LMFDB - Embedded newform 495.2.n.a.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 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			136.2
Root			$-0.227943 - 0.701538i$ of defining polynomial
Character	$\chi$	$=$	495.136
Dual form			495.2.n.a.91.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.212253 - 0.154211i) q^{2} +(-0.596764 - 1.83665i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-0.986854 - 3.03722i) q^{7} +(-0.318714 + 0.980901i) q^{8} +O(q^{10})$	\(q+(-0.212253 - 0.154211i) q^{2} +(-0.596764 - 1.83665i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-0.986854 - 3.03722i) q^{7} +(-0.318714 + 0.980901i) q^{8} -0.262360 q^{10} +(-3.27115 - 0.547326i) q^{11} +(0.905781 + 0.658088i) q^{13} +(-0.258911 + 0.796845i) q^{14} +(-2.90578 + 2.11117i) q^{16} +(-0.0713767 + 0.0518582i) q^{17} +(-0.0212704 + 0.0654637i) q^{19} +(-1.56235 - 1.13511i) q^{20} +(0.609909 + 0.620620i) q^{22} -6.65450 q^{23} +(0.309017 - 0.951057i) q^{25} +(-0.0907705 - 0.279363i) q^{26} +(-4.98940 + 3.62501i) q^{28} +(-1.15444 - 3.55299i) q^{29} +(7.75430 + 5.63383i) q^{31} +3.00509 q^{32} +0.0231471 q^{34} +(-2.58362 - 1.87711i) q^{35} +(-2.57418 - 7.92250i) q^{37} +(0.0146100 - 0.0106148i) q^{38} +(0.318714 + 0.980901i) q^{40} +(3.60489 - 11.0947i) q^{41} -11.8217 q^{43} +(0.946857 + 6.33458i) q^{44} +(1.41244 + 1.02620i) q^{46} +(-0.280594 + 0.863579i) q^{47} +(-2.58773 + 1.88010i) q^{49} +(-0.212253 + 0.154211i) q^{50} +(0.668140 - 2.05632i) q^{52} +(0.705768 + 0.512771i) q^{53} +(-2.96813 + 1.47994i) q^{55} +3.29374 q^{56} +(-0.302877 + 0.932160i) q^{58} +(-0.567369 - 1.74618i) q^{59} +(8.13881 - 5.91319i) q^{61} +(-0.777078 - 2.39160i) q^{62} +(5.17372 + 3.75893i) q^{64} +1.11961 q^{65} +9.53916 q^{67} +(0.137840 + 0.100147i) q^{68} +(0.258911 + 0.796845i) q^{70} +(-3.77370 + 2.74175i) q^{71} +(-2.21267 - 6.80989i) q^{73} +(-0.675360 + 2.07854i) q^{74} +0.132927 q^{76} +(1.56580 + 10.4754i) q^{77} +(-0.640209 - 0.465139i) q^{79} +(-1.10991 + 3.41595i) q^{80} +(-2.47608 + 1.79898i) q^{82} +(0.200012 - 0.145318i) q^{83} +(-0.0272635 + 0.0839083i) q^{85} +(2.50920 + 1.82304i) q^{86} +(1.57943 - 3.03423i) q^{88} +14.5788 q^{89} +(1.10489 - 3.40050i) q^{91} +(3.97116 + 12.2220i) q^{92} +(0.192730 - 0.140027i) q^{94} +(0.0212704 + 0.0654637i) q^{95} +(3.31048 + 2.40521i) q^{97} +0.839188 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 2 q^{4} + 2 q^{5} + 3 q^{7} + q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 + 2 * q^4 + 2 * q^5 + 3 * q^7 + q^8	$ 8 q - 4 q^{2} + 2 q^{4} + 2 q^{5} + 3 q^{7} + q^{8} - 6 q^{10} - 3 q^{11} - 4 q^{13} + 4 q^{14} - 12 q^{16} + 2 q^{19} + 3 q^{20} + 9 q^{22} + 6 q^{23} - 2 q^{25} - 2 q^{26} - 11 q^{28} - 10 q^{29} + 19 q^{31} - 12 q^{32} - 6 q^{34} - 3 q^{35} - q^{37} + 20 q^{38} - q^{40} + 9 q^{41} - 17 q^{44} - 22 q^{46} + 19 q^{47} + q^{49} - 4 q^{50} - 2 q^{52} - 25 q^{53} + 3 q^{55} + 16 q^{56} - 12 q^{58} - 13 q^{59} + 13 q^{61} - 35 q^{62} + 39 q^{64} + 14 q^{65} + 2 q^{67} - 19 q^{68} - 4 q^{70} + 11 q^{71} - 7 q^{73} + 43 q^{74} - 38 q^{76} + 7 q^{77} - 22 q^{79} - 13 q^{80} - 35 q^{82} + 21 q^{83} + 10 q^{85} - 20 q^{86} + 59 q^{88} + 20 q^{89} - 11 q^{91} + 28 q^{92} - 35 q^{94} - 2 q^{95} + 31 q^{97} - 22 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 + 2 * q^4 + 2 * q^5 + 3 * q^7 + q^8 - 6 * q^10 - 3 * q^11 - 4 * q^13 + 4 * q^14 - 12 * q^16 + 2 * q^19 + 3 * q^20 + 9 * q^22 + 6 * q^23 - 2 * q^25 - 2 * q^26 - 11 * q^28 - 10 * q^29 + 19 * q^31 - 12 * q^32 - 6 * q^34 - 3 * q^35 - q^37 + 20 * q^38 - q^40 + 9 * q^41 - 17 * q^44 - 22 * q^46 + 19 * q^47 + q^49 - 4 * q^50 - 2 * q^52 - 25 * q^53 + 3 * q^55 + 16 * q^56 - 12 * q^58 - 13 * q^59 + 13 * q^61 - 35 * q^62 + 39 * q^64 + 14 * q^65 + 2 * q^67 - 19 * q^68 - 4 * q^70 + 11 * q^71 - 7 * q^73 + 43 * q^74 - 38 * q^76 + 7 * q^77 - 22 * q^79 - 13 * q^80 - 35 * q^82 + 21 * q^83 + 10 * q^85 - 20 * q^86 + 59 * q^88 + 20 * q^89 - 11 * q^91 + 28 * q^92 - 35 * q^94 - 2 * q^95 + 31 * q^97 - 22 * 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 $

$2$	−0.212253	−	0.154211i	−0.150086	−	0.109044i	0.510208	−	0.860051i	$-0.329568\pi$
$2$	−0.212253	−	0.154211i	−0.150086	−	0.109044i	−0.660294	+	0.751007i	$0.729568\pi$
$3$		0			0
$3$		0			0
$4$	−0.596764	−	1.83665i	−0.298382	−	0.918325i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$6$		0			0
$7$	−0.986854	−	3.03722i	−0.372996	−	1.14796i	−0.944821	−	0.327587i	$-0.893764\pi$
$7$	−0.986854	−	3.03722i	−0.372996	−	1.14796i	0.571825	−	0.820376i	$-0.306236\pi$
$8$	−0.318714	+	0.980901i	−0.112682	+	0.346801i
$9$		0			0
$10$	−0.262360			−0.0829654
$11$	−3.27115	−	0.547326i	−0.986289	−	0.165025i
$11$	−3.27115	−	0.547326i	−0.986289	−	0.165025i
$12$		0			0
$13$	0.905781	+	0.658088i	0.251218	+	0.182521i	0.706267	−	0.707946i	$-0.250378\pi$
$13$	0.905781	+	0.658088i	0.251218	+	0.182521i	−0.455048	+	0.890467i	$0.650378\pi$
$14$	−0.258911	+	0.796845i	−0.0691968	+	0.212966i
$15$		0			0
$16$	−2.90578	+	2.11117i	−0.726445	+	0.527793i
$17$	−0.0713767	+	0.0518582i	−0.0173114	+	0.0125775i	−0.596407	−	0.802682i	$-0.703406\pi$
$17$	−0.0713767	+	0.0518582i	−0.0173114	+	0.0125775i	0.579096	+	0.815259i	$0.303406\pi$
$18$		0			0
$19$	−0.0212704	+	0.0654637i	−0.00487977	+	0.0150184i	−0.953467	−	0.301498i	$-0.902513\pi$
$19$	−0.0212704	+	0.0654637i	−0.00487977	+	0.0150184i	0.948587	+	0.316517i	$0.102513\pi$
$20$	−1.56235	−	1.13511i	−0.349351	−	0.253819i
$21$		0			0
$22$	0.609909	+	0.620620i	0.130033	+	0.132317i
$23$	−6.65450			−1.38756			−0.693780	−	0.720187i	$-0.744056\pi$
$23$	−6.65450			−1.38756			−0.693780	+	0.720187i	$0.744056\pi$
$24$		0			0
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	−0.0907705	−	0.279363i	−0.0178016	−	0.0547876i
$27$		0			0
$28$	−4.98940	+	3.62501i	−0.942908	+	0.685062i
$29$	−1.15444	−	3.55299i	−0.214373	−	0.659773i	−0.999197	−	0.0400546i	$-0.987247\pi$
$29$	−1.15444	−	3.55299i	−0.214373	−	0.659773i	0.784824	−	0.619718i	$-0.212753\pi$
$30$		0			0
$31$	7.75430	+	5.63383i	1.39271	+	1.01187i	0.995562	+	0.0941130i	$0.0300015\pi$
$31$	7.75430	+	5.63383i	1.39271	+	1.01187i	0.397152	+	0.917753i	$0.369998\pi$
$32$	3.00509			0.531230
$33$		0			0
$34$	0.0231471			0.00396969
$35$	−2.58362	−	1.87711i	−0.436711	−	0.317289i
$36$		0			0
$37$	−2.57418	−	7.92250i	−0.423192	−	1.30245i	−0.904715	−	0.426017i	$-0.859916\pi$
$37$	−2.57418	−	7.92250i	−0.423192	−	1.30245i	0.481523	−	0.876433i	$-0.340084\pi$
$38$	0.0146100	−	0.0106148i	0.00237005	−	0.00172194i
$39$		0			0
$40$	0.318714	+	0.980901i	0.0503931	+	0.155094i
$41$	3.60489	−	11.0947i	0.562989	−	1.73270i	−0.110863	−	0.993836i	$-0.535362\pi$
$41$	3.60489	−	11.0947i	0.562989	−	1.73270i	0.673852	−	0.738866i	$-0.264638\pi$
$42$		0			0
$43$	−11.8217			−1.80280			−0.901399	−	0.432989i	$-0.857459\pi$
$43$	−11.8217			−1.80280			−0.901399	+	0.432989i	$0.857459\pi$
$44$	0.946857	+	6.33458i	0.142744	+	0.954974i
$45$		0			0
$46$	1.41244	+	1.02620i	0.208253	+	0.151305i
$47$	−0.280594	+	0.863579i	−0.0409288	+	0.125966i	−0.969433	−	0.245356i	$-0.921095\pi$
$47$	−0.280594	+	0.863579i	−0.0409288	+	0.125966i	0.928504	+	0.371322i	$0.121095\pi$
$48$		0			0
$49$	−2.58773	+	1.88010i	−0.369676	+	0.268586i
$50$	−0.212253	+	0.154211i	−0.0300172	+	0.0218088i
$51$		0			0
$52$	0.668140	−	2.05632i	0.0926544	−	0.285161i
$53$	0.705768	+	0.512771i	0.0969447	+	0.0704344i	0.635202	−	0.772346i	$-0.280917\pi$
$53$	0.705768	+	0.512771i	0.0969447	+	0.0704344i	−0.538257	+	0.842781i	$0.680917\pi$
$54$		0			0
$55$	−2.96813	+	1.47994i	−0.400222	+	0.199555i
$56$	3.29374			0.440144
$57$		0			0
$58$	−0.302877	+	0.932160i	−0.0397697	+	0.122399i
$59$	−0.567369	−	1.74618i	−0.0738651	−	0.227333i	0.907307	−	0.420469i	$-0.138134\pi$
$59$	−0.567369	−	1.74618i	−0.0738651	−	0.227333i	−0.981172	+	0.193135i	$0.938134\pi$
$60$		0			0
