LMFDB - Embedded newform 162.2.e.b.19.1

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			19.1
Root			$0.500000 - 0.677980i$ of defining polynomial
Character	$\chi$	$=$	162.19
Dual form			162.2.e.b.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(0.766044 - 0.642788i) q^{4} +(-0.617090 - 3.49969i) q^{5} +(-0.244752 - 0.205371i) q^{7} +(0.500000 - 0.866025i) q^{8} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(0.766044 - 0.642788i) q^{4} +(-0.617090 - 3.49969i) q^{5} +(-0.244752 - 0.205371i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.77684 - 3.07758i) q^{10} +(-0.773091 + 4.38442i) q^{11} +(4.39657 + 1.60022i) q^{13} +(-0.300233 - 0.109276i) q^{14} +(0.173648 - 0.984808i) q^{16} +(0.567354 + 0.982686i) q^{17} +(-0.928896 + 1.60890i) q^{19} +(-2.72228 - 2.28426i) q^{20} +(0.773091 + 4.38442i) q^{22} +(-0.110473 + 0.0926974i) q^{23} +(-7.16859 + 2.60915i) q^{25} +4.67874 q^{26} -0.319501 q^{28} +(-4.09634 + 1.49095i) q^{29} +(0.514546 - 0.431755i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(0.869237 + 0.729376i) q^{34} +(-0.567702 + 0.983289i) q^{35} +(-3.79438 - 6.57207i) q^{37} +(-0.322602 + 1.82957i) q^{38} +(-3.33937 - 1.21543i) q^{40} +(2.04599 + 0.744678i) q^{41} +(-1.23250 + 6.98988i) q^{43} +(2.22603 + 3.85559i) q^{44} +(-0.0721058 + 0.124891i) q^{46} +(7.91059 + 6.63778i) q^{47} +(-1.19781 - 6.79312i) q^{49} +(-5.84389 + 4.90360i) q^{50} +(4.39657 - 1.60022i) q^{52} -0.805554 q^{53} +15.8212 q^{55} +(-0.300233 + 0.109276i) q^{56} +(-3.33937 + 2.80206i) q^{58} +(-0.517966 - 2.93753i) q^{59} +(-2.67705 - 2.24631i) q^{61} +(0.335846 - 0.581702i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(2.88720 - 16.3741i) q^{65} +(-6.99437 - 2.54574i) q^{67} +(1.06628 + 0.388093i) q^{68} +(-0.197161 + 1.11816i) q^{70} +(-4.04928 - 7.01356i) q^{71} +(-7.30065 + 12.6451i) q^{73} +(-5.81333 - 4.87797i) q^{74} +(0.322602 + 1.82957i) q^{76} +(1.08965 - 0.914324i) q^{77} +(11.8279 - 4.30501i) q^{79} -3.55368 q^{80} +2.17729 q^{82} +(-5.08715 + 1.85157i) q^{83} +(3.08899 - 2.59197i) q^{85} +(1.23250 + 6.98988i) q^{86} +(3.41047 + 2.86173i) q^{88} +(2.52624 - 4.37558i) q^{89} +(-0.747430 - 1.29459i) q^{91} +(-0.0250421 + 0.142021i) q^{92} +(9.70378 + 3.53189i) q^{94} +(6.20385 + 2.25802i) q^{95} +(3.24273 - 18.3904i) q^{97} +(-3.44896 - 5.97377i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$		0			0
$3$		0			0
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−0.617090	−	3.49969i	−0.275971	−	1.56511i	−0.735860	−	0.677134i	$-0.763222\pi$
$5$	−0.617090	−	3.49969i	−0.275971	−	1.56511i	0.459889	−	0.887977i	$-0.347889\pi$
$6$		0			0
$7$	−0.244752	−	0.205371i	−0.0925075	−	0.0776230i	0.595361	−	0.803458i	$-0.297009\pi$
$7$	−0.244752	−	0.205371i	−0.0925075	−	0.0776230i	−0.687869	+	0.725835i	$0.741453\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$		0			0
$10$	−1.77684	−	3.07758i	−0.561886	−	0.973216i
$11$	−0.773091	+	4.38442i	−0.233096	+	1.32195i	0.613491	+	0.789702i	$0.289765\pi$
$11$	−0.773091	+	4.38442i	−0.233096	+	1.32195i	−0.846587	+	0.532250i	$0.821347\pi$
$12$		0			0
$13$	4.39657	+	1.60022i	1.21939	+	0.443822i	0.869951	−	0.493137i	$-0.164150\pi$
$13$	4.39657	+	1.60022i	1.21939	+	0.443822i	0.349439	+	0.936959i	$0.386372\pi$
$14$	−0.300233	−	0.109276i	−0.0802405	−	0.0292052i
$15$		0			0
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	0.567354	+	0.982686i	0.137604	+	0.238336i	0.926589	−	0.376075i	$-0.122727\pi$
$17$	0.567354	+	0.982686i	0.137604	+	0.238336i	−0.788985	+	0.614412i	$0.789393\pi$
$18$		0			0
$19$	−0.928896	+	1.60890i	−0.213103	+	0.369106i	−0.952684	−	0.303962i	$-0.901690\pi$
$19$	−0.928896	+	1.60890i	−0.213103	+	0.369106i	0.739581	+	0.673068i	$0.235024\pi$
$20$	−2.72228	−	2.28426i	−0.608720	−	0.510777i
$21$		0			0
$22$	0.773091	+	4.38442i	0.164824	+	0.934761i
$23$	−0.110473	+	0.0926974i	−0.0230351	+	0.0193288i	−0.654233	−	0.756293i	$-0.727008\pi$
$23$	−0.110473	+	0.0926974i	−0.0230351	+	0.0193288i	0.631197	+	0.775622i	$0.282564\pi$
$24$		0			0
$25$	−7.16859	+	2.60915i	−1.43372	+	0.521831i
$26$	4.67874			0.917576
$27$		0			0
$28$	−0.319501			−0.0603800
$29$	−4.09634	+	1.49095i	−0.760672	+	0.276862i	−0.693089	−	0.720852i	$-0.743751\pi$
$29$	−4.09634	+	1.49095i	−0.760672	+	0.276862i	−0.0675824	+	0.997714i	$0.521529\pi$
$30$		0			0
$31$	0.514546	−	0.431755i	0.0924152	−	0.0775455i	−0.595410	−	0.803422i	$-0.703010\pi$
$31$	0.514546	−	0.431755i	0.0924152	−	0.0775455i	0.687825	+	0.725877i	$0.258566\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$		0			0
$34$	0.869237	+	0.729376i	0.149073	+	0.125087i
$35$	−0.567702	+	0.983289i	−0.0959592	+	0.166206i
$36$		0			0
$37$	−3.79438	−	6.57207i	−0.623793	−	1.08044i	−0.988773	−	0.149426i	$-0.952258\pi$
$37$	−3.79438	−	6.57207i	−0.623793	−	1.08044i	0.364980	−	0.931015i	$-0.381076\pi$
$38$	−0.322602	+	1.82957i	−0.0523330	+	0.296795i
$39$		0			0
$40$	−3.33937	−	1.21543i	−0.528000	−	0.192176i
$41$	2.04599	+	0.744678i	0.319529	+	0.116299i	0.496805	−	0.867862i	$-0.334506\pi$
$41$	2.04599	+	0.744678i	0.319529	+	0.116299i	−0.177276	+	0.984161i	$0.556729\pi$
$42$		0			0
$43$	−1.23250	+	6.98988i	−0.187955	+	1.06595i	0.734144	+	0.678994i	$0.237584\pi$
$43$	−1.23250	+	6.98988i	−0.187955	+	1.06595i	−0.922099	+	0.386953i	$0.873528\pi$
$44$	2.22603	+	3.85559i	0.335586	+	0.581252i
$45$		0			0
$46$	−0.0721058	+	0.124891i	−0.0106314	+	0.0184142i
$47$	7.91059	+	6.63778i	1.15388	+	0.968219i	0.999803	−	0.0198400i	$-0.00631569\pi$
$47$	7.91059	+	6.63778i	1.15388	+	0.968219i	0.154075	+	0.988059i	$0.450760\pi$
$48$		0			0
$49$	−1.19781	−	6.79312i	−0.171116	−	0.970446i
$50$	−5.84389	+	4.90360i	−0.826450	+	0.693474i
$51$		0			0
$52$	4.39657	−	1.60022i	0.609695	−	0.221911i
$53$	−0.805554			−0.110651			−0.0553257	−	0.998468i	$-0.517620\pi$
$53$	−0.805554			−0.110651			−0.0553257	+	0.998468i	$0.517620\pi$
$54$		0			0
$55$	15.8212			2.13333
$56$	−0.300233	+	0.109276i	−0.0401203	+	0.0146026i
$57$		0			0
$58$	−3.33937	+	2.80206i	−0.438481	+	0.367929i
$59$	−0.517966	−	2.93753i	−0.0674334	−	0.382434i	−0.999782	−	0.0208736i	$-0.993355\pi$
$59$	−0.517966	−	2.93753i	−0.0674334	−	0.382434i	0.932349	−	0.361560i	$-0.117756\pi$
$60$		0			0
$61$	−2.67705	−	2.24631i	−0.342761	−	0.287611i	0.455114	−	0.890433i	$-0.349598\pi$
$61$	−2.67705	−	2.24631i	−0.342761	−	0.287611i	−0.797876	+	0.602822i	$0.794043\pi$
$62$	0.335846	−	0.581702i	0.0426525	−	0.0738763i
$63$		0			0
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	2.88720	−	16.3741i	0.358113	−	2.03096i
$66$		0			0
$67$	−6.99437	−	2.54574i	−0.854498	−	0.311012i	−0.122625	−	0.992453i	$-0.539131\pi$
$67$	−6.99437	−	2.54574i	−0.854498	−	0.311012i	−0.731873	+	0.681441i	$0.761353\pi$
$68$	1.06628	+	0.388093i	0.129305	+	0.0470632i
$69$		0			0
$70$	−0.197161	+	1.11816i	−0.0235652	+	0.133645i
$71$	−4.04928	−	7.01356i	−0.480561	−	0.832356i	0.519190	−	0.854659i	$-0.326234\pi$
$71$	−4.04928	−	7.01356i	−0.480561	−	0.832356i	−0.999751	+	0.0223028i	$0.992900\pi$
$72$		0			0
$73$	−7.30065	+	12.6451i	−0.854477	+	1.48000i	0.0226526	+	0.999743i	$0.492789\pi$
$73$	−7.30065	+	12.6451i	−0.854477	+	1.48000i	−0.877129	+	0.480254i	$0.840545\pi$
$74$	−5.81333	−	4.87797i	−0.675786	−	0.567052i
$75$		0			0
$76$	0.322602	+	1.82957i	0.0370050	+	0.209866i
$77$	1.08965	−	0.914324i	0.124177	−	0.104197i
$78$		0			0
$79$	11.8279	−	4.30501i	1.33074	−	0.484351i	0.423859	−	0.905728i	$-0.360675\pi$
$79$	11.8279	−	4.30501i	1.33074	−	0.484351i	0.906886	+	0.421377i	$0.138453\pi$
$80$	−3.55368			−0.397314
$81$		0			0
$82$	2.17729			0.240442
$83$	−5.08715	+	1.85157i	−0.558387	+	0.203236i	−0.605769	−	0.795641i	$-0.707134\pi$
