LMFDB - Embedded newform 81.2.e.a.10.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,2,Mod(10,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

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("81.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	81.e (of order $9$, degree $6$, 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:	$0.646788256372$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			10.1
Root			$0.500000 + 1.00210i$ of defining polynomial
Character	$\chi$	$=$	81.10
Dual form			81.2.e.a.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.183082 - 1.03831i) q^{2} +(0.834822 - 0.303850i) q^{4} +(1.33735 + 1.12217i) q^{5} +(-2.31094 - 0.841112i) q^{7} +(-1.52266 - 2.63732i) q^{8} +O(q^{10})$	\(q+(-0.183082 - 1.03831i) q^{2} +(0.834822 - 0.303850i) q^{4} +(1.33735 + 1.12217i) q^{5} +(-2.31094 - 0.841112i) q^{7} +(-1.52266 - 2.63732i) q^{8} +(0.920313 - 1.59403i) q^{10} +(0.960783 - 0.806193i) q^{11} +(-0.789931 + 4.47992i) q^{13} +(-0.450243 + 2.55345i) q^{14} +(-1.09847 + 0.921724i) q^{16} +(-3.32358 + 5.75662i) q^{17} +(-0.124578 - 0.215776i) q^{19} +(1.45742 + 0.530458i) q^{20} +(-1.01298 - 0.849989i) q^{22} +(0.791222 - 0.287981i) q^{23} +(-0.339001 - 1.92257i) q^{25} +4.79615 q^{26} -2.18479 q^{28} +(0.0889744 + 0.504599i) q^{29} +(0.770551 - 0.280458i) q^{31} +(-3.50754 - 2.94318i) q^{32} +(6.58563 + 2.39697i) q^{34} +(-2.14666 - 3.71812i) q^{35} +(-1.30403 + 2.25865i) q^{37} +(-0.201233 + 0.168855i) q^{38} +(0.923194 - 5.23570i) q^{40} +(1.41572 - 8.02895i) q^{41} +(3.31478 - 2.78143i) q^{43} +(0.557121 - 0.964962i) q^{44} +(-0.443871 - 0.768808i) q^{46} +(-4.98256 - 1.81351i) q^{47} +(-0.729356 - 0.612002i) q^{49} +(-1.93415 + 0.703974i) q^{50} +(0.701774 + 3.97996i) q^{52} +10.4841 q^{53} +2.18959 q^{55} +(1.30048 + 7.37539i) q^{56} +(0.507639 - 0.184765i) q^{58} +(2.30289 + 1.93235i) q^{59} +(-2.70930 - 0.986103i) q^{61} +(-0.432275 - 0.748722i) q^{62} +(-3.84771 + 6.66442i) q^{64} +(-6.08365 + 5.10479i) q^{65} +(1.75146 - 9.93303i) q^{67} +(-1.02545 + 5.81562i) q^{68} +(-3.46754 + 2.90961i) q^{70} +(0.0447378 - 0.0774882i) q^{71} +(2.66057 + 4.60824i) q^{73} +(2.58391 + 0.940468i) q^{74} +(-0.169564 - 0.142281i) q^{76} +(-2.89841 + 1.05493i) q^{77} +(0.829503 + 4.70435i) q^{79} -2.50337 q^{80} -8.59571 q^{82} +(-1.39625 - 7.91851i) q^{83} +(-10.9047 + 3.96899i) q^{85} +(-3.49486 - 2.93254i) q^{86} +(-3.58913 - 1.30634i) q^{88} +(3.35189 + 5.80564i) q^{89} +(5.59359 - 9.68839i) q^{91} +(0.573026 - 0.480826i) q^{92} +(-0.970760 + 5.50545i) q^{94} +(0.0755324 - 0.428365i) q^{95} +(4.20603 - 3.52928i) q^{97} +(-0.501915 + 0.869342i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 6 q^{4} + 3 q^{5} - 6 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q + 6 * q^2 - 6 * q^4 + 3 * q^5 - 6 * q^7 - 6 * q^8	$ 12 q + 6 q^{2} - 6 q^{4} + 3 q^{5} - 6 q^{7} - 6 q^{8} - 3 q^{10} - 3 q^{11} - 6 q^{13} - 15 q^{14} - 9 q^{17} - 3 q^{19} + 3 q^{20} + 3 q^{22} + 12 q^{23} + 3 q^{25} + 30 q^{26} - 12 q^{28} + 6 q^{29} + 3 q^{31} + 9 q^{34} - 12 q^{35} - 3 q^{37} - 42 q^{38} + 21 q^{40} - 15 q^{41} + 3 q^{43} - 3 q^{44} - 3 q^{46} + 15 q^{47} + 12 q^{49} + 33 q^{50} + 9 q^{52} + 18 q^{53} - 12 q^{55} + 33 q^{56} + 21 q^{58} + 12 q^{59} + 12 q^{61} + 12 q^{62} + 12 q^{64} - 3 q^{65} - 15 q^{67} - 9 q^{68} - 15 q^{70} - 27 q^{71} + 6 q^{73} - 33 q^{74} - 48 q^{76} - 15 q^{77} - 42 q^{79} - 42 q^{80} - 12 q^{82} - 39 q^{83} - 27 q^{85} - 51 q^{86} - 30 q^{88} - 9 q^{89} + 6 q^{91} + 39 q^{92} - 15 q^{94} + 33 q^{95} + 3 q^{97} + 45 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 - 6 * q^4 + 3 * q^5 - 6 * q^7 - 6 * q^8 - 3 * q^10 - 3 * q^11 - 6 * q^13 - 15 * q^14 - 9 * q^17 - 3 * q^19 + 3 * q^20 + 3 * q^22 + 12 * q^23 + 3 * q^25 + 30 * q^26 - 12 * q^28 + 6 * q^29 + 3 * q^31 + 9 * q^34 - 12 * q^35 - 3 * q^37 - 42 * q^38 + 21 * q^40 - 15 * q^41 + 3 * q^43 - 3 * q^44 - 3 * q^46 + 15 * q^47 + 12 * q^49 + 33 * q^50 + 9 * q^52 + 18 * q^53 - 12 * q^55 + 33 * q^56 + 21 * q^58 + 12 * q^59 + 12 * q^61 + 12 * q^62 + 12 * q^64 - 3 * q^65 - 15 * q^67 - 9 * q^68 - 15 * q^70 - 27 * q^71 + 6 * q^73 - 33 * q^74 - 48 * q^76 - 15 * q^77 - 42 * q^79 - 42 * q^80 - 12 * q^82 - 39 * q^83 - 27 * q^85 - 51 * q^86 - 30 * q^88 - 9 * q^89 + 6 * q^91 + 39 * q^92 - 15 * q^94 + 33 * q^95 + 3 * q^97 + 45 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	−0.183082	−	1.03831i	−0.129458	−	0.734194i	−0.978560	−	0.205964i	$-0.933967\pi$
$2$	−0.183082	−	1.03831i	−0.129458	−	0.734194i	0.849101	−	0.528230i	$-0.177144\pi$
$3$		0			0
$3$		0			0
$4$	0.834822	−	0.303850i	0.417411	−	0.151925i
$5$	1.33735	+	1.12217i	0.598081	+	0.501850i	0.890828	−	0.454340i	$-0.150125\pi$
$5$	1.33735	+	1.12217i	0.598081	+	0.501850i	−0.292747	+	0.956190i	$0.594569\pi$
$6$		0			0
$7$	−2.31094	−	0.841112i	−0.873452	−	0.317910i	−0.133888	−	0.990997i	$-0.542746\pi$
$7$	−2.31094	−	0.841112i	−0.873452	−	0.317910i	−0.739564	+	0.673086i	$0.764968\pi$
$8$	−1.52266	−	2.63732i	−0.538340	−	0.932432i
$9$		0			0
$10$	0.920313	−	1.59403i	0.291029	−	0.504076i
$11$	0.960783	−	0.806193i	0.289687	−	0.243076i	−0.486349	−	0.873764i	$-0.661672\pi$
$11$	0.960783	−	0.806193i	0.289687	−	0.243076i	0.776036	+	0.630688i	$0.217227\pi$
$12$		0			0
$13$	−0.789931	+	4.47992i	−0.219087	+	1.24251i	0.654584	+	0.755989i	$0.272844\pi$
$13$	−0.789931	+	4.47992i	−0.219087	+	1.24251i	−0.873671	+	0.486517i	$0.838267\pi$
$14$	−0.450243	+	2.55345i	−0.120332	+	0.682439i
$15$		0			0
$16$	−1.09847	+	0.921724i	−0.274617	+	0.230431i
$17$	−3.32358	+	5.75662i	−0.806088	+	1.39618i	0.109467	+	0.993990i	$0.465086\pi$
$17$	−3.32358	+	5.75662i	−0.806088	+	1.39618i	−0.915554	+	0.402194i	$0.868248\pi$
$18$		0			0
$19$	−0.124578	−	0.215776i	−0.0285802	−	0.0495023i	0.851382	−	0.524547i	$-0.175765\pi$
$19$	−0.124578	−	0.215776i	−0.0285802	−	0.0495023i	−0.879962	+	0.475045i	$0.842432\pi$
$20$	1.45742	+	0.530458i	0.325889	+	0.118614i
$21$		0			0
$22$	−1.01298	−	0.849989i	−0.215967	−	0.181218i
$23$	0.791222	−	0.287981i	0.164981	−	0.0600483i	−0.258209	−	0.966089i	$-0.583132\pi$
$23$	0.791222	−	0.287981i	0.164981	−	0.0600483i	0.423190	+	0.906041i	$0.360910\pi$
$24$		0			0
$25$	−0.339001	−	1.92257i	−0.0678002	−	0.384514i
$26$	4.79615			0.940603
$27$		0			0
$28$	−2.18479			−0.412887
$29$	0.0889744	+	0.504599i	0.0165221	+	0.0937016i	0.991954	−	0.126601i	$-0.0404067\pi$
$29$	0.0889744	+	0.504599i	0.0165221	+	0.0937016i	−0.975432	+	0.220302i	$0.929296\pi$
$30$		0			0
$31$	0.770551	−	0.280458i	0.138395	−	0.0503717i	−0.271894	−	0.962327i	$-0.587650\pi$
$31$	0.770551	−	0.280458i	0.138395	−	0.0503717i	0.410289	+	0.911956i	$0.365428\pi$
$32$	−3.50754	−	2.94318i	−0.620052	−	0.520286i
$33$		0			0
$34$	6.58563	+	2.39697i	1.12943	+	0.411077i
$35$	−2.14666	−	3.71812i	−0.362852	−	0.628478i
$36$		0			0
$37$	−1.30403	+	2.25865i	−0.214381	+	0.371319i	−0.953081	−	0.302715i	$-0.902107\pi$
$37$	−1.30403	+	2.25865i	−0.214381	+	0.371319i	0.738700	+	0.674035i	$0.235440\pi$
$38$	−0.201233	+	0.168855i	−0.0326444	+	0.0273919i
$39$		0			0
$40$	0.923194	−	5.23570i	0.145970	−	0.827836i
$41$	1.41572	−	8.02895i	0.221099	−	1.25391i	−0.648906	−	0.760869i	$-0.724773\pi$
$41$	1.41572	−	8.02895i	0.221099	−	1.25391i	0.870005	−	0.493044i	$-0.164116\pi$
$42$		0			0
$43$	3.31478	−	2.78143i	0.505500	−	0.424165i	−0.354042	−	0.935229i	$-0.615193\pi$
$43$	3.31478	−	2.78143i	0.505500	−	0.424165i	0.859542	+	0.511065i	$0.170749\pi$
$44$	0.557121	−	0.964962i	0.0839891	−	0.145473i
$45$		0			0
$46$	−0.443871	−	0.768808i	−0.0654452	−	0.113354i
$47$	−4.98256	−	1.81351i	−0.726782	−	0.264527i	−0.0479798	−	0.998848i	$-0.515278\pi$
$47$	−4.98256	−	1.81351i	−0.726782	−	0.264527i	−0.678802	+	0.734321i	$0.737501\pi$
$48$		0			0
$49$	−0.729356	−	0.612002i	−0.104194	−	0.0874289i
$50$	−1.93415	+	0.703974i	−0.273530	+	0.0995569i
$51$		0			0
$52$	0.701774	+	3.97996i	0.0973185	+	0.551921i
$53$	10.4841			1.44010			0.720052	−	0.693920i	$-0.244118\pi$
$53$	10.4841			1.44010			0.720052	+	0.693920i	$0.244118\pi$
$54$		0			0
$55$	2.18959			0.295244
$56$	1.30048	+	7.37539i	0.173784	+	0.985578i
$57$		0			0
