LMFDB - Embedded newform 495.2.n.e.136.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(91,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("495.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.n (of order $5$, degree $4$, 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:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			136.2
Root			$0.418926 - 1.28932i$ of defining polynomial
Character	$\chi$	$=$	495.136
Dual form			495.2.n.e.91.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09676 + 0.796845i) q^{2} +(-0.0501062 - 0.154211i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-1.12773 - 3.47080i) q^{7} +(0.905781 - 2.78771i) q^{8} +O(q^{10})$	\(q+(1.09676 + 0.796845i) q^{2} +(-0.0501062 - 0.154211i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-1.12773 - 3.47080i) q^{7} +(0.905781 - 2.78771i) q^{8} -1.35567 q^{10} +(-0.490303 - 3.28018i) q^{11} +(2.29029 + 1.66399i) q^{13} +(1.52884 - 4.70527i) q^{14} +(2.95244 - 2.14507i) q^{16} +(2.98685 - 2.17008i) q^{17} +(-0.0293950 + 0.0904686i) q^{19} +(0.131180 + 0.0953077i) q^{20} +(2.07605 - 3.98828i) q^{22} -1.16215 q^{23} +(0.309017 - 0.951057i) q^{25} +(1.18596 + 3.65001i) q^{26} +(-0.478730 + 0.347817i) q^{28} +(2.08707 + 6.42333i) q^{29} +(-5.48382 - 3.98423i) q^{31} -0.914918 q^{32} +5.00509 q^{34} +(2.95244 + 2.14507i) q^{35} +(3.04066 + 9.35820i) q^{37} +(-0.104329 + 0.0757994i) q^{38} +(0.905781 + 2.78771i) q^{40} +(2.57047 - 7.91110i) q^{41} -2.96862 q^{43} +(-0.481274 + 0.239968i) q^{44} +(-1.27460 - 0.926052i) q^{46} +(0.687534 - 2.11601i) q^{47} +(-5.11155 + 3.71376i) q^{49} +(1.09676 - 0.796845i) q^{50} +(0.141849 - 0.436565i) q^{52} +(2.42214 + 1.75979i) q^{53} +(2.32471 + 2.36553i) q^{55} -10.6970 q^{56} +(-2.82938 + 8.70794i) q^{58} +(2.62930 + 8.09216i) q^{59} +(6.86076 - 4.98464i) q^{61} +(-2.83964 - 8.73951i) q^{62} +(-6.90832 - 5.01919i) q^{64} -2.83095 q^{65} -13.4153 q^{67} +(-0.484310 - 0.351872i) q^{68} +(1.52884 + 4.70527i) q^{70} +(6.71734 - 4.88043i) q^{71} +(-0.407912 - 1.25542i) q^{73} +(-4.12215 + 12.6867i) q^{74} +0.0154241 q^{76} +(-10.8319 + 5.40091i) q^{77} +(11.2179 + 8.15028i) q^{79} +(-1.12773 + 3.47080i) q^{80} +(9.12312 - 6.62834i) q^{82} +(-8.61155 + 6.25666i) q^{83} +(-1.14088 + 3.51126i) q^{85} +(-3.25587 - 2.36553i) q^{86} +(-9.58829 - 1.60431i) q^{88} +12.1612 q^{89} +(3.19256 - 9.82567i) q^{91} +(0.0582308 + 0.179216i) q^{92} +(2.44020 - 1.77291i) q^{94} +(-0.0293950 - 0.0904686i) q^{95} +(3.50412 + 2.54589i) q^{97} -8.56545 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - q^{7} - 4 q^{8}+O(q^{10}) $ 8 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - q^7 - 4 * q^8	$ 8 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - q^{7} - 4 q^{8} + 2 q^{10} - 3 q^{11} - 2 q^{13} + 16 q^{14} + 4 q^{16} + 13 q^{17} + 15 q^{19} + 3 q^{20} - 7 q^{22} - 10 q^{23} - 2 q^{25} - 10 q^{26} - 6 q^{28} + 9 q^{29} - 10 q^{31} - 16 q^{32} + 4 q^{34} + 4 q^{35} + 24 q^{37} - 4 q^{40} - 8 q^{41} - 38 q^{43} + 12 q^{44} + 3 q^{46} + q^{49} + 2 q^{50} - 28 q^{52} - 13 q^{53} + 7 q^{55} - 22 q^{56} + 12 q^{58} + 27 q^{59} + 6 q^{61} + 30 q^{62} - 26 q^{64} - 2 q^{65} - 38 q^{67} - 11 q^{68} + 16 q^{70} + 20 q^{71} + 13 q^{73} - 20 q^{74} - 34 q^{77} + 37 q^{79} - q^{80} + 28 q^{82} - 27 q^{83} - 12 q^{85} + 3 q^{86} - 36 q^{88} + 16 q^{89} + 44 q^{91} - 11 q^{92} + 17 q^{94} + 15 q^{95} + 24 q^{97} - 16 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - q^7 - 4 * q^8 + 2 * q^10 - 3 * q^11 - 2 * q^13 + 16 * q^14 + 4 * q^16 + 13 * q^17 + 15 * q^19 + 3 * q^20 - 7 * q^22 - 10 * q^23 - 2 * q^25 - 10 * q^26 - 6 * q^28 + 9 * q^29 - 10 * q^31 - 16 * q^32 + 4 * q^34 + 4 * q^35 + 24 * q^37 - 4 * q^40 - 8 * q^41 - 38 * q^43 + 12 * q^44 + 3 * q^46 + q^49 + 2 * q^50 - 28 * q^52 - 13 * q^53 + 7 * q^55 - 22 * q^56 + 12 * q^58 + 27 * q^59 + 6 * q^61 + 30 * q^62 - 26 * q^64 - 2 * q^65 - 38 * q^67 - 11 * q^68 + 16 * q^70 + 20 * q^71 + 13 * q^73 - 20 * q^74 - 34 * q^77 + 37 * q^79 - q^80 + 28 * q^82 - 27 * q^83 - 12 * q^85 + 3 * q^86 - 36 * q^88 + 16 * q^89 + 44 * q^91 - 11 * q^92 + 17 * q^94 + 15 * q^95 + 24 * q^97 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

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 $

$2$	1.09676	+	0.796845i	0.775529	+	0.563455i	0.903634	−	0.428306i	$-0.140889\pi$
$2$	1.09676	+	0.796845i	0.775529	+	0.563455i	−0.128105	+	0.991761i	$0.540889\pi$
$3$		0			0
$3$		0			0
$4$	−0.0501062	−	0.154211i	−0.0250531	−	0.0771056i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$6$		0			0
$7$	−1.12773	−	3.47080i	−0.426242	−	1.31184i	−0.901800	−	0.432154i	$-0.857754\pi$
$7$	−1.12773	−	3.47080i	−0.426242	−	1.31184i	0.475558	−	0.879685i	$-0.342246\pi$
$8$	0.905781	−	2.78771i	0.320242	−	0.985603i
$9$		0			0
$10$	−1.35567			−0.428702
$11$	−0.490303	−	3.28018i	−0.147832	−	0.989012i
$11$	−0.490303	−	3.28018i	−0.147832	−	0.989012i
$12$		0			0
$13$	2.29029	+	1.66399i	0.635212	+	0.461509i	0.858202	−	0.513312i	$-0.171582\pi$
$13$	2.29029	+	1.66399i	0.635212	+	0.461509i	−0.222990	+	0.974821i	$0.571582\pi$
$14$	1.52884	−	4.70527i	0.408599	−	1.25754i
$15$		0			0
$16$	2.95244	−	2.14507i	0.738109	−	0.536268i
$17$	2.98685	−	2.17008i	0.724419	−	0.526321i	−0.163374	−	0.986564i	$-0.552238\pi$
$17$	2.98685	−	2.17008i	0.724419	−	0.526321i	0.887793	+	0.460243i	$0.152238\pi$
$18$		0			0
$19$	−0.0293950	+	0.0904686i	−0.00674368	+	0.0207549i	−0.954372	−	0.298621i	$-0.903473\pi$
$19$	−0.0293950	+	0.0904686i	−0.00674368	+	0.0207549i	0.947628	+	0.319376i	$0.103473\pi$
$20$	0.131180	+	0.0953077i	0.0293327	+	0.0213115i
$21$		0			0
$22$	2.07605	−	3.98828i	0.442616	−	0.850304i
$23$	−1.16215			−0.242324			−0.121162	−	0.992633i	$-0.538662\pi$
$23$	−1.16215			−0.242324			−0.121162	+	0.992633i	$0.538662\pi$
$24$		0			0
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	1.18596	+	3.65001i	0.232586	+	0.715827i
$27$		0			0
$28$	−0.478730	+	0.347817i	−0.0904714	+	0.0657313i
$29$	2.08707	+	6.42333i	0.387559	+	1.19278i	0.934607	+	0.355682i	$0.115751\pi$
$29$	2.08707	+	6.42333i	0.387559	+	1.19278i	−0.547049	+	0.837101i	$0.684249\pi$
$30$		0			0
$31$	−5.48382	−	3.98423i	−0.984923	−	0.715588i	−0.0261194	−	0.999659i	$-0.508315\pi$
$31$	−5.48382	−	3.98423i	−0.984923	−	0.715588i	−0.958803	+	0.284071i	$0.908315\pi$
$32$	−0.914918			−0.161736
$33$		0			0
$34$	5.00509			0.858366
$35$	2.95244	+	2.14507i	0.499053	+	0.362583i
$36$		0			0
$37$	3.04066	+	9.35820i	0.499882	+	1.53848i	0.809208	+	0.587523i	$0.199897\pi$
$37$	3.04066	+	9.35820i	0.499882	+	1.53848i	−0.309326	+	0.950956i	$0.600103\pi$
$38$	−0.104329	+	0.0757994i	−0.0169244	+	0.0122963i
$39$		0			0
$40$	0.905781	+	2.78771i	0.143216	+	0.440775i
$41$	2.57047	−	7.91110i	0.401440	−	1.23551i	−0.522391	−	0.852706i	$-0.674960\pi$
$41$	2.57047	−	7.91110i	0.401440	−	1.23551i	0.923831	−	0.382800i	$-0.125040\pi$
$42$		0			0
$43$	−2.96862			−0.452710			−0.226355	−	0.974045i	$-0.572681\pi$
$43$	−2.96862			−0.452710			−0.226355	+	0.974045i	$0.572681\pi$
$44$	−0.481274	+	0.239968i	−0.0725547	+	0.0361765i
$45$		0			0
$46$	−1.27460	−	0.926052i	−0.187930	−	0.136539i
$47$	0.687534	−	2.11601i	0.100287	−	0.308652i	−0.888308	−	0.459248i	$-0.848119\pi$
$47$	0.687534	−	2.11601i	0.100287	−	0.308652i	0.988595	+	0.150595i	$0.0481191\pi$
$48$		0			0
$49$	−5.11155	+	3.71376i	−0.730221	+	0.530537i
$50$	1.09676	−	0.796845i	0.155106	−	0.112691i
$51$		0			0
$52$	0.141849	−	0.436565i	0.0196708	−	0.0605407i
$53$	2.42214	+	1.75979i	0.332706	+	0.241725i	0.741578	−	0.670867i	$-0.234078\pi$
$53$	2.42214	+	1.75979i	0.332706	+	0.241725i	−0.408872	+	0.912592i	$0.634078\pi$
$54$		0			0
$55$	2.32471	+	2.36553i	0.313463	+	0.318968i
$56$	−10.6970			−1.42945
$57$		0			0
$58$	−2.82938	+	8.70794i	−0.371516	+	1.14341i
$59$	2.62930	+	8.09216i	0.342306	+	1.05351i	0.963010	+	0.269465i	$0.0868468\pi$
$59$	2.62930	+	8.09216i	0.342306	+	1.05351i	−0.620704	+	0.784045i	$0.713153\pi$
