LMFDB - Embedded newform 261.2.o.a.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,2,Mod(64,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("261.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.o (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{14})$
Coefficient field:	12.0.7877952219361.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{11} + 13x^{9} - 18x^{8} - 14x^{7} + 57x^{6} - 28x^{5} - 72x^{4} + 104x^{3} - 96x + 64 $ x^12 - 3x^11 + 13x^9 - 18x^8 - 14x^7 + 57x^6 - 28x^5 - 72x^4 + 104x^3 - 96*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			109.1
Root			$1.38491 + 0.286410i$ of defining polynomial
Character	$\chi$	$=$	261.109
Dual form			261.2.o.a.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.536089 - 0.122359i) q^{2} +(-1.52952 + 0.736577i) q^{4} +(-0.610610 - 2.67526i) q^{5} +(-4.03077 - 1.94112i) q^{7} +(-1.58965 + 1.26771i) q^{8} +O(q^{10})$	\(q+(0.536089 - 0.122359i) q^{2} +(-1.52952 + 0.736577i) q^{4} +(-0.610610 - 2.67526i) q^{5} +(-4.03077 - 1.94112i) q^{7} +(-1.58965 + 1.26771i) q^{8} +(-0.654683 - 1.35946i) q^{10} +(-1.16531 - 0.929305i) q^{11} +(0.906494 - 1.13671i) q^{13} +(-2.39836 - 0.547411i) q^{14} +(1.41984 - 1.78042i) q^{16} +2.07293i q^{17} +(-0.236123 - 0.490315i) q^{19} +(2.90447 + 3.64209i) q^{20} +(-0.738420 - 0.355604i) q^{22} +(0.382936 - 1.67775i) q^{23} +(-2.27930 + 1.09766i) q^{25} +(0.346875 - 0.720294i) q^{26} +7.59491 q^{28} +(3.78014 - 3.83543i) q^{29} +(-4.54177 + 1.03663i) q^{31} +(2.30769 - 4.79197i) q^{32} +(0.253641 + 1.11128i) q^{34} +(-2.73175 + 11.9686i) q^{35} +(-2.37655 + 1.89524i) q^{37} +(-0.186578 - 0.233961i) q^{38} +(4.36209 + 3.47865i) q^{40} -0.595175i q^{41} +(0.321297 + 0.0733340i) q^{43} +(2.46687 + 0.563047i) q^{44} -0.946280i q^{46} +(-8.97652 - 7.15853i) q^{47} +(8.11473 + 10.1755i) q^{49} +(-1.08760 + 0.867335i) q^{50} +(-0.549226 + 2.40632i) q^{52} +(2.28813 + 10.0249i) q^{53} +(-1.77458 + 3.68495i) q^{55} +(8.86828 - 2.02413i) q^{56} +(1.55719 - 2.51867i) q^{58} +4.03359 q^{59} +(5.18352 - 10.7637i) q^{61} +(-2.30795 + 1.11145i) q^{62} +(-0.362680 + 1.58901i) q^{64} +(-3.59450 - 1.73102i) q^{65} +(-5.20630 - 6.52849i) q^{67} +(-1.52687 - 3.17058i) q^{68} +6.75049i q^{70} +(5.78348 - 7.25226i) q^{71} +(-3.37292 - 0.769848i) q^{73} +(-1.04215 + 1.30681i) q^{74} +(0.722310 + 0.576023i) q^{76} +(2.89321 + 6.00781i) q^{77} +(6.50888 - 5.19066i) q^{79} +(-5.63005 - 2.71129i) q^{80} +(-0.0728249 - 0.319067i) q^{82} +(0.955764 - 0.460272i) q^{83} +(5.54562 - 1.26575i) q^{85} +0.181217 q^{86} +3.03052 q^{88} +(-4.68343 + 1.06896i) q^{89} +(-5.86034 + 2.82219i) q^{91} +(0.650086 + 2.84821i) q^{92} +(-5.68812 - 2.73926i) q^{94} +(-1.16754 + 0.931082i) q^{95} +(2.09615 + 4.35270i) q^{97} +(5.59529 + 4.46209i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 7 q^{2} - q^{4} + q^{5} - 11 q^{7} - 14 q^{8}+O(q^{10}) $ 12 * q + 7 * q^2 - q^4 + q^5 - 11 * q^7 - 14 * q^8	$ 12 q + 7 q^{2} - q^{4} + q^{5} - 11 q^{7} - 14 q^{8} - 7 q^{10} - 7 q^{11} + 9 q^{13} + 7 q^{14} + 9 q^{16} - 7 q^{19} + 11 q^{20} - 4 q^{22} + 5 q^{23} + 13 q^{25} + 21 q^{26} + 12 q^{28} + 15 q^{29} - 21 q^{31} - 13 q^{34} - 19 q^{35} + 7 q^{37} - 28 q^{38} + 35 q^{40} + 7 q^{43} - 42 q^{44} + 7 q^{47} + 13 q^{49} + 28 q^{50} - 6 q^{52} + 10 q^{53} - 35 q^{55} + 21 q^{56} - 57 q^{58} - 44 q^{59} - 7 q^{61} - 37 q^{62} - 26 q^{64} + 6 q^{65} - 37 q^{67} - 14 q^{68} + 21 q^{71} + 14 q^{73} + 7 q^{76} + 7 q^{77} + 49 q^{79} + 6 q^{80} + 22 q^{82} - 5 q^{83} + 14 q^{85} + 44 q^{86} - 66 q^{88} - 7 q^{89} - 3 q^{91} + 6 q^{92} + 66 q^{94} + 7 q^{95} + 14 q^{97} + 42 q^{98}+O(q^{100}) $ 12 * q + 7 * q^2 - q^4 + q^5 - 11 * q^7 - 14 * q^8 - 7 * q^10 - 7 * q^11 + 9 * q^13 + 7 * q^14 + 9 * q^16 - 7 * q^19 + 11 * q^20 - 4 * q^22 + 5 * q^23 + 13 * q^25 + 21 * q^26 + 12 * q^28 + 15 * q^29 - 21 * q^31 - 13 * q^34 - 19 * q^35 + 7 * q^37 - 28 * q^38 + 35 * q^40 + 7 * q^43 - 42 * q^44 + 7 * q^47 + 13 * q^49 + 28 * q^50 - 6 * q^52 + 10 * q^53 - 35 * q^55 + 21 * q^56 - 57 * q^58 - 44 * q^59 - 7 * q^61 - 37 * q^62 - 26 * q^64 + 6 * q^65 - 37 * q^67 - 14 * q^68 + 21 * q^71 + 14 * q^73 + 7 * q^76 + 7 * q^77 + 49 * q^79 + 6 * q^80 + 22 * q^82 - 5 * q^83 + 14 * q^85 + 44 * q^86 - 66 * q^88 - 7 * q^89 - 3 * q^91 + 6 * q^92 + 66 * q^94 + 7 * q^95 + 14 * q^97 + 42 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{13}{14}\right)$	$1$

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 $

$2$	0.536089	−	0.122359i	0.379072	−	0.0865208i	−0.0287391	−	0.999587i	$-0.509149\pi$
$2$	0.536089	−	0.122359i	0.379072	−	0.0865208i	0.407811	+	0.913066i	$0.366292\pi$
$3$		0			0
$3$		0			0
$4$	−1.52952	+	0.736577i	−0.764759	+	0.368288i
$5$	−0.610610	−	2.67526i	−0.273073	−	1.19641i	−0.906364	−	0.422497i	$-0.861154\pi$
$5$	−0.610610	−	2.67526i	−0.273073	−	1.19641i	0.633291	−	0.773914i	$-0.281704\pi$
$6$		0			0
$7$	−4.03077	−	1.94112i	−1.52349	−	0.733673i	−0.530040	−	0.847972i	$-0.677823\pi$
$7$	−4.03077	−	1.94112i	−1.52349	−	0.733673i	−0.993446	+	0.114300i	$0.963538\pi$
$8$	−1.58965	+	1.26771i	−0.562027	+	0.448201i
$9$		0			0
$10$	−0.654683	−	1.35946i	−0.207029	−	0.429900i
$11$	−1.16531	−	0.929305i	−0.351355	−	0.280196i	0.431869	−	0.901937i	$-0.357854\pi$
$11$	−1.16531	−	0.929305i	−0.351355	−	0.280196i	−0.783223	+	0.621741i	$0.786426\pi$
$12$		0			0
$13$	0.906494	−	1.13671i	0.251416	−	0.315266i	−0.640068	−	0.768319i	$-0.721094\pi$
$13$	0.906494	−	1.13671i	0.251416	−	0.315266i	0.891484	+	0.453053i	$0.149665\pi$
$14$	−2.39836	−	0.547411i	−0.640990	−	0.146302i
$15$		0			0
$16$	1.41984	−	1.78042i	0.354959	−	0.445105i
$17$			2.07293i			0.502759i	0.967889	+	0.251380i	$0.0808843\pi$
$17$			2.07293i			0.502759i	−0.967889	+	0.251380i	$0.919116\pi$
$18$		0			0
$19$	−0.236123	−	0.490315i	−0.0541704	−	0.112486i	0.872126	−	0.489281i	$-0.162741\pi$
$19$	−0.236123	−	0.490315i	−0.0541704	−	0.112486i	−0.926297	+	0.376794i	$0.877026\pi$
$20$	2.90447	+	3.64209i	0.649459	+	0.814396i
$21$		0			0
$22$	−0.738420	−	0.355604i	−0.157432	−	0.0758151i
$23$	0.382936	−	1.67775i	0.0798476	−	0.349835i	−0.919184	−	0.393828i	$-0.871151\pi$
$23$	0.382936	−	1.67775i	0.0798476	−	0.349835i	0.999032	+	0.0439925i	$0.0140078\pi$
$24$		0			0
$25$	−2.27930	+	1.09766i	−0.455861	+	0.219531i
$26$	0.346875	−	0.720294i	0.0680279	−	0.141261i
$27$		0			0
$28$	7.59491			1.43530
$29$	3.78014	−	3.83543i	0.701954	−	0.712222i
$29$	3.78014	−	3.83543i	0.701954	−	0.712222i
$30$		0			0
$31$	−4.54177	+	1.03663i	−0.815726	+	0.186184i	−0.609975	−	0.792420i	$-0.708821\pi$
$31$	−4.54177	+	1.03663i	−0.815726	+	0.186184i	−0.205750	+	0.978604i	$0.565964\pi$
$32$	2.30769	−	4.79197i	0.407946	−	0.847108i
$33$		0			0
$34$	0.253641	+	1.11128i	0.0434992	+	0.190582i
$35$	−2.73175	+	11.9686i	−0.461751	+	2.02306i
$36$		0			0
$37$	−2.37655	+	1.89524i	−0.390703	+	0.311575i	−0.799065	−	0.601245i	$-0.794672\pi$
$37$	−2.37655	+	1.89524i	−0.390703	+	0.311575i	0.408362	+	0.912820i	$0.366100\pi$
$38$	−0.186578	−	0.233961i	−0.0302669	−	0.0379535i
$39$		0			0
$40$	4.36209	+	3.47865i	0.689707	+	0.550023i
$41$		−	0.595175i		−	0.0929507i	−0.998919	−	0.0464753i	$-0.985201\pi$
$41$		−	0.595175i		−	0.0929507i	0.998919	−	0.0464753i	$-0.0147989\pi$
$42$		0			0
$43$	0.321297	+	0.0733340i	0.0489974	+	0.0111833i	0.246949	−	0.969028i	$-0.420572\pi$
$43$	0.321297	+	0.0733340i	0.0489974	+	0.0111833i	−0.197952	+	0.980212i	$0.563429\pi$
$44$	2.46687	+	0.563047i	0.371894	+	0.0848825i
$45$		0			0
$46$		−	0.946280i		−	0.139521i
$47$	−8.97652	−	7.15853i	−1.30936	−	1.04418i	−0.995505	−	0.0947081i	$-0.969808\pi$
$47$	−8.97652	−	7.15853i	−1.30936	−	1.04418i	−0.313854	−	0.949471i	$-0.601620\pi$
$48$		0			0
$49$	8.11473	+	10.1755i	1.15925	+	1.45365i
$50$	−1.08760	+	0.867335i	−0.153810	+	0.122660i
$51$		0			0
$52$	−0.549226	+	2.40632i	−0.0761639	+	0.333696i
$53$	2.28813	+	10.0249i	0.314299	+	1.37703i	0.847389	+	0.530973i	$0.178174\pi$
$53$	2.28813	+	10.0249i	0.314299	+	1.37703i	−0.533090	+	0.846059i	$0.678969\pi$
$54$		0			0
$55$	−1.77458	+	3.68495i	−0.239284	+	0.496878i
$56$	8.86828	−	2.02413i	1.18507	−	0.270485i
$57$		0			0
$58$	1.55719	−	2.51867i	0.204470	−	0.330717i
$59$	4.03359			0.525129			0.262564	−	0.964914i	$-0.415432\pi$
