LMFDB - Embedded newform 495.2.n.e.181.1

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			181.1
Root			$-0.386111 - 0.280526i$ of defining polynomial
Character	$\chi$	$=$	495.181
Dual form			495.2.n.e.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.147481 - 0.453901i) q^{2} +(1.43376 - 1.04169i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-2.17239 + 1.57833i) q^{7} +(-1.45650 - 1.05821i) q^{8} +O(q^{10})$	\(q+(-0.147481 - 0.453901i) q^{2} +(1.43376 - 1.04169i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-2.17239 + 1.57833i) q^{7} +(-1.45650 - 1.05821i) q^{8} -0.477260 q^{10} +(2.79042 - 1.79264i) q^{11} +(-1.44244 - 4.43939i) q^{13} +(1.03679 + 0.753275i) q^{14} +(0.829779 - 2.55380i) q^{16} +(1.42961 - 4.39990i) q^{17} +(3.51149 + 2.55125i) q^{19} +(-0.547647 - 1.68548i) q^{20} +(-1.22522 - 1.00220i) q^{22} -2.77222 q^{23} +(-0.809017 - 0.587785i) q^{25} +(-1.80231 + 1.30945i) q^{26} +(-1.47055 + 4.52590i) q^{28} +(-2.43790 + 1.77124i) q^{29} +(0.737407 + 2.26951i) q^{31} -4.88221 q^{32} -2.20796 q^{34} +(0.829779 + 2.55380i) q^{35} +(8.61029 - 6.25574i) q^{37} +(0.640135 - 1.97013i) q^{38} +(-1.45650 + 1.05821i) q^{40} +(-1.78826 - 1.29924i) q^{41} -7.06719 q^{43} +(2.13343 - 5.47695i) q^{44} +(0.408851 + 1.25832i) q^{46} +(3.52905 + 2.56401i) q^{47} +(0.0650188 - 0.200107i) q^{49} +(-0.147481 + 0.453901i) q^{50} +(-6.69257 - 4.86243i) q^{52} +(1.95733 + 6.02403i) q^{53} +(-0.842610 - 3.20780i) q^{55} +4.83428 q^{56} +(1.16351 + 0.845342i) q^{58} +(9.50375 - 6.90488i) q^{59} +(-1.23070 + 3.78770i) q^{61} +(0.921378 - 0.669420i) q^{62} +(-0.939522 - 2.89155i) q^{64} -4.66785 q^{65} +7.31984 q^{67} +(-2.53359 - 7.79760i) q^{68} +(1.03679 - 0.753275i) q^{70} +(-0.369495 + 1.13719i) q^{71} +(-0.826577 + 0.600544i) q^{73} +(-4.10935 - 2.98562i) q^{74} +7.69223 q^{76} +(-3.23251 + 8.29852i) q^{77} +(1.08222 + 3.33073i) q^{79} +(-2.17239 - 1.57833i) q^{80} +(-0.325994 + 1.00331i) q^{82} +(-3.43498 + 10.5718i) q^{83} +(-3.74278 - 2.71929i) q^{85} +(1.04228 + 3.20780i) q^{86} +(-5.96123 - 0.341876i) q^{88} -2.76978 q^{89} +(10.1404 + 7.36742i) q^{91} +(-3.97470 + 2.88779i) q^{92} +(0.643336 - 1.97998i) q^{94} +(3.51149 - 2.55125i) q^{95} +(5.72738 + 17.6271i) q^{97} -0.100418 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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 $

$2$	−0.147481	−	0.453901i	−0.104285	−	0.320957i	0.885277	−	0.465064i	$-0.153969\pi$
$2$	−0.147481	−	0.453901i	−0.104285	−	0.320957i	−0.989562	+	0.144108i	$0.953969\pi$
$3$		0			0
$3$		0			0
$4$	1.43376	−	1.04169i	0.716879	−	0.520843i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$6$		0			0
$7$	−2.17239	+	1.57833i	−0.821086	+	0.596554i	−0.917023	−	0.398834i	$-0.869415\pi$
$7$	−2.17239	+	1.57833i	−0.821086	+	0.596554i	0.0959376	+	0.995387i	$0.469415\pi$
$8$	−1.45650	−	1.05821i	−0.514950	−	0.374133i
$9$		0			0
$10$	−0.477260			−0.150923
$11$	2.79042	−	1.79264i	0.841344	−	0.540500i
$11$	2.79042	−	1.79264i	0.841344	−	0.540500i
$12$		0			0
$13$	−1.44244	−	4.43939i	−0.400062	−	1.23126i	−0.924949	−	0.380092i	$-0.875892\pi$
$13$	−1.44244	−	4.43939i	−0.400062	−	1.23126i	0.524886	−	0.851172i	$-0.324108\pi$