$60$		0			0
$61$	6.86076	−	4.98464i	0.878431	−	0.638217i	−0.0544052	−	0.998519i	$-0.517326\pi$
$61$	6.86076	−	4.98464i	0.878431	−	0.638217i	0.932836	+	0.360302i	$0.117326\pi$
$62$	−2.83964	−	8.73951i	−0.360634	−	1.10992i
$63$		0			0
$64$	−6.90832	−	5.01919i	−0.863541	−	0.627399i
$65$	−2.83095			−0.351137
$66$		0			0
$67$	−13.4153			−1.63894			−0.819469	−	0.573123i	$-0.805732\pi$
$67$	−13.4153			−1.63894			−0.819469	+	0.573123i	$0.805732\pi$
$68$	−0.484310	−	0.351872i	−0.0587312	−	0.0426707i
$69$		0			0
$70$	1.52884	+	4.70527i	0.182731	+	0.562388i
$71$	6.71734	−	4.88043i	0.797202	−	0.579201i	−0.112890	−	0.993607i	$-0.536011\pi$
$71$	6.71734	−	4.88043i	0.797202	−	0.579201i	0.910092	+	0.414406i	$0.136011\pi$
$72$		0			0
$73$	−0.407912	−	1.25542i	−0.0477425	−	0.146936i	0.924343	−	0.381562i	$-0.124614\pi$
$73$	−0.407912	−	1.25542i	−0.0477425	−	0.146936i	−0.972086	+	0.234625i	$0.924614\pi$
$74$	−4.12215	+	12.6867i	−0.479190	+	1.47480i
$75$		0			0
$76$	0.0154241			0.00176927
$77$	−10.8319	+	5.40091i	−1.23441	+	0.615491i
$78$		0			0
$79$	11.2179	+	8.15028i	1.26211	+	0.916978i	0.998859	−	0.0477484i	$-0.0152046\pi$
$79$	11.2179	+	8.15028i	1.26211	+	0.916978i	0.263253	+	0.964727i	$0.415205\pi$
$80$	−1.12773	+	3.47080i	−0.126084	+	0.388047i
$81$		0			0
$82$	9.12312	−	6.62834i	1.00748	−	0.731977i
$83$	−8.61155	+	6.25666i	−0.945240	+	0.686757i	−0.949676	−	0.313233i	$-0.898588\pi$
$83$	−8.61155	+	6.25666i	−0.945240	+	0.686757i	0.00443607	+	0.999990i	$0.498588\pi$
$84$		0			0
$85$	−1.14088	+	3.51126i	−0.123745	+	0.380849i
$86$	−3.25587	−	2.36553i	−0.351090	−	0.255082i
$87$		0			0
$88$	−9.58829	−	1.60431i	−1.02212	−	0.171020i
$89$	12.1612			1.28908			0.644540	−	0.764570i	$-0.277049\pi$
$89$	12.1612			1.28908			0.644540	+	0.764570i	$0.277049\pi$
$90$		0			0
$91$	3.19256	−	9.82567i	0.334671	−	1.03001i
$92$	0.0582308	+	0.179216i	0.00607098	+	0.0186846i
$93$		0			0
$94$	2.44020	−	1.77291i	0.251687	−	0.182861i
$95$	−0.0293950	−	0.0904686i	−0.00301587	−	0.00928188i
$96$		0			0
$97$	3.50412	+	2.54589i	0.355789	+	0.258496i	0.751294	−	0.659968i	$-0.229430\pi$
$97$	3.50412	+	2.54589i	0.355789	+	0.258496i	−0.395504	+	0.918464i	$0.629430\pi$
$98$	−8.56545			−0.865241
$99$		0			0
$100$	−0.162147			−0.0162147
$101$	8.01388	+	5.82242i	0.797411	+	0.579353i	0.910153	−	0.414271i	$-0.135964\pi$
$101$	8.01388	+	5.82242i	0.797411	+	0.579353i	−0.112743	+	0.993624i	$0.535964\pi$
$102$		0			0
$103$	1.25643	+	3.86690i	0.123800	+	0.381017i	0.993681	−	0.112245i	$-0.0358042\pi$
$103$	1.25643	+	3.86690i	0.123800	+	0.381017i	−0.869880	+	0.493263i	$0.835804\pi$
$104$	6.71323	−	4.87744i	0.658286	−	0.478273i
$105$		0			0
$106$	1.25424	+	3.86014i	0.121822	+	0.374930i
$107$	−0.599053	+	1.84369i	−0.0579126	+	0.178237i	−0.975828	−	0.218539i	$-0.929871\pi$
$107$	−0.599053	+	1.84369i	−0.0579126	+	0.178237i	0.917916	+	0.396776i	$0.129871\pi$
$108$		0			0
$109$	6.12664			0.586825			0.293413	−	0.955986i	$-0.405209\pi$
$109$	6.12664			0.586825			0.293413	+	0.955986i	$0.405209\pi$
$110$	0.664691	+	4.44686i	0.0633758	+	0.423991i
$111$		0			0
$112$	−10.7747	−	7.82825i	−1.01811	−	0.739700i
$113$	−1.78775	+	5.50212i	−0.168177	+	0.517596i	−0.999256	−	0.0385582i	$-0.987724\pi$
$113$	−1.78775	+	5.50212i	−0.168177	+	0.517596i	0.831079	+	0.556154i	$0.187724\pi$
$114$		0			0
$115$	0.940197	−	0.683093i	0.0876738	−	0.0636987i
$116$	0.885974	−	0.643698i	0.0822606	−	0.0597659i
$117$		0			0
$118$	−3.56448	+	10.9703i	−0.328137	+	1.00990i
$119$	−10.9003	−	7.91951i	−0.999226	−	0.725980i
$120$		0			0
$121$	−10.5192	+	3.21657i	−0.956291	+	0.292415i
$122$	11.4966			1.04085
$123$		0			0
$124$	−0.339639	+	1.04530i	−0.0305005	+	0.0938708i
$125$	0.309017	+	0.951057i	0.0276393	+	0.0850651i
$126$		0			0
$127$	−1.97224	+	1.43292i	−0.175008	+	0.127151i	−0.671841	−	0.740695i	$-0.734496\pi$
$127$	−1.97224	+	1.43292i	−0.175008	+	0.127151i	0.496833	+	0.867846i	$0.334496\pi$
$128$	−3.01183	−	9.26945i	−0.266211	−	0.819312i
$129$		0			0
$130$	−3.10489	−	2.25583i	−0.272317	−	0.197850i
$131$	−7.04156			−0.615224			−0.307612	−	0.951512i	$-0.599530\pi$
$131$	−7.04156			−0.615224			−0.307612	+	0.951512i	$0.599530\pi$
$132$		0			0
$133$	0.347148			0.0301016
$134$	−14.7134	−	10.6899i	−1.27104	−	0.923468i
$135$		0			0
$136$	−3.34410	−	10.2921i	−0.286754	−	0.882539i
$137$	−7.74461	+	5.62678i	−0.661666	+	0.480729i	−0.867225	−	0.497916i	$-0.834099\pi$
$137$	−7.74461	+	5.62678i	−0.661666	+	0.480729i	0.205559	+	0.978645i	$0.434099\pi$
$138$		0			0
$139$	0.159299	+	0.490271i	0.0135116	+	0.0415843i	0.957585	−	0.288151i	$-0.0930405\pi$
$139$	0.159299	+	0.490271i	0.0135116	+	0.0415843i	−0.944073	+	0.329735i	$0.893041\pi$
$140$	0.182858	−	0.562780i	0.0154544	−	0.0475636i
$141$		0			0
$142$	11.2563			0.944607
$143$	4.33527	−	8.32843i	0.362533	−	0.696459i
$144$		0			0
$145$	−5.46401	−	3.96984i	−0.453761	−	0.329677i
$146$	0.552996	−	1.70195i	0.0457663	−	0.140854i
$147$		0			0
$148$	1.29078	−	0.937809i	0.106102	−	0.0770874i
$149$	−6.60144	+	4.79623i	−0.540811	+	0.392922i	−0.824386	−	0.566028i	$-0.808479\pi$
$149$	−6.60144	+	4.79623i	−0.540811	+	0.392922i	0.283575	+	0.958950i	$0.408479\pi$
$150$		0			0
$151$	0.599563	−	1.84526i	0.0487917	−	0.150165i	−0.923692	−	0.383135i	$-0.874844\pi$
$151$	0.599563	−	1.84526i	0.0487917	−	0.150165i	0.972484	+	0.232970i	$0.0748443\pi$
$152$	0.225574	+	0.163889i	0.0182965	+	0.0132932i
$153$		0			0
$154$	−16.1838	−	2.70785i	−1.30412	−	0.218205i
$155$	6.77837			0.544452
$156$		0			0
$157$	6.57418	−	20.2332i	0.524676	−	1.61479i	−0.240279	−	0.970704i	$-0.577239\pi$
$157$	6.57418	−	20.2332i	0.524676	−	1.61479i	0.764955	−	0.644084i	$-0.222761\pi$
$158$	5.80887	+	17.8779i	0.462129	+	1.42229i
$159$		0			0
$160$	0.740184	−	0.537775i	0.0585167	−	0.0425149i
$161$	1.31059	+	4.03358i	0.103289	+	0.317891i
$162$		0			0
$163$	12.9289	+	9.39337i	1.01267	+	0.735746i	0.964767	−	0.263107i	$-0.0847471\pi$
$163$	12.9289	+	9.39337i	1.01267	+	0.735746i	0.0479001	+	0.998852i	$0.484747\pi$
$164$	−1.34878			−0.105322
$165$		0			0
$166$	−14.4304			−1.12002
$167$	14.3269	+	10.4091i	1.10865	+	0.805481i	0.982450	−	0.186524i	$-0.0597223\pi$
$167$	14.3269	+	10.4091i	1.10865	+	0.805481i	0.126199	+	0.992005i	$0.459722\pi$
$168$		0			0
$169$	−1.54066	−	4.74168i	−0.118513	−	0.364744i
$170$	−4.04920	+	2.94192i	−0.310560	+	0.225635i
$171$		0			0
$172$	0.148746	+	0.457794i	0.0113418	+	0.0349065i
$173$	−4.90888	+	15.1080i	−0.373216	+	1.14864i	0.571459	+	0.820631i	$0.306378\pi$
$173$	−4.90888	+	15.1080i	−0.373216	+	1.14864i	−0.944675	+	0.328009i	$0.893622\pi$
$174$		0			0
$175$	−3.64941			−0.275870
$176$	−8.48382	−	8.63280i	−0.639492	−	0.650722i
$177$		0			0
$178$	13.3379	+	9.69057i	0.999719	+	0.726339i
$179$	5.21653	−	16.0548i	0.389902	−	1.19999i	−0.542960	−	0.839759i	$-0.682696\pi$
$179$	5.21653	−	16.0548i	0.389902	−	1.19999i	0.932862	−	0.360235i	$-0.117304\pi$
$180$		0			0
$181$	19.4871	−	14.1582i	1.44846	−	1.05237i	0.462277	−	0.886735i	$-0.347032\pi$
$181$	19.4871	−	14.1582i	1.44846	−	1.05237i	0.986187	−	0.165636i	$-0.0529676\pi$
$182$	11.3310	−	8.23247i	0.839911	−	0.610231i
$183$		0			0
$184$	−1.05265	+	3.23972i	−0.0776024	+	0.238836i
$185$	−7.96056	−	5.78369i	−0.585272	−	0.425225i
$186$		0			0
$187$	−8.58271	−	8.73343i	−0.627630	−	0.638652i
$188$	−0.360762			−0.0263113
$189$		0			0
$190$	0.0398501	−	0.122646i	0.00289103	−	0.00889767i
$191$	−1.66337	−	5.11934i	−0.120358	−	0.370422i	0.872669	−	0.488312i	$-0.162387\pi$
$191$	−1.66337	−	5.11934i	−0.120358	−	0.370422i	−0.993027	+	0.117890i	$0.962387\pi$
$192$		0			0
$193$	−14.7921	+	10.7471i	−1.06476	+	0.773593i	−0.974963	−	0.222367i	$-0.928622\pi$
$193$	−14.7921	+	10.7471i	−1.06476	+	0.773593i	−0.0897961	+	0.995960i	$0.528622\pi$
$194$	1.81451	+	5.58448i	0.130274	+	0.400942i
$195$		0			0
$196$	0.828823	+	0.602175i	0.0592017	+	0.0430125i
$197$	−2.64566			−0.188496			−0.0942478	−	0.995549i	$-0.530045\pi$
