LMFDB - Embedded newform 414.2.i.g.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(55,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("414.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.i (of order $11$, degree $10$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 8 x^{18} + 53 x^{16} + 358 x^{14} + 1753 x^{12} + 7149 x^{10} + 23268 x^{8} + 37292 x^{6} + \cdots + 58081 $ x^20 + 8x^18 + 53x^16 + 358x^14 + 1753x^12 + 7149x^10 + 23268x^8 + 37292x^6 + 19057x^4 - 81217*x^2 + 58081
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			361.2
Root			$0.708869 + 1.55221i$ of defining polynomial
Character	$\chi$	$=$	414.361
Dual form			414.2.i.g.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 + 0.755750i) q^{2} +(-0.142315 - 0.989821i) q^{4} +(1.18678 + 2.59868i) q^{5} +(-4.30188 + 1.26315i) q^{7} +(0.841254 + 0.540641i) q^{8} +O(q^{10})$	\(q+(-0.654861 + 0.755750i) q^{2} +(-0.142315 - 0.989821i) q^{4} +(1.18678 + 2.59868i) q^{5} +(-4.30188 + 1.26315i) q^{7} +(0.841254 + 0.540641i) q^{8} +(-2.74112 - 0.804866i) q^{10} +(-0.129901 - 0.149914i) q^{11} +(-3.55849 - 1.04487i) q^{13} +(1.86251 - 4.07833i) q^{14} +(-0.959493 + 0.281733i) q^{16} +(0.0880352 - 0.612298i) q^{17} +(0.0368862 + 0.256549i) q^{19} +(2.40333 - 1.54453i) q^{20} +0.198365 q^{22} +(-4.31411 + 2.09487i) q^{23} +(-2.07038 + 2.38934i) q^{25} +(3.11997 - 2.00509i) q^{26} +(1.86251 + 4.07833i) q^{28} +(-1.06688 + 7.42031i) q^{29} +(-2.36331 - 1.51881i) q^{31} +(0.415415 - 0.909632i) q^{32} +(0.405093 + 0.467502i) q^{34} +(-8.38787 - 9.68012i) q^{35} +(2.45405 - 5.37362i) q^{37} +(-0.218042 - 0.140127i) q^{38} +(-0.406571 + 2.82776i) q^{40} +(3.51171 + 7.68956i) q^{41} +(-8.47267 + 5.44505i) q^{43} +(-0.129901 + 0.149914i) q^{44} +(1.24194 - 4.63223i) q^{46} -9.81259 q^{47} +(11.0219 - 7.08332i) q^{49} +(-0.449936 - 3.12937i) q^{50} +(-0.527806 + 3.67097i) q^{52} +(3.77638 - 1.10884i) q^{53} +(0.235415 - 0.515486i) q^{55} +(-4.30188 - 1.26315i) q^{56} +(-4.90924 - 5.66556i) q^{58} +(9.41528 + 2.76458i) q^{59} +(-4.30653 - 2.76764i) q^{61} +(2.69548 - 0.791464i) q^{62} +(0.415415 + 0.909632i) q^{64} +(-1.50786 - 10.4874i) q^{65} +(4.81731 - 5.55947i) q^{67} -0.618594 q^{68} +12.8086 q^{70} +(-7.26928 + 8.38920i) q^{71} +(2.22470 + 15.4731i) q^{73} +(2.45405 + 5.37362i) q^{74} +(0.248688 - 0.0730215i) q^{76} +(0.748184 + 0.480829i) q^{77} +(14.3558 + 4.21524i) q^{79} +(-1.87083 - 2.15906i) q^{80} +(-8.11106 - 2.38162i) q^{82} +(4.00034 - 8.75953i) q^{83} +(1.69564 - 0.497885i) q^{85} +(1.43332 - 9.96896i) q^{86} +(-0.0282303 - 0.196346i) q^{88} +(12.9011 - 8.29101i) q^{89} +16.6280 q^{91} +(2.68751 + 3.97207i) q^{92} +(6.42588 - 7.41586i) q^{94} +(-0.622913 + 0.400322i) q^{95} +(4.92117 + 10.7759i) q^{97} +(-1.86457 + 12.9684i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{7} - 2 q^{8}+O(q^{10}) $ 20 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^7 - 2 * q^8	$ 20 q - 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{7} - 2 q^{8} - 2 q^{10} + 2 q^{11} + 18 q^{14} - 2 q^{16} - 18 q^{17} + 16 q^{19} - 2 q^{20} + 24 q^{22} + 2 q^{23} + 38 q^{25} + 18 q^{28} + 30 q^{29} + 14 q^{31} - 2 q^{32} + 4 q^{34} - 48 q^{35} - 20 q^{37} + 16 q^{38} - 2 q^{40} + 12 q^{41} - 28 q^{43} + 2 q^{44} + 2 q^{46} - 32 q^{47} + 6 q^{49} - 6 q^{50} + 46 q^{53} - 28 q^{55} - 4 q^{56} - 14 q^{58} - 50 q^{61} - 8 q^{62} - 2 q^{64} - 16 q^{65} - 8 q^{67} + 48 q^{68} - 48 q^{70} - 12 q^{71} - 18 q^{73} - 20 q^{74} - 6 q^{76} + 4 q^{77} - 18 q^{79} - 2 q^{80} - 10 q^{82} + 44 q^{83} + 32 q^{85} - 28 q^{86} + 2 q^{88} + 44 q^{91} + 2 q^{92} + 12 q^{94} - 64 q^{95} + 14 q^{97} + 28 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^7 - 2 * q^8 - 2 * q^10 + 2 * q^11 + 18 * q^14 - 2 * q^16 - 18 * q^17 + 16 * q^19 - 2 * q^20 + 24 * q^22 + 2 * q^23 + 38 * q^25 + 18 * q^28 + 30 * q^29 + 14 * q^31 - 2 * q^32 + 4 * q^34 - 48 * q^35 - 20 * q^37 + 16 * q^38 - 2 * q^40 + 12 * q^41 - 28 * q^43 + 2 * q^44 + 2 * q^46 - 32 * q^47 + 6 * q^49 - 6 * q^50 + 46 * q^53 - 28 * q^55 - 4 * q^56 - 14 * q^58 - 50 * q^61 - 8 * q^62 - 2 * q^64 - 16 * q^65 - 8 * q^67 + 48 * q^68 - 48 * q^70 - 12 * q^71 - 18 * q^73 - 20 * q^74 - 6 * q^76 + 4 * q^77 - 18 * q^79 - 2 * q^80 - 10 * q^82 + 44 * q^83 + 32 * q^85 - 28 * q^86 + 2 * q^88 + 44 * q^91 + 2 * q^92 + 12 * q^94 - 64 * q^95 + 14 * q^97 + 28 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	−0.654861	+	0.755750i	−0.463056	+	0.534396i
$2$	−0.654861	+	0.755750i	−0.463056	+	0.534396i
$3$		0			0
$3$		0			0
$4$	−0.142315	−	0.989821i	−0.0711574	−	0.494911i
$5$	1.18678	+	2.59868i	0.530742	+	1.16216i	0.965210	+	0.261476i	$0.0842092\pi$
$5$	1.18678	+	2.59868i	0.530742	+	1.16216i	−0.434468	+	0.900687i	$0.643064\pi$
$6$		0			0
$7$	−4.30188	+	1.26315i	−1.62596	+	0.477424i	−0.962611	−	0.270887i	$-0.912683\pi$
$7$	−4.30188	+	1.26315i	−1.62596	+	0.477424i	−0.663347	+	0.748312i	$0.730865\pi$
$8$	0.841254	+	0.540641i	0.297428	+	0.191145i
$9$		0			0
$10$	−2.74112	−	0.804866i	−0.866819	−	0.254521i
$11$	−0.129901	−	0.149914i	−0.0391668	−	0.0452009i	0.735828	−	0.677168i	$-0.236793\pi$
$11$	−0.129901	−	0.149914i	−0.0391668	−	0.0452009i	−0.774995	+	0.631967i	$0.782248\pi$
$12$		0			0
$13$	−3.55849	−	1.04487i	−0.986948	−	0.289794i	−0.251858	−	0.967764i	$-0.581042\pi$
$13$	−3.55849	−	1.04487i	−0.986948	−	0.289794i	−0.735090	+	0.677970i	$0.762860\pi$
$14$	1.86251	−	4.07833i	0.497777	−	1.08998i
$15$		0			0
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	0.0880352	−	0.612298i	0.0213517	−	0.148504i	−0.976357	−	0.216166i	$-0.930645\pi$
$17$	0.0880352	−	0.612298i	0.0213517	−	0.148504i	0.997708	+	0.0676618i	$0.0215539\pi$
$18$		0			0
$19$	0.0368862	+	0.256549i	0.00846228	+	0.0588564i	0.993615	−	0.112824i	$-0.0359895\pi$
$19$	0.0368862	+	0.256549i	0.00846228	+	0.0588564i	−0.985153	+	0.171680i	$0.945080\pi$
$20$	2.40333	−	1.54453i	0.537401	−	0.345366i
$21$		0			0
$22$	0.198365			0.0422916
$23$	−4.31411	+	2.09487i	−0.899554	+	0.436810i
$23$	−4.31411	+	2.09487i	−0.899554	+	0.436810i
$24$		0			0
$25$	−2.07038	+	2.38934i	−0.414075	+	0.477868i
$26$	3.11997	−	2.00509i	0.611877	−	0.393230i
$27$		0			0
$28$	1.86251	+	4.07833i	0.351981	+	0.770732i
$29$	−1.06688	+	7.42031i	−0.198114	+	1.37792i	0.611635	+	0.791140i	$0.290512\pi$
$29$	−1.06688	+	7.42031i	−0.198114	+	1.37792i	−0.809749	+	0.586776i	$0.800397\pi$
$30$		0			0
$31$	−2.36331	−	1.51881i	−0.424463	−	0.272786i	0.310922	−	0.950436i	$-0.399362\pi$
$31$	−2.36331	−	1.51881i	−0.424463	−	0.272786i	−0.735385	+	0.677649i	$0.762999\pi$
$32$	0.415415	−	0.909632i	0.0734357	−	0.160802i
$33$		0			0
$34$	0.405093	+	0.467502i	0.0694729	+	0.0801760i
$35$	−8.38787	−	9.68012i	−1.41781	−	1.63624i
$36$		0			0
$37$	2.45405	−	5.37362i	0.403443	−	0.883418i	−0.593466	−	0.804859i	$-0.702241\pi$
$37$	2.45405	−	5.37362i	0.403443	−	0.883418i	0.996909	−	0.0785589i	$-0.0250319\pi$
$38$	−0.218042	−	0.140127i	−0.0353711	−	0.0227316i
$39$		0			0
$40$	−0.406571	+	2.82776i	−0.0642845	+	0.447109i
$41$	3.51171	+	7.68956i	0.548436	+	1.20091i	0.957508	+	0.288406i	$0.0931253\pi$
$41$	3.51171	+	7.68956i	0.548436	+	1.20091i	−0.409072	+	0.912502i	$0.634147\pi$
$42$		0			0
$43$	−8.47267	+	5.44505i	−1.29207	+	0.830363i	−0.992325	−	0.123657i	$-0.960538\pi$
$43$	−8.47267	+	5.44505i	−1.29207	+	0.830363i	−0.299744	+	0.954020i	$0.596901\pi$
$44$	−0.129901	+	0.149914i	−0.0195834	+	0.0226004i
$45$		0			0
$46$	1.24194	−	4.63223i	0.183115	−	0.682985i
$47$	−9.81259			−1.43131			−0.715657	−	0.698452i	$-0.753872\pi$
$47$	−9.81259			−1.43131			−0.715657	+	0.698452i	$0.753872\pi$
$48$		0			0
$49$	11.0219	−	7.08332i	1.57455	−	1.01190i
$50$	−0.449936	−	3.12937i	−0.0636305	−	0.442560i
$51$		0			0
$52$	−0.527806	+	3.67097i	−0.0731935	+	0.509072i
$53$	3.77638	−	1.10884i	0.518725	−	0.152311i	−0.0118818	−	0.999929i	$-0.503782\pi$
$53$	3.77638	−	1.10884i	0.518725	−	0.152311i	0.530607	+	0.847618i	$0.321964\pi$
$54$		0			0
$55$	0.235415	−	0.515486i	0.0317433	−	0.0695082i