$83$	−5.08715	+	1.85157i	−0.558387	+	0.203236i	0.0473820	+	0.998877i	$0.484912\pi$
$84$		0			0
$85$	3.08899	−	2.59197i	0.335048	−	0.281139i
$86$	1.23250	+	6.98988i	0.132904	+	0.753738i
$87$		0			0
$88$	3.41047	+	2.86173i	0.363558	+	0.305061i
$89$	2.52624	−	4.37558i	0.267781	−	0.463810i	−0.700508	−	0.713645i	$-0.747043\pi$
$89$	2.52624	−	4.37558i	0.267781	−	0.463810i	0.968288	+	0.249835i	$0.0803763\pi$
$90$		0			0
$91$	−0.747430	−	1.29459i	−0.0783520	−	0.135710i
$92$	−0.0250421	+	0.142021i	−0.00261082	+	0.0148067i
$93$		0			0
$94$	9.70378	+	3.53189i	1.00087	+	0.364286i
$95$	6.20385	+	2.25802i	0.636502	+	0.231668i
$96$		0			0
$97$	3.24273	−	18.3904i	0.329249	−	1.86726i	−0.148708	−	0.988881i	$-0.547511\pi$
$97$	3.24273	−	18.3904i	0.329249	−	1.86726i	0.477957	−	0.878383i	$-0.341377\pi$
$98$	−3.44896	−	5.97377i	−0.348398	−	0.603442i
$99$		0			0
$100$	−3.81433	+	6.60661i	−0.381433	+	0.660661i
$101$	1.85357	+	1.55533i	0.184438	+	0.154761i	0.730332	−	0.683093i	$-0.239366\pi$
$101$	1.85357	+	1.55533i	0.184438	+	0.154761i	−0.545894	+	0.837854i	$0.683810\pi$
$102$		0			0
$103$	0.346489	+	1.96504i	0.0341406	+	0.193621i	0.997108	−	0.0759967i	$-0.0242138\pi$
$103$	0.346489	+	1.96504i	0.0341406	+	0.193621i	−0.962967	+	0.269618i	$0.913103\pi$
$104$	3.58412	−	3.00743i	0.351452	−	0.294903i
$105$		0			0
$106$	−0.756973	+	0.275516i	−0.0735238	+	0.0267605i
$107$	−8.87072			−0.857565			−0.428783	−	0.903408i	$-0.641057\pi$
$107$	−8.87072			−0.857565			−0.428783	+	0.903408i	$0.641057\pi$
$108$		0			0
$109$	−1.97204			−0.188887			−0.0944434	−	0.995530i	$-0.530107\pi$
$109$	−1.97204			−0.188887			−0.0944434	+	0.995530i	$0.530107\pi$
$110$	14.8671	−	5.41116i	1.41752	−	0.515934i
$111$		0			0
$112$	−0.244752	+	0.205371i	−0.0231269	+	0.0194058i
$113$	1.67200	+	9.48237i	0.157288	+	0.892026i	0.956664	+	0.291195i	$0.0940527\pi$
$113$	1.67200	+	9.48237i	0.157288	+	0.892026i	−0.799375	+	0.600832i	$0.794836\pi$
$114$		0			0
$115$	0.392584	+	0.329417i	0.0366087	+	0.0307183i
$116$	−2.17962	+	3.77521i	−0.202372	+	0.350519i
$117$		0			0
$118$	−1.49142	−	2.58322i	−0.137297	−	0.237805i
$119$	0.0629545	−	0.357033i	0.00577103	−	0.0327291i
$120$		0			0
$121$	−8.28884	−	3.01689i	−0.753530	−	0.274263i
$122$	−3.28389	−	1.19524i	−0.297309	−	0.108212i
$123$		0			0
$124$	0.116638	−	0.661487i	0.0104744	−	0.0594033i
$125$	4.67070	+	8.08988i	0.417760	+	0.723581i
$126$		0			0
$127$	−0.0796049	+	0.137880i	−0.00706379	+	0.0122348i	−0.869536	−	0.493870i	$-0.835582\pi$
$127$	−0.0796049	+	0.137880i	−0.00706379	+	0.0122348i	0.862472	+	0.506105i	$0.168915\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$		0			0
$130$	−2.88720	−	16.3741i	−0.253224	−	1.43611i
$131$	7.26657	−	6.09738i	0.634883	−	0.532730i	−0.267559	−	0.963542i	$-0.586217\pi$
$131$	7.26657	−	6.09738i	0.634883	−	0.532730i	0.902442	+	0.430811i	$0.141773\pi$
$132$		0			0
$133$	0.557770	−	0.203012i	0.0483648	−	0.0176033i
$134$	−7.44325			−0.642999
$135$		0			0
$136$	1.13471			0.0973004
$137$	11.0032	−	4.00484i	0.940067	−	0.342156i	0.173875	−	0.984768i	$-0.444371\pi$
$137$	11.0032	−	4.00484i	0.940067	−	0.342156i	0.766192	+	0.642611i	$0.222149\pi$
$138$		0			0
$139$	−4.02194	+	3.37481i	−0.341136	+	0.286247i	−0.797219	−	0.603690i	$-0.793696\pi$
$139$	−4.02194	+	3.37481i	−0.341136	+	0.286247i	0.456083	+	0.889937i	$0.349252\pi$
$140$	0.197161	+	1.11816i	0.0166631	+	0.0945014i
$141$		0			0
$142$	−6.20385	−	5.20565i	−0.520616	−	0.436849i
$143$	−10.4150	+	18.0393i	−0.870946	+	1.50852i
$144$		0			0
$145$	7.74567	+	13.4159i	0.643243	+	1.11413i
$146$	−2.53549	+	14.3795i	−0.209839	+	1.19005i
$147$		0			0
$148$	−7.13111	−	2.59551i	−0.586174	−	0.213350i
$149$	−15.3097	−	5.57227i	−1.25422	−	0.456499i	−0.372394	−	0.928075i	$-0.621463\pi$
$149$	−15.3097	−	5.57227i	−1.25422	−	0.456499i	−0.881825	+	0.471576i	$0.843685\pi$
$150$		0			0
$151$	−2.71203	+	15.3807i	−0.220702	+	1.25166i	0.650033	+	0.759906i	$0.274755\pi$
$151$	−2.71203	+	15.3807i	−0.220702	+	1.25166i	−0.870734	+	0.491754i	$0.836356\pi$
$152$	0.928896	+	1.60890i	0.0753434	+	0.130499i
$153$		0			0
$154$	0.711218	−	1.23187i	0.0573116	−	0.0992665i
$155$	−1.82853	−	1.53432i	−0.146871	−	0.123240i
$156$		0			0
$157$	3.06168	+	17.3637i	0.244349	+	1.38577i	0.822000	+	0.569488i	$0.192859\pi$
$157$	3.06168	+	17.3637i	0.244349	+	1.38577i	−0.577651	+	0.816284i	$0.696030\pi$
$158$	9.64221	−	8.09077i	0.767093	−	0.643667i
$159$		0			0
$160$	−3.33937	+	1.21543i	−0.264000	+	0.0960882i
$161$	0.0460757			0.00363128
$162$		0			0
$163$	−15.8801			−1.24382			−0.621912	−	0.783087i	$-0.713644\pi$
$163$	−15.8801			−1.24382			−0.621912	+	0.783087i	$0.713644\pi$
$164$	2.04599	−	0.744678i	0.159765	−	0.0581496i
$165$		0			0
$166$	−4.14708	+	3.47981i	−0.321876	+	0.270086i
$167$	2.35787	+	13.3721i	0.182457	+	1.03477i	0.929179	+	0.369630i	$0.120516\pi$
$167$	2.35787	+	13.3721i	0.182457	+	1.03477i	−0.746722	+	0.665137i	$0.768373\pi$
$168$		0			0
$169$	6.81058	+	5.71475i	0.523891	+	0.439596i
$170$	2.01620	−	3.49215i	0.154635	−	0.267836i
$171$		0			0
$172$	3.54885	+	6.14680i	0.270598	+	0.468689i
$173$	−1.11906	+	6.34650i	−0.0850805	+	0.482516i	0.912259	+	0.409615i	$0.134337\pi$
$173$	−1.11906	+	6.34650i	−0.0850805	+	0.482516i	−0.997339	+	0.0729010i	$0.976774\pi$
$174$		0			0
$175$	2.29037	+	0.833627i	0.173136	+	0.0630163i
$176$	4.18356	+	1.52269i	0.315348	+	0.114777i
$177$		0			0
$178$	0.877354	−	4.97572i	0.0657605	−	0.372946i
$179$	−6.25613	−	10.8359i	−0.467605	−	0.809915i	0.531710	−	0.846927i	$-0.321550\pi$
$179$	−6.25613	−	10.8359i	−0.467605	−	0.809915i	−0.999315	+	0.0370111i	$0.988216\pi$
$180$		0			0
$181$	−0.152251	+	0.263707i	−0.0113168	+	0.0196012i	−0.871628	−	0.490167i	$-0.836936\pi$
$181$	−0.152251	+	0.263707i	−0.0113168	+	0.0196012i	0.860312	+	0.509769i	$0.170269\pi$
$182$	−1.14513	−	0.960878i	−0.0848827	−	0.0712250i
$183$		0			0
$184$	0.0250421	+	0.142021i	0.00184613	+	0.0104699i
$185$	−20.6587	+	17.3347i	−1.51886	+	1.27448i
$186$		0			0
$187$	−4.74712	+	1.72781i	−0.347144	+	0.126350i
$188$	10.3265			0.753141
$189$		0			0
$190$	6.60200			0.478960
$191$	−13.5247	+	4.92260i	−0.978615	+	0.356187i	−0.781301	−	0.624154i	$-0.785444\pi$
$191$	−13.5247	+	4.92260i	−0.978615	+	0.356187i	−0.197313	+	0.980341i	$0.563222\pi$
$192$		0			0
$193$	2.33692	−	1.96090i	0.168215	−	0.141149i	−0.554794	−	0.831988i	$-0.687203\pi$
$193$	2.33692	−	1.96090i	0.168215	−	0.141149i	0.723009	+	0.690839i	$0.242759\pi$
$194$	−3.24273	−	18.3904i	−0.232814	−	1.32036i
$195$		0			0
$196$	−5.28411	−	4.43390i	−0.377437	−	0.316707i
$197$	11.1321	−	19.2814i	0.793129	−	1.37374i	−0.130891	−	0.991397i	$-0.541784\pi$
$197$	11.1321	−	19.2814i	0.793129	−	1.37374i	0.924020	−	0.382343i	$-0.124883\pi$
$198$		0			0
$199$	−12.2817	−	21.2725i	−0.870626	−	1.50797i	−0.861350	−	0.508012i	$-0.830381\pi$
$199$	−12.2817	−	21.2725i	−0.870626	−	1.50797i	−0.00927642	−	0.999957i	$-0.502953\pi$
$200$	−1.32470	+	7.51276i	−0.0936705	+	0.531232i
$201$		0			0
$202$	2.27375	+	0.827576i	0.159980	+	0.0582280i
$203$	1.30878	+	0.476359i	0.0918587	+	0.0334338i
$204$		0			0
$205$	1.34359	−	7.61986i	0.0938402	−	0.532194i
$206$	0.997676	+	1.72802i	0.0695114	+	0.120397i
$207$		0			0
$208$	2.33937	−	4.05190i	0.162206	−	0.280949i
$209$	−6.33595	−	5.31649i	−0.438267	−	0.367750i
$210$		0			0
$211$	−0.524297	−	2.97344i	−0.0360941	−	0.204700i	0.961428	−	0.275058i	$-0.0886970\pi$
$211$	−0.524297	−	2.97344i	−0.0360941	−	0.204700i	−0.997522	+	0.0703579i	$0.977586\pi$
$212$	−0.617090	+	0.517800i	−0.0423819	+	0.0355627i
$213$		0			0
$214$	−8.33575	+	3.03397i	−0.569820	+	0.207398i