$58$	0.507639	−	0.184765i	0.0666563	−	0.0242609i
$59$	2.30289	+	1.93235i	0.299810	+	0.251571i	0.780265	−	0.625449i	$-0.215084\pi$
$59$	2.30289	+	1.93235i	0.299810	+	0.251571i	−0.480455	+	0.877019i	$0.659529\pi$
$60$		0			0
$61$	−2.70930	−	0.986103i	−0.346890	−	0.126258i	0.162699	−	0.986676i	$-0.447980\pi$
$61$	−2.70930	−	0.986103i	−0.346890	−	0.126258i	−0.509589	+	0.860418i	$0.670202\pi$
$62$	−0.432275	−	0.748722i	−0.0548990	−	0.0950878i
$63$		0			0
$64$	−3.84771	+	6.66442i	−0.480963	+	0.833053i
$65$	−6.08365	+	5.10479i	−0.754584	+	0.633171i
$66$		0			0
$67$	1.75146	−	9.93303i	0.213975	−	1.21351i	−0.668701	−	0.743531i	$-0.733149\pi$
$67$	1.75146	−	9.93303i	0.213975	−	1.21351i	0.882676	−	0.469982i	$-0.155739\pi$
$68$	−1.02545	+	5.81562i	−0.124354	+	0.705248i
$69$		0			0
$70$	−3.46754	+	2.90961i	−0.414451	+	0.347765i
$71$	0.0447378	−	0.0774882i	0.00530940	−	0.00919615i	−0.863358	−	0.504591i	$-0.831643\pi$
$71$	0.0447378	−	0.0774882i	0.00530940	−	0.00919615i	0.868668	+	0.495395i	$0.164977\pi$
$72$		0			0
$73$	2.66057	+	4.60824i	0.311396	+	0.539354i	0.978665	−	0.205463i	$-0.0658701\pi$
$73$	2.66057	+	4.60824i	0.311396	+	0.539354i	−0.667269	+	0.744817i	$0.732537\pi$
$74$	2.58391	+	0.940468i	0.300374	+	0.109327i
$75$		0			0
$76$	−0.169564	−	0.142281i	−0.0194503	−	0.0163208i
$77$	−2.89841	+	1.05493i	−0.330304	+	0.120221i
$78$		0			0
$79$	0.829503	+	4.70435i	0.0933264	+	0.529280i	0.995247	+	0.0973792i	$0.0310460\pi$
$79$	0.829503	+	4.70435i	0.0933264	+	0.529280i	−0.901921	+	0.431901i	$0.857843\pi$
$80$	−2.50337			−0.279885
$81$		0			0
$82$	−8.59571			−0.949238
$83$	−1.39625	−	7.91851i	−0.153258	−	0.869169i	−0.960361	−	0.278759i	$-0.910077\pi$
$83$	−1.39625	−	7.91851i	−0.153258	−	0.869169i	0.807103	−	0.590410i	$-0.201034\pi$
$84$		0			0
$85$	−10.9047	+	3.96899i	−1.18278	+	0.430497i
$86$	−3.49486	−	2.93254i	−0.376860	−	0.316223i
$87$		0			0
$88$	−3.58913	−	1.30634i	−0.382602	−	0.139256i
$89$	3.35189	+	5.80564i	0.355299	+	0.615396i	0.987169	−	0.159678i	$-0.0510457\pi$
$89$	3.35189	+	5.80564i	0.355299	+	0.615396i	−0.631870	+	0.775074i	$0.717712\pi$
$90$		0			0
$91$	5.59359	−	9.68839i	0.586368	−	1.01562i
$92$	0.573026	−	0.480826i	0.0597421	−	0.0501296i
$93$		0			0
$94$	−0.970760	+	5.50545i	−0.100126	+	0.567844i
$95$	0.0755324	−	0.428365i	0.00774946	−	0.0439494i
$96$		0			0
$97$	4.20603	−	3.52928i	0.427057	−	0.358344i	−0.403783	−	0.914855i	$-0.632305\pi$
$97$	4.20603	−	3.52928i	0.427057	−	0.358344i	0.830840	+	0.556511i	$0.187860\pi$
$98$	−0.501915	+	0.869342i	−0.0507010	+	0.0878168i
$99$		0			0
$100$	−0.867179	−	1.50200i	−0.0867179	−	0.150200i
$101$	4.70360	+	1.71197i	0.468025	+	0.170347i	0.565258	−	0.824914i	$-0.308777\pi$
$101$	4.70360	+	1.71197i	0.468025	+	0.170347i	−0.0972322	+	0.995262i	$0.530999\pi$
$102$		0			0
$103$	8.90079	+	7.46865i	0.877021	+	0.735908i	0.965564	−	0.260164i	$-0.0837767\pi$
$103$	8.90079	+	7.46865i	0.877021	+	0.735908i	−0.0885431	+	0.996072i	$0.528221\pi$
$104$	13.0178	−	4.73808i	1.27650	−	0.464607i
$105$		0			0
$106$	−1.91945	−	10.8857i	−0.186433	−	1.05732i
$107$	−19.4581			−1.88109			−0.940544	−	0.339673i	$-0.889684\pi$
$107$	−19.4581			−1.88109			−0.940544	+	0.339673i	$0.889684\pi$
$108$		0			0
$109$	6.31515			0.604881			0.302441	−	0.953168i	$-0.402199\pi$
$109$	6.31515			0.604881			0.302441	+	0.953168i	$0.402199\pi$
$110$	−0.400873	−	2.27347i	−0.0382218	−	0.216766i
$111$		0			0
$112$	3.31376	−	1.20611i	0.313121	−	0.113967i
$113$	5.29775	+	4.44534i	0.498371	+	0.418183i	0.857015	−	0.515292i	$-0.172316\pi$
$113$	5.29775	+	4.44534i	0.498371	+	0.418183i	−0.358644	+	0.933474i	$0.616761\pi$
$114$		0			0
$115$	1.38131	+	0.502754i	0.128807	+	0.0468821i
$116$	0.227600	+	0.394215i	0.0211322	+	0.0366020i
$117$		0			0
$118$	1.58476	−	2.74488i	0.145889	−	0.252687i
$119$	12.5226	−	10.5077i	1.14794	−	0.963236i
$120$		0			0
$121$	−1.63697	+	9.28373i	−0.148816	+	0.843976i
$122$	−0.527856	+	2.99362i	−0.0477898	+	0.271030i
$123$		0			0
$124$	0.558056	−	0.468265i	0.0501149	−	0.0420514i
$125$	6.06855	−	10.5110i	0.542788	−	0.940136i
$126$		0			0
$127$	−6.01162	−	10.4124i	−0.533445	−	0.923954i	−0.999237	−	0.0390598i	$-0.987564\pi$
$127$	−6.01162	−	10.4124i	−0.533445	−	0.923954i	0.465792	−	0.884894i	$-0.345770\pi$
$128$	−0.981117	−	0.357098i	−0.0867194	−	0.0315633i
$129$		0			0
$130$	6.41414	+	5.38210i	0.562557	+	0.472042i
$131$	−13.2354	+	4.81728i	−1.15638	+	0.420888i	−0.847803	−	0.530311i	$-0.822075\pi$
$131$	−13.2354	+	4.81728i	−1.15638	+	0.420888i	−0.308577	+	0.951199i	$0.599853\pi$
$132$		0			0
$133$	0.106401	+	0.603428i	0.00922610	+	0.0523238i
$134$	−10.6342			−0.918655
$135$		0			0
$136$	20.2427			1.73580
$137$	−0.392122	−	2.22383i	−0.0335012	−	0.189995i	0.963465	−	0.267836i	$-0.0863085\pi$
$137$	−0.392122	−	2.22383i	−0.0335012	−	0.189995i	−0.996966	+	0.0778409i	$0.975197\pi$
$138$		0			0
$139$	7.49414	−	2.72764i	0.635644	−	0.231356i	−0.00404179	−	0.999992i	$-0.501287\pi$
$139$	7.49414	−	2.72764i	0.635644	−	0.231356i	0.639686	+	0.768636i	$0.279064\pi$
$140$	−2.92183	−	2.45171i	−0.246940	−	0.207207i
$141$		0			0
$142$	−0.0886472	−	0.0322649i	−0.00743911	−	0.00270761i
$143$	2.85273	+	4.94107i	0.238557	+	0.413193i
$144$		0			0
$145$	−0.447256	+	0.774670i	−0.0371426	+	0.0643328i
$146$	4.29767	−	3.60617i	0.355678	−	0.298449i
$147$		0			0
$148$	−0.402343	+	2.28180i	−0.0330724	+	0.187563i
$149$	0.0185697	−	0.105314i	0.00152129	−	0.00862764i	−0.984038	−	0.177960i	$-0.943050\pi$
$149$	0.0185697	−	0.105314i	0.00152129	−	0.00862764i	0.985559	+	0.169333i	$0.0541612\pi$
$150$		0			0
$151$	−15.5196	+	13.0225i	−1.26297	+	1.05976i	−0.267609	+	0.963528i	$0.586233\pi$
$151$	−15.5196	+	13.0225i	−1.26297	+	1.05976i	−0.995359	+	0.0962282i	$0.969322\pi$
$152$	−0.379379	+	0.657104i	−0.0307717	+	0.0532982i
$153$		0			0
$154$	1.62599	+	2.81630i	0.131026	+	0.226944i
$155$	1.34522	+	0.489620i	0.108051	+	0.0393272i
$156$		0			0
$157$	−15.8953	−	13.3377i	−1.26858	−	1.06447i	−0.994712	−	0.102701i	$-0.967252\pi$
$157$	−15.8953	−	13.3377i	−1.26858	−	1.06447i	−0.273871	−	0.961767i	$-0.588304\pi$
$158$	4.73269	−	1.72256i	0.376513	−	0.137039i
$159$		0			0
$160$	−1.38807	−	7.87212i	−0.109736	−	0.622346i
$161$	−2.07069			−0.163193
$162$		0			0
$163$	−20.1346			−1.57706			−0.788531	−	0.614995i	$-0.789158\pi$
$163$	−20.1346			−1.57706			−0.788531	+	0.614995i	$0.789158\pi$
$164$	−1.25773	−	7.13292i	−0.0982119	−	0.556987i
$165$		0			0
$166$	−7.96622	+	2.89947i	−0.618298	+	0.225042i
$167$	15.2156	+	12.7674i	1.17742	+	0.987974i	0.999993	+	0.00383999i	$0.00122231\pi$
$167$	15.2156	+	12.7674i	1.17742	+	0.987974i	0.177429	+	0.984134i	$0.443222\pi$
$168$		0			0
$169$	−7.22968	−	2.63139i	−0.556130	−	0.202415i
$170$	6.11748	+	10.5958i	0.469189	+	0.812660i
$171$		0			0
$172$	1.92212	−	3.32920i	0.146560	−	0.253849i
$173$	−14.4975	+	12.1648i	−1.10222	+	0.924875i	−0.997573	−	0.0696342i	$-0.977817\pi$
$173$	−14.4975	+	12.1648i	−1.10222	+	0.924875i	−0.104650	+	0.994509i	$0.533372\pi$
$174$		0			0
$175$	−0.833686	+	4.72807i	−0.0630208	+	0.357409i
$176$	−0.312302	+	1.77115i	−0.0235407	+	0.133506i
$177$		0			0
$178$	5.41436	−	4.54319i	0.405824	−	0.340527i
$179$	5.45683	−	9.45151i	0.407863	−	0.706439i	−0.586787	−	0.809741i	$-0.699608\pi$
$179$	5.45683	−	9.45151i	0.407863	−	0.706439i	0.994650	+	0.103302i	$0.0329409\pi$
$180$		0			0
$181$	8.97393	+	15.5433i	0.667027	+	1.15532i	0.978731	+	0.205146i	$0.0657668\pi$
$181$	8.97393	+	15.5433i	0.667027	+	1.15532i	−0.311704	+	0.950179i	$0.600900\pi$
$182$	−11.0836	−	4.03410i	−0.821572	−	0.299028i
$183$		0			0
$184$	−1.96426	−	1.64821i	−0.144807	−	0.121507i
$185$	−4.27853	+	1.55726i	−0.314564	+	0.114492i
$186$		0			0
$187$	1.44770	+	8.21031i	0.105866	+	0.600397i
$188$	−4.71059			−0.343555
$189$		0			0
$190$	−0.458604			−0.0332706
$191$	4.68261	+	26.5564i	0.338822	+	1.92155i	0.385641	+	0.922649i	$0.373980\pi$
$191$	4.68261	+	26.5564i	0.338822	+	1.92155i	−0.0468192	+	0.998903i	$0.514908\pi$
$192$		0			0
$193$	16.1202	−	5.86729i	1.16036	−	0.422337i	0.311135	−	0.950366i	$-0.399291\pi$
$193$	16.1202	−	5.86729i	1.16036	−	0.422337i	0.849226	+	0.528029i	$0.177069\pi$
$194$	−4.43452	−	3.72100i	−0.318380	−	0.267152i