$61$	8.13881	−	5.91319i	1.04207	−	0.757107i	0.0713799	−	0.997449i	$-0.477260\pi$
$61$	8.13881	−	5.91319i	1.04207	−	0.757107i	0.970688	+	0.240342i	$0.0772597\pi$
$62$	−0.777078	−	2.39160i	−0.0986890	−	0.303733i
$63$		0			0
$64$	5.17372	+	3.75893i	0.646715	+	0.469866i
$65$	1.11961			0.138870
$66$		0			0
$67$	9.53916			1.16539			0.582697	−	0.812690i	$-0.301997\pi$
$67$	9.53916			1.16539			0.582697	+	0.812690i	$0.301997\pi$
$68$	0.137840	+	0.100147i	0.0167156	+	0.0121446i
$69$		0			0
$70$	0.258911	+	0.796845i	0.0309458	+	0.0952412i
$71$	−3.77370	+	2.74175i	−0.447855	+	0.325386i	−0.788748	−	0.614716i	$-0.789271\pi$
$71$	−3.77370	+	2.74175i	−0.447855	+	0.325386i	0.340893	+	0.940102i	$0.389271\pi$
$72$		0			0
$73$	−2.21267	−	6.80989i	−0.258973	−	0.797037i	−0.993021	−	0.117939i	$-0.962371\pi$
$73$	−2.21267	−	6.80989i	−0.258973	−	0.797037i	0.734048	−	0.679098i	$-0.237629\pi$
$74$	−0.675360	+	2.07854i	−0.0785090	+	0.241626i
$75$		0			0
$76$	0.132927			0.0152478
$77$	1.56580	+	10.4754i	0.178439	+	1.19378i
$78$		0			0
$79$	−0.640209	−	0.465139i	−0.0720292	−	0.0523323i	0.551188	−	0.834381i	$-0.314175\pi$
$79$	−0.640209	−	0.465139i	−0.0720292	−	0.0523323i	−0.623217	+	0.782049i	$0.714175\pi$
$80$	−1.10991	+	3.41595i	−0.124092	+	0.381915i
$81$		0			0
$82$	−2.47608	+	1.79898i	−0.273437	+	0.198664i
$83$	0.200012	−	0.145318i	0.0219542	−	0.0159507i	−0.576754	−	0.816918i	$-0.695681\pi$
$83$	0.200012	−	0.145318i	0.0219542	−	0.0159507i	0.598708	+	0.800967i	$0.295681\pi$
$84$		0			0
$85$	−0.0272635	+	0.0839083i	−0.00295714	+	0.00910114i
$86$	2.50920	+	1.82304i	0.270574	+	0.196584i
$87$		0			0
$88$	1.57943	−	3.03423i	0.168368	−	0.323450i
$89$	14.5788			1.54535			0.772673	−	0.634804i	$-0.218919\pi$
$89$	14.5788			1.54535			0.772673	+	0.634804i	$0.218919\pi$
$90$		0			0
$91$	1.10489	−	3.40050i	0.115824	−	0.356469i
$92$	3.97116	+	12.2220i	0.414022	+	1.27423i
$93$		0			0
$94$	0.192730	−	0.140027i	0.0198786	−	0.0144427i
$95$	0.0212704	+	0.0654637i	0.00218230	+	0.00671643i
$96$		0			0
$97$	3.31048	+	2.40521i	0.336128	+	0.244212i	0.743027	−	0.669262i	$-0.233390\pi$
$97$	3.31048	+	2.40521i	0.336128	+	0.244212i	−0.406898	+	0.913474i	$0.633390\pi$
$98$	0.839188			0.0847708
$99$		0			0
$100$	−1.93117			−0.193117
$101$	3.47207	+	2.52261i	0.345484	+	0.251009i	0.746972	−	0.664856i	$-0.231507\pi$
$101$	3.47207	+	2.52261i	0.345484	+	0.251009i	−0.401488	+	0.915864i	$0.631507\pi$
$102$		0			0
$103$	0.646712	+	1.99038i	0.0637224	+	0.196118i	0.977849	−	0.209311i	$-0.0671222\pi$
$103$	0.646712	+	1.99038i	0.0637224	+	0.196118i	−0.914127	+	0.405429i	$0.867122\pi$
$104$	−0.934204	+	0.678739i	−0.0916062	+	0.0665558i
$105$		0			0
$106$	−0.0707268	−	0.217675i	−0.00686959	−	0.0211424i
$107$	4.86421	−	14.9705i	0.470241	−	1.44725i	−0.382029	−	0.924151i	$-0.624774\pi$
$107$	4.86421	−	14.9705i	0.470241	−	1.44725i	0.852270	−	0.523103i	$-0.175226\pi$
$108$		0			0
$109$	−4.13271			−0.395842			−0.197921	−	0.980218i	$-0.563419\pi$
$109$	−4.13271			−0.395842			−0.197921	+	0.980218i	$0.563419\pi$
$110$	0.858218	+	0.143596i	0.0818279	+	0.0136914i
$111$		0			0
$112$	9.27969	+	6.74209i	0.876848	+	0.637067i
$113$	−4.25053	+	13.0818i	−0.399856	+	1.23063i	0.525258	+	0.850943i	$0.323969\pi$
$113$	−4.25053	+	13.0818i	−0.399856	+	1.23063i	−0.925114	+	0.379688i	$0.876031\pi$
$114$		0			0
$115$	−5.38361	+	3.91142i	−0.502024	+	0.364742i
$116$	−5.83666	+	4.24059i	−0.541921	+	0.393728i
$117$		0			0
$118$	−0.148855	+	0.458127i	−0.0137032	+	0.0421740i
$119$	0.227943	+	0.165611i	0.0208955	+	0.0151815i
$120$		0			0
$121$	10.4009	+	3.58078i	0.945533	+	0.325525i
$122$	−2.63937			−0.238957
$123$		0			0
$124$	5.71989	−	17.6040i	0.513661	−	1.58089i
$125$	−0.309017	−	0.951057i	−0.0276393	−	0.0850651i
$126$		0			0
$127$	−6.39106	+	4.64338i	−0.567115	+	0.412033i	−0.834056	−	0.551680i	$-0.813987\pi$
$127$	−6.39106	+	4.64338i	−0.567115	+	0.412033i	0.266941	+	0.963713i	$0.413987\pi$
$128$	−2.37572	−	7.31171i	−0.209986	−	0.646270i
$129$		0			0
$130$	−0.237640	−	0.172656i	−0.0208424	−	0.0151429i
$131$	16.3539			1.42884			0.714422	−	0.699715i	$-0.246690\pi$
$131$	16.3539			1.42884			0.714422	+	0.699715i	$0.246690\pi$
$132$		0			0
$133$	0.219819			0.0190607
$134$	−2.02472	−	1.47104i	−0.174909	−	0.127079i
$135$		0			0
$136$	−0.0281190	−	0.0865414i	−0.00241118	−	0.00742086i
$137$	6.25538	−	4.54480i	0.534433	−	0.388289i	−0.287580	−	0.957757i	$-0.592851\pi$
$137$	6.25538	−	4.54480i	0.534433	−	0.388289i	0.822013	+	0.569468i	$0.192851\pi$
$138$		0			0
$139$	6.23796	+	19.1985i	0.529097	+	1.62839i	0.756069	+	0.654492i	$0.227117\pi$
$139$	6.23796	+	19.1985i	0.529097	+	1.62839i	−0.226972	+	0.973901i	$0.572883\pi$
$140$	−1.90578	+	5.86539i	−0.161068	+	0.495716i
$141$		0			0
$142$	1.22379			0.102698
$143$	−2.60276	−	2.64846i	−0.217653	−	0.221476i
$144$		0			0
$145$	−3.02235	−	2.19587i	−0.250993	−	0.182357i
$146$	−0.580514	+	1.78664i	−0.0480437	+	0.147863i
$147$		0			0
$148$	−13.0147	+	9.45572i	−1.06980	+	0.777255i
$149$	7.84361	−	5.69872i	0.642573	−	0.466857i	−0.218160	−	0.975913i	$-0.570005\pi$
$149$	7.84361	−	5.69872i	0.642573	−	0.466857i	0.860733	+	0.509056i	$0.170005\pi$
$150$		0			0
$151$	4.68515	−	14.4194i	0.381272	−	1.17343i	−0.557877	−	0.829924i	$-0.688384\pi$
$151$	4.68515	−	14.4194i	0.381272	−	1.17343i	0.939149	−	0.343511i	$-0.111616\pi$
$152$	−0.0574342	−	0.0417284i	−0.00465853	−	0.00338462i
$153$		0			0
$154$	1.28307	−	2.46489i	0.103393	−	0.198627i
$155$	9.58484			0.769873
$156$		0			0
$157$	−4.59834	+	14.1522i	−0.366987	+	1.12947i	0.581740	+	0.813375i	$0.302372\pi$
$157$	−4.59834	+	14.1522i	−0.366987	+	1.12947i	−0.948727	+	0.316096i	$0.897628\pi$
$158$	0.0641570	+	0.197455i	0.00510405	+	0.0157087i
$159$		0			0
$160$	2.43117	−	1.76635i	0.192201	−	0.139642i
$161$	6.56702	+	20.2112i	0.517554	+	1.59287i
$162$		0			0
$163$	−2.75158	−	1.99914i	−0.215521	−	0.156585i	0.474787	−	0.880101i	$-0.342525\pi$
$163$	−2.75158	−	1.99914i	−0.215521	−	0.156585i	−0.690308	+	0.723516i	$0.742525\pi$
$164$	−22.5283			−1.75917
$165$		0			0
$166$	−0.0648629			−0.00503434
$167$	−18.2970	−	13.2936i	−1.41587	−	1.02869i	−0.992437	−	0.122757i	$-0.960826\pi$
$167$	−18.2970	−	13.2936i	−1.41587	−	1.02869i	−0.423429	−	0.905929i	$-0.639174\pi$
$168$		0			0
$169$	−3.62986	−	11.1716i	−0.279220	−	0.859351i
$170$	0.0187264	−	0.0136055i	0.00143625	−	0.00104349i
$171$		0			0
$172$	7.05478	+	21.7124i	0.537922	+	1.65555i
$173$	4.04543	−	12.4506i	0.307568	−	0.946598i	−0.671138	−	0.741333i	$-0.734194\pi$
$173$	4.04543	−	12.4506i	0.307568	−	0.946598i	0.978706	−	0.205266i	$-0.0658058\pi$
$174$		0			0
$175$	−3.19353			−0.241408
$176$	10.6607	−	5.31556i	0.803584	−	0.400675i
$177$		0			0
$178$	−3.09439	−	2.24821i	−0.231935	−	0.168510i
$179$	4.69008	−	14.4346i	0.350553	−	1.07889i	−0.607990	−	0.793944i	$-0.708024\pi$
$179$	4.69008	−	14.4346i	0.350553	−	1.07889i	0.958543	−	0.284947i	$-0.0919759\pi$
$180$		0			0
$181$	−1.14353	+	0.830823i	−0.0849978	+	0.0617546i	−0.629473	−	0.777023i	$-0.716729\pi$
$181$	−1.14353	+	0.830823i	−0.0849978	+	0.0617546i	0.544475	+	0.838777i	$0.316729\pi$
$182$	−0.758911	+	0.551381i	−0.0562542	+	0.0408711i
$183$		0			0
$184$	2.12088	−	6.52740i	0.156354	−	0.481207i
$185$	−6.73928	−	4.89637i	−0.495482	−	0.359989i
$186$		0			0
$187$	0.261867	−	0.130570i	0.0191496	−	0.00954820i
$188$	1.75354			0.127890
$189$		0			0
$190$	0.00558051	−	0.0171750i	0.000404853	−	0.00124601i
$191$	−1.51701	−	4.66887i	−0.109767	−	0.337827i	0.881053	−	0.473018i	$-0.156835\pi$
$191$	−1.51701	−	4.66887i	−0.109767	−	0.337827i	−0.990820	+	0.135190i	$0.956835\pi$
$192$		0			0
$193$	−7.86354	+	5.71320i	−0.566030	+	0.411245i	−0.833661	−	0.552276i	$-0.813759\pi$
$193$	−7.86354	+	5.71320i	−0.566030	+	0.411245i	0.267631	+	0.963522i	$0.413759\pi$
$194$	−0.331752	−	1.02103i	−0.0238184	−	0.0733054i
$195$		0			0
$196$	4.99735	+	3.63079i	0.356953	+	0.259342i