$197$	−2.64566			−0.188496			−0.0942478	+	0.995549i	$0.530045\pi$
$198$		0			0
$199$	6.52800			0.462757			0.231379	−	0.972864i	$-0.425676\pi$
$199$	6.52800			0.462757			0.231379	+	0.972864i	$0.425676\pi$
$200$	−2.37136	−	1.72290i	−0.167681	−	0.121827i
$201$		0			0
$202$	4.14976	+	12.7716i	0.291976	+	0.898610i
$203$	19.9404	−	14.4876i	1.39954	−	1.01683i
$204$		0			0
$205$	2.57047	+	7.91110i	0.179530	+	0.552535i
$206$	−1.70331	+	5.24226i	−0.118676	+	0.365246i
$207$		0			0
$208$	10.3313			0.716349
$209$	0.311166	+	0.0520641i	0.0215238	+	0.00360135i
$210$		0			0
$211$	22.2057	+	16.1334i	1.52871	+	1.11067i	0.956953	+	0.290243i	$0.0937362\pi$
$211$	22.2057	+	16.1334i	1.52871	+	1.11067i	0.571752	+	0.820426i	$0.306264\pi$
$212$	0.150014	−	0.461697i	0.0103030	−	0.0317095i
$213$		0			0
$214$	−2.12616	+	1.54474i	−0.145341	+	0.105597i
$215$	2.40166	−	1.74491i	0.163792	−	0.119002i
$216$		0			0
$217$	−7.64418	+	23.5264i	−0.518921	+	1.59707i
$218$	6.71947	+	4.88198i	0.455100	+	0.330650i
$219$		0			0
$220$	0.248309	−	0.477024i	0.0167410	−	0.0321609i
$221$	10.4518			0.703061
$222$		0			0
$223$	−1.57040	+	4.83321i	−0.105162	+	0.323656i	−0.989768	−	0.142683i	$-0.954427\pi$
$223$	−1.57040	+	4.83321i	−0.105162	+	0.323656i	0.884606	+	0.466338i	$0.154427\pi$
$224$	1.03178	+	3.17550i	0.0689388	+	0.212172i
$225$		0			0
$226$	−6.34507	+	4.60997i	−0.422068	+	0.306650i
$227$	−1.15566	−	3.55676i	−0.0767040	−	0.236071i	0.905351	−	0.424663i	$-0.139607\pi$
$227$	−1.15566	−	3.55676i	−0.0767040	−	0.236071i	−0.982055	+	0.188593i	$0.939607\pi$
$228$		0			0
$229$	−21.7821	−	15.8256i	−1.43940	−	1.04578i	−0.988168	−	0.153378i	$-0.950985\pi$
$229$	−21.7821	−	15.8256i	−1.43940	−	1.04578i	−0.451232	−	0.892407i	$-0.649015\pi$
$230$	1.57549			0.103885
$231$		0			0
$232$	19.7968			1.29972
$233$	14.8185	+	10.7663i	0.970794	+	0.705323i	0.955632	−	0.294562i	$-0.0951737\pi$
$233$	14.8185	+	10.7663i	0.970794	+	0.705323i	0.0151615	+	0.999885i	$0.495174\pi$
$234$		0			0
$235$	0.687534	+	2.11601i	0.0448498	+	0.138033i
$236$	1.11616	−	0.810936i	0.0726557	−	0.0527874i
$237$		0			0
$238$	−5.64439	−	17.3717i	−0.365872	−	1.12604i
$239$	3.38555	−	10.4196i	0.218993	−	0.673991i	−0.779853	−	0.625963i	$-0.784706\pi$
$239$	3.38555	−	10.4196i	0.218993	−	0.673991i	0.998846	−	0.0480283i	$-0.0152938\pi$
$240$		0			0
$241$	−9.99444			−0.643798			−0.321899	−	0.946774i	$-0.604321\pi$
$241$	−9.99444			−0.643798			−0.321899	+	0.946774i	$0.604321\pi$
$242$	−14.1002	−	4.85437i	−0.906394	−	0.312050i
$243$		0			0
$244$	−1.11245	−	0.808245i	−0.0712175	−	0.0517426i
$245$	1.95244	−	6.00899i	0.124737	−	0.383900i
$246$		0			0
$247$	−0.217862	+	0.158286i	−0.0138622	+	0.0100715i
$248$	−16.0740	+	11.6784i	−1.02070	+	0.741581i
$249$		0			0
$250$	−0.418926	+	1.28932i	−0.0264952	+	0.0815439i
$251$	7.81303	+	5.67650i	0.493154	+	0.358297i	0.806396	−	0.591376i	$-0.201415\pi$
$251$	7.81303	+	5.67650i	0.493154	+	0.358297i	−0.313242	+	0.949673i	$0.601415\pi$
$252$		0			0
$253$	0.569804	+	3.81206i	0.0358233	+	0.239662i
$254$	−3.30490			−0.207368
$255$		0			0
$256$	−1.19443	+	3.67608i	−0.0746520	+	0.229755i
$257$	−3.22230	−	9.91721i	−0.201001	−	0.618618i	−0.999854	−	0.0170916i	$-0.994559\pi$
$257$	−3.22230	−	9.91721i	−0.201001	−	0.618618i	0.798853	−	0.601527i	$-0.205441\pi$
$258$		0			0
$259$	29.0514	−	21.1071i	1.80517	−	1.31153i
$260$	0.141849	+	0.436565i	0.00879707	+	0.0270746i
$261$		0			0
$262$	−7.72292	−	5.61103i	−0.477124	−	0.346651i
$263$	10.9619			0.675937			0.337968	−	0.941157i	$-0.390260\pi$
$263$	10.9619			0.675937			0.337968	+	0.941157i	$0.390260\pi$
$264$		0			0
$265$	−2.99393			−0.183915
$266$	0.380739	+	0.276623i	0.0233446	+	0.0169609i
$267$		0			0
$268$	0.672190	+	2.06879i	0.0410605	+	0.126371i
$269$	−0.0722816	+	0.0525156i	−0.00440708	+	0.00320193i	−0.589987	−	0.807413i	$-0.700867\pi$
$269$	−0.0722816	+	0.0525156i	−0.00440708	+	0.00320193i	0.585580	+	0.810615i	$0.300867\pi$
$270$		0			0
$271$	−4.14069	−	12.7437i	−0.251529	−	0.774126i	−0.994494	−	0.104796i	$-0.966581\pi$
$271$	−4.14069	−	12.7437i	−0.251529	−	0.774126i	0.742965	−	0.669330i	$-0.233419\pi$
$272$	4.16353	−	12.8140i	0.252451	−	0.776965i
$273$		0			0
$274$	−12.9777			−0.784010
$275$	−3.27115	−	0.547326i	−0.197258	−	0.0330050i
$276$		0			0
$277$	3.16057	+	2.29629i	0.189901	+	0.137971i	0.678673	−	0.734440i	$-0.262555\pi$
$277$	3.16057	+	2.29629i	0.189901	+	0.137971i	−0.488773	+	0.872411i	$0.662555\pi$
$278$	−0.215957	+	0.664648i	−0.0129523	+	0.0398630i
$279$		0			0
$280$	8.65409	−	6.28756i	0.517181	−	0.375754i
$281$	−1.24381	+	0.903680i	−0.0741994	+	0.0539090i	−0.624267	−	0.781211i	$-0.714602\pi$
$281$	−1.24381	+	0.903680i	−0.0741994	+	0.0539090i	0.550067	+	0.835120i	$0.314602\pi$
$282$		0			0
$283$	−1.67231	+	5.14683i	−0.0994083	+	0.305947i	−0.988377	−	0.152020i	$-0.951422\pi$
$283$	−1.67231	+	5.14683i	−0.0994083	+	0.305947i	0.888969	+	0.457967i	$0.151422\pi$
$284$	−1.08920	−	0.791349i	−0.0646320	−	0.0469579i
$285$		0			0
$286$	11.3912	−	5.67979i	0.673578	−	0.335853i
$287$	−30.3566			−1.79190
$288$		0			0
$289$	−1.04122	+	3.20456i	−0.0612484	+	0.188503i
$290$	−2.82938	−	8.70794i	−0.166147	−	0.511348i
$291$		0			0
$292$	−0.173162	+	0.125809i	−0.0101335	+	0.00736243i
$293$	−3.52789	−	10.8577i	−0.206102	−	0.634315i	−0.999666	−	0.0258295i	$-0.991777\pi$
$293$	−3.52789	−	10.8577i	−0.206102	−	0.634315i	0.793565	−	0.608486i	$-0.208223\pi$
$294$		0			0
$295$	−6.88361	−	5.00123i	−0.400779	−	0.291183i
$296$	28.8421			1.67641
$297$		0			0
$298$	−11.0621			−0.640808
$299$	−2.66165	−	1.93381i	−0.153927	−	0.111835i
$300$		0			0
$301$	3.34780	+	10.3035i	0.192964	+	0.593883i
$302$	2.12797	−	1.54606i	0.122451	−	0.0889657i
$303$		0			0
$304$	0.107275	+	0.330157i	0.00615262	+	0.0189358i
$305$	−2.62058	+	8.06531i	−0.150054	+	0.461818i
$306$		0			0
$307$	−4.25008			−0.242565			−0.121282	−	0.992618i	$-0.538701\pi$
$307$	−4.25008			−0.242565			−0.121282	+	0.992618i	$0.538701\pi$
$308$	1.37563	+	1.39978i	0.0783836	+	0.0797601i
$309$		0			0
$310$	7.43427	+	5.40131i	0.422238	+	0.306774i
$311$	5.13570	−	15.8061i	0.291219	−	0.896279i	−0.693247	−	0.720700i	$-0.743820\pi$
$311$	5.13570	−	15.8061i	0.291219	−	0.896279i	0.984465	−	0.175579i	$-0.0561796\pi$
$312$		0			0
$313$	21.5012	−	15.6215i	1.21532	−	0.882982i	0.219617	−	0.975586i	$-0.429519\pi$
$313$	21.5012	−	15.6215i	1.21532	−	0.882982i	0.995703	+	0.0926041i	$0.0295191\pi$
$314$	23.3331	−	16.9525i	1.31676	−	0.956683i
$315$		0			0
$316$	0.694778	−	2.13831i	0.0390843	−	0.120289i
$317$	4.68982	+	3.40736i	0.263407	+	0.191376i	0.711648	−	0.702537i	$-0.247949\pi$
$317$	4.68982	+	3.40736i	0.263407	+	0.191376i	−0.448241	+	0.893913i	$0.647949\pi$
$318$		0			0
$319$	20.0464	−	9.99534i	1.12238	−	0.559632i
$320$	8.53916			0.477353
$321$		0			0
$322$	−1.77673	+	5.46822i	−0.0990134	+	0.304732i
$323$	0.108525	+	0.334006i	0.00603850	+	0.0185846i
$324$		0			0
$325$	2.29029	−	1.66399i	0.127042	−	0.0923018i
$326$	6.69484	+	20.6046i	0.370793	+	1.14118i
$327$		0			0
$328$	−19.7255	−	14.3314i	−1.08916	−	0.791321i
$329$	−8.11961			−0.447648
$330$		0			0
$331$	−12.9230			−0.710311			−0.355155	−	0.934807i	$-0.615572\pi$
$331$	−12.9230			−0.710311			−0.355155	+	0.934807i	$0.615572\pi$
$332$	1.39634	+	1.01450i	0.0766340	+	0.0556779i
$333$		0			0
$334$	7.41878	+	22.8327i	0.405938	+	1.24935i
$335$	10.8532	−	7.88531i	0.592974	−	0.430820i
$336$		0			0
$337$	4.13631	+	12.7303i	0.225319	+	0.693461i	0.998259	+	0.0589818i	$0.0187854\pi$
$337$	4.13631	+	12.7303i	0.225319	+	0.693461i	−0.772940	+	0.634479i	$0.781215\pi$
$338$	2.08864	−	6.42817i	0.113607	−	0.349646i
$339$		0			0
$340$	0.598640			0.0324658
$341$	−10.3803	+	19.9414i	−0.562123	+	1.07989i
$342$		0			0
$343$	−2.01291	−	1.46246i	−0.108687	−	0.0789656i
$344$	−2.68892	+	8.27564i	−0.144977	+	0.446193i
$345$		0			0
$346$	−17.4226	+	12.6583i	−0.936646	+	0.680513i
$347$	−6.83538	+	4.96619i	−0.366942	+	0.266599i	−0.755942	−	0.654639i	$-0.772821\pi$