$195$		0			0
$196$	−0.794839	−	0.289298i	−0.0567742	−	0.0206641i
$197$	1.25612	+	2.17567i	0.0894951	+	0.155010i	0.907298	−	0.420489i	$-0.138141\pi$
$197$	1.25612	+	2.17567i	0.0894951	+	0.155010i	−0.817803	+	0.575499i	$0.804808\pi$
$198$		0			0
$199$	−9.26942	+	16.0551i	−0.657092	+	1.13812i	0.324273	+	0.945964i	$0.394880\pi$
$199$	−9.26942	+	16.0551i	−0.657092	+	1.13812i	−0.981365	+	0.192153i	$0.938453\pi$
$200$	−4.55424	+	3.82146i	−0.322033	+	0.270218i
$201$		0			0
$202$	0.916408	−	5.19721i	0.0644783	−	0.365674i
$203$	0.218810	−	1.24093i	0.0153574	−	0.0870964i
$204$		0			0
$205$	10.9032	−	9.14885i	0.761510	−	0.638983i
$206$	6.12519	−	10.6091i	0.426762	−	0.739173i
$207$		0			0
$208$	−3.26154	−	5.64915i	−0.226147	−	0.391698i
$209$	−0.293649	−	0.106880i	−0.0203121	−	0.00739301i
$210$		0			0
$211$	−2.82761	−	2.37264i	−0.194661	−	0.163340i	0.540248	−	0.841506i	$-0.318330\pi$
$211$	−2.82761	−	2.37264i	−0.194661	−	0.163340i	−0.734908	+	0.678166i	$0.762775\pi$
$212$	8.75237	−	3.18560i	0.601115	−	0.218788i
$213$		0			0
$214$	3.56242	+	20.2035i	0.243522	+	1.38108i
$215$	7.55427			0.515197
$216$		0			0
$217$	−2.01659			−0.136895
$218$	−1.15619	−	6.55706i	−0.0783069	−	0.444100i
$219$		0			0
$220$	1.82792	−	0.665307i	0.123238	−	0.0448550i
$221$	−23.1638	−	19.4367i	−1.55816	−	1.30746i
$222$		0			0
$223$	19.9601	+	7.26487i	1.33662	+	0.486491i	0.908748	−	0.417346i	$-0.137040\pi$
$223$	19.9601	+	7.26487i	1.33662	+	0.486491i	0.427876	+	0.903837i	$0.359262\pi$
$224$	5.63017	+	9.75174i	0.376181	+	0.651565i
$225$		0			0
$226$	3.64571	−	6.31456i	0.242509	−	0.420038i
$227$	10.9851	−	9.21761i	0.729108	−	0.611794i	−0.200781	−	0.979636i	$-0.564348\pi$
$227$	10.9851	−	9.21761i	0.729108	−	0.611794i	0.929888	+	0.367842i	$0.119903\pi$
$228$		0			0
$229$	2.93219	−	16.6293i	0.193765	−	1.09889i	−0.720403	−	0.693556i	$-0.756043\pi$
$229$	2.93219	−	16.6293i	0.193765	−	1.09889i	0.914167	−	0.405337i	$-0.132846\pi$
$230$	0.269122	−	1.52626i	0.0177454	−	0.100639i
$231$		0			0
$232$	1.19531	−	1.00298i	0.0784759	−	0.0658491i
$233$	2.79972	−	4.84926i	0.183416	−	0.317686i	−0.759626	−	0.650361i	$-0.774618\pi$
$233$	2.79972	−	4.84926i	0.183416	−	0.317686i	0.943042	+	0.332675i	$0.107951\pi$
$234$		0			0
$235$	−4.62837	−	8.01658i	−0.301922	−	0.522944i
$236$	2.50964	+	0.913436i	0.163364	+	0.0594596i
$237$		0			0
$238$	−13.2028	−	11.0785i	−0.855813	−	0.718112i
$239$	−4.95620	+	1.80391i	−0.320590	+	0.116685i	−0.497302	−	0.867577i	$-0.665676\pi$
$239$	−4.95620	+	1.80391i	−0.320590	+	0.116685i	0.176712	+	0.984263i	$0.443454\pi$
$240$		0			0
$241$	−1.54590	−	8.76723i	−0.0995801	−	0.564747i	−0.993247	−	0.116017i	$-0.962987\pi$
$241$	−1.54590	−	8.76723i	−0.0995801	−	0.564747i	0.893667	−	0.448730i	$-0.148124\pi$
$242$	9.93907			0.638907
$243$		0			0
$244$	−2.56141			−0.163977
$245$	−0.288634	−	1.63692i	−0.0184401	−	0.104579i
$246$		0			0
$247$	1.06507	−	0.387652i	0.0677685	−	0.0246657i
$248$	−1.91294	−	1.60515i	−0.121472	−	0.101927i
$249$		0			0
$250$	−12.0247	−	4.37665i	−0.760511	−	0.276803i
$251$	−3.89010	−	6.73786i	−0.245541	−	0.425290i	0.716742	−	0.697338i	$-0.245632\pi$
$251$	−3.89010	−	6.73786i	−0.245541	−	0.425290i	−0.962284	+	0.272048i	$0.912299\pi$
$252$		0			0
$253$	0.528024	−	0.914565i	0.0331966	−	0.0574982i
$254$	−9.71069	+	8.14824i	−0.609303	+	0.511266i
$255$		0			0
$256$	−2.86374	+	16.2411i	−0.178984	+	1.01507i
$257$	3.54877	−	20.1261i	0.221366	−	1.25543i	−0.648145	−	0.761517i	$-0.724455\pi$
$257$	3.54877	−	20.1261i	0.221366	−	1.25543i	0.869511	−	0.493913i	$-0.164434\pi$
$258$		0			0
$259$	4.91331	−	4.12275i	0.305298	−	0.256175i
$260$	−3.52767	+	6.11011i	−0.218777	+	0.378933i
$261$		0			0
$262$	7.42498	+	12.8604i	0.458717	+	0.794520i
$263$	10.5996	+	3.85792i	0.653596	+	0.237890i	0.647469	−	0.762092i	$-0.275827\pi$
$263$	10.5996	+	3.85792i	0.653596	+	0.237890i	0.00612723	+	0.999981i	$0.498050\pi$
$264$		0			0
$265$	14.0209	+	11.7650i	0.861299	+	0.722716i
$266$	0.607063	−	0.220953i	0.0372214	−	0.0135475i
$267$		0			0
$268$	−1.55600	−	8.82450i	−0.0950476	−	0.539042i
$269$	0.307761			0.0187645			0.00938226	−	0.999956i	$-0.497013\pi$
$269$	0.307761			0.0187645			0.00938226	+	0.999956i	$0.497013\pi$
$270$		0			0
$271$	−2.22251			−0.135008			−0.0675040	−	0.997719i	$-0.521504\pi$
$271$	−2.22251			−0.135008			−0.0675040	+	0.997719i	$0.521504\pi$
$272$	−1.65516	−	9.38689i	−0.100359	−	0.569164i
$273$		0			0
$274$	−2.23723	+	0.814286i	−0.135156	+	0.0491928i
$275$	−1.87567	−	1.57387i	−0.113107	−	0.0949080i
$276$		0			0
$277$	21.9228	+	7.97924i	1.31721	+	0.479426i	0.902564	−	0.430556i	$-0.141683\pi$
$277$	21.9228	+	7.97924i	1.31721	+	0.479426i	0.414648	+	0.909982i	$0.363905\pi$
$278$	−4.20417	−	7.28184i	−0.252149	−	0.436735i
$279$		0			0
$280$	−6.53725	+	11.3228i	−0.390675	+	0.676670i
$281$	−5.53502	+	4.64443i	−0.330192	+	0.277064i	−0.792778	−	0.609511i	$-0.791366\pi$
$281$	−5.53502	+	4.64443i	−0.330192	+	0.277064i	0.462586	+	0.886574i	$0.346922\pi$
$282$		0			0
$283$	1.23643	−	7.01212i	0.0734979	−	0.416827i	−0.925753	−	0.378129i	$-0.876568\pi$
$283$	1.23643	−	7.01212i	0.0734979	−	0.416827i	0.999251	−	0.0386985i	$-0.0123212\pi$
$284$	0.0138033	−	0.0782824i	0.000819076	−	0.00464521i
$285$		0			0
$286$	4.60806	−	3.86662i	0.272480	−	0.228638i
$287$	−10.0249	+	17.3636i	−0.591751	+	1.02494i
$288$		0			0
$289$	−13.5924	−	23.5428i	−0.799555	−	1.38487i
$290$	0.886230	+	0.322561i	0.0520412	+	0.0189414i
$291$		0			0
$292$	3.62132	+	3.03865i	0.211922	+	0.177823i
$293$	0.519166	−	0.188961i	0.0303300	−	0.0110392i	−0.326811	−	0.945090i	$-0.605974\pi$
$293$	0.519166	−	0.188961i	0.0303300	−	0.0110392i	0.357141	+	0.934051i	$0.383752\pi$
$294$		0			0
$295$	0.911339	+	5.16846i	0.0530602	+	0.300919i
$296$	7.94236			0.461640
$297$		0			0
$298$	−0.112748			−0.00653131
$299$	0.665122	+	3.77210i	0.0384650	+	0.218146i
$300$		0			0
$301$	−9.99975	+	3.63961i	−0.576376	+	0.209784i
$302$	16.3627	+	13.7299i	0.941568	+	0.790069i
$303$		0			0
$304$	0.335731	+	0.122196i	0.0192555	+	0.00700842i
$305$	−2.51670	−	4.35906i	−0.144106	−	0.249599i
$306$		0			0
$307$	−3.36438	+	5.82728i	−0.192015	+	0.332580i	−0.945918	−	0.324406i	$-0.894836\pi$
$307$	−3.36438	+	5.82728i	−0.192015	+	0.332580i	0.753903	+	0.656986i	$0.228169\pi$
$308$	−2.09911	+	1.76136i	−0.119608	+	0.100363i
$309$		0			0
$310$	0.262091	−	1.48639i	0.0148858	−	0.0844213i
$311$	−2.67825	+	15.1891i	−0.151870	+	0.861297i	0.809722	+	0.586814i	$0.199618\pi$
$311$	−2.67825	+	15.1891i	−0.151870	+	0.861297i	−0.961592	+	0.274483i	$0.911493\pi$
$312$		0			0
$313$	−18.0487	+	15.1446i	−1.02017	+	0.856025i	−0.989649	−	0.143509i	$-0.954162\pi$
$313$	−18.0487	+	15.1446i	−1.02017	+	0.856025i	−0.0305223	+	0.999534i	$0.509717\pi$
$314$	−10.9385	+	18.9461i	−0.617297	+	1.06919i
$315$		0			0
$316$	2.12191	+	3.67525i	0.119367	+	0.206749i
$317$	6.81469	+	2.48034i	0.382751	+	0.139310i	0.526228	−	0.850344i	$-0.323606\pi$
$317$	6.81469	+	2.48034i	0.382751	+	0.139310i	−0.143477	+	0.989654i	$0.545828\pi$
$318$		0			0
$319$	0.492289	+	0.413079i	0.0275629	+	0.0231280i
$320$	−12.6243	+	4.59489i	−0.705723	+	0.256862i
$321$		0			0
$322$	0.379105	+	2.15001i	0.0211267	+	0.119815i
$323$	1.65618			0.0921525
$324$		0			0
$325$	8.88074			0.492615
$326$	3.68627	+	20.9059i	0.204164	+	1.15787i
$327$		0			0
$328$	−23.3306	+	8.49163i	−1.28821	+	0.468872i
$329$	9.98903	+	8.38179i	0.550713	+	0.462103i
$330$		0			0
$331$	−27.2835	−	9.93037i	−1.49964	−	0.545823i	−0.543669	−	0.839300i	$-0.682965\pi$
$331$	−27.2835	−	9.93037i	−1.49964	−	0.545823i	−0.955966	+	0.293477i	$0.905188\pi$
$332$	−3.57166	−	6.18629i	−0.196020	−	0.339517i
$333$		0			0
$334$	10.4708	−	18.1360i	0.572938	−	0.992357i
$335$	13.4889	−	11.3185i	0.736976	−	0.618396i
$336$		0			0
$337$	−0.201275	+	1.14149i	−0.0109641	+	0.0621807i	−0.989799	−	0.142471i	$-0.954495\pi$
$337$	−0.201275	+	1.14149i	−0.0109641	+	0.0621807i	0.978835	+	0.204652i	$0.0656063\pi$
$338$	−1.40857	+	7.98839i	−0.0766161	+	0.434511i
$339$		0			0
$340$	−7.89751	+	6.62680i	−0.428303	+	0.359389i
$341$	0.514230	−	0.890672i	0.0278471	−	0.0482326i
$342$		0			0
$343$	9.77810	+	16.9362i	0.527968	+	0.914467i