$197$	8.88764			0.633218			0.316609	−	0.948556i	$-0.397456\pi$
$197$	8.88764			0.633218			0.316609	+	0.948556i	$0.397456\pi$
$198$		0			0
$199$	18.0381			1.27869			0.639343	−	0.768921i	$-0.279206\pi$
$199$	18.0381			1.27869			0.639343	+	0.768921i	$0.279206\pi$
$200$	0.834404	+	0.606230i	0.0590013	+	0.0428669i
$201$		0			0
$202$	−0.347945	−	1.07086i	−0.0244813	−	0.0753457i
$203$	−9.65196	+	7.01256i	−0.677435	+	0.492185i
$204$		0			0
$205$	−3.60489	−	11.0947i	−0.251776	−	0.774888i
$206$	0.169671	−	0.522194i	0.0118216	−	0.0363830i
$207$		0			0
$208$	−4.02134			−0.278830
$209$	0.105409	−	0.202500i	0.00729128	−	0.0140072i
$210$		0			0
$211$	−14.5444	−	10.5671i	−1.00127	−	0.727469i	−0.0389136	−	0.999243i	$-0.512390\pi$
$211$	−14.5444	−	10.5671i	−1.00127	−	0.727469i	−0.962361	+	0.271774i	$0.912390\pi$
$212$	0.520603	−	1.60225i	0.0357552	−	0.110043i
$213$		0			0
$214$	−3.34106	+	2.42743i	−0.228390	+	0.165935i
$215$	−9.56399	+	6.94864i	−0.652258	+	0.473894i
$216$		0			0
$217$	9.45884	−	29.1113i	0.642108	−	1.97621i
$218$	0.877182	+	0.637310i	0.0594103	+	0.0431641i
$219$		0			0
$220$	4.48940	+	4.56824i	0.302675	+	0.307990i
$221$	−0.0987789			−0.00664459
$222$		0			0
$223$	−4.24865	+	13.0760i	−0.284511	+	0.875635i	0.702034	+	0.712144i	$0.252276\pi$
$223$	−4.24865	+	13.0760i	−0.284511	+	0.875635i	−0.986545	+	0.163491i	$0.947724\pi$
$224$	−2.96558	−	9.12713i	−0.198146	−	0.609832i
$225$		0			0
$226$	2.91955	−	2.12118i	0.194205	−	0.141099i
$227$	−0.204796	−	0.630298i	−0.0135928	−	0.0418344i	0.944030	−	0.329859i	$-0.107001\pi$
$227$	−0.204796	−	0.630298i	−0.0135928	−	0.0418344i	−0.957623	+	0.288025i	$0.907001\pi$
$228$		0			0
$229$	6.05987	+	4.40275i	0.400447	+	0.290942i	0.769723	−	0.638378i	$-0.220394\pi$
$229$	6.05987	+	4.40275i	0.400447	+	0.290942i	−0.369276	+	0.929320i	$0.620394\pi$
$230$	1.74587			0.115119
$231$		0			0
$232$	3.85306			0.252966
$233$	8.51520	+	6.18665i	0.557849	+	0.405301i	0.830671	−	0.556763i	$-0.187957\pi$
$233$	8.51520	+	6.18665i	0.557849	+	0.405301i	−0.272822	+	0.962065i	$0.587957\pi$
$234$		0			0
$235$	0.280594	+	0.863579i	0.0183039	+	0.0563337i
$236$	−2.86854	+	2.08411i	−0.186726	+	0.135664i
$237$		0			0
$238$	−0.0228428	−	0.0703028i	−0.00148068	−	0.00455706i
$239$	−5.27684	+	16.2404i	−0.341330	+	1.05051i	0.622189	+	0.782867i	$0.286244\pi$
$239$	−5.27684	+	16.2404i	−0.341330	+	1.05051i	−0.963519	+	0.267640i	$0.913756\pi$
$240$		0			0
$241$	−16.7082			−1.07627			−0.538135	−	0.842859i	$-0.680871\pi$
$241$	−16.7082			−1.07627			−0.538135	+	0.842859i	$0.680871\pi$
$242$	−1.65542	−	2.36396i	−0.106415	−	0.151961i
$243$		0			0
$244$	−15.7174	−	11.4194i	−1.00620	−	0.731050i
$245$	−0.988426	+	3.04206i	−0.0631483	+	0.194350i
$246$		0			0
$247$	−0.0623472	+	0.0452979i	−0.00396706	+	0.00288224i
$248$	−7.99763	+	5.81062i	−0.507850	+	0.368975i
$249$		0			0
$250$	−0.0810736	+	0.249519i	−0.00512754	+	0.0157810i
$251$	−4.15646	−	3.01984i	−0.262353	−	0.190611i	0.448831	−	0.893617i	$-0.351841\pi$
$251$	−4.15646	−	3.01984i	−0.262353	−	0.190611i	−0.711184	+	0.703006i	$0.751841\pi$
$252$		0			0
$253$	21.7679	+	3.64219i	1.36854	+	0.228982i
$254$	2.07259			0.130046
$255$		0			0
$256$	3.32908	−	10.2458i	0.208067	−	0.640366i
$257$	1.14282	+	3.51724i	0.0712872	+	0.219399i	0.980352	−	0.197255i	$-0.0632026\pi$
$257$	1.14282	+	3.51724i	0.0712872	+	0.219399i	−0.909065	+	0.416654i	$0.863203\pi$
$258$		0			0
$259$	−21.5221	+	15.6367i	−1.33732	+	0.971617i
$260$	−0.668140	−	2.05632i	−0.0414363	−	0.127528i
$261$		0			0
$262$	−3.47116	−	2.52195i	−0.214449	−	0.155806i
$263$	−31.6315			−1.95048			−0.975241	−	0.221147i	$-0.929020\pi$
$263$	−31.6315			−1.95048			−0.975241	+	0.221147i	$0.929020\pi$
$264$		0			0
$265$	0.872377			0.0535897
$266$	−0.0466573	−	0.0338985i	−0.00286074	−	0.00207845i
$267$		0			0
$268$	−5.69262	−	17.5201i	−0.347732	−	1.07021i
$269$	−11.9536	+	8.68479i	−0.728823	+	0.529521i	−0.889191	−	0.457536i	$-0.848732\pi$
$269$	−11.9536	+	8.68479i	−0.728823	+	0.529521i	0.160368	+	0.987057i	$0.448732\pi$
$270$		0			0
$271$	−6.05269	−	18.6283i	−0.367675	−	1.13159i	−0.948289	−	0.317408i	$-0.897188\pi$
$271$	−6.05269	−	18.6283i	−0.367675	−	1.13159i	0.580614	−	0.814179i	$-0.302812\pi$
$272$	0.0979234	−	0.301377i	0.00593748	−	0.0182737i
$273$		0			0
$274$	−2.02859			−0.122551
$275$	−1.53138	+	2.94192i	−0.0923457	+	0.177404i
$276$		0			0
$277$	−20.8001	−	15.1122i	−1.24976	−	0.908002i	−0.251550	−	0.967844i	$-0.580940\pi$
$277$	−20.8001	−	15.1122i	−1.24976	−	0.908002i	−0.998208	+	0.0598418i	$0.980940\pi$
$278$	1.63659	−	5.03691i	0.0981561	−	0.302094i
$279$		0			0
$280$	2.66469	−	1.93601i	0.159246	−	0.115699i
$281$	−21.6096	+	15.7003i	−1.28912	+	0.936599i	−0.999787	−	0.0206304i	$-0.993433\pi$
$281$	−21.6096	+	15.7003i	−1.28912	+	0.936599i	−0.289331	+	0.957229i	$0.593433\pi$
$282$		0			0
$283$	2.23535	−	6.87970i	0.132878	−	0.408956i	−0.862376	−	0.506268i	$-0.831025\pi$
$283$	2.23535	−	6.87970i	0.132878	−	0.408956i	0.995254	+	0.0973123i	$0.0310246\pi$
$284$	7.28764	+	5.29478i	0.432442	+	0.314187i
$285$		0			0
$286$	0.144021	+	0.963520i	0.00851616	+	0.0569741i
$287$	−37.2546			−2.19907
$288$		0			0
$289$	−5.25088	+	16.1606i	−0.308876	+	0.950621i
$290$	0.302877	+	0.932160i	0.0177856	+	0.0547383i
$291$		0			0
$292$	−11.1869	+	8.12778i	−0.654666	+	0.475643i
$293$	−4.51002	−	13.8804i	−0.263478	−	0.810902i	−0.992040	−	0.125922i	$-0.959811\pi$
$293$	−4.51002	−	13.8804i	−0.263478	−	0.810902i	0.728562	−	0.684980i	$-0.240189\pi$
$294$		0			0
$295$	−1.48539	−	1.07920i	−0.0864828	−	0.0628334i
$296$	8.59161			0.499377
$297$		0			0
$298$	−2.54364			−0.147349
$299$	−6.02752	−	4.37925i	−0.348580	−	0.253258i
$300$		0			0
$301$	11.6663	+	35.9053i	0.672436	+	2.06955i
$302$	−3.21807	+	2.33807i	−0.185179	+	0.134541i
$303$		0			0
$304$	−0.0763980	−	0.235129i	−0.00438172	−	0.0134856i
$305$	3.10875	−	9.56775i	0.178006	−	0.547848i
$306$		0			0
$307$	28.5445			1.62912			0.814559	−	0.580080i	$-0.196979\pi$
$307$	28.5445			1.62912			0.814559	+	0.580080i	$0.196979\pi$
$308$	18.3051	−	9.12713i	1.04303	−	0.520066i
$309$		0			0
$310$	−2.03442	−	1.47809i	−0.115547	−	0.0839499i
$311$	3.07411	−	9.46113i	0.174317	−	0.536492i	−0.825285	−	0.564717i	$-0.808985\pi$
$311$	3.07411	−	9.46113i	0.174317	−	0.536492i	0.999602	+	0.0282249i	$0.00898547\pi$
$312$		0			0
$313$	13.2929	−	9.65786i	0.751359	−	0.545894i	−0.144889	−	0.989448i	$-0.546282\pi$
$313$	13.2929	−	9.65786i	0.751359	−	0.545894i	0.896248	+	0.443554i	$0.146282\pi$
$314$	3.15844	−	2.29474i	0.178241	−	0.129500i
$315$		0			0
$316$	−0.472244	+	1.45342i	−0.0265658	+	0.0817612i
$317$	11.4966	+	8.35278i	0.645714	+	0.469139i	0.861809	−	0.507234i	$-0.169332\pi$
$317$	11.4966	+	8.35278i	0.645714	+	0.469139i	−0.216094	+	0.976373i	$0.569332\pi$
$318$		0			0
$319$	1.83169	+	12.2542i	0.102555	+	0.686104i
$320$	6.39507			0.357495
$321$		0			0
$322$	1.72292	−	5.30261i	0.0960147	−	0.295503i
$323$	−0.00187662	−	0.00577563i	−0.000104418	−	0.000321365i
$324$		0			0
$325$	0.905781	−	0.658088i	0.0502437	−	0.0365042i
$326$	0.275743	+	0.848650i	0.0152720	+	0.0470024i
$327$		0			0
$328$	9.73387	+	7.07207i	0.537463	+	0.390490i
$329$	2.89979			0.159870
$330$		0			0
$331$	−10.9119			−0.599773			−0.299886	−	0.953975i	$-0.596949\pi$
$331$	−10.9119			−0.599773			−0.299886	+	0.953975i	$0.596949\pi$
$332$	−0.386258	−	0.280633i	−0.0211986	−	0.0154017i
$333$		0			0
$334$	1.83359	+	5.64321i	0.100330	+	0.308783i
$335$	7.71734	−	5.60698i	0.421643	−	0.306342i
$336$		0			0
$337$	−1.81890	−	5.59800i	−0.0990819	−	0.304943i	0.889214	−	0.457491i	$-0.151252\pi$
$337$	−1.81890	−	5.59800i	−0.0990819	−	0.304943i	−0.988296	+	0.152549i	$0.951252\pi$
$338$	−0.952330	+	2.93097i	−0.0517999	+	0.159424i
$339$		0			0
$340$	0.170380			0.00924015
$341$	−22.2820	−	22.6732i	−1.20664	−	1.22783i
$342$		0			0
$343$	−9.82132	−	7.13561i	−0.530302	−	0.385287i
