LMFDB - Embedded newform 162.2.e.b.19.2

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			19.2
Root			$0.500000 + 1.96356i$ of defining polynomial
Character	$\chi$	$=$	162.19
Dual form			162.2.e.b.145.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(0.766044 - 0.642788i) q^{4} +(0.177398 + 1.00607i) q^{5} +(2.04289 + 1.71418i) q^{7} +(0.500000 - 0.866025i) q^{8} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(0.766044 - 0.642788i) q^{4} +(0.177398 + 1.00607i) q^{5} +(2.04289 + 1.71418i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.510796 + 0.884725i) q^{10} +(0.720058 - 4.08365i) q^{11} +(-3.68356 - 1.34071i) q^{13} +(2.50597 + 0.912098i) q^{14} +(0.173648 - 0.984808i) q^{16} +(-0.925795 - 1.60352i) q^{17} +(-3.21653 + 5.57120i) q^{19} +(0.782585 + 0.656667i) q^{20} +(-0.720058 - 4.08365i) q^{22} +(-6.69746 + 5.61984i) q^{23} +(3.71775 - 1.35315i) q^{25} -3.91997 q^{26} +2.66680 q^{28} +(1.17759 - 0.428609i) q^{29} +(-2.56758 + 2.15445i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-1.41840 - 1.19018i) q^{34} +(-1.36219 + 2.35938i) q^{35} +(-4.58887 - 7.94816i) q^{37} +(-1.11709 + 6.33533i) q^{38} +(0.959983 + 0.349405i) q^{40} +(3.53914 + 1.28814i) q^{41} +(0.536567 - 3.04303i) q^{43} +(-2.07332 - 3.59110i) q^{44} +(-4.37146 + 7.57159i) q^{46} +(2.11809 + 1.77729i) q^{47} +(0.0194152 + 0.110109i) q^{49} +(3.03074 - 2.54309i) q^{50} +(-3.68356 + 1.34071i) q^{52} +0.231576 q^{53} +4.23618 q^{55} +(2.50597 - 0.912098i) q^{56} +(0.959983 - 0.805521i) q^{58} +(-0.613793 - 3.48099i) q^{59} +(0.405075 + 0.339899i) q^{61} +(-1.67587 + 2.90269i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(0.695393 - 3.94377i) q^{65} +(7.67276 + 2.79266i) q^{67} +(-1.73993 - 0.633281i) q^{68} +(-0.473084 + 2.68299i) q^{70} +(4.03086 + 6.98165i) q^{71} +(1.57397 - 2.72620i) q^{73} +(-7.03056 - 5.89934i) q^{74} +(1.11709 + 6.33533i) q^{76} +(8.47113 - 7.10812i) q^{77} +(2.43473 - 0.886167i) q^{79} +1.02159 q^{80} +3.76627 q^{82} +(-7.55488 + 2.74975i) q^{83} +(1.44903 - 1.21588i) q^{85} +(-0.536567 - 3.04303i) q^{86} +(-3.17652 - 2.66541i) q^{88} +(6.12693 - 10.6122i) q^{89} +(-5.22688 - 9.05322i) q^{91} +(-1.51819 + 8.61009i) q^{92} +(2.59823 + 0.945677i) q^{94} +(-6.17564 - 2.24775i) q^{95} +(-1.51264 + 8.57862i) q^{97} +(0.0559038 + 0.0968282i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	0.177398	+	1.00607i	0.0793347	+	0.449929i	0.998436	+	0.0559078i	$0.0178053\pi$
$5$	0.177398	+	1.00607i	0.0793347	+	0.449929i	−0.919101	+	0.394021i	$0.871084\pi$
$6$		0			0
$7$	2.04289	+	1.71418i	0.772138	+	0.647901i	0.941256	−	0.337695i	$-0.109647\pi$
$7$	2.04289	+	1.71418i	0.772138	+	0.647901i	−0.169118	+	0.985596i	$0.554092\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$		0			0
$10$	0.510796	+	0.884725i	0.161528	+	0.279775i
$11$	0.720058	−	4.08365i	0.217106	−	1.23127i	−0.660109	−	0.751169i	$-0.729490\pi$
$11$	0.720058	−	4.08365i	0.217106	−	1.23127i	0.877215	−	0.480098i	$-0.159399\pi$
$12$		0			0
$13$	−3.68356	−	1.34071i	−1.02164	−	0.371845i	−0.223746	−	0.974647i	$-0.571829\pi$
$13$	−3.68356	−	1.34071i	−1.02164	−	0.371845i	−0.797891	+	0.602802i	$0.794051\pi$
$14$	2.50597	+	0.912098i	0.669749	+	0.243769i
$15$		0			0
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−0.925795	−	1.60352i	−0.224538	−	0.388912i	0.731643	−	0.681688i	$-0.238754\pi$
$17$	−0.925795	−	1.60352i	−0.224538	−	0.388912i	−0.956181	+	0.292777i	$0.905421\pi$
$18$		0			0
$19$	−3.21653	+	5.57120i	−0.737923	+	1.27812i	0.215505	+	0.976503i	$0.430860\pi$
$19$	−3.21653	+	5.57120i	−0.737923	+	1.27812i	−0.953429	+	0.301618i	$0.902473\pi$
$20$	0.782585	+	0.656667i	0.174991	+	0.146835i
$21$		0			0
$22$	−0.720058	−	4.08365i	−0.153517	−	0.870637i
$23$	−6.69746	+	5.61984i	−1.39652	+	1.17182i	−0.433897	+	0.900963i	$0.642862\pi$
$23$	−6.69746	+	5.61984i	−1.39652	+	1.17182i	−0.962620	+	0.270854i	$0.912694\pi$
$24$		0			0
$25$	3.71775	−	1.35315i	0.743550	−	0.270630i
$26$	−3.91997			−0.768769
$27$		0			0
$28$	2.66680			0.503977
$29$	1.17759	−	0.428609i	0.218674	−	0.0795907i	−0.230360	−	0.973105i	$-0.573990\pi$
$29$	1.17759	−	0.428609i	0.218674	−	0.0795907i	0.449034	+	0.893515i	$0.351768\pi$
$30$		0			0
$31$	−2.56758	+	2.15445i	−0.461151	+	0.386952i	−0.843554	−	0.537044i	$-0.819541\pi$
$31$	−2.56758	+	2.15445i	−0.461151	+	0.386952i	0.382403	+	0.923995i	$0.375096\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$		0			0
$34$	−1.41840	−	1.19018i	−0.243254	−	0.204114i
$35$	−1.36219	+	2.35938i	−0.230252	+	0.398808i
$36$		0			0
$37$	−4.58887	−	7.94816i	−0.754406	−	1.30667i	−0.945669	−	0.325131i	$-0.894592\pi$
$37$	−4.58887	−	7.94816i	−0.754406	−	1.30667i	0.191263	−	0.981539i	$-0.438742\pi$
$38$	−1.11709	+	6.33533i	−0.181216	+	1.02773i
$39$		0			0
$40$	0.959983	+	0.349405i	0.151787	+	0.0552458i
$41$	3.53914	+	1.28814i	0.552720	+	0.201174i	0.603255	−	0.797549i	$-0.293870\pi$
$41$	3.53914	+	1.28814i	0.552720	+	0.201174i	−0.0505345	+	0.998722i	$0.516092\pi$
$42$		0			0
$43$	0.536567	−	3.04303i	0.0818258	−	0.464057i	−0.916171	−	0.400788i	$-0.868736\pi$
$43$	0.536567	−	3.04303i	0.0818258	−	0.464057i	0.997997	−	0.0632688i	$-0.0201526\pi$
$44$	−2.07332	−	3.59110i	−0.312565	−	0.541379i
$45$		0			0
$46$	−4.37146	+	7.57159i	−0.644536	+	1.11637i
$47$	2.11809	+	1.77729i	0.308956	+	0.259244i	0.784060	−	0.620685i	$-0.213145\pi$
$47$	2.11809	+	1.77729i	0.308956	+	0.259244i	−0.475105	+	0.879929i	$0.657590\pi$
$48$		0			0
$49$	0.0194152	+	0.110109i	0.00277360	+	0.0157298i
$50$	3.03074	−	2.54309i	0.428611	−	0.359647i
$51$		0			0
$52$	−3.68356	+	1.34071i	−0.510818	+	0.185923i
$53$	0.231576			0.0318094			0.0159047	−	0.999874i	$-0.494937\pi$
$53$	0.231576			0.0318094			0.0159047	+	0.999874i	$0.494937\pi$
$54$		0			0
$55$	4.23618			0.571207
$56$	2.50597	−	0.912098i	0.334874	−	0.121884i
$57$		0			0
$58$	0.959983	−	0.805521i	0.126052	−	0.105770i
$59$	−0.613793	−	3.48099i	−0.0799090	−	0.453187i	−0.998339	−	0.0576042i	$-0.981654\pi$
$59$	−0.613793	−	3.48099i	−0.0799090	−	0.453187i	0.918430	−	0.395582i	$-0.129457\pi$
$60$		0			0
$61$	0.405075	+	0.339899i	0.0518646	+	0.0435196i	0.668351	−	0.743846i	$-0.267000\pi$
$61$	0.405075	+	0.339899i	0.0518646	+	0.0435196i	−0.616487	+	0.787365i	$0.711445\pi$
$62$	−1.67587	+	2.90269i	−0.212835	+	0.368642i
$63$		0			0
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	0.695393	−	3.94377i	0.0862529	−	0.489164i
$66$		0			0
$67$	7.67276	+	2.79266i	0.937377	+	0.341177i	0.765130	−	0.643876i	$-0.222675\pi$
$67$	7.67276	+	2.79266i	0.937377	+	0.341177i	0.172247	+	0.985054i	$0.444897\pi$
$68$	−1.73993	−	0.633281i	−0.210997	−	0.0767966i
$69$		0			0
$70$	−0.473084	+	2.68299i	−0.0565443	+	0.320679i
$71$	4.03086	+	6.98165i	0.478375	+	0.828570i	0.999693	−	0.0247929i	$-0.00789263\pi$
$71$	4.03086	+	6.98165i	0.478375	+	0.828570i	−0.521318	+	0.853363i	$0.674559\pi$
$72$		0			0
$73$	1.57397	−	2.72620i	0.184219	−	0.319078i	−0.759094	−	0.650981i	$-0.774358\pi$
$73$	1.57397	−	2.72620i	0.184219	−	0.319078i	0.943313	+	0.331904i	$0.107691\pi$
$74$	−7.03056	−	5.89934i	−0.817286	−	0.685784i
$75$		0			0
$76$	1.11709	+	6.33533i	0.128139	+	0.726713i
$77$	8.47113	−	7.10812i	0.965374	−	0.810045i
$78$		0			0
$79$	2.43473	−	0.886167i	0.273928	−	0.0997016i	−0.201404	−	0.979508i	$-0.564550\pi$
$79$	2.43473	−	0.886167i	0.273928	−	0.0997016i	0.475332	+	0.879807i	$0.342328\pi$
$80$	1.02159			0.114218
$81$		0			0
$82$	3.76627			0.415915
$83$	−7.55488	+	2.74975i	−0.829256	+	0.301824i	−0.721553	−	0.692359i	$-0.756572\pi$
$83$	−7.55488	+	2.74975i	−0.829256	+	0.301824i	−0.107702	+	0.994183i	$0.534349\pi$