$56$	−4.30188	−	1.26315i	−0.574863	−	0.168795i
$57$		0			0
$58$	−4.90924	−	5.66556i	−0.644614	−	0.743925i
$59$	9.41528	+	2.76458i	1.22577	+	0.359917i	0.829650	−	0.558284i	$-0.188540\pi$
$59$	9.41528	+	2.76458i	1.22577	+	0.359917i	0.396115	+	0.918201i	$0.370358\pi$
$60$		0			0
$61$	−4.30653	−	2.76764i	−0.551394	−	0.354360i	0.235086	−	0.971975i	$-0.424463\pi$
$61$	−4.30653	−	2.76764i	−0.551394	−	0.354360i	−0.786481	+	0.617615i	$0.788099\pi$
$62$	2.69548	−	0.791464i	0.342326	−	0.100516i
$63$		0			0
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	−1.50786	−	10.4874i	−0.187027	−	1.30080i
$66$		0			0
$67$	4.81731	−	5.55947i	0.588528	−	0.679197i	−0.380888	−	0.924621i	$-0.624382\pi$
$67$	4.81731	−	5.55947i	0.588528	−	0.679197i	0.969416	+	0.245424i	$0.0789271\pi$
$68$	−0.618594			−0.0750156
$69$		0			0
$70$	12.8086			1.53093
$71$	−7.26928	+	8.38920i	−0.862705	+	0.995615i	0.137282	+	0.990532i	$0.456163\pi$
$71$	−7.26928	+	8.38920i	−0.862705	+	0.995615i	−0.999987	+	0.00508295i	$0.998382\pi$
$72$		0			0
$73$	2.22470	+	15.4731i	0.260382	+	1.81099i	0.529968	+	0.848018i	$0.322204\pi$
$73$	2.22470	+	15.4731i	0.260382	+	1.81099i	−0.269586	+	0.962976i	$0.586887\pi$
$74$	2.45405	+	5.37362i	0.285278	+	0.624671i
$75$		0			0
$76$	0.248688	−	0.0730215i	0.0285265	−	0.00837614i
$77$	0.748184	+	0.480829i	0.0852635	+	0.0547955i
$78$		0			0
$79$	14.3558	+	4.21524i	1.61515	+	0.474252i	0.959710	−	0.280992i	$-0.0906635\pi$
$79$	14.3558	+	4.21524i	1.61515	+	0.474252i	0.655444	+	0.755244i	$0.272482\pi$
$80$	−1.87083	−	2.15906i	−0.209166	−	0.241390i
$81$		0			0
$82$	−8.11106	−	2.38162i	−0.895717	−	0.263006i
$83$	4.00034	−	8.75953i	0.439094	−	0.961483i	−0.552669	−	0.833401i	$-0.686391\pi$
$83$	4.00034	−	8.75953i	0.439094	−	0.961483i	0.991764	−	0.128082i	$-0.0408821\pi$
$84$		0			0
$85$	1.69564	−	0.497885i	0.183918	−	0.0540032i
$86$	1.43332	−	9.96896i	0.154559	−	1.07498i
$87$		0			0
$88$	−0.0282303	−	0.196346i	−0.00300936	−	0.0209305i
$89$	12.9011	−	8.29101i	1.36751	−	0.878845i	0.368795	−	0.929511i	$-0.379771\pi$
$89$	12.9011	−	8.29101i	1.36751	−	0.878845i	0.998716	+	0.0506655i	$0.0161342\pi$
$90$		0			0
$91$	16.6280			1.74309
$92$	2.68751	+	3.97207i	0.280192	+	0.414116i
$93$		0			0
$94$	6.42588	−	7.41586i	0.662779	−	0.764888i
$95$	−0.622913	+	0.400322i	−0.0639095	+	0.0410721i
$96$		0			0
$97$	4.92117	+	10.7759i	0.499669	+	1.09412i	0.976577	+	0.215170i	$0.0690304\pi$
$97$	4.92117	+	10.7759i	0.499669	+	1.09412i	−0.476907	+	0.878954i	$0.658242\pi$
$98$	−1.86457	+	12.9684i	−0.188350	+	1.31000i
$99$		0			0
$100$	2.65967	+	1.70926i	0.265967	+	0.170926i
$101$	−7.84546	+	17.1792i	−0.780653	+	1.70939i	−0.0789976	+	0.996875i	$0.525172\pi$
$101$	−7.84546	+	17.1792i	−0.780653	+	1.70939i	−0.701655	+	0.712517i	$0.747555\pi$
$102$		0			0
$103$	2.18569	+	2.52243i	0.215363	+	0.248542i	0.853144	−	0.521676i	$-0.174693\pi$
$103$	2.18569	+	2.52243i	0.215363	+	0.248542i	−0.637781	+	0.770218i	$0.720147\pi$
$104$	−2.42870	−	2.80286i	−0.238153	−	0.274843i
$105$		0			0
$106$	−1.63499	+	3.58013i	−0.158805	+	0.347733i
$107$	4.15997	+	2.67345i	0.402160	+	0.258452i	0.726049	−	0.687643i	$-0.241354\pi$
$107$	4.15997	+	2.67345i	0.402160	+	0.258452i	−0.323890	+	0.946095i	$0.604991\pi$
$108$		0			0
$109$	−0.331389	+	2.30486i	−0.0317413	+	0.220765i	−0.999518	−	0.0310445i	$-0.990117\pi$
$109$	−0.331389	+	2.30486i	−0.0317413	+	0.220765i	0.967777	+	0.251810i	$0.0810257\pi$
$110$	0.235415	+	0.515486i	0.0224459	+	0.0491497i
$111$		0			0
$112$	3.77176	−	2.42396i	0.356397	−	0.229043i
$113$	−5.24375	+	6.05161i	−0.493290	+	0.569287i	−0.946742	−	0.321994i	$-0.895647\pi$
$113$	−5.24375	+	6.05161i	−0.493290	+	0.569287i	0.453452	+	0.891281i	$0.350192\pi$
$114$		0			0
$115$	−10.5638	−	8.72483i	−0.985076	−	0.813595i
$116$	7.49661			0.696043
$117$		0			0
$118$	−8.25503	+	5.30518i	−0.759937	+	0.488382i
$119$	0.394705	+	2.74523i	0.0361826	+	0.251655i
$120$		0			0
$121$	1.55986	−	10.8491i	0.141806	−	0.986281i
$122$	4.91182	−	1.44224i	0.444695	−	0.130574i
$123$		0			0
$124$	−1.16701	+	2.55541i	−0.104801	+	0.229482i
$125$	5.03941	+	1.47970i	0.450738	+	0.132349i
$126$		0			0
$127$	−3.58686	−	4.13945i	−0.318282	−	0.367317i	0.573953	−	0.818888i	$-0.305409\pi$
$127$	−3.58686	−	4.13945i	−0.318282	−	0.367317i	−0.892235	+	0.451571i	$0.850864\pi$
$128$	−0.959493	−	0.281733i	−0.0848080	−	0.0249019i
$129$		0			0
$130$	8.91328	+	5.72822i	0.781746	+	0.502398i
$131$	−5.58385	+	1.63957i	−0.487863	+	0.143250i	−0.516408	−	0.856343i	$-0.672731\pi$
$131$	−5.58385	+	1.63957i	−0.487863	+	0.143250i	0.0285442	+	0.999593i	$0.490913\pi$
$132$		0			0
$133$	−0.482739	−	1.05705i	−0.0418588	−	0.0916580i
$134$	1.04690	+	7.28136i	0.0904385	+	0.629013i
$135$		0			0
$136$	0.405093	−	0.467502i	0.0347365	−	0.0400880i
$137$	6.21674			0.531132			0.265566	−	0.964093i	$-0.414441\pi$
$137$	6.21674			0.531132			0.265566	+	0.964093i	$0.414441\pi$
$138$		0			0
$139$	3.51441			0.298089			0.149044	−	0.988831i	$-0.452380\pi$
$139$	3.51441			0.298089			0.149044	+	0.988831i	$0.452380\pi$
$140$	−8.38787	+	9.68012i	−0.708905	+	0.818120i
$141$		0			0
$142$	−1.57977	−	10.9875i	−0.132571	−	0.922052i
$143$	0.305613	+	0.669198i	0.0255566	+	0.0559612i
$144$		0			0
$145$	−20.5491	+	6.03377i	−1.70651	+	0.501077i
$146$	−13.1507	−	8.45144i	−1.08836	−	0.699446i
$147$		0			0
$148$	−5.66817	−	1.66433i	−0.465921	−	0.136807i
$149$	−2.72485	−	3.14464i	−0.223228	−	0.257619i	0.633078	−	0.774088i	$-0.281791\pi$
$149$	−2.72485	−	3.14464i	−0.223228	−	0.257619i	−0.856306	+	0.516469i	$0.827246\pi$
$150$		0			0
$151$	7.59149	+	2.22906i	0.617787	+	0.181398i	0.575627	−	0.817712i	$-0.304758\pi$
$151$	7.59149	+	2.22906i	0.617787	+	0.181398i	0.0421596	+	0.999111i	$0.486576\pi$
$152$	−0.107670	+	0.235765i	−0.00873322	+	0.0191231i
$153$		0			0
$154$	−0.853343	+	0.250564i	−0.0687643	+	0.0201910i
$155$	1.14217	−	7.94397i	0.0917413	−	0.638075i
$156$		0			0
$157$	−2.55410	−	17.7642i	−0.203840	−	1.41774i	−0.792754	−	0.609541i	$-0.791354\pi$
$157$	−2.55410	−	17.7642i	−0.203840	−	1.41774i	0.588915	−	0.808195i	$-0.299555\pi$
$158$	−12.5867	+	8.08899i	−1.00135	+	0.643526i
$159$		0			0
$160$	2.85684			0.225853
$161$	15.9127	−	14.4612i	1.25409	−	1.13970i
$162$		0			0
$163$	−4.64585	+	5.36159i	−0.363891	+	0.419952i	−0.907939	−	0.419101i	$-0.862345\pi$
$163$	−4.64585	+	5.36159i	−0.363891	+	0.419952i	0.544049	+	0.839054i	$0.316891\pi$
$164$	7.11153	−	4.57030i	0.555317	−	0.356881i
$165$		0			0
$166$	4.00034	+	8.75953i	0.310487	+	0.679871i
$167$	2.32259	−	16.1540i	0.179727	−	1.25003i	−0.677666	−	0.735370i	$-0.737008\pi$
$167$	2.32259	−	16.1540i	0.179727	−	1.25003i	0.857393	−	0.514662i	$-0.172083\pi$
$168$		0			0
$169$	0.634818	+	0.407973i	0.0488321	+	0.0313825i
$170$	−0.734133	+	1.60753i	−0.0563054	+	0.123292i
$171$		0			0
$172$	6.59542	+	7.61152i	0.502896	+	0.580373i
$173$	−10.1331	−	11.6943i	−0.770409	−	0.889099i	0.225969	−	0.974134i	$-0.427445\pi$
$173$	−10.1331	−	11.6943i	−0.770409	−	0.889099i	−0.996378	+	0.0850354i	$0.972900\pi$
$174$		0			0
$175$	5.88842	−	12.8939i	0.445123	−	0.974684i
$176$	0.166875	+	0.107244i	0.0125787	+	0.00808384i
$177$		0			0
$178$	−2.18247	+	15.1794i	−0.163583	+	1.13775i
$179$	−1.94368	−	4.25607i	−0.145278	−	0.318114i	0.822979	−	0.568072i	$-0.192310\pi$
$179$	−1.94368	−	4.25607i	−0.145278	−	0.318114i	−0.968257	+	0.249958i	$0.919583\pi$
$180$		0			0
$181$	−4.56694	+	2.93499i	−0.339458	+	0.218156i	−0.699252	−	0.714876i	$-0.746483\pi$
$181$	−4.56694	+	2.93499i	−0.339458	+	0.218156i	0.359794	+	0.933032i	$0.382847\pi$
$182$	−10.8890	+	12.5666i	−0.807150	+	0.931500i
$183$		0			0
$184$	−4.76183	−	0.570068i	−0.351047	−	0.0420259i
$185$	16.8767			1.24080
$186$		0			0
$187$	−0.103228	+	0.0663407i	−0.00754879	+	0.00485131i
$188$	1.39648	+	9.71271i	0.101849	+	0.708372i
$189$		0			0
$190$	0.105378	−	0.732921i	0.00764493	−	0.0531717i
$191$	5.53506	−	1.62524i	0.400503	−	0.117598i	−0.0752770	−	0.997163i	$-0.523984\pi$
$191$	5.53506	−	1.62524i	0.400503	−	0.117598i	0.475780	+	0.879564i	$0.342166\pi$