$344$	−12.3828	−	4.50697i	−0.667636	−	0.243000i
$345$		0			0
$346$	15.2851	+	12.8257i	0.821730	+	0.689513i
$347$	5.53452	−	2.01440i	0.297108	−	0.108139i	−0.189165	−	0.981945i	$-0.560578\pi$
$347$	5.53452	−	2.01440i	0.297108	−	0.108139i	0.486273	+	0.873807i	$0.338356\pi$
$348$		0			0
$349$	−5.31237	−	30.1279i	−0.284364	−	1.61271i	−0.707547	−	0.706666i	$-0.750198\pi$
$349$	−5.31237	−	30.1279i	−0.284364	−	1.61271i	0.423183	−	0.906044i	$-0.360913\pi$
$350$	5.06182			0.270566
$351$		0			0
$352$	−5.74276			−0.306090
$353$	−6.41826	−	36.3997i	−0.341609	−	1.93736i	−0.348294	−	0.937385i	$-0.613239\pi$
$353$	−6.41826	−	36.3997i	−0.341609	−	1.93736i	0.00668455	−	0.999978i	$-0.497872\pi$
$354$		0			0
$355$	0.146785	−	0.0534254i	0.00779054	−	0.00283553i
$356$	4.56227	+	3.82820i	0.241800	+	0.202894i
$357$		0			0
$358$	−10.8126	−	3.93547i	−0.571464	−	0.207996i
$359$	−13.1880	−	22.8423i	−0.696037	−	1.20557i	−0.969830	−	0.243783i	$-0.921611\pi$
$359$	−13.1880	−	22.8423i	−0.696037	−	1.20557i	0.273792	−	0.961789i	$-0.411722\pi$
$360$		0			0
$361$	9.46896	−	16.4007i	0.498366	−	0.863196i
$362$	14.4958	−	12.1634i	0.761881	−	0.639294i
$363$		0			0
$364$	1.72583	−	9.78769i	0.0904583	−	0.513015i
$365$	−1.61312	+	9.14845i	−0.0844345	+	0.478852i
$366$		0			0
$367$	−8.66636	+	7.27194i	−0.452380	+	0.379592i	−0.840318	−	0.542093i	$-0.817632\pi$
$367$	−8.66636	+	7.27194i	−0.452380	+	0.379592i	0.387938	+	0.921685i	$0.373187\pi$
$368$	−0.603693	+	1.04563i	−0.0314697	+	0.0545071i
$369$		0			0
$370$	2.40023	+	4.15733i	0.124782	+	0.216129i
$371$	−24.2281	−	8.81831i	−1.25786	−	0.457824i
$372$		0			0
$373$	4.47682	+	3.75650i	0.231801	+	0.194504i	0.751289	−	0.659974i	$-0.229433\pi$
$373$	4.47682	+	3.75650i	0.231801	+	0.194504i	−0.519487	+	0.854478i	$0.673877\pi$
$374$	8.25978	−	3.00631i	0.427103	−	0.155453i
$375$		0			0
$376$	2.80394	+	15.9019i	0.144602	+	0.820080i
$377$	−2.33085			−0.120045
$378$		0			0
$379$	24.3265			1.24957			0.624783	−	0.780798i	$-0.285187\pi$
$379$	24.3265			1.24957			0.624783	+	0.780798i	$0.285187\pi$
$380$	−0.0671029	−	0.380559i	−0.00344231	−	0.0195223i
$381$		0			0
$382$	26.7164	−	9.72397i	1.36693	−	0.497522i
$383$	2.92326	+	2.45291i	0.149372	+	0.125338i	0.714411	−	0.699726i	$-0.246695\pi$
$383$	2.92326	+	2.45291i	0.149372	+	0.125338i	−0.565039	+	0.825064i	$0.691139\pi$
$384$		0			0
$385$	−5.06000	−	1.84169i	−0.257881	−	0.0938612i
$386$	−9.04337	−	15.6636i	−0.460295	−	0.797255i
$387$		0			0
$388$	2.43891	−	4.22432i	0.123817	−	0.214457i
$389$	−8.30534	+	6.96901i	−0.421097	+	0.353343i	−0.828580	−	0.559870i	$-0.810851\pi$
$389$	−8.30534	+	6.96901i	−0.421097	+	0.353343i	0.407483	+	0.913213i	$0.366407\pi$
$390$		0			0
$391$	−0.971896	+	5.51189i	−0.0491509	+	0.278748i
$392$	−0.503486	+	2.85541i	−0.0254299	+	0.144220i
$393$		0			0
$394$	2.02904	−	1.70257i	0.102222	−	0.0857741i
$395$	−4.16974	+	7.22221i	−0.209802	+	0.363389i
$396$		0			0
$397$	5.25461	+	9.10124i	0.263721	+	0.456778i	0.967228	−	0.253910i	$-0.0817168\pi$
$397$	5.25461	+	9.10124i	0.263721	+	0.456778i	−0.703507	+	0.710689i	$0.748383\pi$
$398$	18.3672	+	6.68511i	0.920665	+	0.335094i
$399$		0			0
$400$	2.14446	+	1.79942i	0.107223	+	0.0899708i
$401$	13.4992	−	4.91332i	0.674119	−	0.245359i	0.0177987	−	0.999842i	$-0.494334\pi$
$401$	13.4992	−	4.91332i	0.674119	−	0.245359i	0.656320	+	0.754482i	$0.272112\pi$
$402$		0			0
$403$	0.647746	+	3.67355i	0.0322665	+	0.182993i
$404$	4.44685			0.221239
$405$		0			0
$406$	−1.32853			−0.0659338
$407$	0.568014	+	3.22137i	0.0281554	+	0.159677i
$408$		0			0
$409$	−16.6159	+	6.04769i	−0.821603	+	0.299039i	−0.718408	−	0.695622i	$-0.755129\pi$
$409$	−16.6159	+	6.04769i	−0.821603	+	0.299039i	−0.103195	+	0.994661i	$0.532907\pi$
$410$	−11.4955	−	9.64586i	−0.567721	−	0.476375i
$411$		0			0
$412$	9.69993	+	3.53049i	0.477881	+	0.173935i
$413$	−3.69650	−	6.40252i	−0.181893	−	0.315047i
$414$		0			0
$415$	7.01864	−	12.1566i	0.344532	−	0.596746i
$416$	15.9559	−	13.3886i	0.782303	−	0.656431i
$417$		0			0
$418$	−0.0572121	+	0.324466i	−0.00279833	+	0.0158701i
$419$	−1.58606	+	8.99500i	−0.0774842	+	0.439435i	0.921243	+	0.388988i	$0.127175\pi$
$419$	−1.58606	+	8.99500i	−0.0774842	+	0.439435i	−0.998727	+	0.0504461i	$0.983936\pi$
$420$		0			0
$421$	18.5344	−	15.5522i	0.903310	−	0.757967i	−0.0675243	−	0.997718i	$-0.521510\pi$
$421$	18.5344	−	15.5522i	0.903310	−	0.757967i	0.970835	+	0.239750i	$0.0770656\pi$
$422$	−1.94585	+	3.37031i	−0.0947226	+	0.164064i
$423$		0			0
$424$	−15.9637	−	27.6499i	−0.775265	−	1.34280i
$425$	12.1942	+	4.43832i	0.591505	+	0.215290i
$426$		0			0
$427$	5.43159	+	4.55764i	0.262853	+	0.220560i
$428$	−16.2441	+	5.91236i	−0.785187	+	0.285785i
$429$		0			0
$430$	−1.38305	−	7.84366i	−0.0666965	−	0.378255i
$431$	29.5332			1.42256			0.711282	−	0.702907i	$-0.248115\pi$
$431$	29.5332			1.42256			0.711282	+	0.702907i	$0.248115\pi$
$432$		0			0
$433$	0.669754			0.0321863			0.0160932	−	0.999870i	$-0.494877\pi$
$433$	0.669754			0.0321863			0.0160932	+	0.999870i	$0.494877\pi$
$434$	0.369201	+	2.09384i	0.0177222	+	0.100508i
$435$		0			0
$436$	5.27203	−	1.91886i	0.252484	−	0.0918967i
$437$	−0.160708	−	0.134850i	−0.00768772	−	0.00645076i
$438$		0			0
$439$	5.96599	+	2.17144i	0.284741	+	0.103637i	0.480442	−	0.877026i	$-0.340476\pi$
$439$	5.96599	+	2.17144i	0.284741	+	0.103637i	−0.195701	+	0.980664i	$0.562698\pi$
$440$	−3.33399	−	5.77464i	−0.158942	−	0.275295i
$441$		0			0
$442$	−15.9404	+	27.6096i	−0.758209	+	1.31326i
$443$	−11.7618	+	9.86931i	−0.558819	+	0.468905i	−0.877914	−	0.478818i	$-0.841066\pi$
$443$	−11.7618	+	9.86931i	−0.558819	+	0.468905i	0.319095	+	0.947723i	$0.396621\pi$
$444$		0			0
$445$	−2.03227	+	11.5256i	−0.0963387	+	0.546364i
$446$	3.88884	−	22.0547i	0.184142	−	1.04432i
$447$		0			0
$448$	14.4973	−	12.1647i	0.684934	−	0.574728i
$449$	−16.0199	+	27.7473i	−0.756027	+	1.30948i	0.188836	+	0.982009i	$0.439529\pi$
$449$	−16.0199	+	27.7473i	−0.756027	+	1.30948i	−0.944862	+	0.327468i	$0.893805\pi$
$450$		0			0
$451$	−5.11268	−	8.85543i	−0.240747	−	0.416986i
$452$	5.77340	+	2.10135i	0.271558	+	0.0988390i
$453$		0			0
$454$	−11.5819	−	9.71835i	−0.543565	−	0.456105i
$455$	18.3526	−	6.67980i	0.860384	−	0.313154i
$456$		0			0
$457$	3.32849	+	18.8768i	0.155700	+	0.883021i	0.958143	+	0.286291i	$0.0924225\pi$
$457$	3.32849	+	18.8768i	0.155700	+	0.883021i	−0.802442	+	0.596730i	$0.796466\pi$
$458$	−17.8031			−0.831886
$459$		0			0
$460$	1.30591			0.0608882
$461$	0.906494	+	5.14098i	0.0422196	+	0.239440i	0.998614	−	0.0526405i	$-0.0167637\pi$
$461$	0.906494	+	5.14098i	0.0422196	+	0.239440i	−0.956394	+	0.292080i	$0.905653\pi$
$462$		0			0
$463$	−1.59502	+	0.580541i	−0.0741271	+	0.0269800i	−0.378818	−	0.925471i	$-0.623669\pi$
$463$	−1.59502	+	0.580541i	−0.0741271	+	0.0269800i	0.304690	+	0.952451i	$0.401447\pi$
$464$	−0.562837	−	0.472276i	−0.0261290	−	0.0219249i
$465$		0			0
$466$	−5.54760	−	2.01916i	−0.256988	−	0.0935359i
$467$	9.84136	+	17.0457i	0.455404	+	0.788783i	0.998711	−	0.0507511i	$-0.0161615\pi$
$467$	9.84136	+	17.0457i	0.455404	+	0.788783i	−0.543307	+	0.839534i	$0.682828\pi$
$468$		0			0
$469$	−12.4023	+	21.4814i	−0.572685	+	0.991920i
$470$	−7.47630	+	6.27336i	−0.344856	+	0.289369i
$471$		0			0
$472$	1.58972	−	9.01574i	0.0731727	−	0.414983i
$473$	0.942416	−	5.34471i	0.0433324	−	0.245750i
$474$		0			0
$475$	−0.372611	+	0.312658i	−0.0170966	+	0.0143457i
$476$	7.26134	−	12.5770i	0.332823	−	0.576467i
$477$		0			0
$478$	2.78040	+	4.81579i	0.127173	+	0.220269i
$479$	−27.4892	−	10.0053i	−1.25601	−	0.457152i	−0.373585	−	0.927596i	$-0.621872\pi$
$479$	−27.4892	−	10.0053i	−1.25601	−	0.457152i	−0.882430	+	0.470444i	$0.844094\pi$
$480$		0			0
$481$	−9.08847	−	7.62613i	−0.414398	−	0.347722i
$482$	−8.82005	+	3.21024i	−0.401742	+	0.146222i
$483$		0			0
$484$	1.45429	+	8.24766i	0.0661039	+	0.374894i
$485$	9.58538			0.435250
$486$		0			0
$487$	−20.5056			−0.929199			−0.464600	−	0.885521i	$-0.653802\pi$
$487$	−20.5056			−0.929199			−0.464600	+	0.885521i	$0.653802\pi$
$488$	1.52466	+	8.64677i	0.0690180	+	0.391421i
$489$		0			0
$490$	−1.64679	+	0.599381i	−0.0743942	+	0.0270773i