$347$	−6.83538	+	4.96619i	−0.366942	+	0.266599i	0.389000	+	0.921238i	$0.372821\pi$
$348$		0			0
$349$	−3.21341	+	9.88987i	−0.172010	+	0.529393i	−0.999484	−	0.0321111i	$-0.989777\pi$
$349$	−3.21341	+	9.88987i	−0.172010	+	0.529393i	0.827474	+	0.561504i	$0.189777\pi$
$350$	−4.00254	−	2.90802i	−0.213945	−	0.155440i
$351$		0			0
$352$	0.448587	+	3.00110i	0.0239098	+	0.159959i
$353$	−19.1073			−1.01698			−0.508489	−	0.861069i	$-0.669796\pi$
$353$	−19.1073			−1.01698			−0.508489	+	0.861069i	$0.669796\pi$
$354$		0			0
$355$	−2.56580	+	7.89671i	−0.136178	+	0.419114i
$356$	−0.609350	−	1.87539i	−0.0322955	−	0.0993953i
$357$		0			0
$358$	18.5145	−	13.4516i	0.978522	−	0.710938i
$359$	1.36405	+	4.19813i	0.0719920	+	0.221569i	0.980578	−	0.196129i	$-0.0628371\pi$
$359$	1.36405	+	4.19813i	0.0719920	+	0.221569i	−0.908586	+	0.417698i	$0.862837\pi$
$360$		0			0
$361$	15.3640	+	11.1626i	0.808632	+	0.587505i
$362$	32.6546			1.71629
$363$		0			0
$364$	−1.67520			−0.0878041
$365$	1.06793	+	0.775895i	0.0558979	+	0.0406122i
$366$		0			0
$367$	−9.07327	−	27.9247i	−0.473621	−	1.45766i	−0.847809	−	0.530302i	$-0.822078\pi$
$367$	−9.07327	−	27.9247i	−0.473621	−	1.45766i	0.374188	−	0.927353i	$-0.377922\pi$
$368$	−3.43117	+	2.49289i	−0.178862	+	0.129951i
$369$		0			0
$370$	−4.12215	−	12.6867i	−0.214300	−	0.659549i
$371$	3.37634	−	10.3913i	0.175291	−	0.539490i
$372$		0			0
$373$	−4.96478			−0.257067			−0.128533	−	0.991705i	$-0.541027\pi$
$373$	−4.96478			−0.257067			−0.128533	+	0.991705i	$0.541027\pi$
$374$	−2.45401	−	16.4176i	−0.126894	−	0.848934i
$375$		0			0
$376$	−5.27606	−	3.83329i	−0.272092	−	0.197687i
$377$	−5.90839	+	18.1842i	−0.304298	+	0.936532i
$378$		0			0
$379$	−6.40996	+	4.65711i	−0.329258	+	0.239220i	−0.740116	−	0.672480i	$-0.765229\pi$
$379$	−6.40996	+	4.65711i	−0.329258	+	0.239220i	0.410858	+	0.911699i	$0.365229\pi$
$380$	−0.0124784	+	0.00906608i	−0.000640128	+	0.000465080i
$381$		0			0
$382$	2.25499	−	6.94016i	0.115375	−	0.355089i
$383$	−19.8335	−	14.4099i	−1.01344	−	0.736309i	−0.0485140	−	0.998823i	$-0.515449\pi$
$383$	−19.8335	−	14.4099i	−1.01344	−	0.736309i	−0.964928	+	0.262514i	$0.915449\pi$
$384$		0			0
$385$	5.58864	−	10.7363i	0.284823	−	0.547171i
$386$	−24.7872			−1.26164
$387$		0			0
$388$	0.217026	−	0.667939i	0.0110179	−	0.0339095i
$389$	−1.68752	−	5.19366i	−0.0855608	−	0.263329i	0.899118	−	0.437706i	$-0.144209\pi$
$389$	−1.68752	−	5.19366i	−0.0855608	−	0.263329i	−0.984679	+	0.174377i	$0.944209\pi$
$390$		0			0
$391$	−3.47116	+	2.52195i	−0.175544	+	0.127540i
$392$	5.72292	+	17.6133i	0.289051	+	0.889608i
$393$		0			0
$394$	−2.90166	−	2.10818i	−0.146184	−	0.106209i
$395$	−13.8661			−0.697679
$396$		0			0
$397$	−6.43455			−0.322941			−0.161470	−	0.986878i	$-0.551624\pi$
$397$	−6.43455			−0.322941			−0.161470	+	0.986878i	$0.551624\pi$
$398$	7.15967	+	5.20180i	0.358882	+	0.260743i
$399$		0			0
$400$	−1.12773	−	3.47080i	−0.0563865	−	0.173540i
$401$	−11.8947	+	8.64197i	−0.593991	+	0.431560i	−0.843741	−	0.536751i	$-0.819652\pi$
$401$	−11.8947	+	8.64197i	−0.593991	+	0.431560i	0.249750	+	0.968310i	$0.419652\pi$
$402$		0			0
$403$	−5.92981	−	18.2501i	−0.295385	−	0.909101i
$404$	0.496337	−	1.52757i	0.0246937	−	0.0759994i
$405$		0			0
$406$	33.4143			1.65832
$407$	29.2058	−	14.5623i	1.44768	−	0.721826i
$408$		0			0
$409$	−3.55625	−	2.58376i	−0.175845	−	0.127759i	0.496381	−	0.868105i	$-0.334662\pi$
$409$	−3.55625	−	2.58376i	−0.175845	−	0.127759i	−0.672226	+	0.740346i	$0.734662\pi$
$410$	−3.48472	+	10.7249i	−0.172098	+	0.529664i
$411$		0			0
$412$	0.533365	−	0.387512i	0.0262770	−	0.0190914i
$413$	25.1211	−	18.2516i	1.23613	−	0.898101i
$414$		0			0
$415$	3.28932	−	10.1235i	0.161466	−	0.496942i
$416$	−2.09543	−	1.52242i	−0.102737	−	0.0746427i
$417$		0			0
$418$	0.299789	+	0.305053i	0.0146631	+	0.0149206i
$419$	−17.8526			−0.872159			−0.436079	−	0.899908i	$-0.643633\pi$
$419$	−17.8526			−0.872159			−0.436079	+	0.899908i	$0.643633\pi$
$420$		0			0
$421$	−1.49210	+	4.59221i	−0.0727205	+	0.223811i	−0.980810	−	0.194965i	$-0.937541\pi$
$421$	−1.49210	+	4.59221i	−0.0727205	+	0.223811i	0.908090	+	0.418776i	$0.137541\pi$
$422$	11.4986	+	35.3891i	0.559743	+	1.72271i
$423$		0			0
$424$	7.09969	−	5.15823i	0.344792	−	0.250506i
$425$	−1.14088	−	3.51126i	−0.0553407	−	0.170321i
$426$		0			0
$427$	−25.0378	−	18.1910i	−1.21166	−	0.880324i
$428$	0.314335			0.0151939
$429$		0			0
$430$	4.02448			0.194078
$431$	−20.1234	−	14.6205i	−0.969312	−	0.704247i	−0.0140175	−	0.999902i	$-0.504462\pi$
$431$	−20.1234	−	14.6205i	−0.969312	−	0.704247i	−0.955295	+	0.295655i	$0.904462\pi$
$432$		0			0
$433$	−6.56669	−	20.2102i	−0.315575	−	0.971240i	−0.975517	−	0.219923i	$-0.929419\pi$
$433$	−6.56669	−	20.2102i	−0.315575	−	0.971240i	0.659942	−	0.751316i	$-0.270581\pi$
$434$	−27.1307	+	19.7116i	−1.30232	+	0.946188i
$435$		0			0
$436$	−0.306983	−	0.944796i	−0.0147018	−	0.0452475i
$437$	0.0341614	−	0.105138i	0.00163416	−	0.00502943i
$438$		0			0
$439$	−15.9119			−0.759434			−0.379717	−	0.925103i	$-0.623979\pi$
$439$	−15.9119			−0.759434			−0.379717	+	0.925103i	$0.623979\pi$
$440$	8.70008	−	4.33795i	0.414760	−	0.206804i
$441$		0			0
$442$	11.4631	+	8.32843i	0.545244	+	0.396143i
$443$	−8.12332	+	25.0010i	−0.385951	+	1.18783i	0.549838	+	0.835272i	$0.314690\pi$
$443$	−8.12332	+	25.0010i	−0.385951	+	1.18783i	−0.935788	+	0.352562i	$0.885310\pi$
$444$		0			0
$445$	−9.83859	+	7.14815i	−0.466394	+	0.338855i
$446$	−5.57368	+	4.04952i	−0.263922	+	0.191750i
$447$		0			0
$448$	−9.62987	+	29.6377i	−0.454969	+	1.40025i
$449$	−6.62554	−	4.81373i	−0.312678	−	0.227174i	0.420366	−	0.907354i	$-0.361902\pi$
$449$	−6.62554	−	4.81373i	−0.312678	−	0.227174i	−0.733045	+	0.680180i	$0.761902\pi$
$450$		0			0
$451$	−27.2102	−	4.55278i	−1.28128	−	0.214382i
$452$	0.938065			0.0441229
$453$		0			0
$454$	1.56670	−	4.82181i	0.0735289	−	0.226299i
$455$	3.19256	+	9.82567i	0.149669	+	0.460635i
$456$		0			0
$457$	−9.64056	+	7.00428i	−0.450966	+	0.327646i	−0.789977	−	0.613136i	$-0.789908\pi$
$457$	−9.64056	+	7.00428i	−0.450966	+	0.327646i	0.339011	+	0.940782i	$0.389908\pi$
$458$	−11.2792	−	34.7139i	−0.527043	−	1.62207i
$459$		0			0
$460$	−0.152450	−	0.110762i	−0.00710803	−	0.00516429i
$461$	−6.96172			−0.324240			−0.162120	−	0.986771i	$-0.551833\pi$
$461$	−6.96172			−0.324240			−0.162120	+	0.986771i	$0.551833\pi$
$462$		0			0
$463$	12.4762			0.579817			0.289909	−	0.957054i	$-0.406375\pi$
$463$	12.4762			0.579817			0.289909	+	0.957054i	$0.406375\pi$
$464$	19.9404	+	14.4876i	0.925712	+	0.672569i
$465$		0			0
$466$	7.67335	+	23.6161i	0.355461	+	1.09400i
$467$	−4.97235	+	3.61263i	−0.230093	+	0.167172i	−0.696858	−	0.717209i	$-0.745419\pi$
$467$	−4.97235	+	3.61263i	−0.230093	+	0.167172i	0.466765	+	0.884381i	$0.345419\pi$
$468$		0			0
$469$	15.1288	+	46.5618i	0.698585	+	2.15002i
$470$	−0.932072	+	2.86862i	−0.0429933	+	0.132320i
$471$		0			0
$472$	24.9401			1.14796
$473$	1.45552	+	9.73762i	0.0669250	+	0.447736i
$474$		0			0
$475$	0.0769572	+	0.0559127i	0.00353104	+	0.00256545i
$476$	−0.675105	+	2.07776i	−0.0309434	+	0.0952340i
$477$		0			0
$478$	12.0160	−	8.73013i	0.549599	−	0.399307i
$479$	17.9555	−	13.0454i	0.820406	−	0.596060i	−0.0964228	−	0.995340i	$-0.530740\pi$
$479$	17.9555	−	13.0454i	0.820406	−	0.596060i	0.916829	+	0.399281i	$0.130740\pi$
$480$		0			0
$481$	−8.60798	+	26.4926i	−0.392490	+	1.20796i
$482$	−10.9615	−	7.96402i	−0.499284	−	0.362751i
$483$		0			0
$484$	1.02311	+	1.46101i	0.0465049	+	0.0664095i
$485$	−4.33133			−0.196675
$486$		0			0
$487$	−10.5778	+	32.5553i	−0.479328	+	1.47522i	0.360702	+	0.932681i	$0.382537\pi$
$487$	−10.5778	+	32.5553i	−0.479328	+	1.47522i	−0.840030	+	0.542539i	$0.817463\pi$
$488$	−7.68135	−	23.6408i	−0.347719	−	1.07017i
$489$		0			0
$490$	6.92960	−	5.03465i	0.313047	−	0.227442i
$491$	5.25197	+	16.1639i	0.237018	+	0.729467i	0.996847	+	0.0793441i	$0.0252826\pi$
