LMFDB - Embedded newform 162.2.e.b.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(19,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			73.1
Root			$0.500000 - 1.74095i$ of defining polynomial
Character	$\chi$	$=$	162.73
Dual form			162.2.e.b.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 + 0.984808i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(-2.42692 + 2.03643i) q^{5} +(-3.46344 + 1.26059i) q^{7} +(0.500000 - 0.866025i) q^{8} +O(q^{10})$	\(q+(-0.173648 + 0.984808i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(-2.42692 + 2.03643i) q^{5} +(-3.46344 + 1.26059i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.58406 - 2.74367i) q^{10} +(1.75046 + 1.46881i) q^{11} +(0.538357 + 3.05317i) q^{13} +(-0.640018 - 3.62972i) q^{14} +(0.766044 + 0.642788i) q^{16} +(0.862878 + 1.49455i) q^{17} +(1.69740 - 2.93998i) q^{19} +(2.97705 - 1.08356i) q^{20} +(-1.75046 + 1.46881i) q^{22} +(-3.15087 - 1.14682i) q^{23} +(0.874658 - 4.96043i) q^{25} -3.10027 q^{26} +3.68572 q^{28} +(0.101661 - 0.576550i) q^{29} +(4.35827 + 1.58628i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(-1.62168 + 0.590243i) q^{34} +(5.83839 - 10.1124i) q^{35} +(3.65360 + 6.32822i) q^{37} +(2.60057 + 2.18213i) q^{38} +(0.550137 + 3.11998i) q^{40} +(1.22952 + 6.97295i) q^{41} +(1.27004 + 1.06569i) q^{43} +(-1.14253 - 1.97893i) q^{44} +(1.67654 - 2.90386i) q^{46} +(-3.61968 + 1.31746i) q^{47} +(5.04404 - 4.23245i) q^{49} +(4.73319 + 1.72274i) q^{50} +(0.538357 - 3.05317i) q^{52} +2.58267 q^{53} -7.23936 q^{55} +(-0.640018 + 3.62972i) q^{56} +(0.550137 + 0.200234i) q^{58} +(7.40243 - 6.21138i) q^{59} +(-12.3018 + 4.47750i) q^{61} +(-2.31899 + 4.01660i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(-7.52411 - 6.31348i) q^{65} +(-1.49490 - 8.47798i) q^{67} +(-0.299674 - 1.69954i) q^{68} +(8.94493 + 7.50569i) q^{70} +(0.993732 + 1.72119i) q^{71} +(-5.32371 + 9.22094i) q^{73} +(-6.86652 + 2.49921i) q^{74} +(-2.60057 + 2.18213i) q^{76} +(-7.91420 - 2.88053i) q^{77} +(2.44726 - 13.8791i) q^{79} -3.16812 q^{80} -7.08052 q^{82} +(0.538035 - 3.05135i) q^{83} +(-5.13767 - 1.86996i) q^{85} +(-1.27004 + 1.06569i) q^{86} +(2.14726 - 0.781539i) q^{88} +(-8.67300 + 15.0221i) q^{89} +(-5.71337 - 9.89585i) q^{91} +(2.56861 + 2.15532i) q^{92} +(-0.668890 - 3.79346i) q^{94} +(1.86760 + 10.5917i) q^{95} +(7.04084 + 5.90797i) q^{97} +(3.29226 + 5.70237i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q + 3 * q^5 - 3 * q^7 + 6 * q^8	$ 12 q + 3 q^{5} - 3 q^{7} + 6 q^{8} - 3 q^{10} + 12 q^{11} + 12 q^{13} + 3 q^{14} + 6 q^{17} - 9 q^{19} - 6 q^{20} - 12 q^{22} - 30 q^{23} - 9 q^{25} - 18 q^{26} + 12 q^{28} - 15 q^{29} - 15 q^{34} - 3 q^{35} - 15 q^{37} - 3 q^{38} - 3 q^{40} + 12 q^{41} + 9 q^{43} + 3 q^{44} + 3 q^{46} + 9 q^{47} - 39 q^{49} + 27 q^{50} + 12 q^{52} + 12 q^{53} + 18 q^{55} + 3 q^{56} - 3 q^{58} - 12 q^{59} - 36 q^{61} + 12 q^{62} - 6 q^{64} + 15 q^{65} + 36 q^{67} - 3 q^{68} + 39 q^{70} - 12 q^{71} - 21 q^{73} - 33 q^{74} + 3 q^{76} - 3 q^{77} + 39 q^{79} - 6 q^{80} + 6 q^{82} - 18 q^{83} + 45 q^{85} - 9 q^{86} + 6 q^{88} - 12 q^{89} - 6 q^{91} + 6 q^{92} + 36 q^{94} + 15 q^{95} + 39 q^{97} + 12 q^{98}+O(q^{100}) $ 12 * q + 3 * q^5 - 3 * q^7 + 6 * q^8 - 3 * q^10 + 12 * q^11 + 12 * q^13 + 3 * q^14 + 6 * q^17 - 9 * q^19 - 6 * q^20 - 12 * q^22 - 30 * q^23 - 9 * q^25 - 18 * q^26 + 12 * q^28 - 15 * q^29 - 15 * q^34 - 3 * q^35 - 15 * q^37 - 3 * q^38 - 3 * q^40 + 12 * q^41 + 9 * q^43 + 3 * q^44 + 3 * q^46 + 9 * q^47 - 39 * q^49 + 27 * q^50 + 12 * q^52 + 12 * q^53 + 18 * q^55 + 3 * q^56 - 3 * q^58 - 12 * q^59 - 36 * q^61 + 12 * q^62 - 6 * q^64 + 15 * q^65 + 36 * q^67 - 3 * q^68 + 39 * q^70 - 12 * q^71 - 21 * q^73 - 33 * q^74 + 3 * q^76 - 3 * q^77 + 39 * q^79 - 6 * q^80 + 6 * q^82 - 18 * q^83 + 45 * q^85 - 9 * q^86 + 6 * q^88 - 12 * q^89 - 6 * q^91 + 6 * q^92 + 36 * q^94 + 15 * q^95 + 39 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$3$		0			0
$3$		0			0
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	−2.42692	+	2.03643i	−1.08535	+	0.910717i	−0.996354	−	0.0853149i	$-0.972810\pi$
$5$	−2.42692	+	2.03643i	−1.08535	+	0.910717i	−0.0889963	+	0.996032i	$0.528366\pi$
$6$		0			0
$7$	−3.46344	+	1.26059i	−1.30906	+	0.476458i	−0.899936	−	0.436021i	$-0.856387\pi$
$7$	−3.46344	+	1.26059i	−1.30906	+	0.476458i	−0.409122	+	0.912480i	$0.634165\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$		0			0
$10$	−1.58406	−	2.74367i	−0.500923	−	0.867624i
$11$	1.75046	+	1.46881i	0.527785	+	0.442864i	0.867336	−	0.497724i	$-0.165831\pi$
$11$	1.75046	+	1.46881i	0.527785	+	0.442864i	−0.339551	+	0.940588i	$0.610275\pi$
$12$		0			0
$13$	0.538357	+	3.05317i	0.149313	+	0.846798i	0.963802	+	0.266619i	$0.0859065\pi$
$13$	0.538357	+	3.05317i	0.149313	+	0.846798i	−0.814489	+	0.580179i	$0.802982\pi$
$14$	−0.640018	−	3.62972i	−0.171052	−	0.970085i
$15$		0			0
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	0.862878	+	1.49455i	0.209279	+	0.362481i	0.951487	−	0.307687i	$-0.0995551\pi$
$17$	0.862878	+	1.49455i	0.209279	+	0.362481i	−0.742209	+	0.670169i	$0.766222\pi$
$18$		0			0
$19$	1.69740	−	2.93998i	0.389410	−	0.674478i	−0.602960	−	0.797771i	$-0.706012\pi$
$19$	1.69740	−	2.93998i	0.389410	−	0.674478i	0.992370	+	0.123293i	$0.0393456\pi$
$20$	2.97705	−	1.08356i	0.665690	−	0.242291i
$21$		0			0
$22$	−1.75046	+	1.46881i	−0.373200	+	0.313152i
$23$	−3.15087	−	1.14682i	−0.657002	−	0.239129i	−0.00806071	−	0.999968i	$-0.502566\pi$
$23$	−3.15087	−	1.14682i	−0.657002	−	0.239129i	−0.648942	+	0.760838i	$0.724788\pi$
$24$		0			0
$25$	0.874658	−	4.96043i	0.174932	−	0.992086i
$26$	−3.10027			−0.608014
$27$		0			0
$28$	3.68572			0.696535
$29$	0.101661	−	0.576550i	0.0188780	−	0.107063i	−0.973913	−	0.226923i	$-0.927134\pi$
$29$	0.101661	−	0.576550i	0.0188780	−	0.107063i	0.992791	+	0.119860i	$0.0382446\pi$
$30$		0			0
$31$	4.35827	+	1.58628i	0.782769	+	0.284904i	0.702327	−	0.711855i	$-0.252145\pi$
$31$	4.35827	+	1.58628i	0.782769	+	0.284904i	0.0804420	+	0.996759i	$0.474367\pi$
$32$	−0.766044	+	0.642788i	−0.135419	+	0.113630i
$33$		0			0
$34$	−1.62168	+	0.590243i	−0.278116	+	0.101226i
$35$	5.83839	−	10.1124i	0.986868	−	1.70931i
$36$		0			0
$37$	3.65360	+	6.32822i	0.600648	+	1.04035i	0.992723	+	0.120420i	$0.0384240\pi$
$37$	3.65360	+	6.32822i	0.600648	+	1.04035i	−0.392075	+	0.919933i	$0.628243\pi$
$38$	2.60057	+	2.18213i	0.421867	+	0.353989i
$39$		0			0
$40$	0.550137	+	3.11998i	0.0869844	+	0.493313i
$41$	1.22952	+	6.97295i	0.192019	+	1.08899i	0.916601	+	0.399803i	$0.130922\pi$
$41$	1.22952	+	6.97295i	0.192019	+	1.08899i	−0.724582	+	0.689188i	$0.757967\pi$
$42$		0			0
$43$	1.27004	+	1.06569i	0.193679	+	0.162516i	0.734470	−	0.678641i	$-0.237431\pi$
$43$	1.27004	+	1.06569i	0.193679	+	0.162516i	−0.540791	+	0.841157i	$0.681875\pi$
$44$	−1.14253	−	1.97893i	−0.172243	−	0.298334i
$45$		0			0
$46$	1.67654	−	2.90386i	0.247193	−	0.428151i
$47$	−3.61968	+	1.31746i	−0.527984	+	0.192171i	−0.592238	−	0.805763i	$-0.701756\pi$
$47$	−3.61968	+	1.31746i	−0.527984	+	0.192171i	0.0642537	+	0.997934i	$0.479533\pi$
$48$		0			0
$49$	5.04404	−	4.23245i	0.720577	−	0.604636i
$50$	4.73319	+	1.72274i	0.669374	+	0.243632i
$51$		0			0
$52$	0.538357	−	3.05317i	0.0746567	−	0.423399i
$53$	2.58267			0.354757			0.177379	−	0.984143i	$-0.443238\pi$
$53$	2.58267			0.354757			0.177379	+	0.984143i	$0.443238\pi$
$54$		0			0
$55$	−7.23936			−0.976155
$56$	−0.640018	+	3.62972i	−0.0855261	+	0.485042i
$57$		0			0
$58$	0.550137	+	0.200234i	0.0722366	+	0.0262920i
$59$	7.40243	−	6.21138i	0.963714	−	0.808652i	−0.0178389	−	0.999841i	$-0.505679\pi$
$59$	7.40243	−	6.21138i	0.963714	−	0.808652i	0.981553	+	0.191188i	$0.0612342\pi$
$60$		0			0
$61$	−12.3018	+	4.47750i	−1.57509	+	0.573285i	−0.974129	−	0.225994i	$-0.927437\pi$
$61$	−12.3018	+	4.47750i	−1.57509	+	0.573285i	−0.600960	+	0.799279i	$0.705215\pi$
$62$	−2.31899	+	4.01660i	−0.294512	+	0.510109i
$63$		0			0