$192$		0			0
$193$	−1.15744	+	2.53444i	−0.0833142	+	0.182433i	−0.946704	−	0.322105i	$-0.895610\pi$
$193$	−1.15744	+	2.53444i	−0.0833142	+	0.182433i	0.863390	+	0.504537i	$0.168337\pi$
$194$	−11.3665	−	3.33752i	−0.816070	−	0.239620i
$195$		0			0
$196$	−8.57980	−	9.90162i	−0.612843	−	0.707259i
$197$	26.6070	+	7.81253i	1.89567	+	0.556620i	0.991618	+	0.129205i	$0.0412424\pi$
$197$	26.6070	+	7.81253i	1.89567	+	0.556620i	0.904055	+	0.427415i	$0.140576\pi$
$198$		0			0
$199$	−17.2652	−	11.0957i	−1.22390	−	0.786552i	−0.240969	−	0.970533i	$-0.577465\pi$
$199$	−17.2652	−	11.0957i	−1.22390	−	0.786552i	−0.982930	+	0.183981i	$0.941102\pi$
$200$	−3.03349	+	0.890712i	−0.214500	+	0.0629829i
$201$		0			0
$202$	−7.84546	−	17.1792i	−0.552005	−	1.20872i
$203$	−4.78335	−	33.2689i	−0.335725	−	2.33502i
$204$		0			0
$205$	−15.8151	+	18.2516i	−1.10457	+	1.27475i
$206$	−3.33765			−0.232545
$207$		0			0
$208$	3.70872			0.257154
$209$	0.0336688	−	0.0388559i	0.00232892	−	0.00268772i
$210$		0			0
$211$	3.13628	+	21.8133i	0.215910	+	1.50169i	0.752919	+	0.658113i	$0.228645\pi$
$211$	3.13628	+	21.8133i	0.215910	+	1.50169i	−0.537008	+	0.843577i	$0.680446\pi$
$212$	−1.63499	−	3.58013i	−0.112292	−	0.245885i
$213$		0			0
$214$	−4.74466	+	1.39316i	−0.324338	+	0.0952343i
$215$	−24.2051	−	15.5557i	−1.65077	−	1.06089i
$216$		0			0
$217$	12.0852	+	3.54853i	0.820395	+	0.240890i
$218$	−1.52488	−	1.75981i	−0.103278	−	0.119189i
$219$		0			0
$220$	−0.543742	−	0.159657i	−0.0366591	−	0.0107641i
$221$	−0.953042	+	2.08687i	−0.0641086	+	0.140378i
$222$		0			0
$223$	−15.4109	+	4.52504i	−1.03199	+	0.303019i	−0.753519	−	0.657426i	$-0.771645\pi$
$223$	−15.4109	+	4.52504i	−1.03199	+	0.303019i	−0.278469	+	0.960445i	$0.589827\pi$
$224$	−0.638068	+	4.43786i	−0.0426327	+	0.296517i
$225$		0			0
$226$	−1.13958	−	7.92592i	−0.0758034	−	0.527224i
$227$	−19.9564	+	12.8252i	−1.32455	+	0.851237i	−0.995654	−	0.0931286i	$-0.970313\pi$
$227$	−19.9564	+	12.8252i	−1.32455	+	0.851237i	−0.328897	+	0.944366i	$0.606677\pi$
$228$		0			0
$229$	−19.2142			−1.26971			−0.634856	−	0.772630i	$-0.718941\pi$
$229$	−19.2142			−1.26971			−0.634856	+	0.772630i	$0.718941\pi$
$230$	13.5116	−	2.27001i	0.890927	−	0.149680i
$231$		0			0
$232$	−4.90924	+	5.66556i	−0.322307	+	0.371962i
$233$	−18.0142	+	11.5770i	−1.18015	+	0.758436i	−0.975414	−	0.220381i	$-0.929270\pi$
$233$	−18.0142	+	11.5770i	−1.18015	+	0.758436i	−0.204736	+	0.978817i	$0.565634\pi$
$234$		0			0
$235$	−11.6453	−	25.4997i	−0.759658	−	1.66342i
$236$	1.39650	−	9.71289i	0.0909046	−	0.632255i
$237$		0			0
$238$	−2.33319	−	1.49945i	−0.151238	−	0.0971948i
$239$	−2.57759	+	5.64414i	−0.166730	+	0.365089i	−0.974493	−	0.224420i	$-0.927951\pi$
$239$	−2.57759	+	5.64414i	−0.166730	+	0.365089i	0.807762	+	0.589509i	$0.200679\pi$
$240$		0			0
$241$	−5.09410	−	5.87891i	−0.328140	−	0.378694i	0.567576	−	0.823321i	$-0.307881\pi$
$241$	−5.09410	−	5.87891i	−0.328140	−	0.378694i	−0.895715	+	0.444628i	$0.853336\pi$
$242$	7.17770	+	8.28351i	0.461400	+	0.532484i
$243$		0			0
$244$	−2.12658	+	4.65657i	−0.136141	+	0.298106i
$245$	31.4877	+	20.2359i	2.01168	+	1.29283i
$246$		0			0
$247$	0.136801	−	0.951469i	0.00870442	−	0.0605405i
$248$	−1.16701	−	2.55541i	−0.0741055	−	0.162268i
$249$		0			0
$250$	−4.41840	+	2.83953i	−0.279444	+	0.179588i
$251$	−9.03315	+	10.4248i	−0.570167	+	0.658008i	−0.965461	−	0.260547i	$-0.916097\pi$
$251$	−9.03315	+	10.4248i	−0.570167	+	0.658008i	0.395294	+	0.918555i	$0.370643\pi$
$252$		0			0
$253$	0.874460	+	0.374620i	0.0549768	+	0.0235522i
$254$	5.47728			0.343675
$255$		0			0
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	1.74258	+	12.1199i	0.108699	+	0.756019i	0.969147	+	0.246482i	$0.0792745\pi$
$257$	1.74258	+	12.1199i	0.108699	+	0.756019i	−0.860448	+	0.509538i	$0.829816\pi$
$258$		0			0
$259$	−3.76936	+	26.2165i	−0.234217	+	1.62901i
$260$	−10.1661	+	2.98502i	−0.630472	+	0.185123i
$261$		0			0
$262$	2.41754	−	5.29368i	0.149356	−	0.327045i
$263$	12.9262	+	3.79547i	0.797062	+	0.234039i	0.654812	−	0.755792i	$-0.272748\pi$
$263$	12.9262	+	3.79547i	0.797062	+	0.234039i	0.142251	+	0.989831i	$0.454566\pi$
$264$		0			0
$265$	7.36324	+	8.49763i	0.452320	+	0.522005i
$266$	1.11499	+	0.327392i	0.0683646	+	0.0200737i
$267$		0			0
$268$	−6.18846	−	3.97708i	−0.378020	−	0.242939i
$269$	−10.1688	+	2.98582i	−0.620001	+	0.182049i	−0.576623	−	0.817010i	$-0.695630\pi$
$269$	−10.1688	+	2.98582i	−0.620001	+	0.182049i	−0.0433775	+	0.999059i	$0.513812\pi$
$270$		0			0
$271$	−2.64627	−	5.79452i	−0.160749	−	0.351992i	0.812069	−	0.583561i	$-0.198341\pi$
$271$	−2.64627	−	5.79452i	−0.160749	−	0.351992i	−0.972818	+	0.231569i	$0.925614\pi$
$272$	0.0880352	+	0.612298i	0.00533792	+	0.0371260i
$273$		0			0
$274$	−4.07110	+	4.69830i	−0.245944	+	0.283835i
$275$	0.627141			0.0378180
$276$		0			0
$277$	−3.99485			−0.240027			−0.120014	−	0.992772i	$-0.538294\pi$
$277$	−3.99485			−0.240027			−0.120014	+	0.992772i	$0.538294\pi$
$278$	−2.30145	+	2.65602i	−0.138032	+	0.159297i
$279$		0			0
$280$	−1.82286	−	12.6783i	−0.108937	−	0.757671i
$281$	1.51158	+	3.30991i	0.0901736	+	0.197453i	0.949345	−	0.314235i	$-0.101748\pi$
$281$	1.51158	+	3.30991i	0.0901736	+	0.197453i	−0.859172	+	0.511687i	$0.829021\pi$
$282$		0			0
$283$	11.6557	−	3.42243i	0.692862	−	0.203443i	0.0837030	−	0.996491i	$-0.473325\pi$
$283$	11.6557	−	3.42243i	0.692862	−	0.203443i	0.609159	+	0.793048i	$0.291507\pi$
$284$	9.33834	+	6.00139i	0.554128	+	0.356117i
$285$		0			0
$286$	−0.705880	−	0.207265i	−0.0417396	−	0.0122558i
$287$	−24.8200	−	28.6438i	−1.46508	−	1.69079i
$288$		0			0
$289$	15.9442	+	4.68165i	0.937895	+	0.275391i
$290$	8.89680	−	19.4813i	0.522438	−	1.14398i
$291$		0			0
$292$	14.9990	−	4.40412i	0.877752	−	0.257731i
$293$	−2.23532	+	15.5470i	−0.130589	+	0.908264i	0.814200	+	0.580584i	$0.197176\pi$
$293$	−2.23532	+	15.5470i	−0.130589	+	0.908264i	−0.944789	+	0.327680i	$0.893733\pi$
$294$		0			0
$295$	3.98959	+	27.7482i	0.232283	+	1.61556i
$296$	4.96968	−	3.19382i	0.288857	−	0.185637i
$297$		0			0
$298$	4.16095			0.241038
$299$	17.5406	−	2.94690i	1.01440	−	0.170424i
$300$		0			0
$301$	29.5705	−	34.1262i	1.70442	−	1.96700i
$302$	−6.65598	+	4.27754i	−0.383009	+	0.246145i
$303$		0			0
$304$	−0.107670	−	0.235765i	−0.00617532	−	0.0135221i
$305$	2.08131	−	14.4758i	0.119176	−	0.828884i
$306$		0			0
$307$	1.47138	+	0.945596i	0.0839759	+	0.0539680i	0.581955	−	0.813221i	$-0.302288\pi$
$307$	1.47138	+	0.945596i	0.0839759	+	0.0539680i	−0.497979	+	0.867189i	$0.665924\pi$
$308$	0.369457	−	0.808998i	0.0210518	−	0.0460969i
$309$		0			0
$310$	5.25569	+	6.06539i	0.298503	+	0.344491i
$311$	9.39460	+	10.8419i	0.532719	+	0.614790i	0.956769	−	0.290848i	$-0.0939376\pi$
$311$	9.39460	+	10.8419i	0.532719	+	0.614790i	−0.424051	+	0.905639i	$0.639392\pi$
$312$		0			0
$313$	1.33641	−	2.92632i	0.0755382	−	0.165406i	−0.868095	−	0.496397i	$-0.834656\pi$
$313$	1.33641	−	2.92632i	0.0755382	−	0.165406i	0.943634	+	0.330992i	$0.107383\pi$
$314$	15.0979	+	9.70280i	0.852021	+	0.547561i
$315$		0			0
$316$	2.12929	−	14.8096i	0.119782	−	0.833103i
$317$	−3.56387	−	7.80379i	−0.200167	−	0.438304i	0.782754	−	0.622331i	$-0.213814\pi$
$317$	−3.56387	−	7.80379i	−0.200167	−	0.438304i	−0.982921	+	0.184026i	$0.941087\pi$
$318$		0			0
$319$	1.25100	−	0.803968i	0.0700425	−	0.0450136i
$320$	−1.87083	+	2.15906i	−0.104583	+	0.120695i
$321$		0			0
$322$	0.508490	+	21.4961i	0.0283371	+	1.19793i
$323$	0.160332			0.00892110
$324$		0			0
$325$	9.86396	−	6.33918i	0.547154	−	0.351635i
$326$	−1.00964	−	7.02219i	−0.0559187	−	0.388923i
$327$		0			0
$328$	−1.20306	+	8.36744i	−0.0664277	+	0.462015i
$329$	42.2126	−	12.3947i	2.32726	−	0.683344i
$330$		0			0
$331$	13.4913	−	29.5417i	0.741547	−	1.62376i	−0.0394471	−	0.999222i	$-0.512560\pi$
$331$	13.4913	−	29.5417i	0.741547	−	1.62376i	0.780994	−	0.624539i	$-0.214713\pi$
$332$	−9.23967	−	2.71301i	−0.507093	−	0.148896i
$333$		0			0
$334$	10.6874	+	12.3339i	0.584788	+	0.674881i
$335$	20.1643	+	5.92078i	1.10169	+	0.323487i
$336$		0			0