$59$	4.03359			0.525129			0.262564	+	0.964914i	$0.415432\pi$
$60$		0			0
$61$	5.18352	−	10.7637i	0.663682	−	1.37815i	−0.248608	−	0.968604i	$-0.579973\pi$
$61$	5.18352	−	10.7637i	0.663682	−	1.37815i	0.912290	−	0.409545i	$-0.134313\pi$
$62$	−2.30795	+	1.11145i	−0.293110	+	0.141155i
$63$		0			0
$64$	−0.362680	+	1.58901i	−0.0453350	+	0.198626i
$65$	−3.59450	−	1.73102i	−0.445842	−	0.214706i
$66$		0			0
$67$	−5.20630	−	6.52849i	−0.636050	−	0.797582i	0.354453	−	0.935074i	$-0.384667\pi$
$67$	−5.20630	−	6.52849i	−0.636050	−	0.797582i	−0.990503	+	0.137492i	$0.956096\pi$
$68$	−1.52687	−	3.17058i	−0.185161	−	0.384490i
$69$		0			0
$70$			6.75049i			0.806838i
$71$	5.78348	−	7.25226i	0.686373	−	0.860685i	−0.309551	−	0.950883i	$-0.600179\pi$
$71$	5.78348	−	7.25226i	0.686373	−	0.860685i	0.995924	+	0.0901983i	$0.0287501\pi$
$72$		0			0
$73$	−3.37292	−	0.769848i	−0.394771	−	0.0901039i	0.0205272	−	0.999789i	$-0.493466\pi$
$73$	−3.37292	−	0.769848i	−0.394771	−	0.0901039i	−0.415298	+	0.909685i	$0.636323\pi$
$74$	−1.04215	+	1.30681i	−0.121147	+	0.151913i
$75$		0			0
$76$	0.722310	+	0.576023i	0.0828546	+	0.0660744i
$77$	2.89321	+	6.00781i	0.329712	+	0.684654i
$78$		0			0
$79$	6.50888	−	5.19066i	0.732307	−	0.583995i	−0.184734	−	0.982789i	$-0.559142\pi$
$79$	6.50888	−	5.19066i	0.732307	−	0.583995i	0.917041	+	0.398794i	$0.130571\pi$
$80$	−5.63005	−	2.71129i	−0.629458	−	0.303131i
$81$		0			0
$82$	−0.0728249	−	0.319067i	−0.00804217	−	0.0352350i
$83$	0.955764	−	0.460272i	0.104909	−	0.0505214i	−0.380693	−	0.924701i	$-0.624315\pi$
$83$	0.955764	−	0.460272i	0.104909	−	0.0505214i	0.485602	+	0.874180i	$0.338600\pi$
$84$		0			0
$85$	5.54562	−	1.26575i	0.601507	−	0.137290i
$86$	0.181217			0.0195411
$87$		0			0
$88$	3.03052			0.323055
$89$	−4.68343	+	1.06896i	−0.496442	+	0.113310i	−0.463409	−	0.886145i	$-0.653374\pi$
$89$	−4.68343	+	1.06896i	−0.496442	+	0.113310i	−0.0330334	+	0.999454i	$0.510517\pi$
$90$		0			0
$91$	−5.86034	+	2.82219i	−0.614331	+	0.295846i
$92$	0.650086	+	2.84821i	0.0677761	+	0.296947i
$93$		0			0
$94$	−5.68812	−	2.73926i	−0.586685	−	0.282533i
$95$	−1.16754	+	0.931082i	−0.119787	+	0.0955270i
$96$		0			0
$97$	2.09615	+	4.35270i	0.212832	+	0.441950i	0.979866	−	0.199656i	$-0.0639826\pi$
$97$	2.09615	+	4.35270i	0.212832	+	0.441950i	−0.767034	+	0.641606i	$0.778268\pi$
$98$	5.59529	+	4.46209i	0.565209	+	0.450739i
$99$		0			0
$100$	2.67773	−	3.35777i	0.267773	−	0.335777i
$101$	−11.7217	−	2.67540i	−1.16635	−	0.266212i	−0.404856	−	0.914381i	$-0.632678\pi$
$101$	−11.7217	−	2.67540i	−1.16635	−	0.266212i	−0.761497	+	0.648168i	$0.775535\pi$
$102$		0			0
$103$	−4.21214	+	5.28185i	−0.415034	+	0.520436i	−0.944773	−	0.327724i	$-0.893718\pi$
$103$	−4.21214	+	5.28185i	−0.415034	+	0.520436i	0.529739	+	0.848160i	$0.322290\pi$
$104$			2.95614i			0.289873i
$105$		0			0
$106$	2.45328	+	5.09429i	0.238284	+	0.494801i
$107$	8.52897	+	10.6950i	0.824527	+	1.03392i	0.998788	+	0.0492247i	$0.0156751\pi$
$107$	8.52897	+	10.6950i	0.824527	+	1.03392i	−0.174261	+	0.984700i	$0.555754\pi$
$108$		0			0
$109$	0.850324	+	0.409495i	0.0814463	+	0.0392225i	0.474163	−	0.880437i	$-0.342751\pi$
$109$	0.850324	+	0.409495i	0.0814463	+	0.0392225i	−0.392717	+	0.919659i	$0.628465\pi$
$110$	−0.500446	+	2.19260i	−0.0477156	+	0.209056i
$111$		0			0
$112$	−9.17904	+	4.42039i	−0.867337	+	0.417688i
$113$	7.26684	−	15.0897i	0.683606	−	1.41952i	−0.213159	−	0.977017i	$-0.568375\pi$
$113$	7.26684	−	15.0897i	0.683606	−	1.41952i	0.896766	−	0.442506i	$-0.145910\pi$
$114$		0			0
$115$	−4.72224			−0.440351
$116$	−2.95670	+	8.65072i	−0.274523	+	0.803200i
$117$		0			0
$118$	2.16236	−	0.493546i	0.199062	−	0.0454346i
$119$	4.02380	−	8.35550i	0.368861	−	0.765947i
$120$		0			0
$121$	−1.95339	−	8.55835i	−0.177581	−	0.778032i
$122$	1.46180	−	6.40455i	0.132345	−	0.579841i
$123$		0			0
$124$	6.18316	−	4.93091i	0.555264	−	0.442808i
$125$	−4.22618	−	5.29946i	−0.378001	−	0.473998i
$126$		0			0
$127$	−9.64469	−	7.69138i	−0.855828	−	0.682500i	0.0938983	−	0.995582i	$-0.470067\pi$
$127$	−9.64469	−	7.69138i	−0.855828	−	0.682500i	−0.949726	+	0.313082i	$0.898639\pi$
$128$			11.5336i			1.01944i
$129$		0			0
$130$	−2.13878	−	0.488162i	−0.187583	−	0.0428146i
$131$	−12.2846	−	2.80387i	−1.07331	−	0.244975i	−0.350878	−	0.936421i	$-0.614117\pi$
$131$	−12.2846	−	2.80387i	−1.07331	−	0.244975i	−0.722428	+	0.691446i	$0.756974\pi$
$132$		0			0
$133$			2.43469i			0.211114i
$134$	−3.58986	−	2.86282i	−0.310116	−	0.247310i
$135$		0			0
$136$	−2.62786	−	3.29524i	−0.225338	−	0.282564i
$137$	−5.06920	+	4.04255i	−0.433091	+	0.345378i	−0.815643	−	0.578555i	$-0.803617\pi$
$137$	−5.06920	+	4.04255i	−0.433091	+	0.345378i	0.382552	+	0.923934i	$0.375045\pi$
$138$		0			0
$139$	−1.85332	+	8.11994i	−0.157197	+	0.688724i	0.833487	+	0.552540i	$0.186341\pi$
$139$	−1.85332	+	8.11994i	−0.157197	+	0.688724i	−0.990683	+	0.136185i	$0.956516\pi$
$140$	−4.63753	−	20.3183i	−0.391942	−	1.71721i
$141$		0			0
$142$	2.21309	−	4.59552i	0.185718	−	0.385647i
$143$	−2.11269	+	0.482209i	−0.176672	+	0.0403243i
$144$		0			0
$145$	−12.5690	−	7.77089i	−1.04379	−	0.645337i
$146$	−1.90239			−0.157443
$147$		0			0
$148$	2.23899	−	4.64931i	0.184044	−	0.382171i
$149$	14.5448	−	7.00441i	1.19156	−	0.573824i	0.270300	−	0.962776i	$-0.412877\pi$
$149$	14.5448	−	7.00441i	1.19156	−	0.573824i	0.921258	+	0.388953i	$0.127163\pi$
$150$		0			0
$151$	−0.708124	+	3.10249i	−0.0576263	+	0.252477i	−0.995533	−	0.0944090i	$-0.969904\pi$
$151$	−0.708124	+	3.10249i	−0.0576263	+	0.252477i	0.937907	+	0.346886i	$0.112761\pi$
$152$	0.996929	+	0.480096i	0.0808616	+	0.0389409i
$153$		0			0
$154$	2.28613	+	2.86672i	0.184222	+	0.231007i
$155$	5.54650	+	11.5174i	0.445505	+	0.925101i
$156$		0			0
$157$		−	17.6378i		−	1.40765i	−0.710375	−	0.703824i	$-0.751474\pi$
$157$		−	17.6378i		−	1.40765i	0.710375	−	0.703824i	$-0.248526\pi$
$158$	2.85422	−	3.57908i	0.227070	−	0.284736i
$159$		0			0
$160$	−14.2288	−	3.24764i	−1.12489	−	0.256748i
$161$	−4.80023	+	6.01930i	−0.378311	+	0.474387i
$162$		0			0
$163$	−1.98183	−	1.58046i	−0.155229	−	0.123791i	0.542795	−	0.839865i	$-0.317366\pi$
$163$	−1.98183	−	1.58046i	−0.155229	−	0.123791i	−0.698024	+	0.716074i	$0.745937\pi$
$164$	0.438392	+	0.910330i	0.0342327	+	0.0710849i
$165$		0			0
$166$	0.456057	−	0.363693i	0.0353969	−	0.0282281i
$167$	−12.3660	−	5.95514i	−0.956908	−	0.460823i	−0.110805	−	0.993842i	$-0.535343\pi$
$167$	−12.3660	−	5.95514i	−0.956908	−	0.460823i	−0.846103	+	0.533020i	$0.821057\pi$
$168$		0			0
$169$	2.42240	+	10.6132i	0.186338	+	0.816402i
$170$	2.81807	−	1.35711i	0.216136	−	0.104086i
$171$		0			0
$172$	−0.545446	+	0.124494i	−0.0415899	+	0.00949262i
$173$	7.05351			0.536268			0.268134	−	0.963382i	$-0.413593\pi$
$173$	7.05351			0.536268			0.268134	+	0.963382i	$0.413593\pi$
$174$		0			0
$175$	11.3180			0.855562
$176$	−3.30911	+	0.755282i	−0.249433	+	0.0569315i
$177$		0			0
$178$	−2.37994	+	1.14612i	−0.178384	+	0.0859052i
$179$	−1.19772	−	5.24757i	−0.0895222	−	0.392222i	0.910239	−	0.414084i	$-0.135898\pi$
$179$	−1.19772	−	5.24757i	−0.0895222	−	0.392222i	−0.999761	+	0.0218614i	$0.993041\pi$
$180$		0			0
$181$	14.1408	+	6.80987i	1.05108	+	0.506174i	0.877964	−	0.478727i	$-0.158902\pi$
$181$	14.1408	+	6.80987i	1.05108	+	0.506174i	0.173117	+	0.984901i	$0.444616\pi$
$182$	−2.79635	+	2.23001i	−0.207279	+	0.165300i
$183$		0			0
$184$	1.51816	+	3.15249i	0.111920	+	0.232405i
$185$	6.52139	+	5.20063i	0.479462	+	0.382358i
$186$		0			0
$187$	1.92638	−	2.41561i	0.140871	−	0.176647i
$188$	19.0025	+	4.33721i	1.38590	+	0.316323i
$189$		0			0
$190$	−0.511979	+	0.642002i	−0.0371429	+	0.0465757i
$191$			4.28271i			0.309886i	0.987923	+	0.154943i	$0.0495194\pi$
$191$			4.28271i			0.309886i	−0.987923	+	0.154943i	$0.950481\pi$
$192$		0			0
$193$	10.2525	+	21.2896i	0.737994	+	1.53246i	0.842955	+	0.537984i	$0.180814\pi$
$193$	10.2525	+	21.2896i	0.737994	+	1.53246i	−0.104961	+	0.994476i	$0.533472\pi$
$194$	1.65632	+	2.07695i	0.118917	+	0.149117i
$195$		0			0
$196$	−19.9067	−	9.58656i	−1.42191	−	0.684754i
$197$	−1.12719	+	4.93853i	−0.0803088	+	0.351856i	−0.999078	−	0.0429401i	$-0.986328\pi$
$197$	−1.12719	+	4.93853i	−0.0803088	+	0.351856i	0.918769	+	0.394796i	$0.129185\pi$