$491$	5.25197	+	16.1639i	0.237018	+	0.729467i	−0.759829	+	0.650123i	$0.774717\pi$
$492$		0			0
$493$	20.1729	+	14.6565i	0.908541	+	0.660094i
$494$	−0.365073			−0.0164254
$495$		0			0
$496$	−24.7371			−1.11073
$497$	−24.5144	−	17.8107i	−1.09962	−	0.798920i
$498$		0			0
$499$	1.61599	+	4.97352i	0.0723418	+	0.222645i	0.980690	−	0.195570i	$-0.0626558\pi$
$499$	1.61599	+	4.97352i	0.0723418	+	0.222645i	−0.908348	+	0.418215i	$0.862656\pi$
$500$	0.131180	−	0.0953077i	0.00586654	−	0.00426229i
$501$		0			0
$502$	4.04575	+	12.4515i	0.180571	+	0.555740i
$503$	−12.9617	+	39.8919i	−0.577931	+	1.77869i	0.0480416	+	0.998845i	$0.484702\pi$
$503$	−12.9617	+	39.8919i	−0.577931	+	1.77869i	−0.625973	+	0.779845i	$0.715298\pi$
$504$		0			0
$505$	−9.90570			−0.440798
$506$	−2.41268	+	4.63497i	−0.107257	+	0.206050i
$507$		0			0
$508$	0.319794	+	0.232344i	0.0141886	+	0.0103086i
$509$	−6.29399	+	19.3709i	−0.278976	+	0.858601i	0.709163	+	0.705044i	$0.249073\pi$
$509$	−6.29399	+	19.3709i	−0.278976	+	0.858601i	−0.988140	+	0.153557i	$0.950927\pi$
$510$		0			0
$511$	−3.89731	+	2.83156i	−0.172407	+	0.125261i
$512$	−20.0094	+	14.5377i	−0.884300	+	0.642481i
$513$		0			0
$514$	4.36838	−	13.4445i	0.192681	−	0.593012i
$515$	−3.28939	−	2.38988i	−0.144948	−	0.105311i
$516$		0			0
$517$	−7.27801	−	1.21775i	−0.320086	−	0.0535566i
$518$	48.6816			2.13895
$519$		0			0
$520$	−2.56422	+	7.89187i	−0.112449	+	0.346081i
$521$	−4.47391	−	13.7693i	−0.196005	−	0.603243i	−0.999963	−	0.00855656i	$-0.997276\pi$
$521$	−4.47391	−	13.7693i	−0.196005	−	0.603243i	0.803958	−	0.594686i	$-0.202724\pi$
$522$		0			0
$523$	−9.02873	+	6.55975i	−0.394799	+	0.286838i	−0.767419	−	0.641146i	$-0.778459\pi$
$523$	−9.02873	+	6.55975i	−0.394799	+	0.286838i	0.372620	+	0.927984i	$0.378459\pi$
$524$	0.352826	+	1.08589i	0.0154133	+	0.0474372i
$525$		0			0
$526$	12.0226	+	8.73490i	0.524209	+	0.380860i
$527$	−25.0254			−1.09013
$528$		0			0
$529$	−21.6494			−0.941279
$530$	−3.28363	−	2.38570i	−0.142632	−	0.103628i
$531$		0			0
$532$	−0.0173943	−	0.0535341i	−0.000754138	−	0.00232100i
$533$	19.0511	−	13.8415i	0.825197	−	0.599540i
$534$		0			0
$535$	−0.599053	−	1.84369i	−0.0258993	−	0.0797099i
$536$	−12.1513	+	37.3979i	−0.524857	+	1.61534i
$537$		0			0
$538$	−0.121123			−0.00522197
$539$	14.6880	+	14.9459i	0.632658	+	0.643768i
$540$		0			0
$541$	−8.64094	−	6.27801i	−0.371503	−	0.269913i	0.386331	−	0.922360i	$-0.373742\pi$
$541$	−8.64094	−	6.27801i	−0.371503	−	0.269913i	−0.757834	+	0.652447i	$0.773742\pi$
$542$	5.61343	−	17.2763i	0.241117	−	0.742083i
$543$		0			0
$544$	−2.73273	+	1.98544i	−0.117165	+	0.0851251i
$545$	−4.95655	+	3.60115i	−0.212315	+	0.154256i
$546$		0			0
$547$	0.540038	−	1.66207i	0.0230904	−	0.0710648i	−0.938847	−	0.344334i	$-0.888105\pi$
$547$	0.540038	−	1.66207i	0.0230904	−	0.0710648i	0.961938	+	0.273269i	$0.0881049\pi$
$548$	1.25577	+	0.912367i	0.0536437	+	0.0389744i
$549$		0			0
$550$	−3.15155	−	3.20689i	−0.134382	−	0.136742i
$551$	−0.642459			−0.0273697
$552$		0			0
$553$	15.6372	−	48.1264i	0.664962	−	2.04654i
$554$	1.63661	+	5.03698i	0.0695331	+	0.214001i
$555$		0			0
$556$	0.0676235	−	0.0491313i	0.00286787	−	0.00208363i
$557$	6.02100	+	18.5307i	0.255118	+	0.785173i	0.993806	+	0.111126i	$0.0354456\pi$
$557$	6.02100	+	18.5307i	0.255118	+	0.785173i	−0.738688	+	0.674047i	$0.764554\pi$
$558$		0			0
$559$	−6.79900	−	4.93976i	−0.287567	−	0.208930i
$560$	13.3182			0.562798
$561$		0			0
$562$	−2.08426			−0.0879191
$563$	−11.8838	−	8.63407i	−0.500842	−	0.363883i	0.308497	−	0.951225i	$-0.400174\pi$
$563$	−11.8838	−	8.63407i	−0.500842	−	0.363883i	−0.809338	+	0.587343i	$0.800174\pi$
$564$		0			0
$565$	−1.78775	−	5.50212i	−0.0752111	−	0.231476i
$566$	−5.93535	+	4.31228i	−0.249481	+	0.181259i
$567$		0			0
$568$	−7.52078	−	23.1466i	−0.315565	−	0.971209i
$569$	−6.15980	+	18.9579i	−0.258232	+	0.794758i	0.734943	+	0.678129i	$0.237209\pi$
$569$	−6.15980	+	18.9579i	−0.258232	+	0.794758i	−0.993176	+	0.116629i	$0.962791\pi$
$570$		0			0
$571$	5.24422			0.219464			0.109732	−	0.993961i	$-0.465001\pi$
$571$	5.24422			0.219464			0.109732	+	0.993961i	$0.465001\pi$
$572$	−1.50156	−	0.251240i	−0.0627834	−	0.0105049i
$573$		0			0
$574$	−33.2940	−	24.1895i	−1.38967	−	1.00965i
$575$	−0.359123	+	1.10527i	−0.0149765	+	0.0460928i
$576$		0			0
$577$	−30.4194	+	22.1010i	−1.26637	+	0.920075i	−0.999052	−	0.0435320i	$-0.986139\pi$
$577$	−30.4194	+	22.1010i	−1.26637	+	0.920075i	−0.267323	+	0.963607i	$0.586139\pi$
$578$	−3.69551	+	2.68495i	−0.153713	+	0.111679i
$579$		0			0
$580$	−0.338412	+	1.04153i	−0.0140518	+	0.0432470i
$581$	31.4271	+	22.8331i	1.30382	+	0.947278i
$582$		0			0
$583$	4.58484	−	8.80789i	0.189885	−	0.364785i
$584$	−3.86923			−0.160110
$585$		0			0
$586$	4.78267	−	14.7195i	0.197570	−	0.608059i
$587$	−7.90191	−	24.3196i	−0.326147	−	1.00378i	−0.970920	−	0.239403i	$-0.923048\pi$
$587$	−7.90191	−	24.3196i	−0.326147	−	1.00378i	0.644774	−	0.764373i	$-0.276952\pi$
$588$		0			0
$589$	0.521644	−	0.378997i	0.0214940	−	0.0156163i
$590$	−3.56448	−	10.9703i	−0.146747	−	0.451642i
$591$		0			0
$592$	29.0514	+	21.1071i	1.19400	+	0.867495i
$593$	−40.2260			−1.65188			−0.825942	−	0.563754i	$-0.809356\pi$
$593$	−40.2260			−1.65188			−0.825942	+	0.563754i	$0.809356\pi$
$594$		0			0
$595$	13.4735			0.552358
$596$	1.07040	+	0.777695i	0.0438455	+	0.0318556i
$597$		0			0
$598$	−1.37826	−	4.24185i	−0.0563613	−	0.173462i
$599$	3.98843	−	2.89776i	0.162963	−	0.118399i	−0.503315	−	0.864103i	$-0.667886\pi$
$599$	3.98843	−	2.89776i	0.162963	−	0.118399i	0.666278	+	0.745704i	$0.267886\pi$
$600$		0			0
$601$	14.2425	+	43.8338i	0.580963	+	1.78802i	0.614912	+	0.788596i	$0.289191\pi$
$601$	14.2425	+	43.8338i	0.580963	+	1.78802i	−0.0339497	+	0.999424i	$0.510809\pi$
$602$	−4.53853	+	13.9682i	−0.184977	+	0.569300i
$603$		0			0
$604$	−0.314602			−0.0128010
$605$	6.61956	−	8.78529i	0.269124	−	0.357173i
$606$		0			0
$607$	36.5162	+	26.5306i	1.48215	+	1.07684i	0.976857	+	0.213891i	$0.0686139\pi$
$607$	36.5162	+	26.5306i	1.48215	+	1.07684i	0.505288	+	0.862951i	$0.331386\pi$
$608$	0.0268941	−	0.0827714i	0.00109070	−	0.00335682i
$609$		0			0
$610$	−9.30096	+	6.75754i	−0.376585	+	0.273605i
$611$	5.09568	−	3.70223i	0.206149	−	0.149776i
$612$		0			0
$613$	1.46294	−	4.50247i	0.0590877	−	0.181853i	−0.917156	−	0.398528i	$-0.869521\pi$
$613$	1.46294	−	4.50247i	0.0590877	−	0.181853i	0.976244	+	0.216675i	$0.0695212\pi$
$614$	−4.66133	−	3.38666i	−0.188116	−	0.136674i
$615$		0			0
$616$	5.24479	+	35.0883i	0.211319	+	1.41375i
$617$	−17.8468			−0.718486			−0.359243	−	0.933244i	$-0.616965\pi$
$617$	−17.8468			−0.718486			−0.359243	+	0.933244i	$0.616965\pi$
$618$		0			0
$619$	0.110304	−	0.339482i	0.00443351	−	0.0136449i	−0.948815	−	0.315832i	$-0.897717\pi$
$619$	0.110304	−	0.339482i	0.00443351	−	0.0136449i	0.953249	+	0.302187i	$0.0977166\pi$
$620$	−0.339639	−	1.04530i	−0.0136402	−	0.0419803i
$621$		0			0
$622$	18.2276	−	13.2431i	0.730861	−	0.531002i
$623$	−13.7145	−	42.2089i	−0.549461	−	1.69107i
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	36.0297			1.44004
$627$		0			0
$628$	−3.44960			−0.137654
$629$	29.3900	+	21.3531i	1.17186	+	0.851404i
$630$		0			0
$631$	−9.88614	−	30.4264i	−0.393561	−	1.21126i	−0.930077	−	0.367366i	$-0.880260\pi$
$631$	−9.88614	−	30.4264i	−0.393561	−	1.21126i	0.536516	−	0.843890i	$-0.319740\pi$
$632$	32.8815	−	23.8898i	1.30796	−	0.950287i
$633$		0			0
$634$	2.42849	+	7.47413i	0.0964477	+	0.296836i
$635$	0.753330	−	2.31851i	0.0298950	−	0.0920073i
$636$		0			0
$637$	−17.8866			−0.708693
$638$	29.9509	+	5.01136i	1.18577	+	0.198402i
$639$		0			0
$640$	7.88507	+	5.72884i	0.311685	+	0.226452i
$641$	−0.312987	+	0.963274i	−0.0123622	+	0.0380470i	−0.957047	−	0.289932i	$-0.906367\pi$
$641$	−0.312987	+	0.963274i	−0.0123622	+	0.0380470i	0.944685	+	0.327979i	$0.106367\pi$
$642$		0			0
$643$	12.1130	−	8.80057i	0.477688	−	0.347061i	−0.322742	−	0.946487i	$-0.604605\pi$
$643$	12.1130	−	8.80057i	0.477688	−	0.347061i	0.800430	+	0.599426i	$0.204605\pi$