$337$	−16.7128	−	10.7407i	−0.910404	−	0.585081i	−0.000545257	−	1.00000i	$-0.500174\pi$
$337$	−16.7128	−	10.7407i	−0.910404	−	0.585081i	−0.909858	+	0.414919i	$0.863810\pi$
$338$	−0.724042	+	0.212598i	−0.0393827	+	0.0115638i
$339$		0			0
$340$	−0.734133	−	1.60753i	−0.0398139	−	0.0871803i
$341$	0.0793066	+	0.551590i	0.00429469	+	0.0298703i
$342$		0			0
$343$	−17.9150	+	20.6751i	−0.967321	+	1.11635i
$344$	−10.0715			−0.543018
$345$		0			0
$346$	15.4737			0.831873
$347$	−12.3901	+	14.2989i	−0.665133	+	0.767605i	−0.983607	−	0.180327i	$-0.942284\pi$
$347$	−12.3901	+	14.2989i	−0.665133	+	0.767605i	0.318473	+	0.947932i	$0.396830\pi$
$348$		0			0
$349$	0.0474615	+	0.330102i	0.00254055	+	0.0176699i	0.991052	−	0.133474i	$-0.0426133\pi$
$349$	0.0474615	+	0.330102i	0.00254055	+	0.0176699i	−0.988512	+	0.151144i	$0.951704\pi$
$350$	5.88842	+	12.8939i	0.314750	+	0.689205i
$351$		0			0
$352$	−0.190330	+	0.0558859i	−0.0101446	+	0.00297873i
$353$	−6.42828	−	4.13121i	−0.342143	−	0.219882i	0.358273	−	0.933617i	$-0.383366\pi$
$353$	−6.42828	−	4.13121i	−0.342143	−	0.219882i	−0.700416	+	0.713735i	$0.747002\pi$
$354$		0			0
$355$	−30.4278	−	8.93441i	−1.61494	−	0.474189i
$356$	−10.0426	−	11.5898i	−0.532259	−	0.614259i
$357$		0			0
$358$	4.48937	+	1.31820i	0.237270	+	0.0696689i
$359$	6.04768	−	13.2426i	0.319184	−	0.698916i	−0.680235	−	0.732994i	$-0.738122\pi$
$359$	6.04768	−	13.2426i	0.319184	−	0.698916i	0.999419	+	0.0340781i	$0.0108495\pi$
$360$		0			0
$361$	18.1659	−	5.33399i	0.956101	−	0.280736i
$362$	0.772589	−	5.37347i	0.0406064	−	0.282423i
$363$		0			0
$364$	−2.36642	−	16.4588i	−0.124034	−	0.862674i
$365$	−37.5695	+	24.1444i	−1.96648	+	1.26378i
$366$		0			0
$367$	24.3518			1.27116			0.635578	−	0.772037i	$-0.280762\pi$
$367$	24.3518			1.27116			0.635578	+	0.772037i	$0.280762\pi$
$368$	3.54916	−	3.22544i	0.185013	−	0.168137i
$369$		0			0
$370$	−11.0519	+	12.7546i	−0.574561	+	0.663078i
$371$	−14.8449	+	9.54023i	−0.770708	+	0.495304i
$372$		0			0
$373$	6.82929	+	14.9541i	0.353607	+	0.774292i	0.999937	+	0.0112335i	$0.00357581\pi$
$373$	6.82929	+	14.9541i	0.353607	+	0.774292i	−0.646330	+	0.763058i	$0.723697\pi$
$374$	0.0174631	−	0.121458i	0.000902995	−	0.00628047i
$375$		0			0
$376$	−8.25488	−	5.30509i	−0.425713	−	0.273589i
$377$	11.5497	−	25.2904i	0.594841	−	1.30252i
$378$		0			0
$379$	−4.82648	−	5.57006i	−0.247920	−	0.286115i	0.618126	−	0.786079i	$-0.287892\pi$
$379$	−4.82648	−	5.57006i	−0.247920	−	0.286115i	−0.866046	+	0.499964i	$0.833347\pi$
$380$	0.484897	+	0.559600i	0.0248747	+	0.0287069i
$381$		0			0
$382$	−2.39642	+	5.24742i	−0.122611	+	0.268482i
$383$	19.5183	+	12.5436i	0.997337	+	0.640950i	0.934086	−	0.357048i	$-0.116217\pi$
$383$	19.5183	+	12.5436i	0.997337	+	0.640950i	0.0632510	+	0.997998i	$0.479853\pi$
$384$		0			0
$385$	−0.361592	+	2.51492i	−0.0184284	+	0.128172i
$386$	−1.15744	−	2.53444i	−0.0589120	−	0.128999i
$387$		0			0
$388$	9.96582	−	6.40465i	0.505938	−	0.325147i
$389$	−13.2408	+	15.2807i	−0.671334	+	0.774760i	−0.984584	−	0.174910i	$-0.944036\pi$
$389$	−13.2408	+	15.2807i	−0.671334	+	0.774760i	0.313251	+	0.949670i	$0.398582\pi$
$390$		0			0
$391$	0.902890	+	2.82594i	0.0456611	+	0.142914i
$392$	13.1017			0.661737
$393$		0			0
$394$	−23.3282	+	14.9921i	−1.17526	+	0.755293i
$395$	6.08306	+	42.3086i	0.306072	+	2.12878i
$396$		0			0
$397$	−2.59852	+	18.0731i	−0.130416	+	0.907062i	0.814597	+	0.580028i	$0.196958\pi$
$397$	−2.59852	+	18.0731i	−0.130416	+	0.907062i	−0.945013	+	0.327034i	$0.893951\pi$
$398$	19.6919	−	5.78205i	0.987064	−	0.289828i
$399$		0			0
$400$	1.31336	−	2.87585i	0.0656678	−	0.143792i
$401$	−34.4511	−	10.1158i	−1.72041	−	0.505157i	−0.735394	−	0.677639i	$-0.763003\pi$
$401$	−34.4511	−	10.1158i	−1.72041	−	0.505157i	−0.985013	+	0.172482i	$0.944821\pi$
$402$		0			0
$403$	6.82287	+	7.87402i	0.339872	+	0.392233i
$404$	18.1208	+	5.32076i	0.901545	+	0.264718i
$405$		0			0
$406$	28.2754	+	18.1715i	1.40328	+	0.901836i
$407$	−1.12437	+	0.330144i	−0.0557328	+	0.0163646i
$408$		0			0
$409$	−10.9223	−	23.9164i	−0.540072	−	1.18259i	−0.961266	−	0.275621i	$-0.911116\pi$
$409$	−10.9223	−	23.9164i	−0.540072	−	1.18259i	0.421195	−	0.906970i	$-0.361611\pi$
$410$	−3.43694	−	23.9045i	−0.169739	−	1.18056i
$411$		0			0
$412$	2.18569	−	2.52243i	0.107681	−	0.124271i
$413$	−43.9955			−2.16488
$414$		0			0
$415$	27.5107			1.35045
$416$	−2.42870	+	2.80286i	−0.119077	+	0.137422i
$417$		0			0
$418$	0.00731693	+	0.0508904i	0.000357883	+	0.00248913i
$419$	3.02321	+	6.61990i	0.147693	+	0.323403i	0.968991	−	0.247097i	$-0.0794767\pi$
$419$	3.02321	+	6.61990i	0.147693	+	0.323403i	−0.821297	+	0.570500i	$0.806749\pi$
$420$		0			0
$421$	32.9426	−	9.67282i	1.60552	−	0.471424i	0.648447	−	0.761260i	$-0.275419\pi$
$421$	32.9426	−	9.67282i	1.60552	−	0.471424i	0.957076	+	0.289836i	$0.0936007\pi$
$422$	−18.5392	−	11.9144i	−0.902475	−	0.579986i
$423$		0			0
$424$	3.77638	+	1.10884i	0.183397	+	0.0538502i
$425$	1.28072	+	1.47803i	0.0621242	+	0.0716951i
$426$		0			0
$427$	22.0221	+	6.46627i	1.06572	+	0.312925i
$428$	2.05421	−	4.49810i	0.0992942	−	0.217424i
$429$		0			0
$430$	27.6071	−	8.10619i	1.33133	−	0.390915i
$431$	2.59391	−	18.0410i	0.124944	−	0.869005i	−0.826884	−	0.562373i	$-0.809889\pi$
$431$	2.59391	−	18.0410i	0.124944	−	0.869005i	0.951828	−	0.306633i	$-0.0992023\pi$
$432$		0			0
$433$	−0.732840	−	5.09701i	−0.0352180	−	0.244947i	0.964606	−	0.263695i	$-0.0849411\pi$
$433$	−0.732840	−	5.09701i	−0.0352180	−	0.244947i	−0.999824	+	0.0187478i	$0.994032\pi$
$434$	−10.5959	+	6.80957i	−0.508619	+	0.326870i
$435$		0			0
$436$	2.32856			0.111518
$437$	−0.696568	−	1.02951i	−0.0333214	−	0.0492481i
$438$		0			0
$439$	−11.6229	+	13.4135i	−0.554731	+	0.640193i	−0.961979	−	0.273124i	$-0.911943\pi$
$439$	−11.6229	+	13.4135i	−0.554731	+	0.640193i	0.407248	+	0.913318i	$0.366488\pi$
$440$	0.476736	−	0.306380i	0.0227275	−	0.0146061i
$441$		0			0
$442$	−0.953042	−	2.08687i	−0.0453316	−	0.0992624i
$443$	−0.465019	+	3.23428i	−0.0220937	+	0.153665i	−0.997882	−	0.0650528i	$-0.979278\pi$
$443$	−0.465019	+	3.23428i	−0.0220937	+	0.153665i	0.975788	+	0.218718i	$0.0701875\pi$
$444$		0			0
$445$	36.8563	+	23.6861i	1.74716	+	1.12283i
$446$	6.67218	−	14.6100i	0.315937	−	0.691805i
$447$		0			0
$448$	−2.93606	−	3.38840i	−0.138716	−	0.160087i
$449$	−26.3854	−	30.4503i	−1.24520	−	1.43704i	−0.856880	−	0.515516i	$-0.827600\pi$
$449$	−26.3854	−	30.4503i	−1.24520	−	1.43704i	−0.388323	−	0.921524i	$-0.626945\pi$
$450$		0			0
$451$	0.696600	−	1.52534i	0.0328016	−	0.0718255i
$452$	6.73627	+	4.32914i	0.316848	+	0.203626i
$453$		0			0
$454$	3.37602	−	23.4807i	0.158444	−	1.10201i
$455$	19.7337	+	43.2109i	0.925132	+	2.02576i
$456$		0			0
$457$	25.1688	−	16.1750i	1.17735	−	0.756636i	0.202451	−	0.979292i	$-0.435109\pi$
$457$	25.1688	−	16.1750i	1.17735	−	0.756636i	0.974897	+	0.222657i	$0.0714728\pi$
$458$	12.5826	−	14.5211i	0.587948	−	0.678529i
$459$		0			0
$460$	−7.13264	+	11.6979i	−0.332561	+	0.545418i
$461$	8.18649			0.381283			0.190642	−	0.981660i	$-0.438943\pi$
$461$	8.18649			0.381283			0.190642	+	0.981660i	$0.438943\pi$
$462$		0			0
$463$	−2.46230	+	1.58242i	−0.114433	+	0.0735414i	−0.596605	−	0.802535i	$-0.703484\pi$
$463$	−2.46230	+	1.58242i	−0.114433	+	0.0735414i	0.482173	+	0.876076i	$0.339848\pi$
$464$	−1.06688	−	7.42031i	−0.0495286	−	0.344479i
$465$		0			0
$466$	3.04746	−	21.1956i	0.141171	−	0.981866i
$467$	−31.8781	+	9.36025i	−1.47514	+	0.433141i	−0.917767	−	0.397120i	$-0.870010\pi$
$467$	−31.8781	+	9.36025i	−1.47514	+	0.433141i	−0.557375	+	0.830261i	$0.688192\pi$
$468$		0			0
$469$	−13.7011	+	30.0011i	−0.632656	+	1.38532i
$470$	26.8975	+	7.89782i	1.24069	+	0.364299i
$471$		0			0
$472$	6.42600	+	7.41599i	0.295780	+	0.341349i
$473$	1.91690	+	0.562853i	0.0881393	+	0.0258800i
$474$		0			0
$475$	−0.689352	−	0.443020i	−0.0316296	−	0.0203271i
$476$	2.66112	−	0.781375i	0.121972	−	0.0358143i
$477$		0			0
$478$	−2.57759	−	5.64414i	−0.117896	−	0.258157i
$479$	−3.91803	−	27.2505i	−0.179019	−	1.24511i	−0.859038	−	0.511911i	$-0.828938\pi$