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−7.52411	−	6.31348i	−0.933251	−	0.783091i
$66$		0			0
$67$	−1.49490	−	8.47798i	−0.182631	−	1.03575i	−0.928962	−	0.370175i	$-0.879298\pi$
$67$	−1.49490	−	8.47798i	−0.182631	−	1.03575i	0.746331	−	0.665574i	$-0.231813\pi$
$68$	−0.299674	−	1.69954i	−0.0363408	−	0.206099i
$69$		0			0
$70$	8.94493	+	7.50569i	1.06912	+	0.897102i
$71$	0.993732	+	1.72119i	0.117934	+	0.204268i	0.918949	−	0.394377i	$-0.129039\pi$
$71$	0.993732	+	1.72119i	0.117934	+	0.204268i	−0.801015	+	0.598645i	$0.795706\pi$
$72$		0			0
$73$	−5.32371	+	9.22094i	−0.623094	+	1.07923i	0.365812	+	0.930689i	$0.380791\pi$
$73$	−5.32371	+	9.22094i	−0.623094	+	1.07923i	−0.988906	+	0.148541i	$0.952542\pi$
$74$	−6.86652	+	2.49921i	−0.798217	+	0.290527i
$75$		0			0
$76$	−2.60057	+	2.18213i	−0.298305	+	0.250308i
$77$	−7.91420	−	2.88053i	−0.901907	−	0.328267i
$78$		0			0
$79$	2.44726	−	13.8791i	0.275338	−	1.56152i	−0.462548	−	0.886594i	$-0.653065\pi$
$79$	2.44726	−	13.8791i	0.275338	−	1.56152i	0.737886	−	0.674925i	$-0.235824\pi$
$80$	−3.16812			−0.354206
$81$		0			0
$82$	−7.08052			−0.781912
$83$	0.538035	−	3.05135i	0.0590571	−	0.334929i	−0.940936	−	0.338584i	$-0.890052\pi$
$83$	0.538035	−	3.05135i	0.0590571	−	0.334929i	0.999993	+	0.00365453i	$0.00116328\pi$
$84$		0			0
$85$	−5.13767	−	1.86996i	−0.557258	−	0.202825i
$86$	−1.27004	+	1.06569i	−0.136952	+	0.114916i
$87$		0			0
$88$	2.14726	−	0.781539i	0.228899	−	0.0833123i
$89$	−8.67300	+	15.0221i	−0.919336	+	1.59234i	−0.118911	+	0.992905i	$0.537940\pi$
$89$	−8.67300	+	15.0221i	−0.919336	+	1.59234i	−0.800425	+	0.599432i	$0.795393\pi$
$90$		0			0
$91$	−5.71337	−	9.89585i	−0.598924	−	1.03737i
$92$	2.56861	+	2.15532i	0.267797	+	0.224708i
$93$		0			0
$94$	−0.668890	−	3.79346i	−0.0689907	−	0.391266i
$95$	1.86760	+	10.5917i	0.191612	+	1.08669i
$96$		0			0
$97$	7.04084	+	5.90797i	0.714889	+	0.599863i	0.925966	−	0.377606i	$-0.123253\pi$
$97$	7.04084	+	5.90797i	0.714889	+	0.599863i	−0.211077	+	0.977469i	$0.567697\pi$
$98$	3.29226	+	5.70237i	0.332569	+	0.576026i
$99$		0			0
$100$	−2.51848	+	4.36213i	−0.251848	+	0.436213i
$101$	11.2389	−	4.09062i	1.11831	−	0.407032i	0.284276	−	0.958743i	$-0.408247\pi$
$101$	11.2389	−	4.09062i	1.11831	−	0.407032i	0.834036	+	0.551710i	$0.186025\pi$
$102$		0			0
$103$	−9.76437	+	8.19328i	−0.962112	+	0.807308i	−0.981295	−	0.192508i	$-0.938338\pi$
$103$	−9.76437	+	8.19328i	−0.962112	+	0.807308i	0.0191837	+	0.999816i	$0.493893\pi$
$104$	2.91331	+	1.06036i	0.285673	+	0.103977i
$105$		0			0
$106$	−0.448476	+	2.54343i	−0.0435599	+	0.247040i
$107$	−6.09894			−0.589607			−0.294803	−	0.955558i	$-0.595254\pi$
$107$	−6.09894			−0.589607			−0.294803	+	0.955558i	$0.595254\pi$
$108$		0			0
$109$	11.2390			1.07650			0.538250	−	0.842785i	$-0.319086\pi$
$109$	11.2390			1.07650			0.538250	+	0.842785i	$0.319086\pi$
$110$	1.25710	−	7.12937i	0.119860	−	0.679759i
$111$		0			0
$112$	−3.46344	−	1.26059i	−0.327265	−	0.119115i
$113$	5.39062	−	4.52327i	0.507107	−	0.425513i	−0.353003	−	0.935622i	$-0.614839\pi$
$113$	5.39062	−	4.52327i	0.507107	−	0.425513i	0.860110	+	0.510109i	$0.170395\pi$
$114$		0			0
$115$	9.98233	−	3.63327i	0.930857	−	0.338804i
$116$	−0.292722	+	0.507009i	−0.0271786	+	0.0470746i
$117$		0			0
$118$	4.83159	+	8.36857i	0.444784	+	0.770389i
$119$	−4.87254	−	4.08855i	−0.446665	−	0.374796i
$120$		0			0
$121$	−1.00342	−	5.69068i	−0.0912200	−	0.517334i
$122$	−2.27329	−	12.8925i	−0.205814	−	1.16723i
$123$		0			0
$124$	−3.55290	−	2.98123i	−0.319059	−	0.267723i
$125$	0.0585380	+	0.101391i	0.00523579	+	0.00906866i
$126$		0			0
$127$	−2.99250	+	5.18316i	−0.265541	+	0.459931i	−0.967705	−	0.252084i	$-0.918884\pi$
$127$	−2.99250	+	5.18316i	−0.265541	+	0.459931i	0.702164	+	0.712015i	$0.252217\pi$
$128$	0.939693	−	0.342020i	0.0830579	−	0.0302306i
$129$		0			0
$130$	7.52411	−	6.31348i	0.659908	−	0.553729i
$131$	15.4251	+	5.61427i	1.34770	+	0.490521i	0.912228	−	0.409683i	$-0.134361\pi$
$131$	15.4251	+	5.61427i	1.34770	+	0.490521i	0.435468	+	0.900204i	$0.356583\pi$
$132$		0			0
$133$	−2.17273	+	12.3222i	−0.188400	+	1.06847i
$134$	8.60876			0.743684
$135$		0			0
$136$	1.72576			0.147982
$137$	0.0366673	−	0.207951i	0.00313270	−	0.0177664i	−0.983201	−	0.182524i	$-0.941573\pi$
$137$	0.0366673	−	0.207951i	0.00313270	−	0.0177664i	0.986334	+	0.164758i	$0.0526843\pi$
$138$		0			0
$139$	−3.45009	−	1.25573i	−0.292633	−	0.106510i	0.191532	−	0.981486i	$-0.438654\pi$
$139$	−3.45009	−	1.25573i	−0.292633	−	0.106510i	−0.484165	+	0.874977i	$0.660877\pi$
$140$	−8.94493	+	7.50569i	−0.755985	+	0.634347i
$141$		0			0
$142$	−1.86760	+	0.679753i	−0.156726	+	0.0570436i
$143$	−3.54217	+	6.13522i	−0.296211	+	0.513053i
$144$		0			0
$145$	0.927377	+	1.60626i	0.0770145	+	0.133393i
$146$	−8.15640	−	6.84404i	−0.675029	−	0.566416i
$147$		0			0
$148$	−1.26888	−	7.19618i	−0.104301	−	0.591523i
$149$	−2.68710	−	15.2393i	−0.220136	−	1.24845i	−0.871769	−	0.489918i	$-0.837027\pi$
$149$	−2.68710	−	15.2393i	−0.220136	−	1.24845i	0.651633	−	0.758535i	$-0.274084\pi$
$150$		0			0
$151$	15.4325	+	12.9494i	1.25588	+	1.05381i	0.996108	+	0.0881390i	$0.0280920\pi$
$151$	15.4325	+	12.9494i	1.25588	+	1.05381i	0.259772	+	0.965670i	$0.416352\pi$
$152$	−1.69740	−	2.93998i	−0.137677	−	0.238464i
$153$		0			0
$154$	4.21106	−	7.29377i	0.339337	−	0.587748i
$155$	−13.8075	+	5.02552i	−1.10905	+	0.403660i
$156$		0			0
$157$	13.7868	−	11.5685i	1.10031	−	0.923269i	0.102863	−	0.994695i	$-0.467200\pi$
$157$	13.7868	−	11.5685i	1.10031	−	0.923269i	0.997446	+	0.0714264i	$0.0227551\pi$
$158$	13.2433	+	4.82016i	1.05358	+	0.383471i
$159$		0			0
$160$	0.550137	−	3.11998i	0.0434922	−	0.246656i
$161$	12.3585			0.973989
$162$		0			0
$163$	3.05289			0.239121			0.119560	−	0.992827i	$-0.461851\pi$
$163$	3.05289			0.239121			0.119560	+	0.992827i	$0.461851\pi$
$164$	1.22952	−	6.97295i	0.0960093	−	0.544496i
$165$		0			0
$166$	2.91156	+	1.05972i	0.225981	+	0.0822504i
$167$	3.14170	−	2.63620i	0.243112	−	0.203995i	−0.513088	−	0.858336i	$-0.671498\pi$
$167$	3.14170	−	2.63620i	0.243112	−	0.203995i	0.756199	+	0.654341i	$0.227054\pi$
$168$		0			0
$169$	3.18396	−	1.15887i	0.244920	−	0.0891435i
$170$	2.73370	−	4.73490i	0.209665	−	0.363150i
$171$		0			0
$172$	−0.828957	−	1.43580i	−0.0632074	−	0.109478i
$173$	13.0435	+	10.9448i	0.991680	+	0.832118i	0.985810	−	0.167864i	$-0.0536871\pi$
$173$	13.0435	+	10.9448i	0.991680	+	0.832118i	0.00586990	+	0.999983i	$0.498132\pi$
$174$		0			0
$175$	3.22374	+	18.2828i	0.243692	+	1.38205i
$176$	0.396798	+	2.25035i	0.0299098	+	0.169627i
$177$		0			0
$178$	−13.2878	−	11.1498i	−0.995964	−	0.835713i
$179$	−7.27802	−	12.6059i	−0.543985	−	0.942210i	−0.998670	−	0.0515575i	$-0.983581\pi$
$179$	−7.27802	−	12.6059i	−0.543985	−	0.942210i	0.454685	−	0.890652i	$-0.349752\pi$
$180$		0			0
$181$	6.51190	−	11.2789i	0.484026	−	0.838357i	−0.515806	−	0.856706i	$-0.672507\pi$
$181$	6.51190	−	11.2789i	0.484026	−	0.838357i	0.999832	+	0.0183482i	$0.00584075\pi$
$182$	10.7376	−	3.90818i	0.795926	−	0.289693i
$183$		0			0
$184$	−2.56861	+	2.15532i	−0.189361	+	0.158893i
$185$	−21.7539	−	7.91778i	−1.59938	−	0.582127i
$186$		0			0
$187$	−0.684776	+	3.88356i	−0.0500758	+	0.283994i
$188$	3.85198			0.280935
$189$		0			0
$190$	−10.7551			−0.780258
$191$	−0.625632	+	3.54814i	−0.0452692	+	0.256734i	−0.999040	−	0.0437996i	$-0.986054\pi$
$191$	−0.625632	+	3.54814i	−0.0452692	+	0.256734i	0.953771	+	0.300534i	$0.0971648\pi$
$192$		0			0
$193$	−1.38592	−	0.504435i	−0.0997610	−	0.0363100i	0.291657	−	0.956523i	$-0.405793\pi$
$193$	−1.38592	−	0.504435i	−0.0997610	−	0.0363100i	−0.391418	+	0.920213i	$0.628015\pi$
$194$	−7.04084	+	5.90797i	−0.505503	+	0.424167i
$195$		0			0
$196$	−6.18743	+	2.25204i	−0.441959	+	0.160860i
$197$	1.26931	−	2.19851i	0.0904346	−	0.156637i	−0.817259	−	0.576270i	$-0.804508\pi$
$197$	1.26931	−	2.19851i	0.0904346	−	0.156637i	0.907694	+	0.419633i	$0.137841\pi$
$198$		0			0
$199$	0.925891	+	1.60369i	0.0656347	+	0.113683i	0.896975	−	0.442081i	$-0.145759\pi$