$344$	3.76775	−	11.5959i	0.203144	−	0.625212i
$345$		0			0
$346$	−2.77867	+	2.01882i	−0.149382	+	0.108533i
$347$	27.9145	−	20.2811i	1.49853	−	1.08875i	0.527569	−	0.849512i	$-0.323104\pi$
$347$	27.9145	−	20.2811i	1.49853	−	1.08875i	0.970962	−	0.239234i	$-0.0768962\pi$
$348$		0			0
$349$	−1.70378	+	5.24371i	−0.0912014	+	0.280689i	−0.986245	−	0.165289i	$-0.947144\pi$
$349$	−1.70378	+	5.24371i	−0.0912014	+	0.280689i	0.895044	+	0.445978i	$0.147144\pi$
$350$	0.677837	+	0.492478i	0.0362319	+	0.0263240i
$351$		0			0
$352$	−9.83010	−	1.64476i	−0.523946	−	0.0876662i
$353$	29.8740			1.59003			0.795016	−	0.606589i	$-0.207463\pi$
$353$	29.8740			1.59003			0.795016	+	0.606589i	$0.207463\pi$
$354$		0			0
$355$	−1.44142	+	4.43625i	−0.0765028	+	0.235451i
$356$	−8.70008	−	26.7761i	−0.461103	−	1.41913i
$357$		0			0
$358$	−3.22146	+	2.34053i	−0.170259	+	0.123701i
$359$	11.0978	+	34.1554i	0.585717	+	1.80265i	0.596372	+	0.802708i	$0.296608\pi$
$359$	11.0978	+	34.1554i	0.585717	+	1.80265i	−0.0106548	+	0.999943i	$0.503392\pi$
$360$		0			0
$361$	15.3675	+	11.1651i	0.808815	+	0.587639i
$362$	0.370840			0.0194909
$363$		0			0
$364$	−6.90488			−0.361914
$365$	−5.79283	−	4.20874i	−0.303211	−	0.220296i
$366$		0			0
$367$	−2.79069	−	8.58887i	−0.145673	−	0.448335i	0.851424	−	0.524478i	$-0.175740\pi$
$367$	−2.79069	−	8.58887i	−0.145673	−	0.448335i	−0.997097	+	0.0761428i	$0.975740\pi$
$368$	19.3365	−	14.0488i	1.00799	−	0.732345i
$369$		0			0
$370$	0.675360	+	2.07854i	0.0351103	+	0.108058i
$371$	0.860909	−	2.64961i	0.0446962	−	0.137561i
$372$		0			0
$373$	17.1994			0.890553			0.445277	−	0.895393i	$-0.353105\pi$
$373$	17.1994			0.890553			0.445277	+	0.895393i	$0.353105\pi$
$374$	−0.0757176	−	0.0126690i	−0.00391526	−	0.000655098i
$375$		0			0
$376$	−0.757656	−	0.550469i	−0.0390731	−	0.0283883i
$377$	1.29251	−	3.97795i	0.0665678	−	0.204875i
$378$		0			0
$379$	6.47382	−	4.70350i	0.332538	−	0.241603i	−0.408969	−	0.912548i	$-0.634112\pi$
$379$	6.47382	−	4.70350i	0.332538	−	0.241603i	0.741507	+	0.670946i	$0.234112\pi$
$380$	0.107540	−	0.0781327i	0.00551671	−	0.00400812i
$381$		0			0
$382$	−0.398002	+	1.22492i	−0.0203635	+	0.0626725i
$383$	24.0384	+	17.4649i	1.22831	+	0.892417i	0.996762	−	0.0804076i	$-0.0256222\pi$
$383$	24.0384	+	17.4649i	1.22831	+	0.892417i	0.231544	+	0.972824i	$0.425622\pi$
$384$		0			0
$385$	7.42401	+	7.55439i	0.378363	+	0.385007i
$386$	2.55010			0.129797
$387$		0			0
$388$	2.44194	−	7.51553i	0.123971	−	0.381543i
$389$	0.183988	+	0.566256i	0.00932855	+	0.0287103i	0.955612	−	0.294627i	$-0.0951953\pi$
$389$	0.183988	+	0.566256i	0.00932855	+	0.0287103i	−0.946284	+	0.323337i	$0.895195\pi$
$390$		0			0
$391$	0.474976	−	0.345090i	0.0240206	−	0.0174520i
$392$	−1.01944	−	3.13752i	−0.0514897	−	0.158469i
$393$		0			0
$394$	−1.88643	−	1.37057i	−0.0950371	−	0.0690485i
$395$	−0.791342			−0.0398167
$396$		0			0
$397$	1.66950			0.0837898			0.0418949	−	0.999122i	$-0.486661\pi$
$397$	1.66950			0.0837898			0.0418949	+	0.999122i	$0.486661\pi$
$398$	−3.82865	−	2.78168i	−0.191913	−	0.139433i
$399$		0			0
$400$	1.10991	+	3.41595i	0.0554955	+	0.170797i
$401$	−9.19771	+	6.68253i	−0.459312	+	0.333710i	−0.793261	−	0.608881i	$-0.791619\pi$
$401$	−9.19771	+	6.68253i	−0.459312	+	0.333710i	0.333949	+	0.942591i	$0.391619\pi$
$402$		0			0
$403$	3.31614	+	10.2060i	0.165189	+	0.508398i
$404$	2.56114	−	7.88237i	0.127421	−	0.392163i
$405$		0			0
$406$	3.13008			0.155343
$407$	4.08433	+	27.3246i	0.202453	+	1.35443i
$408$		0			0
$409$	6.95565	+	5.05358i	0.343935	+	0.249883i	0.746320	−	0.665587i	$-0.231819\pi$
$409$	6.95565	+	5.05358i	0.343935	+	0.249883i	−0.402385	+	0.915470i	$0.631819\pi$
$410$	−0.945777	+	2.91080i	−0.0467086	+	0.143754i
$411$		0			0
$412$	3.26969	−	2.37557i	0.161086	−	0.117036i
$413$	−4.74363	+	3.44645i	−0.233419	+	0.169589i
$414$		0			0
$415$	0.0763980	−	0.235129i	0.00375023	−	0.0115420i
$416$	2.72195	+	1.97761i	0.133455	+	0.0969604i
$417$		0			0
$418$	−0.0536011	+	0.0267261i	−0.00262172	+	0.00130721i
$419$	−31.3915			−1.53358			−0.766789	−	0.641899i	$-0.778147\pi$
$419$	−31.3915			−1.53358			−0.766789	+	0.641899i	$0.778147\pi$
$420$		0			0
$421$	−1.41497	+	4.35482i	−0.0689613	+	0.212241i	−0.979598	−	0.200967i	$-0.935592\pi$
$421$	−1.41497	+	4.35482i	−0.0689613	+	0.212241i	0.910637	+	0.413208i	$0.135592\pi$
$422$	1.45753	+	4.48580i	0.0709513	+	0.218366i
$423$		0			0
$424$	−0.727915	+	0.528861i	−0.0353507	+	0.0256838i
$425$	0.0272635	+	0.0839083i	0.00132247	+	0.00407015i
$426$		0			0
$427$	−25.9915	−	18.8839i	−1.25782	−	0.913858i
$428$	−30.3983			−1.46936
$429$		0			0
$430$	3.10155			0.149570
$431$	12.8694	+	9.35015i	0.619896	+	0.450381i	0.852885	−	0.522098i	$-0.174851\pi$
$431$	12.8694	+	9.35015i	0.619896	+	0.450381i	−0.232989	+	0.972479i	$0.574851\pi$
$432$		0			0
$433$	4.88338	+	15.0295i	0.234680	+	0.722272i	0.997164	+	0.0752639i	$0.0239799\pi$
$433$	4.88338	+	15.0295i	0.234680	+	0.722272i	−0.762483	+	0.647008i	$0.776020\pi$
$434$	−6.49696	+	4.72032i	−0.311864	+	0.226583i
$435$		0			0
$436$	2.46625	+	7.59034i	0.118112	+	0.363511i
$437$	0.141544	−	0.435628i	0.00677098	−	0.0208389i
$438$		0			0
$439$	21.5227			1.02722			0.513611	−	0.858023i	$-0.328307\pi$
$439$	21.5227			1.02722			0.513611	+	0.858023i	$0.328307\pi$
$440$	−0.505689	−	3.38312i	−0.0241078	−	0.161284i
$441$		0			0
$442$	0.0209662	+	0.0152328i	0.000997258	+	0.000724551i
$443$	−3.14484	+	9.67881i	−0.149416	+	0.459854i	−0.997552	−	0.0699233i	$-0.977725\pi$
$443$	−3.14484	+	9.67881i	−0.149416	+	0.459854i	0.848137	+	0.529777i	$0.177725\pi$
$444$		0			0
$445$	11.7945	−	8.56919i	0.559112	−	0.406218i
$446$	2.91826	−	2.12024i	0.138184	−	0.100396i
$447$		0			0
$448$	6.31100	−	19.4233i	0.298167	−	0.917663i
$449$	31.2352	+	22.6937i	1.47408	+	1.07098i	0.979406	+	0.201902i	$0.0647121\pi$
$449$	31.2352	+	22.6937i	1.47408	+	1.07098i	0.494673	+	0.869079i	$0.335288\pi$
$450$		0			0
$451$	−17.8646	+	34.3194i	−0.841209	+	1.61604i
$452$	26.5632			1.24943
$453$		0			0
$454$	−0.0537303	+	0.165365i	−0.00252169	+	0.00776096i
$455$	−1.10489	−	3.40050i	−0.0517980	−	0.159418i
$456$		0			0
$457$	−18.9017	+	13.7329i	−0.884183	+	0.642396i	−0.934355	−	0.356344i	$-0.884023\pi$
$457$	−18.9017	+	13.7329i	−0.884183	+	0.642396i	0.0501720	+	0.998741i	$0.484023\pi$
$458$	−0.607275	−	1.86900i	−0.0283761	−	0.0873326i
$459$		0			0
$460$	10.3966	+	7.55360i	0.484746	+	0.352189i
$461$	−4.93120			−0.229669			−0.114834	−	0.993385i	$-0.536634\pi$
$461$	−4.93120			−0.229669			−0.114834	+	0.993385i	$0.536634\pi$
$462$		0			0
$463$	26.9648			1.25316			0.626580	−	0.779357i	$-0.284454\pi$
$463$	26.9648			1.25316			0.626580	+	0.779357i	$0.284454\pi$
$464$	10.8555	+	7.88699i	0.503954	+	0.366144i
$465$		0			0
$466$	−0.853329	−	2.62628i	−0.0395297	−	0.121660i
$467$	−19.1558	+	13.9175i	−0.886423	+	0.644024i	−0.934943	−	0.354798i	$-0.884550\pi$
$467$	−19.1558	+	13.9175i	−0.886423	+	0.644024i	0.0485201	+	0.998822i	$0.484550\pi$
$468$		0			0
$469$	−9.41376	−	28.9726i	−0.434687	−	1.33783i
$470$	0.0736165	−	0.226568i	0.00339568	−	0.0104508i
$471$		0			0
$472$	1.89366			0.0871627
$473$	38.6707	+	6.47035i	1.77808	+	0.297507i
$474$		0			0
$475$	0.0556868	+	0.0404588i	0.00255508	+	0.00185638i
$476$	0.168140	−	0.517482i	0.00770669	−	0.0237188i
$477$		0			0
$478$	3.62449	−	2.63334i	0.165780	−	0.120446i
$479$	−10.9412	+	7.94922i	−0.499915	+	0.363209i	−0.808984	−	0.587830i	$-0.799982\pi$
$479$	−10.9412	+	7.94922i	−0.499915	+	0.363209i	0.309070	+	0.951039i	$0.399982\pi$
$480$		0			0
$481$	2.88206	−	8.87008i	0.131411	−	0.404441i
$482$	3.54637	+	2.57659i	0.161533	+	0.117361i
$483$		0			0
$484$	0.369771	−	21.2396i	0.0168078	−	0.965437i
$485$	4.09198			0.185807
$486$		0			0
$487$	−2.66590	+	8.20480i	−0.120803	+	0.371795i	−0.993113	−	0.117159i	$-0.962621\pi$
$487$	−2.66590	+	8.20480i	−0.120803	+	0.371795i	0.872310	+	0.488954i	$0.162621\pi$