$198$		0			0
$199$	21.1994	−	10.2091i	1.50279	−	0.723703i	0.511980	−	0.858997i	$-0.328912\pi$
$199$	21.1994	−	10.2091i	1.50279	−	0.723703i	0.990806	+	0.135294i	$0.0431978\pi$
$200$	2.23180	−	4.63438i	0.157812	−	0.327700i
$201$		0			0
$202$	−6.61124			−0.465165
$203$	−22.6819	+	8.12204i	−1.59196	+	0.570056i
$204$		0			0
$205$	−1.59224	+	0.363419i	−0.111207	+	0.0253823i
$206$	−1.61180	+	3.34694i	−0.112299	+	0.233192i
$207$		0			0
$208$	−0.736742	−	3.22788i	−0.0510839	−	0.223813i
$209$	−0.180495	+	0.790801i	−0.0124851	+	0.0547008i
$210$		0			0
$211$	−14.3321	+	11.4295i	−0.986663	+	0.786838i	−0.977027	−	0.213116i	$-0.931639\pi$
$211$	−14.3321	+	11.4295i	−0.986663	+	0.786838i	−0.00963631	+	0.999954i	$0.503067\pi$
$212$	−10.8839	−	13.6479i	−0.747508	−	0.937345i
$213$		0			0
$214$	5.88092	+	4.68988i	0.402011	+	0.320593i
$215$		−	0.904331i		−	0.0616749i
$216$		0			0
$217$	20.3190	+	4.63769i	1.37935	+	0.314827i
$218$	0.505955	+	0.115481i	0.0342676	+	0.00782136i
$219$		0			0
$220$		−	6.94331i		−	0.468118i
$221$	2.35631	+	1.87910i	0.158503	+	0.126402i
$222$		0			0
$223$	−2.98934	−	3.74852i	−0.200181	−	0.251019i	0.671601	−	0.740913i	$-0.265607\pi$
$223$	−2.98934	−	3.74852i	−0.200181	−	0.251019i	−0.871782	+	0.489894i	$0.837036\pi$
$224$	−18.6035	+	14.8358i	−1.24300	+	0.991260i
$225$		0			0
$226$	2.04931	−	8.97861i	0.136318	−	0.597248i
$227$	0.759662	+	3.32830i	0.0504206	+	0.220907i	0.993861	−	0.110635i	$-0.0352884\pi$
$227$	0.759662	+	3.32830i	0.0504206	+	0.220907i	−0.943441	+	0.331542i	$0.892431\pi$
$228$		0			0
$229$	8.66379	−	17.9906i	0.572520	−	1.18885i	−0.390796	−	0.920477i	$-0.627800\pi$
$229$	8.66379	−	17.9906i	0.572520	−	1.18885i	0.963315	−	0.268372i	$-0.0864855\pi$
$230$	−2.53154	+	0.577808i	−0.166925	+	0.0380995i
$231$		0			0
$232$	−1.14691	+	10.8891i	−0.0752984	+	0.714905i
$233$	4.14336			0.271440			0.135720	−	0.990747i	$-0.456665\pi$
$233$	4.14336			0.271440			0.135720	+	0.990747i	$0.456665\pi$
$234$		0			0
$235$	−13.6698	+	28.3855i	−0.891717	+	1.85167i
$236$	−6.16945	+	2.97105i	−0.401597	+	0.193399i
$237$		0			0
$238$	1.13474	−	4.97164i	0.0735546	−	0.322264i
$239$	18.8278	+	9.06700i	1.21787	+	0.586495i	0.928718	−	0.370788i	$-0.120912\pi$
$239$	18.8278	+	9.06700i	1.21787	+	0.586495i	0.289152	+	0.957283i	$0.406627\pi$
$240$		0			0
$241$	−2.28011	−	2.85917i	−0.146875	−	0.184176i	0.702952	−	0.711238i	$-0.251865\pi$
$241$	−2.28011	−	2.85917i	−0.146875	−	0.184176i	−0.849827	+	0.527062i	$0.823294\pi$
$242$	−2.09438	−	4.34902i	−0.134632	−	0.279566i
$243$		0			0
$244$			20.2813i			1.29838i
$245$	22.2673	−	27.9223i	1.42260	−	1.78389i
$246$		0			0
$247$	−0.771389	−	0.176065i	−0.0490823	−	0.0112027i
$248$	5.90569	−	7.40550i	0.375012	−	0.470250i
$249$		0			0
$250$	−2.91404	−	2.32387i	−0.184300	−	0.146975i
$251$	6.00009	+	12.4593i	0.378722	+	0.786425i	0.999996	+	0.00283143i	$0.000901275\pi$
$251$	6.00009	+	12.4593i	0.378722	+	0.786425i	−0.621274	+	0.783594i	$0.713384\pi$
$252$		0			0
$253$	−2.00538	+	1.59924i	−0.126077	+	0.100543i
$254$	−6.11152	−	2.94316i	−0.383471	−	0.184670i
$255$		0			0
$256$	0.685877	+	3.00502i	0.0428673	+	0.187814i
$257$	15.1065	−	7.27489i	0.942315	−	0.453795i	0.101330	−	0.994853i	$-0.467690\pi$
$257$	15.1065	−	7.27489i	0.942315	−	0.453795i	0.840985	+	0.541058i	$0.181976\pi$
$258$		0			0
$259$	13.2582	−	3.02610i	0.823825	−	0.188033i
$260$	6.77287			0.420036
$261$		0			0
$262$	−6.92870			−0.428056
$263$	3.43964	−	0.785076i	0.212097	−	0.0484099i	−0.115152	−	0.993348i	$-0.536735\pi$
$263$	3.43964	−	0.785076i	0.212097	−	0.0484099i	0.327249	+	0.944938i	$0.393878\pi$
$264$		0			0
$265$	25.4221	−	12.2427i	1.56167	−	0.752060i
$266$	0.297906	+	1.30521i	0.0182658	+	0.0800276i
$267$		0			0
$268$	12.7719	+	6.15060i	0.780165	+	0.375708i
$269$	18.7417	−	14.9460i	1.14270	−	0.911274i	0.145751	−	0.989321i	$-0.453440\pi$
$269$	18.7417	−	14.9460i	1.14270	−	0.911274i	0.996950	+	0.0780476i	$0.0248686\pi$
$270$		0			0
$271$	9.85146	+	20.4568i	0.598434	+	1.24266i	0.951669	+	0.307126i	$0.0993673\pi$
$271$	9.85146	+	20.4568i	0.598434	+	1.24266i	−0.353235	+	0.935535i	$0.614918\pi$
$272$	3.69069	+	2.94322i	0.223781	+	0.178459i
$273$		0			0
$274$	−2.22290	+	2.78743i	−0.134290	+	0.168395i
$275$	3.67616	+	0.839059i	0.221681	+	0.0505971i
$276$		0			0
$277$	−12.7570	+	15.9968i	−0.766495	+	0.961154i	−0.999937	−	0.0112168i	$-0.996430\pi$
$277$	−12.7570	+	15.9968i	−0.766495	+	0.961154i	0.233442	+	0.972371i	$0.425001\pi$
$278$			4.57978i			0.274677i
$279$		0			0
$280$	−10.8301	−	22.4890i	−0.647223	−	1.34397i
$281$	−1.78761	−	2.24159i	−0.106640	−	0.133722i	0.725647	−	0.688067i	$-0.241540\pi$
$281$	−1.78761	−	2.24159i	−0.106640	−	0.133722i	−0.832287	+	0.554345i	$0.812969\pi$
$282$		0			0
$283$	4.70357	+	2.26512i	0.279598	+	0.134647i	0.568428	−	0.822733i	$-0.307552\pi$
$283$	4.70357	+	2.26512i	0.279598	+	0.134647i	−0.288830	+	0.957380i	$0.593266\pi$
$284$	−3.50409	+	15.3524i	−0.207930	+	0.910999i
$285$		0			0
$286$	−1.07359	+	0.517014i	−0.0634827	+	0.0305717i
$287$	−1.15530	+	2.39901i	−0.0681954	+	0.141609i
$288$		0			0
$289$	12.7030			0.747233
$290$	−7.68892	−	2.62797i	−0.451509	−	0.154320i
$291$		0			0
$292$	5.72600	−	1.30692i	0.335089	−	0.0764818i
$293$	−11.8669	+	24.6418i	−0.693271	+	1.43959i	0.195249	+	0.980754i	$0.437448\pi$
$293$	−11.8669	+	24.6418i	−0.693271	+	1.43959i	−0.888520	+	0.458838i	$0.848266\pi$
$294$		0			0
$295$	−2.46295	−	10.7909i	−0.143398	−	0.628270i
$296$	1.37529	−	6.02553i	0.0799370	−	0.350227i
$297$		0			0
$298$	6.94027	−	5.53468i	0.402039	−	0.320615i
$299$	−1.55998	−	1.95616i	−0.0902162	−	0.113127i
$300$		0			0
$301$	−1.15272	−	0.919267i	−0.0664420	−	0.0529857i
$302$			1.74986i			0.100693i
$303$		0			0
$304$	−1.20822	−	0.275769i	−0.0692964	−	0.0158165i
$305$	−31.9607	−	7.29483i	−1.83007	−	0.417701i
$306$		0			0
$307$			5.31763i			0.303493i	0.988419	+	0.151746i	$0.0484897\pi$
$307$			5.31763i			0.303493i	−0.988419	+	0.151746i	$0.951510\pi$
$308$	−8.85043	−	7.05799i	−0.504300	−	0.402166i
$309$		0			0
$310$	4.38268	+	5.49570i	0.248919	+	0.312135i
$311$	−5.17845	+	4.12968i	−0.293643	+	0.234173i	−0.759219	−	0.650835i	$-0.774419\pi$
$311$	−5.17845	+	4.12968i	−0.293643	+	0.234173i	0.465576	+	0.885008i	$0.345847\pi$
$312$		0			0
$313$	0.329444	−	1.44339i	0.0186213	−	0.0815852i	−0.964763	−	0.263119i	$-0.915249\pi$
$313$	0.329444	−	1.44339i	0.0186213	−	0.0815852i	0.983385	+	0.181533i	$0.0581061\pi$
$314$	−2.15814	−	9.45542i	−0.121791	−	0.533600i
$315$		0			0
$316$	−6.13213	+	12.7335i	−0.344959	+	0.716315i
$317$	4.49826	−	1.02670i	0.252648	−	0.0576652i	−0.0943212	−	0.995542i	$-0.530068\pi$
$317$	4.49826	−	1.02670i	0.252648	−	0.0576652i	0.346969	+	0.937877i	$0.387211\pi$
$318$		0			0
$319$	−7.96933	+	0.956570i	−0.446197	+	0.0535576i
$320$	4.47245			0.250018
$321$		0			0
$322$	−1.83684	+	3.81424i	−0.102363	+	0.212559i
$323$	1.01639	−	0.489467i	0.0565534	−	0.0272347i
$324$		0			0
$325$	−0.818463	+	3.58592i	−0.0454001	+	0.198911i
$326$	−1.25582	−	0.604771i	−0.0695535	−	0.0334952i
$327$		0			0
$328$	0.754506	+	0.946121i	0.0416606	+	0.0522408i
$329$	22.2867	+	46.2788i	1.22871	+	2.55143i
$330$		0			0
$331$			1.65763i			0.0911116i	0.998962	+	0.0455558i	$0.0145059\pi$
$331$			1.65763i			0.0911116i	−0.998962	+	0.0455558i	$0.985494\pi$
$332$	−1.12283	+	1.40799i	−0.0616235	+	0.0772734i
$333$		0			0
$334$	−7.35793	−	1.67940i	−0.402608	−	0.0918927i
$335$	−14.2864	+	17.9145i	−0.780547	+	0.978775i
$336$		0			0
$337$	−13.9220	−	11.1024i	−0.758378	−	0.604786i	0.166061	−	0.986115i	$-0.446895\pi$
$337$	−13.9220	−	11.1024i	−0.758378	−	0.604786i	−0.924439	+	0.381329i	$0.875466\pi$
$338$	2.59725	+	5.39324i	0.141272	+	0.293353i
$339$		0			0
$340$	−7.54980	+	6.02076i	−0.409445	+	0.326522i
$341$	6.25592	+	3.01269i	0.338777	+	0.163146i
$342$		0			0
$343$	−5.98805	−	26.2354i	−0.323324	−	1.41658i
$344$	−0.603717	+	0.290735i	−0.0325502	+	0.0156754i
$345$		0			0
$346$	3.78131	−	0.863060i	0.203285	−	0.0463984i
$347$	−3.69857			−0.198550			−0.0992748	−	0.995060i	$-0.531652\pi$
$347$	−3.69857			−0.198550			−0.0992748	+	0.995060i	$0.531652\pi$
$348$		0			0
$349$	−22.2918			−1.19325			−0.596626	−	0.802520i	$-0.703492\pi$