$491$	−13.4265	−	11.2661i	−0.605927	−	0.508433i	0.287417	−	0.957805i	$-0.407203\pi$
$491$	−13.4265	−	11.2661i	−0.605927	−	0.508433i	−0.893345	+	0.449372i	$0.851648\pi$
$492$		0			0
$493$	−3.20050	−	1.16489i	−0.144143	−	0.0524638i
$494$	−0.597496	−	1.03489i	−0.0268826	−	0.0465620i
$495$		0			0
$496$	−0.587922	+	1.01831i	−0.0263985	+	0.0457235i
$497$	−0.168562	+	0.141441i	−0.00756106	+	0.00634448i
$498$		0			0
$499$	−3.31772	+	18.8157i	−0.148522	+	0.842307i	0.815950	+	0.578122i	$0.196214\pi$
$499$	−3.31772	+	18.8157i	−0.148522	+	0.842307i	−0.964472	+	0.264185i	$0.914897\pi$
$500$	1.87238	−	10.6188i	0.0837353	−	0.474887i
$501$		0			0
$502$	−6.28376	+	5.27270i	−0.280458	+	0.235332i
$503$	−5.48381	+	9.49824i	−0.244511	+	0.423506i	−0.961994	−	0.273070i	$-0.911961\pi$
$503$	−5.48381	+	9.49824i	−0.244511	+	0.423506i	0.717483	+	0.696576i	$0.245294\pi$
$504$		0			0
$505$	4.36924	+	7.56774i	0.194429	+	0.336760i
$506$	−1.04627	−	0.380811i	−0.0465124	−	0.0169291i
$507$		0			0
$508$	−8.18246	−	6.86590i	−0.363038	−	0.304625i
$509$	−18.6993	+	6.80598i	−0.828831	+	0.301670i	−0.721379	−	0.692540i	$-0.756491\pi$
$509$	−18.6993	+	6.80598i	−0.828831	+	0.301670i	−0.107452	+	0.994210i	$0.534269\pi$
$510$		0			0
$511$	−2.27236	−	12.8872i	−0.100523	−	0.570096i
$512$	15.2994			0.676143
$513$		0			0
$514$	−21.5468			−0.950387
$515$	3.52238	+	19.9764i	0.155215	+	0.880266i
$516$		0			0
$517$	−6.24920	+	2.27452i	−0.274839	+	0.100033i
$518$	−5.18022	−	4.34672i	−0.227606	−	0.190984i
$519$		0			0
$520$	22.7262	+	8.27167i	0.996611	+	0.362737i
$521$	17.5583	+	30.4119i	0.769244	+	1.33237i	0.937973	+	0.346708i	$0.112700\pi$
$521$	17.5583	+	30.4119i	0.769244	+	1.33237i	−0.168729	+	0.985662i	$0.553966\pi$
$522$		0			0
$523$	7.12269	−	12.3369i	0.311453	−	0.539453i	−0.667224	−	0.744857i	$-0.732518\pi$
$523$	7.12269	−	12.3369i	0.311453	−	0.539453i	0.978677	+	0.205404i	$0.0658509\pi$
$524$	−9.58545	+	8.04315i	−0.418742	+	0.351367i
$525$		0			0
$526$	2.06513	−	11.7119i	0.0900437	−	0.510663i
$527$	−0.946505	+	5.36789i	−0.0412304	+	0.233829i
$528$		0			0
$529$	−17.0759	+	14.3284i	−0.742431	+	0.622974i
$530$	9.64867	−	16.7120i	0.419111	−	0.725922i
$531$		0			0
$532$	0.272177	+	0.471425i	0.0118004	+	0.0204389i
$533$	34.8507	+	12.6846i	1.50955	+	0.549433i
$534$		0			0
$535$	−26.0223	−	21.8353i	−1.12504	−	0.944023i
$536$	−28.8634	+	10.5054i	−1.24671	+	0.453765i
$537$		0			0
$538$	−0.0563454	−	0.319550i	−0.00242922	−	0.0137768i
$539$	−1.19414			−0.0514354
$540$		0			0
$541$	−13.2368			−0.569094			−0.284547	−	0.958662i	$-0.591843\pi$
$541$	−13.2368			−0.569094			−0.284547	+	0.958662i	$0.591843\pi$
$542$	0.406901	+	2.30765i	0.0174779	+	0.0991222i
$543$		0			0
$544$	28.6004	−	10.4097i	1.22623	−	0.446312i
$545$	8.44557	+	7.08667i	0.361768	+	0.303560i
$546$		0			0
$547$	15.3216	+	5.57661i	0.655105	+	0.238439i	0.648121	−	0.761537i	$-0.275555\pi$
$547$	15.3216	+	5.57661i	0.655105	+	0.238439i	0.00698326	+	0.999976i	$0.497777\pi$
$548$	−1.00306	−	1.73736i	−0.0428488	−	0.0742163i
$549$		0			0
$550$	−1.29076	+	2.23567i	−0.0550383	+	0.0953291i
$551$	0.0977958	−	0.0820605i	0.00416624	−	0.00349589i
$552$		0			0
$553$	2.03995	−	11.5692i	0.0867476	−	0.491970i
$554$	4.27124	−	24.2234i	0.181468	−	1.02915i
$555$		0			0
$556$	5.42748	−	4.55419i	0.230176	−	0.193141i
$557$	15.4486	−	26.7577i	0.654577	−	1.13376i	−0.327422	−	0.944878i	$-0.606180\pi$
$557$	15.4486	−	26.7577i	0.654577	−	1.13376i	0.982000	−	0.188883i	$-0.0604867\pi$
$558$		0			0
$559$	9.84215	+	17.0471i	0.416279	+	0.721016i
$560$	5.78513	+	2.10561i	0.244466	+	0.0889784i
$561$		0			0
$562$	5.83571	+	4.89674i	0.246165	+	0.206557i
$563$	25.1612	−	9.15791i	1.06042	−	0.385960i	0.247832	−	0.968803i	$-0.420282\pi$
$563$	25.1612	−	9.15791i	1.06042	−	0.385960i	0.812585	+	0.582843i	$0.198060\pi$
$564$		0			0
$565$	2.09652	+	11.8900i	0.0882013	+	0.500214i
$566$	−7.50710			−0.315547
$567$		0			0
$568$	−0.272481			−0.0114331
$569$	−3.30985	−	18.7711i	−0.138756	−	0.786924i	−0.972170	−	0.234275i	$-0.924728\pi$
$569$	−3.30985	−	18.7711i	−0.138756	−	0.786924i	0.833414	−	0.552649i	$-0.186383\pi$
$570$		0			0
$571$	17.6420	−	6.42116i	0.738294	−	0.268717i	0.0546227	−	0.998507i	$-0.482604\pi$
$571$	17.6420	−	6.42116i	0.738294	−	0.268717i	0.683671	+	0.729790i	$0.260382\pi$
$572$	3.88286	+	3.25811i	0.162351	+	0.136228i
$573$		0			0
$574$	19.8641	+	7.22996i	0.829113	+	0.301773i
$575$	−0.821889	−	1.42355i	−0.0342751	−	0.0593663i
$576$		0			0
$577$	2.42981	−	4.20856i	0.101154	−	0.175204i	−0.811006	−	0.585038i	$-0.801080\pi$
$577$	2.42981	−	4.20856i	0.101154	−	0.175204i	0.912161	+	0.409833i	$0.134413\pi$
$578$	−21.9561	+	18.4234i	−0.913254	+	0.766311i
$579$		0			0
$580$	−0.137995	+	0.782610i	−0.00572994	+	0.0324961i
$581$	−3.43371	+	19.4736i	−0.142454	+	0.807899i
$582$		0			0
$583$	10.0730	−	8.45221i	0.417179	−	0.350055i
$584$	8.10226	−	14.0335i	0.335274	−	0.580712i
$585$		0			0
$586$	−0.291249	−	0.504459i	−0.0120314	−	0.0208390i
$587$	−30.8194	−	11.2174i	−1.27205	−	0.462990i	−0.384257	−	0.923226i	$-0.625542\pi$
$587$	−30.8194	−	11.2174i	−1.27205	−	0.462990i	−0.887796	+	0.460236i	$0.847765\pi$
$588$		0			0
$589$	−0.156510	−	0.131327i	−0.00644887	−	0.00541125i
$590$	5.19960	−	1.89250i	0.214064	−	0.0779130i
$591$		0			0
$592$	−0.649414	−	3.68301i	−0.0266908	−	0.151371i
$593$	−17.3446			−0.712258			−0.356129	−	0.934437i	$-0.615904\pi$
$593$	−17.3446			−0.712258			−0.356129	+	0.934437i	$0.615904\pi$
$594$		0			0
$595$	28.5384			1.16996
$596$	−0.0164973	−	0.0935607i	−0.000675754	−	0.00383239i
$597$		0			0
$598$	3.79482	−	1.38120i	0.155182	−	0.0564816i
$599$	−18.6975	−	15.6891i	−0.763961	−	0.641039i	0.175194	−	0.984534i	$-0.443945\pi$
$599$	−18.6975	−	15.6891i	−0.763961	−	0.641039i	−0.939155	+	0.343495i	$0.888389\pi$
$600$		0			0
$601$	−7.39563	−	2.69179i	−0.301674	−	0.109800i	0.186748	−	0.982408i	$-0.440205\pi$
$601$	−7.39563	−	2.69179i	−0.301674	−	0.109800i	−0.488422	+	0.872607i	$0.662427\pi$
$602$	5.60981	+	9.71647i	0.228639	+	0.396014i
$603$		0			0
$604$	−8.99922	+	15.5871i	−0.366173	+	0.634230i
$605$	−12.6071	+	10.5786i	−0.512553	+	0.430083i
$606$		0			0
$607$	−1.77772	+	10.0819i	−0.0721553	+	0.409213i	0.927241	+	0.374466i	$0.122174\pi$
$607$	−1.77772	+	10.0819i	−0.0721553	+	0.409213i	−0.999396	+	0.0347476i	$0.988937\pi$
$608$	−0.198103	+	1.12350i	−0.00803414	+	0.0455639i
$609$		0			0
$610$	−4.06528	+	3.41117i	−0.164598	+	0.138114i
$611$	12.0602	−	20.8889i	0.487905	−	0.845076i
$612$		0			0
$613$	−1.11753	−	1.93563i	−0.0451368	−	0.0781792i	0.842574	−	0.538580i	$-0.181039\pi$
$613$	−1.11753	−	1.93563i	−0.0451368	−	0.0781792i	−0.887711	+	0.460401i	$0.847706\pi$
$614$	6.66646	+	2.42639i	0.269036	+	0.0979213i
$615$		0			0
$616$	7.19547	+	6.03771i	0.289914	+	0.243266i
$617$	31.9267	−	11.6204i	1.28532	−	0.467818i	0.393132	−	0.919482i	$-0.371391\pi$
$617$	31.9267	−	11.6204i	1.28532	−	0.467818i	0.892188	+	0.451664i	$0.149169\pi$
$618$		0			0
$619$	−5.01079	−	28.4176i	−0.201401	−	1.14220i	−0.903004	−	0.429632i	$-0.858643\pi$
$619$	−5.01079	−	28.4176i	−0.201401	−	1.14220i	0.701604	−	0.712567i	$-0.252468\pi$
$620$	1.27179			0.0510763
$621$		0			0
$622$	16.2613			0.652020
$623$	−2.86280	−	16.2358i	−0.114696	−	0.650472i
$624$		0			0
$625$	10.7385	−	3.90849i	0.429540	−	0.156340i
$626$	19.0292	+	15.9674i	0.760558	+	0.638184i
$627$		0			0
$628$	−17.3224	−	6.30485i	−0.691240	−	0.251591i
$629$	−8.66811	−	15.0136i	−0.345620	−	0.598632i
$630$		0			0
$631$	1.57039	−	2.71999i	0.0625162	−	0.108281i	−0.833073	−	0.553163i	$-0.813421\pi$
$631$	1.57039	−	2.71999i	0.0625162	−	0.108281i	0.895590	+	0.444881i	$0.146754\pi$
$632$	11.1438	−	9.35076i	0.443277	−	0.371953i
$633$		0			0
$634$	1.32772	−	7.52985i	0.0527303	−	0.299049i
$635$	3.64488	−	20.6711i	0.144643	−	0.820309i
$636$		0			0
$637$	3.31786	−	2.78402i	0.131458	−	0.110307i
$638$	0.338774	−	0.586774i	0.0134122	−	0.0232306i
$639$		0			0
$640$	−0.911374	−	1.57855i	−0.0360252	−	0.0623975i
$641$	−29.9034	−	10.8839i	−1.18111	−	0.429890i	−0.324518	−	0.945879i	$-0.605202\pi$
$641$	−29.9034	−	10.8839i	−1.18111	−	0.429890i	−0.856595	+	0.515989i	$0.827424\pi$
$642$		0			0