$14$	1.03679	+	0.753275i	0.277095	+	0.201321i
$15$		0			0
$16$	0.829779	−	2.55380i	0.207445	−	0.638449i
$17$	1.42961	−	4.39990i	0.346732	−	1.06713i	−0.613918	−	0.789370i	$-0.710407\pi$
$17$	1.42961	−	4.39990i	0.346732	−	1.06713i	0.960650	−	0.277762i	$-0.0895926\pi$
$18$		0			0
$19$	3.51149	+	2.55125i	0.805592	+	0.585297i	0.912549	−	0.408967i	$-0.134111\pi$
$19$	3.51149	+	2.55125i	0.805592	+	0.585297i	−0.106958	+	0.994264i	$0.534111\pi$
$20$	−0.547647	−	1.68548i	−0.122458	−	0.376886i
$21$		0			0
$22$	−1.22522	−	1.00220i	−0.261217	−	0.213669i
$23$	−2.77222			−0.578048			−0.289024	−	0.957322i	$-0.593331\pi$
$23$	−2.77222			−0.578048			−0.289024	+	0.957322i	$0.593331\pi$
$24$		0			0
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	−1.80231	+	1.30945i	−0.353462	+	0.256805i
$27$		0			0
$28$	−1.47055	+	4.52590i	−0.277908	+	0.855314i
$29$	−2.43790	+	1.77124i	−0.452707	+	0.328911i	−0.790664	−	0.612251i	$-0.790264\pi$
$29$	−2.43790	+	1.77124i	−0.452707	+	0.328911i	0.337956	+	0.941162i	$0.390264\pi$
$30$		0			0
$31$	0.737407	+	2.26951i	0.132442	+	0.407615i	0.995183	−	0.0980305i	$-0.0312543\pi$
$31$	0.737407	+	2.26951i	0.132442	+	0.407615i	−0.862741	+	0.505646i	$0.831254\pi$
$32$	−4.88221			−0.863061
$33$		0			0
$34$	−2.20796			−0.378662
$35$	0.829779	+	2.55380i	0.140258	+	0.431670i
$36$		0			0
$37$	8.61029	−	6.25574i	1.41552	−	1.02844i	0.423033	−	0.906114i	$-0.360965\pi$
$37$	8.61029	−	6.25574i	1.41552	−	1.02844i	0.992490	−	0.122324i	$-0.0390346\pi$
$38$	0.640135	−	1.97013i	0.103844	−	0.319598i
$39$		0			0
$40$	−1.45650	+	1.05821i	−0.230293	+	0.167317i
$41$	−1.78826	−	1.29924i	−0.279279	−	0.202908i	0.439324	−	0.898329i	$-0.355218\pi$
$41$	−1.78826	−	1.29924i	−0.279279	−	0.202908i	−0.718603	+	0.695421i	$0.755218\pi$
$42$		0			0
$43$	−7.06719			−1.07774			−0.538868	−	0.842390i	$-0.681148\pi$
$43$	−7.06719			−1.07774			−0.538868	+	0.842390i	$0.681148\pi$
$44$	2.13343	−	5.47695i	0.321626	−	0.825682i
$45$		0			0
$46$	0.408851	+	1.25832i	0.0602819	+	0.185528i
$47$	3.52905	+	2.56401i	0.514765	+	0.373999i	0.814628	−	0.579983i	$-0.196941\pi$
$47$	3.52905	+	2.56401i	0.514765	+	0.373999i	−0.299863	+	0.953982i	$0.596941\pi$
$48$		0			0
$49$	0.0650188	−	0.200107i	0.00928840	−	0.0285868i
$50$	−0.147481	+	0.453901i	−0.0208570	+	0.0641913i
$51$		0			0
$52$	−6.69257	−	4.86243i	−0.928092	−	0.674298i
$53$	1.95733	+	6.02403i	0.268859	+	0.827464i	0.990779	+	0.135487i	$0.0432600\pi$
$53$	1.95733	+	6.02403i	0.268859	+	0.827464i	−0.721920	+	0.691977i	$0.756740\pi$
$54$		0			0
$55$	−0.842610	−	3.20780i	−0.113617	−	0.432540i
$56$	4.83428			0.646008
$57$		0			0
$58$	1.16351	+	0.845342i	0.152777	+	0.110999i
$59$	9.50375	−	6.90488i	1.23728	−	0.898939i	0.239869	−	0.970805i	$-0.422896\pi$
$59$	9.50375	−	6.90488i	1.23728	−	0.898939i	0.997414	+	0.0718667i	$0.0228956\pi$
$60$		0			0
$61$	−1.23070	+	3.78770i	−0.157575	+	0.484966i	−0.998413	−	0.0563214i	$-0.982063\pi$
$61$	−1.23070	+	3.78770i	−0.157575	+	0.484966i	0.840838	+	0.541287i	$0.182063\pi$
$62$	0.921378	−	0.669420i	0.117015	−	0.0850164i
$63$		0			0
$64$	−0.939522	−	2.89155i	−0.117440	−	0.361444i
$65$	−4.66785			−0.578975
$66$		0			0
$67$	7.31984			0.894260			0.447130	−	0.894469i	$-0.352446\pi$