$349$	−22.2918			−1.19325			−0.596626	+	0.802520i	$0.703492\pi$
$350$	6.06747	−	1.38486i	0.324320	−	0.0740239i
$351$		0			0
$352$	−7.14238	+	3.43959i	−0.380690	+	0.183331i
$353$	−5.28701	−	23.1639i	−0.281399	−	1.23289i	−0.896001	−	0.444053i	$-0.853540\pi$
$353$	−5.28701	−	23.1639i	−0.281399	−	1.23289i	0.614601	−	0.788838i	$-0.289317\pi$
$354$		0			0
$355$	−22.9331	−	11.0440i	−1.21716	−	0.586154i
$356$	6.37601	−	5.08470i	0.337928	−	0.269489i
$357$		0			0
$358$	−1.28417	−	2.66662i	−0.0678708	−	0.140935i
$359$	−27.9498	−	22.2893i	−1.47514	−	1.17638i	−0.944380	−	0.328857i	$-0.893336\pi$
$359$	−27.9498	−	22.2893i	−1.47514	−	1.17638i	−0.530757	−	0.847524i	$-0.678092\pi$
$360$		0			0
$361$	11.6617	−	14.6232i	0.613771	−	0.769645i
$362$	8.41400	+	1.92044i	0.442230	+	0.100936i
$363$		0			0
$364$	6.88474	−	8.63319i	0.360858	−	0.452502i
$365$			9.49351i			0.496913i
$366$		0			0
$367$	0.613081	+	1.27308i	0.0320026	+	0.0664540i	0.916357	−	0.400362i	$-0.131115\pi$
$367$	0.613081	+	1.27308i	0.0320026	+	0.0664540i	−0.884355	+	0.466816i	$0.845401\pi$
$368$	−2.44340	−	3.06392i	−0.127371	−	0.159718i
$369$		0			0
$370$	4.13239	+	1.99005i	0.214833	+	0.103458i
$371$	10.2367	−	44.8497i	0.531461	−	2.32848i
$372$		0			0
$373$	−3.25539	+	1.56771i	−0.168557	+	0.0811730i	−0.516260	−	0.856432i	$-0.672676\pi$
$373$	−3.25539	+	1.56771i	−0.168557	+	0.0811730i	0.347703	+	0.937605i	$0.386962\pi$
$374$	0.737143	−	1.53069i	0.0381167	−	0.0791502i
$375$		0			0
$376$	23.3444			1.20390
$377$	−0.933089	−	7.77371i	−0.0480565	−	0.400366i
$378$		0			0
$379$	5.57574	−	1.27263i	0.286407	−	0.0653704i	−0.0769040	−	0.997038i	$-0.524504\pi$
$379$	5.57574	−	1.27263i	0.286407	−	0.0653704i	0.363311	+	0.931668i	$0.381646\pi$
$380$	1.09996	−	2.28409i	0.0564267	−	0.117171i
$381$		0			0
$382$	0.524028	+	2.29592i	0.0268116	+	0.117469i
$383$	2.41813	−	10.5945i	0.123561	−	0.541354i	−0.874819	−	0.484450i	$-0.839020\pi$
$383$	2.41813	−	10.5945i	0.123561	−	0.541354i	0.998380	−	0.0569044i	$-0.0181230\pi$
$384$		0			0
$385$	14.3058	−	11.4085i	0.729092	−	0.581431i
$386$	8.10125	+	10.1586i	0.412343	+	0.517062i
$387$		0			0
$388$	−6.41220	−	5.11356i	−0.325530	−	0.259602i
$389$			27.0337i			1.37066i	0.728232	+	0.685331i	$0.240342\pi$
$389$			27.0337i			1.37066i	−0.728232	+	0.685331i	$0.759658\pi$
$390$		0			0
$391$	3.47786	+	0.793799i	0.175883	+	0.0401442i
$392$	−25.7992	−	5.88850i	−1.30306	−	0.297414i
$393$		0			0
$394$			2.78541i			0.140327i
$395$	−17.8607	−	14.2435i	−0.898671	−	0.716666i
$396$		0			0
$397$	−18.3457	−	23.0047i	−0.920742	−	1.15457i	−0.987628	−	0.156813i	$-0.949878\pi$
$397$	−18.3457	−	23.0047i	−0.920742	−	1.15457i	0.0668862	−	0.997761i	$-0.478694\pi$
$398$	10.1156	−	8.06692i	0.507049	−	0.404358i
$399$		0			0
$400$	−1.28196	+	5.61661i	−0.0640978	+	0.280831i
$401$	1.76229	+	7.72111i	0.0880047	+	0.385574i	0.999679	−	0.0253400i	$-0.00806685\pi$
$401$	1.76229	+	7.72111i	0.0880047	+	0.385574i	−0.911674	+	0.410914i	$0.865210\pi$
$402$		0			0
$403$	−2.93874	+	6.10236i	−0.146389	+	0.303980i
$404$	19.8992	−	4.54186i	0.990022	−	0.225966i
$405$		0			0
$406$	−11.1657	+	7.12947i	−0.554145	+	0.353830i
$407$	4.53068			0.224577
$408$		0			0
$409$	11.1814	−	23.2184i	0.552883	−	1.14807i	−0.417984	−	0.908454i	$-0.637263\pi$
$409$	11.1814	−	23.2184i	0.552883	−	1.14807i	0.970867	−	0.239619i	$-0.0770226\pi$
$410$	−0.809118	+	0.389651i	−0.0399595	+	0.0192435i
$411$		0			0
$412$	2.55205	−	11.1812i	0.125730	−	0.550860i
$413$	−16.2585	−	7.82966i	−0.800027	−	0.385272i
$414$		0			0
$415$	−1.81494	−	2.27587i	−0.0890921	−	0.111718i
$416$	−3.35516	−	6.96706i	−0.164500	−	0.341588i
$417$		0			0
$418$			0.446025i			0.0218158i
$419$	−0.231745	+	0.290599i	−0.0113215	+	0.0141967i	−0.787460	−	0.616366i	$-0.788604\pi$
$419$	−0.231745	+	0.290599i	−0.0113215	+	0.0141967i	0.776139	+	0.630562i	$0.217176\pi$
$420$		0			0
$421$	21.8509	+	4.98733i	1.06495	+	0.243068i	0.718875	−	0.695139i	$-0.244657\pi$
$421$	21.8509	+	4.98733i	1.06495	+	0.243068i	0.346074	+	0.938207i	$0.387515\pi$
$422$	−6.28479	+	7.88088i	−0.305939	+	0.383635i
$423$		0			0
$424$	−16.3460	−	13.0355i	−0.793832	−	0.633060i
$425$	−2.27536	−	4.72484i	−0.110371	−	0.229188i
$426$		0			0
$427$	−41.7871	+	33.3241i	−2.02222	+	1.61267i
$428$	−20.9229	−	10.0759i	−1.01135	−	0.487039i
$429$		0			0
$430$	−0.110653	−	0.484802i	−0.00533616	−	0.0233792i
$431$	31.3909	−	15.1171i	1.51205	−	0.728164i	0.520016	−	0.854156i	$-0.325926\pi$
$431$	31.3909	−	15.1171i	1.51205	−	0.728164i	0.992031	+	0.125992i	$0.0402115\pi$
$432$		0			0
$433$	−21.0132	+	4.79613i	−1.00983	+	0.230488i	−0.695269	−	0.718749i	$-0.744715\pi$
$433$	−21.0132	+	4.79613i	−1.00983	+	0.230488i	−0.314562	+	0.949237i	$0.601858\pi$
$434$	11.4603			0.550111
$435$		0			0
$436$	−1.60221			−0.0767319
$437$	−0.913047	+	0.208397i	−0.0436770	+	0.00996898i
$438$		0			0
$439$	1.48009	−	0.712776i	0.0706411	−	0.0340189i	−0.398230	−	0.917286i	$-0.630375\pi$
$439$	1.48009	−	0.712776i	0.0706411	−	0.0340189i	0.468871	+	0.883267i	$0.344661\pi$
$440$	−1.85047	−	8.10743i	−0.0882176	−	0.386506i
$441$		0			0
$442$	1.49312	+	0.719049i	0.0710205	+	0.0342017i
$443$	−27.6581	+	22.0566i	−1.31407	+	1.04794i	−0.319109	+	0.947718i	$0.603384\pi$
$443$	−27.6581	+	22.0566i	−1.31407	+	1.04794i	−0.994965	+	0.100221i	$0.968045\pi$
$444$		0			0
$445$	5.71949	+	11.8766i	0.271130	+	0.563007i
$446$	−2.06122	−	1.64377i	−0.0976016	−	0.0778347i
$447$		0			0
$448$	4.54632	−	5.70091i	0.214794	−	0.269343i
$449$	−12.0435	−	2.74885i	−0.568367	−	0.129726i	−0.0713260	−	0.997453i	$-0.522723\pi$
$449$	−12.0435	−	2.74885i	−0.568367	−	0.129726i	−0.497041	+	0.867727i	$0.665580\pi$
$450$		0			0
$451$	−0.553099	+	0.693564i	−0.0260444	+	0.0326587i
$452$			28.4326i			1.33736i
$453$		0			0
$454$	0.814494	+	1.69131i	0.0382261	+	0.0793773i
$455$	11.1285	+	13.9547i	0.521711	+	0.654205i
$456$		0			0
$457$	−28.2167	−	13.5884i	−1.31992	−	0.635640i	−0.364586	−	0.931170i	$-0.618790\pi$
$457$	−28.2167	−	13.5884i	−1.31992	−	0.635640i	−0.955334	+	0.295530i	$0.904504\pi$
$458$	2.44326	−	10.7046i	0.114166	−	0.500195i
$459$		0			0
$460$	7.22275	−	3.47829i	0.336762	−	0.162176i
$461$	−2.80526	+	5.82519i	−0.130654	+	0.271306i	−0.956025	−	0.293285i	$-0.905252\pi$
$461$	−2.80526	+	5.82519i	−0.130654	+	0.271306i	0.825371	+	0.564591i	$0.190966\pi$
$462$		0			0
$463$	−14.5214			−0.674867			−0.337434	−	0.941349i	$-0.609559\pi$
$463$	−14.5214			−0.674867			−0.337434	+	0.941349i	$0.609559\pi$
$464$	−1.46149	−	12.1759i	−0.0678482	−	0.565253i
$465$		0			0
$466$	2.22121	−	0.506977i	0.102896	−	0.0234852i
$467$	11.3476	−	23.5636i	0.525105	−	1.09039i	−0.454738	−	0.890625i	$-0.650267\pi$
$467$	11.3476	−	23.5636i	0.525105	−	1.09039i	0.979843	−	0.199767i	$-0.0640187\pi$
$468$		0			0
$469$	8.31282	+	36.4208i	0.383850	+	1.68176i
$470$	−3.85499	+	16.8898i	−0.177817	+	0.779069i
$471$		0			0
$472$	−6.41200	+	5.11340i	−0.295136	+	0.235363i
$473$	−0.306262	−	0.384040i	−0.0140819	−	0.0176582i
$474$		0			0
$475$	1.07639	+	0.858396i	0.0493884	+	0.0393859i
$476$			15.7437i			0.721612i
$477$		0			0
$478$	11.2028	+	2.55697i	0.512405	+	0.116953i
$479$	24.5946	+	5.61357i	1.12376	+	0.256490i	0.743727	−	0.668483i	$-0.233056\pi$
$479$	24.5946	+	5.61357i	1.12376	+	0.256490i	0.380031	+	0.924974i	$0.375913\pi$
$480$		0			0
$481$			4.41946i			0.201510i
$482$	−1.57219	−	1.25378i	−0.0716113	−	0.0571081i
$483$		0			0
$484$	9.29162	+	11.6513i	0.422346	+	0.529606i
$485$	10.3647	−	8.26554i	0.470635	−	0.375319i
$486$		0			0
$487$	8.92818	−	39.1169i	0.404575	−	1.77256i	−0.203909	−	0.978990i	$-0.565365\pi$
$487$	8.92818	−	39.1169i	0.404575	−	1.77256i	0.608483	−	0.793567i	$-0.291778\pi$
$488$	5.40519	+	23.6817i	0.244682	+	1.07202i
$489$		0			0
$490$	8.52070	−	17.6934i	0.384926	−	0.799307i
$491$	−9.91823	+	2.26377i	−0.447604	+	0.102163i	−0.440380	−	0.897811i	$-0.645156\pi$
$491$	−9.91823	+	2.26377i	−0.447604	+	0.102163i	−0.00722326	+	0.999974i	$0.502299\pi$
$492$		0			0
$493$	7.95058	+	7.83597i	0.358076	+	0.352914i
$494$	−0.435077			−0.0195750
$495$		0			0
$496$	−4.60294	+	9.55810i	−0.206678	+	0.429171i
$497$	−37.3893	+	18.0058i	−1.67714	+	0.807669i
$498$		0			0
$499$	−1.83329	+	8.03215i	−0.0820691	+	0.359568i	−0.999242	−	0.0389205i	$-0.987608\pi$