$488$	3.20630	+	9.86798i	0.145142	+	0.446703i
$489$		0			0
$490$	0.678917	−	0.493262i	0.0306703	−	0.0222833i
$491$	8.00565	+	24.6388i	0.361290	+	1.11194i	0.952272	+	0.305251i	$0.0987404\pi$
$491$	8.00565	+	24.6388i	0.361290	+	1.11194i	−0.590982	+	0.806685i	$0.701260\pi$
$492$		0			0
$493$	0.266651	+	0.193733i	0.0120094	+	0.00872532i
$494$	0.0202189			0.000909690
$495$		0			0
$496$	−34.4263			−1.54579
$497$	12.0514	+	8.75585i	0.540579	+	0.392754i
$498$		0			0
$499$	−8.66717	−	26.6748i	−0.387996	−	1.19413i	−0.934284	−	0.356531i	$-0.883960\pi$
$499$	−8.66717	−	26.6748i	−0.387996	−	1.19413i	0.546288	−	0.837597i	$-0.316040\pi$
$500$	−1.56235	+	1.13511i	−0.0698703	+	0.0507637i
$501$		0			0
$502$	0.416529	+	1.28194i	0.0185906	+	0.0572160i
$503$	−9.08507	+	27.9610i	−0.405083	+	1.24672i	0.515743	+	0.856744i	$0.327516\pi$
$503$	−9.08507	+	27.9610i	−0.405083	+	1.24672i	−0.920826	+	0.389974i	$0.872484\pi$
$504$		0			0
$505$	4.29171			0.190979
$506$	−4.05864	−	4.12992i	−0.180429	−	0.183597i
$507$		0			0
$508$	12.3422	+	8.96714i	0.547597	+	0.397853i
$509$	5.99195	−	18.4413i	0.265589	−	0.817398i	−0.725969	−	0.687728i	$-0.758608\pi$
$509$	5.99195	−	18.4413i	0.265589	−	0.817398i	0.991557	−	0.129670i	$-0.0413918\pi$
$510$		0			0
$511$	−18.4996	+	13.4407i	−0.818373	+	0.594583i
$512$	−14.7261	+	10.6991i	−0.650806	+	0.472838i
$513$		0			0
$514$	0.299830	−	0.922782i	0.0132249	−	0.0407022i
$515$	1.69311	+	1.23012i	0.0746075	+	0.0542056i
$516$		0			0
$517$	1.39052	−	2.67132i	0.0611552	−	0.117485i
$518$	6.97949			0.306661
$519$		0			0
$520$	−0.356834	+	1.09822i	−0.0156482	+	0.0481602i
$521$	−7.72734	−	23.7823i	−0.338541	−	1.04192i	−0.964951	−	0.262429i	$-0.915477\pi$
$521$	−7.72734	−	23.7823i	−0.338541	−	1.04192i	0.626410	−	0.779493i	$-0.284523\pi$
$522$		0			0
$523$	1.76982	−	1.28585i	0.0773887	−	0.0562262i	−0.548418	−	0.836204i	$-0.684770\pi$
$523$	1.76982	−	1.28585i	0.0773887	−	0.0562262i	0.625807	+	0.779978i	$0.284770\pi$
$524$	−9.75939	−	30.0363i	−0.426341	−	1.31214i
$525$		0			0
$526$	6.71389	+	4.87793i	0.292740	+	0.212688i
$527$	−0.845637			−0.0368365
$528$		0			0
$529$	21.2824			0.925322
$530$	−0.185165	−	0.134530i	−0.00804306	−	0.00584362i
$531$		0			0
$532$	−0.131180	−	0.403730i	−0.00568737	−	0.0175039i
$533$	10.5665	−	7.67703i	0.457687	−	0.332529i
$534$		0			0
$535$	−4.86421	−	14.9705i	−0.210298	−	0.647231i
$536$	−3.04026	+	9.35697i	−0.131319	+	0.404159i
$537$		0			0
$538$	3.87648			0.167127
$539$	9.49390	−	4.73375i	0.408931	−	0.203897i
$540$		0			0
$541$	−10.9689	−	7.96939i	−0.471591	−	0.342631i	0.326470	−	0.945208i	$-0.394141\pi$
$541$	−10.9689	−	7.96939i	−0.471591	−	0.342631i	−0.798061	+	0.602577i	$0.794141\pi$
$542$	−1.58798	+	4.88731i	−0.0682097	+	0.209928i
$543$		0			0
$544$	−0.214493	+	0.155838i	−0.00919632	+	0.00668152i
$545$	−3.34343	+	2.42915i	−0.143217	+	0.104053i
$546$		0			0
$547$	−1.14732	+	3.53110i	−0.0490560	+	0.150979i	−0.972584	−	0.232553i	$-0.925292\pi$
$547$	−1.14732	+	3.53110i	−0.0490560	+	0.150979i	0.923528	+	0.383531i	$0.125292\pi$
$548$	−12.0802	−	8.77677i	−0.516040	−	0.374925i
$549$		0			0
$550$	0.778717	−	0.388276i	0.0332046	−	0.0165562i
$551$	0.257147			0.0109548
$552$		0			0
$553$	−0.780939	+	2.40348i	−0.0332089	+	0.102207i
$554$	2.08443	+	6.41522i	0.0885590	+	0.272557i
$555$		0			0
$556$	31.5383	−	22.9139i	1.33752	−	0.971766i
$557$	−2.03185	−	6.25339i	−0.0860922	−	0.264964i	0.898738	−	0.438486i	$-0.144485\pi$
$557$	−2.03185	−	6.25339i	−0.0860922	−	0.264964i	−0.984830	+	0.173522i	$0.944485\pi$
$558$		0			0
$559$	−10.7079	−	7.77974i	−0.452896	−	0.329048i
$560$	11.4703			0.484710
$561$		0			0
$562$	7.00786			0.295609
$563$	−5.58931	−	4.06087i	−0.235561	−	0.171145i	0.463742	−	0.885970i	$-0.346506\pi$
$563$	−5.58931	−	4.06087i	−0.235561	−	0.171145i	−0.699303	+	0.714825i	$0.746506\pi$
$564$		0			0
$565$	4.25053	+	13.0818i	0.178821	+	0.550355i
$566$	−1.53539	+	1.11552i	−0.0645372	+	0.0468890i
$567$		0			0
$568$	−1.48666	−	4.57545i	−0.0623787	−	0.191982i
$569$	2.08515	−	6.41743i	0.0874140	−	0.269033i	−0.897789	−	0.440427i	$-0.854827\pi$
$569$	2.08515	−	6.41743i	0.0874140	−	0.269033i	0.985203	+	0.171394i	$0.0548272\pi$
$570$		0			0
$571$	9.68928			0.405484			0.202742	−	0.979232i	$-0.435015\pi$
$571$	9.68928			0.405484			0.202742	+	0.979232i	$0.435015\pi$
$572$	−3.31107	+	6.36086i	−0.138443	+	0.265961i
$573$		0			0
$574$	7.90742	+	5.74508i	0.330049	+	0.239795i
$575$	−2.05635	+	6.32881i	−0.0857559	+	0.263930i
$576$		0			0
$577$	−12.2565	+	8.90484i	−0.510243	+	0.370713i	−0.812916	−	0.582381i	$-0.802121\pi$
$577$	−12.2565	+	8.90484i	−0.510243	+	0.370713i	0.302673	+	0.953095i	$0.402121\pi$
$578$	3.60666	−	2.62039i	0.150017	−	0.108994i
$579$		0			0
$580$	−2.22941	+	6.86141i	−0.0925711	+	0.284905i
$581$	−0.638745	−	0.464076i	−0.0264996	−	0.0192531i
$582$		0			0
$583$	−2.02802	−	2.06364i	−0.0839921	−	0.0854671i
$584$	7.38503			0.305595
$585$		0			0
$586$	−1.18325	+	3.64166i	−0.0488795	+	0.150436i
$587$	8.34693	+	25.6892i	0.344514	+	1.06031i	0.961843	+	0.273601i	$0.0882149\pi$
$587$	8.34693	+	25.6892i	0.344514	+	1.06031i	−0.617329	+	0.786705i	$0.711785\pi$
$588$		0			0
$589$	−0.533749	+	0.387791i	−0.0219927	+	0.0159787i
$590$	0.148855	+	0.458127i	0.00612825	+	0.0188608i
$591$		0			0
$592$	24.2058	+	17.5865i	0.994850	+	0.722801i
$593$	22.1863			0.911084			0.455542	−	0.890214i	$-0.349446\pi$
$593$	22.1863			0.911084			0.455542	+	0.890214i	$0.349446\pi$
$594$		0			0
$595$	0.281754			0.0115508
$596$	−15.1473	−	11.0052i	−0.620458	−	0.450789i
$597$		0			0
$598$	0.604033	+	1.85902i	0.0247007	+	0.0760210i
$599$	9.50487	−	6.90569i	0.388359	−	0.282159i	−0.376424	−	0.926448i	$-0.622846\pi$
$599$	9.50487	−	6.90569i	0.388359	−	0.282159i	0.764783	+	0.644289i	$0.222846\pi$
$600$		0			0
$601$	10.6242	+	32.6979i	0.433370	+	1.33378i	0.894747	+	0.446572i	$0.147355\pi$
$601$	10.6242	+	32.6979i	0.433370	+	1.33378i	−0.461377	+	0.887204i	$0.652645\pi$
$602$	3.06077	−	9.42010i	0.124748	−	0.383934i
$603$		0			0
$604$	−29.2793			−1.19136
$605$	10.5192	−	3.21657i	0.427667	−	0.130772i
$606$		0			0
$607$	−11.0267	−	8.01137i	−0.447560	−	0.325172i	0.341071	−	0.940037i	$-0.389210\pi$
$607$	−11.0267	−	8.01137i	−0.447560	−	0.325172i	−0.788632	+	0.614866i	$0.789210\pi$
$608$	−0.0639196	+	0.196724i	−0.00259228	+	0.00797822i
$609$		0			0
$610$	−2.13530	+	1.55138i	−0.0864556	+	0.0628137i
$611$	−0.822467	+	0.597557i	−0.0332735	+	0.0241746i
$612$		0			0
$613$	−2.11057	+	6.49565i	−0.0852450	+	0.262357i	−0.984589	−	0.174885i	$-0.944045\pi$
$613$	−2.11057	+	6.49565i	−0.0852450	+	0.262357i	0.899344	+	0.437242i	$0.144045\pi$
$614$	−6.05866	−	4.40187i	−0.244508	−	0.177645i
$615$		0			0
$616$	−10.7743	−	1.80275i	−0.434110	−	0.0726349i
$617$	−30.3730			−1.22277			−0.611386	−	0.791333i	$-0.709388\pi$
$617$	−30.3730			−1.22277			−0.611386	+	0.791333i	$0.709388\pi$
$618$		0			0
$619$	−7.96890	+	24.5258i	−0.320297	+	0.985773i	0.653222	+	0.757167i	$0.273417\pi$
$619$	−7.96890	+	24.5258i	−0.320297	+	0.985773i	−0.973519	+	0.228607i	$0.926583\pi$
$620$	−5.71989	−	17.6040i	−0.229716	−	0.706994i
$621$		0			0
$622$	−2.11150	+	1.53410i	−0.0846635	+	0.0615117i
$623$	−14.3871	−	44.2790i	−0.576408	−	1.77400i
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	−4.31081			−0.172295
$627$		0			0
$628$	28.7368			1.14672
$629$	0.594583	+	0.431990i	0.0237076	+	0.0172246i
$630$		0			0
$631$	−7.90021	−	24.3143i	−0.314502	−	0.967939i	−0.975959	−	0.217955i	$-0.930061\pi$
$631$	−7.90021	−	24.3143i	−0.314502	−	0.967939i	0.661456	−	0.749984i	$-0.269939\pi$
$632$	0.660299	−	0.479735i	0.0262653	−	0.0190828i
$633$		0			0
$634$	−1.15210	−	3.54581i	−0.0457559	−	0.140822i
$635$	−2.44117	+	7.51314i	−0.0968748	+	0.298150i
$636$		0			0
$637$	−3.58119			−0.141892
$638$	1.50095	−	2.88347i	0.0594233	−	0.114157i
$639$		0			0
$640$	−6.21971	−	4.51888i	−0.245856	−	0.178625i