$215$	25.2230			1.72019
$216$		0			0
$217$	−0.214606			−0.0145684
$218$	−1.85311	+	0.674476i	−0.125508	+	0.0456813i
$219$		0			0
$220$	12.1197	−	10.1697i	0.817112	−	0.685638i
$221$	0.921898	+	5.22835i	0.0620136	+	0.351697i
$222$		0			0
$223$	7.64543	+	6.41527i	0.511976	+	0.429599i	0.861824	−	0.507208i	$-0.169322\pi$
$223$	7.64543	+	6.41527i	0.511976	+	0.429599i	−0.349848	+	0.936806i	$0.613767\pi$
$224$	−0.159750	+	0.276696i	−0.0106738	+	0.0184875i
$225$		0			0
$226$	4.81433	+	8.33866i	0.320244	+	0.554679i
$227$	3.66786	−	20.8015i	0.243444	−	1.38064i	−0.580633	−	0.814165i	$-0.697195\pi$
$227$	3.66786	−	20.8015i	0.243444	−	1.38064i	0.824078	−	0.566477i	$-0.191694\pi$
$228$		0			0
$229$	21.8767	+	7.96248i	1.44566	+	0.526176i	0.941374	−	0.337364i	$-0.109535\pi$
$229$	21.8767	+	7.96248i	1.44566	+	0.526176i	0.504281	+	0.863539i	$0.331757\pi$
$230$	0.481576	+	0.175279i	0.0317542	+	0.0115576i
$231$		0			0
$232$	−0.756973	+	4.29301i	−0.0496977	+	0.281850i
$233$	13.3621	+	23.1439i	0.875383	+	1.51621i	0.856354	+	0.516390i	$0.172724\pi$
$233$	13.3621	+	23.1439i	0.875383	+	1.51621i	0.0190296	+	0.999819i	$0.493942\pi$
$234$		0			0
$235$	18.3486	−	31.7808i	1.19693	−	2.07315i
$236$	−2.28499	−	1.91734i	−0.148740	−	0.124808i
$237$		0			0
$238$	−0.0629545	−	0.357033i	−0.00408073	−	0.0231430i
$239$	18.4309	−	15.4654i	1.19220	−	1.00037i	0.192379	−	0.981321i	$-0.438380\pi$
$239$	18.4309	−	15.4654i	1.19220	−	1.00037i	0.999818	−	0.0190518i	$-0.00606474\pi$
$240$		0			0
$241$	1.40157	−	0.510130i	0.0902831	−	0.0328604i	−0.296484	−	0.955038i	$-0.595814\pi$
$241$	1.40157	−	0.510130i	0.0902831	−	0.0328604i	0.386767	+	0.922178i	$0.373592\pi$
$242$	−8.82079			−0.567022
$243$		0			0
$244$	−3.49464			−0.223721
$245$	−23.0347	+	8.38394i	−1.47163	+	0.535630i
$246$		0			0
$247$	−6.65855	+	5.58719i	−0.423674	+	0.355504i
$248$	−0.116638	−	0.661487i	−0.00740653	−	0.0420045i
$249$		0			0
$250$	7.15592	+	6.00453i	0.452580	+	0.379760i
$251$	7.28748	−	12.6223i	0.459982	−	0.796711i	−0.538978	−	0.842320i	$-0.681189\pi$
$251$	7.28748	−	12.6223i	0.459982	−	0.796711i	0.998959	+	0.0456086i	$0.0145227\pi$
$252$		0			0
$253$	−0.321019	−	0.556021i	−0.0201823	−	0.0349568i
$254$	−0.0276465	+	0.156791i	−0.00173469	+	0.00983794i
$255$		0			0
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−10.3598	−	3.77064i	−0.646224	−	0.235206i	−0.00194649	−	0.999998i	$-0.500620\pi$
$257$	−10.3598	−	3.77064i	−0.646224	−	0.235206i	−0.644277	+	0.764792i	$0.722842\pi$
$258$		0			0
$259$	−0.421030	+	2.38778i	−0.0261616	+	0.148370i
$260$	−8.31337	−	14.3992i	−0.515573	−	0.892999i
$261$		0			0
$262$	4.74292	−	8.21497i	0.293018	−	0.507523i
$263$	10.0659	+	8.44626i	0.620688	+	0.520819i	0.898020	−	0.439955i	$-0.145006\pi$
$263$	10.0659	+	8.44626i	0.620688	+	0.520819i	−0.277332	+	0.960774i	$0.589450\pi$
$264$		0			0
$265$	0.497100	+	2.81919i	0.0305366	+	0.173182i
$266$	0.454698	−	0.381537i	0.0278793	−	0.0233935i
$267$		0			0
$268$	−6.99437	+	2.54574i	−0.427249	+	0.155506i
$269$	10.3086			0.628528			0.314264	−	0.949336i	$-0.398242\pi$
$269$	10.3086			0.628528			0.314264	+	0.949336i	$0.398242\pi$
$270$		0			0
$271$	1.01454			0.0616288			0.0308144	−	0.999525i	$-0.490190\pi$
$271$	1.01454			0.0616288			0.0308144	+	0.999525i	$0.490190\pi$
$272$	1.06628	−	0.388093i	0.0646525	−	0.0235316i
$273$		0			0
$274$	8.96989	−	7.52663i	0.541891	−	0.454700i
$275$	−5.89764	−	33.4472i	−0.355641	−	2.01694i
$276$		0			0
$277$	−8.29755	−	6.96247i	−0.498552	−	0.418334i	0.358528	−	0.933519i	$-0.383279\pi$
$277$	−8.29755	−	6.96247i	−0.498552	−	0.418334i	−0.857079	+	0.515185i	$0.827723\pi$
$278$	−2.62513	+	4.54686i	−0.157445	+	0.272703i
$279$		0			0
$280$	0.567702	+	0.983289i	0.0339267	+	0.0587628i
$281$	1.47197	−	8.34795i	0.0878103	−	0.497997i	−0.908904	−	0.417004i	$-0.863080\pi$
$281$	1.47197	−	8.34795i	0.0878103	−	0.497997i	0.996715	−	0.0809924i	$-0.0258089\pi$
$282$		0			0
$283$	−5.92408	−	2.15619i	−0.352150	−	0.128172i	0.159887	−	0.987135i	$-0.448887\pi$
$283$	−5.92408	−	2.15619i	−0.352150	−	0.128172i	−0.512037	+	0.858963i	$0.671109\pi$
$284$	−7.61015	−	2.76987i	−0.451580	−	0.164362i
$285$		0			0
$286$	−3.61709	+	20.5135i	−0.213883	+	1.21299i
$287$	−0.347824	−	0.602448i	−0.0205314	−	0.0355614i
$288$		0			0
$289$	7.85622	−	13.6074i	0.462130	−	0.800434i
$290$	11.8671	+	9.95764i	0.696857	+	0.584733i
$291$		0			0
$292$	2.53549	+	14.3795i	0.148378	+	0.841495i
$293$	1.86383	−	1.56394i	0.108886	−	0.0913662i	−0.586719	−	0.809790i	$-0.699581\pi$
$293$	1.86383	−	1.56394i	0.108886	−	0.0913662i	0.695605	+	0.718424i	$0.255136\pi$
$294$		0			0
$295$	−9.96083	+	3.62544i	−0.579942	+	0.211082i
$296$	−7.58877			−0.441088
$297$		0			0
$298$	−16.2922			−0.943784
$299$	−0.634037	+	0.230771i	−0.0366673	+	0.0133458i
$300$		0			0
$301$	1.73718	−	1.45767i	0.100129	−	0.0840184i
$302$	2.71203	+	15.3807i	0.156060	+	0.885058i
$303$		0			0
$304$	1.42315	+	1.19417i	0.0816233	+	0.0684901i
$305$	−6.20942	+	10.7550i	−0.355550	+	0.615831i
$306$		0			0
$307$	11.8629	+	20.5471i	0.677050	+	1.17269i	0.975865	+	0.218374i	$0.0700754\pi$
$307$	11.8629	+	20.5471i	0.677050	+	1.17269i	−0.298815	+	0.954311i	$0.596591\pi$
$308$	0.247003	−	1.40083i	0.0140743	−	0.0798194i
$309$		0			0
$310$	−2.24303	−	0.816395i	−0.127395	−	0.0463681i
$311$	−10.1493	−	3.69403i	−0.575511	−	0.209469i	0.0378338	−	0.999284i	$-0.487954\pi$
$311$	−10.1493	−	3.69403i	−0.575511	−	0.209469i	−0.613345	+	0.789815i	$0.710176\pi$
$312$		0			0
$313$	−2.75948	+	15.6498i	−0.155975	+	0.884577i	0.801914	+	0.597439i	$0.203815\pi$
$313$	−2.75948	+	15.6498i	−0.155975	+	0.884577i	−0.957889	+	0.287138i	$0.907296\pi$
$314$	8.81577	+	15.2694i	0.497503	+	0.861700i
$315$		0			0
$316$	6.29350	−	10.9007i	0.354037	−	0.613210i
$317$	2.47819	+	2.07944i	0.139189	+	0.116793i	0.709724	−	0.704480i	$-0.248820\pi$
$317$	2.47819	+	2.07944i	0.139189	+	0.116793i	−0.570535	+	0.821273i	$0.693264\pi$
$318$		0			0
$319$	−3.37009	−	19.1127i	−0.188689	−	1.07011i
$320$	−2.72228	+	2.28426i	−0.152180	+	0.127694i
$321$		0			0
$322$	0.0432970	−	0.0157588i	0.00241285	−	0.000878205i
$323$	−2.10805			−0.117295
$324$		0			0
$325$	−35.6925			−1.97986
$326$	−14.9224	+	5.43131i	−0.826475	+	0.300812i
$327$		0			0
$328$	1.66790	−	1.39954i	0.0920946	−	0.0772765i
$329$	−0.572924	−	3.24922i	−0.0315863	−	0.179135i
$330$		0			0
$331$	−13.5311	−	11.3540i	−0.743739	−	0.624071i	0.190100	−	0.981765i	$-0.439119\pi$
$331$	−13.5311	−	11.3540i	−0.743739	−	0.624071i	−0.933839	+	0.357693i	$0.883563\pi$
$332$	−2.70681	+	4.68834i	−0.148556	+	0.257306i
$333$		0			0
$334$	6.78921	+	11.7593i	0.371489	+	0.643438i
$335$	−4.59316	+	26.0491i	−0.250951	+	1.42321i
$336$		0			0
$337$	9.90706	+	3.60588i	0.539672	+	0.196425i	0.597452	−	0.801905i	$-0.296180\pi$
$337$	9.90706	+	3.60588i	0.539672	+	0.196425i	−0.0577798	+	0.998329i	$0.518402\pi$
$338$	8.35441	+	3.04076i	0.454420	+	0.165395i
$339$		0			0
$340$	0.700218	−	3.97113i	0.0379746	−	0.215365i
$341$	1.49520	+	2.58977i	0.0809699	+	0.140244i
$342$		0			0
$343$	−2.22020	+	3.84550i	−0.119879	+	0.207637i
$344$	5.43716	+	4.56232i	0.293152	+	0.245984i
$345$		0			0
$346$	1.11906	+	6.34650i	0.0601610	+	0.341190i
$347$	−24.9000	+	20.8936i	−1.33670	+	1.12163i	−0.354243	+	0.935153i	$0.615261\pi$
$347$	−24.9000	+	20.8936i	−1.33670	+	1.12163i	−0.982460	+	0.186473i	$0.940294\pi$
$348$		0			0
$349$	18.8599	−	6.86444i	1.00955	−	0.367445i	0.216289	−	0.976329i	$-0.430605\pi$
$349$	18.8599	−	6.86444i	1.00955	−	0.367445i	0.793259	+	0.608884i	$0.208383\pi$
$350$	2.43736			0.130282
$351$		0			0
$352$	4.45206			0.237295
$353$	10.3705	−	3.77455i	0.551966	−	0.200899i	−0.0509539	−	0.998701i	$-0.516226\pi$