$499$	−1.83329	+	8.03215i	−0.0820691	+	0.359568i	0.917173	+	0.398489i	$0.130465\pi$
$500$	10.3675	+	4.99271i	0.463647	+	0.223281i
$501$		0			0
$502$	4.74109	+	5.94514i	0.211605	+	0.265345i
$503$	−1.18362	−	2.45782i	−0.0527751	−	0.109589i	0.872914	−	0.487875i	$-0.162228\pi$
$503$	−1.18362	−	2.45782i	−0.0527751	−	0.109589i	−0.925689	+	0.378286i	$0.876513\pi$
$504$		0			0
$505$			32.9922i			1.46813i
$506$	−0.879383	+	1.10271i	−0.0390933	+	0.0490215i
$507$		0			0
$508$	20.4170	+	4.66005i	0.905859	+	0.206756i
$509$	−21.3596	+	26.7840i	−0.946746	+	1.18718i	0.0354598	+	0.999371i	$0.488710\pi$
$509$	−21.3596	+	26.7840i	−0.946746	+	1.18718i	−0.982205	+	0.187810i	$0.939861\pi$
$510$		0			0
$511$	12.1011	+	9.65031i	0.535321	+	0.426905i
$512$	−9.27309	−	19.2558i	−0.409817	−	0.850993i
$513$		0			0
$514$	7.20827	−	5.74840i	0.317943	−	0.253551i
$515$	16.7023	+	8.04339i	0.735990	+	0.354434i
$516$		0			0
$517$	3.80798	+	16.6838i	0.167475	+	0.733754i
$518$	6.73731	−	3.24452i	0.296020	−	0.142556i
$519$		0			0
$520$	7.90842	−	1.80504i	0.346807	−	0.0791565i
$521$	30.8597			1.35199			0.675994	−	0.736907i	$-0.263715\pi$
$521$	30.8597			1.35199			0.675994	+	0.736907i	$0.263715\pi$
$522$		0			0
$523$	31.8103			1.39097			0.695484	−	0.718542i	$-0.255190\pi$
$523$	31.8103			1.39097			0.695484	+	0.718542i	$0.255190\pi$
$524$	20.8547	−	4.75995i	0.911042	−	0.207939i
$525$		0			0
$526$	1.74789	−	0.841742i	0.0762118	−	0.0367017i
$527$	−2.14886	−	9.41477i	−0.0936058	−	0.410114i
$528$		0			0
$529$	18.0541	+	8.69438i	0.784960	+	0.378017i
$530$	12.1305	−	9.67378i	0.526917	−	0.420202i
$531$		0			0
$532$	−1.79334	−	3.72390i	−0.0777510	−	0.161452i
$533$	−0.676539	−	0.539522i	−0.0293042	−	0.0233693i
$534$		0			0
$535$	23.4040	−	29.3477i	1.01184	−	1.26881i
$536$	16.5524	+	3.77798i	0.714955	+	0.163184i
$537$		0			0
$538$	8.21844	−	10.3056i	0.354322	−	0.444306i
$539$		−	19.3987i		−	0.835563i
$540$		0			0
$541$	−15.2290	−	31.6234i	−0.654747	−	1.35960i	−0.918660	−	0.395049i	$-0.870727\pi$
$541$	−15.2290	−	31.6234i	−0.654747	−	1.35960i	0.263913	−	0.964546i	$-0.414987\pi$
$542$	7.78433	+	9.76124i	0.334366	+	0.419281i
$543$		0			0
$544$	9.93342	+	4.78368i	0.425892	+	0.205099i
$545$	0.576286	−	2.52488i	0.0246854	−	0.108154i
$546$		0			0
$547$	−2.77683	+	1.33725i	−0.118729	+	0.0571768i	−0.492305	−	0.870423i	$-0.663846\pi$
$547$	−2.77683	+	1.33725i	−0.118729	+	0.0571768i	0.373576	+	0.927599i	$0.378131\pi$
$548$	4.77578	−	9.91701i	0.204011	−	0.423634i
$549$		0			0
$550$	2.07341			0.0884107
$551$	−2.77315	−	0.947826i	−0.118140	−	0.0403787i
$552$		0			0
$553$	−36.3115	+	8.28785i	−1.54412	+	0.352435i
$554$	−4.88155	+	10.1366i	−0.207397	+	0.430665i
$555$		0			0
$556$	−3.14627	−	13.7847i	−0.133432	−	0.584602i
$557$	−4.85165	+	21.2565i	−0.205571	+	0.900666i	0.761902	+	0.647692i	$0.224266\pi$
$557$	−4.85165	+	21.2565i	−0.205571	+	0.900666i	−0.967473	+	0.252974i	$0.918591\pi$
$558$		0			0
$559$	0.374613	−	0.298744i	0.0158445	−	0.0126355i
$560$	17.4305	+	21.8571i	0.736572	+	0.923632i
$561$		0			0
$562$	−1.23260	−	0.982965i	−0.0519940	−	0.0414639i
$563$		−	5.22049i		−	0.220017i	−0.993931	−	0.110009i	$-0.964912\pi$
$563$		−	5.22049i		−	0.220017i	0.993931	−	0.110009i	$-0.0350879\pi$
$564$		0			0
$565$	−44.8061	−	10.2267i	−1.88501	−	0.430241i
$566$	2.79869	+	0.638783i	0.117638	+	0.0268500i
$567$		0			0
$568$			18.8603i			0.791361i
$569$	−20.0881	−	16.0197i	−0.842138	−	0.671583i	0.104272	−	0.994549i	$-0.466749\pi$
$569$	−20.0881	−	16.0197i	−0.842138	−	0.671583i	−0.946411	+	0.322966i	$0.895320\pi$
$570$		0			0
$571$	26.2637	+	32.9337i	1.09910	+	1.37823i	0.918848	+	0.394611i	$0.129121\pi$
$571$	26.2637	+	32.9337i	1.09910	+	1.37823i	0.180254	+	0.983620i	$0.442308\pi$
$572$	2.87622	−	2.29371i	0.120261	−	0.0959048i
$573$		0			0
$574$	−0.325805	+	1.42745i	−0.0135988	+	0.0595804i
$575$	0.968765	+	4.24444i	0.0404003	+	0.177005i
$576$		0			0
$577$	−3.03601	+	6.30433i	−0.126391	+	0.262453i	−0.954556	−	0.298030i	$-0.903670\pi$
$577$	−3.03601	+	6.30433i	−0.126391	+	0.262453i	0.828166	+	0.560483i	$0.189385\pi$
$578$	6.80992	−	1.55432i	0.283255	−	0.0646512i
$579$		0			0
$580$	24.9483	+	2.62772i	1.03592	+	0.109110i
$581$	−4.74590			−0.196893
$582$		0			0
$583$	6.64985	−	13.8085i	0.275409	−	0.571892i
$584$	6.33771	−	3.05208i	0.262256	−	0.126296i
$585$		0			0
$586$	−3.34656	+	14.6622i	−0.138245	+	0.605692i
$587$	−27.7213	−	13.3499i	−1.14418	−	0.551009i	−0.236900	−	0.971534i	$-0.576131\pi$
$587$	−27.7213	−	13.3499i	−1.14418	−	0.551009i	−0.907281	+	0.420525i	$0.861846\pi$
$588$		0			0
$589$	1.58069	+	1.98213i	0.0651313	+	0.0816721i
$590$	−2.64072	−	5.48351i	−0.108717	−	0.225753i
$591$		0			0
$592$			6.92219i			0.284500i
$593$	17.5078	−	21.9541i	0.718961	−	0.901549i	−0.279317	−	0.960199i	$-0.590108\pi$
$593$	17.5078	−	21.9541i	0.718961	−	0.901549i	0.998279	+	0.0586500i	$0.0186796\pi$
$594$		0			0
$595$	−24.8101	−	5.66274i	−1.01711	−	0.232150i
$596$	−17.0873	+	21.4267i	−0.699921	+	0.877674i
$597$		0			0
$598$	−1.07564	−	0.857797i	−0.0439863	−	0.0350779i
$599$	15.9299	+	33.0787i	0.650877	+	1.35156i	0.921313	+	0.388822i	$0.127118\pi$
$599$	15.9299	+	33.0787i	0.650877	+	1.35156i	−0.270436	+	0.962738i	$0.587168\pi$
$600$		0			0
$601$	16.6833	−	13.3045i	0.680525	−	0.542701i	−0.221083	−	0.975255i	$-0.570959\pi$
$601$	16.6833	−	13.3045i	0.680525	−	0.542701i	0.901608	+	0.432554i	$0.142388\pi$
$602$	−0.730444	−	0.351763i	−0.0297707	−	0.0143368i
$603$		0			0
$604$	−1.20214	−	5.26691i	−0.0489143	−	0.214307i
$605$	−21.7030	+	10.4516i	−0.882353	+	0.424919i
$606$		0			0
$607$	10.2345	−	2.33595i	0.415405	−	0.0948134i	−0.00971006	−	0.999953i	$-0.503091\pi$
$607$	10.2345	−	2.33595i	0.415405	−	0.0948134i	0.425115	+	0.905139i	$0.360234\pi$
$608$	−2.89447			−0.117386
$609$		0			0
$610$	−18.0264			−0.729867
$611$	−16.2743	+	3.71451i	−0.658388	+	0.150273i
$612$		0			0
$613$	−22.5656	+	10.8670i	−0.911417	+	0.438915i	−0.829999	−	0.557765i	$-0.811659\pi$
$613$	−22.5656	+	10.8670i	−0.911417	+	0.438915i	−0.0814179	+	0.996680i	$0.525945\pi$
$614$	0.650659	+	2.85072i	0.0262585	+	0.115046i
$615$		0			0
$616$	−12.2153	−	5.88260i	−0.492170	−	0.237017i
$617$	26.2440	−	20.9289i	1.05654	−	0.842565i	0.0686411	−	0.997641i	$-0.478134\pi$
$617$	26.2440	−	20.9289i	1.05654	−	0.842565i	0.987903	+	0.155076i	$0.0495622\pi$
$618$		0			0
$619$	−16.7105	−	34.6998i	−0.671653	−	1.39470i	−0.906306	−	0.422622i	$-0.861110\pi$
$619$	−16.7105	−	34.6998i	−0.671653	−	1.39470i	0.234654	−	0.972079i	$-0.424604\pi$
$620$	−16.9669	−	13.5307i	−0.681408	−	0.543405i
$621$		0			0
$622$	−2.27081	+	2.84751i	−0.0910512	+	0.114175i
$623$	20.9528	+	4.78234i	0.839456	+	0.191600i
$624$		0			0
$625$	−19.4835	+	24.4315i	−0.779340	+	0.977262i
$626$		−	0.814096i		−	0.0325378i
$627$		0			0
$628$	12.9916	+	26.9773i	0.518420	+	1.07651i
$629$	−3.92869	−	4.92643i	−0.156647	−	0.196430i
$630$		0			0
$631$	35.2889	+	16.9943i	1.40483	+	0.676531i	0.974135	−	0.225967i	$-0.0725540\pi$
$631$	35.2889	+	16.9943i	1.40483	+	0.676531i	0.430696	+	0.902497i	$0.358268\pi$
$632$	−3.76663	+	16.5027i	−0.149829	+	0.656442i
$633$		0			0
$634$	2.28585	−	1.10081i	0.0907825	−	0.0437186i
$635$	−14.6873	+	30.4984i	−0.582847	+	1.21029i
$636$		0			0
$637$	18.9226			0.749739
$638$	−4.15523	+	1.48792i	−0.164507	+	0.0589075i
$639$		0			0
$640$	30.8553	−	7.04252i	1.21966	−	0.278380i
$641$	18.3563	−	38.1173i	0.725032	−	1.50554i	−0.132539	−	0.991178i	$-0.542313\pi$
$641$	18.3563	−	38.1173i	0.725032	−	1.50554i	0.857571	−	0.514366i	$-0.171973\pi$
$642$		0			0
$643$	−5.21491	−	22.8480i	−0.205656	−	0.901038i	−0.967419	−	0.253182i	$-0.918523\pi$
$643$	−5.21491	−	22.8480i	−0.205656	−	0.901038i	0.761763	−	0.647856i	$-0.224334\pi$
$644$	2.90836	−	12.7424i	0.114606	−	0.502120i
$645$		0			0
$646$	0.484985	−	0.386763i	0.0190815	−	0.0152170i
$647$	−10.5713	−	13.2560i	−0.415602	−	0.521149i	0.529329	−	0.848416i	$-0.322444\pi$
$647$	−10.5713	−	13.2560i	−0.415602	−	0.521149i	−0.944932	+	0.327268i	$0.893872\pi$
$648$		0			0
$649$	−4.70039	−	3.74843i	−0.184506	−	0.147139i
$650$			2.02252i			0.0793297i
$651$		0			0
$652$	4.19537	+	0.957566i	0.164303	+	0.0375012i
$653$	−6.30263	−	1.43853i	−0.246641	−	0.0562942i	0.0974130	−	0.995244i	$-0.468943\pi$