$84$		0			0
$85$	1.44903	−	1.21588i	0.157169	−	0.131880i
$86$	−0.536567	−	3.04303i	−0.0578596	−	0.328138i
$87$		0			0
$88$	−3.17652	−	2.66541i	−0.338618	−	0.284134i
$89$	6.12693	−	10.6122i	0.649453	−	1.12489i	−0.333800	−	0.942644i	$-0.608331\pi$
$89$	6.12693	−	10.6122i	0.649453	−	1.12489i	0.983254	−	0.182242i	$-0.0583355\pi$
$90$		0			0
$91$	−5.22688	−	9.05322i	−0.547926	−	0.949035i
$92$	−1.51819	+	8.61009i	−0.158282	+	0.897664i
$93$		0			0
$94$	2.59823	+	0.945677i	0.267986	+	0.0975391i
$95$	−6.17564	−	2.24775i	−0.633607	−	0.230614i
$96$		0			0
$97$	−1.51264	+	8.57862i	−0.153586	+	0.871027i	0.806482	+	0.591259i	$0.201369\pi$
$97$	−1.51264	+	8.57862i	−0.153586	+	0.871027i	−0.960068	+	0.279768i	$0.909742\pi$
$98$	0.0559038	+	0.0968282i	0.00564713	+	0.00978112i
$99$		0			0
$100$	1.97817	−	3.42630i	0.197817	−	0.342630i
$101$	4.14121	+	3.47489i	0.412066	+	0.345764i	0.825135	−	0.564935i	$-0.191099\pi$
$101$	4.14121	+	3.47489i	0.412066	+	0.345764i	−0.413069	+	0.910700i	$0.635543\pi$
$102$		0			0
$103$	1.87292	+	10.6218i	0.184544	+	1.04660i	0.926540	+	0.376197i	$0.122768\pi$
$103$	1.87292	+	10.6218i	0.184544	+	1.04660i	−0.741996	+	0.670405i	$0.766120\pi$
$104$	−3.00287	+	2.51971i	−0.294455	+	0.247077i
$105$		0			0
$106$	0.217610	−	0.0792037i	0.0211362	−	0.00769295i
$107$	14.8511			1.43571			0.717856	−	0.696191i	$-0.245124\pi$
$107$	14.8511			1.43571			0.717856	+	0.696191i	$0.245124\pi$
$108$		0			0
$109$	17.6598			1.69150			0.845752	−	0.533576i	$-0.179152\pi$
$109$	17.6598			1.69150			0.845752	+	0.533576i	$0.179152\pi$
$110$	3.98071	−	1.44886i	0.379546	−	0.138143i
$111$		0			0
$112$	2.04289	−	1.71418i	0.193035	−	0.161975i
$113$	−0.339716	−	1.92663i	−0.0319578	−	0.181242i	0.964651	−	0.263532i	$-0.0848876\pi$
$113$	−0.339716	−	1.92663i	−0.0319578	−	0.181242i	−0.996608	+	0.0822905i	$0.973776\pi$
$114$		0			0
$115$	−6.84208	−	5.74118i	−0.638027	−	0.535368i
$116$	0.626584	−	1.08528i	0.0581769	−	0.100765i
$117$		0			0
$118$	−1.76735	−	3.06113i	−0.162697	−	0.281800i
$119$	0.857442	−	4.86280i	0.0786016	−	0.445772i
$120$		0			0
$121$	−5.82110	−	2.11871i	−0.529191	−	0.192610i
$122$	0.496899	+	0.180856i	0.0449871	+	0.0163740i
$123$		0			0
$124$	−0.582023	+	3.30082i	−0.0522672	+	0.296422i
$125$	4.57487	+	7.92391i	0.409189	+	0.708736i
$126$		0			0
$127$	−2.78998	+	4.83239i	−0.247571	+	0.428805i	−0.962851	−	0.270032i	$-0.912966\pi$
$127$	−2.78998	+	4.83239i	−0.247571	+	0.428805i	0.715281	+	0.698837i	$0.246299\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$		0			0
$130$	−0.695393	−	3.94377i	−0.0609900	−	0.345891i
$131$	−1.18532	+	0.994600i	−0.103562	+	0.0868986i	−0.693098	−	0.720843i	$-0.743755\pi$
$131$	−1.18532	+	0.994600i	−0.103562	+	0.0868986i	0.589537	+	0.807742i	$0.299310\pi$
$132$		0			0
$133$	−16.1211	+	5.86759i	−1.39787	+	0.508785i
$134$	8.16518			0.705364
$135$		0			0
$136$	−1.85159			−0.158773
$137$	−18.8496	+	6.86070i	−1.61043	+	0.586149i	−0.981525	−	0.191332i	$-0.938719\pi$
$137$	−18.8496	+	6.86070i	−1.61043	+	0.586149i	−0.628906	+	0.777481i	$0.716497\pi$
$138$		0			0
$139$	2.98779	−	2.50705i	0.253421	−	0.212645i	−0.507223	−	0.861815i	$-0.669328\pi$
$139$	2.98779	−	2.50705i	0.253421	−	0.212645i	0.760644	+	0.649170i	$0.224883\pi$
$140$	0.473084	+	2.68299i	0.0399829	+	0.226754i
$141$		0			0
$142$	6.17564	+	5.18197i	0.518248	+	0.434862i
$143$	−8.12736	+	14.0770i	−0.679644	+	1.17718i
$144$		0			0
$145$	0.640114	+	1.10871i	0.0531586	+	0.0920734i
$146$	0.546635	−	3.10012i	0.0452398	−	0.256568i
$147$		0			0
$148$	−8.62426	−	3.13897i	−0.708910	−	0.258022i
$149$	−9.24128	−	3.36355i	−0.757075	−	0.275553i	−0.0654951	−	0.997853i	$-0.520863\pi$
$149$	−9.24128	−	3.36355i	−0.757075	−	0.275553i	−0.691580	+	0.722300i	$0.743085\pi$
$150$		0			0
$151$	0.697011	−	3.95294i	0.0567219	−	0.321686i	−0.943223	−	0.332160i	$-0.892223\pi$
$151$	0.697011	−	3.95294i	0.0567219	−	0.321686i	0.999945	+	0.0104735i	$0.00333387\pi$
$152$	3.21653	+	5.57120i	0.260895	+	0.451884i
$153$		0			0
$154$	5.52913	−	9.57674i	0.445550	−	0.771716i
$155$	−2.62302	−	2.20098i	−0.210686	−	0.176787i
$156$		0			0
$157$	−2.48817	−	14.1111i	−0.198578	−	1.12619i	−0.907231	−	0.420634i	$-0.861808\pi$
$157$	−2.48817	−	14.1111i	−0.198578	−	1.12619i	0.708653	−	0.705557i	$-0.249303\pi$
$158$	1.98481	−	1.66545i	0.157903	−	0.132496i
$159$		0			0
$160$	0.959983	−	0.349405i	0.0758933	−	0.0276229i
$161$	−23.3156			−1.83753
$162$		0			0
$163$	−14.2911			−1.11937			−0.559683	−	0.828707i	$-0.689077\pi$
$163$	−14.2911			−1.11937			−0.559683	+	0.828707i	$0.689077\pi$
$164$	3.53914	−	1.28814i	0.276360	−	0.100587i
$165$		0			0
$166$	−6.15879	+	5.16784i	−0.478015	+	0.401102i
$167$	1.65921	+	9.40983i	0.128393	+	0.728154i	0.979234	+	0.202731i	$0.0649818\pi$
$167$	1.65921	+	9.40983i	0.128393	+	0.728154i	−0.850841	+	0.525423i	$0.823907\pi$
$168$		0			0
$169$	1.81256	+	1.52092i	0.139428	+	0.116994i
$170$	0.945785	−	1.63815i	0.0725384	−	0.125640i
$171$		0			0
$172$	−1.54498	−	2.67599i	−0.117804	−	0.204042i
$173$	−1.73345	+	9.83089i	−0.131792	+	0.747429i	0.845248	+	0.534374i	$0.179453\pi$
$173$	−1.73345	+	9.83089i	−0.131792	+	0.747429i	−0.977040	+	0.213055i	$0.931659\pi$
$174$		0			0
$175$	9.91449	+	3.60858i	0.749465	+	0.272783i
$176$	−3.89657	−	1.41824i	−0.293715	−	0.106904i
$177$		0			0
$178$	2.12786	−	12.0677i	0.159490	−	0.904512i
$179$	−11.2541	−	19.4927i	−0.841174	−	1.45696i	−0.888903	−	0.458096i	$-0.848532\pi$
$179$	−11.2541	−	19.4927i	−0.841174	−	1.45696i	0.0477290	−	0.998860i	$-0.484802\pi$
$180$		0			0
$181$	−0.248078	+	0.429684i	−0.0184395	+	0.0319382i	−0.875098	−	0.483946i	$-0.839203\pi$
$181$	−0.248078	+	0.429684i	−0.0184395	+	0.0319382i	0.856658	+	0.515884i	$0.172536\pi$
$182$	−8.00804	−	6.71954i	−0.593595	−	0.498086i
$183$		0			0
$184$	1.51819	+	8.61009i	0.111923	+	0.634744i
$185$	7.18237	−	6.02672i	0.528058	−	0.443093i
$186$		0			0
$187$	−7.21486	+	2.62599i	−0.527603	+	0.192032i
$188$	2.76497			0.201656
$189$		0			0
$190$	−6.57197			−0.476781
$191$	6.75481	−	2.45855i	0.488761	−	0.177894i	−0.0858713	−	0.996306i	$-0.527367\pi$
$191$	6.75481	−	2.45855i	0.488761	−	0.177894i	0.574632	+	0.818412i	$0.305145\pi$
$192$		0			0
$193$	−10.3185	+	8.65825i	−0.742742	+	0.623234i	−0.933572	−	0.358389i	$-0.883326\pi$
$193$	−10.3185	+	8.65825i	−0.742742	+	0.623234i	0.190831	+	0.981623i	$0.438882\pi$
$194$	1.51264	+	8.57862i	0.108601	+	0.615909i
$195$		0			0
$196$	0.0856496	+	0.0718685i	0.00611783	+	0.00513346i
$197$	2.53340	−	4.38797i	0.180497	−	0.312630i	−0.761553	−	0.648103i	$-0.775563\pi$
$197$	2.53340	−	4.38797i	0.180497	−	0.312630i	0.942050	+	0.335473i	$0.108896\pi$
$198$		0			0
$199$	8.97242	+	15.5407i	0.636038	+	1.10165i	0.986294	+	0.164996i	$0.0527611\pi$
$199$	8.97242	+	15.5407i	0.636038	+	1.10165i	−0.350256	+	0.936654i	$0.613906\pi$
$200$	0.687013	−	3.89624i	0.0485791	−	0.275506i
$201$		0			0
$202$	5.07995	+	1.84895i	0.357424	+	0.130092i
$203$	3.14040	+	1.14301i	0.220413	+	0.0802238i
$204$		0			0
$205$	−0.668128	+	3.78914i	−0.0466641	+	0.264645i
$206$	5.39285	+	9.34070i	0.375738	+	0.650797i
$207$		0			0
$208$	−1.95998	+	3.39479i	−0.135900	+	0.235386i
$209$	20.4347	+	17.1468i	1.41350	+	1.18607i
$210$		0			0
$211$	−0.884489	−	5.01618i	−0.0608907	−	0.345328i	−0.999999	−	0.00170581i	$-0.999457\pi$
$211$	−0.884489	−	5.01618i	−0.0608907	−	0.345328i	0.939108	−	0.343623i	$-0.111654\pi$
$212$	0.177398	−	0.148854i	0.0121837	−	0.0102234i
$213$		0			0
$214$	13.9555	−	5.07938i	0.953978	−	0.347220i
$215$	3.15669			0.215284
$216$		0			0
$217$	−8.93840			−0.606778
$218$	16.5948	−	6.04001i	1.12394	−	0.409081i