$644$	0.556354	−	0.404215i	0.0219234	−	0.0159283i
$645$		0			0
$646$	−0.147125	+	0.452803i	−0.00578855	+	0.0178153i
$647$	14.4712	+	10.5139i	0.568920	+	0.413345i	0.834713	−	0.550686i	$-0.185634\pi$
$647$	14.4712	+	10.5139i	0.568920	+	0.413345i	−0.265793	+	0.964030i	$0.585634\pi$
$648$		0			0
$649$	25.2546	−	12.5922i	0.991331	−	0.494287i
$650$	3.83785			0.150533
$651$		0			0
$652$	0.800746	−	2.46444i	0.0313596	−	0.0965150i
$653$	−14.1419	−	43.5244i	−0.553416	−	1.70324i	−0.700089	−	0.714055i	$-0.746856\pi$
$653$	−14.1419	−	43.5244i	−0.553416	−	1.70324i	0.146673	−	0.989185i	$-0.453144\pi$
$654$		0			0
$655$	5.69674	−	4.13892i	0.222590	−	0.161721i
$656$	−9.38072	−	28.8709i	−0.366255	−	1.12722i
$657$		0			0
$658$	−8.90529	−	6.47007i	−0.347164	−	0.252230i
$659$	9.54036			0.371640			0.185820	−	0.982584i	$-0.440506\pi$
$659$	9.54036			0.371640			0.185820	+	0.982584i	$0.440506\pi$
$660$		0			0
$661$	15.7769			0.613651			0.306825	−	0.951766i	$-0.400733\pi$
$661$	15.7769			0.613651			0.306825	+	0.951766i	$0.400733\pi$
$662$	−14.1734	−	10.2976i	−0.550866	−	0.400228i
$663$		0			0
$664$	9.64154	+	29.6736i	0.374164	+	1.15156i
$665$	−0.280849	+	0.204048i	−0.0108908	+	0.00791266i
$666$		0			0
$667$	−2.42548	−	7.46486i	−0.0939149	−	0.289040i
$668$	0.887333	−	2.73093i	0.0343319	−	0.105663i
$669$		0			0
$670$	18.1868			0.702616
$671$	−19.7144	−	20.0606i	−0.761065	−	0.774430i
$672$		0			0
$673$	−38.2690	−	27.8041i	−1.47516	−	1.07177i	−0.979076	−	0.203494i	$-0.934770\pi$
$673$	−38.2690	−	27.8041i	−1.47516	−	1.07177i	−0.496086	−	0.868273i	$-0.665230\pi$
$674$	−5.60749	+	17.2581i	−0.215992	+	0.664756i
$675$		0			0
$676$	−0.654023	+	0.475175i	−0.0251547	+	0.0182760i
$677$	22.2828	−	16.1894i	0.856399	−	0.622210i	−0.0705039	−	0.997512i	$-0.522461\pi$
$677$	22.2828	−	16.1894i	0.856399	−	0.622210i	0.926903	+	0.375301i	$0.122461\pi$
$678$		0			0
$679$	4.88457	−	15.0332i	0.187453	−	0.576920i
$680$	8.75497	+	6.36086i	0.335738	+	0.243928i
$681$		0			0
$682$	−27.2749	+	13.5995i	−1.04441	+	0.520753i
$683$	27.1617			1.03931			0.519656	−	0.854375i	$-0.326060\pi$
$683$	27.1617			1.03931			0.519656	+	0.854375i	$0.326060\pi$
$684$		0			0
$685$	2.95818	−	9.10433i	0.113026	−	0.347859i
$686$	−1.04233	−	3.20795i	−0.0397962	−	0.122480i
$687$		0			0
$688$	−8.76467	+	6.36790i	−0.334150	+	0.242774i
$689$	2.61913	+	8.06084i	0.0997808	+	0.307094i
$690$		0			0
$691$	6.08931	+	4.42414i	0.231648	+	0.168302i	0.697554	−	0.716532i	$-0.254272\pi$
$691$	6.08931	+	4.42414i	0.231648	+	0.168302i	−0.465906	+	0.884834i	$0.654272\pi$
$692$	2.57579			0.0979167
$693$		0			0
$694$	−11.4541			−0.434791
$695$	−0.417050	−	0.303004i	−0.0158196	−	0.0114936i
$696$		0			0
$697$	−9.49007	−	29.2074i	−0.359462	−	1.10631i
$698$	−11.4051	+	8.28625i	−0.431688	+	0.313639i
$699$		0			0
$700$	0.182858	+	0.562780i	0.00691140	+	0.0212711i
$701$	9.83315	−	30.2633i	0.371393	−	1.14303i	−0.574487	−	0.818513i	$-0.694799\pi$
$701$	9.83315	−	30.2633i	0.371393	−	1.14303i	0.945880	−	0.324516i	$-0.105201\pi$
$702$		0			0
$703$	−0.936004			−0.0353021
$704$	−13.0767	+	25.1215i	−0.492847	+	0.946802i
$705$		0			0
$706$	−20.9562	−	15.2255i	−0.788696	−	0.573021i
$707$	11.1710	−	34.3807i	0.420127	−	1.29302i
$708$		0			0
$709$	11.6807	−	8.48651i	0.438677	−	0.318718i	−0.346432	−	0.938075i	$-0.612607\pi$
$709$	11.6807	−	8.48651i	0.438677	−	0.318718i	0.785109	+	0.619357i	$0.212607\pi$
$710$	−9.10653	+	6.61628i	−0.341762	+	0.248305i
$711$		0			0
$712$	11.0153	−	33.9017i	0.412817	−	1.27052i
$713$	6.37300	+	4.63026i	0.238671	+	0.173405i
$714$		0			0
$715$	1.38803	+	9.28605i	0.0519092	+	0.347279i
$716$	−2.73721			−0.102294
$717$		0			0
$718$	−1.84921	+	5.69129i	−0.0690120	+	0.212397i
$719$	−1.67179	−	5.14526i	−0.0623474	−	0.191886i	0.915031	−	0.403383i	$-0.132166\pi$
$719$	−1.67179	−	5.14526i	−0.0623474	−	0.191886i	−0.977378	+	0.211498i	$0.932166\pi$
$720$		0			0
$721$	12.0043	−	8.72166i	0.447065	−	0.324811i
$722$	7.95581	+	24.4855i	0.296085	+	0.911255i
$723$		0			0
$724$	−3.15978	−	2.29571i	−0.117432	−	0.0853195i
$725$	6.75389			0.250833
$726$		0			0
$727$	−16.7753			−0.622161			−0.311080	−	0.950384i	$-0.600691\pi$
$727$	−16.7753			−0.622161			−0.311080	+	0.950384i	$0.600691\pi$
$728$	−24.4993	−	17.7998i	−0.908006	−	0.659705i
$729$		0			0
$730$	0.552996	+	1.70195i	0.0204673	+	0.0629919i
$731$	−8.86684	+	6.44213i	−0.327952	+	0.238271i
$732$		0			0
$733$	−4.35252	−	13.3957i	−0.160764	−	0.494781i	0.837935	−	0.545770i	$-0.183763\pi$
$733$	−4.35252	−	13.3957i	−0.160764	−	0.494781i	−0.998699	+	0.0509889i	$0.983763\pi$
$734$	12.3004	−	37.8567i	0.454016	−	1.39732i
$735$		0			0
$736$	1.06327			0.0391926
$737$	6.57756	+	44.0046i	0.242287	+	1.62093i
$738$		0			0
$739$	29.4043	+	21.3635i	1.08165	+	0.785868i	0.977971	−	0.208743i	$-0.0669371\pi$
$739$	29.4043	+	21.3635i	1.08165	+	0.785868i	0.103683	+	0.994610i	$0.466937\pi$
$740$	−0.493035	+	1.51741i	−0.0181243	+	0.0557810i
$741$		0			0
$742$	11.9833	−	8.70640i	0.439922	−	0.319622i
$743$	−1.58338	+	1.15039i	−0.0580884	+	0.0422037i	−0.616451	−	0.787394i	$-0.711430\pi$
$743$	−1.58338	+	1.15039i	−0.0580884	+	0.0422037i	0.558362	+	0.829597i	$0.311430\pi$
$744$		0			0
$745$	2.52153	−	7.76046i	0.0923815	−	0.284321i
$746$	−5.44519	−	3.95617i	−0.199363	−	0.144846i
$747$		0			0
$748$	−0.916745	+	1.76115i	−0.0335195	+	0.0643940i
$749$	7.07466			0.258503
$750$		0			0
$751$	5.78189	−	17.7948i	0.210984	−	0.649342i	−0.788430	−	0.615124i	$-0.789106\pi$
$751$	5.78189	−	17.7948i	0.210984	−	0.649342i	0.999414	−	0.0342181i	$-0.0108941\pi$
$752$	−2.50910	−	7.72220i	−0.0914973	−	0.281600i
$753$		0			0
$754$	−20.9701	+	15.2356i	−0.763685	+	0.554850i
$755$	0.599563	+	1.84526i	0.0218203	+	0.0671560i
$756$		0			0
$757$	11.7688	+	8.55054i	0.427744	+	0.310775i	0.780746	−	0.624848i	$-0.214839\pi$
$757$	11.7688	+	8.55054i	0.427744	+	0.310775i	−0.353002	+	0.935623i	$0.614839\pi$
$758$	−10.7412			−0.390138
$759$		0			0
$760$	−0.278825			−0.0101141
$761$	10.6309	+	7.72383i	0.385371	+	0.279989i	0.763556	−	0.645741i	$-0.223452\pi$
$761$	10.6309	+	7.72383i	0.385371	+	0.279989i	−0.378185	+	0.925730i	$0.623452\pi$
$762$		0			0
$763$	−6.90920	−	21.2643i	−0.250130	−	0.769820i
$764$	−0.706114	+	0.513022i	−0.0255463	+	0.0185605i
$765$		0			0
$766$	−10.2702	−	31.6084i	−0.371077	−	1.14206i
$767$	−7.44344	+	22.9085i	−0.268767	+	0.827180i
$768$		0			0
$769$	38.9767			1.40554			0.702768	−	0.711419i	$-0.251947\pi$
$769$	38.9767			1.40554			0.702768	+	0.711419i	$0.251947\pi$
$770$	14.6846	−	7.32187i	0.529195	−	0.263862i
$771$		0			0
$772$	2.39850	+	1.74261i	0.0863239	+	0.0627179i
$773$	11.9756	−	36.8571i	0.430733	−	1.32566i	−0.466664	−	0.884435i	$-0.654544\pi$
$773$	11.9756	−	36.8571i	0.430733	−	1.32566i	0.897397	−	0.441225i	$-0.145456\pi$
$774$		0			0
$775$	−5.48382	+	3.98423i	−0.196985	+	0.143118i
$776$	10.2712	−	7.46243i	0.368713	−	0.267886i
$777$		0			0
$778$	2.28773	−	7.04091i	0.0820192	−	0.252429i
$779$	0.640147	+	0.465094i	0.0229356	+	0.0166637i
$780$		0			0
$781$	−19.3023	−	19.6412i	−0.690689	−	0.702818i
$782$	−5.81665			−0.208003
$783$		0			0
$784$	−7.12525	+	21.9293i	−0.254473	+	0.783188i
$785$	6.57418	+	20.2332i	0.234642	+	0.722155i
$786$		0			0
$787$	17.3002	−	12.5693i	0.616685	−	0.448048i	−0.235077	−	0.971977i	$-0.575534\pi$
$787$	17.3002	−	12.5693i	0.616685	−	0.448048i	0.851762	+	0.523929i	$0.175534\pi$
$788$	0.132564	+	0.407990i	0.00472240	+	0.0145341i
$789$		0			0
$790$	−15.2078	−	11.0491i	−0.541070	−	0.393110i
$791$	21.1128			0.750686
$792$		0			0
$793$	24.0075			0.852533
$794$	−7.05718	−	5.12734i	−0.250450	−	0.181963i
$795$		0			0
$796$	−0.327093	−	1.00669i	−0.0115935	−	0.0356812i
$797$	−1.79970	+	1.30756i	−0.0637488	+	0.0463162i	−0.619203	−	0.785231i	$-0.712544\pi$
$797$	−1.79970	+	1.30756i	−0.0637488	+	0.0463162i	0.555454	+	0.831547i	$0.312544\pi$
$798$		0			0
$799$	−2.53834	−	7.81222i	−0.0898002	−	0.276377i