$479$	−3.91803	−	27.2505i	−0.179019	−	1.24511i	0.680019	−	0.733194i	$-0.261971\pi$
$480$		0			0
$481$	−14.3474	+	16.5578i	−0.654187	+	0.754972i
$482$	7.77891			0.354319
$483$		0			0
$484$	−10.9607			−0.498211
$485$	−22.1626	+	25.5771i	−1.00635	+	1.16139i
$486$		0			0
$487$	−1.96809	−	13.6884i	−0.0891827	−	0.620279i	−0.984570	−	0.174991i	$-0.944010\pi$
$487$	−1.96809	−	13.6884i	−0.0891827	−	0.620279i	0.895387	−	0.445288i	$-0.146899\pi$
$488$	−2.12658	−	4.65657i	−0.0962660	−	0.210793i
$489$		0			0
$490$	−35.9134	+	10.5451i	−1.62240	+	0.476380i
$491$	5.38908	+	3.46335i	0.243206	+	0.156299i	0.656566	−	0.754269i	$-0.272008\pi$
$491$	5.38908	+	3.46335i	0.243206	+	0.156299i	−0.413360	+	0.910568i	$0.635645\pi$
$492$		0			0
$493$	4.44952	+	1.30650i	0.200396	+	0.0588416i
$494$	0.629487	+	0.726467i	0.0283220	+	0.0326853i
$495$		0			0
$496$	2.69548	+	0.791464i	0.121031	+	0.0355378i
$497$	20.6748	−	45.2715i	0.927392	−	2.03070i
$498$		0			0
$499$	−4.24270	+	1.24577i	−0.189929	+	0.0557683i	−0.375314	−	0.926898i	$-0.622465\pi$
$499$	−4.24270	+	1.24577i	−0.189929	+	0.0557683i	0.185385	+	0.982666i	$0.440647\pi$
$500$	0.747460	−	5.19870i	0.0334274	−	0.232493i
$501$		0			0
$502$	−1.96309	−	13.6536i	−0.0876170	−	0.609390i
$503$	20.6268	−	13.2561i	0.919705	−	0.591058i	0.00713290	−	0.999975i	$-0.497730\pi$
$503$	20.6268	−	13.2561i	0.919705	−	0.591058i	0.912572	+	0.408916i	$0.134093\pi$
$504$		0			0
$505$	−53.9539			−2.40092
$506$	−0.855768	+	0.415549i	−0.0380435	+	0.0184734i
$507$		0			0
$508$	−3.58686	+	4.13945i	−0.159141	+	0.183659i
$509$	−4.06575	+	2.61290i	−0.180211	+	0.115815i	−0.627636	−	0.778507i	$-0.715977\pi$
$509$	−4.06575	+	2.61290i	−0.180211	+	0.115815i	0.447425	+	0.894321i	$0.352341\pi$
$510$		0			0
$511$	−29.1152	−	63.7535i	−1.28798	−	2.82029i
$512$	−0.142315	+	0.989821i	−0.00628949	+	0.0437443i
$513$		0			0
$514$	−10.3008	−	6.61990i	−0.454347	−	0.291991i
$515$	−3.96104	+	8.67346i	−0.174544	+	0.382198i
$516$		0			0
$517$	1.27467	+	1.47105i	0.0560599	+	0.0646966i
$518$	−17.3447	−	20.0169i	−0.762083	−	0.879490i
$519$		0			0
$520$	4.40142	−	9.63776i	0.193015	−	0.422644i
$521$	−0.290245	−	0.186529i	−0.0127159	−	0.00817200i	0.534267	−	0.845316i	$-0.320588\pi$
$521$	−0.290245	−	0.186529i	−0.0127159	−	0.00817200i	−0.546983	+	0.837144i	$0.684224\pi$
$522$		0			0
$523$	−4.65718	+	32.3914i	−0.203644	+	1.41638i	0.589709	+	0.807616i	$0.299242\pi$
$523$	−4.65718	+	32.3914i	−0.203644	+	1.41638i	−0.793354	+	0.608761i	$0.791667\pi$
$524$	2.41754	+	5.29368i	0.105611	+	0.231256i
$525$		0			0
$526$	−11.3333	+	7.28345i	−0.494154	+	0.317574i
$527$	−1.13802	+	1.31334i	−0.0495728	+	0.0572101i
$528$		0			0
$529$	14.2231	−	18.0750i	0.618394	−	0.785868i
$530$	−11.2440			−0.488407
$531$		0			0
$532$	−0.977591	+	0.628260i	−0.0423840	+	0.0272385i
$533$	−4.46180	−	31.0325i	−0.193262	−	1.34417i
$534$		0			0
$535$	−2.01048	+	13.9832i	−0.0869207	+	0.604547i
$536$	7.05825	−	2.07249i	0.304870	−	0.0895179i
$537$		0			0
$538$	4.40260	−	9.64034i	0.189809	−	0.415625i
$539$	−2.49365	−	0.732201i	−0.107409	−	0.0315381i
$540$		0			0
$541$	3.86632	+	4.46197i	0.166226	+	0.191835i	0.832751	−	0.553648i	$-0.186765\pi$
$541$	3.86632	+	4.46197i	0.166226	+	0.191835i	−0.666525	+	0.745483i	$0.732219\pi$
$542$	6.11214	+	1.79469i	0.262539	+	0.0770884i
$543$		0			0
$544$	−0.520395	−	0.334437i	−0.0223117	−	0.0143389i
$545$	−6.38286	+	1.87418i	−0.273412	+	0.0802809i
$546$		0			0
$547$	4.44603	+	9.73545i	0.190099	+	0.416258i	0.980551	−	0.196266i	$-0.0628816\pi$
$547$	4.44603	+	9.73545i	0.190099	+	0.416258i	−0.790452	+	0.612524i	$0.790154\pi$
$548$	−0.884734	−	6.15346i	−0.0377940	−	0.262863i
$549$		0			0
$550$	−0.410690	+	0.473962i	−0.0175119	+	0.0202098i
$551$	−1.94303			−0.0827757
$552$		0			0
$553$	−67.0814			−2.85259
$554$	2.61607	−	3.01911i	0.111146	−	0.128270i
$555$		0			0
$556$	−0.500153	−	3.47864i	−0.0212112	−	0.147527i
$557$	14.6781	+	32.1405i	0.621931	+	1.36184i	0.914107	+	0.405474i	$0.132893\pi$
$557$	14.6781	+	32.1405i	0.621931	+	1.36184i	−0.292176	+	0.956365i	$0.594379\pi$
$558$		0			0
$559$	35.8393	−	10.5234i	1.51584	−	0.445091i
$560$	10.7753	+	6.92487i	0.455340	+	0.292629i
$561$		0			0
$562$	−3.49134	−	1.02515i	−0.147273	−	0.0432433i
$563$	8.18713	+	9.44845i	0.345046	+	0.398205i	0.901574	−	0.432624i	$-0.142412\pi$
$563$	8.18713	+	9.44845i	0.345046	+	0.398205i	−0.556528	+	0.830829i	$0.687867\pi$
$564$		0			0
$565$	−21.9493	−	6.44490i	−0.923415	−	0.271139i
$566$	−5.04638	+	11.0500i	−0.212115	+	0.464468i
$567$		0			0
$568$	−10.6509	+	3.12737i	−0.446900	+	0.131222i
$569$	−1.59184	+	11.0715i	−0.0667333	+	0.464141i	0.928865	+	0.370418i	$0.120786\pi$
$569$	−1.59184	+	11.0715i	−0.0667333	+	0.464141i	−0.995598	+	0.0937223i	$0.970123\pi$
$570$		0			0
$571$	2.14329	+	14.9069i	0.0896941	+	0.623836i	0.984237	+	0.176854i	$0.0565921\pi$
$571$	2.14329	+	14.9069i	0.0896941	+	0.623836i	−0.894543	+	0.446982i	$0.852499\pi$
$572$	0.618894	−	0.397739i	0.0258772	−	0.0166303i
$573$		0			0
$574$	37.9012			1.58196
$575$	3.92647	−	14.6450i	0.163745	−	0.610741i
$576$		0			0
$577$	19.1687	−	22.1218i	0.798002	−	0.920943i	−0.200268	−	0.979741i	$-0.564181\pi$
$577$	19.1687	−	22.1218i	0.798002	−	0.920943i	0.998270	+	0.0587982i	$0.0187268\pi$
$578$	−13.9794	+	8.98401i	−0.581466	+	0.373686i
$579$		0			0
$580$	8.89680	+	19.4813i	0.369419	+	0.808916i
$581$	−6.14443	+	42.7355i	−0.254914	+	1.77297i
$582$		0			0
$583$	−0.656788	−	0.422092i	−0.0272014	−	0.0174813i
$584$	−6.49387	+	14.2196i	−0.268718	+	0.588411i
$585$		0			0
$586$	−10.2858	−	11.8704i	−0.424902	−	0.490363i
$587$	14.8648	+	17.1549i	0.613535	+	0.708057i	0.974466	−	0.224536i	$-0.0720865\pi$
$587$	14.8648	+	17.1549i	0.613535	+	0.708057i	−0.360931	+	0.932592i	$0.617541\pi$
$588$		0			0
$589$	0.302476	−	0.662329i	0.0124633	−	0.0272908i
$590$	−23.5833	−	15.1561i	−0.970910	−	0.623966i
$591$		0			0
$592$	−0.840720	+	5.84734i	−0.0345534	+	0.240324i
$593$	−3.41490	−	7.47759i	−0.140233	−	0.307068i	0.826465	−	0.562989i	$-0.190349\pi$
$593$	−3.41490	−	7.47759i	−0.140233	−	0.307068i	−0.966698	+	0.255921i	$0.917621\pi$
$594$		0			0
$595$	−6.66555	+	4.28369i	−0.273261	+	0.175614i
$596$	−2.72485	+	3.14464i	−0.111614	+	0.128809i
$597$		0			0
$598$	−9.25952	+	15.1861i	−0.378650	+	0.621005i
$599$	28.8240			1.17771			0.588857	−	0.808237i	$-0.299578\pi$
$599$	28.8240			1.17771			0.588857	+	0.808237i	$0.299578\pi$
$600$		0			0
$601$	1.23258	−	0.792132i	0.0502780	−	0.0323117i	−0.515260	−	0.857034i	$-0.672305\pi$
$601$	1.23258	−	0.792132i	0.0502780	−	0.0323117i	0.565538	+	0.824722i	$0.308668\pi$
$602$	6.42629	+	44.6958i	0.261916	+	1.82166i
$603$		0			0
$604$	1.12599	−	7.83145i	0.0458160	−	0.318657i
$605$	30.0445	−	8.82185i	1.22148	−	0.358659i
$606$		0			0
$607$	−6.59758	+	14.4467i	−0.267787	+	0.586372i	−0.994981	−	0.100059i	$-0.968097\pi$
$607$	−6.59758	+	14.4467i	−0.267787	+	0.586372i	0.727194	+	0.686432i	$0.240824\pi$
$608$	0.248688	+	0.0730215i	0.0100856	+	0.00296141i
$609$		0			0
$610$	9.57714	+	11.0526i	0.387767	+	0.447507i
$611$	34.9180	+	10.2529i	1.41263	+	0.414786i
$612$		0			0
$613$	−22.4682	−	14.4395i	−0.907484	−	0.583204i	0.00151697	−	0.999999i	$-0.499517\pi$
$613$	−22.4682	−	14.4395i	−0.907484	−	0.583204i	−0.909001	+	0.416794i	$0.863153\pi$
$614$	−1.67818	+	0.492758i	−0.0677259	+	0.0198861i
$615$		0			0
$616$	0.369457	+	0.808998i	0.0148858	+	0.0325955i
$617$	−5.79400	−	40.2981i	−0.233258	−	1.62234i	−0.683857	−	0.729616i	$-0.739699\pi$
$617$	−5.79400	−	40.2981i	−0.233258	−	1.62234i	0.450600	−	0.892726i	$-0.351210\pi$
$618$		0			0
$619$	13.6103	−	15.7072i	0.547046	−	0.631325i	−0.413146	−	0.910665i	$-0.635570\pi$
$619$	13.6103	−	15.7072i	0.547046	−	0.631325i	0.960192	+	0.279340i	$0.0901157\pi$
$620$	−8.02566			−0.322318
$621$		0			0
$622$	−14.3459			−0.575220
$623$	−45.0261	+	51.9629i	−1.80393	+	2.08185i
$624$		0			0
$625$	4.38505	+	30.4987i	0.175402	+	1.21995i
$626$	1.33641	+	2.92632i	0.0534136	+	0.116959i
$627$		0			0
$628$	−17.2199	+	5.05621i	−0.687148	+	0.201765i