$653$	−6.30263	−	1.43853i	−0.246641	−	0.0562942i	−0.344054	+	0.938950i	$0.611800\pi$
$654$		0			0
$655$			34.5764i			1.35101i
$656$	−1.05966	−	0.845052i	−0.0413728	−	0.0329937i
$657$		0			0
$658$	17.6103	+	22.0826i	0.686521	+	0.860870i
$659$	−16.1927	+	12.9133i	−0.630780	+	0.503030i	−0.885898	−	0.463880i	$-0.846457\pi$
$659$	−16.1927	+	12.9133i	−0.630780	+	0.503030i	0.255119	+	0.966910i	$0.417885\pi$
$660$		0			0
$661$	−1.12801	+	4.94211i	−0.0438743	+	0.192226i	−0.992116	−	0.125324i	$-0.960003\pi$
$661$	−1.12801	+	4.94211i	−0.0438743	+	0.192226i	0.948242	+	0.317550i	$0.102860\pi$
$662$	0.202826	+	0.888638i	0.00788305	+	0.0345379i
$663$		0			0
$664$	−0.935844	+	1.94330i	−0.0363178	+	0.0754147i
$665$	6.51342	−	1.48664i	0.252579	−	0.0576496i
$666$		0			0
$667$	−4.98735	−	7.81086i	−0.193111	−	0.302438i
$668$	23.3004			0.901519
$669$		0			0
$670$	−5.46676	+	11.3519i	−0.211199	+	0.438560i
$671$	−16.0432	+	7.72598i	−0.619339	+	0.298258i
$672$		0			0
$673$	−1.39139	+	6.09608i	−0.0536342	+	0.234987i	−0.994639	−	0.103406i	$-0.967026\pi$
$673$	−1.39139	+	6.09608i	−0.0536342	+	0.234987i	0.941005	+	0.338392i	$0.109883\pi$
$674$	−8.82190	−	4.24840i	−0.339807	−	0.163642i
$675$		0			0
$676$	−11.5226	−	14.4488i	−0.443175	−	0.555724i
$677$	−14.3011	−	29.6966i	−0.549637	−	1.14133i	−0.972016	−	0.234914i	$-0.924519\pi$
$677$	−14.3011	−	29.6966i	−0.549637	−	1.14133i	0.422379	−	0.906419i	$-0.361195\pi$
$678$		0			0
$679$		−	21.6136i		−	0.829454i
$680$	−7.21100	+	9.04231i	−0.276529	+	0.346757i
$681$		0			0
$682$	3.72236	+	0.849605i	0.142537	+	0.0325330i
$683$	19.6682	−	24.6631i	0.752582	−	0.943708i	−0.247098	−	0.968990i	$-0.579477\pi$
$683$	19.6682	−	24.6631i	0.752582	−	0.943708i	0.999680	+	0.0252824i	$0.00804850\pi$
$684$		0			0
$685$	13.9102	+	11.0930i	0.531480	+	0.423841i
$686$	−6.42026	−	13.3318i	−0.245127	−	0.509011i
$687$		0			0
$688$	0.586755	−	0.467922i	0.0223698	−	0.0178393i
$689$	13.4696	+	6.48662i	0.513151	+	0.247120i
$690$		0			0
$691$	−2.32737	−	10.1969i	−0.0885372	−	0.387907i	0.911172	−	0.412026i	$-0.135179\pi$
$691$	−2.32737	−	10.1969i	−0.0885372	−	0.387907i	−0.999709	+	0.0241197i	$0.992322\pi$
$692$	−10.7885	+	5.19545i	−0.410116	+	0.197501i
$693$		0			0
$694$	−1.98276	+	0.452553i	−0.0752646	+	0.0171787i
$695$	22.8546			0.866923
$696$		0			0
$697$	1.23376			0.0467318
$698$	−11.9504	+	2.72760i	−0.452329	+	0.103241i
$699$		0			0
$700$	−17.3111	+	8.33659i	−0.654299	+	0.315094i
$701$	−1.34313	−	5.88465i	−0.0507294	−	0.222260i	0.943209	−	0.332201i	$-0.107791\pi$
$701$	−1.34313	−	5.88465i	−0.0507294	−	0.222260i	−0.993938	+	0.109940i	$0.964934\pi$
$702$		0			0
$703$	1.49042	+	0.717750i	0.0562124	+	0.0270705i
$704$	1.89931	−	1.51465i	0.0715828	−	0.0570854i
$705$		0			0
$706$	−5.66862	−	11.7710i	−0.213341	−	0.443008i
$707$	42.0542	+	33.5371i	1.58161	+	1.26129i
$708$		0			0
$709$	−11.4416	+	14.3473i	−0.429698	+	0.538824i	−0.948796	−	0.315891i	$-0.897697\pi$
$709$	−11.4416	+	14.3473i	−0.429698	+	0.538824i	0.519097	+	0.854715i	$0.326268\pi$
$710$	−13.6455	−	3.11450i	−0.512107	−	0.116885i
$711$		0			0
$712$	6.08989	−	7.63648i	0.228228	−	0.286189i
$713$			8.01692i			0.300236i
$714$		0			0
$715$	2.58006	+	5.35756i	0.0964889	+	0.200361i
$716$	5.69718	+	7.14404i	0.212914	+	0.266985i
$717$		0			0
$718$	−17.7109	−	8.52912i	−0.660965	−	0.318304i
$719$	2.01071	−	8.80950i	0.0749868	−	0.328539i	−0.923496	−	0.383609i	$-0.874681\pi$
$719$	2.01071	−	8.80950i	0.0749868	−	0.328539i	0.998482	+	0.0550701i	$0.0175382\pi$
$720$		0			0
$721$	27.2308	−	13.1137i	1.01413	−	0.488379i
$722$	4.46240	−	9.26627i	0.166073	−	0.344855i
$723$		0			0
$724$	−26.6447			−0.990241
$725$	−4.40611	+	12.8914i	−0.163639	+	0.478775i
$726$		0			0
$727$	5.64989	−	1.28955i	0.209543	−	0.0478268i	−0.116461	−	0.993195i	$-0.537155\pi$
$727$	5.64989	−	1.28955i	0.209543	−	0.0478268i	0.326004	+	0.945368i	$0.394298\pi$
$728$	5.73820	−	11.9155i	0.212672	−	0.441618i
$729$		0			0
$730$	1.16162	+	5.08937i	0.0429933	+	0.188366i
$731$	−0.152016	+	0.666027i	−0.00562253	+	0.0246339i
$732$		0			0
$733$	−5.33969	+	4.25826i	−0.197226	+	0.157282i	−0.717123	−	0.696946i	$-0.754542\pi$
$733$	−5.33969	+	4.25826i	−0.197226	+	0.157282i	0.519897	+	0.854229i	$0.325970\pi$
$734$	0.484438	+	0.607466i	0.0178809	+	0.0224220i
$735$		0			0
$736$	−7.15603	−	5.70675i	−0.263775	−	0.210353i
$737$			12.4460i			0.458453i
$738$		0			0
$739$	−33.0680	−	7.54755i	−1.21643	−	0.277641i	−0.434304	−	0.900767i	$-0.643005\pi$
$739$	−33.0680	−	7.54755i	−1.21643	−	0.277641i	−0.782122	+	0.623125i	$0.785863\pi$
$740$	−13.8052	−	3.15096i	−0.507491	−	0.115832i
$741$		0			0
$742$		−	25.2960i		−	0.928646i
$743$	24.7299	+	19.7214i	0.907252	+	0.723509i	0.961438	−	0.275021i	$-0.0886850\pi$
$743$	24.7299	+	19.7214i	0.907252	+	0.723509i	−0.0541860	+	0.998531i	$0.517256\pi$
$744$		0			0
$745$	−27.6198	−	34.6341i	−1.01191	−	1.26890i
$746$	−1.55335	+	1.23876i	−0.0568723	+	0.0453542i
$747$		0			0
$748$	−1.16716	+	5.11365i	−0.0426755	+	0.186973i
$749$	−13.6181	−	59.6648i	−0.497594	−	2.18010i
$750$		0			0
$751$	10.0485	−	20.8659i	0.366675	−	0.761408i	−0.633247	−	0.773950i	$-0.718278\pi$
$751$	10.0485	−	20.8659i	0.366675	−	0.761408i	0.999921	+	0.0125423i	$0.00399245\pi$
$752$	−25.4904	+	5.81802i	−0.929539	+	0.212161i
$753$		0			0
$754$	−1.45140	−	4.05323i	−0.0528569	−	0.147610i
$755$	8.73235			0.317803
$756$		0			0
$757$	0.873631	−	1.81411i	0.0317527	−	0.0659351i	−0.884489	−	0.466561i	$-0.845493\pi$
$757$	0.873631	−	1.81411i	0.0317527	−	0.0659351i	0.916242	+	0.400626i	$0.131207\pi$
$758$	2.83338	−	1.36448i	0.102913	−	0.0495603i
$759$		0			0
$760$	0.675644	−	2.96019i	0.0245082	−	0.107377i
$761$	6.54560	+	3.15220i	0.237278	+	0.114267i	0.548745	−	0.835990i	$-0.315106\pi$
$761$	6.54560	+	3.15220i	0.237278	+	0.114267i	−0.311467	+	0.950257i	$0.600820\pi$
$762$		0			0
$763$	−2.63258	−	3.30115i	−0.0953059	−	0.119510i
$764$	−3.15455	−	6.55048i	−0.114128	−	0.236988i
$765$		0			0
$766$		−	5.97548i		−	0.215903i
$767$	3.65642	−	4.58501i	0.132026	−	0.165555i
$768$		0			0
$769$	−25.9802	−	5.92981i	−0.936869	−	0.213834i	−0.273283	−	0.961934i	$-0.588109\pi$
$769$	−25.9802	−	5.92981i	−0.936869	−	0.213834i	−0.663587	+	0.748099i	$0.730967\pi$
$770$	6.27326	−	7.86642i	0.226073	−	0.283486i
$771$		0			0
$772$	−31.3629	−	25.0111i	−1.12877	−	0.900168i
$773$	7.26841	+	15.0930i	0.261427	+	0.542858i	0.989824	−	0.142297i	$-0.0454488\pi$
$773$	7.26841	+	15.0930i	0.261427	+	0.542858i	−0.728397	+	0.685155i	$0.759734\pi$
$774$		0			0
$775$	9.21422	−	7.34809i	0.330984	−	0.263951i
$776$	−8.85009	−	4.26198i	−0.317700	−	0.152996i
$777$		0			0
$778$	3.30781	+	14.4925i	0.118591	+	0.519580i
$779$	−0.291823	+	0.140535i	−0.0104557	+	0.00503518i
$780$		0			0
$781$	−13.4791	+	3.07652i	−0.482321	+	0.110087i
$782$	1.96157			0.0701457
$783$		0			0
$784$	29.6383			1.05851
$785$	−47.1856	+	10.7698i	−1.68412	+	0.384391i
$786$		0			0
$787$	21.2463	−	10.2317i	0.757349	−	0.364720i	−0.0150260	−	0.999887i	$-0.504783\pi$
$787$	21.2463	−	10.2317i	0.757349	−	0.364720i	0.772375	+	0.635167i	$0.219069\pi$
$788$	−1.91355	−	8.38383i	−0.0681675	−	0.298662i
$789$		0			0
$790$	−11.3178	−	5.45035i	−0.402668	−	0.193915i
$791$	−58.5818	+	46.7175i	−2.08293	+	1.66108i
$792$		0			0
$793$	−7.53634	−	15.6494i	−0.267623	−	0.555725i
$794$	−12.6497	−	10.0878i	−0.448923	−	0.358004i
$795$		0			0
$796$	−24.9051	+	31.2300i	−0.882737	+	1.10692i
$797$	−27.8945	−	6.36673i	−0.988073	−	0.225521i	−0.302202	−	0.953244i	$-0.597722\pi$
$797$	−27.8945	−	6.36673i	−0.988073	−	0.225521i	−0.685871	+	0.727723i	$0.740579\pi$
$798$		0			0
$799$	14.8391	−	18.6077i	0.524971	−	0.658293i
$800$			13.4554i			0.475720i
$801$		0			0
$802$	1.88949	+	3.92357i	0.0667203	+	0.138546i
$803$	3.21508	+	4.03159i	0.113458	+	0.142272i
$804$		0			0
$805$	19.0342	+	9.16641i	0.670869	+	0.323073i
$806$	−0.828750	+	3.63099i	−0.0291915	+	0.127896i
$807$		0			0
$808$	22.0250	−	10.6067i	0.774838	−	0.373142i
$809$	−4.98171	+	10.3446i	−0.175148	+	0.363698i	−0.970000	−	0.243105i	$-0.921834\pi$
$809$	−4.98171	+	10.3446i	−0.175148	+	0.363698i	0.794852	+	0.606803i	$0.207548\pi$
$810$		0			0
$811$	−26.3454			−0.925111			−0.462555	−	0.886590i	$-0.653067\pi$