$641$	1.25851	−	3.87329i	0.0497081	−	0.152986i	−0.923121	−	0.384509i	$-0.874371\pi$
$641$	1.25851	−	3.87329i	0.0497081	−	0.152986i	0.972829	+	0.231523i	$0.0743708\pi$
$642$		0			0
$643$	−9.16601	+	6.65950i	−0.361472	+	0.262625i	−0.753666	−	0.657258i	$-0.771716\pi$
$643$	−9.16601	+	6.65950i	−0.361472	+	0.262625i	0.392194	+	0.919883i	$0.371716\pi$
$644$	33.2020	−	24.1226i	1.30834	−	0.950565i
$645$		0			0
$646$	−0.000492348		0.00151529i	−1.93712e−5		5.96184e-5i
$647$	−29.8107	−	21.6587i	−1.17198	−	0.851492i	−0.180734	−	0.983532i	$-0.557847\pi$
$647$	−29.8107	−	21.6587i	−1.17198	−	0.851492i	−0.991244	+	0.132040i	$0.957847\pi$
$648$		0			0
$649$	0.900218	+	6.02256i	0.0353366	+	0.236406i
$650$	−0.293740			−0.0115214
$651$		0			0
$652$	−2.02968	+	6.24671i	−0.0794883	+	0.244640i
$653$	−4.72079	−	14.5291i	−0.184739	−	0.568568i	0.815205	−	0.579173i	$-0.196624\pi$
$653$	−4.72079	−	14.5291i	−0.184739	−	0.568568i	−0.999944	+	0.0106050i	$0.996624\pi$
$654$		0			0
$655$	13.2306	−	9.61256i	0.516961	−	0.375594i
$656$	12.9478	+	39.8493i	0.505528	+	1.55585i
$657$		0			0
$658$	−0.615490	−	0.447180i	−0.0239943	−	0.0174329i
$659$	−11.8996			−0.463544			−0.231772	−	0.972770i	$-0.574452\pi$
$659$	−11.8996			−0.463544			−0.231772	+	0.972770i	$0.574452\pi$
$660$		0			0
$661$	−44.8648			−1.74504			−0.872520	−	0.488578i	$-0.837516\pi$
$661$	−44.8648			−1.74504			−0.872520	+	0.488578i	$0.837516\pi$
$662$	2.31609	+	1.68274i	0.0900174	+	0.0654015i
$663$		0			0
$664$	0.0787953	+	0.242507i	0.00305785	+	0.00941110i
$665$	0.177837	−	0.129206i	0.00689623	−	0.00501040i
$666$		0			0
$667$	7.68219	+	23.6434i	0.297456	+	0.915474i
$668$	−13.4966	+	41.5383i	−0.522200	+	1.60717i
$669$		0			0
$670$	−2.50269			−0.0966874
$671$	−29.8597	+	14.8884i	−1.15272	+	0.574759i
$672$		0			0
$673$	15.4576	+	11.2306i	0.595848	+	0.432909i	0.844403	−	0.535709i	$-0.179956\pi$
$673$	15.4576	+	11.2306i	0.595848	+	0.432909i	−0.248555	+	0.968618i	$0.579956\pi$
$674$	−0.477207	+	1.46869i	−0.0183813	+	0.0565719i
$675$		0			0
$676$	−18.3521	+	13.3336i	−0.705849	+	0.512830i
$677$	37.5881	−	27.3093i	1.44463	−	1.04958i	0.457578	−	0.889170i	$-0.348717\pi$
$677$	37.5881	−	27.3093i	1.44463	−	1.04958i	0.987050	−	0.160414i	$-0.0512829\pi$
$678$		0			0
$679$	4.03819	−	12.4283i	0.154971	−	0.476953i
$680$	−0.0736165	−	0.0534855i	−0.00282306	−	0.00205108i
$681$		0			0
$682$	1.23295	+	8.24860i	0.0472122	+	0.315855i
$683$	42.5651			1.62871			0.814355	−	0.580367i	$-0.197091\pi$
$683$	42.5651			1.62871			0.814355	+	0.580367i	$0.197091\pi$
$684$		0			0
$685$	2.38934	−	7.35364i	0.0912921	−	0.280968i
$686$	0.984219	+	3.02912i	0.0375777	+	0.115652i
$687$		0			0
$688$	34.3514	−	24.9577i	1.30963	−	0.951505i
$689$	0.301823	+	0.928915i	0.0114985	+	0.0353888i
$690$		0			0
$691$	−28.4249	−	20.6519i	−1.08134	−	0.785636i	−0.103420	−	0.994638i	$-0.532979\pi$
$691$	−28.4249	−	20.6519i	−1.08134	−	0.785636i	−0.977915	+	0.209001i	$0.932979\pi$
$692$	−25.2815			−0.961057
$693$		0			0
$694$	−9.05253			−0.343629
$695$	16.3312	+	11.8653i	0.619478	+	0.450077i
$696$		0			0
$697$	0.318046	+	0.978846i	0.0120469	+	0.0370764i
$698$	1.17027	−	0.850252i	0.0442954	−	0.0321825i
$699$		0			0
$700$	1.90578	+	5.86539i	0.0720317	+	0.221691i
$701$	9.47794	−	29.1701i	0.357977	−	1.10174i	−0.596286	−	0.802772i	$-0.703358\pi$
$701$	9.47794	−	29.1701i	0.357977	−	1.10174i	0.954263	−	0.298968i	$-0.0966423\pi$
$702$		0			0
$703$	0.573390			0.0216258
$704$	−14.8667	−	15.1277i	−0.560309	−	0.570148i
$705$		0			0
$706$	−6.34086	−	4.60690i	−0.238641	−	0.173383i
$707$	4.23530	−	13.0349i	0.159285	−	0.490228i
$708$		0			0
$709$	−12.2100	+	8.87107i	−0.458555	+	0.333160i	−0.792964	−	0.609268i	$-0.791463\pi$
$709$	−12.2100	+	8.87107i	−0.458555	+	0.333160i	0.334409	+	0.942428i	$0.391463\pi$
$710$	0.990066	−	0.719325i	0.0371565	−	0.0269958i
$711$		0			0
$712$	−4.64646	+	14.3003i	−0.174133	+	0.535927i
$713$	−51.6010	−	37.4903i	−1.93247	−	1.40402i
$714$		0			0
$715$	−3.66240	−	0.612790i	−0.136966	−	0.0229171i
$716$	−29.3101			−1.09537
$717$		0			0
$718$	2.91160	−	8.96099i	0.108660	−	0.334421i
$719$	1.91288	+	5.88723i	0.0713383	+	0.219557i	0.980369	−	0.197173i	$-0.0631761\pi$
$719$	1.91288	+	5.88723i	0.0713383	+	0.219557i	−0.909030	+	0.416730i	$0.863176\pi$
$720$		0			0
$721$	5.40701	−	3.92842i	0.201367	−	0.146302i
$722$	−1.54001	−	4.73968i	−0.0573134	−	0.176393i
$723$		0			0
$724$	2.20835	+	1.60446i	0.0820725	+	0.0596292i
$725$	−3.73583			−0.138745
$726$		0			0
$727$	−18.1515			−0.673200			−0.336600	−	0.941648i	$-0.609277\pi$
$727$	−18.1515			−0.673200			−0.336600	+	0.941648i	$0.609277\pi$
$728$	2.98341	+	2.16757i	0.110572	+	0.0803355i
$729$		0			0
$730$	0.580514	+	1.78664i	0.0214858	+	0.0661265i
$731$	0.843796	−	0.613054i	0.0312089	−	0.0226746i
$732$		0			0
$733$	−8.88142	−	27.3342i	−0.328043	−	1.00961i	−0.970048	−	0.242912i	$-0.921897\pi$
$733$	−8.88142	−	27.3342i	−0.328043	−	1.00961i	0.642005	−	0.766700i	$-0.278103\pi$
$734$	−0.732165	+	2.25337i	−0.0270247	+	0.0831735i
$735$		0			0
$736$	−19.9974			−0.737113
$737$	−31.2040	−	5.22103i	−1.14942	−	0.192319i
$738$		0			0
$739$	37.8896	+	27.5284i	1.39379	+	1.01265i	0.995437	+	0.0954172i	$0.0304185\pi$
$739$	37.8896	+	27.5284i	1.39379	+	1.01265i	0.398354	+	0.917232i	$0.369581\pi$
$740$	−4.97116	+	15.2997i	−0.182744	+	0.562427i
$741$		0			0
$742$	−0.591330	+	0.429626i	−0.0217084	+	0.0157721i
$743$	21.5286	−	15.6414i	0.789806	−	0.573828i	−0.118100	−	0.993002i	$-0.537680\pi$
$743$	21.5286	−	15.6414i	0.789806	−	0.573828i	0.907906	+	0.419174i	$0.137680\pi$
$744$		0			0
$745$	2.99599	−	9.22071i	0.109765	−	0.337821i
$746$	−3.65064	−	2.65235i	−0.133659	−	0.0971093i
$747$		0			0
$748$	−0.396084	−	0.403039i	−0.0144823	−	0.0147366i
$749$	−50.2691			−1.83679
$750$		0			0
$751$	12.5406	−	38.5959i	0.457612	−	1.40838i	−0.410430	−	0.911892i	$-0.634621\pi$
$751$	12.5406	−	38.5959i	0.457612	−	1.40838i	0.868041	−	0.496492i	$-0.165379\pi$
$752$	−1.00782	−	3.10175i	−0.0367514	−	0.113109i
$753$		0			0
$754$	−0.887784	+	0.645013i	−0.0323312	+	0.0234900i
$755$	−4.68515	−	14.4194i	−0.170510	−	0.524776i
$756$		0			0
$757$	−26.4693	−	19.2311i	−0.962045	−	0.698966i	−0.00841989	−	0.999965i	$-0.502680\pi$
$757$	−26.4693	−	19.2311i	−0.962045	−	0.698966i	−0.953625	+	0.300998i	$0.902680\pi$
$758$	−2.09942			−0.0762545
$759$		0			0
$760$	−0.0709926			−0.00257517
$761$	−2.12721	−	1.54551i	−0.0771113	−	0.0560246i	0.548562	−	0.836110i	$-0.315176\pi$
$761$	−2.12721	−	1.54551i	−0.0771113	−	0.0560246i	−0.625673	+	0.780085i	$0.715176\pi$
$762$		0			0
$763$	4.07838	+	12.5520i	0.147647	+	0.454412i
$764$	−7.66978	+	5.57242i	−0.277483	+	0.201603i
$765$		0			0
$766$	−2.40895	−	7.41399i	−0.0870389	−	0.267878i
$767$	0.635229	−	1.95503i	0.0229368	−	0.0705922i
$768$		0			0
$769$	3.23559			0.116678			0.0583392	−	0.998297i	$-0.481419\pi$
$769$	3.23559			0.116678			0.0583392	+	0.998297i	$0.481419\pi$
$770$	−0.410802	−	2.74831i	−0.0148043	−	0.0990422i
$771$		0			0
$772$	15.1858	+	11.0331i	0.546550	+	0.397092i
$773$	−13.4844	+	41.5008i	−0.485001	+	1.49268i	0.346979	+	0.937873i	$0.387208\pi$
$773$	−13.4844	+	41.5008i	−0.485001	+	1.49268i	−0.831980	+	0.554806i	$0.812792\pi$
$774$		0			0
$775$	7.75430	−	5.63383i	0.278543	−	0.202373i
$776$	−3.41436	+	2.48068i	−0.122569	+	0.0890512i
$777$		0			0
$778$	0.0482710	−	0.148563i	0.00173060	−	0.00532623i
$779$	0.649623	+	0.471979i	0.0232752	+	0.0169104i
$780$		0			0
$781$	13.8450	−	6.90324i	0.495412	−	0.247017i
$782$	−0.154032			−0.00550818
$783$		0			0
$784$	3.55017	−	10.9263i	0.126792	−	0.390225i
$785$	4.59834	+	14.1522i	0.164122	+	0.505114i
$786$		0			0
$787$	3.69251	−	2.68277i	0.131624	−	0.0956304i	−0.520025	−	0.854151i	$-0.674077\pi$
$787$	3.69251	−	2.68277i	0.131624	−	0.0956304i	0.651649	+	0.758521i	$0.274077\pi$
$788$	−5.30382	−	16.3235i	−0.188941	−	0.581500i
$789$		0			0