$199$	0.925891	+	1.60369i	0.0656347	+	0.113683i	−0.831341	+	0.555763i	$0.812426\pi$
$200$	−3.85853	−	3.23769i	−0.272839	−	0.228939i
$201$		0			0
$202$	2.07686	+	11.7785i	0.146128	+	0.828731i
$203$	0.374695	+	2.12500i	0.0262984	+	0.149146i
$204$		0			0
$205$	−17.1838	−	14.4189i	−1.20017	−	1.00706i
$206$	−6.37324	−	11.0388i	−0.444045	−	0.769108i
$207$		0			0
$208$	−1.55014	+	2.68492i	−0.107483	+	0.186165i
$209$	7.28951	−	2.65317i	0.504226	−	0.183523i
$210$		0			0
$211$	−14.5459	+	12.2054i	−1.00138	+	0.840257i	−0.987175	−	0.159642i	$-0.948966\pi$
$211$	−14.5459	+	12.2054i	−1.00138	+	0.840257i	−0.0142043	+	0.999899i	$0.504522\pi$
$212$	−2.42692	−	0.883326i	−0.166681	−	0.0606671i
$213$		0			0
$214$	1.05907	−	6.00628i	0.0723965	−	0.410581i
$215$	−5.25247			−0.358215
$216$		0			0
$217$	−17.0943			−1.16043
$218$	−1.95163	+	11.0683i	−0.132181	+	0.749637i
$219$		0			0
$220$	6.80277	+	2.47601i	0.458643	+	0.166932i
$221$	−4.09858	+	3.43912i	−0.275700	+	0.231340i
$222$		0			0
$223$	6.81687	−	2.48114i	0.456491	−	0.166149i	−0.103532	−	0.994626i	$-0.533014\pi$
$223$	6.81687	−	2.48114i	0.456491	−	0.166149i	0.560023	+	0.828477i	$0.310792\pi$
$224$	1.84286	−	3.19193i	0.123131	−	0.213270i
$225$		0			0
$226$	3.51848	+	6.09418i	0.234046	+	0.405379i
$227$	21.8531	+	18.3369i	1.45044	+	1.21706i	0.932258	+	0.361793i	$0.117835\pi$
$227$	21.8531	+	18.3369i	1.45044	+	1.21706i	0.518182	+	0.855271i	$0.326609\pi$
$228$		0			0
$229$	0.322184	+	1.82720i	0.0212905	+	0.120744i	0.993601	−	0.112949i	$-0.0360298\pi$
$229$	0.322184	+	1.82720i	0.0212905	+	0.120744i	−0.972310	+	0.233694i	$0.924919\pi$
$230$	1.84466	+	10.4616i	0.121633	+	0.689816i
$231$		0			0
$232$	−0.448476	−	0.376316i	−0.0294439	−	0.0247064i
$233$	4.26735	+	7.39126i	0.279563	+	0.484218i	0.971276	−	0.237955i	$-0.0764770\pi$
$233$	4.26735	+	7.39126i	0.279563	+	0.484218i	−0.691713	+	0.722172i	$0.743144\pi$
$234$		0			0
$235$	6.10176	−	10.5686i	0.398035	−	0.689417i
$236$	−9.08043	+	3.30500i	−0.591085	+	0.215137i
$237$		0			0
$238$	4.87254	−	4.08855i	0.315840	−	0.265021i
$239$	−6.84845	−	2.49263i	−0.442989	−	0.161235i	0.110889	−	0.993833i	$-0.464630\pi$
$239$	−6.84845	−	2.49263i	−0.442989	−	0.161235i	−0.553878	+	0.832598i	$0.686853\pi$
$240$		0			0
$241$	−0.231806	+	1.31464i	−0.0149319	+	0.0846833i	−0.991363	−	0.131146i	$-0.958134\pi$
$241$	−0.231806	+	1.31464i	−0.0149319	+	0.0846833i	0.976431	+	0.215829i	$0.0692455\pi$
$242$	5.77847			0.371454
$243$		0			0
$244$	13.0913			0.838087
$245$	−3.62239	+	20.5436i	−0.231426	+	1.31248i
$246$		0			0
$247$	9.89008	+	3.59969i	0.629291	+	0.229043i
$248$	3.55290	−	2.98123i	0.225609	−	0.189308i
$249$		0			0
$250$	−0.110015	+	0.0400423i	−0.00695798	+	0.00253250i
$251$	−1.43928	+	2.49291i	−0.0908466	+	0.157351i	−0.907868	−	0.419257i	$-0.862291\pi$
$251$	−1.43928	+	2.49291i	−0.0908466	+	0.157351i	0.817021	+	0.576608i	$0.195624\pi$
$252$		0			0
$253$	−3.83102	−	6.63552i	−0.240854	−	0.417171i
$254$	−4.58477	−	3.84708i	−0.287674	−	0.241387i
$255$		0			0
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	4.47629	+	25.3863i	0.279223	+	1.58355i	0.725219	+	0.688518i	$0.241738\pi$
$257$	4.47629	+	25.3863i	0.279223	+	1.58355i	−0.445996	+	0.895035i	$0.647150\pi$
$258$		0			0
$259$	−20.6313	−	17.3117i	−1.28197	−	1.07570i
$260$	4.91101	+	8.50613i	0.304568	+	0.527528i
$261$		0			0
$262$	−8.20752	+	14.2158i	−0.507062	+	0.878257i
$263$	−14.1609	+	5.15414i	−0.873197	+	0.317818i	−0.739461	−	0.673199i	$-0.764920\pi$
$263$	−14.1609	+	5.15414i	−0.873197	+	0.317818i	−0.133736	+	0.991017i	$0.542697\pi$
$264$		0			0
$265$	−6.26793	+	5.25942i	−0.385036	+	0.323083i
$266$	−11.7577	−	4.27945i	−0.720910	−	0.262390i
$267$		0			0
$268$	−1.49490	+	8.47798i	−0.0913153	+	0.517875i
$269$	−16.0615			−0.979286			−0.489643	−	0.871923i	$-0.662873\pi$
$269$	−16.0615			−0.979286			−0.489643	+	0.871923i	$0.662873\pi$
$270$		0			0
$271$	9.41446			0.571888			0.285944	−	0.958246i	$-0.407693\pi$
$271$	9.41446			0.571888			0.285944	+	0.958246i	$0.407693\pi$
$272$	−0.299674	+	1.69954i	−0.0181704	+	0.103050i
$273$		0			0
$274$	0.198424	+	0.0722205i	0.0119872	+	0.00436300i
$275$	8.81700	−	7.39834i	0.531685	−	0.446137i
$276$		0			0
$277$	−5.23856	+	1.90668i	−0.314755	+	0.114561i	−0.494567	−	0.869140i	$-0.664673\pi$
$277$	−5.23856	+	1.90668i	−0.314755	+	0.114561i	0.179812	+	0.983701i	$0.442451\pi$
$278$	1.83576	−	3.17962i	0.110101	−	0.190701i
$279$		0			0
$280$	−5.83839	−	10.1124i	−0.348911	−	0.604331i
$281$	−21.4529	−	18.0011i	−1.27977	−	1.07386i	−0.993275	−	0.115777i	$-0.963064\pi$
$281$	−21.4529	−	18.0011i	−1.27977	−	1.07386i	−0.286499	−	0.958081i	$-0.592491\pi$
$282$		0			0
$283$	1.06884	+	6.06171i	0.0635361	+	0.360331i	0.999955	+	0.00944797i	$0.00300743\pi$
$283$	1.06884	+	6.06171i	0.0635361	+	0.360331i	−0.936419	+	0.350883i	$0.885881\pi$
$284$	−0.345119	−	1.95727i	−0.0204791	−	0.116143i
$285$		0			0
$286$	−5.42692	−	4.55372i	−0.320900	−	0.269267i
$287$	−13.0484	−	22.6005i	−0.770222	−	1.33406i
$288$		0			0
$289$	7.01088	−	12.1432i	0.412405	−	0.714306i
$290$	−1.74290	+	0.634363i	−0.102347	+	0.0372511i
$291$		0			0
$292$	8.15640	−	6.84404i	0.477317	−	0.400517i
$293$	2.19428	+	0.798651i	0.128191	+	0.0466577i	0.405319	−	0.914175i	$-0.367160\pi$
$293$	2.19428	+	0.798651i	0.128191	+	0.0466577i	−0.277128	+	0.960833i	$0.589383\pi$
$294$		0			0
$295$	−5.31608	+	30.1490i	−0.309514	+	1.75534i
$296$	7.30720			0.424722
$297$		0			0
$298$	15.4744			0.896408
$299$	1.80516	−	10.2376i	0.104395	−	0.592054i
$300$		0			0
$301$	−5.74209	−	2.08995i	−0.330969	−	0.120463i
$302$	−15.4325	+	12.9494i	−0.888042	+	0.745155i
$303$		0			0
$304$	3.19007	−	1.16109i	0.182963	−	0.0665930i
$305$	20.7374	−	35.9183i	1.18742	−	2.05668i
$306$		0			0
$307$	−3.41265	−	5.91088i	−0.194770	−	0.337351i	0.752055	−	0.659100i	$-0.229063\pi$
$307$	−3.41265	−	5.91088i	−0.194770	−	0.337351i	−0.946825	+	0.321749i	$0.895729\pi$
$308$	6.45172	+	5.41363i	0.367621	+	0.308470i
$309$		0			0
$310$	−2.55152	−	14.4704i	−0.144917	−	0.821864i
$311$	−1.49254	−	8.46464i	−0.0846344	−	0.479986i	−0.997435	−	0.0715798i	$-0.977196\pi$
$311$	−1.49254	−	8.46464i	−0.0846344	−	0.479986i	0.912800	−	0.408406i	$-0.133915\pi$
$312$		0			0
$313$	−16.5993	−	13.9285i	−0.938250	−	0.787285i	0.0390299	−	0.999238i	$-0.487573\pi$
$313$	−16.5993	−	13.9285i	−0.938250	−	0.787285i	−0.977280	+	0.211953i	$0.932018\pi$
$314$	8.99872	+	15.5862i	0.507827	+	0.879582i
$315$		0			0
$316$	−7.04660	+	12.2051i	−0.396402	+	0.686588i
$317$	33.1899	−	12.0801i	1.86413	−	0.678488i	0.888577	−	0.458728i	$-0.151695\pi$
$317$	33.1899	−	12.0801i	1.86413	−	0.678488i	0.975554	−	0.219760i	$-0.0705273\pi$
$318$		0			0
$319$	1.02480	−	0.859908i	0.0573777	−	0.0481456i
$320$	2.97705	+	1.08356i	0.166422	+	0.0605728i
$321$		0			0
$322$	−2.14604	+	12.1708i	−0.119594	+	0.678251i
$323$	5.85859			0.325981
$324$		0			0
$325$	15.6159			0.866217
$326$	−0.530129	+	3.00651i	−0.0293611	+	0.166515i
$327$		0			0
$328$	6.65351	+	2.42168i	0.367379	+	0.133715i
$329$	10.8758	−	9.12586i	0.599601	−	0.503125i
$330$		0			0
$331$	24.2569	−	8.82879i	1.33328	−	0.485274i	0.425590	−	0.904916i	$-0.360067\pi$
$331$	24.2569	−	8.82879i	1.33328	−	0.485274i	0.907690	+	0.419642i	$0.137844\pi$
$332$	−1.54921	+	2.68331i	−0.0850240	+	0.147266i
$333$		0			0
$334$	2.05060	+	3.55174i	0.112204	+	0.194343i
$335$	20.8928	+	17.5311i	1.14149	+	0.957826i
$336$		0			0
$337$	−0.587727	−	3.33317i	−0.0320156	−	0.181569i	0.964607	−	0.263693i	$-0.0849407\pi$
$337$	−0.587727	−	3.33317i	−0.0320156	−	0.181569i	−0.996622	+	0.0821241i	$0.973830\pi$
$338$	0.588371	+	3.33682i	0.0320032	+	0.181499i
$339$		0			0
$340$	4.18826	+	3.51437i	0.227141	+	0.190594i
$341$	5.29904	+	9.17821i	0.286959	+	0.497028i
$342$		0			0
$343$	0.765664	−	1.32617i	0.0413420	−	0.0716064i
$344$	1.55793	−	0.567040i	0.0839980	−	0.0305728i
$345$		0			0
$346$	−13.0435	+	10.9448i	−0.701224	+	0.588397i