$811$	−26.3454			−0.925111			−0.462555	+	0.886590i	$0.653067\pi$
$812$	28.7098	−	29.1298i	1.00752	−	1.02225i
$813$		0			0
$814$	2.42885	−	0.554368i	0.0851310	−	0.0194306i
$815$	−3.01800	+	6.26694i	−0.105716	+	0.219521i
$816$		0			0
$817$	−0.0399090	−	0.174853i	−0.00139624	−	0.00611733i
$818$	3.15324	−	13.8153i	0.110250	−	0.483039i
$819$		0			0
$820$	2.16768	−	1.72867i	0.0756987	−	0.0603677i
$821$	7.84675	+	9.83951i	0.273853	+	0.343401i	0.899671	−	0.436568i	$-0.143806\pi$
$821$	7.84675	+	9.83951i	0.273853	+	0.343401i	−0.625818	+	0.779969i	$0.715235\pi$
$822$		0			0
$823$	37.3908	+	29.8182i	1.30336	+	1.03940i	0.996142	+	0.0877587i	$0.0279704\pi$
$823$	37.3908	+	29.8182i	1.30336	+	1.03940i	0.307221	+	0.951638i	$0.400601\pi$
$824$		−	13.7360i		−	0.478518i
$825$		0			0
$826$	−9.67402	−	2.20803i	−0.336602	−	0.0768272i
$827$	9.20610	+	2.10123i	0.320128	+	0.0730670i	0.379565	−	0.925165i	$-0.376074\pi$
$827$	9.20610	+	2.10123i	0.320128	+	0.0730670i	−0.0594376	+	0.998232i	$0.518931\pi$
$828$		0			0
$829$		−	22.2232i		−	0.771843i	−0.922532	−	0.385921i	$-0.873884\pi$
$829$		−	22.2232i		−	0.771843i	0.922532	−	0.385921i	$-0.126116\pi$
$830$	−1.25144	−	0.997994i	−0.0434383	−	0.0346409i
$831$		0			0
$832$	1.47747	+	1.85268i	0.0512220	+	0.0642303i
$833$	−21.0932	+	16.8213i	−0.730836	+	0.582822i
$834$		0			0
$835$	−8.38074	+	36.7184i	−0.290027	+	1.27069i
$836$	−0.306415	−	1.34249i	−0.0105976	−	0.0464311i
$837$		0			0
$838$	−0.0886786	+	0.184143i	−0.00306335	+	0.00636112i
$839$	40.5091	−	9.24594i	1.39853	−	0.319205i	0.544208	−	0.838950i	$-0.316830\pi$
$839$	40.5091	−	9.24594i	1.39853	−	0.319205i	0.854321	+	0.519745i	$0.173973\pi$
$840$		0			0
$841$	−0.421076	−	28.9969i	−0.0145198	−	0.999895i
$842$	12.3243			0.424723
$843$		0			0
$844$	13.5025	−	28.0383i	0.464776	−	0.965118i
$845$	26.9140	−	12.9611i	0.925868	−	0.445875i
$846$		0			0
$847$	−8.73909	+	38.2885i	−0.300279	+	1.31561i
$848$	21.0974	+	10.1600i	0.724487	+	0.348895i
$849$		0			0
$850$	−1.79792	−	2.25453i	−0.0616683	−	0.0773296i
$851$	2.26967	+	4.71302i	0.0778033	+	0.161560i
$852$		0			0
$853$			1.76038i			0.0602743i	0.999546	+	0.0301371i	$0.00959440\pi$
$853$			1.76038i			0.0602743i	−0.999546	+	0.0301371i	$0.990406\pi$
$854$	−18.3241	+	22.9777i	−0.627039	+	0.786282i
$855$		0			0
$856$	−27.1162	−	6.18910i	−0.926813	−	0.211539i
$857$	8.71902	−	10.9333i	0.297836	−	0.373474i	−0.610285	−	0.792182i	$-0.708945\pi$
$857$	8.71902	−	10.9333i	0.297836	−	0.373474i	0.908121	+	0.418707i	$0.137517\pi$
$858$		0			0
$859$	0.625735	+	0.499007i	0.0213498	+	0.0170259i	0.634107	−	0.773246i	$-0.281368\pi$
$859$	0.625735	+	0.499007i	0.0213498	+	0.0170259i	−0.612757	+	0.790272i	$0.709939\pi$
$860$	0.666109	+	1.38319i	0.0227141	+	0.0471664i
$861$		0			0
$862$	14.9786	−	11.9451i	0.510174	−	0.406850i
$863$	−9.60543	−	4.62573i	−0.326973	−	0.157462i	0.263194	−	0.964743i	$-0.415224\pi$
$863$	−9.60543	−	4.62573i	−0.326973	−	0.157462i	−0.590167	+	0.807281i	$0.700938\pi$
$864$		0			0
$865$	−4.30694	−	18.8699i	−0.146440	−	0.641597i
$866$	−10.6781	+	5.14231i	−0.362857	+	0.174743i
$867$		0			0
$868$	−34.4943	+	7.87311i	−1.17081	+	0.267231i
$869$	−12.4086			−0.420932
$870$		0			0
$871$	−12.1405			−0.411364
$872$	−1.87084	+	0.427007i	−0.0633546	+	0.0144603i
$873$		0			0
$874$	−0.463976	+	0.223439i	−0.0156942	+	0.00755793i
$875$	6.74788	+	29.5644i	0.228120	+	0.999458i
$876$		0			0
$877$	14.6169	+	7.03914i	0.493578	+	0.237695i	0.664078	−	0.747663i	$-0.268824\pi$
$877$	14.6169	+	7.03914i	0.493578	+	0.237695i	−0.170500	+	0.985358i	$0.554538\pi$
$878$	0.706248	−	0.563214i	0.0238347	−	0.0190076i
$879$		0			0
$880$	4.04114	+	8.39152i	0.136227	+	0.282878i
$881$	17.6471	+	14.0731i	0.594545	+	0.474134i	0.873934	−	0.486044i	$-0.161561\pi$
$881$	17.6471	+	14.0731i	0.594545	+	0.474134i	−0.279389	+	0.960178i	$0.590132\pi$
$882$		0			0
$883$	−6.36666	+	7.98354i	−0.214255	+	0.268668i	−0.877332	−	0.479884i	$-0.840679\pi$
$883$	−6.36666	+	7.98354i	−0.214255	+	0.268668i	0.663077	+	0.748551i	$0.269250\pi$
$884$	−4.98813	−	1.13851i	−0.167769	−	0.0382921i
$885$		0			0
$886$	−12.1284	+	15.2085i	−0.407461	+	0.510939i
$887$		−	45.7130i		−	1.53489i	−0.641113	−	0.767447i	$-0.721527\pi$
$887$		−	45.7130i		−	1.53489i	0.641113	−	0.767447i	$-0.278473\pi$
$888$		0			0
$889$	23.9456	+	49.7236i	0.803111	+	1.66768i
$890$	4.51937	+	5.66711i	0.151490	+	0.189962i
$891$		0			0
$892$	7.33333	+	3.53154i	0.245538	+	0.118245i
$893$	−1.39037	+	6.09162i	−0.0465270	+	0.203848i
$894$		0			0
$895$	−13.3073	+	6.40844i	−0.444813	+	0.214211i
$896$	22.3880	−	46.4892i	0.747932	−	1.55310i
$897$		0			0
$898$	−6.79273			−0.226676
$899$	−13.1926	+	21.3383i	−0.439998	+	0.711671i
$900$		0			0
$901$	−20.7810	+	4.74313i	−0.692316	+	0.158017i
$902$	−0.211647	+	0.439489i	−0.00704706	+	0.0146334i
$903$		0			0
$904$	7.57760	+	33.1996i	0.252027	+	1.10420i
$905$	9.58361	−	41.9886i	0.318570	−	1.39575i
$906$		0			0
$907$	25.2645	−	20.1478i	0.838894	−	0.668996i	−0.106719	−	0.994289i	$-0.534035\pi$
$907$	25.2645	−	20.1478i	0.838894	−	0.668996i	0.945613	+	0.325293i	$0.105463\pi$
$908$	−3.61346	−	4.53114i	−0.119917	−	0.150371i
$909$		0			0
$910$	7.67333	+	6.11928i	0.254368	+	0.202852i
$911$		−	10.6165i		−	0.351739i	−0.984413	−	0.175870i	$-0.943726\pi$
$911$		−	10.6165i		−	0.351739i	0.984413	−	0.175870i	$-0.0562737\pi$
$912$		0			0
$913$	−1.54150	−	0.351836i	−0.0510161	−	0.0116441i
$914$	−16.7893	−	3.83205i	−0.555341	−	0.126753i
$915$		0			0
$916$			33.8984i			1.12004i
$917$	44.0736	+	35.1475i	1.45544	+	1.16067i
$918$		0			0
$919$	11.4579	+	14.3678i	0.377962	+	0.473949i	0.934034	−	0.357185i	$-0.116263\pi$
$919$	11.4579	+	14.3678i	0.377962	+	0.473949i	−0.556072	+	0.831134i	$0.687692\pi$
$920$	7.50672	−	5.98641i	0.247489	−	0.197366i
$921$		0			0
$922$	−0.791108	+	3.46607i	−0.0260537	+	0.114149i
$923$	−3.00100	−	13.1483i	−0.0987792	−	0.432780i
$924$		0			0
$925$	3.33657	−	6.92846i	0.109706	−	0.227806i
$926$	−7.78478	+	1.77682i	−0.255824	+	0.0583901i
$927$		0			0
$928$	−9.65587	−	26.9653i	−0.316970	−	0.885179i
$929$	−56.4863			−1.85325			−0.926627	−	0.375981i	$-0.877306\pi$
$929$	−56.4863			−1.85325			−0.926627	+	0.375981i	$0.877306\pi$
$930$		0			0
$931$	3.07315	−	6.38146i	0.100718	−	0.209144i
$932$	−6.33734	+	3.05190i	−0.207586	+	0.0999684i
$933$		0			0
$934$	3.20013	−	14.0207i	0.104711	−	0.458770i
$935$	−7.63864	−	3.67858i	−0.249810	−	0.120302i
$936$		0			0
$937$	18.0257	+	22.6035i	0.588874	+	0.738425i	0.983598	−	0.180375i	$-0.0577312\pi$
$937$	18.0257	+	22.6035i	0.588874	+	0.738425i	−0.394724	+	0.918800i	$0.629160\pi$
$938$	8.91283	+	18.5077i	0.291014	+	0.604297i
$939$		0			0
$940$		−	53.4850i		−	1.74449i
$941$	1.55635	−	1.95160i	0.0507355	−	0.0636202i	−0.755816	−	0.654784i	$-0.772760\pi$
$941$	1.55635	−	1.95160i	0.0507355	−	0.0636202i	0.806552	+	0.591163i	$0.201331\pi$
$942$		0			0
$943$	−0.998555	−	0.227914i	−0.0325174	−	0.00742189i
$944$	5.72704	−	7.18148i	0.186399	−	0.233737i
$945$		0			0
$946$	−0.211174	−	0.168406i	−0.00686587	−	0.00547535i
$947$	4.44526	+	9.23068i	0.144452	+	0.299957i	0.960624	−	0.277852i	$-0.0896224\pi$
$947$	4.44526	+	9.23068i	0.144452	+	0.299957i	−0.816172	+	0.577808i	$0.803908\pi$
$948$		0			0
$949$	−3.93263	+	3.13616i	−0.127658	+	0.101804i
$950$	0.682076	+	0.328470i	0.0221295	+	0.0106570i
$951$		0			0
$952$	4.19587	+	18.3833i	0.135989	+	0.595807i
$953$	−3.97726	+	1.91535i	−0.128836	+	0.0620442i	−0.497191	−	0.867641i	$-0.665635\pi$
$953$	−3.97726	+	1.91535i	−0.128836	+	0.0620442i	0.368355	+	0.929685i	$0.379921\pi$
$954$		0			0
$955$	11.4574	−	2.61507i	0.370751	−	0.0846215i
$956$	−35.4760			−1.14738
$957$		0			0
$958$	13.8718			0.448177
$959$	28.2798	−	6.45468i	0.913203	−	0.208433i
$960$		0			0
$961$	−8.37697	+	4.03413i	−0.270225	+	0.130133i
$962$	0.540761	+	2.36923i	0.0174348	+	0.0763870i
$963$		0			0
$964$	5.59348	+	2.69368i	0.180154	+	0.0867575i
$965$	50.6949	−	40.4278i	1.63193	−	1.30142i
$966$		0			0
$967$	7.82186	+	16.2423i	0.251534	+	0.522316i	0.988056	−	0.154098i	$-0.0492473\pi$
$967$	7.82186	+	16.2423i	0.251534	+	0.522316i	−0.736521	+	0.676414i	$0.763533\pi$
$968$	13.9547	+	11.1285i	0.448520	+	0.357683i
$969$		0			0
$970$	4.54502	−	5.69928i	0.145932	−	0.182993i