$219$		0			0
$220$	3.24511	−	2.72297i	0.218785	−	0.183582i
$221$	1.26037	+	7.14790i	0.0847815	+	0.480820i
$222$		0			0
$223$	2.92334	+	2.45297i	0.195761	+	0.164263i	0.735399	−	0.677634i	$-0.236995\pi$
$223$	2.92334	+	2.45297i	0.195761	+	0.164263i	−0.539638	+	0.841897i	$0.681439\pi$
$224$	1.33340	−	2.30951i	0.0890914	−	0.154311i
$225$		0			0
$226$	−0.978174	−	1.69425i	−0.0650672	−	0.112700i
$227$	3.53875	−	20.0693i	0.234875	−	1.33204i	−0.608001	−	0.793936i	$-0.708028\pi$
$227$	3.53875	−	20.0693i	0.234875	−	1.33204i	0.842876	−	0.538108i	$-0.180861\pi$
$228$		0			0
$229$	1.41711	+	0.515787i	0.0936455	+	0.0340842i	0.388418	−	0.921483i	$-0.373022\pi$
$229$	1.41711	+	0.515787i	0.0936455	+	0.0340842i	−0.294773	+	0.955567i	$0.595244\pi$
$230$	−8.39305	−	3.05482i	−0.553421	−	0.201429i
$231$		0			0
$232$	0.217610	−	1.23413i	0.0142868	−	0.0810246i
$233$	−10.0838	−	17.4656i	−0.660610	−	1.14421i	−0.980456	−	0.196741i	$-0.936964\pi$
$233$	−10.0838	−	17.4656i	−0.660610	−	1.14421i	0.319845	−	0.947470i	$-0.396369\pi$
$234$		0			0
$235$	−1.41234	+	2.44624i	−0.0921308	+	0.159575i
$236$	−2.70773	−	2.27206i	−0.176258	−	0.147898i
$237$		0			0
$238$	−0.857442	−	4.86280i	−0.0555797	−	0.315208i
$239$	9.68541	−	8.12702i	0.626497	−	0.525693i	−0.273341	−	0.961917i	$-0.588129\pi$
$239$	9.68541	−	8.12702i	0.626497	−	0.525693i	0.899838	+	0.436224i	$0.143684\pi$
$240$		0			0
$241$	26.1605	−	9.52166i	1.68515	−	0.613344i	0.691148	−	0.722713i	$-0.257105\pi$
$241$	26.1605	−	9.52166i	1.68515	−	0.613344i	0.994001	+	0.109369i	$0.0348831\pi$
$242$	−6.19469			−0.398210
$243$		0			0
$244$	0.528788			0.0338522
$245$	−0.107333	+	0.0390661i	−0.00685728	+	0.00249584i
$246$		0			0
$247$	19.3177	−	16.2094i	1.22915	−	1.03138i
$248$	0.582023	+	3.30082i	0.0369585	+	0.209602i
$249$		0			0
$250$	7.00911	+	5.88134i	0.443295	+	0.371969i
$251$	−0.336641	+	0.583079i	−0.0212486	+	0.0368036i	−0.876454	−	0.481485i	$-0.840097\pi$
$251$	−0.336641	+	0.583079i	−0.0212486	+	0.0368036i	0.855206	+	0.518289i	$0.173431\pi$
$252$		0			0
$253$	18.1269	+	31.3967i	1.13963	+	1.97389i
$254$	−0.968950	+	5.49519i	−0.0607973	+	0.344799i
$255$		0			0
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	28.7904	+	10.4789i	1.79590	+	0.653653i	0.998756	+	0.0498599i	$0.0158775\pi$
$257$	28.7904	+	10.4789i	1.79590	+	0.653653i	0.797141	+	0.603793i	$0.206345\pi$
$258$		0			0
$259$	4.25007	−	24.1033i	0.264087	−	1.49771i
$260$	−2.00230	−	3.46809i	−0.124178	−	0.215082i
$261$		0			0
$262$	−0.773661	+	1.34002i	−0.0477969	+	0.0827867i
$263$	4.54929	+	3.81731i	0.280521	+	0.235385i	0.772182	−	0.635402i	$-0.219165\pi$
$263$	4.54929	+	3.81731i	0.280521	+	0.235385i	−0.491661	+	0.870787i	$0.663610\pi$
$264$		0			0
$265$	0.0410811	+	0.232982i	0.00252359	+	0.0143120i
$266$	−13.1420	+	11.0275i	−0.805789	+	0.676137i
$267$		0			0
$268$	7.67276	−	2.79266i	0.468688	−	0.170589i
$269$	−15.3624			−0.936661			−0.468330	−	0.883553i	$-0.655144\pi$
$269$	−15.3624			−0.936661			−0.468330	+	0.883553i	$0.655144\pi$
$270$		0			0
$271$	−14.5939			−0.886516			−0.443258	−	0.896394i	$-0.646177\pi$
$271$	−14.5939			−0.886516			−0.443258	+	0.896394i	$0.646177\pi$
$272$	−1.73993	+	0.633281i	−0.105498	+	0.0383983i
$273$		0			0
$274$	−15.3663	+	12.8939i	−0.928315	+	0.778949i
$275$	−2.84880	−	16.1563i	−0.171789	−	0.974264i
$276$		0			0
$277$	4.35786	+	3.65668i	0.261838	+	0.219709i	0.764250	−	0.644920i	$-0.223109\pi$
$277$	4.35786	+	3.65668i	0.261838	+	0.219709i	−0.502412	+	0.864629i	$0.667554\pi$
$278$	1.95014	−	3.37774i	0.116962	−	0.202584i
$279$		0			0
$280$	1.36219	+	2.35938i	0.0814064	+	0.141000i
$281$	−2.37136	+	13.4487i	−0.141464	+	0.802281i	0.828675	+	0.559730i	$0.189095\pi$
$281$	−2.37136	+	13.4487i	−0.141464	+	0.802281i	−0.970139	+	0.242551i	$0.922016\pi$
$282$		0			0
$283$	−24.3720	−	8.87068i	−1.44876	−	0.527307i	−0.506519	−	0.862229i	$-0.669068\pi$
$283$	−24.3720	−	8.87068i	−1.44876	−	0.527307i	−0.942246	+	0.334922i	$0.891290\pi$
$284$	7.57554	+	2.75727i	0.449525	+	0.163614i
$285$		0			0
$286$	−2.82260	+	16.0078i	−0.166904	+	0.946559i
$287$	5.02194	+	8.69825i	0.296436	+	0.513442i
$288$		0			0
$289$	6.78581	−	11.7534i	0.399165	−	0.691374i
$290$	0.980712	+	0.822915i	0.0575894	+	0.0483232i
$291$		0			0
$292$	−0.546635	−	3.10012i	−0.0319894	−	0.181421i
$293$	−15.2378	+	12.7860i	−0.890199	+	0.746966i	−0.968250	−	0.249984i	$-0.919575\pi$
$293$	−15.2378	+	12.7860i	−0.890199	+	0.746966i	0.0780511	+	0.996949i	$0.475130\pi$
$294$		0			0
$295$	3.39325	−	1.23504i	0.197562	−	0.0719068i
$296$	−9.17774			−0.533446
$297$		0			0
$298$	−9.83436			−0.569689
$299$	32.2051	−	11.7217i	1.86247	−	0.677883i
$300$		0			0
$301$	6.31245	−	5.29678i	0.363844	−	0.305301i
$302$	−0.697011	−	3.95294i	−0.0401085	−	0.227466i
$303$		0			0
$304$	4.92802	+	4.13510i	0.282641	+	0.237164i
$305$	−0.270103	+	0.467832i	−0.0154661	+	0.0267880i
$306$		0			0
$307$	4.75733	+	8.23993i	0.271515	+	0.470278i	0.969250	−	0.246078i	$-0.0791420\pi$
$307$	4.75733	+	8.23993i	0.271515	+	0.470278i	−0.697735	+	0.716356i	$0.745809\pi$
$308$	1.92025	−	10.8903i	0.109416	−	0.620531i
$309$		0			0
$310$	−3.21761	−	1.17111i	−0.182748	−	0.0665148i
$311$	−13.5916	−	4.94693i	−0.770707	−	0.280514i	−0.0734150	−	0.997301i	$-0.523390\pi$
$311$	−13.5916	−	4.94693i	−0.770707	−	0.280514i	−0.697292	+	0.716787i	$0.745612\pi$
$312$		0			0
$313$	−2.32518	+	13.1867i	−0.131427	+	0.745359i	0.845855	+	0.533414i	$0.179091\pi$
$313$	−2.32518	+	13.1867i	−0.131427	+	0.745359i	−0.977281	+	0.211946i	$0.932020\pi$
$314$	−7.16441	−	12.4091i	−0.404311	−	0.700287i
$315$		0			0
$316$	1.29549	−	2.24385i	0.0728770	−	0.126227i
$317$	−19.2768	−	16.1751i	−1.08269	−	0.908487i	−0.0865506	−	0.996247i	$-0.527584\pi$
$317$	−19.2768	−	16.1751i	−1.08269	−	0.908487i	−0.996142	+	0.0877609i	$0.972029\pi$
$318$		0			0
$319$	−0.902354	−	5.11750i	−0.0505221	−	0.286525i
$320$	0.782585	−	0.656667i	0.0437479	−	0.0367088i
$321$		0			0
$322$	−21.9095	+	7.97440i	−1.22097	+	0.444396i
$323$	11.9114			0.662768
$324$		0			0
$325$	−15.5088			−0.860271
$326$	−13.4292	+	4.88784i	−0.743777	+	0.270713i
$327$		0			0
$328$	2.88513	−	2.42091i	0.159305	−	0.133672i
$329$	1.28042	+	7.26160i	0.0705916	+	0.400345i
$330$		0			0
$331$	−16.1905	−	13.5855i	−0.889912	−	0.746725i	0.0782802	−	0.996931i	$-0.475057\pi$
$331$	−16.1905	−	13.5855i	−0.889912	−	0.746725i	−0.968193	+	0.250206i	$0.919502\pi$
$332$	−4.01987	+	6.96261i	−0.220619	+	0.382123i
$333$		0			0
$334$	4.77749	+	8.27486i	0.261413	+	0.452780i
$335$	−1.44848	+	8.21476i	−0.0791392	+	0.448820i
$336$		0			0
$337$	−4.48414	−	1.63209i	−0.244267	−	0.0889058i	0.216986	−	0.976175i	$-0.430378\pi$
$337$	−4.48414	−	1.63209i	−0.244267	−	0.0889058i	−0.461252	+	0.887269i	$0.652600\pi$
$338$	2.22344	+	0.809266i	0.120939	+	0.0440183i
$339$		0			0
$340$	0.328468	−	1.86283i	0.0178137	−	0.101026i
$341$	6.94924	+	12.0364i	0.376322	+	0.651809i
$342$		0			0
$343$	9.18471	−	15.9084i	0.495928	−	0.858972i
$344$	−2.36705	−	1.98619i	−0.127623	−	0.107088i
$345$		0			0
$346$	1.73345	+	9.83089i	0.0931909	+	0.528512i
$347$	−12.0020	+	10.0708i	−0.644299	+	0.540631i	−0.905335	−	0.424698i	$-0.860380\pi$
$347$	−12.0020	+	10.0708i	−0.644299	+	0.540631i	0.261036	+	0.965329i	$0.415936\pi$
$348$		0			0
$349$	−18.6170	+	6.77604i	−0.996547	+	0.362713i	−0.788252	−	0.615353i	$-0.789014\pi$
$349$	−18.6170	+	6.77604i	−0.996547	+	0.362713i	−0.208295	+	0.978066i	$0.566791\pi$
$350$	10.5508			0.563963
$351$		0			0
$352$	−4.14665			−0.221017
$353$	−14.8445	+	5.40296i	−0.790093	+	0.287570i	−0.705375	−	0.708835i	$-0.749221\pi$