$353$	10.3705	−	3.77455i	0.551966	−	0.200899i	0.602920	+	0.797802i	$0.294004\pi$
$354$		0			0
$355$	−22.0465	+	18.4992i	−1.17011	+	0.981837i
$356$	−0.877354	−	4.97572i	−0.0464997	−	0.263713i
$357$		0			0
$358$	−9.58494	−	8.04272i	−0.506580	−	0.425071i
$359$	−1.96044	+	3.39557i	−0.103468	+	0.179212i	−0.913111	−	0.407711i	$-0.866327\pi$
$359$	−1.96044	+	3.39557i	−0.103468	+	0.179212i	0.809643	+	0.586922i	$0.199661\pi$
$360$		0			0
$361$	7.77430	+	13.4655i	0.409174	+	0.708710i
$362$	−0.0528764	+	0.299877i	−0.00277912	+	0.0157612i
$363$		0			0
$364$	−1.40471	−	0.511272i	−0.0736268	−	0.0267980i
$365$	48.7591	+	17.7469i	2.55217	+	0.928914i
$366$		0			0
$367$	5.06206	−	28.7084i	0.264237	−	1.49856i	−0.506961	−	0.861969i	$-0.669231\pi$
$367$	5.06206	−	28.7084i	0.264237	−	1.49856i	0.771198	−	0.636595i	$-0.219658\pi$
$368$	0.0721058	+	0.124891i	0.00375878	+	0.00651039i
$369$		0			0
$370$	−13.4840	+	23.3550i	−0.701001	+	1.21417i
$371$	0.197161	+	0.165438i	0.0102361	+	0.00858909i
$372$		0			0
$373$	1.08909	+	6.17653i	0.0563909	+	0.319809i	0.999935	−	0.0114395i	$-0.00364140\pi$
$373$	1.08909	+	6.17653i	0.0563909	+	0.319809i	−0.943544	+	0.331248i	$0.892530\pi$
$374$	−3.86989	+	3.24722i	−0.200107	+	0.167910i
$375$		0			0
$376$	9.70378	−	3.53189i	0.500434	−	0.182143i
$377$	−20.3957			−1.05043
$378$		0			0
$379$	−26.9562			−1.38465			−0.692324	−	0.721587i	$-0.743413\pi$
$379$	−26.9562			−1.38465			−0.692324	+	0.721587i	$0.743413\pi$
$380$	6.20385	−	2.25802i	0.318251	−	0.115834i
$381$		0			0
$382$	−11.0255	+	9.25146i	−0.564111	+	0.473346i
$383$	0.565446	+	3.20680i	0.0288929	+	0.163860i	0.995840	−	0.0911163i	$-0.0290435\pi$
$383$	0.565446	+	3.20680i	0.0288929	+	0.163860i	−0.966947	+	0.254976i	$0.917932\pi$
$384$		0			0
$385$	−3.87226	−	3.24922i	−0.197349	−	0.165595i
$386$	1.52531	−	2.64192i	0.0776364	−	0.134470i
$387$		0			0
$388$	−9.33706	−	16.1723i	−0.474018	−	0.821022i
$389$	−0.241315	+	1.36857i	−0.0122352	+	0.0693891i	−0.990314	−	0.138846i	$-0.955661\pi$
$389$	−0.241315	+	1.36857i	−0.0122352	+	0.0693891i	0.978079	+	0.208235i	$0.0667719\pi$
$390$		0			0
$391$	−0.153770	−	0.0559675i	−0.00777646	−	0.00283040i
$392$	−6.48192	−	2.35923i	−0.327387	−	0.119159i
$393$		0			0
$394$	3.86614	−	21.9260i	0.194773	−	1.10461i
$395$	−22.3651	−	38.7375i	−1.12531	−	1.94909i
$396$		0			0
$397$	−1.07010	+	1.85347i	−0.0537069	+	0.0930230i	−0.891629	−	0.452767i	$-0.850437\pi$
$397$	−1.07010	+	1.85347i	−0.0537069	+	0.0930230i	0.837922	+	0.545790i	$0.183770\pi$
$398$	−18.8167	−	15.7890i	−0.943193	−	0.791433i
$399$		0			0
$400$	1.32470	+	7.51276i	0.0662351	+	0.375638i
$401$	6.55222	−	5.49796i	0.327202	−	0.274555i	−0.464357	−	0.885648i	$-0.653714\pi$
$401$	6.55222	−	5.49796i	0.327202	−	0.274555i	0.791559	+	0.611093i	$0.209270\pi$
$402$		0			0
$403$	2.95314	−	1.07486i	0.147107	−	0.0535424i
$404$	2.41967			0.120383
$405$		0			0
$406$	1.39278			0.0691225
$407$	31.7481	−	11.5554i	1.57369	−	0.572778i
$408$		0			0
$409$	20.8915	−	17.5300i	1.03302	−	0.866804i	0.0418096	−	0.999126i	$-0.486688\pi$
$409$	20.8915	−	17.5300i	1.03302	−	0.866804i	0.991207	+	0.132322i	$0.0422433\pi$
$410$	−1.34359	−	7.61986i	−0.0663550	−	0.376318i
$411$		0			0
$412$	1.52853	+	1.28259i	0.0753052	+	0.0631885i
$413$	−0.476511	+	0.825342i	−0.0234476	+	0.0406124i
$414$		0			0
$415$	9.61916	+	16.6609i	0.472186	+	0.817850i
$416$	0.812454	−	4.60766i	0.0398338	−	0.225909i
$417$		0			0
$418$	−7.77219	−	2.82885i	−0.380150	−	0.138363i
$419$	15.0495	+	5.47757i	0.735216	+	0.267597i	0.682371	−	0.731006i	$-0.260949\pi$
$419$	15.0495	+	5.47757i	0.735216	+	0.267597i	0.0528448	+	0.998603i	$0.483171\pi$
$420$		0			0
$421$	−3.15120	+	17.8713i	−0.153580	+	0.870995i	0.806493	+	0.591244i	$0.201363\pi$
$421$	−3.15120	+	17.8713i	−0.153580	+	0.870995i	−0.960073	+	0.279751i	$0.909748\pi$
$422$	−1.50965	−	2.61480i	−0.0734888	−	0.127286i
$423$		0			0
$424$	−0.402777	+	0.697630i	−0.0195606	+	0.0338799i
$425$	−6.63111	−	5.56416i	−0.321656	−	0.269901i
$426$		0			0
$427$	0.193885	+	1.09958i	0.00938276	+	0.0532123i
$428$	−6.79537	+	5.70199i	−0.328467	+	0.275616i
$429$		0			0
$430$	23.7019	−	8.62677i	1.14301	−	0.416020i
$431$	−2.13698			−0.102935			−0.0514673	−	0.998675i	$-0.516390\pi$
$431$	−2.13698			−0.102935			−0.0514673	+	0.998675i	$0.516390\pi$
$432$		0			0
$433$	25.1733			1.20975			0.604876	−	0.796320i	$-0.293223\pi$
$433$	25.1733			1.20975			0.604876	+	0.796320i	$0.293223\pi$
$434$	−0.201664	+	0.0733996i	−0.00968017	+	0.00352329i
$435$		0			0
$436$	−1.51067	+	1.26760i	−0.0723478	+	0.0607071i
$437$	−0.0465230	−	0.263845i	−0.00222550	−	0.0126214i
$438$		0			0
$439$	19.8037	+	16.6173i	0.945179	+	0.793099i	0.978479	−	0.206346i	$-0.0661573\pi$
$439$	19.8037	+	16.6173i	0.945179	+	0.793099i	−0.0333002	+	0.999445i	$0.510602\pi$
$440$	7.91059	−	13.7015i	0.377123	−	0.653196i
$441$		0			0
$442$	2.65450	+	4.59773i	0.126262	+	0.218692i
$443$	−2.42041	+	13.7268i	−0.114997	+	0.652181i	0.871755	+	0.489943i	$0.162982\pi$
$443$	−2.42041	+	13.7268i	−0.114997	+	0.652181i	−0.986752	+	0.162238i	$0.948129\pi$
$444$		0			0
$445$	−16.8721	−	6.14094i	−0.799814	−	0.291108i
$446$	9.37850	+	3.41350i	0.444085	+	0.161634i
$447$		0			0
$448$	−0.0554807	+	0.314647i	−0.00262122	+	0.0148657i
$449$	14.5769	+	25.2479i	0.687927	+	1.19152i	0.972507	+	0.232872i	$0.0748123\pi$
$449$	14.5769	+	25.2479i	0.687927	+	1.19152i	−0.284581	+	0.958652i	$0.591854\pi$
$450$		0			0
$451$	−4.84672	+	8.39476i	−0.228223	+	0.395294i
$452$	7.37598	+	6.18918i	0.346937	+	0.291114i
$453$		0			0
$454$	−3.66786	−	20.8015i	−0.172141	−	0.976261i
$455$	−4.06943	+	3.41465i	−0.190778	+	0.160081i
$456$		0			0
$457$	−22.3630	+	8.13945i	−1.04609	+	0.380747i	−0.807188	−	0.590295i	$-0.799011\pi$
$457$	−22.3630	+	8.13945i	−1.04609	+	0.380747i	−0.238907	+	0.971042i	$0.576789\pi$
$458$	23.2807			1.08784
$459$		0			0
$460$	0.512482			0.0238946
$461$	28.9550	−	10.5388i	1.34857	−	0.490839i	0.436069	−	0.899913i	$-0.356370\pi$
$461$	28.9550	−	10.5388i	1.34857	−	0.490839i	0.912501	+	0.409074i	$0.134148\pi$
$462$		0			0
$463$	27.6849	−	23.2304i	1.28663	−	1.07961i	0.294334	−	0.955703i	$-0.404902\pi$
$463$	27.6849	−	23.2304i	1.28663	−	1.07961i	0.992294	−	0.123907i	$-0.0395424\pi$
$464$	0.756973	+	4.29301i	0.0351416	+	0.199298i
$465$		0			0
$466$	20.4720	+	17.1780i	0.948347	+	0.795758i
$467$	−18.4877	+	32.0217i	−0.855509	+	1.48179i	0.0206626	+	0.999787i	$0.493422\pi$
$467$	−18.4877	+	32.0217i	−0.855509	+	1.48179i	−0.876172	+	0.481999i	$0.839911\pi$
$468$		0			0
$469$	1.18906	+	2.05952i	0.0549058	+	0.0950996i
$470$	6.37241	−	36.1397i	0.293937	−	1.66700i
$471$		0			0
$472$	−2.80296	−	1.02019i	−0.129017	−	0.0469582i
$473$	−29.6937	−	10.8076i	−1.36532	−	0.496935i
$474$		0			0
$475$	2.46102	−	13.9571i	0.112919	−	0.640398i
$476$	−0.181270	−	0.313969i	−0.00830850	−	0.0143908i
$477$		0			0
$478$	12.0299	−	20.8365i	0.550236	−	0.953037i
$479$	−29.4015	−	24.6708i	−1.34339	−	1.12724i	−0.980741	−	0.195311i	$-0.937429\pi$
$479$	−29.4015	−	24.6708i	−1.34339	−	1.12724i	−0.362647	−	0.931926i	$-0.618127\pi$
$480$		0			0
$481$	−6.16553	−	34.9664i	−0.281124	−	1.59433i
$482$	1.14257	−	0.958731i	0.0520427	−	0.0436690i
$483$		0			0
$484$	−8.28884	+	3.01689i	−0.376765	+	0.137131i
$485$	−66.3619			−3.01334
$486$		0			0
$487$	34.3088			1.55468			0.777339	−	0.629082i	$-0.216569\pi$
$487$	34.3088			1.55468			0.777339	+	0.629082i	$0.216569\pi$
$488$	−3.28389	+	1.19524i	−0.148655	+	0.0541059i
$489$		0			0
$490$	−18.7781	+	15.7567i	−0.848306	+	0.711813i
$491$	3.02281	+	17.1432i	0.136417	+	0.773661i	0.973862	+	0.227139i	$0.0729373\pi$