$347$	−15.2230	−	5.54073i	−0.817216	−	0.297442i	−0.100615	−	0.994925i	$-0.532081\pi$
$347$	−15.2230	−	5.54073i	−0.817216	−	0.297442i	−0.716601	+	0.697483i	$0.754303\pi$
$348$		0			0
$349$	0.780120	−	4.42428i	0.0417589	−	0.236826i	−0.956783	−	0.290801i	$-0.906078\pi$
$349$	0.780120	−	4.42428i	0.0417589	−	0.236826i	0.998542	+	0.0539752i	$0.0171892\pi$
$350$	−18.5648			−0.992330
$351$		0			0
$352$	−2.28507			−0.121795
$353$	4.03327	−	22.8738i	0.214669	−	1.21745i	−0.666810	−	0.745228i	$-0.732341\pi$
$353$	4.03327	−	22.8738i	0.214669	−	1.21745i	0.881479	−	0.472222i	$-0.156548\pi$
$354$		0			0
$355$	−5.91679	−	2.15353i	−0.314030	−	0.114298i
$356$	13.2878	−	11.1498i	0.704253	−	0.590938i
$357$		0			0
$358$	13.6782	−	4.97846i	0.722916	−	0.263120i
$359$	−5.77697	+	10.0060i	−0.304897	+	0.528097i	−0.977238	−	0.212144i	$-0.931955\pi$
$359$	−5.77697	+	10.0060i	−0.304897	+	0.528097i	0.672341	+	0.740241i	$0.265289\pi$
$360$		0			0
$361$	3.73768	+	6.47385i	0.196720	+	0.340729i
$362$	9.97681	+	8.37154i	0.524370	+	0.439998i
$363$		0			0
$364$	1.98423	+	11.2531i	0.104002	+	0.589825i
$365$	−5.85755	−	33.2198i	−0.306598	−	1.73880i
$366$		0			0
$367$	11.9271	+	10.0080i	0.622589	+	0.522414i	0.898616	−	0.438735i	$-0.144573\pi$
$367$	11.9271	+	10.0080i	0.622589	+	0.522414i	−0.276027	+	0.961150i	$0.589018\pi$
$368$	−1.67654	−	2.90386i	−0.0873959	−	0.151374i
$369$		0			0
$370$	11.5750	−	20.0485i	0.601757	−	1.04227i
$371$	−8.94493	+	3.25569i	−0.464398	+	0.169027i
$372$		0			0
$373$	−7.47450	+	6.27185i	−0.387015	+	0.324744i	−0.815449	−	0.578829i	$-0.803510\pi$
$373$	−7.47450	+	6.27185i	−0.387015	+	0.324744i	0.428434	+	0.903573i	$0.359065\pi$
$374$	−3.70565	−	1.34875i	−0.191614	−	0.0697420i
$375$		0			0
$376$	−0.668890	+	3.79346i	−0.0344953	+	0.195633i
$377$	1.81504			0.0934792
$378$		0			0
$379$	−18.7904			−0.965197			−0.482599	−	0.875842i	$-0.660307\pi$
$379$	−18.7904			−0.965197			−0.482599	+	0.875842i	$0.660307\pi$
$380$	1.86760	−	10.5917i	0.0958061	−	0.543343i
$381$		0			0
$382$	−3.38559	−	1.23226i	−0.173222	−	0.0630477i
$383$	−23.5697	+	19.7773i	−1.20435	+	1.01057i	−0.204859	+	0.978791i	$0.565674\pi$
$383$	−23.5697	+	19.7773i	−1.20435	+	1.01057i	−0.999495	+	0.0317817i	$0.989882\pi$
$384$		0			0
$385$	25.0731	−	9.12586i	1.27784	−	0.465097i
$386$	0.737435	−	1.27727i	0.0375344	−	0.0650116i
$387$		0			0
$388$	−4.59558	−	7.95978i	−0.233305	−	0.404097i
$389$	−22.6754	−	19.0269i	−1.14969	−	0.964704i	−0.149978	−	0.988689i	$-0.547920\pi$
$389$	−22.6754	−	19.0269i	−1.14969	−	0.964704i	−0.999712	+	0.0239850i	$0.992365\pi$
$390$		0			0
$391$	−1.00483	−	5.69870i	−0.0508167	−	0.288196i
$392$	−1.14339	−	6.48449i	−0.0577499	−	0.327516i
$393$		0			0
$394$	1.94470	+	1.63179i	0.0979724	+	0.0822086i
$395$	22.3244	+	38.6670i	1.12326	+	1.94555i
$396$		0			0
$397$	−8.07134	+	13.9800i	−0.405089	+	0.701635i	−0.994332	−	0.106321i	$-0.966093\pi$
$397$	−8.07134	+	13.9800i	−0.405089	+	0.701635i	0.589243	+	0.807956i	$0.299426\pi$
$398$	−1.74011	+	0.633347i	−0.0872237	+	0.0317468i
$399$		0			0
$400$	3.85853	−	3.23769i	0.192927	−	0.161885i
$401$	23.8328	+	8.67444i	1.19016	+	0.433181i	0.859778	−	0.510668i	$-0.170602\pi$
$401$	23.8328	+	8.67444i	1.19016	+	0.433181i	0.330377	+	0.943849i	$0.392824\pi$
$402$		0			0
$403$	−2.49689	+	14.1605i	−0.124379	+	0.705387i
$404$	−11.9602			−0.595041
$405$		0			0
$406$	−2.15778			−0.107089
$407$	−2.89948	+	16.4438i	−0.143722	+	0.815087i
$408$		0			0
$409$	21.3980	+	7.78825i	1.05806	+	0.385104i	0.811701	−	0.584073i	$-0.198542\pi$
$409$	21.3980	+	7.78825i	1.05806	+	0.385104i	0.246364	+	0.969177i	$0.420764\pi$
$410$	17.1838	−	14.4189i	0.848649	−	0.712101i
$411$		0			0
$412$	11.9778	−	4.35955i	0.590102	−	0.214780i
$413$	−17.8079	+	30.8442i	−0.876269	+	1.51774i
$414$		0			0
$415$	4.90808	+	8.50104i	0.240928	+	0.417300i
$416$	−2.37495	−	1.99282i	−0.116441	−	0.0977060i
$417$		0			0
$418$	1.34705	+	7.63949i	0.0658863	+	0.373660i
$419$	0.854828	+	4.84797i	0.0417611	+	0.236839i	0.998543	−	0.0539688i	$-0.0171872\pi$
$419$	0.854828	+	4.84797i	0.0417611	+	0.236839i	−0.956782	+	0.290808i	$0.906076\pi$
$420$		0			0
$421$	15.1046	+	12.6742i	0.736151	+	0.617704i	0.931801	−	0.362970i	$-0.118237\pi$
$421$	15.1046	+	12.6742i	0.736151	+	0.617704i	−0.195650	+	0.980674i	$0.562682\pi$
$422$	−9.49415	−	16.4443i	−0.462168	−	0.800498i
$423$		0			0
$424$	1.29134	−	2.23666i	0.0627128	−	0.108622i
$425$	8.16833	−	2.97303i	0.396222	−	0.144213i
$426$		0			0
$427$	36.9624	−	31.0151i	1.78874	−	1.50093i
$428$	5.73113	+	2.08596i	0.277025	+	0.100829i
$429$		0			0
$430$	0.912081	−	5.17267i	0.0439845	−	0.249448i
$431$	6.16323			0.296873			0.148436	−	0.988922i	$-0.452576\pi$
$431$	6.16323			0.296873			0.148436	+	0.988922i	$0.452576\pi$
$432$		0			0
$433$	−14.7838			−0.710466			−0.355233	−	0.934778i	$-0.615599\pi$
$433$	−14.7838			−0.710466			−0.355233	+	0.934778i	$0.615599\pi$
$434$	2.96839	−	16.8346i	0.142487	−	0.808085i
$435$		0			0
$436$	−10.5612	−	3.84396i	−0.505790	−	0.184092i
$437$	−8.71993	+	7.31689i	−0.417131	+	0.350014i
$438$		0			0
$439$	−27.9719	+	10.1809i	−1.33502	+	0.485909i	−0.908242	−	0.418445i	$-0.862575\pi$
$439$	−27.9719	+	10.1809i	−1.33502	+	0.485909i	−0.426782	+	0.904354i	$0.640353\pi$
$440$	−3.61968	+	6.26947i	−0.172561	+	0.298885i
$441$		0			0
$442$	−2.67516	−	4.63351i	−0.127244	−	0.220394i
$443$	−23.3447	−	19.5885i	−1.10914	−	0.930680i	−0.111136	−	0.993805i	$-0.535449\pi$
$443$	−23.3447	−	19.5885i	−1.10914	−	0.930680i	−0.998006	+	0.0631253i	$0.979893\pi$
$444$		0			0
$445$	−9.54269	−	54.1193i	−0.452367	−	2.56550i
$446$	1.25971	+	7.14415i	0.0596488	+	0.338285i
$447$		0			0
$448$	2.82342	+	2.36913i	0.133394	+	0.111931i
$449$	5.92055	+	10.2547i	0.279408	+	0.483949i	0.971238	−	0.238112i	$-0.0765284\pi$
$449$	5.92055	+	10.2547i	0.279408	+	0.483949i	−0.691830	+	0.722061i	$0.743195\pi$
$450$		0			0
$451$	−8.08973	+	14.0118i	−0.380930	+	0.659791i
$452$	−6.61257	+	2.40678i	−0.311029	+	0.113205i
$453$		0			0
$454$	−21.8531	+	18.3369i	−1.02562	+	0.860594i
$455$	34.0180	+	12.3816i	1.59479	+	0.580456i
$456$		0			0
$457$	−0.0323668	+	0.183561i	−0.00151406	+	0.00858664i	−0.985555	−	0.169353i	$-0.945832\pi$
$457$	−0.0323668	+	0.183561i	−0.00151406	+	0.00858664i	0.984041	+	0.177940i	$0.0569432\pi$
$458$	−1.85538			−0.0866963
$459$		0			0
$460$	−10.6230			−0.495299
$461$	−1.80687	+	10.2473i	−0.0841543	+	0.477263i	0.913382	+	0.407105i	$0.133462\pi$
$461$	−1.80687	+	10.2473i	−0.0841543	+	0.477263i	−0.997536	+	0.0701583i	$0.977650\pi$
$462$		0			0
$463$	−24.2332	−	8.82016i	−1.12621	−	0.409907i	−0.289296	−	0.957240i	$-0.593421\pi$
$463$	−24.2332	−	8.82016i	−1.12621	−	0.409907i	−0.836915	+	0.547332i	$0.815643\pi$
$464$	0.448476	−	0.376316i	0.0208200	−	0.0174700i
$465$		0			0
$466$	−8.01999	+	2.91904i	−0.371519	+	0.135222i
$467$	10.8506	−	18.7937i	0.502104	−	0.869670i	−0.497893	−	0.867239i	$-0.665893\pi$
$467$	10.8506	−	18.7937i	0.502104	−	0.869670i	0.999997	−	0.00243153i	$-0.000773982\pi$
$468$		0			0
$469$	15.8647	+	27.4785i	0.732566	+	1.26884i
$470$	9.34844	+	7.84427i	0.431211	+	0.361829i
$471$		0			0
$472$	−1.67799	−	9.51638i	−0.0772360	−	0.438027i
$473$	0.657857	+	3.73089i	0.0302483	+	0.171547i
$474$		0			0
$475$	−13.0989	−	10.9913i	−0.601020	−	0.504316i
$476$	3.18032	+	5.50848i	0.145770	+	0.252481i
$477$		0			0
$478$	3.64398	−	6.31156i	0.166672	−	0.288684i
$479$	−36.7619	+	13.3802i	−1.67970	+	0.611359i	−0.993268	−	0.115839i	$-0.963044\pi$
$479$	−36.7619	+	13.3802i	−1.67970	+	0.611359i	−0.686427	+	0.727199i	$0.740822\pi$
$480$		0			0
$481$	−17.3542	+	14.5619i	−0.791284	+	0.663966i
$482$	−1.25441	−	0.456569i	−0.0571370	−	0.0207962i
$483$		0			0
$484$	−1.00342	+	5.69068i	−0.0456100	+	0.258667i
$485$	−29.1187			−1.32221
$486$		0			0
$487$	−10.4833			−0.475043			−0.237522	−	0.971382i	$-0.576335\pi$
$487$	−10.4833			−0.475043			−0.237522	+	0.971382i	$0.576335\pi$
$488$	−2.27329	+	12.8925i	−0.102907	+	0.583614i
$489$		0			0
$490$	−19.6025	−	7.13472i	−0.885550	−	0.322314i