$643$	−9.84142	−	8.25794i	−0.388108	−	0.325661i	0.427768	−	0.903889i	$-0.359300\pi$
$643$	−9.84142	−	8.25794i	−0.388108	−	0.325661i	−0.815876	+	0.578228i	$0.803745\pi$
$644$	−1.72866	+	0.629179i	−0.0681186	+	0.0247931i
$645$		0			0
$646$	−0.303217	−	1.71963i	−0.0119299	−	0.0676578i
$647$	−28.2444			−1.11040			−0.555200	−	0.831717i	$-0.687358\pi$
$647$	−28.2444			−1.11040			−0.555200	+	0.831717i	$0.687358\pi$
$648$		0			0
$649$	3.77042			0.148002
$650$	−1.62590	−	9.22094i	−0.0637730	−	0.361675i
$651$		0			0
$652$	−16.8088	+	6.11790i	−0.658283	+	0.239595i
$653$	−19.9099	−	16.7064i	−0.779134	−	0.653771i	0.163897	−	0.986477i	$-0.447594\pi$
$653$	−19.9099	−	16.7064i	−0.779134	−	0.653771i	−0.943030	+	0.332707i	$0.892038\pi$
$654$		0			0
$655$	−23.1062	−	8.40995i	−0.902832	−	0.328604i
$656$	5.84536	+	10.1245i	0.228223	+	0.395294i
$657$		0			0
$658$	6.87407	−	11.9062i	0.267979	−	0.464153i
$659$	36.4774	−	30.6081i	1.42096	−	1.19232i	0.470131	−	0.882597i	$-0.344207\pi$
$659$	36.4774	−	30.6081i	1.42096	−	1.19232i	0.950826	−	0.309727i	$-0.100238\pi$
$660$		0			0
$661$	−0.152204	+	0.863192i	−0.00592005	+	0.0335743i	−0.987625	−	0.156836i	$-0.949871\pi$
$661$	−0.152204	+	0.863192i	−0.00592005	+	0.0335743i	0.981705	+	0.190410i	$0.0609818\pi$
$662$	−5.31568	+	30.1467i	−0.206600	+	1.17168i
$663$		0			0
$664$	−18.7576	+	15.7395i	−0.727936	+	0.610811i
$665$	−0.534854	+	0.926394i	−0.0207407	+	0.0359240i
$666$		0			0
$667$	0.215714	+	0.373627i	0.00835246	+	0.0144669i
$668$	16.5817	+	6.03526i	0.641567	+	0.233511i
$669$		0			0
$670$	−14.2217	−	11.9334i	−0.549430	−	0.461027i
$671$	−3.39803	+	1.23678i	−0.131180	+	0.0477455i
$672$		0			0
$673$	6.48393	+	36.7722i	0.249937	+	1.41746i	0.808742	+	0.588164i	$0.200149\pi$
$673$	6.48393	+	36.7722i	0.249937	+	1.41746i	−0.558805	+	0.829299i	$0.688740\pi$
$674$	1.22206			0.0470721
$675$		0			0
$676$	−6.83505			−0.262886
$677$	2.38231	+	13.5107i	0.0915596	+	0.519260i	0.995747	+	0.0921251i	$0.0293660\pi$
$677$	2.38231	+	13.5107i	0.0915596	+	0.519260i	−0.904188	+	0.427135i	$0.859523\pi$
$678$		0			0
$679$	−12.6884	+	4.61819i	−0.486935	+	0.177230i
$680$	27.0716	+	22.7158i	1.03815	+	0.871109i
$681$		0			0
$682$	−1.01894	−	0.370863i	−0.0390171	−	0.0142011i
$683$	24.9943	+	43.2914i	0.956381	+	1.65650i	0.731175	+	0.682190i	$0.238972\pi$
$683$	24.9943	+	43.2914i	0.956381	+	1.65650i	0.225206	+	0.974311i	$0.427694\pi$
$684$		0			0
$685$	1.97112	−	3.41407i	0.0753125	−	0.130445i
$686$	15.7947	−	13.2534i	0.603046	−	0.506016i
$687$		0			0
$688$	−1.07747	+	6.11064i	−0.0410782	+	0.232966i
$689$	−8.28172	+	46.9680i	−0.315509	+	1.78934i
$690$		0			0
$691$	18.2434	−	15.3080i	0.694011	−	0.582345i	−0.226052	−	0.974115i	$-0.572582\pi$
$691$	18.2434	−	15.3080i	0.694011	−	0.582345i	0.920063	+	0.391771i	$0.128137\pi$
$692$	−8.40653	+	14.5605i	−0.319568	+	0.553508i
$693$		0			0
$694$	−3.10483	−	5.37773i	−0.117858	−	0.204136i
$695$	13.0832	+	4.76188i	0.496273	+	0.180629i
$696$		0			0
$697$	41.5144	+	34.8347i	1.57247	+	1.31946i
$698$	−30.3094	+	11.0317i	−1.14723	+	0.417557i
$699$		0			0
$700$	0.740646	+	4.20041i	0.0279938	+	0.158761i
$701$	−34.4493			−1.30113			−0.650565	−	0.759450i	$-0.725468\pi$
$701$	−34.4493			−1.30113			−0.650565	+	0.759450i	$0.725468\pi$
$702$		0			0
$703$	0.649815			0.0245082
$704$	1.67600	+	9.50506i	0.0631665	+	0.358235i
$705$		0			0
$706$	−36.6191	+	13.3282i	−1.37818	+	0.501615i
$707$	−9.42975	−	7.91250i	−0.354642	−	0.297580i
$708$		0			0
$709$	−14.5871	−	5.30927i	−0.547830	−	0.199394i	0.0532520	−	0.998581i	$-0.483041\pi$
$709$	−14.5871	−	5.30927i	−0.547830	−	0.199394i	−0.601082	+	0.799187i	$0.705264\pi$
$710$	−0.0823456	−	0.142627i	−0.00309038	−	0.00535269i
$711$		0			0
$712$	10.2075	−	17.6800i	0.382543	−	0.662585i
$713$	0.528911	−	0.443809i	0.0198079	−	0.0166208i
$714$		0			0
$715$	−1.72962	+	9.80918i	−0.0646842	+	0.366843i
$716$	1.68364	−	9.54839i	0.0629205	−	0.356840i
$717$		0			0
$718$	−21.3029	+	17.8752i	−0.795016	+	0.667098i
$719$	6.02686	−	10.4388i	0.224764	−	0.389303i	−0.731485	−	0.681858i	$-0.761172\pi$
$719$	6.02686	−	10.4388i	0.224764	−	0.389303i	0.956249	+	0.292555i	$0.0945056\pi$
$720$		0			0
$721$	−14.2872	−	24.7461i	−0.532083	−	0.921594i
$722$	−18.7626	−	6.82902i	−0.698271	−	0.254150i
$723$		0			0
$724$	12.2145	+	10.2492i	0.453947	+	0.380907i
$725$	0.939963	−	0.342119i	0.0349094	−	0.0127060i
$726$		0			0
$727$	−5.49253	−	31.1497i	−0.203707	−	1.15528i	−0.899462	−	0.437000i	$-0.856041\pi$
$727$	−5.49253	−	31.1497i	−0.203707	−	1.15528i	0.695755	−	0.718279i	$-0.255070\pi$
$728$	−34.0685			−1.26266
$729$		0			0
$730$	9.79423			0.362501
$731$	4.99469	+	28.3263i	0.184735	+	1.04769i
$732$		0			0
$733$	17.8831	−	6.50891i	0.660527	−	0.240412i	0.0100630	−	0.999949i	$-0.496797\pi$
$733$	17.8831	−	6.50891i	0.660527	−	0.240412i	0.650464	+	0.759537i	$0.274575\pi$
$734$	9.13716	+	7.66699i	0.337259	+	0.282994i
$735$		0			0
$736$	−3.62283	−	1.31860i	−0.133539	−	0.0486043i
$737$	−6.32516	−	10.9555i	−0.232990	−	0.403551i
$738$		0			0
$739$	−8.30036	+	14.3767i	−0.305334	+	0.528854i	−0.977336	−	0.211696i	$-0.932101\pi$
$739$	−8.30036	+	14.3767i	−0.305334	+	0.528854i	0.672002	+	0.740550i	$0.265435\pi$
$740$	−3.09864	+	2.60007i	−0.113908	+	0.0955804i
$741$		0			0
$742$	−4.72040	+	26.7707i	−0.173291	+	0.982783i
$743$	5.78310	−	32.7976i	0.212161	−	1.20323i	−0.673604	−	0.739093i	$-0.735255\pi$
$743$	5.78310	−	32.7976i	0.212161	−	1.20323i	0.885765	−	0.464134i	$-0.153634\pi$
$744$		0			0
$745$	0.143014	−	0.120003i	0.00523963	−	0.00439657i
$746$	3.08078	−	5.33606i	0.112795	−	0.195367i
$747$		0			0
$748$	3.70328	+	6.41426i	0.135405	+	0.234529i
$749$	44.9665	+	16.3665i	1.64304	+	0.598017i
$750$		0			0
$751$	21.2819	+	17.8577i	0.776589	+	0.651636i	0.942387	−	0.334524i	$-0.108576\pi$
$751$	21.2819	+	17.8577i	0.776589	+	0.651636i	−0.165798	+	0.986160i	$0.553020\pi$
$752$	7.14474	−	2.60047i	0.260542	−	0.0948295i
$753$		0			0
$754$	0.426735	+	2.42013i	0.0155408	+	0.0881361i
$755$	−35.3686			−1.28720
$756$		0			0
$757$	−3.12036			−0.113411			−0.0567057	−	0.998391i	$-0.518060\pi$
$757$	−3.12036			−0.113411			−0.0567057	+	0.998391i	$0.518060\pi$
$758$	−4.45373	−	25.2583i	−0.161767	−	0.917424i
$759$		0			0
$760$	−1.24475	+	0.453050i	−0.0451517	+	0.0164339i
$761$	33.6747	+	28.2564i	1.22071	+	1.02429i	0.998787	+	0.0492297i	$0.0156767\pi$
$761$	33.6747	+	28.2564i	1.22071	+	1.02429i	0.221919	+	0.975065i	$0.428768\pi$
$762$		0			0
$763$	−14.5939	−	5.31175i	−0.528335	−	0.192298i
$764$	11.9783	+	20.7470i	0.433360	+	0.750602i
$765$		0			0
$766$	2.01168	−	3.48433i	0.0726849	−	0.125894i
$767$	−10.4759	+	8.79032i	−0.378263	+	0.317400i
$768$		0			0
$769$	0.644731	−	3.65645i	0.0232496	−	0.131855i	−0.970974	−	0.239186i	$-0.923119\pi$
$769$	0.644731	−	3.65645i	0.0232496	−	0.131855i	0.994223	+	0.107331i	$0.0342305\pi$
$770$	−0.985846	+	5.59101i	−0.0355274	+	0.201486i
$771$		0			0
$772$	11.6748	−	9.79629i	0.420184	−	0.352576i
$773$	−4.48452	+	7.76741i	−0.161297	+	0.279374i	−0.935334	−	0.353766i	$-0.884901\pi$
$773$	−4.48452	+	7.76741i	−0.161297	+	0.279374i	0.774037	+	0.633140i	$0.218234\pi$
$774$		0			0
$775$	−0.800417	−	1.38636i	−0.0287518	−	0.0497996i
$776$	−15.7121	−	5.71875i	−0.564033	−	0.205291i
$777$		0			0
$778$	8.75652	+	7.34760i	0.313937	+	0.263424i
$779$	−1.90882	+	0.694754i	−0.0683906	+	0.0248921i
$780$		0			0
$781$	−0.0194871	−	0.110517i	−0.000697302	−	0.00395459i
$782$	5.90098			0.211018
$783$		0			0
$784$	1.36527			0.0487597
$785$	−6.29037	−	35.6745i	−0.224513	−	1.27328i
$786$		0			0
$787$	−41.2069	+	14.9981i	−1.46887	+	0.534624i	−0.947792	−	0.318888i	$-0.896691\pi$
$787$	−41.2069	+	14.9981i	−1.46887	+	0.534624i	−0.521074	+	0.853512i	$0.674468\pi$
$788$	1.70972	+	1.43462i	0.0609062	+	0.0511063i
$789$		0			0
$790$	8.26227	+	3.00722i	0.293958	+	0.106992i
$791$	−8.50374	−	14.7289i	−0.302358	−	0.523699i
$792$		0			0
$793$	6.55782	−	11.3585i	0.232875	−	0.403351i
$794$	8.48787	−	7.12217i	0.301223	−	0.252756i
$795$		0			0
$796$	−2.85997	+	16.2197i	−0.101369	+	0.574891i
$797$	−2.08656	+	11.8335i	−0.0739097	+	0.419163i	0.925294	+	0.379252i	$0.123819\pi$
$797$	−2.08656	+	11.8335i	−0.0739097	+	0.419163i	−0.999203	+	0.0399111i	$0.987293\pi$