$491$	3.02281	+	17.1432i	0.136417	+	0.773661i	−0.837445	+	0.546522i	$0.815952\pi$
$492$		0			0
$493$	−3.78921	−	3.17952i	−0.170657	−	0.143199i
$494$	−4.34606	+	7.52760i	−0.195539	+	0.338683i
$495$		0			0
$496$	−0.335846	−	0.581702i	−0.0150799	−	0.0261192i
$497$	−0.449314	+	2.54819i	−0.0201545	+	0.114302i
$498$		0			0
$499$	−24.6982	−	8.98939i	−1.10564	−	0.402421i	−0.276248	−	0.961086i	$-0.589091\pi$
$499$	−24.6982	−	8.98939i	−1.10564	−	0.402421i	−0.829393	+	0.558666i	$0.811313\pi$
$500$	8.77804	+	3.19494i	0.392566	+	0.142882i
$501$		0			0
$502$	2.53091	−	14.3535i	0.112960	−	0.640629i
$503$	−9.08930	−	15.7431i	−0.405272	−	0.701952i	0.589081	−	0.808074i	$-0.299490\pi$
$503$	−9.08930	−	15.7431i	−0.405272	−	0.701952i	−0.994353	+	0.106122i	$0.966157\pi$
$504$		0			0
$505$	4.29937	−	7.44672i	0.191319	−	0.331375i
$506$	−0.491830	−	0.412694i	−0.0218645	−	0.0183465i
$507$		0			0
$508$	0.0276465	+	0.156791i	0.00122661	+	0.00695647i
$509$	18.8746	−	15.8376i	0.836600	−	0.701991i	−0.120196	−	0.992750i	$-0.538352\pi$
$509$	18.8746	−	15.8376i	0.836600	−	0.701991i	0.956796	+	0.290759i	$0.0939078\pi$
$510$		0			0
$511$	4.38379	−	1.59557i	0.193927	−	0.0705838i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−11.0246			−0.486275
$515$	6.66321	−	2.42521i	0.293616	−	0.106868i
$516$		0			0
$517$	−35.2184	+	29.5517i	−1.54890	+	1.29968i
$518$	0.421030	+	2.38778i	0.0184990	+	0.104913i
$519$		0			0
$520$	−12.7368	−	10.6875i	−0.558547	−	0.468676i
$521$	15.0065	−	25.9921i	0.657449	−	1.13873i	−0.323825	−	0.946117i	$-0.604969\pi$
$521$	15.0065	−	25.9921i	0.657449	−	1.13873i	0.981274	−	0.192618i	$-0.0616977\pi$
$522$		0			0
$523$	13.6719	+	23.6804i	0.597829	+	1.03547i	0.993141	+	0.116924i	$0.0373033\pi$
$523$	13.6719	+	23.6804i	0.597829	+	1.03547i	−0.395312	+	0.918547i	$0.629363\pi$
$524$	1.64720	−	9.34172i	0.0719582	−	0.408095i
$525$		0			0
$526$	12.3476	+	4.49416i	0.538381	+	0.195955i
$527$	0.716210	+	0.260679i	0.0311986	+	0.0113554i
$528$		0			0
$529$	−3.99030	+	22.6301i	−0.173491	+	0.983917i
$530$	1.43134	+	2.47916i	0.0621735	+	0.107688i
$531$		0			0
$532$	0.296783	−	0.514044i	0.0128672	−	0.0222866i
$533$	7.80368	+	6.54807i	0.338015	+	0.283628i
$534$		0			0
$535$	5.47404	+	31.0448i	0.236663	+	1.34218i
$536$	−5.70186	+	4.78443i	−0.246283	+	0.206656i
$537$		0			0
$538$	9.68695	−	3.52576i	0.417634	−	0.152006i
$539$	30.7099			1.32277
$540$		0			0
$541$	8.65632			0.372164			0.186082	−	0.982534i	$-0.440421\pi$
$541$	8.65632			0.372164			0.186082	+	0.982534i	$0.440421\pi$
$542$	0.953353	−	0.346992i	0.0409500	−	0.0149046i
$543$		0			0
$544$	0.869237	−	0.729376i	0.0372682	−	0.0312718i
$545$	1.21692	+	6.90152i	0.0521273	+	0.295629i
$546$		0			0
$547$	21.1005	+	17.7055i	0.902194	+	0.757031i	0.970618	−	0.240625i	$-0.0773525\pi$
$547$	21.1005	+	17.7055i	0.902194	+	0.757031i	−0.0684237	+	0.997656i	$0.521797\pi$
$548$	5.85468	−	10.1406i	0.250100	−	0.433185i
$549$		0			0
$550$	−16.9816	−	29.4130i	−0.724097	−	1.25417i
$551$	1.40630	−	7.97552i	0.0599104	−	0.339769i
$552$		0			0
$553$	−3.77903	−	1.37545i	−0.160701	−	0.0584903i
$554$	−10.1785	−	3.70465i	−0.432441	−	0.157396i
$555$		0			0
$556$	−0.911699	+	5.17050i	−0.0386647	+	0.219278i
$557$	−13.0903	−	22.6730i	−0.554653	−	0.960687i	−0.997930	−	0.0643022i	$-0.979518\pi$
$557$	−13.0903	−	22.6730i	−0.554653	−	0.960687i	0.443278	−	0.896384i	$-0.353816\pi$
$558$		0			0
$559$	−16.6042	+	28.7592i	−0.702281	+	1.21639i
$560$	0.869770	+	0.729824i	0.0367545	+	0.0308407i
$561$		0			0
$562$	−1.47197	−	8.34795i	−0.0620912	−	0.352137i
$563$	3.04293	−	2.55332i	0.128244	−	0.107610i	−0.576410	−	0.817161i	$-0.695547\pi$
$563$	3.04293	−	2.55332i	0.128244	−	0.107610i	0.704654	+	0.709551i	$0.251102\pi$
$564$		0			0
$565$	32.1536	−	11.7030i	1.35271	−	0.492347i
$566$	−6.30428			−0.264988
$567$		0			0
$568$	−8.09856			−0.339808
$569$	−38.0492	+	13.8488i	−1.59511	+	0.580571i	−0.978418	−	0.206636i	$-0.933748\pi$
$569$	−38.0492	+	13.8488i	−1.59511	+	0.580571i	−0.616688	+	0.787207i	$0.711526\pi$
$570$		0			0
$571$	29.3406	−	24.6197i	1.22787	−	1.03030i	0.229493	−	0.973310i	$-0.426293\pi$
$571$	29.3406	−	24.6197i	1.22787	−	1.03030i	0.998375	−	0.0569933i	$-0.0181514\pi$
$572$	3.61709	+	20.5135i	0.151238	+	0.857714i
$573$		0			0
$574$	−0.532897	−	0.447153i	−0.0222427	−	0.0186638i
$575$	0.550070	−	0.952749i	0.0229395	−	0.0397324i
$576$		0			0
$577$	−4.13928	−	7.16944i	−0.172320	−	0.298468i	0.766910	−	0.641754i	$-0.221793\pi$
$577$	−4.13928	−	7.16944i	−0.172320	−	0.298468i	−0.939231	+	0.343287i	$0.888460\pi$
$578$	2.72844	−	15.4737i	0.113488	−	0.643622i
$579$		0			0
$580$	14.5571	+	5.29835i	0.604450	+	0.220002i
$581$	1.62535	+	0.591578i	0.0674308	+	0.0245428i
$582$		0			0
$583$	0.622767	−	3.53189i	0.0257924	−	0.146276i
$584$	7.30065	+	12.6451i	0.302103	+	0.523258i
$585$		0			0
$586$	1.21653	−	2.10709i	0.0502543	−	0.0870430i
$587$	10.6808	+	8.96228i	0.440845	+	0.369913i	0.836025	−	0.548691i	$-0.184874\pi$
$587$	10.6808	+	8.96228i	0.440845	+	0.369913i	−0.395181	+	0.918603i	$0.629318\pi$
$588$		0			0
$589$	0.216689	+	1.22891i	0.00892853	+	0.0506362i
$590$	−8.12014	+	6.81361i	−0.334301	+	0.280512i
$591$		0			0
$592$	−7.13111	+	2.59551i	−0.293087	+	0.106675i
$593$	41.2342			1.69329			0.846644	−	0.532160i	$-0.178620\pi$
$593$	41.2342			1.69329			0.846644	+	0.532160i	$0.178620\pi$
$594$		0			0
$595$	−1.28835			−0.0528173
$596$	−15.3097	+	5.57227i	−0.627110	+	0.228249i
$597$		0			0
$598$	−0.516872	+	0.433707i	−0.0211365	+	0.0177356i
$599$	0.544602	+	3.08859i	0.0222518	+	0.126196i	0.993910	−	0.110193i	$-0.0351470\pi$
$599$	0.544602	+	3.08859i	0.0222518	+	0.126196i	−0.971658	+	0.236390i	$0.924036\pi$
$600$		0			0
$601$	−26.6855	−	22.3918i	−1.08853	−	0.913382i	−0.0919256	−	0.995766i	$-0.529302\pi$
$601$	−26.6855	−	22.3918i	−1.08853	−	0.913382i	−0.996601	+	0.0823839i	$0.973747\pi$
$602$	1.13386	−	1.96391i	0.0462128	−	0.0800429i
$603$		0			0
$604$	7.80897	+	13.5255i	0.317742	+	0.550346i
$605$	−5.44323	+	30.8701i	−0.221299	+	1.25505i
$606$		0			0
$607$	0.726574	+	0.264451i	0.0294907	+	0.0107338i	0.356723	−	0.934210i	$-0.383894\pi$
$607$	0.726574	+	0.264451i	0.0294907	+	0.0107338i	−0.327233	+	0.944944i	$0.606116\pi$
$608$	1.74575	+	0.635402i	0.0707997	+	0.0257690i
$609$		0			0
$610$	−2.15651	+	12.2302i	−0.0873145	+	0.495185i
$611$	24.1576	+	41.8422i	0.977312	+	1.69275i
$612$		0			0
$613$	−6.99919	+	12.1230i	−0.282695	+	0.489642i	−0.972048	−	0.234784i	$-0.924562\pi$
$613$	−6.99919	+	12.1230i	−0.282695	+	0.489642i	0.689353	+	0.724426i	$0.257895\pi$
$614$	18.1750	+	15.2506i	0.733483	+	0.615465i
$615$		0			0
$616$	−0.247003	−	1.40083i	−0.00995205	−	0.0564409i
$617$	−8.97302	+	7.52926i	−0.361240	+	0.303117i	−0.805285	−	0.592888i	$-0.797988\pi$
$617$	−8.97302	+	7.52926i	−0.361240	+	0.303117i	0.444045	+	0.896005i	$0.353543\pi$
$618$		0			0
$619$	−45.1425	+	16.4305i	−1.81443	+	0.660398i	−0.818073	+	0.575114i	$0.804958\pi$
$619$	−45.1425	+	16.4305i	−1.81443	+	0.660398i	−0.996357	+	0.0852845i	$0.972820\pi$
$620$	−2.38698			−0.0958634
$621$		0			0
$622$	−10.8006			−0.433065
$623$	−1.51692	+	0.552114i	−0.0607741	+	0.0221200i
$624$		0			0
$625$	−3.78956	+	3.17982i	−0.151583	+	0.127193i
$626$	2.75948	+	15.6498i	0.110291	+	0.625490i
$627$		0			0
$628$	13.5065	+	11.3333i	0.538970	+	0.452249i
$629$	4.30552	−	7.45738i	0.171672	−	0.297345i
$630$		0			0
$631$	−19.7725	−	34.2469i	−0.787130	−	1.36335i	−0.927719	−	0.373280i	$-0.878233\pi$
$631$	−19.7725	−	34.2469i	−0.787130	−	1.36335i	0.140589	−	0.990068i	$-0.455100\pi$
$632$	2.18571	−	12.3958i	0.0869429	−	0.493078i
$633$		0			0
$634$	3.03994	+	1.10645i	0.120732	+	0.0439427i