$353$	−14.8445	+	5.40296i	−0.790093	+	0.287570i	−0.0847183	+	0.996405i	$0.526999\pi$
$354$		0			0
$355$	−6.30898	+	5.29387i	−0.334846	+	0.280969i
$356$	−2.12786	−	12.0677i	−0.112776	−	0.639587i
$357$		0			0
$358$	−17.2423	−	14.4680i	−0.911286	−	0.764660i
$359$	2.43474	−	4.21710i	0.128501	−	0.222570i	−0.794595	−	0.607140i	$-0.792317\pi$
$359$	2.43474	−	4.21710i	0.128501	−	0.222570i	0.923096	+	0.384570i	$0.125650\pi$
$360$		0			0
$361$	−11.1922	−	19.3854i	−0.589062	−	1.02028i
$362$	−0.0861567	+	0.488619i	−0.00452830	+	0.0256812i
$363$		0			0
$364$	−9.82332	−	3.57539i	−0.514882	−	0.187402i
$365$	3.02197	+	1.09991i	0.158177	+	0.0575718i
$366$		0			0
$367$	−1.47394	+	8.35914i	−0.0769392	+	0.436344i	0.921868	+	0.387505i	$0.126663\pi$
$367$	−1.47394	+	8.35914i	−0.0769392	+	0.436344i	−0.998807	+	0.0488385i	$0.984448\pi$
$368$	4.37146	+	7.57159i	0.227878	+	0.394696i
$369$		0			0
$370$	4.68796	−	8.11978i	0.243715	−	0.422127i
$371$	0.473084	+	0.396964i	0.0245613	+	0.0206094i
$372$		0			0
$373$	0.783900	+	4.44572i	0.0405888	+	0.230190i	0.998353	−	0.0573629i	$-0.0182692\pi$
$373$	0.783900	+	4.44572i	0.0405888	+	0.230190i	−0.957765	+	0.287553i	$0.907158\pi$
$374$	−5.88161	+	4.93525i	−0.304131	+	0.255196i
$375$		0			0
$376$	2.59823	−	0.945677i	0.133993	−	0.0487695i
$377$	−4.91238			−0.253000
$378$		0			0
$379$	11.1018			0.570262			0.285131	−	0.958489i	$-0.407963\pi$
$379$	11.1018			0.570262			0.285131	+	0.958489i	$0.407963\pi$
$380$	−6.17564	+	2.24775i	−0.316803	+	0.115307i
$381$		0			0
$382$	5.50657	−	4.62056i	0.281741	−	0.236408i
$383$	3.82767	+	21.7078i	0.195585	+	1.10922i	0.911584	+	0.411114i	$0.134860\pi$
$383$	3.82767	+	21.7078i	0.195585	+	1.10922i	−0.715999	+	0.698101i	$0.754029\pi$
$384$		0			0
$385$	8.65404	+	7.26160i	0.441051	+	0.370085i
$386$	−6.73492	+	11.6652i	−0.342798	+	0.593744i
$387$		0			0
$388$	4.35548	+	7.54391i	0.221116	+	0.382984i
$389$	2.95836	−	16.7777i	0.149995	−	0.850663i	−0.813225	−	0.581949i	$-0.802290\pi$
$389$	2.95836	−	16.7777i	0.149995	−	0.850663i	0.963220	−	0.268714i	$-0.0865985\pi$
$390$		0			0
$391$	15.2120	+	5.53672i	0.769305	+	0.280004i
$392$	0.105065	+	0.0382404i	0.00530657	+	0.00193143i
$393$		0			0
$394$	0.879840	−	4.98982i	0.0443257	−	0.251383i
$395$	1.32346	+	2.29231i	0.0665907	+	0.115338i
$396$		0			0
$397$	7.80452	−	13.5178i	0.391698	−	0.678441i	−0.600976	−	0.799267i	$-0.705221\pi$
$397$	7.80452	−	13.5178i	0.391698	−	0.678441i	0.992674	+	0.120827i	$0.0385545\pi$
$398$	13.7465	+	11.5347i	0.689052	+	0.578183i
$399$		0			0
$400$	−0.687013	−	3.89624i	−0.0343506	−	0.194812i
$401$	2.82242	−	2.36829i	0.140945	−	0.118267i	−0.569589	−	0.821929i	$-0.692898\pi$
$401$	2.82242	−	2.36829i	0.140945	−	0.118267i	0.710534	+	0.703663i	$0.248453\pi$
$402$		0			0
$403$	12.3463	−	4.49370i	0.615015	−	0.223847i
$404$	5.40597			0.268957
$405$		0			0
$406$	3.34195			0.165858
$407$	−35.7618	+	13.0162i	−1.77264	+	0.645190i
$408$		0			0
$409$	−10.3077	+	8.64918i	−0.509682	+	0.427674i	−0.861017	−	0.508576i	$-0.830172\pi$
$409$	−10.3077	+	8.64918i	−0.509682	+	0.427674i	0.351335	+	0.936250i	$0.385728\pi$
$410$	0.668128	+	3.78914i	0.0329965	+	0.187132i
$411$		0			0
$412$	8.26233	+	6.93292i	0.407056	+	0.341560i
$413$	4.71316	−	8.16342i	0.231919	−	0.401696i
$414$		0			0
$415$	−4.10667	−	7.11296i	−0.201588	−	0.349161i
$416$	−0.680695	+	3.86041i	−0.0333738	+	0.189272i
$417$		0			0
$418$	25.0669	+	9.12361i	1.22606	+	0.446251i
$419$	1.29440	+	0.471124i	0.0632357	+	0.0230159i	0.373444	−	0.927653i	$-0.378177\pi$
$419$	1.29440	+	0.471124i	0.0632357	+	0.0230159i	−0.310209	+	0.950668i	$0.600399\pi$
$420$		0			0
$421$	−1.39368	+	7.90398i	−0.0679240	+	0.385216i	0.931827	+	0.362903i	$0.118214\pi$
$421$	−1.39368	+	7.90398i	−0.0679240	+	0.385216i	−0.999751	+	0.0223134i	$0.992897\pi$
$422$	−2.54678	−	4.41116i	−0.123975	−	0.214732i
$423$		0			0
$424$	0.115788	−	0.200551i	0.00562317	−	0.00973961i
$425$	−5.61168	−	4.70876i	−0.272207	−	0.228409i
$426$		0			0
$427$	0.244874	+	1.38875i	0.0118503	+	0.0672062i
$428$	11.3766	−	9.54612i	0.549910	−	0.461429i
$429$		0			0
$430$	2.96632	−	1.07965i	0.143049	−	0.0520654i
$431$	34.6923			1.67107			0.835534	−	0.549438i	$-0.185158\pi$
$431$	34.6923			1.67107			0.835534	+	0.549438i	$0.185158\pi$
$432$		0			0
$433$	0.605990			0.0291220			0.0145610	−	0.999894i	$-0.495365\pi$
$433$	0.605990			0.0291220			0.0145610	+	0.999894i	$0.495365\pi$
$434$	−8.39935	+	3.05711i	−0.403182	+	0.146746i
$435$		0			0
$436$	13.5282	−	11.3515i	0.647884	−	0.543639i
$437$	−9.76663	−	55.3893i	−0.467201	−	2.64963i
$438$		0			0
$439$	−0.853735	−	0.716369i	−0.0407466	−	0.0341904i	0.622187	−	0.782869i	$-0.286244\pi$
$439$	−0.853735	−	0.716369i	−0.0407466	−	0.0341904i	−0.662934	+	0.748678i	$0.730689\pi$
$440$	2.11809	−	3.66864i	0.100976	−	0.174896i
$441$		0			0
$442$	3.62908	+	6.28576i	0.172618	+	0.298983i
$443$	−1.06252	+	6.02583i	−0.0504817	+	0.286296i	−0.999589	−	0.0286559i	$-0.990877\pi$
$443$	−1.06252	+	6.02583i	−0.0504817	+	0.286296i	0.949108	+	0.314952i	$0.101988\pi$
$444$		0			0
$445$	11.7635	+	4.28156i	0.557643	+	0.202966i
$446$	3.58600	+	1.30520i	0.169802	+	0.0618029i
$447$		0			0
$448$	0.463084	−	2.62628i	0.0218787	−	0.124080i
$449$	18.1443	+	31.4269i	0.856283	+	1.48313i	0.875450	+	0.483310i	$0.160565\pi$
$449$	18.1443	+	31.4269i	0.856283	+	1.48313i	−0.0191664	+	0.999816i	$0.506101\pi$
$450$		0			0
$451$	7.80870	−	13.5251i	0.367697	−	0.636870i
$452$	−1.49865	−	1.25752i	−0.0704906	−	0.0591486i
$453$		0			0
$454$	−3.53875	−	20.0693i	−0.166082	−	0.941897i
$455$	8.18096	−	6.86464i	0.383529	−	0.321819i
$456$		0			0
$457$	−19.4942	+	7.09531i	−0.911900	+	0.331905i	−0.755011	−	0.655712i	$-0.772369\pi$
$457$	−19.4942	+	7.09531i	−0.911900	+	0.331905i	−0.156889	+	0.987616i	$0.550146\pi$
$458$	1.50806			0.0704670
$459$		0			0
$460$	−8.93170			−0.416443
$461$	38.8668	−	14.1464i	1.81021	−	0.658861i	0.813162	−	0.582037i	$-0.197744\pi$
$461$	38.8668	−	14.1464i	1.81021	−	0.658861i	0.997045	−	0.0768243i	$-0.0244780\pi$
$462$		0			0
$463$	−18.1032	+	15.1904i	−0.841328	+	0.705958i	−0.957862	−	0.287229i	$-0.907266\pi$
$463$	−18.1032	+	15.1904i	−0.841328	+	0.705958i	0.116534	+	0.993187i	$0.462822\pi$
$464$	−0.217610	−	1.23413i	−0.0101023	−	0.0572931i
$465$		0			0
$466$	−15.4492	−	12.9635i	−0.715672	−	0.600520i
$467$	−10.5877	+	18.3384i	−0.489939	+	0.848599i	−0.999933	−	0.0115789i	$-0.996314\pi$
$467$	−10.5877	+	18.3384i	−0.489939	+	0.848599i	0.509994	+	0.860178i	$0.329648\pi$
$468$		0			0
$469$	10.8874	+	18.8576i	0.502735	+	0.870763i
$470$	−0.490500	+	2.78176i	−0.0226251	+	0.128313i
$471$		0			0
$472$	−3.32153	−	1.20894i	−0.152886	−	0.0556458i
$473$	−12.0403	−	4.38231i	−0.553613	−	0.201499i
$474$		0			0
$475$	−4.41960	+	25.0648i	−0.202785	+	1.15005i
$476$	−2.46891	−	4.27627i	−0.113162	−	0.196003i
$477$		0			0
$478$	6.32170	−	10.9495i	0.289148	−	0.500819i
$479$	−10.2101	−	8.56728i	−0.466511	−	0.391449i	0.379009	−	0.925393i	$-0.376265\pi$
$479$	−10.2101	−	8.56728i	−0.466511	−	0.391449i	−0.845520	+	0.533944i	$0.820709\pi$
$480$		0			0
$481$	6.24724	+	35.4299i	0.284850	+	1.61546i
$482$	21.3263	−	17.8949i	0.971385	−	0.815089i
$483$		0			0
$484$	−5.82110	+	2.11871i	−0.264596	+	0.0963049i
$485$	−8.89905			−0.404085
$486$		0			0
$487$	−18.3872			−0.833202			−0.416601	−	0.909090i	$-0.636779\pi$
$487$	−18.3872			−0.833202			−0.416601	+	0.909090i	$0.636779\pi$
$488$	0.496899	−	0.180856i	0.0224935	−	0.00818698i
$489$		0			0
$490$	−0.0874990	+	0.0734203i	−0.00395280	+	0.00331679i
$491$	−3.35081	−	19.0034i	−0.151220	−	0.857610i	−0.962161	−	0.272482i	$-0.912155\pi$