$790$	0.167965	+	0.122034i	0.00597593	+	0.00434177i
$791$	43.9270			1.56186
$792$		0			0
$793$	11.2634			0.399974
$794$	−0.354357	−	0.257455i	−0.0125757	−	0.00913675i
$795$		0			0
$796$	−10.7645	−	33.1297i	−0.381537	−	1.17425i
$797$	−9.04526	+	6.57177i	−0.320400	+	0.232784i	−0.736346	−	0.676605i	$-0.763450\pi$
$797$	−9.04526	+	6.57177i	−0.320400	+	0.232784i	0.415946	+	0.909389i	$0.363450\pi$
$798$		0			0
$799$	−0.0247558	−	0.0761905i	−0.000875797	−	0.00269543i
$800$	0.928623	−	2.85801i	0.0328318	−	0.101046i
$801$		0			0
$802$	2.98277			0.105325
$803$	3.51074	+	23.4872i	0.123891	+	0.828846i
$804$		0			0
$805$	17.1927	+	12.4912i	0.605963	+	0.440258i
$806$	0.870021	−	2.67765i	0.0306452	−	0.0943162i
$807$		0			0
$808$	−3.58102	+	2.60176i	−0.125980	+	0.0915298i
$809$	−36.8440	+	26.7687i	−1.29537	+	0.941139i	−0.999899	−	0.0142137i	$-0.995475\pi$
$809$	−36.8440	+	26.7687i	−1.29537	+	0.941139i	−0.295468	+	0.955353i	$0.595475\pi$
$810$		0			0
$811$	0.872550	−	2.68543i	0.0306394	−	0.0942983i	−0.934567	−	0.355786i	$-0.884213\pi$
$811$	0.872550	−	2.68543i	0.0306394	−	0.0942983i	0.965207	+	0.261488i	$0.0842131\pi$
$812$	18.6395	+	13.5424i	0.654120	+	0.475246i
$813$		0			0
$814$	3.34685	−	6.42959i	0.117307	−	0.225357i
$815$	−3.40114			−0.119137
$816$		0			0
$817$	0.251454	−	0.773895i	0.00879725	−	0.0270751i
$818$	−0.697043	−	2.14528i	−0.0243715	−	0.0750079i
$819$		0			0
$820$	−18.2258	+	13.2418i	−0.636473	+	0.462425i
$821$	7.23460	+	22.2658i	0.252489	+	0.777083i	0.994314	+	0.106488i	$0.0339607\pi$
$821$	7.23460	+	22.2658i	0.252489	+	0.777083i	−0.741825	+	0.670594i	$0.766039\pi$
$822$		0			0
$823$	−37.2994	−	27.0996i	−1.30018	−	0.944633i	−0.300218	−	0.953870i	$-0.597060\pi$
$823$	−37.2994	−	27.0996i	−1.30018	−	0.944633i	−0.999957	+	0.00923747i	$0.997060\pi$
$824$	−2.15848			−0.0751941
$825$		0			0
$826$	1.53833			0.0535255
$827$	−35.1515	−	25.5390i	−1.22234	−	0.888079i	−0.226044	−	0.974117i	$-0.572579\pi$
$827$	−35.1515	−	25.5390i	−1.22234	−	0.888079i	−0.996292	+	0.0860379i	$0.972579\pi$
$828$		0			0
$829$	4.78085	+	14.7139i	0.166046	+	0.511036i	0.999112	−	0.0421372i	$-0.0134167\pi$
$829$	4.78085	+	14.7139i	0.166046	+	0.511036i	−0.833066	+	0.553173i	$0.813417\pi$
$830$	−0.0524752	+	0.0381255i	−0.00182144	+	0.00132335i
$831$		0			0
$832$	2.21255	+	6.80953i	0.0767064	+	0.236078i
$833$	0.0872053	−	0.268390i	0.00302149	−	0.00929918i
$834$		0			0
$835$	−22.6164			−0.782671
$836$	−0.434825	−	0.0727546i	−0.0150387	−	0.00251627i
$837$		0			0
$838$	6.66296	+	4.84093i	0.230168	+	0.167227i
$839$	−9.33790	+	28.7391i	−0.322380	+	0.992184i	0.650229	+	0.759738i	$0.274673\pi$
$839$	−9.33790	+	28.7391i	−0.322380	+	0.992184i	−0.972609	+	0.232446i	$0.925327\pi$
$840$		0			0
$841$	12.1705	−	8.84239i	0.419673	−	0.304910i
$842$	0.971894	−	0.706122i	0.0334937	−	0.0243346i
$843$		0			0
$844$	−10.7285	+	33.0189i	−0.369290	+	1.13656i
$845$	−9.50310	−	6.90441i	−0.326917	−	0.237519i
$846$		0			0
$847$	0.611482	−	35.1235i	0.0210108	−	1.20686i
$848$	−3.13335			−0.107600
$849$		0			0
$850$	0.00715284	−	0.0220142i	0.000245340	−	0.000755080i
$851$	17.1299	+	52.7203i	0.587204	+	1.80723i
$852$		0			0
$853$	1.62538	−	1.18091i	0.0556521	−	0.0404336i	−0.559611	−	0.828755i	$-0.689050\pi$
$853$	1.62538	−	1.18091i	0.0556521	−	0.0404336i	0.615263	+	0.788322i	$0.289050\pi$
$854$	2.60467	+	8.01636i	0.0891301	+	0.274314i
$855$		0			0
$856$	13.1343	+	9.54262i	0.448921	+	0.326160i
$857$	33.6095			1.14808			0.574039	−	0.818828i	$-0.305376\pi$
$857$	33.6095			1.14808			0.574039	+	0.818828i	$0.305376\pi$
$858$		0			0
$859$	−13.7301			−0.468466			−0.234233	−	0.972180i	$-0.575258\pi$
$859$	−13.7301			−0.468466			−0.234233	+	0.972180i	$0.575258\pi$
$860$	18.4697	+	13.4190i	0.629810	+	0.457584i
$861$		0			0
$862$	−1.28967	−	3.96920i	−0.0439264	−	0.135192i
$863$	7.08560	−	5.14799i	0.241197	−	0.175240i	−0.460620	−	0.887598i	$-0.652373\pi$
$863$	7.08560	−	5.14799i	0.241197	−	0.175240i	0.701816	+	0.712358i	$0.252373\pi$
$864$		0			0
$865$	−4.04543	−	12.4506i	−0.137549	−	0.423332i
$866$	1.28120	−	3.94314i	0.0435370	−	0.133993i
$867$		0			0
$868$	−59.1120			−2.00639
$869$	1.83964	+	1.87194i	0.0624055	+	0.0635014i
$870$		0			0
$871$	8.64038	+	6.27761i	0.292768	+	0.212709i
$872$	1.31715	−	4.05378i	0.0446044	−	0.137278i
$873$		0			0
$874$	−0.0972220	+	0.0706359i	−0.00328858	+	0.00238930i
$875$	−2.58362	+	1.87711i	−0.0873422	+	0.0634578i
$876$		0			0
$877$	−4.71136	+	14.5001i	−0.159091	+	0.489633i	−0.998552	−	0.0537871i	$-0.982871\pi$
$877$	−4.71136	+	14.5001i	−0.159091	+	0.489633i	0.839461	+	0.543420i	$0.182871\pi$
$878$	−4.56827	−	3.31904i	−0.154172	−	0.112012i
$879$		0			0
$880$	5.50032	−	10.5666i	0.185416	−	0.356200i
$881$	15.8486			0.533953			0.266977	−	0.963703i	$-0.413975\pi$
$881$	15.8486			0.533953			0.266977	+	0.963703i	$0.413975\pi$
$882$		0			0
$883$	−10.1854	+	31.3474i	−0.342765	+	1.05492i	0.620004	+	0.784598i	$0.287131\pi$
$883$	−10.1854	+	31.3474i	−0.342765	+	1.05492i	−0.962769	+	0.270324i	$0.912869\pi$
$884$	0.0589476	+	0.181422i	0.00198262	+	0.00610189i
$885$		0			0
$886$	2.16008	−	1.56939i	0.0725694	−	0.0527247i
$887$	−3.47720	−	10.7017i	−0.116753	−	0.359328i	0.875556	−	0.483117i	$-0.160495\pi$
$887$	−3.47720	−	10.7017i	−0.116753	−	0.359328i	−0.992309	+	0.123789i	$0.960495\pi$
$888$		0			0
$889$	20.4100	+	14.8288i	0.684530	+	0.497340i
$890$	−3.82488			−0.128210
$891$		0			0
$892$	26.5515			0.889010
$893$	−0.0505647	−	0.0367374i	−0.00169208	−	0.00122937i
$894$		0			0
$895$	−4.69008	−	14.4346i	−0.156772	−	0.482495i
$896$	−19.8628	+	14.4312i	−0.663570	+	0.482112i
$897$		0			0
$898$	−3.13015	−	9.63362i	−0.104455	−	0.321478i
$899$	11.0651	−	34.0548i	0.369041	−	1.13579i
$900$		0			0
$901$	−0.0769667			−0.00256413
$902$	9.08425	−	4.52950i	0.302472	−	0.150816i
$903$		0			0
$904$	−11.4772	−	8.33870i	−0.381727	−	0.277341i
$905$	−0.436789	+	1.34430i	−0.0145194	+	0.0446860i
$906$		0			0
$907$	20.5284	−	14.9147i	0.681634	−	0.495236i	−0.192266	−	0.981343i	$-0.561583\pi$
$907$	20.5284	−	14.9147i	0.681634	−	0.495236i	0.873899	+	0.486107i	$0.161583\pi$
$908$	−1.03542	+	0.752278i	−0.0343617	+	0.0249652i
$909$		0			0
$910$	−0.289878	+	0.892153i	−0.00960937	+	0.0295746i
$911$	−14.0825	−	10.2316i	−0.466575	−	0.338986i	0.329530	−	0.944145i	$-0.393110\pi$
$911$	−14.0825	−	10.2316i	−0.466575	−	0.338986i	−0.796105	+	0.605159i	$0.793110\pi$
$912$		0			0
$913$	−0.733807	+	0.365884i	−0.0242855	+	0.0121090i
$914$	6.12971			0.202753
$915$		0			0
$916$	4.47000	−	13.7573i	0.147693	−	0.454553i
$917$	−16.1389	−	49.6704i	−0.532953	−	1.64026i
$918$		0			0
$919$	26.6133	−	19.3357i	0.877890	−	0.637825i	−0.0548022	−	0.998497i	$-0.517453\pi$
$919$	26.6133	−	19.3357i	0.877890	−	0.637825i	0.932692	+	0.360673i	$0.117453\pi$
$920$	−2.12088	−	6.52740i	−0.0699234	−	0.215202i
$921$		0			0
$922$	1.04666	+	0.760446i	0.0344701	+	0.0250440i
$923$	−5.22245			−0.171899
$924$		0			0
$925$	−8.33021			−0.273896
$926$	−5.72337	−	4.15827i	−0.188082	−	0.136649i
$927$		0			0
$928$	−3.46918	−	10.6770i	−0.113881	−	0.350491i
$929$	26.9509	−	19.5810i	0.884230	−	0.642431i	−0.0501368	−	0.998742i	$-0.515966\pi$
$929$	26.9509	−	19.5810i	0.884230	−	0.642431i	0.934367	+	0.356311i	$0.115966\pi$
$930$		0			0
$931$	−0.0680360	−	0.209393i	−0.00222979	−	0.00686258i
$932$	6.28115	−	19.3314i	0.205746	−	0.633221i
$933$		0			0
$934$	6.21211			0.203266
$935$	0.135108	−	0.259555i	0.00441851	−	0.00848835i
$936$		0			0
$937$	19.3061	+	14.0267i	0.630704	+	0.458233i	0.856644	−	0.515908i	$-0.172545\pi$
$937$	19.3061	+	14.0267i	0.630704	+	0.458233i	−0.225940	+	0.974141i	$0.572545\pi$
$938$	−2.46979	+	7.60123i	−0.0806415	+	0.248189i
$939$		0			0
$940$	1.41864	−	1.03070i	0.0462710	−	0.0336179i
$941$	−6.41192	+	4.65853i	−0.209023	+	0.151864i	−0.687371	−	0.726306i	$-0.741235\pi$
$941$	−6.41192	+	4.65853i	−0.209023	+	0.151864i	0.478349	+	0.878170i	$0.341235\pi$