$635$	0.531660	+	0.193508i	0.0210983	+	0.00767915i
$636$		0			0
$637$	5.60424	−	31.7832i	0.222048	−	1.25930i
$638$	−9.70378	−	16.8074i	−0.384176	−	0.665413i
$639$		0			0
$640$	−1.77684	+	3.07758i	−0.0702358	+	0.121652i
$641$	−0.506596	−	0.425085i	−0.0200093	−	0.0167898i	0.632728	−	0.774374i	$-0.281935\pi$
$641$	−0.506596	−	0.425085i	−0.0200093	−	0.0167898i	−0.652737	+	0.757584i	$0.726380\pi$
$642$		0			0
$643$	0.314901	+	1.78589i	0.0124185	+	0.0704288i	0.990387	−	0.138323i	$-0.0441711\pi$
$643$	0.314901	+	1.78589i	0.0124185	+	0.0704288i	−0.977969	+	0.208752i	$0.933060\pi$
$644$	0.0352961	−	0.0296169i	0.00139086	−	0.00116707i
$645$		0			0
$646$	−1.98092	+	0.720997i	−0.0779383	+	0.0283672i
$647$	−4.13765			−0.162668			−0.0813339	−	0.996687i	$-0.525918\pi$
$647$	−4.13765			−0.162668			−0.0813339	+	0.996687i	$0.525918\pi$
$648$		0			0
$649$	13.2798			0.521278
$650$	−33.5399	+	12.2075i	−1.31554	+	0.478819i
$651$		0			0
$652$	−12.1648	+	10.2075i	−0.476412	+	0.399757i
$653$	−4.66662	−	26.4657i	−0.182619	−	1.03568i	−0.928976	−	0.370139i	$-0.879310\pi$
$653$	−4.66662	−	26.4657i	−0.182619	−	1.03568i	0.746357	−	0.665545i	$-0.231801\pi$
$654$		0			0
$655$	−25.8231	−	21.6681i	−1.00899	−	0.846644i
$656$	1.08865	−	1.88559i	0.0425045	−	0.0736200i
$657$		0			0
$658$	−1.64967	−	2.85731i	−0.0643108	−	0.111390i
$659$	−2.51054	+	14.2380i	−0.0977969	+	0.554634i	0.896058	+	0.443938i	$0.146419\pi$
$659$	−2.51054	+	14.2380i	−0.0977969	+	0.554634i	−0.993854	+	0.110696i	$0.964692\pi$
$660$		0			0
$661$	−20.9378	−	7.62074i	−0.814387	−	0.296413i	−0.0989522	−	0.995092i	$-0.531549\pi$
$661$	−20.9378	−	7.62074i	−0.814387	−	0.296413i	−0.715435	+	0.698680i	$0.753771\pi$
$662$	−16.5984	−	6.04133i	−0.645116	−	0.234803i
$663$		0			0
$664$	−0.940067	+	5.33138i	−0.0364817	+	0.206898i
$665$	−1.05467	−	1.82675i	−0.0408985	−	0.0708382i
$666$		0			0
$667$	0.314326	−	0.544429i	0.0121708	−	0.0210804i
$668$	10.4017	+	8.72804i	0.402453	+	0.337698i
$669$		0			0
$670$	4.59316	+	26.0491i	0.177449	+	1.00636i
$671$	11.9184	−	10.0007i	0.460104	−	0.386073i
$672$		0			0
$673$	−23.4002	+	8.51699i	−0.902012	+	0.328306i	−0.751059	−	0.660235i	$-0.770457\pi$
$673$	−23.4002	+	8.51699i	−0.902012	+	0.328306i	−0.150954	+	0.988541i	$0.548234\pi$
$674$	10.5429			0.406096
$675$		0			0
$676$	8.89058			0.341945
$677$	7.50239	−	2.73065i	0.288340	−	0.104947i	−0.193801	−	0.981041i	$-0.562082\pi$
$677$	7.50239	−	2.73065i	0.288340	−	0.104947i	0.482141	+	0.876094i	$0.339859\pi$
$678$		0			0
$679$	−4.57053	+	3.83513i	−0.175401	+	0.147179i
$680$	−0.700218	−	3.97113i	−0.0268521	−	0.152286i
$681$		0			0
$682$	2.29079	+	1.92220i	0.0877187	+	0.0736048i
$683$	−17.5306	+	30.3639i	−0.670789	+	1.16184i	0.306891	+	0.951745i	$0.400711\pi$
$683$	−17.5306	+	30.3639i	−0.670789	+	1.16184i	−0.977681	+	0.210097i	$0.932622\pi$
$684$		0			0
$685$	−20.8057	−	36.0365i	−0.794944	−	1.37688i
$686$	−0.771067	+	4.37294i	−0.0294395	+	0.166960i
$687$		0			0
$688$	6.66967	+	2.42756i	0.254279	+	0.0925498i
$689$	−3.54168	−	1.28907i	−0.134927	−	0.0491095i
$690$		0			0
$691$	−0.344177	+	1.95193i	−0.0130931	+	0.0742548i	−0.990654	−	0.136397i	$-0.956448\pi$
$691$	−0.344177	+	1.95193i	−0.0130931	+	0.0742548i	0.977561	+	0.210652i	$0.0675587\pi$
$692$	3.22220	+	5.58102i	0.122490	+	0.212159i
$693$		0			0
$694$	−16.2523	+	28.1499i	−0.616930	+	1.06855i
$695$	14.2927	+	11.9930i	0.542152	+	0.454920i
$696$		0			0
$697$	0.429014	+	2.43306i	0.0162501	+	0.0921587i
$698$	15.3747	−	12.9009i	0.581942	−	0.488308i
$699$		0			0
$700$	2.29037	−	0.833627i	0.0865679	−	0.0315081i
$701$	−42.8694			−1.61916			−0.809578	−	0.587013i	$-0.800304\pi$
$701$	−42.8694			−1.61916			−0.809578	+	0.587013i	$0.800304\pi$
$702$		0			0
$703$	14.0984			0.531730
$704$	4.18356	−	1.52269i	0.157674	−	0.0573886i
$705$		0			0
$706$	8.45411	−	7.09384i	0.318174	−	0.266980i
$707$	−0.134245	−	0.761342i	−0.00504881	−	0.0286332i
$708$		0			0
$709$	26.9016	+	22.5731i	1.01031	+	0.847752i	0.988379	−	0.152008i	$-0.0485738\pi$
$709$	26.9016	+	22.5731i	1.01031	+	0.847752i	0.0219320	+	0.999759i	$0.493018\pi$
$710$	−14.3898	+	24.9239i	−0.540041	+	0.935379i
$711$		0			0
$712$	−2.52624	−	4.37558i	−0.0946748	−	0.163982i
$713$	−0.0168206	+	0.0953942i	−0.000629935	+	0.00357254i
$714$		0			0
$715$	69.5590	+	25.3174i	2.60136	+	0.946818i
$716$	−11.7577	−	4.27944i	−0.439405	−	0.159930i
$717$		0			0
$718$	−0.680852	+	3.86130i	−0.0254092	+	0.144103i
$719$	7.52422	+	13.0323i	0.280606	+	0.486024i	0.971534	−	0.236899i	$-0.0761312\pi$
$719$	7.52422	+	13.0323i	0.280606	+	0.486024i	−0.690928	+	0.722924i	$0.742798\pi$
$720$		0			0
$721$	0.318758	−	0.552105i	0.0118712	−	0.0205615i
$722$	11.9109	+	9.99445i	0.443279	+	0.371955i
$723$		0			0
$724$	0.0528764	+	0.299877i	0.00196513	+	0.0111448i
$725$	25.4749	−	21.3760i	0.946113	−	0.793883i
$726$		0			0
$727$	−13.7436	+	5.00226i	−0.509721	+	0.185523i	−0.584061	−	0.811710i	$-0.698537\pi$
$727$	−13.7436	+	5.00226i	−0.509721	+	0.185523i	0.0743399	+	0.997233i	$0.476315\pi$
$728$	−1.49486			−0.0554032
$729$		0			0
$730$	51.8884			1.92048
$731$	−7.56813	+	2.75457i	−0.279917	+	0.101882i
$732$		0			0
$733$	11.5481	−	9.69000i	0.426539	−	0.357908i	−0.404105	−	0.914713i	$-0.632417\pi$
$733$	11.5481	−	9.69000i	0.426539	−	0.357908i	0.830644	+	0.556804i	$0.187973\pi$
$734$	−5.06206	−	28.7084i	−0.186844	−	1.05964i
$735$		0			0
$736$	0.110473	+	0.0926974i	0.00407207	+	0.00341687i
$737$	16.5689	−	28.6981i	0.610322	−	1.05711i
$738$		0			0
$739$	−23.9031	−	41.4014i	−0.879290	−	1.52297i	−0.852122	−	0.523343i	$-0.824685\pi$
$739$	−23.9031	−	41.4014i	−0.879290	−	1.52297i	−0.0271676	−	0.999631i	$-0.508649\pi$
$740$	−4.68296	+	26.5584i	−0.172149	+	0.976305i
$741$		0			0
$742$	0.241854	+	0.0880275i	0.00887873	+	0.00323159i
$743$	−43.7125	−	15.9101i	−1.60366	−	0.583683i	−0.623485	−	0.781835i	$-0.714284\pi$
$743$	−43.7125	−	15.9101i	−1.60366	−	0.583683i	−0.980171	+	0.198152i	$0.936506\pi$
$744$		0			0
$745$	−10.0538	+	57.0178i	−0.368342	+	2.08897i
$746$	3.13591	+	5.43155i	0.114814	+	0.198863i
$747$		0			0
$748$	−2.52589	+	4.37497i	−0.0923558	+	0.159965i
$749$	2.17113	+	1.82179i	0.0793312	+	0.0665668i
$750$		0			0
$751$	0.306626	+	1.73897i	0.0111890	+	0.0634557i	0.989891	−	0.141830i	$-0.0452987\pi$
$751$	0.306626	+	1.73897i	0.0111890	+	0.0634557i	−0.978702	+	0.205286i	$0.934188\pi$
$752$	7.91059	−	6.63778i	0.288470	−	0.242055i
$753$		0			0
$754$	−19.1657	+	6.97575i	−0.697974	+	0.254042i
$755$	55.5012			2.01989
$756$		0			0
$757$	3.34143			0.121446			0.0607232	−	0.998155i	$-0.480659\pi$
$757$	3.34143			0.121446			0.0607232	+	0.998155i	$0.480659\pi$
$758$	−25.3306	+	9.21957i	−0.920048	+	0.334870i
$759$		0			0
$760$	5.05743	−	4.24369i	0.183452	−	0.153935i
$761$	−8.29207	−	47.0267i	−0.300587	−	1.70472i	−0.643581	−	0.765378i	$-0.722552\pi$
$761$	−8.29207	−	47.0267i	−0.300587	−	1.70472i	0.342994	−	0.939338i	$-0.388559\pi$
$762$		0			0
$763$	0.482660	+	0.404999i	0.0174735	+	0.0146620i
$764$	−7.19635	+	12.4645i	−0.260355	+	0.450948i
$765$		0			0
$766$	1.62814	+	2.82001i	0.0588269	+	0.101891i
$767$	2.42343	−	13.7439i	0.0875049	−	0.496265i
$768$		0			0
$769$	6.37595	+	2.32066i	0.229923	+	0.0836850i	0.454412	−	0.890791i	$-0.349849\pi$
$769$	6.37595	+	2.32066i	0.229923	+	0.0836850i	−0.224490	+	0.974476i	$0.572071\pi$
$770$	−4.75004	−	1.72887i	−0.171179	−	0.0623042i
$771$		0			0
$772$	0.529736	−	3.00428i	0.0190656	−	0.108126i
$773$	−15.0683	−	26.0991i	−0.541970	−	0.938720i	−0.998791	−	0.0491615i	$-0.984345\pi$
$773$	−15.0683	−	26.0991i	−0.541970	−	0.938720i	0.456820	−	0.889559i	$-0.348988\pi$
$774$		0			0
$775$	−2.56205	+	4.43760i	−0.0920316	+	0.159403i