$491$	−3.35081	−	19.0034i	−0.151220	−	0.857610i	0.810941	−	0.585128i	$-0.198956\pi$
$492$		0			0
$493$	−1.77749	−	1.49150i	−0.0800543	−	0.0671736i
$494$	12.6087	−	21.8389i	0.567292	−	0.982579i
$495$		0			0
$496$	1.67587	+	2.90269i	0.0752487	+	0.130335i
$497$	−3.73326	+	21.1724i	−0.167459	+	0.949710i
$498$		0			0
$499$	15.3641	+	5.59206i	0.687790	+	0.250335i	0.662189	−	0.749337i	$-0.269628\pi$
$499$	15.3641	+	5.59206i	0.687790	+	0.250335i	0.0256013	+	0.999672i	$0.491850\pi$
$500$	8.59794	+	3.12940i	0.384512	+	0.139951i
$501$		0			0
$502$	−0.116914	+	0.663053i	−0.00521814	+	0.0295935i
$503$	−19.9756	−	34.5988i	−0.890670	−	1.54269i	−0.839074	−	0.544018i	$-0.816902\pi$
$503$	−19.9756	−	34.5988i	−0.890670	−	1.54269i	−0.0515962	−	0.998668i	$-0.516431\pi$
$504$		0			0
$505$	−2.76135	+	4.78280i	−0.122878	+	0.212832i
$506$	27.7720	+	23.3035i	1.23462	+	1.03597i
$507$		0			0
$508$	0.968950	+	5.49519i	0.0429902	+	0.243810i
$509$	−24.7041	+	20.7292i	−1.09499	+	0.918805i	−0.997078	−	0.0763905i	$-0.975660\pi$
$509$	−24.7041	+	20.7292i	−1.09499	+	0.918805i	−0.0979108	+	0.995195i	$0.531216\pi$
$510$		0			0
$511$	7.88865	−	2.87123i	0.348973	−	0.127016i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	30.6381			1.35139
$515$	−10.3541	+	3.76858i	−0.456256	+	0.166064i
$516$		0			0
$517$	8.78298	−	7.36980i	0.386275	−	0.324123i
$518$	−4.25007	−	24.1033i	−0.186737	−	1.05904i
$519$		0			0
$520$	−3.06771	−	2.57411i	−0.134528	−	0.112882i
$521$	18.6915	−	32.3746i	0.818890	−	1.41836i	−0.0876112	−	0.996155i	$-0.527923\pi$
$521$	18.6915	−	32.3746i	0.818890	−	1.41836i	0.906501	−	0.422204i	$-0.138743\pi$
$522$		0			0
$523$	−14.5920	−	25.2740i	−0.638062	−	1.10516i	−0.985858	−	0.167586i	$-0.946403\pi$
$523$	−14.5920	−	25.2740i	−0.638062	−	1.10516i	0.347795	−	0.937570i	$-0.386930\pi$
$524$	−0.268690	+	1.52382i	−0.0117378	+	0.0665682i
$525$		0			0
$526$	5.58053	+	2.03115i	0.243323	+	0.0885622i
$527$	5.83177	+	2.12259i	0.254036	+	0.0924615i
$528$		0			0
$529$	9.27951	−	52.6267i	0.403457	−	2.28812i
$530$	0.118288	+	0.204881i	0.00513812	+	0.00889948i
$531$		0			0
$532$	−8.57784	+	14.8573i	−0.371897	+	0.644144i
$533$	−11.3096	−	9.48989i	−0.489874	−	0.411053i
$534$		0			0
$535$	2.63456	+	14.9413i	0.113902	+	0.645969i
$536$	6.25489	−	5.24848i	0.270170	−	0.226700i
$537$		0			0
$538$	−14.4359	+	5.25424i	−0.622377	+	0.226527i
$539$	0.463627			0.0199698
$540$		0			0
$541$	12.6132			0.542283			0.271142	−	0.962539i	$-0.412599\pi$
$541$	12.6132			0.542283			0.271142	+	0.962539i	$0.412599\pi$
$542$	−13.7138	+	4.99141i	−0.589057	+	0.214399i
$543$		0			0
$544$	−1.41840	+	1.19018i	−0.0608134	+	0.0510285i
$545$	3.13281	+	17.7671i	0.134195	+	0.761057i
$546$		0			0
$547$	22.3688	+	18.7696i	0.956419	+	0.802531i	0.980367	−	0.197182i	$-0.0631790\pi$
$547$	22.3688	+	18.7696i	0.956419	+	0.802531i	−0.0239476	+	0.999713i	$0.507623\pi$
$548$	−10.0297	+	17.3719i	−0.428446	+	0.742091i
$549$		0			0
$550$	−8.20279	−	14.2077i	−0.349768	−	0.605816i
$551$	−1.39990	+	7.93924i	−0.0596379	+	0.338223i
$552$		0			0
$553$	6.49292	+	2.36323i	0.276107	+	0.100495i
$554$	5.34571	+	1.94568i	0.227117	+	0.0826639i
$555$		0			0
$556$	0.677277	−	3.84103i	0.0287229	−	0.162896i
$557$	21.6137	+	37.4361i	0.915804	+	1.58622i	0.805720	+	0.592296i	$0.201778\pi$
$557$	21.6137	+	37.4361i	0.915804	+	1.58622i	0.110083	+	0.993922i	$0.464888\pi$
$558$		0			0
$559$	−6.05629	+	10.4898i	−0.256154	+	0.443671i
$560$	2.08700	+	1.75120i	0.0881917	+	0.0740016i
$561$		0			0
$562$	2.37136	+	13.4487i	0.100030	+	0.567298i
$563$	5.18375	−	4.34968i	0.218469	−	0.183317i	−0.526984	−	0.849875i	$-0.676677\pi$
$563$	5.18375	−	4.34968i	0.218469	−	0.183317i	0.745454	+	0.666558i	$0.232233\pi$
$564$		0			0
$565$	1.87806	−	0.683558i	0.0790106	−	0.0287575i
$566$	−25.9361			−1.09018
$567$		0			0
$568$	8.06172			0.338262
$569$	−1.78951	+	0.651329i	−0.0750203	+	0.0273051i	−0.379258	−	0.925291i	$-0.623821\pi$
$569$	−1.78951	+	0.651329i	−0.0750203	+	0.0273051i	0.304237	+	0.952596i	$0.401598\pi$
$570$		0			0
$571$	−8.59231	+	7.20980i	−0.359577	+	0.301721i	−0.804622	−	0.593787i	$-0.797632\pi$
$571$	−8.59231	+	7.20980i	−0.359577	+	0.301721i	0.445045	+	0.895508i	$0.353188\pi$
$572$	2.82260	+	16.0078i	0.118019	+	0.669319i
$573$		0			0
$574$	7.69406	+	6.45608i	0.321144	+	0.269472i
$575$	−17.2950	+	29.9558i	−0.721252	+	1.24924i
$576$		0			0
$577$	−19.6634	−	34.0581i	−0.818600	−	1.41786i	−0.906714	−	0.421746i	$-0.861417\pi$
$577$	−19.6634	−	34.0581i	−0.818600	−	1.41786i	0.0881143	−	0.996110i	$-0.471916\pi$
$578$	2.35669	−	13.3654i	0.0980252	−	0.555929i
$579$		0			0
$580$	1.20302	+	0.437864i	0.0499527	+	0.0181813i
$581$	−20.1473	−	7.33303i	−0.835852	−	0.304225i
$582$		0			0
$583$	0.166748	−	0.945677i	0.00690601	−	0.0391659i
$584$	−1.57397	−	2.72620i	−0.0651314	−	0.112811i
$585$		0			0
$586$	−9.94574	+	17.2265i	−0.410855	+	0.711621i
$587$	−5.98030	−	5.01807i	−0.246834	−	0.207118i	0.510974	−	0.859596i	$-0.329285\pi$
$587$	−5.98030	−	5.01807i	−0.246834	−	0.207118i	−0.757807	+	0.652478i	$0.773729\pi$
$588$		0			0
$589$	−3.74419	−	21.2344i	−0.154277	−	0.874947i
$590$	2.76620	−	2.32112i	0.113883	−	0.0955589i
$591$		0			0
$592$	−8.62426	+	3.13897i	−0.354455	+	0.129011i
$593$	12.2602			0.503465			0.251733	−	0.967797i	$-0.419000\pi$
$593$	12.2602			0.503465			0.251733	+	0.967797i	$0.419000\pi$
$594$		0			0
$595$	5.04444			0.206802
$596$	−9.24128	+	3.36355i	−0.378537	+	0.137776i
$597$		0			0
$598$	26.2538	−	22.0296i	1.07360	−	0.900856i
$599$	3.40179	+	19.2925i	0.138993	+	0.788271i	0.971995	+	0.235001i	$0.0755093\pi$
$599$	3.40179	+	19.2925i	0.138993	+	0.788271i	−0.833002	+	0.553270i	$0.813380\pi$
$600$		0			0
$601$	−3.14380	−	2.63796i	−0.128238	−	0.107605i	0.576413	−	0.817159i	$-0.304452\pi$
$601$	−3.14380	−	2.63796i	−0.128238	−	0.107605i	−0.704651	+	0.709554i	$0.748896\pi$
$602$	4.12016	−	7.13633i	0.167925	−	0.290855i
$603$		0			0
$604$	−2.00696	−	3.47616i	−0.0816622	−	0.141443i
$605$	1.09892	−	6.23230i	0.0446776	−	0.253379i
$606$		0			0
$607$	−15.2753	−	5.55976i	−0.620006	−	0.225664i	0.0128694	−	0.999917i	$-0.495903\pi$
$607$	−15.2753	−	5.55976i	−0.620006	−	0.225664i	−0.632876	+	0.774253i	$0.718126\pi$
$608$	6.04511	+	2.20024i	0.245161	+	0.0892315i
$609$		0			0
$610$	−0.0938059	+	0.531999i	−0.00379809	+	0.0215400i
$611$	−5.41930	−	9.38650i	−0.219241	−	0.379737i
$612$		0			0
$613$	−8.52562	+	14.7668i	−0.344347	+	0.596426i	−0.985235	−	0.171208i	$-0.945233\pi$
$613$	−8.52562	+	14.7668i	−0.344347	+	0.596426i	0.640888	+	0.767634i	$0.278566\pi$
$614$	7.28865	+	6.11590i	0.294146	+	0.246818i
$615$		0			0
$616$	−1.92025	−	10.8903i	−0.0773690	−	0.438781i
$617$	21.2848	−	17.8601i	0.856895	−	0.719020i	−0.104402	−	0.994535i	$-0.533293\pi$
$617$	21.2848	−	17.8601i	0.856895	−	0.719020i	0.961297	+	0.275515i	$0.0888484\pi$
$618$		0			0
$619$	−7.09199	+	2.58127i	−0.285051	+	0.103750i	−0.480589	−	0.876946i	$-0.659577\pi$
$619$	−7.09199	+	2.58127i	−0.285051	+	0.103750i	0.195538	+	0.980696i	$0.437355\pi$
$620$	−3.42411			−0.137516
$621$		0			0
$622$	−14.4638			−0.579947
$623$	30.7078	−	11.1767i	1.23028	−	0.447786i
$624$		0			0
$625$	7.99324	−	6.70713i	0.319730	−	0.268285i
$626$	2.32518	+	13.1867i	0.0929329	+	0.527048i
$627$		0			0
$628$	−10.9765	−	9.21039i	−0.438011	−	0.367534i
$629$	−8.49671	+	14.7167i	−0.338786	+	0.586794i
$630$		0			0
$631$	12.3054	+	21.3136i	0.489872	+	0.848483i	0.999932	−	0.0116559i	$-0.00371028\pi$
$631$	12.3054	+	21.3136i	0.489872	+	0.848483i	−0.510060	+	0.860139i	$0.670377\pi$
$632$	0.449919	−	2.55162i	0.0178968	−	0.101498i
$633$		0			0
$634$	−23.6465	−	8.60661i	−0.939122	−	0.341812i