$942$		0			0
$943$	−23.9887	+	73.8297i	−0.781181	+	2.40423i
$944$	5.33514	+	3.87620i	0.173644	+	0.126160i
$945$		0			0
$946$	−7.21019	−	7.33681i	−0.234423	−	0.238540i
$947$	2.15429			0.0700050			0.0350025	−	0.999387i	$-0.488856\pi$
$947$	2.15429			0.0700050			0.0350025	+	0.999387i	$0.488856\pi$
$948$		0			0
$949$	2.47731	−	7.62439i	0.0804170	−	0.247498i
$950$	−0.00558051	−	0.0171750i	−0.000181056	−	0.000557232i
$951$		0			0
$952$	−0.235096	+	0.170807i	−0.00761951	+	0.00553590i
$953$	1.85195	+	5.69971i	0.0599904	+	0.184632i	0.976561	−	0.215242i	$-0.0690540\pi$
$953$	1.85195	+	5.69971i	0.0599904	+	0.184632i	−0.916570	+	0.399874i	$0.869054\pi$
$954$		0			0
$955$	−3.97158	−	2.88552i	−0.128517	−	0.0933732i
$956$	32.9770			1.06655
$957$		0			0
$958$	3.54816			0.114636
$959$	−19.9767	−	14.5139i	−0.645082	−	0.468680i
$960$		0			0
$961$	18.8096	+	57.8901i	0.606762	+	1.86742i
$962$	−1.97959	+	1.43826i	−0.0638246	+	0.0463713i
$963$		0			0
$964$	9.97085	+	30.6871i	0.321139	+	0.988365i
$965$	−3.00361	+	9.24415i	−0.0966895	+	0.297580i
$966$		0			0
$967$	22.2784			0.716424			0.358212	−	0.933640i	$-0.383387\pi$
$967$	22.2784			0.716424			0.358212	+	0.933640i	$0.383387\pi$
$968$	−6.82729	+	9.06097i	−0.219437	+	0.291231i
$969$		0			0
$970$	−0.868537	−	0.631029i	−0.0278870	−	0.0202611i
$971$	11.3381	−	34.8952i	0.363858	−	1.11984i	−0.586835	−	0.809706i	$-0.699626\pi$
$971$	11.3381	−	34.8952i	0.363858	−	1.11984i	0.950693	−	0.310133i	$-0.100374\pi$
$972$		0			0
$973$	52.1541	−	37.8922i	1.67198	−	1.21477i
$974$	1.83112	−	1.33039i	0.0586728	−	0.0426283i
$975$		0			0
$976$	−11.1658	+	34.3649i	−0.357409	+	1.09999i
$977$	22.5751	+	16.4018i	0.722242	+	0.524739i	0.887100	−	0.461578i	$-0.152717\pi$
$977$	22.5751	+	16.4018i	0.722242	+	0.524739i	−0.164858	+	0.986317i	$0.552717\pi$
$978$		0			0
$979$	−47.6894	−	7.97935i	−1.52416	−	0.255021i
$980$	6.17706			0.197319
$981$		0			0
$982$	2.10036	−	6.46424i	0.0670252	−	0.206282i
$983$	−3.02596	−	9.31294i	−0.0965130	−	0.297037i	0.891132	−	0.453744i	$-0.149912\pi$
$983$	−3.02596	−	9.31294i	−0.0965130	−	0.297037i	−0.987645	+	0.156708i	$0.949912\pi$
$984$		0			0
$985$	7.19025	−	5.22402i	0.229101	−	0.166451i
$986$	−0.0267218	−	0.0822412i	−0.000850995	−	0.00261909i
$987$		0			0
$988$	0.120403	+	0.0874779i	0.00383053	+	0.00278304i
$989$	78.6678			2.50149
$990$		0			0
$991$	34.9794			1.11116			0.555578	−	0.831464i	$-0.312497\pi$
$991$	34.9794			1.11116			0.555578	+	0.831464i	$0.312497\pi$
$992$	23.3024	+	16.9302i	0.739851	+	0.537533i
$993$		0			0
$994$	−1.20770	−	3.71692i	−0.0383059	−	0.117894i
$995$	14.5931	−	10.6025i	0.462633	−	0.336123i
$996$		0			0
$997$	−3.94779	−	12.1501i	−0.125028	−	0.384796i	0.868878	−	0.495026i	$-0.164841\pi$
$997$	−3.94779	−	12.1501i	−0.125028	−	0.384796i	−0.993906	+	0.110230i	$0.964841\pi$
$998$	−2.27392	+	6.99839i	−0.0719795	+	0.221530i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.n.a.136.2		8
3.2	odd	2		165.2.m.d.136.1	yes	8
11.3	even	5	inner	495.2.n.a.91.2		8
11.5	even	5		5445.2.a.bt.1.2		4
11.6	odd	10		5445.2.a.bf.1.3		4
15.2	even	4		825.2.bx.f.499.2		16
15.8	even	4		825.2.bx.f.499.3		16
15.14	odd	2		825.2.n.g.301.2		8
33.5	odd	10		1815.2.a.p.1.3		4
33.14	odd	10		165.2.m.d.91.1	✓	8
33.17	even	10		1815.2.a.w.1.2		4
165.14	odd	10		825.2.n.g.751.2		8
165.47	even	20		825.2.bx.f.124.3		16
165.104	odd	10		9075.2.a.di.1.2		4
165.113	even	20		825.2.bx.f.124.2		16
165.149	even	10		9075.2.a.cm.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.d.91.1	✓	8	33.14	odd	10
165.2.m.d.136.1	yes	8	3.2	odd	2
495.2.n.a.91.2		8	11.3	even	5	inner
495.2.n.a.136.2		8	1.1	even	1	trivial
825.2.n.g.301.2		8	15.14	odd	2
825.2.n.g.751.2		8	165.14	odd	10
825.2.bx.f.124.2		16	165.113	even	20
825.2.bx.f.124.3		16	165.47	even	20
825.2.bx.f.499.2		16	15.2	even	4
825.2.bx.f.499.3		16	15.8	even	4
1815.2.a.p.1.3		4	33.5	odd	10
1815.2.a.w.1.2		4	33.17	even	10
5445.2.a.bf.1.3		4	11.6	odd	10
5445.2.a.bt.1.2		4	11.5	even	5
9075.2.a.cm.1.3		4	165.149	even	10
9075.2.a.di.1.2		4	165.104	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.212253 - 0.154211i) q^{2} +(-0.596764 - 1.83665i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-0.986854 - 3.03722i) q^{7} +(-0.318714 + 0.980901i) q^{8} +O(q^{10})\)	\(q+(-0.212253 - 0.154211i) q^{2} +(-0.596764 - 1.83665i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-0.986854 - 3.03722i) q^{7} +(-0.318714 + 0.980901i) q^{8} -0.262360 q^{10} +(-3.27115 - 0.547326i) q^{11} +(0.905781 + 0.658088i) q^{13} +(-0.258911 + 0.796845i) q^{14} +(-2.90578 + 2.11117i) q^{16} +(-0.0713767 + 0.0518582i) q^{17} +(-0.0212704 + 0.0654637i) q^{19} +(-1.56235 - 1.13511i) q^{20} +(0.609909 + 0.620620i) q^{22} -6.65450 q^{23} +(0.309017 - 0.951057i) q^{25} +(-0.0907705 - 0.279363i) q^{26} +(-4.98940 + 3.62501i) q^{28} +(-1.15444 - 3.55299i) q^{29} +(7.75430 + 5.63383i) q^{31} +3.00509 q^{32} +0.0231471 q^{34} +(-2.58362 - 1.87711i) q^{35} +(-2.57418 - 7.92250i) q^{37} +(0.0146100 - 0.0106148i) q^{38} +(0.318714 + 0.980901i) q^{40} +(3.60489 - 11.0947i) q^{41} -11.8217 q^{43} +(0.946857 + 6.33458i) q^{44} +(1.41244 + 1.02620i) q^{46} +(-0.280594 + 0.863579i) q^{47} +(-2.58773 + 1.88010i) q^{49} +(-0.212253 + 0.154211i) q^{50} +(0.668140 - 2.05632i) q^{52} +(0.705768 + 0.512771i) q^{53} +(-2.96813 + 1.47994i) q^{55} +3.29374 q^{56} +(-0.302877 + 0.932160i) q^{58} +(-0.567369 - 1.74618i) q^{59} +(8.13881 - 5.91319i) q^{61} +(-0.777078 - 2.39160i) q^{62} +(5.17372 + 3.75893i) q^{64} +1.11961 q^{65} +9.53916 q^{67} +(0.137840 + 0.100147i) q^{68} +(0.258911 + 0.796845i) q^{70} +(-3.77370 + 2.74175i) q^{71} +(-2.21267 - 6.80989i) q^{73} +(-0.675360 + 2.07854i) q^{74} +0.132927 q^{76} +(1.56580 + 10.4754i) q^{77} +(-0.640209 - 0.465139i) q^{79} +(-1.10991 + 3.41595i) q^{80} +(-2.47608 + 1.79898i) q^{82} +(0.200012 - 0.145318i) q^{83} +(-0.0272635 + 0.0839083i) q^{85} +(2.50920 + 1.82304i) q^{86} +(1.57943 - 3.03423i) q^{88} +14.5788 q^{89} +(1.10489 - 3.40050i) q^{91} +(3.97116 + 12.2220i) q^{92} +(0.192730 - 0.140027i) q^{94} +(0.0212704 + 0.0654637i) q^{95} +(3.31048 + 2.40521i) q^{97} +0.839188 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 2 q^{4} + 2 q^{5} + 3 q^{7} + q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 + 2 * q^4 + 2 * q^5 + 3 * q^7 + q^8	\( 8 q - 4 q^{2} + 2 q^{4} + 2 q^{5} + 3 q^{7} + q^{8} - 6 q^{10} - 3 q^{11} - 4 q^{13} + 4 q^{14} - 12 q^{16} + 2 q^{19} + 3 q^{20} + 9 q^{22} + 6 q^{23} - 2 q^{25} - 2 q^{26} - 11 q^{28} - 10 q^{29} + 19 q^{31} - 12 q^{32} - 6 q^{34} - 3 q^{35} - q^{37} + 20 q^{38} - q^{40} + 9 q^{41} - 17 q^{44} - 22 q^{46} + 19 q^{47} + q^{49} - 4 q^{50} - 2 q^{52} - 25 q^{53} + 3 q^{55} + 16 q^{56} - 12 q^{58} - 13 q^{59} + 13 q^{61} - 35 q^{62} + 39 q^{64} + 14 q^{65} + 2 q^{67} - 19 q^{68} - 4 q^{70} + 11 q^{71} - 7 q^{73} + 43 q^{74} - 38 q^{76} + 7 q^{77} - 22 q^{79} - 13 q^{80} - 35 q^{82} + 21 q^{83} + 10 q^{85} - 20 q^{86} + 59 q^{88} + 20 q^{89} - 11 q^{91} + 28 q^{92} - 35 q^{94} - 2 q^{95} + 31 q^{97} - 22 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 + 2 * q^4 + 2 * q^5 + 3 * q^7 + q^8 - 6 * q^10 - 3 * q^11 - 4 * q^13 + 4 * q^14 - 12 * q^16 + 2 * q^19 + 3 * q^20 + 9 * q^22 + 6 * q^23 - 2 * q^25 - 2 * q^26 - 11 * q^28 - 10 * q^29 + 19 * q^31 - 12 * q^32 - 6 * q^34 - 3 * q^35 - q^37 + 20 * q^38 - q^40 + 9 * q^41 - 17 * q^44 - 22 * q^46 + 19 * q^47 + q^49 - 4 * q^50 - 2 * q^52 - 25 * q^53 + 3 * q^55 + 16 * q^56 - 12 * q^58 - 13 * q^59 + 13 * q^61 - 35 * q^62 + 39 * q^64 + 14 * q^65 + 2 * q^67 - 19 * q^68 - 4 * q^70 + 11 * q^71 - 7 * q^73 + 43 * q^74 - 38 * q^76 + 7 * q^77 - 22 * q^79 - 13 * q^80 - 35 * q^82 + 21 * q^83 + 10 * q^85 - 20 * q^86 + 59 * q^88 + 20 * q^89 - 11 * q^91 + 28 * q^92 - 35 * q^94 - 2 * q^95 + 31 * q^97 - 22 * q^98

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