$491$	−5.25278	+	4.40761i	−0.237055	+	0.198913i	−0.753574	−	0.657363i	$-0.771672\pi$
$491$	−5.25278	+	4.40761i	−0.237055	+	0.198913i	0.516519	+	0.856276i	$0.327227\pi$
$492$		0			0
$493$	0.949403	−	0.345554i	0.0427589	−	0.0155630i
$494$	−5.26240	+	9.11475i	−0.236767	+	0.410092i
$495$		0			0
$496$	2.31899	+	4.01660i	0.104126	+	0.180351i
$497$	−5.61145	−	4.70857i	−0.251708	−	0.211208i
$498$		0			0
$499$	3.26002	+	18.4885i	0.145939	+	0.827659i	0.966609	+	0.256257i	$0.0824892\pi$
$499$	3.26002	+	18.4885i	0.145939	+	0.827659i	−0.820670	+	0.571402i	$0.806400\pi$
$500$	−0.0203300	−	0.115297i	−0.000909186	−	0.00515625i
$501$		0			0
$502$	−2.20511	−	1.85030i	−0.0984187	−	0.0825831i
$503$	−6.21350	−	10.7621i	−0.277046	−	0.479858i	0.693603	−	0.720357i	$-0.256022\pi$
$503$	−6.21350	−	10.7621i	−0.277046	−	0.479858i	−0.970649	+	0.240499i	$0.922689\pi$
$504$		0			0
$505$	−18.9456	+	32.8148i	−0.843069	+	1.46024i
$506$	7.19996	−	2.62057i	0.320077	−	0.116499i
$507$		0			0
$508$	4.58477	−	3.84708i	0.203416	−	0.170687i
$509$	30.9889	+	11.2790i	1.37356	+	0.499935i	0.920219	−	0.391403i	$-0.128010\pi$
$509$	30.9889	+	11.2790i	1.37356	+	0.499935i	0.453340	+	0.891338i	$0.350232\pi$
$510$		0			0
$511$	6.81455	−	38.6472i	0.301458	−	1.70965i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−25.7779			−1.13702
$515$	7.01231	−	39.7688i	0.308999	−	1.75242i
$516$		0			0
$517$	−8.27121	−	3.01047i	−0.363767	−	0.132400i
$518$	20.6313	−	17.3117i	0.906488	−	0.760634i
$519$		0			0
$520$	−9.22969	+	3.35933i	−0.404749	+	0.147316i
$521$	7.16598	−	12.4118i	0.313947	−	0.543773i	−0.665266	−	0.746607i	$-0.731682\pi$
$521$	7.16598	−	12.4118i	0.313947	−	0.543773i	0.979213	+	0.202834i	$0.0650151\pi$
$522$		0			0
$523$	2.85442	+	4.94400i	0.124815	+	0.216186i	0.921661	−	0.387997i	$-0.126833\pi$
$523$	2.85442	+	4.94400i	0.124815	+	0.216186i	−0.796846	+	0.604183i	$0.793500\pi$
$524$	−12.5746	−	10.5514i	−0.549326	−	0.460939i
$525$		0			0
$526$	−2.61682	−	14.8408i	−0.114099	−	0.647087i
$527$	1.38988	+	7.88241i	0.0605442	+	0.343363i
$528$		0			0
$529$	−9.00623	−	7.55712i	−0.391575	−	0.328571i
$530$	−4.09110	−	7.08599i	−0.177706	−	0.307796i
$531$		0			0
$532$	6.25613	−	10.8359i	0.271238	−	0.469798i
$533$	−20.6277	+	7.50787i	−0.893485	+	0.325202i
$534$		0			0
$535$	14.8016	−	12.4200i	0.639930	−	0.536965i
$536$	−8.08959	−	2.94437i	−0.349417	−	0.127177i
$537$		0			0
$538$	2.78905	−	15.8175i	0.120244	−	0.681939i
$539$	15.0461			0.648081
$540$		0			0
$541$	18.0099			0.774305			0.387153	−	0.922016i	$-0.373459\pi$
$541$	18.0099			0.774305			0.387153	+	0.922016i	$0.373459\pi$
$542$	−1.63480	+	9.27143i	−0.0702208	+	0.398242i
$543$		0			0
$544$	−1.62168	−	0.590243i	−0.0695289	−	0.0253065i
$545$	−27.2761	+	22.8874i	−1.16838	+	0.980387i
$546$		0			0
$547$	19.3837	−	7.05509i	0.828788	−	0.301654i	0.107426	−	0.994213i	$-0.465739\pi$
$547$	19.3837	−	7.05509i	0.828788	−	0.301654i	0.721361	+	0.692559i	$0.243517\pi$
$548$	−0.105579	+	0.182869i	−0.00451012	+	0.00781176i
$549$		0			0
$550$	5.75489	+	9.96776i	0.245389	+	0.425027i
$551$	−1.52249	−	1.27752i	−0.0648601	−	0.0544241i
$552$		0			0
$553$	9.01990	+	51.1544i	0.383565	+	2.17531i
$554$	−0.968047	−	5.49007i	−0.0411284	−	0.233251i
$555$		0			0
$556$	2.81254	+	2.36000i	0.119278	+	0.100086i
$557$	−1.90209	−	3.29452i	−0.0805942	−	0.139593i	0.822911	−	0.568170i	$-0.192348\pi$
$557$	−1.90209	−	3.29452i	−0.0805942	−	0.139593i	−0.903505	+	0.428577i	$0.859015\pi$
$558$		0			0
$559$	−2.57000	+	4.45136i	−0.108699	+	0.188273i
$560$	10.9726	−	3.99369i	0.463676	−	0.168764i
$561$		0			0
$562$	21.4529	−	18.0011i	0.904937	−	0.759332i
$563$	−10.4037	−	3.78663i	−0.438463	−	0.159587i	0.113351	−	0.993555i	$-0.463842\pi$
$563$	−10.4037	−	3.78663i	−0.438463	−	0.159587i	−0.551813	+	0.833968i	$0.686064\pi$
$564$		0			0
$565$	−3.87129	+	21.9552i	−0.162866	+	0.923662i
$566$	−6.15522			−0.258723
$567$		0			0
$568$	1.98746			0.0833921
$569$	−8.11202	+	46.0056i	−0.340074	+	1.92865i	0.0297623	+	0.999557i	$0.490525\pi$
$569$	−8.11202	+	46.0056i	−0.340074	+	1.92865i	−0.369836	+	0.929097i	$0.620586\pi$
$570$		0			0
$571$	29.7753	+	10.8373i	1.24606	+	0.453528i	0.879068	−	0.476697i	$-0.158166\pi$
$571$	29.7753	+	10.8373i	1.24606	+	0.453528i	0.366990	+	0.930225i	$0.380388\pi$
$572$	5.42692	−	4.55372i	0.226911	−	0.190401i
$573$		0			0
$574$	24.5230	−	8.92563i	1.02357	−	0.372549i
$575$	−8.44468	+	14.6266i	−0.352167	+	0.609972i
$576$		0			0
$577$	−22.1642	−	38.3895i	−0.922707	−	1.59818i	−0.795208	−	0.606336i	$-0.792639\pi$
$577$	−22.1642	−	38.3895i	−0.922707	−	1.59818i	−0.127499	−	0.991839i	$-0.540695\pi$
$578$	10.7413	+	9.01302i	0.446779	+	0.374892i
$579$		0			0
$580$	−0.322075	−	1.82658i	−0.0133734	−	0.0758445i
$581$	1.98305	+	11.2464i	0.0822707	+	0.466580i
$582$		0			0
$583$	4.52087	+	3.79346i	0.187235	+	0.157109i
$584$	5.32371	+	9.22094i	0.220297	+	0.381565i
$585$		0			0
$586$	−1.16755	+	2.02226i	−0.0482310	+	0.0835386i
$587$	38.5694	−	14.0381i	1.59193	−	0.579414i	0.614174	−	0.789170i	$-0.289489\pi$
$587$	38.5694	−	14.0381i	1.59193	−	0.579414i	0.977754	+	0.209756i	$0.0672669\pi$
$588$		0			0
$589$	12.0614	−	10.1207i	0.496980	−	0.417015i
$590$	−28.7678	−	10.4706i	−1.18435	−	0.431069i
$591$		0			0
$592$	−1.26888	+	7.19618i	−0.0521507	+	0.295761i
$593$	9.69265			0.398029			0.199015	−	0.979996i	$-0.436226\pi$
$593$	9.69265			0.398029			0.199015	+	0.979996i	$0.436226\pi$
$594$		0			0
$595$	20.1513			0.826121
$596$	−2.68710	+	15.2393i	−0.110068	+	0.624226i
$597$		0			0
$598$	9.76857	+	3.55547i	0.399467	+	0.145394i
$599$	22.8572	−	19.1794i	0.933918	−	0.783651i	−0.0425983	−	0.999092i	$-0.513564\pi$
$599$	22.8572	−	19.1794i	0.933918	−	0.783651i	0.976517	+	0.215442i	$0.0691191\pi$
$600$		0			0
$601$	−11.7938	+	4.29259i	−0.481079	+	0.175098i	−0.571165	−	0.820836i	$-0.693508\pi$
$601$	−11.7938	+	4.29259i	−0.481079	+	0.175098i	0.0900856	+	0.995934i	$0.471286\pi$
$602$	3.05530	−	5.29194i	0.124525	−	0.215683i
$603$		0			0
$604$	−10.0729	−	17.4467i	−0.409859	−	0.709896i
$605$	14.0239	+	11.7674i	0.570151	+	0.478413i
$606$		0			0
$607$	−0.482765	−	2.73790i	−0.0195948	−	0.111128i	0.973442	−	0.228935i	$-0.0735245\pi$
$607$	−0.482765	−	2.73790i	−0.0195948	−	0.111128i	−0.993036	+	0.117808i	$0.962413\pi$
$608$	0.589500	+	3.34322i	0.0239074	+	0.135586i
$609$		0			0
$610$	31.7716	+	26.6595i	1.28639	+	1.07941i
$611$	−5.97110	−	10.3422i	−0.241565	−	0.418403i
$612$		0			0
$613$	4.29646	−	7.44168i	0.173532	−	0.300567i	−0.766120	−	0.642697i	$-0.777815\pi$
$613$	4.29646	−	7.44168i	0.173532	−	0.300567i	0.939652	+	0.342131i	$0.111149\pi$
$614$	6.41368	−	2.33439i	0.258835	−	0.0942082i
$615$		0			0
$616$	−6.45172	+	5.41363i	−0.259947	+	0.218121i
$617$	−18.8681	−	6.86743i	−0.759602	−	0.276472i	−0.0669615	−	0.997756i	$-0.521330\pi$
$617$	−18.8681	−	6.86743i	−0.759602	−	0.276472i	−0.692640	+	0.721283i	$0.743553\pi$
$618$		0			0
$619$	1.45723	−	8.26436i	0.0585710	−	0.332173i	−0.941416	−	0.337247i	$-0.890504\pi$
$619$	1.45723	−	8.26436i	0.0585710	−	0.332173i	0.999987	+	0.00507458i	$0.00161530\pi$
$620$	14.6936			0.590111
$621$		0			0
$622$	8.59522			0.344637
$623$	11.1018	−	62.9612i	0.444783	−	2.52249i
$624$		0			0
$625$	23.3174	+	8.48684i	0.932696	+	0.339474i
$626$	16.5993	−	13.9285i	0.663443	−	0.556695i
$627$		0			0
$628$	−16.9121	+	6.15549i	−0.674865	+	0.245631i
$629$	−6.30522	+	10.9210i	−0.251405	+	0.435447i
$630$		0			0
$631$	−8.78157	−	15.2101i	−0.349589	−	0.605506i	0.636588	−	0.771204i	$-0.280345\pi$
$631$	−8.78157	−	15.2101i	−0.349589	−	0.605506i	−0.986176	+	0.165699i	$0.947012\pi$
$632$	−10.7960	−	9.05893i	−0.429442	−	0.360345i
$633$		0			0
$634$	6.13325	+	34.7834i	0.243582	+	1.38142i
$635$	−3.29257	−	18.6731i	−0.130662	−	0.741019i
$636$		0			0
$637$	15.6379	+	13.1218i	0.619596	+	0.519903i
$638$	0.668890	+	1.15855i	0.0264816	+	0.0458675i
$639$		0			0
$640$	−1.58406	+	2.74367i	−0.0626154	+	0.108453i
$641$	−12.6056	+	4.58808i	−0.497893	+	0.181218i	−0.578746	−	0.815508i	$-0.696458\pi$