$635$	−5.35667	−	1.94967i	−0.212573	−	0.0773702i
$636$		0			0
$637$	0.0761068	−	0.431623i	0.00301546	−	0.0171015i
$638$	−2.59823	−	4.50026i	−0.102865	−	0.178167i
$639$		0			0
$640$	0.510796	−	0.884725i	0.0201910	−	0.0349718i
$641$	−23.1248	−	19.4040i	−0.913373	−	0.766411i	0.0593849	−	0.998235i	$-0.481086\pi$
$641$	−23.1248	−	19.4040i	−0.913373	−	0.766411i	−0.972758	+	0.231824i	$0.925531\pi$
$642$		0			0
$643$	−2.06856	−	11.7314i	−0.0815762	−	0.462641i	−0.998043	−	0.0625308i	$-0.980083\pi$
$643$	−2.06856	−	11.7314i	−0.0815762	−	0.462641i	0.916467	−	0.400111i	$-0.131028\pi$
$644$	−17.8608	+	14.9870i	−0.703813	+	0.590569i
$645$		0			0
$646$	11.1931	−	4.07394i	0.440385	−	0.160287i
$647$	−20.4896			−0.805528			−0.402764	−	0.915304i	$-0.631951\pi$
$647$	−20.4896			−0.805528			−0.402764	+	0.915304i	$0.631951\pi$
$648$		0			0
$649$	−14.6571			−0.575343
$650$	−14.5735	+	5.30431i	−0.571618	+	0.208052i
$651$		0			0
$652$	−10.9476	+	9.18614i	−0.428742	+	0.359757i
$653$	8.53662	+	48.4136i	0.334064	+	1.89457i	0.436286	+	0.899808i	$0.356294\pi$
$653$	8.53662	+	48.4136i	0.334064	+	1.89457i	−0.102222	+	0.994762i	$0.532595\pi$
$654$		0			0
$655$	−1.21091	−	1.01608i	−0.0473142	−	0.0397014i
$656$	1.88313	−	3.26169i	0.0735241	−	0.127347i
$657$		0			0
$658$	3.68681	+	6.38574i	0.143727	+	0.248942i
$659$	−4.93483	+	27.9868i	−0.192234	+	1.09021i	0.724070	+	0.689727i	$0.242269\pi$
$659$	−4.93483	+	27.9868i	−0.192234	+	1.09021i	−0.916303	+	0.400485i	$0.868842\pi$
$660$		0			0
$661$	−40.5404	−	14.7555i	−1.57684	−	0.573923i	−0.602326	−	0.798251i	$-0.705759\pi$
$661$	−40.5404	−	14.7555i	−1.57684	−	0.573923i	−0.974514	+	0.224328i	$0.927981\pi$
$662$	−19.8606	−	7.22868i	−0.771905	−	0.280951i
$663$		0			0
$664$	−1.39609	+	7.91759i	−0.0541786	+	0.307262i
$665$	−8.76306	−	15.1781i	−0.339817	−	0.588580i
$666$		0			0
$667$	−5.47817	+	9.48848i	−0.212116	+	0.367395i
$668$	7.31955	+	6.14183i	0.283202	+	0.237634i
$669$		0			0
$670$	1.44848	+	8.21476i	0.0559598	+	0.317364i
$671$	1.67971	−	1.40944i	0.0648443	−	0.0544108i
$672$		0			0
$673$	33.9219	−	12.3466i	1.30759	−	0.475926i	0.408132	−	0.912923i	$-0.366180\pi$
$673$	33.9219	−	12.3466i	1.30759	−	0.475926i	0.899463	+	0.436997i	$0.143958\pi$
$674$	−4.77192			−0.183808
$675$		0			0
$676$	2.36613			0.0910052
$677$	40.5216	−	14.7487i	1.55737	−	0.566837i	0.587239	−	0.809413i	$-0.300215\pi$
$677$	40.5216	−	14.7487i	1.55737	−	0.566837i	0.970132	+	0.242576i	$0.0779925\pi$
$678$		0			0
$679$	−17.7955	+	14.9322i	−0.682928	+	0.573045i
$680$	−0.328468	−	1.86283i	−0.0125962	−	0.0714364i
$681$		0			0
$682$	10.6468	+	8.93377i	0.407689	+	0.342092i
$683$	0.0895535	−	0.155111i	0.00342667	−	0.00593517i	−0.864307	−	0.502965i	$-0.832243\pi$
$683$	0.0895535	−	0.155111i	0.00342667	−	0.00593517i	0.867734	+	0.497029i	$0.165576\pi$
$684$		0			0
$685$	−10.2462	−	17.7470i	−0.391489	−	0.678078i
$686$	3.18982	−	18.0903i	0.121788	−	0.690692i
$687$		0			0
$688$	−2.90362	−	1.05683i	−0.110700	−	0.0402913i
$689$	−0.853026	−	0.310476i	−0.0324977	−	0.0118282i
$690$		0			0
$691$	−5.97830	+	33.9046i	−0.227425	+	1.28979i	0.630568	+	0.776134i	$0.282822\pi$
$691$	−5.97830	+	33.9046i	−0.227425	+	1.28979i	−0.857994	+	0.513660i	$0.828289\pi$
$692$	4.99127	+	8.64514i	0.189740	+	0.328639i
$693$		0			0
$694$	−7.83372	+	13.5684i	−0.297364	+	0.515050i
$695$	3.05230	+	2.56119i	0.115780	+	0.0971514i
$696$		0			0
$697$	−1.21095	−	6.86764i	−0.0458680	−	0.260130i
$698$	−15.1767	+	12.7348i	−0.574448	+	0.482019i
$699$		0			0
$700$	9.91449	−	3.60858i	0.374732	−	0.136391i
$701$	17.3215			0.654224			0.327112	−	0.944985i	$-0.393924\pi$
$701$	17.3215			0.654224			0.327112	+	0.944985i	$0.393924\pi$
$702$		0			0
$703$	59.0410			2.22677
$704$	−3.89657	+	1.41824i	−0.146858	+	0.0534518i
$705$		0			0
$706$	−12.1013	+	10.1542i	−0.455440	+	0.382160i
$707$	2.50342	+	14.1976i	0.0941508	+	0.533956i
$708$		0			0
$709$	−28.0038	−	23.4980i	−1.05171	−	0.882485i	−0.0584333	−	0.998291i	$-0.518611\pi$
$709$	−28.0038	−	23.4980i	−1.05171	−	0.882485i	−0.993272	+	0.115806i	$0.963055\pi$
$710$	−4.11790	+	7.13241i	−0.154542	+	0.267674i
$711$		0			0
$712$	−6.12693	−	10.6122i	−0.229616	−	0.397707i
$713$	5.08858	−	28.8588i	0.190569	−	1.08077i
$714$		0			0
$715$	−15.6043	−	5.67948i	−0.583566	−	0.212401i
$716$	−21.1509	−	7.69828i	−0.790445	−	0.287698i
$717$		0			0
$718$	0.845577	−	4.79551i	0.0315567	−	0.178967i
$719$	−22.8804	−	39.6301i	−0.853296	−	1.47795i	−0.878216	−	0.478263i	$-0.841266\pi$
$719$	−22.8804	−	39.6301i	−0.853296	−	1.47795i	0.0249200	−	0.999689i	$-0.492067\pi$
$720$		0			0
$721$	−14.3816	+	24.9097i	−0.535601	+	0.927687i
$722$	−17.1474	−	14.3884i	−0.638160	−	0.535480i
$723$		0			0
$724$	0.0861567	+	0.488619i	0.00320199	+	0.0181594i
$725$	3.79803	−	3.18692i	0.141055	−	0.118359i
$726$		0			0
$727$	−8.24873	+	3.00229i	−0.305928	+	0.111349i	−0.490423	−	0.871485i	$-0.663158\pi$
$727$	−8.24873	+	3.00229i	−0.305928	+	0.111349i	0.184494	+	0.982834i	$0.440935\pi$
$728$	−10.4538			−0.387442
$729$		0			0
$730$	3.21592			0.119026
$731$	−5.37632	+	1.95682i	−0.198850	+	0.0723756i
$732$		0			0
$733$	25.4717	−	21.3733i	0.940820	−	0.789441i	−0.0369082	−	0.999319i	$-0.511751\pi$
$733$	25.4717	−	21.3733i	0.940820	−	0.789441i	0.977728	+	0.209877i	$0.0673065\pi$
$734$	1.47394	+	8.35914i	0.0544042	+	0.308542i
$735$		0			0
$736$	6.69746	+	5.61984i	0.246872	+	0.207150i
$737$	16.9291	−	29.3220i	0.623590	−	1.08009i
$738$		0			0
$739$	1.03598	+	1.79437i	0.0381091	+	0.0660069i	0.884451	−	0.466633i	$-0.154533\pi$
$739$	1.03598	+	1.79437i	0.0381091	+	0.0660069i	−0.846342	+	0.532640i	$0.821200\pi$
$740$	1.62811	−	9.23347i	0.0598505	−	0.339429i
$741$		0			0
$742$	0.580323	+	0.211220i	0.0213043	+	0.00775414i
$743$	3.31599	+	1.20692i	0.121652	+	0.0442777i	0.402129	−	0.915583i	$-0.368270\pi$
$743$	3.31599	+	1.20692i	0.121652	+	0.0442777i	−0.280477	+	0.959861i	$0.590493\pi$
$744$		0			0
$745$	1.74459	−	9.89408i	0.0639169	−	0.362491i
$746$	2.25715	+	3.90950i	0.0826401	+	0.143137i
$747$		0			0
$748$	−3.83895	+	6.64925i	−0.140366	+	0.243121i
$749$	30.3391	+	25.4576i	1.10857	+	0.930199i
$750$		0			0
$751$	−6.65211	−	37.7260i	−0.242739	−	1.37664i	−0.825685	−	0.564131i	$-0.809211\pi$
$751$	−6.65211	−	37.7260i	−0.242739	−	1.37664i	0.582946	−	0.812511i	$-0.301900\pi$
$752$	2.11809	−	1.77729i	0.0772389	−	0.0648111i
$753$		0			0
$754$	−4.61613	+	1.68013i	−0.168109	+	0.0611868i
$755$	4.10060			0.149236
$756$		0			0
$757$	12.3900			0.450322			0.225161	−	0.974322i	$-0.427709\pi$
$757$	12.3900			0.450322			0.225161	+	0.974322i	$0.427709\pi$
$758$	10.4323	−	3.79705i	0.378918	−	0.137915i
$759$		0			0
$760$	−5.03442	+	4.22438i	−0.182618	+	0.153234i
$761$	1.41032	+	7.99834i	0.0511241	+	0.289939i	0.999641	−	0.0267867i	$-0.00852750\pi$
$761$	1.41032	+	7.99834i	0.0511241	+	0.289939i	−0.948517	+	0.316726i	$0.897416\pi$
$762$		0			0
$763$	36.0770	+	30.2722i	1.30607	+	1.09593i
$764$	3.59416	−	6.22526i	0.130032	−	0.225222i
$765$		0			0
$766$	11.0213	+	19.0895i	0.398217	+	0.689732i
$767$	−2.40605	+	13.6454i	−0.0868774	+	0.492706i
$768$		0			0
$769$	24.7906	+	9.02303i	0.893971	+	0.325379i	0.747834	−	0.663885i	$-0.231094\pi$
$769$	24.7906	+	9.02303i	0.893971	+	0.325379i	0.146137	+	0.989264i	$0.453316\pi$
$770$	10.6158	+	3.86382i	0.382565	+	0.139242i
$771$		0			0
$772$	−2.33901	+	13.2652i	−0.0841829	+	0.477425i
$773$	5.39129	+	9.33798i	0.193911	+	0.335864i	0.946543	−	0.322578i	$-0.104549\pi$
$773$	5.39129	+	9.33798i	0.193911	+	0.335864i	−0.752632	+	0.658442i	$0.771216\pi$
$774$		0			0
$775$	−6.63032	+	11.4840i	−0.238168	+	0.412519i
$776$	6.67298	+	5.59930i	0.239546	+	0.201003i