$800$	−0.282725	+	0.870139i	−0.00999585	+	0.0307641i
$801$		0			0
$802$	−19.9319			−0.703821
$803$	−3.91802	+	1.95356i	−0.138264	+	0.0689398i
$804$		0			0
$805$	−3.43117	−	2.49289i	−0.120933	−	0.0878628i
$806$	8.03889	−	24.7412i	0.283158	−	0.871470i
$807$		0			0
$808$	23.4900	−	17.0665i	0.826376	−	0.600397i
$809$	17.1254	−	12.4424i	0.602098	−	0.437450i	−0.244525	−	0.969643i	$-0.578632\pi$
$809$	17.1254	−	12.4424i	0.602098	−	0.437450i	0.846623	+	0.532193i	$0.178632\pi$
$810$		0			0
$811$	−11.3462	+	34.9201i	−0.398420	+	1.22621i	0.527845	+	0.849341i	$0.323000\pi$
$811$	−11.3462	+	34.9201i	−0.398420	+	1.22621i	−0.926266	+	0.376871i	$0.877000\pi$
$812$	−3.23329	−	2.34912i	−0.113466	−	0.0824380i
$813$		0			0
$814$	43.6357	+	7.30109i	1.52943	+	0.255903i
$815$	−15.9810			−0.559788
$816$		0			0
$817$	0.0872627	−	0.268567i	0.00305294	−	0.00939597i
$818$	−1.84150	−	5.66756i	−0.0643866	−	0.198161i
$819$		0			0
$820$	1.09118	−	0.792791i	0.0381058	−	0.0276855i
$821$	12.2585	+	37.7278i	0.427825	+	1.31671i	0.900264	+	0.435345i	$0.143374\pi$
$821$	12.2585	+	37.7278i	0.427825	+	1.31671i	−0.472439	+	0.881363i	$0.656626\pi$
$822$		0			0
$823$	37.1568	+	26.9960i	1.29520	+	0.941021i	0.999897	−	0.0143810i	$-0.00457777\pi$
$823$	37.1568	+	26.9960i	1.29520	+	0.941021i	0.295308	+	0.955402i	$0.404578\pi$
$824$	11.9178			0.415178
$825$		0			0
$826$	42.0956			1.46469
$827$	−32.1139	−	23.3321i	−1.11671	−	0.811337i	−0.133002	−	0.991116i	$-0.542462\pi$
$827$	−32.1139	−	23.3321i	−1.11671	−	0.811337i	−0.983707	+	0.179779i	$0.942462\pi$
$828$		0			0
$829$	2.36578	+	7.28113i	0.0821671	+	0.252884i	0.983697	−	0.179832i	$-0.0575553\pi$
$829$	2.36578	+	7.28113i	0.0821671	+	0.252884i	−0.901530	+	0.432716i	$0.857555\pi$
$830$	11.6745	−	8.48199i	0.405226	−	0.294414i
$831$		0			0
$832$	−7.47017	−	22.9908i	−0.258982	−	0.797063i
$833$	−7.20831	+	22.1849i	−0.249753	+	0.768661i
$834$		0			0
$835$	−17.7090			−0.612846
$836$	−0.00756251	−	0.0505940i	−0.000261555	−	0.00174983i
$837$		0			0
$838$	−19.5801	−	14.2258i	−0.676384	−	0.491422i
$839$	−8.52536	+	26.2383i	−0.294328	+	0.905848i	0.689118	+	0.724649i	$0.257998\pi$
$839$	−8.52536	+	26.2383i	−0.294328	+	0.905848i	−0.983446	+	0.181200i	$0.942002\pi$
$840$		0			0
$841$	−13.4418	+	9.76607i	−0.463512	+	0.336761i
$842$	−5.29576	+	3.84760i	−0.182504	+	0.132597i
$843$		0			0
$844$	1.37531	−	4.23276i	0.0473400	−	0.145697i
$845$	4.03351	+	2.93052i	0.138757	+	0.100813i
$846$		0			0
$847$	23.0269	+	32.8826i	0.791213	+	1.12986i
$848$	10.9261			0.375203
$849$		0			0
$850$	1.54666	−	4.76012i	0.0530499	−	0.163271i
$851$	−3.53370	−	10.8756i	−0.121134	−	0.372811i
$852$		0			0
$853$	−34.0998	+	24.7749i	−1.16755	+	0.848277i	−0.990714	−	0.135962i	$-0.956587\pi$
$853$	−34.0998	+	24.7749i	−1.16755	+	0.848277i	−0.176840	+	0.984240i	$0.556587\pi$
$854$	−12.9651	−	39.9024i	−0.443656	−	1.36543i
$855$		0			0
$856$	4.59707	+	3.33997i	0.157125	+	0.114158i
$857$	45.0850			1.54008			0.770038	−	0.637998i	$-0.220237\pi$
$857$	45.0850			1.54008			0.770038	+	0.637998i	$0.220237\pi$
$858$		0			0
$859$	−11.8257			−0.403488			−0.201744	−	0.979438i	$-0.564661\pi$
$859$	−11.8257			−0.403488			−0.201744	+	0.979438i	$0.564661\pi$
$860$	−0.389423	−	0.282932i	−0.0132792	−	0.00964792i
$861$		0			0
$862$	−10.4204	−	32.0705i	−0.354919	−	1.09233i
$863$	22.5484	−	16.3823i	0.767555	−	0.557662i	−0.133663	−	0.991027i	$-0.542674\pi$
$863$	22.5484	−	16.3823i	0.767555	−	0.557662i	0.901218	+	0.433365i	$0.142674\pi$
$864$		0			0
$865$	−4.90888	−	15.1080i	−0.166907	−	0.513687i
$866$	8.90229	−	27.3984i	0.302512	−	0.931037i
$867$		0			0
$868$	4.01105			0.136144
$869$	21.2342	−	40.7929i	0.720323	−	1.38380i
$870$		0			0
$871$	−30.7249	−	22.3230i	−1.04107	−	0.756384i
$872$	5.54939	−	17.0793i	0.187926	−	0.578377i
$873$		0			0
$874$	0.121246	−	0.0880900i	0.00410119	−	0.00297969i
$875$	2.95244	−	2.14507i	0.0998106	−	0.0725167i
$876$		0			0
$877$	−3.53736	+	10.8869i	−0.119448	+	0.367624i	−0.992849	−	0.119379i	$-0.961910\pi$
$877$	−3.53736	+	10.8869i	−0.119448	+	0.367624i	0.873401	+	0.487003i	$0.161910\pi$
$878$	−17.4516	−	12.6793i	−0.588963	−	0.427907i
$879$		0			0
$880$	11.9378	+	1.99742i	0.402423	+	0.0673330i
$881$	−47.0037			−1.58360			−0.791798	−	0.610783i	$-0.790855\pi$
$881$	−47.0037			−1.58360			−0.791798	+	0.610783i	$0.790855\pi$
$882$		0			0
$883$	−14.4974	+	44.6185i	−0.487877	+	1.50153i	0.339894	+	0.940464i	$0.389609\pi$
$883$	−14.4974	+	44.6185i	−0.487877	+	1.50153i	−0.827770	+	0.561067i	$0.810391\pi$
$884$	−0.523698	−	1.61178i	−0.0176139	−	0.0542099i
$885$		0			0
$886$	−28.8313	+	20.9472i	−0.968607	+	0.703734i
$887$	8.60386	+	26.4800i	0.288889	+	0.889110i	0.985206	+	0.171375i	$0.0548210\pi$
$887$	8.60386	+	26.4800i	0.288889	+	0.889110i	−0.696316	+	0.717735i	$0.745179\pi$
$888$		0			0
$889$	7.19754	+	5.22932i	0.241398	+	0.175386i
$890$	−16.4866			−0.552631
$891$		0			0
$892$	0.824022			0.0275903
$893$	0.171223	+	0.124401i	0.00572975	+	0.00416290i
$894$		0			0
$895$	5.21653	+	16.0548i	0.174369	+	0.536653i
$896$	−28.7759	+	20.9069i	−0.961335	+	0.698451i
$897$		0			0
$898$	−3.43085	−	10.5591i	−0.114489	−	0.352360i
$899$	14.1469	−	43.5397i	0.471826	−	1.45213i
$900$		0			0
$901$	11.0534			0.368244
$902$	−26.2153	−	26.6756i	−0.872872	−	0.888201i
$903$		0			0
$904$	13.7190	+	9.96742i	0.456287	+	0.331512i
$905$	−7.44341	+	22.9085i	−0.247427	+	0.761503i
$906$		0			0
$907$	23.1567	−	16.8243i	0.768907	−	0.558643i	−0.132723	−	0.991153i	$-0.542372\pi$
$907$	23.1567	−	16.8243i	0.768907	−	0.558643i	0.901629	+	0.432510i	$0.142372\pi$
$908$	−0.490586	+	0.356432i	−0.0162807	+	0.0118286i
$909$		0			0
$910$	−4.32807	+	13.3204i	−0.143474	+	0.441567i
$911$	4.14883	+	3.01430i	0.137457	+	0.0998682i	0.654389	−	0.756158i	$-0.272926\pi$
$911$	4.14883	+	3.01430i	0.137457	+	0.0998682i	−0.516932	+	0.856026i	$0.672926\pi$
$912$		0			0
$913$	24.7452	+	25.1798i	0.818948	+	0.833330i
$914$	−16.1547			−0.534351
$915$		0			0
$916$	−1.34907	+	4.15200i	−0.0445744	+	0.137186i
$917$	7.94098	+	24.4398i	0.262234	+	0.807074i
$918$		0			0
$919$	−28.5429	+	20.7376i	−0.941544	+	0.684072i	−0.948792	−	0.315902i	$-0.897693\pi$
$919$	−28.5429	+	20.7376i	−0.941544	+	0.684072i	0.00724799	+	0.999974i	$0.497693\pi$
$920$	−1.05265	−	3.23972i	−0.0347049	−	0.106811i
$921$		0			0
$922$	−7.63536	−	5.54742i	−0.251457	−	0.182694i
$923$	23.5057			0.773699
$924$		0			0
$925$	9.83980			0.323531
$926$	13.6834	+	9.94159i	0.449665	+	0.326701i
$927$		0			0
$928$	−1.90950	−	5.87682i	−0.0626823	−	0.192916i
$929$	−47.8474	+	34.7632i	−1.56982	+	1.14054i	−0.642498	+	0.766287i	$0.722102\pi$
$929$	−47.8474	+	34.7632i	−1.56982	+	1.14054i	−0.927325	+	0.374256i	$0.877898\pi$
$930$		0			0
$931$	−0.185724	−	0.571601i	−0.00608687	−	0.0187335i
$932$	0.917781	−	2.82464i	0.0300629	−	0.0925242i
$933$		0			0
$934$	−8.33220			−0.272638
$935$	12.0769	+	2.02070i	0.394958	+	0.0660841i
$936$		0			0
$937$	−11.6843	−	8.48911i	−0.381708	−	0.277327i	0.380341	−	0.924846i	$-0.375807\pi$
$937$	−11.6843	−	8.48911i	−0.381708	−	0.277327i	−0.762049	+	0.647519i	$0.775807\pi$
$938$	−20.5098	+	63.1226i	−0.669668	+	2.06103i
$939$		0			0
$940$	0.291863	−	0.212051i	0.00951952	−	0.00691634i
$941$	−15.0955	+	10.9675i	−0.492100	+	0.357532i	−0.805991	−	0.591927i	$-0.798367\pi$
$941$	−15.0955	+	10.9675i	−0.492100	+	0.357532i	0.313891	+	0.949459i	$0.398367\pi$
$942$		0			0
$943$	−2.98727	+	9.19386i	−0.0972788	+	0.299393i
$944$	25.1211	+	18.2516i	0.817623	+	0.594038i
$945$		0			0
$946$	−6.16301	+	11.8397i	−0.200377	+	0.384942i
$947$	0.991391			0.0322159			0.0161079	−	0.999870i	$-0.494872\pi$
$947$	0.991391			0.0322159			0.0161079	+	0.999870i	$0.494872\pi$
$948$		0			0
$949$	1.15478	−	3.55405i	0.0374858	−	0.115369i
$950$	0.0398501	+	0.122646i	0.00129291	+	0.00397916i
$951$		0			0
$952$	−31.9505	+	23.2134i	−1.03552	+	0.752351i
$953$	2.55373	+	7.85957i	0.0827234	+	0.254597i	0.983860	−	0.178938i	$-0.0572662\pi$