$641$	−12.6056	+	4.58808i	−0.497893	+	0.181218i	0.0808532	+	0.996726i	$0.474235\pi$
$642$		0			0
$643$	−7.99375	+	6.70755i	−0.315243	+	0.264520i	−0.786655	−	0.617393i	$-0.788189\pi$
$643$	−7.99375	+	6.70755i	−0.315243	+	0.264520i	0.471412	+	0.881913i	$0.343744\pi$
$644$	−11.6132	−	4.22687i	−0.457625	−	0.166562i
$645$		0			0
$646$	−1.01733	+	5.76958i	−0.0400264	+	0.227001i
$647$	37.9585			1.49230			0.746152	−	0.665775i	$-0.231899\pi$
$647$	37.9585			1.49230			0.746152	+	0.665775i	$0.231899\pi$
$648$		0			0
$649$	22.0810			0.866756
$650$	−2.71168	+	15.3787i	−0.106361	+	0.603202i
$651$		0			0
$652$	−2.86878	−	1.04415i	−0.112350	−	0.0408921i
$653$	20.9178	−	17.5521i	0.818578	−	0.686868i	−0.134061	−	0.990973i	$-0.542802\pi$
$653$	20.9178	−	17.5521i	0.818578	−	0.686868i	0.952639	+	0.304105i	$0.0983573\pi$
$654$		0			0
$655$	−48.8684	+	17.7867i	−1.90945	+	0.694982i
$656$	−3.54026	+	6.13191i	−0.138224	+	0.239411i
$657$		0			0
$658$	7.09866	+	12.2952i	0.276735	+	0.479318i
$659$	26.3174	+	22.0829i	1.02518	+	0.860228i	0.990270	−	0.139162i	$-0.0444410\pi$
$659$	26.3174	+	22.0829i	1.02518	+	0.860228i	0.0349104	+	0.999390i	$0.488885\pi$
$660$		0			0
$661$	−4.26787	−	24.2043i	−0.166001	−	0.941439i	−0.948026	−	0.318192i	$-0.896924\pi$
$661$	−4.26787	−	24.2043i	−0.166001	−	0.941439i	0.782025	−	0.623247i	$-0.214187\pi$
$662$	4.48249	+	25.4215i	0.174217	+	0.988034i
$663$		0			0
$664$	−2.37353	−	1.99163i	−0.0921108	−	0.0772901i
$665$	−19.8202	−	34.3295i	−0.768593	−	1.33124i
$666$		0			0
$667$	−0.981523	+	1.70005i	−0.0380047	+	0.0658261i
$668$	−3.85386	+	1.40269i	−0.149110	+	0.0542718i
$669$		0			0
$670$	−20.8928	+	17.5311i	−0.807157	+	0.677285i
$671$	−28.1105	−	10.2314i	−1.08519	−	0.394979i
$672$		0			0
$673$	7.44524	−	42.2241i	0.286993	−	1.62762i	−0.411085	−	0.911597i	$-0.634850\pi$
$673$	7.44524	−	42.2241i	0.286993	−	1.62762i	0.698078	−	0.716021i	$-0.254039\pi$
$674$	3.38459			0.130369
$675$		0			0
$676$	−3.38830			−0.130319
$677$	−1.30018	+	7.37368i	−0.0499699	+	0.283393i	−0.999546	−	0.0301446i	$-0.990403\pi$
$677$	−1.30018	+	7.37368i	−0.0499699	+	0.283393i	0.949576	+	0.313538i	$0.101514\pi$
$678$		0			0
$679$	−31.8331	−	11.5863i	−1.22164	−	0.444641i
$680$	−4.18826	+	3.51437i	−0.160613	+	0.134770i
$681$		0			0
$682$	−9.95894	+	3.62476i	−0.381348	+	0.138799i
$683$	8.37724	−	14.5098i	0.320546	−	0.555202i	−0.660055	−	0.751218i	$-0.729467\pi$
$683$	8.37724	−	14.5098i	0.320546	−	0.555202i	0.980601	+	0.196015i	$0.0628002\pi$
$684$		0			0
$685$	0.334487	+	0.579349i	0.0127801	+	0.0221358i
$686$	1.17307	+	0.984318i	0.0447878	+	0.0375815i
$687$		0			0
$688$	0.287894	+	1.63273i	0.0109759	+	0.0622471i
$689$	1.39040	+	7.88535i	0.0529700	+	0.300408i
$690$		0			0
$691$	−11.4550	−	9.61189i	−0.435769	−	0.365653i	0.398354	−	0.917232i	$-0.369581\pi$
$691$	−11.4550	−	9.61189i	−0.435769	−	0.365653i	−0.834123	+	0.551578i	$0.814026\pi$
$692$	−8.51355	−	14.7459i	−0.323637	−	0.560555i
$693$		0			0
$694$	8.10001	−	14.0296i	0.307472	−	0.532558i
$695$	10.9303	−	3.97830i	0.414609	−	0.150905i
$696$		0			0
$697$	−9.36048	+	7.85437i	−0.354553	+	0.297506i
$698$	4.22160	+	1.53654i	0.159790	+	0.0581587i
$699$		0			0
$700$	3.22374	−	18.2828i	0.121846	−	0.691023i
$701$	42.1025			1.59019			0.795094	−	0.606486i	$-0.207421\pi$
$701$	42.1025			1.59019			0.795094	+	0.606486i	$0.207421\pi$
$702$		0			0
$703$	24.8065			0.935593
$704$	0.396798	−	2.25035i	0.0149549	−	0.0848133i
$705$		0			0
$706$	21.8259	+	7.94399i	0.821430	+	0.298976i
$707$	−33.7687	+	28.3353i	−1.27000	+	1.06566i
$708$		0			0
$709$	−26.7677	+	9.74265i	−1.00528	+	0.365893i	−0.791619	−	0.611015i	$-0.790762\pi$
$709$	−26.7677	+	9.74265i	−1.00528	+	0.365893i	−0.213663	+	0.976907i	$0.568539\pi$
$710$	3.14826	−	5.45294i	0.118152	−	0.204645i
$711$		0			0
$712$	8.67300	+	15.0221i	0.325035	+	0.562976i
$713$	−11.9132	−	9.99634i	−0.446152	−	0.374366i
$714$		0			0
$715$	−3.89736	−	22.1030i	−0.145753	−	0.826606i
$716$	2.52763	+	14.3349i	0.0944620	+	0.535721i
$717$		0			0
$718$	−8.85083	−	7.42673i	−0.330310	−	0.277163i
$719$	1.26744	+	2.19526i	0.0472674	+	0.0818695i	0.888691	−	0.458506i	$-0.151615\pi$
$719$	1.26744	+	2.19526i	0.0472674	+	0.0818695i	−0.841424	+	0.540376i	$0.818282\pi$
$720$		0			0
$721$	23.4900	−	40.6858i	0.874812	−	1.51522i
$722$	−7.02454	+	2.55672i	−0.261426	+	0.0951513i
$723$		0			0
$724$	−9.97681	+	8.37154i	−0.370785	+	0.311126i
$725$	−2.77102	−	1.00857i	−0.102913	−	0.0374573i
$726$		0			0
$727$	3.45271	−	19.5813i	0.128054	−	0.726231i	−0.851393	−	0.524529i	$-0.824242\pi$
$727$	3.45271	−	19.5813i	0.128054	−	0.726231i	0.979447	−	0.201702i	$-0.0646473\pi$
$728$	−11.4267			−0.423503
$729$		0			0
$730$	33.7323			1.24849
$731$	−0.496834	+	2.81769i	−0.0183761	+	0.104216i
$732$		0			0
$733$	9.40733	+	3.42399i	0.347468	+	0.126468i	0.509858	−	0.860259i	$-0.329698\pi$
$733$	9.40733	+	3.42399i	0.347468	+	0.126468i	−0.162390	+	0.986727i	$0.551920\pi$
$734$	−11.9271	+	10.0080i	−0.440237	+	0.369403i
$735$		0			0
$736$	3.15087	−	1.14682i	0.116143	−	0.0422725i
$737$	9.83580	−	17.0361i	0.362306	−	0.627533i
$738$		0			0
$739$	20.1957	+	34.9800i	0.742911	+	1.28676i	0.951164	+	0.308685i	$0.0998890\pi$
$739$	20.1957	+	34.9800i	0.742911	+	1.28676i	−0.208253	+	0.978075i	$0.566778\pi$
$740$	17.7340	+	14.8806i	0.651913	+	0.547020i
$741$		0			0
$742$	−1.65296	−	9.37439i	−0.0606820	−	0.344145i
$743$	−6.19059	−	35.1086i	−0.227111	−	1.28801i	−0.858609	−	0.512631i	$-0.828671\pi$
$743$	−6.19059	−	35.1086i	−0.227111	−	1.28801i	0.631498	−	0.775377i	$-0.282440\pi$
$744$		0			0
$745$	37.5551	+	31.5124i	1.37591	+	1.15453i
$746$	−4.87863	−	8.45004i	−0.178619	−	0.309378i
$747$		0			0
$748$	1.97173	−	3.41514i	0.0720937	−	0.124870i
$749$	21.1233	−	7.68826i	0.771830	−	0.280923i
$750$		0			0
$751$	−7.25347	+	6.08638i	−0.264683	+	0.222095i	−0.765464	−	0.643479i	$-0.777491\pi$
$751$	−7.25347	+	6.08638i	−0.264683	+	0.222095i	0.500781	+	0.865574i	$0.333046\pi$
$752$	−3.61968	−	1.31746i	−0.131996	−	0.0480426i
$753$		0			0
$754$	−0.315178	+	1.78746i	−0.0114781	+	0.0650956i
$755$	−63.8240			−2.32279
$756$		0			0
$757$	−37.9651			−1.37987			−0.689933	−	0.723873i	$-0.742360\pi$
$757$	−37.9651			−1.37987			−0.689933	+	0.723873i	$0.742360\pi$
$758$	3.26292	−	18.5049i	0.118514	−	0.672129i
$759$		0			0
$760$	10.1065	+	3.67846i	0.366601	+	0.133432i
$761$	−34.3845	+	28.8520i	−1.24644	+	1.04588i	−0.249444	+	0.968389i	$0.580248\pi$
$761$	−34.3845	+	28.8520i	−1.24644	+	1.04588i	−0.996993	+	0.0774952i	$0.975308\pi$
$762$		0			0
$763$	−38.9256	+	14.1678i	−1.40920	+	0.512908i
$764$	1.80144	−	3.12018i	0.0651737	−	0.112884i
$765$		0			0
$766$	−15.3840	−	26.6459i	−0.555847	−	0.962755i
$767$	22.9496	+	19.2570i	0.828661	+	0.695329i
$768$		0			0
$769$	7.94212	+	45.0420i	0.286400	+	1.62426i	0.700241	+	0.713906i	$0.253076\pi$
$769$	7.94212	+	45.0420i	0.286400	+	1.62426i	−0.413841	+	0.910349i	$0.635813\pi$
$770$	4.63332	+	26.2769i	0.166973	+	0.946953i
$771$		0			0
$772$	1.12982	+	0.948028i	0.0406630	+	0.0341203i
$773$	−10.2853	−	17.8147i	−0.369938	−	0.640752i	0.619617	−	0.784904i	$-0.287288\pi$
$773$	−10.2853	−	17.8147i	−0.369938	−	0.640752i	−0.989556	+	0.144152i	$0.953954\pi$
$774$		0			0
$775$	11.6806	−	20.2315i	0.419581	−	0.726735i
$776$	8.63687	−	3.14356i	0.310046	−	0.112847i
$777$		0			0
$778$	22.6754	−	19.0269i	0.812954	−	0.682149i
$779$	22.5873	+	8.22111i	0.809274	+	0.294552i
$780$		0			0
$781$	−0.788621	+	4.47249i	−0.0282191	+	0.160038i
$782$	5.78661			0.206929
$783$		0			0
$784$	6.58452			0.235162
$785$	−9.90106	+	56.1517i	−0.353384	+	2.00414i
$786$		0			0
$787$	−41.8760	−	15.2416i	−1.49272	−	0.543305i	−0.538555	−	0.842590i	$-0.681030\pi$
$787$	−41.8760	−	15.2416i	−1.49272	−	0.543305i	−0.954164	+	0.299285i	$0.903252\pi$
$788$	−1.94470	+	1.63179i	−0.0692769	+	0.0581302i
$789$		0			0
$790$	−41.9562	+	15.2708i	−1.49273	+	0.543311i
$791$	−12.9681	+	22.4614i	−0.461093	+	0.798637i
$792$		0			0