$777$		0			0
$778$	−2.95836	−	16.7777i	−0.106062	−	0.601509i
$779$	−18.5602	+	15.5739i	−0.664989	+	0.557992i
$780$		0			0
$781$	31.4131	−	11.4334i	1.12405	−	0.409120i
$782$	16.1883			0.578892
$783$		0			0
$784$	0.111808			0.00399313
$785$	13.7554	−	5.00657i	0.490952	−	0.178692i
$786$		0			0
$787$	21.9933	−	18.4546i	0.783976	−	0.657834i	−0.160270	−	0.987073i	$-0.551237\pi$
$787$	21.9933	−	18.4546i	0.783976	−	0.657834i	0.944247	+	0.329239i	$0.106792\pi$
$788$	−0.879840	−	4.98982i	−0.0313430	−	0.177755i
$789$		0			0
$790$	2.02766	+	1.70141i	0.0721410	+	0.0605335i
$791$	2.60859	−	4.51821i	0.0927509	−	0.160649i
$792$		0			0
$793$	−1.03642	−	1.79513i	−0.0368042	−	0.0637468i
$794$	2.71048	−	15.3719i	0.0961914	−	0.545529i
$795$		0			0
$796$	16.8626	+	6.13750i	0.597680	+	0.217538i
$797$	−18.3516	−	6.67942i	−0.650045	−	0.236597i	−0.00411268	−	0.999992i	$-0.501309\pi$
$797$	−18.3516	−	6.67942i	−0.650045	−	0.236597i	−0.645933	+	0.763394i	$0.723531\pi$
$798$		0			0
$799$	0.889009	−	5.04182i	0.0314509	−	0.178367i
$800$	−1.97817	−	3.42630i	−0.0699390	−	0.121138i
$801$		0			0
$802$	1.84220	−	3.19079i	0.0650505	−	0.112671i
$803$	−9.99950	−	8.39057i	−0.352875	−	0.296097i
$804$		0			0
$805$	−4.13613	−	23.4572i	−0.145779	−	0.826756i
$806$	10.0648	−	8.44539i	0.354518	−	0.297476i
$807$		0			0
$808$	5.07995	−	1.84895i	0.178712	−	0.0650458i
$809$	−44.3315			−1.55861			−0.779307	−	0.626643i	$-0.784429\pi$
$809$	−44.3315			−1.55861			−0.779307	+	0.626643i	$0.784429\pi$
$810$		0			0
$811$	47.8398			1.67988			0.839941	−	0.542677i	$-0.182589\pi$
$811$	47.8398			1.67988			0.839941	+	0.542677i	$0.182589\pi$
$812$	3.14040	−	1.14301i	0.110207	−	0.0401119i
$813$		0			0
$814$	−29.1533	+	24.4625i	−1.02182	+	0.857410i
$815$	−2.53521	−	14.3779i	−0.0888045	−	0.503635i
$816$		0			0
$817$	15.2274	+	12.7773i	0.532740	+	0.447022i
$818$	−6.72786	+	11.6530i	−0.235234	+	0.407438i
$819$		0			0
$820$	1.92380	+	3.33211i	0.0671819	+	0.116362i
$821$	5.56302	−	31.5494i	0.194151	−	1.10108i	−0.719473	−	0.694521i	$-0.755616\pi$
$821$	5.56302	−	31.5494i	0.194151	−	1.10108i	0.913623	−	0.406562i	$-0.133272\pi$
$822$		0			0
$823$	−7.96990	−	2.90081i	−0.277813	−	0.101116i	0.199356	−	0.979927i	$-0.436115\pi$
$823$	−7.96990	−	2.90081i	−0.277813	−	0.101116i	−0.477169	+	0.878811i	$0.658337\pi$
$824$	10.1353	+	3.68893i	0.353078	+	0.128510i
$825$		0			0
$826$	1.63686	−	9.28310i	0.0569537	−	0.323000i
$827$	10.8012	+	18.7083i	0.375596	+	0.650552i	0.990416	−	0.138116i	$-0.0441047\pi$
$827$	10.8012	+	18.7083i	0.375596	+	0.650552i	−0.614820	+	0.788668i	$0.710771\pi$
$828$		0			0
$829$	−23.3196	+	40.3907i	−0.809922	+	1.40283i	0.102996	+	0.994682i	$0.467157\pi$
$829$	−23.3196	+	40.3907i	−0.809922	+	1.40283i	−0.912918	+	0.408144i	$0.866176\pi$
$830$	−6.29178	−	5.27943i	−0.218391	−	0.183252i
$831$		0			0
$832$	0.680695	+	3.86041i	0.0235989	+	0.133836i
$833$	0.158588	−	0.133071i	0.00549474	−	0.00461064i
$834$		0			0
$835$	−9.17263	+	3.33856i	−0.317432	+	0.115536i
$836$	26.6757			0.922597
$837$		0			0
$838$	1.37747			0.0475840
$839$	12.8905	−	4.69176i	0.445030	−	0.161978i	−0.109778	−	0.993956i	$-0.535014\pi$
$839$	12.8905	−	4.69176i	0.445030	−	0.161978i	0.554808	+	0.831978i	$0.312792\pi$
$840$		0			0
$841$	−21.0123	+	17.6314i	−0.724561	+	0.607979i
$842$	1.39368	+	7.90398i	0.0480295	+	0.272389i
$843$		0			0
$844$	−3.90190	−	3.27408i	−0.134309	−	0.112699i
$845$	−1.20861	+	2.09338i	−0.0415775	+	0.0720144i
$846$		0			0
$847$	−8.25999	−	14.3067i	−0.283817	−	0.491585i
$848$	0.0402128	−	0.228058i	0.00138091	−	0.00783155i
$849$		0			0
$850$	−6.88375	−	2.50548i	−0.236111	−	0.0859373i
$851$	75.4011	+	27.4438i	2.58472	+	0.940760i
$852$		0			0
$853$	3.39926	−	19.2781i	0.116388	−	0.660071i	−0.869665	−	0.493642i	$-0.835665\pi$
$853$	3.39926	−	19.2781i	0.116388	−	0.660071i	0.986053	−	0.166429i	$-0.0532236\pi$
$854$	0.705086	+	1.22124i	0.0241275	+	0.0417901i
$855$		0			0
$856$	7.42556	−	12.8615i	0.253800	−	0.439595i
$857$	4.11703	+	3.45460i	0.140635	+	0.118007i	0.710391	−	0.703807i	$-0.248518\pi$
$857$	4.11703	+	3.45460i	0.140635	+	0.118007i	−0.569756	+	0.821814i	$0.692962\pi$
$858$		0			0
$859$	5.41073	+	30.6858i	0.184612	+	1.04698i	0.926453	+	0.376410i	$0.122841\pi$
$859$	5.41073	+	30.6858i	0.184612	+	1.04698i	−0.741842	+	0.670575i	$0.766047\pi$
$860$	2.41816	−	2.02908i	0.0824587	−	0.0691911i
$861$		0			0
$862$	32.6001	−	11.8655i	1.11036	−	0.404139i
$863$	2.34241			0.0797367			0.0398683	−	0.999205i	$-0.487306\pi$
$863$	2.34241			0.0797367			0.0398683	+	0.999205i	$0.487306\pi$
$864$		0			0
$865$	−10.1981			−0.346746
$866$	0.569445	−	0.207261i	0.0193505	−	0.00704301i
$867$		0			0
$868$	−6.84721	+	5.74549i	−0.232410	+	0.195015i
$869$	−1.86566	−	10.5807i	−0.0632880	−	0.358924i
$870$		0			0
$871$	−24.5190	−	20.5739i	−0.830793	−	0.697118i
$872$	8.82991	−	15.2939i	0.299019	−	0.517915i
$873$		0			0
$874$	−28.1219	−	48.7085i	−0.951237	−	1.64759i
$875$	−4.23710	+	24.0298i	−0.143240	+	0.812356i
$876$		0			0
$877$	42.5834	+	15.4991i	1.43794	+	0.523367i	0.939196	−	0.343383i	$-0.111573\pi$
$877$	42.5834	+	15.4991i	1.43794	+	0.523367i	0.498743	+	0.866750i	$0.333795\pi$
$878$	−1.04726	−	0.381172i	−0.0353434	−	0.0128639i
$879$		0			0
$880$	0.735606	−	4.17183i	0.0247973	−	0.140632i
$881$	−5.46101	−	9.45874i	−0.183986	−	0.318673i	0.759248	−	0.650801i	$-0.225567\pi$
$881$	−5.46101	−	9.45874i	−0.183986	−	0.318673i	−0.943234	+	0.332128i	$0.892233\pi$
$882$		0			0
$883$	−12.8886	+	22.3238i	−0.433737	+	0.751254i	−0.997192	−	0.0748928i	$-0.976139\pi$
$883$	−12.8886	+	22.3238i	−0.433737	+	0.751254i	0.563455	+	0.826147i	$0.309472\pi$
$884$	5.56008	+	4.66546i	0.187006	+	0.156916i
$885$		0			0
$886$	1.06252	+	6.02583i	0.0356960	+	0.202442i
$887$	31.1646	−	26.1502i	1.04640	−	0.878038i	0.0536937	−	0.998557i	$-0.482901\pi$
$887$	31.1646	−	26.1502i	1.04640	−	0.878038i	0.992711	+	0.120520i	$0.0384561\pi$
$888$		0			0
$889$	−13.9832	+	5.08947i	−0.468982	+	0.170695i
$890$	12.5185			0.419620
$891$		0			0
$892$	3.81615			0.127774
$893$	−16.7146	+	6.08360i	−0.559331	+	0.203580i
$894$		0			0
$895$	17.6147	−	14.7804i	0.588793	−	0.494056i
$896$	−0.463084	−	2.62628i	−0.0154706	−	0.0877379i
$897$		0			0
$898$	27.7987	+	23.3259i	0.927655	+	0.778395i
$899$	−2.10015	+	3.63756i	−0.0700438	+	0.121319i
$900$		0			0
$901$	−0.214392	−	0.371338i	−0.00714244	−	0.0123711i
$902$	2.71193	−	15.3801i	0.0902975	−	0.512102i
$903$		0			0
$904$	−1.83837	−	0.669111i	−0.0611432	−	0.0222543i
$905$	−0.476302	−	0.173360i	−0.0158328	−	0.00576267i
$906$		0			0
$907$	−0.940619	+	5.33451i	−0.0312327	+	0.177130i	−0.996434	−	0.0843797i	$-0.973109\pi$
$907$	−0.940619	+	5.33451i	−0.0312327	+	0.177130i	0.965201	+	0.261509i	$0.0842202\pi$
$908$	−10.1894	−	17.6486i	−0.338148	−	0.585690i
$909$		0			0
$910$	5.33974	−	9.24870i	0.177011	−	0.306591i
$911$	−3.30707	−	2.77496i	−0.109568	−	0.0919385i	0.586358	−	0.810052i	$-0.300561\pi$
$911$	−3.30707	−	2.77496i	−0.109568	−	0.0919385i	−0.695926	+	0.718114i	$0.745006\pi$
$912$		0			0
$913$	5.78907	+	32.8315i	0.191590	+	1.08656i
$914$	−15.8918	+	13.3348i	−0.525655	+	0.441077i
$915$		0			0
$916$	1.41711	−	0.515787i	0.0468227	−	0.0170421i
$917$	−4.12640			−0.136266
$918$		0			0
$919$	−33.7655			−1.11382			−0.556911	−	0.830572i	$-0.688013\pi$
$919$	−33.7655			−1.11382			−0.556911	+	0.830572i	$0.688013\pi$
$920$	−8.39305	+	3.05482i	−0.276711	+	0.100714i
$921$		0			0
$922$	31.6845	−	26.5864i	1.04347	−	0.875578i
$923$	−5.48757	−	31.1216i	−0.180626	−	1.02438i
$924$		0			0
$925$	−27.8153	−	23.3398i	−0.914563	−	0.767409i