$629$	−3.07421	−	1.97568i	−0.122577	−	0.0787754i
$630$		0			0
$631$	18.0358	+	5.29579i	0.717994	+	0.210822i	0.620266	−	0.784391i	$-0.287025\pi$
$631$	18.0358	+	5.29579i	0.717994	+	0.210822i	0.0977273	+	0.995213i	$0.468843\pi$
$632$	9.79793	+	11.3074i	0.389741	+	0.449785i
$633$		0			0
$634$	8.23155	+	2.41700i	0.326917	+	0.0959914i
$635$	6.50031	−	14.2337i	0.257957	−	0.564847i
$636$		0			0
$637$	−46.6224	+	13.6896i	−1.84725	+	0.542400i
$638$	−0.211631	+	1.47193i	−0.00837857	+	0.0582742i
$639$		0			0
$640$	−0.406571	−	2.82776i	−0.0160711	−	0.111777i
$641$	18.7311	−	12.0378i	0.739836	−	0.475464i	−0.115650	−	0.993290i	$-0.536895\pi$
$641$	18.7311	−	12.0378i	0.739836	−	0.475464i	0.855486	+	0.517826i	$0.173259\pi$
$642$		0			0
$643$	−25.8885			−1.02094			−0.510472	−	0.859894i	$-0.670529\pi$
$643$	−25.8885			−1.02094			−0.510472	+	0.859894i	$0.670529\pi$
$644$	−16.5786	−	13.6926i	−0.653290	−	0.539566i
$645$		0			0
$646$	−0.104995	+	0.121171i	−0.00413097	+	0.00476740i
$647$	12.2459	−	7.86995i	0.481435	−	0.309400i	−0.277318	−	0.960778i	$-0.589445\pi$
$647$	12.2459	−	7.86995i	0.481435	−	0.309400i	0.758753	+	0.651379i	$0.225809\pi$
$648$		0			0
$649$	−0.808609	−	1.77061i	−0.0317407	−	0.0695024i
$650$	−1.66869	+	11.6060i	−0.0654513	+	0.455223i
$651$		0			0
$652$	5.96819	+	3.83552i	0.233732	+	0.150211i
$653$	−12.8963	+	28.2390i	−0.504673	+	1.10508i	0.470249	+	0.882534i	$0.344164\pi$
$653$	−12.8963	+	28.2390i	−0.504673	+	1.10508i	−0.974922	+	0.222546i	$0.928563\pi$
$654$		0			0
$655$	−10.8875	−	12.5648i	−0.425409	−	0.490948i
$656$	−5.53586	−	6.38872i	−0.216139	−	0.249438i
$657$		0			0
$658$	−18.2761	+	40.0190i	−0.712475	+	1.56010i
$659$	−27.4006	−	17.6093i	−1.06738	−	0.685962i	−0.115770	−	0.993276i	$-0.536933\pi$
$659$	−27.4006	−	17.6093i	−1.06738	−	0.685962i	−0.951608	+	0.307314i	$0.900570\pi$
$660$		0			0
$661$	−2.57193	+	17.8882i	−0.100037	+	0.695769i	0.876655	+	0.481120i	$0.159770\pi$
$661$	−2.57193	+	17.8882i	−0.100037	+	0.695769i	−0.976691	+	0.214649i	$0.931139\pi$
$662$	13.4913	+	29.5417i	0.524353	+	1.14817i
$663$		0			0
$664$	8.10106	−	5.20623i	0.314382	−	0.202041i
$665$	2.17403	−	2.50897i	0.0843053	−	0.0972935i
$666$		0			0
$667$	−10.9419	−	34.2470i	−0.423673	−	1.32605i
$668$	−16.3201			−0.631443
$669$		0			0
$670$	−17.6794	+	11.3619i	−0.683017	+	0.438948i
$671$	0.144516	+	1.00513i	0.00557898	+	0.0388026i
$672$		0			0
$673$	−1.78082	+	12.3859i	−0.0686456	+	0.477440i	0.926281	+	0.376834i	$0.122987\pi$
$673$	−1.78082	+	12.3859i	−0.0686456	+	0.477440i	−0.994926	+	0.100606i	$0.967922\pi$
$674$	19.0618	−	5.59705i	0.734233	−	0.215590i
$675$		0			0
$676$	0.313476	−	0.686417i	0.0120568	−	0.0264006i
$677$	−9.59019	−	2.81593i	−0.368581	−	0.108225i	0.0921966	−	0.995741i	$-0.470611\pi$
$677$	−9.59019	−	2.81593i	−0.368581	−	0.108225i	−0.460777	+	0.887516i	$0.652429\pi$
$678$		0			0
$679$	−34.7818	−	40.1403i	−1.33480	−	1.54044i
$680$	1.69564	+	0.497885i	0.0650249	+	0.0190930i
$681$		0			0
$682$	−0.468798	−	0.301278i	−0.0179512	−	0.0115366i
$683$	40.5553	−	11.9081i	1.55180	−	0.455651i	0.610165	−	0.792274i	$-0.291103\pi$
$683$	40.5553	−	11.9081i	1.55180	−	0.455651i	0.941639	+	0.336623i	$0.109285\pi$
$684$		0			0
$685$	7.37787	+	16.1553i	0.281894	+	0.617262i
$686$	−3.89331	−	27.0786i	−0.148647	−	1.03386i
$687$		0			0
$688$	6.59542	−	7.61152i	0.251448	−	0.290186i
$689$	−14.5968			−0.556094
$690$		0			0
$691$	−1.03010			−0.0391870			−0.0195935	−	0.999808i	$-0.506237\pi$
$691$	−1.03010			−0.0391870			−0.0195935	+	0.999808i	$0.506237\pi$
$692$	−10.1331	+	11.6943i	−0.385204	+	0.444550i
$693$		0			0
$694$	−2.69262	−	18.7276i	−0.102210	−	0.710889i
$695$	4.17082	+	9.13282i	0.158208	+	0.346428i
$696$		0			0
$697$	5.01746	−	1.47326i	0.190050	−	0.0558036i
$698$	−0.280555	−	0.180302i	−0.0106192	−	0.00682452i
$699$		0			0
$700$	−13.6006	−	3.99350i	−0.514055	−	0.150940i
$701$	−3.99234	−	4.60740i	−0.150788	−	0.174019i	0.675330	−	0.737516i	$-0.264001\pi$
$701$	−3.99234	−	4.60740i	−0.150788	−	0.174019i	−0.826118	+	0.563497i	$0.809456\pi$
$702$		0			0
$703$	1.46912	+	0.431372i	0.0554089	+	0.0162695i
$704$	0.0824038	−	0.180439i	0.00310571	−	0.00680056i
$705$		0			0
$706$	7.33179	−	2.15281i	0.275936	−	0.0810220i
$707$	12.0504	−	83.8127i	0.453204	−	3.15210i
$708$		0			0
$709$	−2.67735	−	18.6214i	−0.100550	−	0.699340i	−0.976276	−	0.216531i	$-0.930526\pi$
$709$	−2.67735	−	18.6214i	−0.100550	−	0.699340i	0.875726	−	0.482809i	$-0.160383\pi$
$710$	26.6782	−	17.1450i	1.00121	−	0.643441i
$711$		0			0
$712$	15.3355			0.574723
$713$	13.3773	+	1.60148i	0.500983	+	0.0599758i
$714$		0			0
$715$	−1.37634	+	1.58838i	−0.0514721	+	0.0594019i
$716$	−3.93614	+	2.52960i	−0.147100	+	0.0945357i
$717$		0			0
$718$	6.04768	+	13.2426i	0.225697	+	0.494208i
$719$	−5.55047	+	38.6043i	−0.206997	+	1.43970i	0.575886	+	0.817530i	$0.304657\pi$
$719$	−5.55047	+	38.6043i	−0.206997	+	1.43970i	−0.782883	+	0.622169i	$0.786252\pi$
$720$		0			0
$721$	−12.5888	−	8.09032i	−0.468831	−	0.301299i
$722$	−7.86498	+	17.2219i	−0.292704	+	0.640933i
$723$		0			0
$724$	3.55506	+	4.10276i	0.132123	+	0.152478i
$725$	−15.5208	−	17.9120i	−0.576428	−	0.665234i
$726$		0			0
$727$	−6.46581	+	14.1582i	−0.239804	+	0.525097i	−0.990820	−	0.135187i	$-0.956837\pi$
$727$	−6.46581	+	14.1582i	−0.239804	+	0.525097i	0.751016	+	0.660283i	$0.229564\pi$
$728$	13.9884	+	8.98979i	0.518444	+	0.333184i
$729$		0			0
$730$	6.35562	−	44.2043i	0.235232	−	1.63608i
$731$	2.58810	+	5.66715i	0.0957244	+	0.209607i
$732$		0			0
$733$	−21.9229	+	14.0890i	−0.809742	+	0.520390i	−0.878782	−	0.477224i	$-0.841643\pi$
$733$	−21.9229	+	14.0890i	−0.809742	+	0.520390i	0.0690394	+	0.997614i	$0.478007\pi$
$734$	−15.9471	+	18.4039i	−0.588617	+	0.679300i
$735$		0			0
$736$	0.113414	+	4.79449i	0.00418049	+	0.176727i
$737$	−1.45922			−0.0537510
$738$		0			0
$739$	8.34738	−	5.36454i	0.307063	−	0.197338i	−0.378029	−	0.925794i	$-0.623398\pi$
$739$	8.34738	−	5.36454i	0.307063	−	0.197338i	0.685093	+	0.728456i	$0.259762\pi$
$740$	−2.40181	−	16.7049i	−0.0882921	−	0.614085i
$741$		0			0
$742$	2.51131	−	17.4665i	0.0921931	−	0.641217i
$743$	27.0561	−	7.94440i	0.992594	−	0.291452i	0.255180	−	0.966894i	$-0.417865\pi$
$743$	27.0561	−	7.94440i	0.992594	−	0.291452i	0.737413	+	0.675442i	$0.236047\pi$
$744$		0			0
$745$	4.93812	−	10.8130i	0.180919	−	0.396157i
$746$	−15.7738	−	4.63159i	−0.577518	−	0.169575i
$747$		0			0
$748$	0.0803563	+	0.0927361i	0.00293812	+	0.00339077i
$749$	−21.2727	−	6.24622i	−0.777286	−	0.228232i
$750$		0			0
$751$	31.3924	+	20.1746i	1.14552	+	0.736183i	0.968743	−	0.248067i	$-0.0797954\pi$
$751$	31.3924	+	20.1746i	1.14552	+	0.736183i	0.176781	+	0.984250i	$0.443432\pi$
$752$	9.41511	−	2.76453i	0.343334	−	0.100812i
$753$		0			0
$754$	11.5497	+	25.2904i	0.420616	+	0.921020i
$755$	3.21678	+	22.3732i	0.117071	+	0.814245i
$756$		0			0
$757$	21.6478	−	24.9829i	0.786801	−	0.908017i	−0.210779	−	0.977534i	$-0.567600\pi$
$757$	21.6478	−	24.9829i	0.786801	−	0.908017i	0.997581	+	0.0695164i	$0.0221456\pi$
$758$	7.37024			0.267699
$759$		0			0
$760$	−0.740458			−0.0268592
$761$	−2.17056	+	2.50496i	−0.0786826	+	0.0908046i	−0.793726	−	0.608276i	$-0.791862\pi$
$761$	−2.17056	+	2.50496i	−0.0786826	+	0.0908046i	0.715043	+	0.699080i	$0.246407\pi$
$762$		0			0
$763$	−1.48578	−	10.3338i	−0.0537888	−	0.374109i
$764$	−2.39642	−	5.24742i	−0.0866994	−	0.189845i
$765$		0			0
$766$	−22.2616	+	6.53659i	−0.804344	+	0.236177i
$767$	−30.6156	−	19.6754i	−1.10546	−	0.710439i
$768$		0			0
$769$	4.69152	+	1.37755i	0.169181	+	0.0496759i	0.365226	−	0.930919i	$-0.380992\pi$
$769$	4.69152	+	1.37755i	0.169181	+	0.0496759i	−0.196045	+	0.980595i	$0.562810\pi$
$770$	−1.66386	−	1.92020i	−0.0599614	−	0.0691991i
$771$		0			0
$772$	2.67336	+	0.784969i	0.0962163	+	0.0282517i
$773$	−8.12531	+	17.7919i	−0.292247	+	0.639932i	−0.997623	−	0.0689013i	$-0.978051\pi$
$773$	−8.12531	+	17.7919i	−0.292247	+	0.639932i	0.705377	+	0.708833i	$0.250778\pi$
$774$		0			0
$775$	8.52190	−	2.50226i	0.306116	−	0.0898837i