$793$	−20.2934	−	35.1492i	−0.720639	−	1.24818i
$794$	−12.3660	−	10.3763i	−0.438853	−	0.368242i
$795$		0			0
$796$	−0.321559	−	1.82365i	−0.0113973	−	0.0646376i
$797$	−7.61623	−	43.1938i	−0.269781	−	1.53000i	−0.755067	−	0.655647i	$-0.772396\pi$
$797$	−7.61623	−	43.1938i	−0.269781	−	1.53000i	0.485287	−	0.874355i	$-0.338715\pi$
$798$		0			0
$799$	−5.09234	−	4.27298i	−0.180154	−	0.151167i
$800$	2.51848	+	4.36213i	0.0890416	+	0.154225i
$801$		0			0
$802$	−12.6812	+	21.9645i	−0.447788	+	0.775592i
$803$	−22.8628	+	8.32138i	−0.806811	+	0.293655i
$804$		0			0
$805$	−29.9932	+	25.1672i	−1.05712	+	0.887029i
$806$	−13.5118	−	4.91791i	−0.475934	−	0.173226i
$807$		0			0
$808$	2.07686	−	11.7785i	0.0730638	−	0.414365i
$809$	15.5821			0.547836			0.273918	−	0.961753i	$-0.411680\pi$
$809$	15.5821			0.547836			0.273918	+	0.961753i	$0.411680\pi$
$810$		0			0
$811$	−30.4691			−1.06992			−0.534958	−	0.844879i	$-0.679673\pi$
$811$	−30.4691			−1.06992			−0.534958	+	0.844879i	$0.679673\pi$
$812$	0.374695	−	2.12500i	0.0131492	−	0.0745729i
$813$		0			0
$814$	−15.6905	−	5.71086i	−0.549950	−	0.200166i
$815$	−7.40912	+	6.21699i	−0.259530	+	0.217772i
$816$		0			0
$817$	5.28886	−	1.92499i	0.185034	−	0.0673468i
$818$	−11.3857	+	19.7205i	−0.398090	+	0.689512i
$819$		0			0
$820$	11.2159	+	19.4266i	0.391678	+	0.678406i
$821$	1.45626	+	1.22195i	0.0508240	+	0.0426464i	0.667846	−	0.744300i	$-0.267217\pi$
$821$	1.45626	+	1.22195i	0.0508240	+	0.0426464i	−0.617022	+	0.786946i	$0.711661\pi$
$822$		0			0
$823$	−3.82738	−	21.7062i	−0.133414	−	0.756629i	−0.975951	−	0.217991i	$-0.930050\pi$
$823$	−3.82738	−	21.7062i	−0.133414	−	0.756629i	0.842537	−	0.538639i	$-0.181061\pi$
$824$	2.21340	+	12.5528i	0.0771075	+	0.437298i
$825$		0			0
$826$	−27.2833	−	22.8934i	−0.949307	−	0.796563i
$827$	24.2488	+	42.0001i	0.843213	+	1.46049i	0.887164	+	0.461454i	$0.152672\pi$
$827$	24.2488	+	42.0001i	0.843213	+	1.46049i	−0.0439508	+	0.999034i	$0.513994\pi$
$828$		0			0
$829$	10.1593	−	17.5964i	0.352846	−	0.611148i	−0.633900	−	0.773415i	$-0.718547\pi$
$829$	10.1593	−	17.5964i	0.352846	−	0.611148i	0.986747	+	0.162267i	$0.0518805\pi$
$830$	−9.22417	+	3.35732i	−0.320176	+	0.116534i
$831$		0			0
$832$	2.37495	−	1.99282i	0.0823365	−	0.0690885i
$833$	10.6780	+	3.88647i	0.369970	+	0.134658i
$834$		0			0
$835$	−2.25622	+	12.7957i	−0.0780797	+	0.442812i
$836$	−7.75734			−0.268293
$837$		0			0
$838$	−4.92276			−0.170054
$839$	0.879762	−	4.98938i	0.0303728	−	0.172253i	−0.965848	−	0.259109i	$-0.916571\pi$
$839$	0.879762	−	4.98938i	0.0303728	−	0.172253i	0.996221	+	0.0868566i	$0.0276822\pi$
$840$		0			0
$841$	26.9290	+	9.80136i	0.928587	+	0.337978i
$842$	−15.1046	+	12.6742i	−0.520538	+	0.436783i
$843$		0			0
$844$	17.8432	−	6.49438i	0.614187	−	0.223546i
$845$	−5.36726	+	9.29636i	−0.184639	+	0.319804i
$846$		0			0
$847$	10.6489	+	18.4444i	0.365901	+	0.633758i
$848$	1.97844	+	1.66011i	0.0679399	+	0.0570084i
$849$		0			0
$850$	1.50945	+	8.56049i	0.0517736	+	0.293622i
$851$	−4.25467	−	24.1294i	−0.145848	−	0.827147i
$852$		0			0
$853$	20.2756	+	17.0132i	0.694222	+	0.582521i	0.920123	−	0.391629i	$-0.128088\pi$
$853$	20.2756	+	17.0132i	0.694222	+	0.582521i	−0.225902	+	0.974150i	$0.572533\pi$
$854$	24.1255	+	41.7866i	0.825558	+	1.42991i
$855$		0			0
$856$	−3.04947	+	5.28184i	−0.104229	+	0.180529i
$857$	−17.2073	+	6.26295i	−0.587790	+	0.213938i	−0.618757	−	0.785582i	$-0.712364\pi$
$857$	−17.2073	+	6.26295i	−0.587790	+	0.213938i	0.0309669	+	0.999520i	$0.490141\pi$
$858$		0			0
$859$	−7.23097	+	6.06751i	−0.246718	+	0.207021i	−0.757757	−	0.652536i	$-0.773705\pi$
$859$	−7.23097	+	6.06751i	−0.246718	+	0.207021i	0.511040	+	0.859557i	$0.329260\pi$
$860$	4.93570	+	1.79645i	0.168306	+	0.0612584i
$861$		0			0
$862$	−1.07023	+	6.06960i	−0.0364523	+	0.206731i
$863$	14.2154			0.483898			0.241949	−	0.970289i	$-0.422213\pi$
$863$	14.2154			0.483898			0.241949	+	0.970289i	$0.422213\pi$
$864$		0			0
$865$	−53.9438			−1.83414
$866$	2.56719	−	14.5592i	0.0872366	−	0.494743i
$867$		0			0
$868$	16.0634	+	5.84659i	0.545226	+	0.198446i
$869$	24.6696	−	20.7003i	0.836859	−	0.702208i
$870$		0			0
$871$	25.0800	−	9.12836i	0.849802	−	0.309303i
$872$	5.61950	−	9.73326i	0.190300	−	0.329610i
$873$		0			0
$874$	−5.69153	−	9.85801i	−0.192519	−	0.333452i
$875$	−0.330555	−	0.277369i	−0.0111748	−	0.00937677i
$876$		0			0
$877$	6.79059	+	38.5113i	0.229302	+	1.30044i	0.854288	+	0.519800i	$0.173993\pi$
$877$	6.79059	+	38.5113i	0.229302	+	1.30044i	−0.624986	+	0.780636i	$0.714895\pi$
$878$	−5.16899	−	29.3148i	−0.174445	−	0.989327i
$879$		0			0
$880$	−5.54567	−	4.65337i	−0.186944	−	0.156865i
$881$	−11.4469	−	19.8266i	−0.385657	−	0.667977i	0.606203	−	0.795310i	$-0.292692\pi$
$881$	−11.4469	−	19.8266i	−0.385657	−	0.667977i	−0.991860	+	0.127333i	$0.959358\pi$
$882$		0			0
$883$	8.57546	−	14.8531i	0.288587	−	0.499847i	−0.684886	−	0.728651i	$-0.740148\pi$
$883$	8.57546	−	14.8531i	0.288587	−	0.499847i	0.973473	+	0.228803i	$0.0734812\pi$
$884$	5.02765	−	1.82992i	0.169098	−	0.0615467i
$885$		0			0
$886$	23.3447	−	19.5885i	0.784281	−	0.658090i
$887$	17.1560	+	6.24427i	0.576042	+	0.209662i	0.613579	−	0.789633i	$-0.289729\pi$
$887$	17.1560	+	6.24427i	0.576042	+	0.209662i	−0.0375373	+	0.999295i	$0.511951\pi$
$888$		0			0
$889$	3.83051	−	21.7239i	0.128471	−	0.728596i
$890$	54.9541			1.84207
$891$		0			0
$892$	−7.25436			−0.242894
$893$	−2.27074	+	12.8780i	−0.0759876	+	0.430947i
$894$		0			0
$895$	43.3342	+	15.7723i	1.44850	+	0.527211i
$896$	−2.82342	+	2.36913i	−0.0943240	+	0.0791472i
$897$		0			0
$898$	−11.1270	+	4.04990i	−0.371313	+	0.135147i
$899$	1.35764	−	2.35150i	0.0452797	−	0.0784268i
$900$		0			0
$901$	2.22853	+	3.85993i	0.0742431	+	0.128593i
$902$	−12.3942	−	10.4000i	−0.412681	−	0.346281i
$903$		0			0
$904$	−1.22195	−	6.93005i	−0.0406416	−	0.230490i
$905$	7.16488	+	40.6341i	0.238169	+	1.35072i
$906$		0			0
$907$	22.3621	+	18.7640i	0.742521	+	0.623049i	0.933513	−	0.358542i	$-0.116726\pi$
$907$	22.3621	+	18.7640i	0.742521	+	0.623049i	−0.190992	+	0.981592i	$0.561171\pi$
$908$	−14.2636	−	24.7053i	−0.473354	−	0.819873i
$909$		0			0
$910$	−18.1006	+	31.3512i	−0.600030	+	1.03928i
$911$	51.3409	−	18.6866i	1.70100	−	0.619114i	0.705062	−	0.709145i	$-0.250919\pi$
$911$	51.3409	−	18.6866i	1.70100	−	0.619114i	0.995939	+	0.0900315i	$0.0286968\pi$
$912$		0			0
$913$	5.42367	−	4.55100i	0.179497	−	0.150616i
$914$	−0.175152	−	0.0637502i	−0.00579352	−	0.00210867i
$915$		0			0
$916$	0.322184	−	1.82720i	0.0106453	−	0.0603722i
$917$	−60.5012			−1.99793
$918$		0			0
$919$	41.0995			1.35575			0.677873	−	0.735179i	$-0.262902\pi$
$919$	41.0995			1.35575			0.677873	+	0.735179i	$0.262902\pi$
$920$	1.84466	−	10.4616i	0.0608166	−	0.344908i
$921$		0			0
$922$	−9.77783	−	3.55884i	−0.322016	−	0.117204i
$923$	−4.72012	+	3.96065i	−0.155365	+	0.130367i
$924$		0			0
$925$	34.5863	−	12.5884i	1.13719	−	0.413904i
$926$	12.8942	−	22.3334i	0.423730	−	0.733922i
$927$		0			0
$928$	0.292722	+	0.507009i	0.00960907	+	0.0166434i
$929$	−11.1812	−	9.38218i	−0.366845	−	0.307819i	0.440667	−	0.897671i	$-0.354742\pi$
$929$	−11.1812	−	9.38218i	−0.366845	−	0.307819i	−0.807512	+	0.589851i	$0.799186\pi$
$930$		0			0
$931$	−3.88158	−	22.0135i	−0.127214	−	0.721464i
$932$	−1.48203	−	8.40503i	−0.0485456	−	0.275316i
$933$		0			0
$934$	16.6240	+	13.9492i	0.543955	+	0.456432i
$935$	−6.24668	−	10.8196i	−0.204288	−	0.353838i
$936$		0			0
$937$	−12.4641	+	21.5885i	−0.407185	+	0.705265i	−0.994573	−	0.104041i	$-0.966823\pi$
$937$	−12.4641	+	21.5885i	−0.407185	+	0.705265i	0.587388	+	0.809305i	$0.300156\pi$
$938$	−29.8160	+	10.8521i	−0.973525	+	0.354334i
$939$		0			0
$940$	−9.34844	+	7.84427i	−0.304912	+	0.255852i
$941$	19.5873	+	7.12918i	0.638526	+	0.232405i	0.640938	−	0.767592i	$-0.278545\pi$
$941$	19.5873	+	7.12918i	0.638526	+	0.232405i	−0.00241179	+	0.999997i	$0.500768\pi$
$942$		0			0
$943$	4.12268	−	23.3809i	0.134253	−	0.761387i
$944$	9.66319			0.314510
$945$		0			0