$953$	2.55373	+	7.85957i	0.0827234	+	0.254597i	−0.901137	+	0.433535i	$0.857266\pi$
$954$		0			0
$955$	4.35477	+	3.16393i	0.140917	+	0.102382i
$956$	−1.77646			−0.0574549
$957$		0			0
$958$	30.0881			0.972101
$959$	28.2633	+	20.5345i	0.912669	+	0.663093i
$960$		0			0
$961$	4.61867	+	14.2148i	0.148989	+	0.458542i
$962$	−30.5515	+	22.1969i	−0.985019	+	0.715658i
$963$		0			0
$964$	0.500784	+	1.54125i	0.0161292	+	0.0496404i
$965$	5.65008	−	17.3892i	0.181883	−	0.559777i
$966$		0			0
$967$	7.36029			0.236691			0.118345	−	0.992972i	$-0.462241\pi$
$967$	7.36029			0.236691			0.118345	+	0.992972i	$0.462241\pi$
$968$	−0.561246	+	32.2380i	−0.0180391	+	1.03617i
$969$		0			0
$970$	−4.75044	−	3.45140i	−0.152527	−	0.110818i
$971$	1.53808	−	4.73372i	0.0493593	−	0.151912i	−0.923339	−	0.383986i	$-0.874551\pi$
$971$	1.53808	−	4.73372i	0.0493593	−	0.151912i	0.972698	+	0.232074i	$0.0745511\pi$
$972$		0			0
$973$	1.52199	−	1.10579i	0.0487927	−	0.0354500i
$974$	−37.5429	+	27.2765i	−1.20295	+	0.873996i
$975$		0			0
$976$	9.56357	−	29.4337i	0.306123	−	0.942148i
$977$	8.36266	+	6.07583i	0.267545	+	0.194383i	0.713467	−	0.700689i	$-0.247124\pi$
$977$	8.36266	+	6.07583i	0.267545	+	0.194383i	−0.445922	+	0.895072i	$0.647124\pi$
$978$		0			0
$979$	−5.96266	−	39.8908i	−0.190567	−	1.27492i
$980$	−1.02448			−0.0327259
$981$		0			0
$982$	−7.11996	+	21.9130i	−0.227207	+	0.699272i
$983$	8.98045	+	27.6390i	0.286432	+	0.881547i	0.985966	+	0.166947i	$0.0533910\pi$
$983$	8.98045	+	27.6390i	0.286432	+	0.881547i	−0.699534	+	0.714599i	$0.746609\pi$
$984$		0			0
$985$	2.14038	−	1.55508i	0.0681983	−	0.0495490i
$986$	10.4460	+	32.1493i	0.332667	+	1.02384i
$987$		0			0
$988$	0.0353258	+	0.0256657i	0.00112386	+	0.000816534i
$989$	3.44997			0.109703
$990$		0			0
$991$	7.70381			0.244719			0.122360	−	0.992486i	$-0.460954\pi$
$991$	7.70381			0.244719			0.122360	+	0.992486i	$0.460954\pi$
$992$	5.01724	+	3.64524i	0.159298	+	0.115737i
$993$		0			0
$994$	−12.6941	−	39.0683i	−0.402631	−	1.23917i
$995$	−5.28126	+	3.83706i	−0.167427	+	0.121643i
$996$		0			0
$997$	−0.885080	−	2.72400i	−0.0280308	−	0.0862698i	0.936062	−	0.351834i	$-0.114442\pi$
$997$	−0.885080	−	2.72400i	−0.0280308	−	0.0862698i	−0.964093	+	0.265564i	$0.914442\pi$
$998$	−2.19076	+	6.74247i	−0.0693473	+	0.213429i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.n.e.136.2		8
3.2	odd	2		55.2.g.b.26.1	✓	8
11.3	even	5	inner	495.2.n.e.91.2		8
11.5	even	5		5445.2.a.bp.1.1		4
11.6	odd	10		5445.2.a.bi.1.4		4
12.11	even	2		880.2.bo.h.81.1		8
15.2	even	4		275.2.z.a.224.4		16
15.8	even	4		275.2.z.a.224.1		16
15.14	odd	2		275.2.h.a.26.2		8
33.2	even	10		605.2.g.e.511.1		8
33.5	odd	10		605.2.a.j.1.4		4
33.8	even	10		605.2.g.k.366.2		8
33.14	odd	10		55.2.g.b.36.1	yes	8
33.17	even	10		605.2.a.k.1.1		4
33.20	odd	10		605.2.g.m.511.2		8
33.26	odd	10		605.2.g.m.251.2		8
33.29	even	10		605.2.g.e.251.1		8
33.32	even	2		605.2.g.k.81.2		8
132.47	even	10		880.2.bo.h.641.1		8
132.71	even	10		9680.2.a.cn.1.2		4
132.83	odd	10		9680.2.a.cm.1.2		4
165.14	odd	10		275.2.h.a.201.2		8
165.47	even	20		275.2.z.a.124.1		16
165.104	odd	10		3025.2.a.bd.1.1		4
165.113	even	20		275.2.z.a.124.4		16
165.149	even	10		3025.2.a.w.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.26.1	✓	8	3.2	odd	2
55.2.g.b.36.1	yes	8	33.14	odd	10
275.2.h.a.26.2		8	15.14	odd	2
275.2.h.a.201.2		8	165.14	odd	10
275.2.z.a.124.1		16	165.47	even	20
275.2.z.a.124.4		16	165.113	even	20
275.2.z.a.224.1		16	15.8	even	4
275.2.z.a.224.4		16	15.2	even	4
495.2.n.e.91.2		8	11.3	even	5	inner
495.2.n.e.136.2		8	1.1	even	1	trivial
605.2.a.j.1.4		4	33.5	odd	10
605.2.a.k.1.1		4	33.17	even	10
605.2.g.e.251.1		8	33.29	even	10
605.2.g.e.511.1		8	33.2	even	10
605.2.g.k.81.2		8	33.32	even	2
605.2.g.k.366.2		8	33.8	even	10
605.2.g.m.251.2		8	33.26	odd	10
605.2.g.m.511.2		8	33.20	odd	10
880.2.bo.h.81.1		8	12.11	even	2
880.2.bo.h.641.1		8	132.47	even	10
3025.2.a.w.1.4		4	165.149	even	10
3025.2.a.bd.1.1		4	165.104	odd	10
5445.2.a.bi.1.4		4	11.6	odd	10
5445.2.a.bp.1.1		4	11.5	even	5
9680.2.a.cm.1.2		4	132.83	odd	10
9680.2.a.cn.1.2		4	132.71	even	10

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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.09676 + 0.796845i) q^{2} +(-0.0501062 - 0.154211i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-1.12773 - 3.47080i) q^{7} +(0.905781 - 2.78771i) q^{8} +O(q^{10})\)	\(q+(1.09676 + 0.796845i) q^{2} +(-0.0501062 - 0.154211i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-1.12773 - 3.47080i) q^{7} +(0.905781 - 2.78771i) q^{8} -1.35567 q^{10} +(-0.490303 - 3.28018i) q^{11} +(2.29029 + 1.66399i) q^{13} +(1.52884 - 4.70527i) q^{14} +(2.95244 - 2.14507i) q^{16} +(2.98685 - 2.17008i) q^{17} +(-0.0293950 + 0.0904686i) q^{19} +(0.131180 + 0.0953077i) q^{20} +(2.07605 - 3.98828i) q^{22} -1.16215 q^{23} +(0.309017 - 0.951057i) q^{25} +(1.18596 + 3.65001i) q^{26} +(-0.478730 + 0.347817i) q^{28} +(2.08707 + 6.42333i) q^{29} +(-5.48382 - 3.98423i) q^{31} -0.914918 q^{32} +5.00509 q^{34} +(2.95244 + 2.14507i) q^{35} +(3.04066 + 9.35820i) q^{37} +(-0.104329 + 0.0757994i) q^{38} +(0.905781 + 2.78771i) q^{40} +(2.57047 - 7.91110i) q^{41} -2.96862 q^{43} +(-0.481274 + 0.239968i) q^{44} +(-1.27460 - 0.926052i) q^{46} +(0.687534 - 2.11601i) q^{47} +(-5.11155 + 3.71376i) q^{49} +(1.09676 - 0.796845i) q^{50} +(0.141849 - 0.436565i) q^{52} +(2.42214 + 1.75979i) q^{53} +(2.32471 + 2.36553i) q^{55} -10.6970 q^{56} +(-2.82938 + 8.70794i) q^{58} +(2.62930 + 8.09216i) q^{59} +(6.86076 - 4.98464i) q^{61} +(-2.83964 - 8.73951i) q^{62} +(-6.90832 - 5.01919i) q^{64} -2.83095 q^{65} -13.4153 q^{67} +(-0.484310 - 0.351872i) q^{68} +(1.52884 + 4.70527i) q^{70} +(6.71734 - 4.88043i) q^{71} +(-0.407912 - 1.25542i) q^{73} +(-4.12215 + 12.6867i) q^{74} +0.0154241 q^{76} +(-10.8319 + 5.40091i) q^{77} +(11.2179 + 8.15028i) q^{79} +(-1.12773 + 3.47080i) q^{80} +(9.12312 - 6.62834i) q^{82} +(-8.61155 + 6.25666i) q^{83} +(-1.14088 + 3.51126i) q^{85} +(-3.25587 - 2.36553i) q^{86} +(-9.58829 - 1.60431i) q^{88} +12.1612 q^{89} +(3.19256 - 9.82567i) q^{91} +(0.0582308 + 0.179216i) q^{92} +(2.44020 - 1.77291i) q^{94} +(-0.0293950 - 0.0904686i) q^{95} +(3.50412 + 2.54589i) q^{97} -8.56545 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - q^{7} - 4 q^{8}+O(q^{10}) \) 8 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - q^7 - 4 * q^8	\( 8 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - q^{7} - 4 q^{8} + 2 q^{10} - 3 q^{11} - 2 q^{13} + 16 q^{14} + 4 q^{16} + 13 q^{17} + 15 q^{19} + 3 q^{20} - 7 q^{22} - 10 q^{23} - 2 q^{25} - 10 q^{26} - 6 q^{28} + 9 q^{29} - 10 q^{31} - 16 q^{32} + 4 q^{34} + 4 q^{35} + 24 q^{37} - 4 q^{40} - 8 q^{41} - 38 q^{43} + 12 q^{44} + 3 q^{46} + q^{49} + 2 q^{50} - 28 q^{52} - 13 q^{53} + 7 q^{55} - 22 q^{56} + 12 q^{58} + 27 q^{59} + 6 q^{61} + 30 q^{62} - 26 q^{64} - 2 q^{65} - 38 q^{67} - 11 q^{68} + 16 q^{70} + 20 q^{71} + 13 q^{73} - 20 q^{74} - 34 q^{77} + 37 q^{79} - q^{80} + 28 q^{82} - 27 q^{83} - 12 q^{85} + 3 q^{86} - 36 q^{88} + 16 q^{89} + 44 q^{91} - 11 q^{92} + 17 q^{94} + 15 q^{95} + 24 q^{97} - 16 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - q^7 - 4 * q^8 + 2 * q^10 - 3 * q^11 - 2 * q^13 + 16 * q^14 + 4 * q^16 + 13 * q^17 + 15 * q^19 + 3 * q^20 - 7 * q^22 - 10 * q^23 - 2 * q^25 - 10 * q^26 - 6 * q^28 + 9 * q^29 - 10 * q^31 - 16 * q^32 + 4 * q^34 + 4 * q^35 + 24 * q^37 - 4 * q^40 - 8 * q^41 - 38 * q^43 + 12 * q^44 + 3 * q^46 + q^49 + 2 * q^50 - 28 * q^52 - 13 * q^53 + 7 * q^55 - 22 * q^56 + 12 * q^58 + 27 * q^59 + 6 * q^61 + 30 * q^62 - 26 * q^64 - 2 * q^65 - 38 * q^67 - 11 * q^68 + 16 * q^70 + 20 * q^71 + 13 * q^73 - 20 * q^74 - 34 * q^77 + 37 * q^79 - q^80 + 28 * q^82 - 27 * q^83 - 12 * q^85 + 3 * q^86 - 36 * q^88 + 16 * q^89 + 44 * q^91 - 11 * q^92 + 17 * q^94 + 15 * q^95 + 24 * q^97 - 16 * q^98

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