$926$	−11.8160	+	20.4660i	−0.388299	+	0.672554i
$927$		0			0
$928$	−0.626584	−	1.08528i	−0.0205686	−	0.0356259i
$929$	−7.86087	+	44.5812i	−0.257907	+	1.46266i	0.530593	+	0.847626i	$0.321969\pi$
$929$	−7.86087	+	44.5812i	−0.257907	+	1.46266i	−0.788500	+	0.615035i	$0.789142\pi$
$930$		0			0
$931$	−0.675888	−	0.246003i	−0.0221513	−	0.00806243i
$932$	−18.9513	−	6.89771i	−0.620771	−	0.225942i
$933$		0			0
$934$	−3.67706	+	20.8536i	−0.120317	+	0.682352i
$935$	−3.92184	−	6.79282i	−0.128258	−	0.222149i
$936$		0			0
$937$	6.86473	−	11.8901i	0.224261	−	0.388431i	−0.731837	−	0.681480i	$-0.761337\pi$
$937$	6.86473	−	11.8901i	0.224261	−	0.388431i	0.956097	+	0.293049i	$0.0946699\pi$
$938$	16.6805	+	13.9966i	0.544639	+	0.457006i
$939$		0			0
$940$	0.490500	+	2.78176i	0.0159983	+	0.0907311i
$941$	5.27589	−	4.42700i	0.171989	−	0.144316i	−0.552730	−	0.833360i	$-0.686414\pi$
$941$	5.27589	−	4.42700i	0.171989	−	0.144316i	0.724719	+	0.689044i	$0.241969\pi$
$942$		0			0
$943$	−30.9424	+	11.2621i	−1.00762	+	0.366744i
$944$	−3.53469			−0.115044
$945$		0			0
$946$	−12.8130			−0.416587
$947$	−39.5384	+	14.3908i	−1.28483	+	0.467639i	−0.892026	−	0.451985i	$-0.850716\pi$
$947$	−39.5384	+	14.3908i	−1.28483	+	0.467639i	−0.392801	+	0.919624i	$0.628494\pi$
$948$		0			0
$949$	−9.45286	+	7.93189i	−0.306853	+	0.257480i
$950$	4.41960	+	25.0648i	0.143391	+	0.813209i
$951$		0			0
$952$	−3.78259	−	3.17397i	−0.122594	−	0.102869i
$953$	−7.20010	+	12.4709i	−0.233234	+	0.403973i	−0.958758	−	0.284224i	$-0.908264\pi$
$953$	−7.20010	+	12.4709i	−0.233234	+	0.403973i	0.725524	+	0.688197i	$0.241597\pi$
$954$		0			0
$955$	3.67177	+	6.35968i	0.118816	+	0.205795i
$956$	2.19550	−	12.4513i	0.0710077	−	0.402704i
$957$		0			0
$958$	−12.5245	−	4.55855i	−0.404649	−	0.147280i
$959$	−50.2681	−	18.2961i	−1.62324	−	0.590812i
$960$		0			0
$961$	−3.43231	+	19.4656i	−0.110720	+	0.627922i
$962$	17.9882	+	31.1565i	0.579964	+	1.00453i
$963$		0			0
$964$	13.9197	−	24.1097i	0.448325	−	0.776521i
$965$	−10.5413	−	8.84520i	−0.339336	−	0.284737i
$966$		0			0
$967$	−0.257613	−	1.46100i	−0.00828429	−	0.0469825i	0.980385	−	0.197090i	$-0.0631491\pi$
$967$	−0.257613	−	1.46100i	−0.00828429	−	0.0469825i	−0.988670	+	0.150107i	$0.952038\pi$
$968$	−4.74541	+	3.98187i	−0.152523	+	0.127982i
$969$		0			0
$970$	−8.36237	+	3.04366i	−0.268500	+	0.0977259i
$971$	−57.7537			−1.85340			−0.926702	−	0.375797i	$-0.877369\pi$
$971$	−57.7537			−1.85340			−0.926702	+	0.375797i	$0.877369\pi$
$972$		0			0
$973$	10.4013			0.333449
$974$	−17.2783	+	6.28878i	−0.553632	+	0.201505i
$975$		0			0
$976$	0.405075	−	0.339899i	0.0129661	−	0.0108799i
$977$	−6.17780	−	35.0361i	−0.197645	−	1.12090i	−0.908601	−	0.417666i	$-0.862848\pi$
$977$	−6.17780	−	35.0361i	−0.197645	−	1.12090i	0.710955	−	0.703237i	$-0.248263\pi$
$978$		0			0
$979$	−38.9246	−	32.6616i	−1.24404	−	1.04387i
$980$	−0.0571109	+	0.0989190i	−0.00182434	+	0.00315985i
$981$		0			0
$982$	−9.64826	−	16.7113i	−0.307888	−	0.533278i
$983$	−4.42114	+	25.0735i	−0.141012	+	0.799722i	0.829470	+	0.558551i	$0.188642\pi$
$983$	−4.42114	+	25.0735i	−0.141012	+	0.799722i	−0.970483	+	0.241171i	$0.922469\pi$
$984$		0			0
$985$	4.86404	+	1.77036i	0.154981	+	0.0564085i
$986$	−2.18042	−	0.793608i	−0.0694387	−	0.0252736i
$987$		0			0
$988$	4.37896	−	24.8343i	0.139313	−	0.790084i
$989$	13.5077	+	23.3960i	0.429519	+	0.743948i
$990$		0			0
$991$	22.5583	−	39.0722i	0.716589	−	1.24117i	−0.245755	−	0.969332i	$-0.579036\pi$
$991$	22.5583	−	39.0722i	0.716589	−	1.24117i	0.962344	−	0.271836i	$-0.0876309\pi$
$992$	2.56758	+	2.15445i	0.0815207	+	0.0684040i
$993$		0			0
$994$	3.73326	+	21.1724i	0.118412	+	0.671546i
$995$	−14.0434	+	11.7838i	−0.445205	+	0.373571i
$996$		0			0
$997$	−49.8376	+	18.1394i	−1.57837	+	0.574481i	−0.974849	−	0.222865i	$-0.928459\pi$
$997$	−49.8376	+	18.1394i	−1.57837	+	0.574481i	−0.603523	+	0.797345i	$0.706237\pi$
$998$	16.3501			0.517553
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.e.b.19.2		12
3.2	odd	2		54.2.e.b.7.2	✓	12
9.2	odd	6		486.2.e.f.379.2		12
9.4	even	3		486.2.e.e.217.2		12
9.5	odd	6		486.2.e.h.217.1		12
9.7	even	3		486.2.e.g.379.1		12
12.11	even	2		432.2.u.b.385.1		12
27.2	odd	18		1458.2.a.g.1.2		6
27.4	even	9	inner	162.2.e.b.145.2		12
27.5	odd	18		486.2.e.h.271.1		12
27.7	even	9		1458.2.c.g.487.2		12
27.11	odd	18		1458.2.c.f.973.5		12
27.13	even	9		486.2.e.g.109.1		12
27.14	odd	18		486.2.e.f.109.2		12
27.16	even	9		1458.2.c.g.973.2		12
27.20	odd	18		1458.2.c.f.487.5		12
27.22	even	9		486.2.e.e.271.2		12
27.23	odd	18		54.2.e.b.31.2	yes	12
27.25	even	9		1458.2.a.f.1.5		6
108.23	even	18		432.2.u.b.193.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.b.7.2	✓	12	3.2	odd	2
54.2.e.b.31.2	yes	12	27.23	odd	18
162.2.e.b.19.2		12	1.1	even	1	trivial
162.2.e.b.145.2		12	27.4	even	9	inner
432.2.u.b.193.1		12	108.23	even	18
432.2.u.b.385.1		12	12.11	even	2
486.2.e.e.217.2		12	9.4	even	3
486.2.e.e.271.2		12	27.22	even	9
486.2.e.f.109.2		12	27.14	odd	18
486.2.e.f.379.2		12	9.2	odd	6
486.2.e.g.109.1		12	27.13	even	9
486.2.e.g.379.1		12	9.7	even	3
486.2.e.h.217.1		12	9.5	odd	6
486.2.e.h.271.1		12	27.5	odd	18
1458.2.a.f.1.5		6	27.25	even	9
1458.2.a.g.1.2		6	27.2	odd	18
1458.2.c.f.487.5		12	27.20	odd	18
1458.2.c.f.973.5		12	27.11	odd	18
1458.2.c.g.487.2		12	27.7	even	9
1458.2.c.g.973.2		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)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(0.766044 - 0.642788i) q^{4} +(0.177398 + 1.00607i) q^{5} +(2.04289 + 1.71418i) q^{7} +(0.500000 - 0.866025i) q^{8} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(0.766044 - 0.642788i) q^{4} +(0.177398 + 1.00607i) q^{5} +(2.04289 + 1.71418i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.510796 + 0.884725i) q^{10} +(0.720058 - 4.08365i) q^{11} +(-3.68356 - 1.34071i) q^{13} +(2.50597 + 0.912098i) q^{14} +(0.173648 - 0.984808i) q^{16} +(-0.925795 - 1.60352i) q^{17} +(-3.21653 + 5.57120i) q^{19} +(0.782585 + 0.656667i) q^{20} +(-0.720058 - 4.08365i) q^{22} +(-6.69746 + 5.61984i) q^{23} +(3.71775 - 1.35315i) q^{25} -3.91997 q^{26} +2.66680 q^{28} +(1.17759 - 0.428609i) q^{29} +(-2.56758 + 2.15445i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-1.41840 - 1.19018i) q^{34} +(-1.36219 + 2.35938i) q^{35} +(-4.58887 - 7.94816i) q^{37} +(-1.11709 + 6.33533i) q^{38} +(0.959983 + 0.349405i) q^{40} +(3.53914 + 1.28814i) q^{41} +(0.536567 - 3.04303i) q^{43} +(-2.07332 - 3.59110i) q^{44} +(-4.37146 + 7.57159i) q^{46} +(2.11809 + 1.77729i) q^{47} +(0.0194152 + 0.110109i) q^{49} +(3.03074 - 2.54309i) q^{50} +(-3.68356 + 1.34071i) q^{52} +0.231576 q^{53} +4.23618 q^{55} +(2.50597 - 0.912098i) q^{56} +(0.959983 - 0.805521i) q^{58} +(-0.613793 - 3.48099i) q^{59} +(0.405075 + 0.339899i) q^{61} +(-1.67587 + 2.90269i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(0.695393 - 3.94377i) q^{65} +(7.67276 + 2.79266i) q^{67} +(-1.73993 - 0.633281i) q^{68} +(-0.473084 + 2.68299i) q^{70} +(4.03086 + 6.98165i) q^{71} +(1.57397 - 2.72620i) q^{73} +(-7.03056 - 5.89934i) q^{74} +(1.11709 + 6.33533i) q^{76} +(8.47113 - 7.10812i) q^{77} +(2.43473 - 0.886167i) q^{79} +1.02159 q^{80} +3.76627 q^{82} +(-7.55488 + 2.74975i) q^{83} +(1.44903 - 1.21588i) q^{85} +(-0.536567 - 3.04303i) q^{86} +(-3.17652 - 2.66541i) q^{88} +(6.12693 - 10.6122i) q^{89} +(-5.22688 - 9.05322i) q^{91} +(-1.51819 + 8.61009i) q^{92} +(2.59823 + 0.945677i) q^{94} +(-6.17564 - 2.24775i) q^{95} +(-1.51264 + 8.57862i) q^{97} +(0.0559038 + 0.0968282i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) \) 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