$971$	23.6230	+	5.39179i	0.758097	+	0.173031i	0.584062	−	0.811709i	$-0.301462\pi$
$971$	23.6230	+	5.39179i	0.758097	+	0.173031i	0.174035	+	0.984739i	$0.444319\pi$
$972$		0			0
$973$	23.2321	−	29.1321i	0.744785	−	0.933931i
$974$		−	22.0626i		−	0.706931i
$975$		0			0
$976$	−11.8041	−	24.5115i	−0.377841	−	0.784595i
$977$	−3.03471	−	3.80541i	−0.0970890	−	0.121746i	0.730914	−	0.682470i	$-0.239094\pi$
$977$	−3.03471	−	3.80541i	−0.0970890	−	0.121746i	−0.828003	+	0.560724i	$0.810523\pi$
$978$		0			0
$979$	6.45104	+	3.10666i	0.206176	+	0.0992892i
$980$	−13.4913	+	59.1091i	−0.430963	+	1.88817i
$981$		0			0
$982$	−5.04007	+	2.42717i	−0.160835	+	0.0774540i
$983$	−10.0684	+	20.9073i	−0.321133	+	0.666840i	−0.997571	−	0.0696600i	$-0.977809\pi$
$983$	−10.0684	+	20.9073i	−0.321133	+	0.666840i	0.676438	+	0.736500i	$0.263523\pi$
$984$		0			0
$985$	13.9001			0.442894
$986$	5.22102	+	3.22795i	0.166271	+	0.102799i
$987$		0			0
$988$	1.30954	−	0.298894i	0.0416620	−	0.00950907i
$989$	0.246072	−	0.510975i	0.00782465	−	0.0162481i
$990$		0			0
$991$	−5.94679	−	26.0546i	−0.188906	−	0.827651i	−0.977195	−	0.212346i	$-0.931890\pi$
$991$	−5.94679	−	26.0546i	−0.188906	−	0.827651i	0.788289	−	0.615306i	$-0.210967\pi$
$992$	−5.51350	+	24.1562i	−0.175054	+	0.766961i
$993$		0			0
$994$	−17.8409	+	14.2276i	−0.565878	+	0.451272i
$995$	−40.2565	−	50.4801i	−1.27622	−	1.60033i
$996$		0			0
$997$	23.2732	+	18.5597i	0.737069	+	0.587793i	0.918411	−	0.395627i	$-0.129473\pi$
$997$	23.2732	+	18.5597i	0.737069	+	0.587793i	−0.181342	+	0.983420i	$0.558044\pi$
$998$			4.53027i			0.143403i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.o.a.109.1		12
3.2	odd	2		29.2.e.a.22.2	yes	12
12.11	even	2		464.2.y.d.225.1		12
15.2	even	4		725.2.p.a.399.2		24
15.8	even	4		725.2.p.a.399.3		24
15.14	odd	2		725.2.q.a.51.1		12
29.2	odd	28		7569.2.a.bp.1.8		12
29.4	even	14	inner	261.2.o.a.91.1		12
29.27	odd	28		7569.2.a.bp.1.5		12
87.2	even	28		841.2.a.k.1.5		12
87.5	odd	14		841.2.b.e.840.8		12
87.8	even	28		841.2.d.l.190.2		24
87.11	even	28		841.2.d.k.574.2		24
87.14	even	28		841.2.d.l.571.3		24
87.17	even	4		841.2.d.m.645.3		24
87.20	odd	14		841.2.e.a.651.2		12
87.23	odd	14		841.2.e.h.270.1		12
87.26	even	28		841.2.d.k.778.3		24
87.32	even	28		841.2.d.k.778.2		24
87.35	odd	14		841.2.e.a.270.2		12
87.38	odd	14		841.2.e.h.651.1		12
87.41	even	4		841.2.d.m.645.2		24
87.44	even	28		841.2.d.l.571.2		24
87.47	even	28		841.2.d.k.574.3		24
87.50	even	28		841.2.d.l.190.3		24
87.53	odd	14		841.2.b.e.840.5		12
87.56	even	28		841.2.a.k.1.8		12
87.62	odd	14		29.2.e.a.4.2	✓	12
87.65	odd	14		841.2.e.e.63.1		12
87.68	even	28		841.2.d.m.605.2		24
87.71	odd	14		841.2.e.e.267.1		12
87.74	odd	14		841.2.e.f.267.2		12
87.77	even	28		841.2.d.m.605.3		24
87.80	odd	14		841.2.e.f.63.2		12
87.83	odd	14		841.2.e.i.236.1		12
87.86	odd	2		841.2.e.i.196.1		12
348.323	even	14		464.2.y.d.33.1		12
435.62	even	28		725.2.p.a.149.3		24
435.149	odd	14		725.2.q.a.526.1		12
435.323	even	28		725.2.p.a.149.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.e.a.4.2	✓	12	87.62	odd	14
29.2.e.a.22.2	yes	12	3.2	odd	2
261.2.o.a.91.1		12	29.4	even	14	inner
261.2.o.a.109.1		12	1.1	even	1	trivial
464.2.y.d.33.1		12	348.323	even	14
464.2.y.d.225.1		12	12.11	even	2
725.2.p.a.149.2		24	435.323	even	28
725.2.p.a.149.3		24	435.62	even	28
725.2.p.a.399.2		24	15.2	even	4
725.2.p.a.399.3		24	15.8	even	4
725.2.q.a.51.1		12	15.14	odd	2
725.2.q.a.526.1		12	435.149	odd	14
841.2.a.k.1.5		12	87.2	even	28
841.2.a.k.1.8		12	87.56	even	28
841.2.b.e.840.5		12	87.53	odd	14
841.2.b.e.840.8		12	87.5	odd	14
841.2.d.k.574.2		24	87.11	even	28
841.2.d.k.574.3		24	87.47	even	28
841.2.d.k.778.2		24	87.32	even	28
841.2.d.k.778.3		24	87.26	even	28
841.2.d.l.190.2		24	87.8	even	28
841.2.d.l.190.3		24	87.50	even	28
841.2.d.l.571.2		24	87.44	even	28
841.2.d.l.571.3		24	87.14	even	28
841.2.d.m.605.2		24	87.68	even	28
841.2.d.m.605.3		24	87.77	even	28
841.2.d.m.645.2		24	87.41	even	4
841.2.d.m.645.3		24	87.17	even	4
841.2.e.a.270.2		12	87.35	odd	14
841.2.e.a.651.2		12	87.20	odd	14
841.2.e.e.63.1		12	87.65	odd	14
841.2.e.e.267.1		12	87.71	odd	14
841.2.e.f.63.2		12	87.80	odd	14
841.2.e.f.267.2		12	87.74	odd	14
841.2.e.h.270.1		12	87.23	odd	14
841.2.e.h.651.1		12	87.38	odd	14
841.2.e.i.196.1		12	87.86	odd	2
841.2.e.i.236.1		12	87.83	odd	14
7569.2.a.bp.1.5		12	29.27	odd	28
7569.2.a.bp.1.8		12	29.2	odd	28

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.o (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.536089 - 0.122359i) q^{2} +(-1.52952 + 0.736577i) q^{4} +(-0.610610 - 2.67526i) q^{5} +(-4.03077 - 1.94112i) q^{7} +(-1.58965 + 1.26771i) q^{8} +O(q^{10})\)	\(q+(0.536089 - 0.122359i) q^{2} +(-1.52952 + 0.736577i) q^{4} +(-0.610610 - 2.67526i) q^{5} +(-4.03077 - 1.94112i) q^{7} +(-1.58965 + 1.26771i) q^{8} +(-0.654683 - 1.35946i) q^{10} +(-1.16531 - 0.929305i) q^{11} +(0.906494 - 1.13671i) q^{13} +(-2.39836 - 0.547411i) q^{14} +(1.41984 - 1.78042i) q^{16} +2.07293i q^{17} +(-0.236123 - 0.490315i) q^{19} +(2.90447 + 3.64209i) q^{20} +(-0.738420 - 0.355604i) q^{22} +(0.382936 - 1.67775i) q^{23} +(-2.27930 + 1.09766i) q^{25} +(0.346875 - 0.720294i) q^{26} +7.59491 q^{28} +(3.78014 - 3.83543i) q^{29} +(-4.54177 + 1.03663i) q^{31} +(2.30769 - 4.79197i) q^{32} +(0.253641 + 1.11128i) q^{34} +(-2.73175 + 11.9686i) q^{35} +(-2.37655 + 1.89524i) q^{37} +(-0.186578 - 0.233961i) q^{38} +(4.36209 + 3.47865i) q^{40} -0.595175i q^{41} +(0.321297 + 0.0733340i) q^{43} +(2.46687 + 0.563047i) q^{44} -0.946280i q^{46} +(-8.97652 - 7.15853i) q^{47} +(8.11473 + 10.1755i) q^{49} +(-1.08760 + 0.867335i) q^{50} +(-0.549226 + 2.40632i) q^{52} +(2.28813 + 10.0249i) q^{53} +(-1.77458 + 3.68495i) q^{55} +(8.86828 - 2.02413i) q^{56} +(1.55719 - 2.51867i) q^{58} +4.03359 q^{59} +(5.18352 - 10.7637i) q^{61} +(-2.30795 + 1.11145i) q^{62} +(-0.362680 + 1.58901i) q^{64} +(-3.59450 - 1.73102i) q^{65} +(-5.20630 - 6.52849i) q^{67} +(-1.52687 - 3.17058i) q^{68} +6.75049i q^{70} +(5.78348 - 7.25226i) q^{71} +(-3.37292 - 0.769848i) q^{73} +(-1.04215 + 1.30681i) q^{74} +(0.722310 + 0.576023i) q^{76} +(2.89321 + 6.00781i) q^{77} +(6.50888 - 5.19066i) q^{79} +(-5.63005 - 2.71129i) q^{80} +(-0.0728249 - 0.319067i) q^{82} +(0.955764 - 0.460272i) q^{83} +(5.54562 - 1.26575i) q^{85} +0.181217 q^{86} +3.03052 q^{88} +(-4.68343 + 1.06896i) q^{89} +(-5.86034 + 2.82219i) q^{91} +(0.650086 + 2.84821i) q^{92} +(-5.68812 - 2.73926i) q^{94} +(-1.16754 + 0.931082i) q^{95} +(2.09615 + 4.35270i) q^{97} +(5.59529 + 4.46209i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 7 q^{2} - q^{4} + q^{5} - 11 q^{7} - 14 q^{8}+O(q^{10}) \) 12 * q + 7 * q^2 - q^4 + q^5 - 11 * q^7 - 14 * q^8	\( 12 q + 7 q^{2} - q^{4} + q^{5} - 11 q^{7} - 14 q^{8} - 7 q^{10} - 7 q^{11} + 9 q^{13} + 7 q^{14} + 9 q^{16} - 7 q^{19} + 11 q^{20} - 4 q^{22} + 5 q^{23} + 13 q^{25} + 21 q^{26} + 12 q^{28} + 15 q^{29} - 21 q^{31} - 13 q^{34} - 19 q^{35} + 7 q^{37} - 28 q^{38} + 35 q^{40} + 7 q^{43} - 42 q^{44} + 7 q^{47} + 13 q^{49} + 28 q^{50} - 6 q^{52} + 10 q^{53} - 35 q^{55} + 21 q^{56} - 57 q^{58} - 44 q^{59} - 7 q^{61} - 37 q^{62} - 26 q^{64} + 6 q^{65} - 37 q^{67} - 14 q^{68} + 21 q^{71} + 14 q^{73} + 7 q^{76} + 7 q^{77} + 49 q^{79} + 6 q^{80} + 22 q^{82} - 5 q^{83} + 14 q^{85} + 44 q^{86} - 66 q^{88} - 7 q^{89} - 3 q^{91} + 6 q^{92} + 66 q^{94} + 7 q^{95} + 14 q^{97} + 42 q^{98}+O(q^{100}) \) 12 * q + 7 * q^2 - q^4 + q^5 - 11 * q^7 - 14 * q^8 - 7 * q^10 - 7 * q^11 + 9 * q^13 + 7 * q^14 + 9 * q^16 - 7 * q^19 + 11 * q^20 - 4 * q^22 + 5 * q^23 + 13 * q^25 + 21 * q^26 + 12 * q^28 + 15 * q^29 - 21 * q^31 - 13 * q^34 - 19 * q^35 + 7 * q^37 - 28 * q^38 + 35 * q^40 + 7 * q^43 - 42 * q^44 + 7 * q^47 + 13 * q^49 + 28 * q^50 - 6 * q^52 + 10 * q^53 - 35 * q^55 + 21 * q^56 - 57 * q^58 - 44 * q^59 - 7 * q^61 - 37 * q^62 - 26 * q^64 + 6 * q^65 - 37 * q^67 - 14 * q^68 + 21 * q^71 + 14 * q^73 + 7 * q^76 + 7 * q^77 + 49 * q^79 + 6 * q^80 + 22 * q^82 - 5 * q^83 + 14 * q^85 + 44 * q^86 - 66 * q^88 - 7 * q^89 - 3 * q^91 + 6 * q^92 + 66 * q^94 + 7 * q^95 + 14 * q^97 + 42 * q^98

Introduction

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