$946$	−3.78845			−0.123173
$947$	−6.23623	+	35.3674i	−0.202650	+	1.14929i	0.698445	+	0.715664i	$0.253876\pi$
$947$	−6.23623	+	35.3674i	−0.202650	+	1.14929i	−0.901095	+	0.433622i	$0.857235\pi$
$948$		0			0
$949$	−31.0192	−	11.2901i	−1.00693	−	0.366491i
$950$	13.0989	−	10.9913i	0.424985	−	0.356605i
$951$		0			0
$952$	−5.97705	+	2.17547i	−0.193717	+	0.0705074i
$953$	2.90103	−	5.02474i	0.0939737	−	0.162767i	−0.815206	−	0.579171i	$-0.803376\pi$
$953$	2.90103	−	5.02474i	0.0939737	−	0.162767i	0.909180	+	0.416404i	$0.136710\pi$
$954$		0			0
$955$	−5.70716	−	9.88509i	−0.184679	−	0.319874i
$956$	5.58290	+	4.68461i	0.180564	+	0.151511i
$957$		0			0
$958$	−6.79333	−	38.5269i	−0.219482	−	1.24475i
$959$	0.135145	+	0.766447i	0.00436407	+	0.0247499i
$960$		0			0
$961$	−7.26914	−	6.09953i	−0.234488	−	0.196759i
$962$	−11.3272	−	19.6192i	−0.365202	−	0.632549i
$963$		0			0
$964$	0.667459	−	1.15607i	0.0214974	−	0.0372346i
$965$	4.39077	−	1.59811i	0.141344	−	0.0514449i
$966$		0			0
$967$	22.7200	−	19.0644i	0.730627	−	0.613069i	−0.199675	−	0.979862i	$-0.563989\pi$
$967$	22.7200	−	19.0644i	0.730627	−	0.613069i	0.930303	+	0.366793i	$0.119544\pi$
$968$	−5.42998	−	1.97635i	−0.174526	−	0.0635224i
$969$		0			0
$970$	5.05640	−	28.6763i	0.162351	−	0.920740i
$971$	−47.1522			−1.51318			−0.756592	−	0.653887i	$-0.773137\pi$
$971$	−47.1522			−1.51318			−0.756592	+	0.653887i	$0.773137\pi$
$972$		0			0
$973$	13.5322			0.433821
$974$	1.82040	−	10.3240i	0.0583295	−	0.330803i
$975$		0			0
$976$	−12.3018	−	4.47750i	−0.393772	−	0.143321i
$977$	18.2341	−	15.3002i	0.583361	−	0.489498i	−0.302688	−	0.953090i	$-0.597884\pi$
$977$	18.2341	−	15.3002i	0.583361	−	0.489498i	0.886049	+	0.463592i	$0.153440\pi$
$978$		0			0
$979$	−37.2464	+	13.5566i	−1.19040	+	0.433270i
$980$	10.4303	−	18.0657i	0.333183	−	0.577089i
$981$		0			0
$982$	−3.42851	−	5.93835i	−0.109408	−	0.189501i
$983$	−8.48950	−	7.12353i	−0.270773	−	0.227205i	0.497283	−	0.867589i	$-0.334331\pi$
$983$	−8.48950	−	7.12353i	−0.270773	−	0.227205i	−0.768056	+	0.640383i	$0.778776\pi$
$984$		0			0
$985$	1.39659	+	7.92046i	0.0444991	+	0.252367i
$986$	0.175443	+	0.994984i	0.00558723	+	0.0316867i
$987$		0			0
$988$	−8.06247	−	6.76521i	−0.256501	−	0.215230i
$989$	−2.77957	−	4.81435i	−0.0883851	−	0.153087i
$990$		0			0
$991$	−5.71846	+	9.90466i	−0.181653	+	0.314632i	−0.942443	−	0.334365i	$-0.891478\pi$
$991$	−5.71846	+	9.90466i	−0.181653	+	0.314632i	0.760791	+	0.648997i	$0.224811\pi$
$992$	−4.35827	+	1.58628i	−0.138375	+	0.0503645i
$993$		0			0
$994$	5.61145	−	4.70857i	0.177984	−	0.149347i
$995$	−5.51286	−	2.00652i	−0.174769	−	0.0636108i
$996$		0			0
$997$	−4.84383	+	27.4707i	−0.153406	+	0.870007i	0.806823	+	0.590793i	$0.201185\pi$
$997$	−4.84383	+	27.4707i	−0.153406	+	0.870007i	−0.960229	+	0.279214i	$0.909926\pi$
$998$	−18.7737			−0.594271
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.e.b.73.1		12
3.2	odd	2		54.2.e.b.25.1	yes	12
9.2	odd	6		486.2.e.f.55.2		12
9.4	even	3		486.2.e.e.379.2		12
9.5	odd	6		486.2.e.h.379.1		12
9.7	even	3		486.2.e.g.55.1		12
12.11	even	2		432.2.u.b.241.2		12
27.2	odd	18		1458.2.c.f.487.2		12
27.4	even	9		486.2.e.e.109.2		12
27.5	odd	18		486.2.e.f.433.2		12
27.7	even	9		1458.2.c.g.973.5		12
27.11	odd	18		1458.2.a.g.1.5		6
27.13	even	9	inner	162.2.e.b.91.1		12
27.14	odd	18		54.2.e.b.13.1	✓	12
27.16	even	9		1458.2.a.f.1.2		6
27.20	odd	18		1458.2.c.f.973.2		12
27.22	even	9		486.2.e.g.433.1		12
27.23	odd	18		486.2.e.h.109.1		12
27.25	even	9		1458.2.c.g.487.5		12
108.95	even	18		432.2.u.b.337.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.b.13.1	✓	12	27.14	odd	18
54.2.e.b.25.1	yes	12	3.2	odd	2
162.2.e.b.73.1		12	1.1	even	1	trivial
162.2.e.b.91.1		12	27.13	even	9	inner
432.2.u.b.241.2		12	12.11	even	2
432.2.u.b.337.2		12	108.95	even	18
486.2.e.e.109.2		12	27.4	even	9
486.2.e.e.379.2		12	9.4	even	3
486.2.e.f.55.2		12	9.2	odd	6
486.2.e.f.433.2		12	27.5	odd	18
486.2.e.g.55.1		12	9.7	even	3
486.2.e.g.433.1		12	27.22	even	9
486.2.e.h.109.1		12	27.23	odd	18
486.2.e.h.379.1		12	9.5	odd	6
1458.2.a.f.1.2		6	27.16	even	9
1458.2.a.g.1.5		6	27.11	odd	18
1458.2.c.f.487.2		12	27.2	odd	18
1458.2.c.f.973.2		12	27.20	odd	18
1458.2.c.g.487.5		12	27.25	even	9
1458.2.c.g.973.5		12	27.7	even	9

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(-2.42692 + 2.03643i) q^{5} +(-3.46344 + 1.26059i) q^{7} +(0.500000 - 0.866025i) q^{8} +O(q^{10})\)	\(q+(-0.173648 + 0.984808i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(-2.42692 + 2.03643i) q^{5} +(-3.46344 + 1.26059i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.58406 - 2.74367i) q^{10} +(1.75046 + 1.46881i) q^{11} +(0.538357 + 3.05317i) q^{13} +(-0.640018 - 3.62972i) q^{14} +(0.766044 + 0.642788i) q^{16} +(0.862878 + 1.49455i) q^{17} +(1.69740 - 2.93998i) q^{19} +(2.97705 - 1.08356i) q^{20} +(-1.75046 + 1.46881i) q^{22} +(-3.15087 - 1.14682i) q^{23} +(0.874658 - 4.96043i) q^{25} -3.10027 q^{26} +3.68572 q^{28} +(0.101661 - 0.576550i) q^{29} +(4.35827 + 1.58628i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(-1.62168 + 0.590243i) q^{34} +(5.83839 - 10.1124i) q^{35} +(3.65360 + 6.32822i) q^{37} +(2.60057 + 2.18213i) q^{38} +(0.550137 + 3.11998i) q^{40} +(1.22952 + 6.97295i) q^{41} +(1.27004 + 1.06569i) q^{43} +(-1.14253 - 1.97893i) q^{44} +(1.67654 - 2.90386i) q^{46} +(-3.61968 + 1.31746i) q^{47} +(5.04404 - 4.23245i) q^{49} +(4.73319 + 1.72274i) q^{50} +(0.538357 - 3.05317i) q^{52} +2.58267 q^{53} -7.23936 q^{55} +(-0.640018 + 3.62972i) q^{56} +(0.550137 + 0.200234i) q^{58} +(7.40243 - 6.21138i) q^{59} +(-12.3018 + 4.47750i) q^{61} +(-2.31899 + 4.01660i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(-7.52411 - 6.31348i) q^{65} +(-1.49490 - 8.47798i) q^{67} +(-0.299674 - 1.69954i) q^{68} +(8.94493 + 7.50569i) q^{70} +(0.993732 + 1.72119i) q^{71} +(-5.32371 + 9.22094i) q^{73} +(-6.86652 + 2.49921i) q^{74} +(-2.60057 + 2.18213i) q^{76} +(-7.91420 - 2.88053i) q^{77} +(2.44726 - 13.8791i) q^{79} -3.16812 q^{80} -7.08052 q^{82} +(0.538035 - 3.05135i) q^{83} +(-5.13767 - 1.86996i) q^{85} +(-1.27004 + 1.06569i) q^{86} +(2.14726 - 0.781539i) q^{88} +(-8.67300 + 15.0221i) q^{89} +(-5.71337 - 9.89585i) q^{91} +(2.56861 + 2.15532i) q^{92} +(-0.668890 - 3.79346i) q^{94} +(1.86760 + 10.5917i) q^{95} +(7.04084 + 5.90797i) q^{97} +(3.29226 + 5.70237i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q + 3 * q^5 - 3 * q^7 + 6 * q^8	\( 12 q + 3 q^{5} - 3 q^{7} + 6 q^{8} - 3 q^{10} + 12 q^{11} + 12 q^{13} + 3 q^{14} + 6 q^{17} - 9 q^{19} - 6 q^{20} - 12 q^{22} - 30 q^{23} - 9 q^{25} - 18 q^{26} + 12 q^{28} - 15 q^{29} - 15 q^{34} - 3 q^{35} - 15 q^{37} - 3 q^{38} - 3 q^{40} + 12 q^{41} + 9 q^{43} + 3 q^{44} + 3 q^{46} + 9 q^{47} - 39 q^{49} + 27 q^{50} + 12 q^{52} + 12 q^{53} + 18 q^{55} + 3 q^{56} - 3 q^{58} - 12 q^{59} - 36 q^{61} + 12 q^{62} - 6 q^{64} + 15 q^{65} + 36 q^{67} - 3 q^{68} + 39 q^{70} - 12 q^{71} - 21 q^{73} - 33 q^{74} + 3 q^{76} - 3 q^{77} + 39 q^{79} - 6 q^{80} + 6 q^{82} - 18 q^{83} + 45 q^{85} - 9 q^{86} + 6 q^{88} - 12 q^{89} - 6 q^{91} + 6 q^{92} + 36 q^{94} + 15 q^{95} + 39 q^{97} + 12 q^{98}+O(q^{100}) \) 12 * q + 3 * q^5 - 3 * q^7 + 6 * q^8 - 3 * q^10 + 12 * q^11 + 12 * q^13 + 3 * q^14 + 6 * q^17 - 9 * q^19 - 6 * q^20 - 12 * q^22 - 30 * q^23 - 9 * q^25 - 18 * q^26 + 12 * q^28 - 15 * q^29 - 15 * q^34 - 3 * q^35 - 15 * q^37 - 3 * q^38 - 3 * q^40 + 12 * q^41 + 9 * q^43 + 3 * q^44 + 3 * q^46 + 9 * q^47 - 39 * q^49 + 27 * q^50 + 12 * q^52 + 12 * q^53 + 18 * q^55 + 3 * q^56 - 3 * q^58 - 12 * q^59 - 36 * q^61 + 12 * q^62 - 6 * q^64 + 15 * q^65 + 36 * q^67 - 3 * q^68 + 39 * q^70 - 12 * q^71 - 21 * q^73 - 33 * q^74 + 3 * q^76 - 3 * q^77 + 39 * q^79 - 6 * q^80 + 6 * q^82 - 18 * q^83 + 45 * q^85 - 9 * q^86 + 6 * q^88 - 12 * q^89 - 6 * q^91 + 6 * q^92 + 36 * q^94 + 15 * q^95 + 39 * q^97 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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