$776$	−1.68592	+	11.7258i	−0.0605209	+	0.420932i
$777$		0			0
$778$	−2.87749	−	20.0134i	−0.103163	−	0.717515i
$779$	−1.84322	+	1.18456i	−0.0660401	+	0.0424414i
$780$		0			0
$781$	2.20195			0.0787920
$782$	−2.72697	−	1.16824i	−0.0975163	−	0.0417761i
$783$		0			0
$784$	−8.57980	+	9.90162i	−0.306421	+	0.353629i
$785$	43.1322	−	27.7194i	1.53945	−	0.989347i
$786$		0			0
$787$	5.96649	+	13.0648i	0.212683	+	0.465710i	0.985664	−	0.168718i	$-0.0539629\pi$
$787$	5.96649	+	13.0648i	0.212683	+	0.465710i	−0.772982	+	0.634428i	$0.781236\pi$
$788$	3.94644	−	27.4481i	0.140586	−	0.977797i
$789$		0			0
$790$	−35.9583	−	23.1090i	−1.27934	−	0.822181i
$791$	14.9139	−	32.6569i	0.530278	−	1.16115i
$792$		0			0
$793$	12.4329	+	14.3484i	0.441506	+	0.509525i
$794$	−11.9571	−	13.7992i	−0.424340	−	0.489714i
$795$		0			0
$796$	−8.52565	+	18.6686i	−0.302184	+	0.661690i
$797$	−29.1603	−	18.7402i	−1.03291	−	0.663811i	−0.0896863	−	0.995970i	$-0.528586\pi$
$797$	−29.1603	−	18.7402i	−1.03291	−	0.663811i	−0.943223	+	0.332159i	$0.892223\pi$
$798$		0			0
$799$	−0.863853	+	6.00823i	−0.0305609	+	0.212556i
$800$	1.31336	+	2.87585i	0.0464342	+	0.101677i
$801$		0			0
$802$	30.2057	−	19.4120i	1.06660	−	0.685462i
$803$	2.03065	−	2.34350i	0.0716602	−	0.0827003i
$804$		0			0
$805$	56.4648	+	24.1896i	1.99012	+	0.852572i
$806$	−10.4188			−0.366987
$807$		0			0
$808$	−15.8878	+	10.2105i	−0.558930	+	0.359203i
$809$	−5.20644	−	36.2116i	−0.183049	−	1.27313i	−0.849503	−	0.527584i	$-0.823098\pi$
$809$	−5.20644	−	36.2116i	−0.183049	−	1.27313i	0.666454	−	0.745546i	$-0.267811\pi$
$810$		0			0
$811$	4.18543	−	29.1103i	0.146970	−	1.02220i	−0.774172	−	0.632975i	$-0.781834\pi$
$811$	4.18543	−	29.1103i	0.146970	−	1.02220i	0.921142	−	0.389226i	$-0.127257\pi$
$812$	−32.2495	+	9.46932i	−1.13174	+	0.332308i
$813$		0			0
$814$	0.486798	−	1.06594i	0.0170623	−	0.0373611i
$815$	−19.4466	−	5.71004i	−0.681185	−	0.200014i
$816$		0			0
$817$	−1.70945	−	1.97281i	−0.0598060	−	0.0690198i
$818$	25.2274	+	7.40743i	0.882055	+	0.258995i
$819$		0			0
$820$	20.3165	+	13.0566i	0.709484	+	0.455957i
$821$	−0.283242	+	0.0831673i	−0.00988521	+	0.00290256i	−0.286671	−	0.958029i	$-0.592549\pi$
$821$	−0.283242	+	0.0831673i	−0.00988521	+	0.00290256i	0.276786	+	0.960932i	$0.410731\pi$
$822$		0			0
$823$	18.4021	+	40.2950i	0.641457	+	1.40460i	0.898836	+	0.438285i	$0.144414\pi$
$823$	18.4021	+	40.2950i	0.641457	+	1.40460i	−0.257379	+	0.966311i	$0.582859\pi$
$824$	0.474997	+	3.30367i	0.0165473	+	0.115089i
$825$		0			0
$826$	28.8109	−	33.2496i	1.00246	−	1.15690i
$827$	28.7630			1.00019			0.500094	−	0.865971i	$-0.333299\pi$
$827$	28.7630			1.00019			0.500094	+	0.865971i	$0.333299\pi$
$828$		0			0
$829$	22.7583			0.790428			0.395214	−	0.918589i	$-0.370670\pi$
$829$	22.7583			0.790428			0.395214	+	0.918589i	$0.370670\pi$
$830$	−18.0157	+	20.7912i	−0.625333	+	0.721672i
$831$		0			0
$832$	−0.527806	−	3.67097i	−0.0182984	−	0.127268i
$833$	−3.36679	−	7.37225i	−0.116652	−	0.255433i
$834$		0			0
$835$	44.7353	−	13.1355i	1.54813	−	0.454572i
$836$	−0.0432520	−	0.0277963i	−0.00149590	−	0.000961357i
$837$		0			0
$838$	−6.98276	−	2.05032i	−0.241216	−	0.0708273i
$839$	12.4906	+	14.4149i	0.431222	+	0.497656i	0.929223	−	0.369520i	$-0.120478\pi$
$839$	12.4906	+	14.4149i	0.431222	+	0.497656i	−0.498001	+	0.867176i	$0.665932\pi$
$840$		0			0
$841$	−26.0974	−	7.66290i	−0.899912	−	0.264238i
$842$	−14.2626	+	31.2307i	−0.491521	+	1.07628i
$843$		0			0
$844$	21.1449	−	6.20872i	0.727839	−	0.213713i
$845$	−0.306802	+	2.13386i	−0.0105543	+	0.0734069i
$846$		0			0
$847$	6.99364	+	48.6418i	0.240304	+	1.67135i
$848$	−3.31101	+	2.12786i	−0.113701	+	0.0730709i
$849$		0			0
$850$	−1.95572			−0.0670806
$851$	0.669989	+	28.3233i	0.0229669	+	0.970910i
$852$		0			0
$853$	−16.5886	+	19.1443i	−0.567984	+	0.655489i	−0.964977	−	0.262333i	$-0.915508\pi$
$853$	−16.5886	+	19.1443i	−0.567984	+	0.655489i	0.396993	+	0.917822i	$0.370054\pi$
$854$	−19.3083	+	12.4087i	−0.660716	+	0.424617i
$855$		0			0
$856$	2.05421	+	4.49810i	0.0702116	+	0.153742i
$857$	−1.17691	+	8.18561i	−0.0402026	+	0.279615i	−0.999999	−	0.00108060i	$-0.999656\pi$
$857$	−1.17691	+	8.18561i	−0.0402026	+	0.279615i	0.959797	+	0.280696i	$0.0905651\pi$
$858$		0			0
$859$	1.59066	+	1.02225i	0.0542725	+	0.0348788i	0.567496	−	0.823376i	$-0.307912\pi$
$859$	1.59066	+	1.02225i	0.0542725	+	0.0348788i	−0.513223	+	0.858255i	$0.671549\pi$
$860$	−11.9526	+	26.1725i	−0.407580	+	0.892475i
$861$		0			0
$862$	11.9358	+	13.7747i	0.406536	+	0.469168i
$863$	5.36458	+	6.19106i	0.182612	+	0.210746i	0.839674	−	0.543091i	$-0.182746\pi$
$863$	5.36458	+	6.19106i	0.182612	+	0.210746i	−0.657061	+	0.753837i	$0.728201\pi$
$864$		0			0
$865$	18.3639	−	40.2112i	0.624390	−	1.36722i
$866$	4.33197	+	2.78399i	0.147206	+	0.0946038i
$867$		0			0
$868$	1.79251	−	12.4672i	0.0608417	−	0.423163i
$869$	−1.23291	−	2.69971i	−0.0418237	−	0.0915812i
$870$		0			0
$871$	−22.9513	+	14.7499i	−0.777674	+	0.499780i
$872$	−1.52488	+	1.75981i	−0.0516390	+	0.0595946i
$873$		0			0
$874$	1.23421	+	0.147754i	0.0417476	+	0.00499786i
$875$	−23.5480			−0.796068
$876$		0			0
$877$	42.4152	−	27.2586i	1.43226	−	0.920458i	0.432437	−	0.901664i	$-0.357654\pi$
$877$	42.4152	−	27.2586i	1.43226	−	0.920458i	0.999823	−	0.0187937i	$-0.00598256\pi$
$878$	−2.52590	−	17.5680i	−0.0852449	−	0.592891i
$879$		0			0
$880$	−0.0806495	+	0.560930i	−0.00271869	+	0.0189089i
$881$	2.26471	−	0.664979i	0.0763001	−	0.0224037i	−0.243360	−	0.969936i	$-0.578250\pi$
$881$	2.26471	−	0.664979i	0.0763001	−	0.0224037i	0.319660	+	0.947532i	$0.396431\pi$
$882$		0			0
$883$	−9.31625	+	20.3998i	−0.313517	+	0.686506i	−0.999141	−	0.0414499i	$-0.986802\pi$
$883$	−9.31625	+	20.3998i	−0.313517	+	0.686506i	0.685624	+	0.727956i	$0.259530\pi$
$884$	2.20126	+	0.646349i	0.0740365	+	0.0217391i
$885$		0			0
$886$	−2.13978	−	2.46944i	−0.0718874	−	0.0829625i
$887$	35.5956	+	10.4518i	1.19518	+	0.350938i	0.818010	−	0.575205i	$-0.195078\pi$
$887$	35.5956	+	10.4518i	1.19518	+	0.350938i	0.377174	+	0.926142i	$0.376896\pi$
$888$		0			0
$889$	20.6590	+	13.2767i	0.692880	+	0.445287i
$890$	−42.0365	+	12.3430i	−1.40907	+	0.413740i
$891$		0			0
$892$	6.67218	+	14.6100i	0.223401	+	0.489180i
$893$	−0.361949	−	2.51741i	−0.0121122	−	0.0842420i
$894$		0			0
$895$	8.75344	−	10.1020i	0.292595	−	0.337673i
$896$	4.48349			0.149783
$897$		0			0
$898$	40.2916			1.34455
$899$	13.7914	−	15.9161i	0.459969	−	0.530832i
$900$		0			0
$901$	−0.346489	−	2.40989i	−0.0115432	−	0.0802849i
$902$	0.696600	+	1.52534i	0.0231942	+	0.0507883i
$903$		0			0
$904$	−7.68307	+	2.25595i	−0.255535	+	0.0750318i
$905$	−13.0470	−	8.38481i	−0.433698	−	0.278721i
$906$		0			0
$907$	11.8105	+	3.46787i	0.392161	+	0.115149i	0.471867	−	0.881670i	$-0.343580\pi$
$907$	11.8105	+	3.46787i	0.392161	+	0.115149i	−0.0797065	+	0.996818i	$0.525398\pi$
$908$	15.5347	+	17.9280i	0.515538	+	0.594963i
$909$		0			0
$910$	−45.5794	−	13.3833i	−1.51094	−	0.443653i
$911$	6.54460	−	14.3307i	0.216832	−	0.474796i	−0.769691	−	0.638416i	$-0.779590\pi$
$911$	6.54460	−	14.3307i	0.216832	−	0.474796i	0.986523	+	0.163620i	$0.0523171\pi$
$912$		0			0
$913$	−1.83283	+	0.538167i	−0.0606578	+	0.0178107i
$914$	−4.25781	+	29.6137i	−0.140836	+	0.979535i
$915$		0			0
$916$	2.73447	+	19.0187i	0.0903494	+	0.628394i
$917$	21.9501	−	14.1064i	0.724855	−	0.465836i
$918$		0			0
$919$	5.16750			0.170460			0.0852300	−	0.996361i	$-0.472837\pi$
$919$	5.16750			0.170460			0.0852300	+	0.996361i	$0.472837\pi$
$920$	−4.16980	−	13.0510i	−0.137474	−	0.430279i
$921$		0			0
$922$	−5.36101	+	6.18694i	−0.176556	+	0.203756i
$923$	34.6333	−	22.2575i	1.13997	−	0.732613i
$924$		0			0
$925$	7.75861	+	16.9890i	0.255101	+	0.558594i
$926$	0.416547	−	2.89715i	0.0136886	−	0.0952061i
$927$		0			0
$928$	6.30655	+	4.05297i	0.207023	+	0.133045i
$929$	−7.97268	+	17.4577i	−0.261575	+	0.572770i	−0.994161	−	0.107905i	$-0.965586\pi$
$929$	−7.97268	+	17.4577i	−0.261575	+	0.572770i	0.732586	+	0.680674i	$0.238313\pi$
$930$		0			0
$931$	2.22378	+	2.56637i	0.0728813	+	0.0841095i