$776$	−14.3052	−	12.0035i	−0.513527	−	0.430900i
$777$		0			0
$778$	0.241315	+	1.36857i	0.00865158	+	0.0490655i
$779$	−3.09862	+	2.60005i	−0.111020	+	0.0931565i
$780$		0			0
$781$	33.8808	−	12.3316i	1.21235	−	0.441260i
$782$	−0.163638			−0.00585169
$783$		0			0
$784$	−6.89792			−0.246354
$785$	58.8782	−	21.4299i	2.10145	−	0.764866i
$786$		0			0
$787$	12.3752	−	10.3840i	0.441127	−	0.370150i	−0.395004	−	0.918679i	$-0.629257\pi$
$787$	12.3752	−	10.3840i	0.441127	−	0.370150i	0.836131	+	0.548530i	$0.184812\pi$
$788$	−3.86614	−	21.9260i	−0.137725	−	0.781080i
$789$		0			0
$790$	−34.2653	−	28.7520i	−1.21911	−	1.02295i
$791$	1.53818	−	2.66421i	0.0546914	−	0.0947284i
$792$		0			0
$793$	−8.17525	−	14.1599i	−0.290312	−	0.502835i
$794$	−0.371642	+	2.10769i	−0.0131891	+	0.0747991i
$795$		0			0
$796$	−23.0820	−	8.40117i	−0.818121	−	0.297772i
$797$	−0.518033	−	0.188548i	−0.0183497	−	0.00667873i	0.332829	−	0.942987i	$-0.391997\pi$
$797$	−0.518033	−	0.188548i	−0.0183497	−	0.00667873i	−0.351179	+	0.936308i	$0.614219\pi$
$798$		0			0
$799$	−2.03474	+	11.5396i	−0.0719840	+	0.408242i
$800$	3.81433	+	6.60661i	0.134857	+	0.233579i
$801$		0			0
$802$	4.27666	−	7.40739i	0.151014	−	0.261564i
$803$	−49.7973	−	41.7849i	−1.75731	−	1.47456i
$804$		0			0
$805$	−0.0284329	−	0.161251i	−0.00100213	−	0.00568335i
$806$	2.40742	−	2.02007i	0.0847979	−	0.0711539i
$807$		0			0
$808$	2.27375	−	0.827576i	0.0799901	−	0.0291140i
$809$	3.04561			0.107078			0.0535389	−	0.998566i	$-0.482950\pi$
$809$	3.04561			0.107078			0.0535389	+	0.998566i	$0.482950\pi$
$810$		0			0
$811$	−7.71732			−0.270992			−0.135496	−	0.990778i	$-0.543263\pi$
$811$	−7.71732			−0.270992			−0.135496	+	0.990778i	$0.543263\pi$
$812$	1.30878	−	0.476359i	0.0459293	−	0.0167169i
$813$		0			0
$814$	25.8813	−	21.7170i	0.907138	−	0.761179i
$815$	9.79944	+	55.5754i	0.343259	+	1.94672i
$816$		0			0
$817$	−10.1011	−	8.47584i	−0.353393	−	0.296532i
$818$	13.6359	−	23.6181i	0.476769	−	0.825789i
$819$		0			0
$820$	−3.86870	−	6.70079i	−0.135101	−	0.234002i
$821$	−4.07282	+	23.0981i	−0.142142	+	0.806129i	0.827475	+	0.561502i	$0.189776\pi$
$821$	−4.07282	+	23.0981i	−0.142142	+	0.806129i	−0.969617	+	0.244627i	$0.921335\pi$
$822$		0			0
$823$	28.0764	+	10.2190i	0.978683	+	0.356211i	0.781328	−	0.624121i	$-0.214543\pi$
$823$	28.0764	+	10.2190i	0.978683	+	0.356211i	0.197355	+	0.980332i	$0.436765\pi$
$824$	1.87502	+	0.682450i	0.0653193	+	0.0237743i
$825$		0			0
$826$	−0.165491	+	0.938544i	−0.00575816	+	0.0326561i
$827$	−9.72093	−	16.8371i	−0.338030	−	0.585485i	0.646032	−	0.763310i	$-0.276427\pi$
$827$	−9.72093	−	16.8371i	−0.338030	−	0.585485i	−0.984062	+	0.177825i	$0.943094\pi$
$828$		0			0
$829$	5.13594	−	8.89571i	0.178379	−	0.308961i	−0.762947	−	0.646461i	$-0.776248\pi$
$829$	5.13594	−	8.89571i	0.178379	−	0.308961i	0.941325	+	0.337501i	$0.109581\pi$
$830$	14.7374	+	12.3661i	0.511543	+	0.429235i
$831$		0			0
$832$	−0.812454	−	4.60766i	−0.0281668	−	0.159742i
$833$	5.99593	−	5.03118i	0.207747	−	0.174320i
$834$		0			0
$835$	45.3433	−	16.5036i	1.56917	−	0.571132i
$836$	−8.27099			−0.286058
$837$		0			0
$838$	16.0153			0.553241
$839$	−12.6630	+	4.60894i	−0.437174	+	0.159118i	−0.551225	−	0.834357i	$-0.685839\pi$
$839$	−12.6630	+	4.60894i	−0.437174	+	0.159118i	0.114051	+	0.993475i	$0.463617\pi$
$840$		0			0
$841$	−7.65820	+	6.42599i	−0.264076	+	0.221586i
$842$	3.15120	+	17.8713i	0.108597	+	0.615887i
$843$		0			0
$844$	−2.31292	−	1.94077i	−0.0796141	−	0.0668042i
$845$	15.7971	−	27.3614i	0.543438	−	0.941262i
$846$		0			0
$847$	1.40913	+	2.44068i	0.0484181	+	0.0838627i
$848$	−0.139883	+	0.793316i	−0.00480360	+	0.0272426i
$849$		0			0
$850$	−8.13426	−	2.96063i	−0.279003	−	0.101549i
$851$	1.02839	+	0.374303i	0.0352527	+	0.0128309i
$852$		0			0
$853$	8.25045	−	46.7906i	0.282490	−	1.60208i	−0.431625	−	0.902053i	$-0.642060\pi$
$853$	8.25045	−	46.7906i	0.282490	−	1.60208i	0.714115	−	0.700028i	$-0.246829\pi$
$854$	0.558270	+	0.966953i	0.0191036	+	0.0330884i
$855$		0			0
$856$	−4.43536	+	7.68227i	−0.151598	+	0.262575i
$857$	−17.7848	−	14.9232i	−0.607516	−	0.509766i	0.286336	−	0.958129i	$-0.407563\pi$
$857$	−17.7848	−	14.9232i	−0.607516	−	0.509766i	−0.893851	+	0.448363i	$0.852007\pi$
$858$		0			0
$859$	3.20736	+	18.1898i	0.109434	+	0.620629i	0.989356	+	0.145513i	$0.0464831\pi$
$859$	3.20736	+	18.1898i	0.109434	+	0.620629i	−0.879923	+	0.475117i	$0.842406\pi$
$860$	19.3219	−	16.2130i	0.658873	−	0.552860i
$861$		0			0
$862$	−2.00810	+	0.730889i	−0.0683962	+	0.0248942i
$863$	21.1288			0.719233			0.359616	−	0.933100i	$-0.382908\pi$
$863$	21.1288			0.719233			0.359616	+	0.933100i	$0.382908\pi$
$864$		0			0
$865$	22.9014			0.778670
$866$	23.6552	−	8.60978i	0.803836	−	0.292572i
$867$		0			0
$868$	−0.164398	+	0.137946i	−0.00558003	+	0.00468220i
$869$	9.73090	+	55.1867i	0.330098	+	1.87208i
$870$		0			0
$871$	−26.6775	−	22.3851i	−0.903932	−	0.758489i
$872$	−0.986018	+	1.70783i	−0.0333908	+	0.0578345i
$873$		0			0
$874$	−0.133958	−	0.232021i	−0.00453118	−	0.00784824i
$875$	0.518268	−	2.93924i	0.0175206	−	0.0993645i
$876$		0			0
$877$	−15.2356	−	5.54531i	−0.514471	−	0.187252i	0.0717206	−	0.997425i	$-0.477151\pi$
$877$	−15.2356	−	5.54531i	−0.514471	−	0.187252i	−0.586191	+	0.810173i	$0.699373\pi$
$878$	24.2928	+	8.84187i	0.819843	+	0.298399i
$879$		0			0
$880$	2.74732	−	15.5808i	0.0926121	−	0.525230i
$881$	22.2510	+	38.5398i	0.749655	+	1.29844i	0.947988	+	0.318306i	$0.103114\pi$
$881$	22.2510	+	38.5398i	0.749655	+	1.29844i	−0.198333	+	0.980135i	$0.563553\pi$
$882$		0			0
$883$	−8.13325	+	14.0872i	−0.273706	+	0.474072i	−0.969808	−	0.243871i	$-0.921583\pi$
$883$	−8.13325	+	14.0872i	−0.273706	+	0.474072i	0.696102	+	0.717943i	$0.254916\pi$
$884$	4.06693	+	3.41256i	0.136786	+	0.114777i
$885$		0			0
$886$	2.42041	+	13.7268i	0.0813152	+	0.461162i
$887$	−15.7565	+	13.2213i	−0.529052	+	0.443928i	−0.867774	−	0.496959i	$-0.834450\pi$
$887$	−15.7565	+	13.2213i	−0.529052	+	0.443928i	0.338722	+	0.940887i	$0.390005\pi$
$888$		0			0
$889$	0.0478000	−	0.0173978i	0.00160316	−	0.000583502i
$890$	−17.9549			−0.601850
$891$		0			0
$892$	9.98040			0.334168
$893$	−18.0276	+	6.56151i	−0.603271	+	0.219573i
$894$		0			0
$895$	−34.0618	+	28.5813i	−1.13856	+	0.955367i
$896$	0.0554807	+	0.314647i	0.00185348	+	0.0105116i
$897$		0			0
$898$	22.3331	+	18.7397i	0.745266	+	0.625352i
$899$	−1.46403	+	2.53578i	−0.0488282	+	0.0845729i
$900$		0			0
$901$	−0.457035	−	0.791607i	−0.0152260	−	0.0263723i
$902$	−1.68325	+	9.54617i	−0.0560460	+	0.317853i
$903$		0			0
$904$	9.04797	+	3.29319i	0.300931	+	0.109530i
$905$	1.01685	+	0.370102i	0.0338011	+	0.0123026i
$906$		0			0
$907$	2.87345	−	16.2961i	0.0954113	−	0.541104i	−0.899209	−	0.437519i	$-0.855857\pi$
$907$	2.87345	−	16.2961i	0.0954113	−	0.541104i	0.994621	−	0.103585i	$-0.0330315\pi$
$908$	−10.5612	−	18.2925i	−0.350485	−	0.607058i
$909$		0			0
$910$	−2.65613	+	4.60055i	−0.0880498	+	0.152507i
$911$	−20.5555	−	17.2481i	−0.681033	−	0.571454i	0.235275	−	0.971929i	$-0.424401\pi$
$911$	−20.5555	−	17.2481i	−0.681033	−	0.571454i	−0.916308	+	0.400474i	$0.868845\pi$
$912$		0			0
$913$	−4.18523	−	23.7356i	−0.138511	−	0.785534i
$914$	−18.2304	+	15.2972i	−0.603010	+	0.505985i
$915$		0			0
$916$	21.8767	−	7.96248i	0.722828	−	0.263088i
$917$	−3.03073			−0.100084
$918$		0			0
$919$	−26.3725			−0.869947			−0.434974	−	0.900443i	$-0.643242\pi$
$919$	−26.3725			−0.869947			−0.434974	+	0.900443i	$0.643242\pi$
$920$	0.481576	−	0.175279i	0.0158771	−	0.00577879i
$921$		0			0
$922$	23.6044	−	19.8064i	0.777368	−	0.652289i
$923$	−6.57970	−	37.3154i	−0.216574	−	1.22825i
$924$		0			0