$798$		0			0
$799$	26.9996	−	22.6554i	0.955178	−	0.801490i
$800$	−4.46940	+	7.74124i	−0.158017	+	0.273694i
$801$		0			0
$802$	−7.57299	−	13.1168i	−0.267412	−	0.463171i
$803$	6.27136	+	2.28259i	0.221311	+	0.0805508i
$804$		0			0
$805$	−2.76924	−	2.32366i	−0.0976027	−	0.0818984i
$806$	3.69568	−	1.34512i	0.130175	−	0.0473798i
$807$		0			0
$808$	−2.64695	−	15.0116i	−0.0931195	−	0.528107i
$809$	8.02937			0.282298			0.141149	−	0.989988i	$-0.454920\pi$
$809$	8.02937			0.282298			0.141149	+	0.989988i	$0.454920\pi$
$810$		0			0
$811$	−12.8345			−0.450681			−0.225341	−	0.974280i	$-0.572349\pi$
$811$	−12.8345			−0.450681			−0.225341	+	0.974280i	$0.572349\pi$
$812$	−0.194391	−	1.10244i	−0.00682177	−	0.0386882i
$813$		0			0
$814$	3.24078	−	1.17955i	0.113589	−	0.0413431i
$815$	−26.9270	−	22.5944i	−0.943211	−	0.791448i
$816$		0			0
$817$	−1.01312	−	0.368744i	−0.0354444	−	0.0129007i
$818$	9.32142	+	16.1452i	0.325916	+	0.564503i
$819$		0			0
$820$	6.32233	−	10.9506i	0.220785	−	0.382411i
$821$	22.7250	−	19.0685i	0.793108	−	0.665497i	−0.153404	−	0.988163i	$-0.549024\pi$
$821$	22.7250	−	19.0685i	0.793108	−	0.665497i	0.946513	+	0.322667i	$0.104579\pi$
$822$		0			0
$823$	8.60266	−	48.7881i	0.299870	−	1.70065i	−0.346852	−	0.937920i	$-0.612749\pi$
$823$	8.60266	−	48.7881i	0.299870	−	1.70065i	0.646722	−	0.762726i	$-0.276139\pi$
$824$	6.14436	−	34.8464i	0.214049	−	1.21393i
$825$		0			0
$826$	−5.97102	+	5.01028i	−0.207758	+	0.174330i
$827$	20.4215	−	35.3711i	0.710126	−	1.22997i	−0.254683	−	0.967025i	$-0.581971\pi$
$827$	20.4215	−	35.3711i	0.710126	−	1.22997i	0.964809	−	0.262950i	$-0.0846955\pi$
$828$		0			0
$829$	4.72638	+	8.18633i	0.164154	+	0.284323i	0.936355	−	0.351056i	$-0.114177\pi$
$829$	4.72638	+	8.18633i	0.164154	+	0.284323i	−0.772201	+	0.635379i	$0.780844\pi$
$830$	−13.9073	−	5.06185i	−0.482730	−	0.175699i
$831$		0			0
$832$	−26.8167	−	22.5018i	−0.929700	−	0.780111i
$833$	5.94714	−	2.16458i	0.206056	−	0.0749983i
$834$		0			0
$835$	6.02140	+	34.1491i	0.208379	+	1.18178i
$836$	−0.277620			−0.00960170
$837$		0			0
$838$	9.62995			0.332661
$839$	2.13360	+	12.1002i	0.0736599	+	0.417746i	0.999232	+	0.0391756i	$0.0124732\pi$
$839$	2.13360	+	12.1002i	0.0736599	+	0.417746i	−0.925572	+	0.378571i	$0.876416\pi$
$840$		0			0
$841$	27.0044	−	9.82879i	0.931186	−	0.338924i
$842$	−19.5413	−	16.3971i	−0.673436	−	0.565080i
$843$		0			0
$844$	−3.08148	−	1.12157i	−0.106069	−	0.0386059i
$845$	−6.71575	−	11.6320i	−0.231029	−	0.400154i
$846$		0			0
$847$	11.5916	−	20.0772i	0.398292	−	0.689862i
$848$	−11.5165	+	9.66346i	−0.395477	+	0.331845i
$849$		0			0
$850$	2.37581	−	13.4739i	0.0814896	−	0.462151i
$851$	−0.381330	+	2.16263i	−0.0130718	+	0.0741339i
$852$		0			0
$853$	−23.6446	+	19.8402i	−0.809576	+	0.679315i	−0.950507	−	0.310704i	$-0.899435\pi$
$853$	−23.6446	+	19.8402i	−0.809576	+	0.679315i	0.140930	+	0.990020i	$0.454991\pi$
$854$	3.73781	−	6.47408i	0.127905	−	0.221538i
$855$		0			0
$856$	29.6280	+	51.3172i	1.01266	+	1.75399i
$857$	10.4738	+	3.81217i	0.357780	+	0.130221i	0.514655	−	0.857397i	$-0.327920\pi$
$857$	10.4738	+	3.81217i	0.357780	+	0.130221i	−0.156876	+	0.987618i	$0.550142\pi$
$858$		0			0
$859$	3.17807	+	2.66672i	0.108434	+	0.0909872i	0.695393	−	0.718630i	$-0.255230\pi$
$859$	3.17807	+	2.66672i	0.108434	+	0.0909872i	−0.586958	+	0.809617i	$0.699675\pi$
$860$	6.30647	−	2.29537i	0.215049	−	0.0782714i
$861$		0			0
$862$	−5.40698	−	30.6645i	−0.184163	−	1.04444i
$863$	47.2534			1.60852			0.804262	−	0.594275i	$-0.202561\pi$
$863$	47.2534			1.60852			0.804262	+	0.594275i	$0.202561\pi$
$864$		0			0
$865$	−33.0392			−1.12337
$866$	−0.122620	−	0.695411i	−0.00416678	−	0.0236310i
$867$		0			0
$868$	−1.68349	+	0.612742i	−0.0571415	+	0.0207978i
$869$	4.58958	+	3.85112i	0.155691	+	0.130640i
$870$		0			0
$871$	43.1156	+	15.6928i	1.46092	+	0.531731i
$872$	−9.61579	−	16.6550i	−0.325632	−	0.564011i
$873$		0			0
$874$	−0.110593	+	0.191553i	−0.00374087	+	0.00647938i
$875$	−22.8650	+	19.1860i	−0.772978	+	0.648606i
$876$		0			0
$877$	6.10381	−	34.6164i	0.206111	−	1.16891i	−0.689571	−	0.724218i	$-0.742201\pi$
$877$	6.10381	−	34.6164i	0.206111	−	1.16891i	0.895682	−	0.444695i	$-0.146688\pi$
$878$	1.16236	−	6.59208i	0.0392278	−	0.222472i
$879$		0			0
$880$	−2.40519	+	2.01820i	−0.0810791	+	0.0680334i
$881$	−9.67981	+	16.7659i	−0.326121	+	0.564858i	−0.981739	−	0.190235i	$-0.939075\pi$
$881$	−9.67981	+	16.7659i	−0.326121	+	0.564858i	0.655618	+	0.755093i	$0.272408\pi$
$882$		0			0
$883$	6.89302	+	11.9391i	0.231969	+	0.401781i	0.958387	−	0.285471i	$-0.0921500\pi$
$883$	6.89302	+	11.9391i	0.231969	+	0.401781i	−0.726419	+	0.687252i	$0.758817\pi$
$884$	−25.2435	−	9.18788i	−0.849031	−	0.309022i
$885$		0			0
$886$	12.4007	+	10.4055i	0.416611	+	0.349578i
$887$	−28.0192	+	10.1982i	−0.940794	+	0.342421i	−0.766479	−	0.642269i	$-0.777993\pi$
$887$	−28.0192	+	10.1982i	−0.940794	+	0.342421i	−0.174315	+	0.984690i	$0.555771\pi$
$888$		0			0
$889$	5.13445	+	29.1189i	0.172204	+	0.976617i
$890$	12.3391			0.413609
$891$		0			0
$892$	18.8705			0.631832
$893$	0.229408	+	1.30104i	0.00767685	+	0.0435376i
$894$		0			0
$895$	17.9039	−	6.51649i	0.598461	−	0.217822i
$896$	1.96694	+	1.65046i	0.0657109	+	0.0551380i
$897$		0			0
$898$	31.7432	+	11.5536i	1.05928	+	0.385548i
$899$	0.210078	+	0.363866i	0.00700649	+	0.0121356i
$900$		0			0
$901$	−34.8448	+	60.3530i	−1.16085	+	2.01065i
$902$	−8.25862	+	6.92980i	−0.274982	+	0.230737i
$903$		0			0
$904$	3.65712	−	20.7406i	0.121634	−	0.689821i
$905$	−5.44094	+	30.8571i	−0.180863	+	1.02573i
$906$		0			0
$907$	−4.77366	+	4.00558i	−0.158507	+	0.133003i	−0.718592	−	0.695432i	$-0.755213\pi$
$907$	−4.77366	+	4.00558i	−0.158507	+	0.133003i	0.560085	+	0.828435i	$0.310769\pi$
$908$	6.36984	−	11.0329i	0.211391	−	0.366139i
$909$		0			0
$910$	−10.2957	−	17.8327i	−0.341300	−	0.591148i
$911$	−29.7314	−	10.8213i	−0.985044	−	0.358527i	−0.201245	−	0.979541i	$-0.564499\pi$
$911$	−29.7314	−	10.8213i	−0.985044	−	0.358527i	−0.783799	+	0.621014i	$0.786721\pi$
$912$		0			0
$913$	−7.72533	−	6.48232i	−0.255671	−	0.214534i
$914$	18.9906	−	6.91200i	0.628152	−	0.228629i
$915$		0			0
$916$	−2.60496	−	14.7734i	−0.0860701	−	0.488128i
$917$	34.6380			1.14385
$918$		0			0
$919$	36.0031			1.18763			0.593816	−	0.804601i	$-0.297621\pi$
$919$	36.0031			1.18763			0.593816	+	0.804601i	$0.297621\pi$
$920$	−0.777331	−	4.40846i	−0.0256278	−	0.145343i
$921$		0			0
$922$	5.17196	−	1.88244i	0.170329	−	0.0619948i
$923$	0.311801	+	0.261632i	0.0102631	+	0.00861173i
$924$		0			0
$925$	4.78447	+	1.74141i	0.157313	+	0.0572571i
$926$	0.894800	+	1.54984i	0.0294049	+	0.0509309i
$927$		0			0
$928$	1.17304	−	2.03177i	0.0385070	−	0.0666961i
$929$	−19.4941	+	16.3575i	−0.639580	+	0.536672i	−0.903889	−	0.427767i	$-0.859301\pi$
$929$	−19.4941	+	16.3575i	−0.639580	+	0.536672i	0.264309	+	0.964438i	$0.414856\pi$
$930$		0			0
$931$	−0.0411934	+	0.233619i	−0.00135006	+	0.00765656i
$932$	0.863820	−	4.89897i	0.0282954	−	0.160471i
$933$		0			0
$934$	15.8969	−	13.3391i	0.520164	−	0.436469i
$935$	−7.27728	+	12.6046i	−0.237993	+	0.412215i
$936$		0			0
$937$	−14.1524	−	24.5127i	−0.462338	−	0.800794i	0.536739	−	0.843749i	$-0.319656\pi$
$937$	−14.1524	−	24.5127i	−0.462338	−	0.800794i	−0.999077	+	0.0429549i	$0.986323\pi$
$938$	24.5750	+	8.94455i	0.802401	+	0.292050i
$939$		0			0
$940$	−6.29971	−	5.28608i	−0.205474	−	0.172413i
$941$	7.79422	−	2.83687i	0.254084	−	0.0924792i	−0.211838	−	0.977305i	$-0.567945\pi$
$941$	7.79422	−	2.83687i	0.254084	−	0.0924792i	0.465922	+	0.884826i	$0.345723\pi$
$942$		0			0
$943$	−1.19204	−	6.76039i	−0.0388181	−	0.220149i
$944$	−4.31074			−0.140303
$945$		0			0
$946$	−5.72199			−0.186038
$947$	7.71877	+	43.7753i	0.250826	+	1.42251i	0.806563	+	0.591148i	$0.201325\pi$
$947$	7.71877	+	43.7753i	0.250826	+	1.42251i	−0.555737	+	0.831358i	$0.687564\pi$
$948$		0			0
$949$	−22.7462	+	8.27895i	−0.738373	+	0.268746i
$950$	0.392853	+	0.329643i	0.0127458	+	0.0106950i
$951$		0			0
$952$	−46.7796	−	17.0264i	−1.51613	−	0.551828i
$953$	−4.83574	−	8.37576i	−0.156645	−	0.271317i	0.777012	−	0.629486i	$-0.216735\pi$