$932$	14.0229	+	16.1833i	0.459335	+	0.530101i
$933$		0			0
$934$	13.8017	−	30.2215i	0.451606	−	0.988878i
$935$	−0.294906	−	0.189525i	−0.00964447	−	0.00619813i
$936$		0			0
$937$	0.861022	−	5.98854i	0.0281284	−	0.195637i	−0.970912	−	0.239437i	$-0.923037\pi$
$937$	0.861022	−	5.98854i	0.0281284	−	0.195637i	0.999040	+	0.0437997i	$0.0139463\pi$
$938$	−13.7011	−	30.0011i	−0.447356	−	0.979572i
$939$		0			0
$940$	−23.5829	+	15.1558i	−0.769189	+	0.494328i
$941$	−6.34225	+	7.31935i	−0.206751	+	0.238604i	−0.849649	−	0.527348i	$-0.823186\pi$
$941$	−6.34225	+	7.31935i	−0.206751	+	0.238604i	0.642898	+	0.765952i	$0.277732\pi$
$942$		0			0
$943$	−31.2585	−	25.8170i	−1.01792	−	0.840719i
$944$	−9.81277			−0.319378
$945$		0			0
$946$	−1.68068	+	1.08011i	−0.0546436	+	0.0351173i
$947$	3.27668	+	22.7898i	0.106478	+	0.740570i	0.971191	+	0.238303i	$0.0765913\pi$
$947$	3.27668	+	22.7898i	0.106478	+	0.740570i	−0.864713	+	0.502267i	$0.832500\pi$
$948$		0			0
$949$	8.25080	−	57.3856i	0.267832	−	1.86281i
$950$	0.786241	−	0.230861i	0.0255090	−	0.00749013i
$951$		0			0
$952$	−1.15214	+	2.52283i	−0.0373410	+	0.0817654i
$953$	−28.3650	−	8.32873i	−0.918834	−	0.269794i	−0.212079	−	0.977253i	$-0.568023\pi$
$953$	−28.3650	−	8.32873i	−0.918834	−	0.269794i	−0.706755	+	0.707459i	$0.749842\pi$
$954$		0			0
$955$	10.7923	+	12.4550i	0.349232	+	0.403035i
$956$	5.95352	+	1.74811i	0.192550	+	0.0565379i
$957$		0			0
$958$	23.1603	+	14.8842i	0.748275	+	0.480887i
$959$	−26.7437	+	7.85265i	−0.863598	+	0.253575i
$960$		0			0
$961$	−9.59940	−	21.0198i	−0.309658	−	0.678057i
$962$	−3.11800	−	21.6861i	−0.100528	−	0.699189i
$963$		0			0
$964$	−5.09410	+	5.87891i	−0.164070	+	0.189347i
$965$	−7.95979			−0.256235
$966$		0			0
$967$	−54.4705			−1.75165			−0.875826	−	0.482627i	$-0.839683\pi$
$967$	−54.4705			−1.75165			−0.875826	+	0.482627i	$0.839683\pi$
$968$	7.17770	−	8.28351i	0.230700	−	0.266242i
$969$		0			0
$970$	−4.81640	−	33.4988i	−0.154645	−	1.07558i
$971$	21.8594	+	47.8653i	0.701500	+	1.53607i	0.838143	+	0.545450i	$0.183641\pi$
$971$	21.8594	+	47.8653i	0.701500	+	1.53607i	−0.136643	+	0.990620i	$0.543631\pi$
$972$		0			0
$973$	−15.1186	+	4.43922i	−0.484680	+	0.142315i
$974$	11.6338	+	7.47659i	0.372771	+	0.239565i
$975$		0			0
$976$	4.91182	+	1.44224i	0.157223	+	0.0461650i
$977$	−9.28784	−	10.7187i	−0.297144	−	0.342923i	0.587470	−	0.809246i	$-0.300124\pi$
$977$	−9.28784	−	10.7187i	−0.297144	−	0.342923i	−0.884615	+	0.466323i	$0.845579\pi$
$978$		0			0
$979$	−2.91881	−	0.857039i	−0.0932855	−	0.0273911i
$980$	15.5488	−	34.0471i	0.496688	−	1.08760i
$981$		0			0
$982$	−6.14652	+	1.80478i	−0.196143	+	0.0575929i
$983$	−6.38642	+	44.4185i	−0.203695	+	1.41673i	0.589502	+	0.807767i	$0.299324\pi$
$983$	−6.38642	+	44.4185i	−0.203695	+	1.41673i	−0.793198	+	0.608964i	$0.791585\pi$
$984$		0			0
$985$	11.2743	+	78.4148i	0.359231	+	2.49850i
$986$	−3.90120	+	2.50715i	−0.124239	+	0.0798438i
$987$		0			0
$988$	−0.961253			−0.0305815
$989$	25.1453	−	41.2397i	0.799575	−	1.31134i
$990$		0			0
$991$	−4.13669	+	4.77400i	−0.131406	+	0.151651i	−0.817639	−	0.575731i	$-0.804718\pi$
$991$	−4.13669	+	4.77400i	−0.131406	+	0.151651i	0.686233	+	0.727382i	$0.259263\pi$
$992$	−2.36331	+	1.51881i	−0.0750352	+	0.0482222i
$993$		0			0
$994$	20.6748	+	45.2715i	0.655765	+	1.43593i
$995$	8.34414	−	58.0348i	0.264527	−	1.83983i
$996$		0			0
$997$	26.8042	+	17.2260i	0.848898	+	0.545554i	0.891231	−	0.453550i	$-0.149843\pi$
$997$	26.8042	+	17.2260i	0.848898	+	0.545554i	−0.0423327	+	0.999104i	$0.513479\pi$
$998$	1.83689	−	4.02223i	0.0581457	−	0.127321i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.g.361.2	yes	20
3.2	odd	2		414.2.i.h.361.1	yes	20
23.6	even	11		9522.2.a.cj.1.8		10
23.13	even	11	inner	414.2.i.g.289.2	✓	20
23.17	odd	22		9522.2.a.ci.1.3		10
69.17	even	22		9522.2.a.ch.1.8		10
69.29	odd	22		9522.2.a.cg.1.3		10
69.59	odd	22		414.2.i.h.289.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.i.g.289.2	✓	20	23.13	even	11	inner
414.2.i.g.361.2	yes	20	1.1	even	1	trivial
414.2.i.h.289.1	yes	20	69.59	odd	22
414.2.i.h.361.1	yes	20	3.2	odd	2
9522.2.a.cg.1.3		10	69.29	odd	22
9522.2.a.ch.1.8		10	69.17	even	22
9522.2.a.ci.1.3		10	23.17	odd	22
9522.2.a.cj.1.8		10	23.6	even	11

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.654861 + 0.755750i) q^{2} +(-0.142315 - 0.989821i) q^{4} +(1.18678 + 2.59868i) q^{5} +(-4.30188 + 1.26315i) q^{7} +(0.841254 + 0.540641i) q^{8} +O(q^{10})\)	\(q+(-0.654861 + 0.755750i) q^{2} +(-0.142315 - 0.989821i) q^{4} +(1.18678 + 2.59868i) q^{5} +(-4.30188 + 1.26315i) q^{7} +(0.841254 + 0.540641i) q^{8} +(-2.74112 - 0.804866i) q^{10} +(-0.129901 - 0.149914i) q^{11} +(-3.55849 - 1.04487i) q^{13} +(1.86251 - 4.07833i) q^{14} +(-0.959493 + 0.281733i) q^{16} +(0.0880352 - 0.612298i) q^{17} +(0.0368862 + 0.256549i) q^{19} +(2.40333 - 1.54453i) q^{20} +0.198365 q^{22} +(-4.31411 + 2.09487i) q^{23} +(-2.07038 + 2.38934i) q^{25} +(3.11997 - 2.00509i) q^{26} +(1.86251 + 4.07833i) q^{28} +(-1.06688 + 7.42031i) q^{29} +(-2.36331 - 1.51881i) q^{31} +(0.415415 - 0.909632i) q^{32} +(0.405093 + 0.467502i) q^{34} +(-8.38787 - 9.68012i) q^{35} +(2.45405 - 5.37362i) q^{37} +(-0.218042 - 0.140127i) q^{38} +(-0.406571 + 2.82776i) q^{40} +(3.51171 + 7.68956i) q^{41} +(-8.47267 + 5.44505i) q^{43} +(-0.129901 + 0.149914i) q^{44} +(1.24194 - 4.63223i) q^{46} -9.81259 q^{47} +(11.0219 - 7.08332i) q^{49} +(-0.449936 - 3.12937i) q^{50} +(-0.527806 + 3.67097i) q^{52} +(3.77638 - 1.10884i) q^{53} +(0.235415 - 0.515486i) q^{55} +(-4.30188 - 1.26315i) q^{56} +(-4.90924 - 5.66556i) q^{58} +(9.41528 + 2.76458i) q^{59} +(-4.30653 - 2.76764i) q^{61} +(2.69548 - 0.791464i) q^{62} +(0.415415 + 0.909632i) q^{64} +(-1.50786 - 10.4874i) q^{65} +(4.81731 - 5.55947i) q^{67} -0.618594 q^{68} +12.8086 q^{70} +(-7.26928 + 8.38920i) q^{71} +(2.22470 + 15.4731i) q^{73} +(2.45405 + 5.37362i) q^{74} +(0.248688 - 0.0730215i) q^{76} +(0.748184 + 0.480829i) q^{77} +(14.3558 + 4.21524i) q^{79} +(-1.87083 - 2.15906i) q^{80} +(-8.11106 - 2.38162i) q^{82} +(4.00034 - 8.75953i) q^{83} +(1.69564 - 0.497885i) q^{85} +(1.43332 - 9.96896i) q^{86} +(-0.0282303 - 0.196346i) q^{88} +(12.9011 - 8.29101i) q^{89} +16.6280 q^{91} +(2.68751 + 3.97207i) q^{92} +(6.42588 - 7.41586i) q^{94} +(-0.622913 + 0.400322i) q^{95} +(4.92117 + 10.7759i) q^{97} +(-1.86457 + 12.9684i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{7} - 2 q^{8}+O(q^{10}) \) 20 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^7 - 2 * q^8	\( 20 q - 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{7} - 2 q^{8} - 2 q^{10} + 2 q^{11} + 18 q^{14} - 2 q^{16} - 18 q^{17} + 16 q^{19} - 2 q^{20} + 24 q^{22} + 2 q^{23} + 38 q^{25} + 18 q^{28} + 30 q^{29} + 14 q^{31} - 2 q^{32} + 4 q^{34} - 48 q^{35} - 20 q^{37} + 16 q^{38} - 2 q^{40} + 12 q^{41} - 28 q^{43} + 2 q^{44} + 2 q^{46} - 32 q^{47} + 6 q^{49} - 6 q^{50} + 46 q^{53} - 28 q^{55} - 4 q^{56} - 14 q^{58} - 50 q^{61} - 8 q^{62} - 2 q^{64} - 16 q^{65} - 8 q^{67} + 48 q^{68} - 48 q^{70} - 12 q^{71} - 18 q^{73} - 20 q^{74} - 6 q^{76} + 4 q^{77} - 18 q^{79} - 2 q^{80} - 10 q^{82} + 44 q^{83} + 32 q^{85} - 28 q^{86} + 2 q^{88} + 44 q^{91} + 2 q^{92} + 12 q^{94} - 64 q^{95} + 14 q^{97} + 28 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^7 - 2 * q^8 - 2 * q^10 + 2 * q^11 + 18 * q^14 - 2 * q^16 - 18 * q^17 + 16 * q^19 - 2 * q^20 + 24 * q^22 + 2 * q^23 + 38 * q^25 + 18 * q^28 + 30 * q^29 + 14 * q^31 - 2 * q^32 + 4 * q^34 - 48 * q^35 - 20 * q^37 + 16 * q^38 - 2 * q^40 + 12 * q^41 - 28 * q^43 + 2 * q^44 + 2 * q^46 - 32 * q^47 + 6 * q^49 - 6 * q^50 + 46 * q^53 - 28 * q^55 - 4 * q^56 - 14 * q^58 - 50 * q^61 - 8 * q^62 - 2 * q^64 - 16 * q^65 - 8 * q^67 + 48 * q^68 - 48 * q^70 - 12 * q^71 - 18 * q^73 - 20 * q^74 - 6 * q^76 + 4 * q^77 - 18 * q^79 - 2 * q^80 - 10 * q^82 + 44 * q^83 + 32 * q^85 - 28 * q^86 + 2 * q^88 + 44 * q^91 + 2 * q^92 + 12 * q^94 - 64 * q^95 + 14 * q^97 + 28 * q^98

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