$925$	44.3479	+	37.2123i	1.45815	+	1.22353i
$926$	18.0701	−	31.2983i	0.593819	−	1.02852i
$927$		0			0
$928$	2.17962	+	3.77521i	0.0715495	+	0.123927i
$929$	−7.43411	+	42.1609i	−0.243905	+	1.38326i	0.579116	+	0.815245i	$0.303398\pi$
$929$	−7.43411	+	42.1609i	−0.243905	+	1.38326i	−0.823021	+	0.568011i	$0.807713\pi$
$930$		0			0
$931$	12.0421	+	4.38296i	0.394663	+	0.143646i
$932$	25.1126	+	9.14025i	0.822591	+	0.299399i
$933$		0			0
$934$	−6.42071	+	36.4137i	−0.210092	+	1.19149i
$935$	8.97622	+	15.5473i	0.293554	+	0.508450i
$936$		0			0
$937$	7.07409	−	12.2527i	0.231100	−	0.400278i	−0.727032	−	0.686604i	$-0.759101\pi$
$937$	7.07409	−	12.2527i	0.231100	−	0.400278i	0.958132	+	0.286326i	$0.0924341\pi$
$938$	1.82175	+	1.52863i	0.0594822	+	0.0499115i
$939$		0			0
$940$	−6.37241	−	36.1397i	−0.207845	−	1.17875i
$941$	−19.8548	+	16.6602i	−0.647249	+	0.543107i	−0.906235	−	0.422775i	$-0.861056\pi$
$941$	−19.8548	+	16.6602i	−0.647249	+	0.543107i	0.258986	+	0.965881i	$0.416612\pi$
$942$		0			0
$943$	−0.295055	+	0.107391i	−0.00960831	+	0.00349714i
$944$	−2.98285			−0.0970834
$945$		0			0
$946$	−31.5994			−1.02738
$947$	15.4336	−	5.61735i	0.501523	−	0.182539i	−0.0788559	−	0.996886i	$-0.525127\pi$
$947$	15.4336	−	5.61735i	0.501523	−	0.182539i	0.580379	+	0.814347i	$0.302904\pi$
$948$		0			0
$949$	−52.3328	+	43.9125i	−1.69880	+	1.42546i
$950$	−2.46102	−	13.9571i	−0.0798461	−	0.452830i
$951$		0			0
$952$	−0.277722	−	0.233036i	−0.00900102	−	0.00755275i
$953$	−18.6267	+	32.2624i	−0.603379	+	1.04508i	0.388927	+	0.921269i	$0.372846\pi$
$953$	−18.6267	+	32.2624i	−0.603379	+	1.04508i	−0.992305	+	0.123814i	$0.960487\pi$
$954$		0			0
$955$	25.5736	+	44.2947i	0.827541	+	1.43334i
$956$	4.17795	−	23.6943i	0.135125	−	0.766330i
$957$		0			0
$958$	−36.0663	−	13.1271i	−1.16525	−	0.424116i
$959$	−3.51553	−	1.27955i	−0.113522	−	0.0413188i
$960$		0			0
$961$	−5.30475	+	30.0847i	−0.171121	+	0.970475i
$962$	−17.7529	−	30.7490i	−0.572377	−	0.991386i
$963$		0			0
$964$	0.745760	−	1.29169i	0.0240193	−	0.0416027i
$965$	−8.30465	−	6.96843i	−0.267336	−	0.224322i
$966$		0			0
$967$	−1.72904	−	9.80587i	−0.0556022	−	0.315336i	0.944303	−	0.329076i	$-0.106737\pi$
$967$	−1.72904	−	9.80587i	−0.0556022	−	0.315336i	−0.999906	+	0.0137404i	$0.995626\pi$
$968$	−6.75712	+	5.66990i	−0.217182	+	0.182237i
$969$		0			0
$970$	−62.3598	+	22.6971i	−2.00225	+	0.728760i
$971$	−2.62332			−0.0841864			−0.0420932	−	0.999114i	$-0.513403\pi$
$971$	−2.62332			−0.0841864			−0.0420932	+	0.999114i	$0.513403\pi$
$972$		0			0
$973$	1.67746			0.0537771
$974$	32.2397	−	11.7343i	1.03303	−	0.375991i
$975$		0			0
$976$	−2.67705	+	2.24631i	−0.0856903	+	0.0719027i
$977$	1.15268	+	6.53720i	0.0368776	+	0.209143i	0.997679	−	0.0680947i	$-0.0216920\pi$
$977$	1.15268	+	6.53720i	0.0368776	+	0.209143i	−0.960801	+	0.277238i	$0.910581\pi$
$978$		0			0
$979$	17.2313	+	14.4588i	0.550716	+	0.462106i
$980$	−12.2565	+	21.2289i	−0.391520	+	0.678132i
$981$		0			0
$982$	8.70382	+	15.0755i	0.277750	+	0.481077i
$983$	8.23026	−	46.6761i	0.262504	−	1.48874i	−0.513544	−	0.858063i	$-0.671668\pi$
$983$	8.23026	−	46.6761i	0.262504	−	1.48874i	0.776048	−	0.630673i	$-0.217221\pi$
$984$		0			0
$985$	−74.3484	−	27.0606i	−2.36894	−	0.862222i
$986$	−4.64815	−	1.69179i	−0.148027	−	0.0538775i
$987$		0			0
$988$	−1.50937	+	8.56007i	−0.0480195	+	0.272332i
$989$	−0.511786	−	0.886440i	−0.0162739	−	0.0281871i
$990$		0			0
$991$	−22.0574	+	38.2046i	−0.700678	+	1.21361i	0.267551	+	0.963544i	$0.413786\pi$
$991$	−22.0574	+	38.2046i	−0.700678	+	1.21361i	−0.968229	+	0.250066i	$0.919548\pi$
$992$	−0.514546	−	0.431755i	−0.0163368	−	0.0137082i
$993$		0			0
$994$	0.449314	+	2.54819i	0.0142514	+	0.0808236i
$995$	−66.8684	+	56.1092i	−2.11987	+	1.77878i
$996$		0			0
$997$	−46.8105	+	17.0376i	−1.48250	+	0.539587i	−0.951464	−	0.307761i	$-0.900420\pi$
$997$	−46.8105	+	17.0376i	−1.48250	+	0.539587i	−0.531039	+	0.847348i	$0.678198\pi$
$998$	−26.2832			−0.831981
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.e.b.19.1		12
3.2	odd	2		54.2.e.b.7.1	✓	12
9.2	odd	6		486.2.e.f.379.1		12
9.4	even	3		486.2.e.e.217.1		12
9.5	odd	6		486.2.e.h.217.2		12
9.7	even	3		486.2.e.g.379.2		12
12.11	even	2		432.2.u.b.385.2		12
27.2	odd	18		1458.2.a.g.1.6		6
27.4	even	9	inner	162.2.e.b.145.1		12
27.5	odd	18		486.2.e.h.271.2		12
27.7	even	9		1458.2.c.g.487.6		12
27.11	odd	18		1458.2.c.f.973.1		12
27.13	even	9		486.2.e.g.109.2		12
27.14	odd	18		486.2.e.f.109.1		12
27.16	even	9		1458.2.c.g.973.6		12
27.20	odd	18		1458.2.c.f.487.1		12
27.22	even	9		486.2.e.e.271.1		12
27.23	odd	18		54.2.e.b.31.1	yes	12
27.25	even	9		1458.2.a.f.1.1		6
108.23	even	18		432.2.u.b.193.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.b.7.1	✓	12	3.2	odd	2
54.2.e.b.31.1	yes	12	27.23	odd	18
162.2.e.b.19.1		12	1.1	even	1	trivial
162.2.e.b.145.1		12	27.4	even	9	inner
432.2.u.b.193.2		12	108.23	even	18
432.2.u.b.385.2		12	12.11	even	2
486.2.e.e.217.1		12	9.4	even	3
486.2.e.e.271.1		12	27.22	even	9
486.2.e.f.109.1		12	27.14	odd	18
486.2.e.f.379.1		12	9.2	odd	6
486.2.e.g.109.2		12	27.13	even	9
486.2.e.g.379.2		12	9.7	even	3
486.2.e.h.217.2		12	9.5	odd	6
486.2.e.h.271.2		12	27.5	odd	18
1458.2.a.f.1.1		6	27.25	even	9
1458.2.a.g.1.6		6	27.2	odd	18
1458.2.c.f.487.1		12	27.20	odd	18
1458.2.c.f.973.1		12	27.11	odd	18
1458.2.c.g.487.6		12	27.7	even	9
1458.2.c.g.973.6		12	27.16	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)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(0.766044 - 0.642788i) q^{4} +(-0.617090 - 3.49969i) q^{5} +(-0.244752 - 0.205371i) q^{7} +(0.500000 - 0.866025i) q^{8} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(0.766044 - 0.642788i) q^{4} +(-0.617090 - 3.49969i) q^{5} +(-0.244752 - 0.205371i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.77684 - 3.07758i) q^{10} +(-0.773091 + 4.38442i) q^{11} +(4.39657 + 1.60022i) q^{13} +(-0.300233 - 0.109276i) q^{14} +(0.173648 - 0.984808i) q^{16} +(0.567354 + 0.982686i) q^{17} +(-0.928896 + 1.60890i) q^{19} +(-2.72228 - 2.28426i) q^{20} +(0.773091 + 4.38442i) q^{22} +(-0.110473 + 0.0926974i) q^{23} +(-7.16859 + 2.60915i) q^{25} +4.67874 q^{26} -0.319501 q^{28} +(-4.09634 + 1.49095i) q^{29} +(0.514546 - 0.431755i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(0.869237 + 0.729376i) q^{34} +(-0.567702 + 0.983289i) q^{35} +(-3.79438 - 6.57207i) q^{37} +(-0.322602 + 1.82957i) q^{38} +(-3.33937 - 1.21543i) q^{40} +(2.04599 + 0.744678i) q^{41} +(-1.23250 + 6.98988i) q^{43} +(2.22603 + 3.85559i) q^{44} +(-0.0721058 + 0.124891i) q^{46} +(7.91059 + 6.63778i) q^{47} +(-1.19781 - 6.79312i) q^{49} +(-5.84389 + 4.90360i) q^{50} +(4.39657 - 1.60022i) q^{52} -0.805554 q^{53} +15.8212 q^{55} +(-0.300233 + 0.109276i) q^{56} +(-3.33937 + 2.80206i) q^{58} +(-0.517966 - 2.93753i) q^{59} +(-2.67705 - 2.24631i) q^{61} +(0.335846 - 0.581702i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(2.88720 - 16.3741i) q^{65} +(-6.99437 - 2.54574i) q^{67} +(1.06628 + 0.388093i) q^{68} +(-0.197161 + 1.11816i) q^{70} +(-4.04928 - 7.01356i) q^{71} +(-7.30065 + 12.6451i) q^{73} +(-5.81333 - 4.87797i) q^{74} +(0.322602 + 1.82957i) q^{76} +(1.08965 - 0.914324i) q^{77} +(11.8279 - 4.30501i) q^{79} -3.55368 q^{80} +2.17729 q^{82} +(-5.08715 + 1.85157i) q^{83} +(3.08899 - 2.59197i) q^{85} +(1.23250 + 6.98988i) q^{86} +(3.41047 + 2.86173i) q^{88} +(2.52624 - 4.37558i) q^{89} +(-0.747430 - 1.29459i) q^{91} +(-0.0250421 + 0.142021i) q^{92} +(9.70378 + 3.53189i) q^{94} +(6.20385 + 2.25802i) q^{95} +(3.24273 - 18.3904i) q^{97} +(-3.44896 - 5.97377i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more