$953$	−4.83574	−	8.37576i	−0.156645	−	0.271317i	−0.933657	+	0.358169i	$0.883401\pi$
$954$		0			0
$955$	−23.5385	+	40.7699i	−0.761688	+	1.31928i
$956$	−3.58942	+	3.01188i	−0.116090	+	0.0974113i
$957$		0			0
$958$	−5.35576	+	30.3740i	−0.173037	+	0.981341i
$959$	−0.964325	+	5.46896i	−0.0311397	+	0.176602i
$960$		0			0
$961$	−23.2323	+	19.4942i	−0.749429	+	0.628845i
$962$	−6.25433	+	10.8328i	−0.201648	+	0.349264i
$963$		0			0
$964$	−3.95448	−	6.84936i	−0.127365	−	0.220603i
$965$	28.1425	+	10.2430i	0.905940	+	0.329735i
$966$		0			0
$967$	−25.3676	−	21.2860i	−0.815768	−	0.684510i	0.136209	−	0.990680i	$-0.456508\pi$
$967$	−25.3676	−	21.2860i	−0.815768	−	0.684510i	−0.951977	+	0.306170i	$0.900953\pi$
$968$	26.9767	−	9.81871i	0.867064	−	0.315585i
$969$		0			0
$970$	−1.75491	−	9.95257i	−0.0563466	−	0.319558i
$971$	27.4309			0.880298			0.440149	−	0.897925i	$-0.354926\pi$
$971$	27.4309			0.880298			0.440149	+	0.897925i	$0.354926\pi$
$972$		0			0
$973$	−19.6127			−0.628755
$974$	3.75420	+	21.2912i	0.120292	+	0.682213i
$975$		0			0
$976$	3.88499	−	1.41402i	0.124356	−	0.0452617i
$977$	−27.8668	−	23.3831i	−0.891539	−	0.748090i	0.0769792	−	0.997033i	$-0.475473\pi$
$977$	−27.8668	−	23.3831i	−0.891539	−	0.748090i	−0.968518	+	0.248943i	$0.919917\pi$
$978$		0			0
$979$	7.90089	+	2.87569i	0.252514	+	0.0919075i
$980$	−0.738337	−	1.27884i	−0.0235853	−	0.0408510i
$981$		0			0
$982$	−9.23957	+	16.0034i	−0.294847	+	0.510689i
$983$	−32.2790	+	27.0853i	−1.02954	+	0.863886i	−0.990796	−	0.135363i	$-0.956780\pi$
$983$	−32.2790	+	27.0853i	−1.02954	+	0.863886i	−0.0387434	+	0.999249i	$0.512335\pi$
$984$		0			0
$985$	−0.761595	+	4.31922i	−0.0242664	+	0.137622i
$986$	−0.623557	+	3.53637i	−0.0198581	+	0.112621i
$987$		0			0
$988$	0.771352	−	0.647241i	0.0245400	−	0.0205915i
$989$	1.82173	−	3.15533i	0.0579276	−	0.100334i
$990$		0			0
$991$	−12.7705	−	22.1191i	−0.405667	−	0.702635i	0.588732	−	0.808328i	$-0.299627\pi$
$991$	−12.7705	−	22.1191i	−0.405667	−	0.702635i	−0.994399	+	0.105693i	$0.966294\pi$
$992$	−3.52818	−	1.28415i	−0.112020	−	0.0407719i
$993$		0			0
$994$	0.177720	+	0.149124i	0.00563692	+	0.00472994i
$995$	−30.4130	+	11.0694i	−0.964158	+	0.350925i
$996$		0			0
$997$	4.08644	+	23.1754i	0.129419	+	0.733971i	0.978585	+	0.205845i	$0.0659942\pi$
$997$	4.08644	+	23.1754i	0.129419	+	0.733971i	−0.849166	+	0.528126i	$0.822895\pi$
$998$	20.1439			0.637644
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.2.e.a.10.1		12
3.2	odd	2		27.2.e.a.13.2	✓	12
9.2	odd	6		243.2.e.c.109.2		12
9.4	even	3		243.2.e.a.190.2		12
9.5	odd	6		243.2.e.d.190.1		12
9.7	even	3		243.2.e.b.109.1		12
12.11	even	2		432.2.u.c.337.2		12
15.2	even	4		675.2.u.b.499.2		24
15.8	even	4		675.2.u.b.499.3		24
15.14	odd	2		675.2.l.c.526.1		12
27.2	odd	18		27.2.e.a.25.2	yes	12
27.4	even	9		729.2.c.b.487.5		12
27.5	odd	18		729.2.a.a.1.5		6
27.7	even	9		243.2.e.b.136.1		12
27.11	odd	18		243.2.e.d.55.1		12
27.13	even	9		729.2.c.b.244.5		12
27.14	odd	18		729.2.c.e.244.2		12
27.16	even	9		243.2.e.a.55.2		12
27.20	odd	18		243.2.e.c.136.2		12
27.22	even	9		729.2.a.d.1.2		6
27.23	odd	18		729.2.c.e.487.2		12
27.25	even	9	inner	81.2.e.a.73.1		12
108.83	even	18		432.2.u.c.241.2		12
135.2	even	36		675.2.u.b.349.3		24
135.29	odd	18		675.2.l.c.376.1		12
135.83	even	36		675.2.u.b.349.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.13.2	✓	12	3.2	odd	2
27.2.e.a.25.2	yes	12	27.2	odd	18
81.2.e.a.10.1		12	1.1	even	1	trivial
81.2.e.a.73.1		12	27.25	even	9	inner
243.2.e.a.55.2		12	27.16	even	9
243.2.e.a.190.2		12	9.4	even	3
243.2.e.b.109.1		12	9.7	even	3
243.2.e.b.136.1		12	27.7	even	9
243.2.e.c.109.2		12	9.2	odd	6
243.2.e.c.136.2		12	27.20	odd	18
243.2.e.d.55.1		12	27.11	odd	18
243.2.e.d.190.1		12	9.5	odd	6
432.2.u.c.241.2		12	108.83	even	18
432.2.u.c.337.2		12	12.11	even	2
675.2.l.c.376.1		12	135.29	odd	18
675.2.l.c.526.1		12	15.14	odd	2
675.2.u.b.349.2		24	135.83	even	36
675.2.u.b.349.3		24	135.2	even	36
675.2.u.b.499.2		24	15.2	even	4
675.2.u.b.499.3		24	15.8	even	4
729.2.a.a.1.5		6	27.5	odd	18
729.2.a.d.1.2		6	27.22	even	9
729.2.c.b.244.5		12	27.13	even	9
729.2.c.b.487.5		12	27.4	even	9
729.2.c.e.244.2		12	27.14	odd	18
729.2.c.e.487.2		12	27.23	odd	18

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	81.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.183082 - 1.03831i) q^{2} +(0.834822 - 0.303850i) q^{4} +(1.33735 + 1.12217i) q^{5} +(-2.31094 - 0.841112i) q^{7} +(-1.52266 - 2.63732i) q^{8} +O(q^{10})\)	\(q+(-0.183082 - 1.03831i) q^{2} +(0.834822 - 0.303850i) q^{4} +(1.33735 + 1.12217i) q^{5} +(-2.31094 - 0.841112i) q^{7} +(-1.52266 - 2.63732i) q^{8} +(0.920313 - 1.59403i) q^{10} +(0.960783 - 0.806193i) q^{11} +(-0.789931 + 4.47992i) q^{13} +(-0.450243 + 2.55345i) q^{14} +(-1.09847 + 0.921724i) q^{16} +(-3.32358 + 5.75662i) q^{17} +(-0.124578 - 0.215776i) q^{19} +(1.45742 + 0.530458i) q^{20} +(-1.01298 - 0.849989i) q^{22} +(0.791222 - 0.287981i) q^{23} +(-0.339001 - 1.92257i) q^{25} +4.79615 q^{26} -2.18479 q^{28} +(0.0889744 + 0.504599i) q^{29} +(0.770551 - 0.280458i) q^{31} +(-3.50754 - 2.94318i) q^{32} +(6.58563 + 2.39697i) q^{34} +(-2.14666 - 3.71812i) q^{35} +(-1.30403 + 2.25865i) q^{37} +(-0.201233 + 0.168855i) q^{38} +(0.923194 - 5.23570i) q^{40} +(1.41572 - 8.02895i) q^{41} +(3.31478 - 2.78143i) q^{43} +(0.557121 - 0.964962i) q^{44} +(-0.443871 - 0.768808i) q^{46} +(-4.98256 - 1.81351i) q^{47} +(-0.729356 - 0.612002i) q^{49} +(-1.93415 + 0.703974i) q^{50} +(0.701774 + 3.97996i) q^{52} +10.4841 q^{53} +2.18959 q^{55} +(1.30048 + 7.37539i) q^{56} +(0.507639 - 0.184765i) q^{58} +(2.30289 + 1.93235i) q^{59} +(-2.70930 - 0.986103i) q^{61} +(-0.432275 - 0.748722i) q^{62} +(-3.84771 + 6.66442i) q^{64} +(-6.08365 + 5.10479i) q^{65} +(1.75146 - 9.93303i) q^{67} +(-1.02545 + 5.81562i) q^{68} +(-3.46754 + 2.90961i) q^{70} +(0.0447378 - 0.0774882i) q^{71} +(2.66057 + 4.60824i) q^{73} +(2.58391 + 0.940468i) q^{74} +(-0.169564 - 0.142281i) q^{76} +(-2.89841 + 1.05493i) q^{77} +(0.829503 + 4.70435i) q^{79} -2.50337 q^{80} -8.59571 q^{82} +(-1.39625 - 7.91851i) q^{83} +(-10.9047 + 3.96899i) q^{85} +(-3.49486 - 2.93254i) q^{86} +(-3.58913 - 1.30634i) q^{88} +(3.35189 + 5.80564i) q^{89} +(5.59359 - 9.68839i) q^{91} +(0.573026 - 0.480826i) q^{92} +(-0.970760 + 5.50545i) q^{94} +(0.0755324 - 0.428365i) q^{95} +(4.20603 - 3.52928i) q^{97} +(-0.501915 + 0.869342i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 6 q^{4} + 3 q^{5} - 6 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q + 6 * q^2 - 6 * q^4 + 3 * q^5 - 6 * q^7 - 6 * q^8	\( 12 q + 6 q^{2} - 6 q^{4} + 3 q^{5} - 6 q^{7} - 6 q^{8} - 3 q^{10} - 3 q^{11} - 6 q^{13} - 15 q^{14} - 9 q^{17} - 3 q^{19} + 3 q^{20} + 3 q^{22} + 12 q^{23} + 3 q^{25} + 30 q^{26} - 12 q^{28} + 6 q^{29} + 3 q^{31} + 9 q^{34} - 12 q^{35} - 3 q^{37} - 42 q^{38} + 21 q^{40} - 15 q^{41} + 3 q^{43} - 3 q^{44} - 3 q^{46} + 15 q^{47} + 12 q^{49} + 33 q^{50} + 9 q^{52} + 18 q^{53} - 12 q^{55} + 33 q^{56} + 21 q^{58} + 12 q^{59} + 12 q^{61} + 12 q^{62} + 12 q^{64} - 3 q^{65} - 15 q^{67} - 9 q^{68} - 15 q^{70} - 27 q^{71} + 6 q^{73} - 33 q^{74} - 48 q^{76} - 15 q^{77} - 42 q^{79} - 42 q^{80} - 12 q^{82} - 39 q^{83} - 27 q^{85} - 51 q^{86} - 30 q^{88} - 9 q^{89} + 6 q^{91} + 39 q^{92} - 15 q^{94} + 33 q^{95} + 3 q^{97} + 45 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 + 3 * q^5 - 6 * q^7 - 6 * q^8 - 3 * q^10 - 3 * q^11 - 6 * q^13 - 15 * q^14 - 9 * q^17 - 3 * q^19 + 3 * q^20 + 3 * q^22 + 12 * q^23 + 3 * q^25 + 30 * q^26 - 12 * q^28 + 6 * q^29 + 3 * q^31 + 9 * q^34 - 12 * q^35 - 3 * q^37 - 42 * q^38 + 21 * q^40 - 15 * q^41 + 3 * q^43 - 3 * q^44 - 3 * q^46 + 15 * q^47 + 12 * q^49 + 33 * q^50 + 9 * q^52 + 18 * q^53 - 12 * q^55 + 33 * q^56 + 21 * q^58 + 12 * q^59 + 12 * q^61 + 12 * q^62 + 12 * q^64 - 3 * q^65 - 15 * q^67 - 9 * q^68 - 15 * q^70 - 27 * q^71 + 6 * q^73 - 33 * q^74 - 48 * q^76 - 15 * q^77 - 42 * q^79 - 42 * q^80 - 12 * q^82 - 39 * q^83 - 27 * q^85 - 51 * q^86 - 30 * q^88 - 9 * q^89 + 6 * q^91 + 39 * q^92 - 15 * q^94 + 33 * q^95 + 3 * q^97 + 45 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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