$67$	7.31984			0.894260			0.447130	+	0.894469i	$0.352446\pi$
$68$	−2.53359	−	7.79760i	−0.307243	−	0.945598i
$69$		0			0
$70$	1.03679	−	0.753275i	0.123921	−	0.0900336i
$71$	−0.369495	+	1.13719i	−0.0438510	+	0.134960i	−0.970585	−	0.240758i	$-0.922604\pi$
$71$	−0.369495	+	1.13719i	−0.0438510	+	0.134960i	0.926734	+	0.375718i	$0.122604\pi$
$72$		0			0
$73$	−0.826577	+	0.600544i	−0.0967436	+	0.0702883i	−0.635105	−	0.772425i	$-0.719043\pi$
$73$	−0.826577	+	0.600544i	−0.0967436	+	0.0702883i	0.538362	+	0.842714i	$0.319043\pi$
$74$	−4.10935	−	2.98562i	−0.477702	−	0.347071i
$75$		0			0
$76$	7.69223			0.882360
$77$	−3.23251	+	8.29852i	−0.368378	+	0.945704i
$78$		0			0
$79$	1.08222	+	3.33073i	0.121759	+	0.374736i	0.993297	−	0.115593i	$-0.0368767\pi$
$79$	1.08222	+	3.33073i	0.121759	+	0.374736i	−0.871538	+	0.490329i	$0.836877\pi$
$80$	−2.17239	−	1.57833i	−0.242880	−	0.176463i
$81$		0			0
$82$	−0.325994	+	1.00331i	−0.0360000	+	0.110797i
$83$	−3.43498	+	10.5718i	−0.377038	+	1.16040i	0.565055	+	0.825053i	$0.308855\pi$
$83$	−3.43498	+	10.5718i	−0.377038	+	1.16040i	−0.942093	+	0.335351i	$0.891145\pi$
$84$		0			0
$85$	−3.74278	−	2.71929i	−0.405961	−	0.294948i
$86$	1.04228	+	3.20780i	0.112392	+	0.345906i
$87$		0			0
$88$	−5.96123	−	0.341876i	−0.635469	−	0.0364442i
$89$	−2.76978			−0.293596			−0.146798	−	0.989167i	$-0.546897\pi$
$89$	−2.76978			−0.293596			−0.146798	+	0.989167i	$0.546897\pi$
$90$		0			0
$91$	10.1404	+	7.36742i	1.06300	+	0.772315i
$92$	−3.97470	+	2.88779i	−0.414391	+	0.301073i
$93$		0			0
$94$	0.643336	−	1.97998i	0.0663550	−	0.204220i
$95$	3.51149	−	2.55125i	0.360271	−	0.261753i
$96$		0			0
$97$	5.72738	+	17.6271i	0.581528	+	1.78976i	0.612789	+	0.790247i	$0.290048\pi$
$97$	5.72738	+	17.6271i	0.581528	+	1.78976i	−0.0312615	+	0.999511i	$0.509952\pi$
$98$	−0.100418			−0.0101438
$99$		0			0
$100$	−1.77222			−0.177222
$101$	2.19852	+	6.76634i	0.218761	+	0.673276i	0.998865	+	0.0476270i	$0.0151659\pi$
$101$	2.19852	+	6.76634i	0.218761	+	0.673276i	−0.780104	+	0.625649i	$0.784834\pi$
$102$		0			0
$103$	−6.09056	+	4.42505i	−0.600121	+	0.436014i	−0.845922	−	0.533307i	$-0.820949\pi$
$103$	−6.09056	+	4.42505i	−0.600121	+	0.436014i	0.245801	+	0.969320i	$0.420949\pi$
$104$	−2.59688	+	7.99237i	−0.254645	+	0.783716i
$105$		0			0
$106$	2.44565	−	1.77687i	0.237542	−	0.172584i
$107$	14.5859	+	10.5973i	1.41008	+	1.02448i	0.993312	+	0.115465i	$0.0368358\pi$
$107$	14.5859	+	10.5973i	1.41008	+	1.02448i	0.416764	+	0.909015i	$0.363164\pi$
$108$		0			0
$109$	−16.3653			−1.56751			−0.783756	−	0.621068i	$-0.786699\pi$
$109$	−16.3653			−1.56751			−0.783756	+	0.621068i	$0.786699\pi$
$110$	−1.33176	+	0.855553i	−0.126978	+	0.0815738i
$111$		0			0
$112$	2.22814	+	6.85750i	0.210539	+	0.647973i
$113$	−1.66154	−	1.20718i	−0.156304	−	0.113562i	0.506884	−	0.862014i	$-0.330797\pi$
$113$	−1.66154	−	1.20718i	−0.156304	−	0.113562i	−0.663188	+	0.748453i	$0.730797\pi$
$114$		0			0
$115$	−0.856664	+	2.63654i	−0.0798843	+	0.245859i
$116$	−1.65029	+	5.07906i	−0.153225	+	0.471579i
$117$		0			0
$118$	−4.53576	−	3.29542i	−0.417551	−	0.303368i
$119$	3.83883	+	11.8147i	0.351905	+	1.08305i
$120$		0			0
$121$	4.57291	−	10.0044i	0.415720	−	0.909493i
$122$	1.90075			0.172086
$123$		0			0
$124$	3.42138	+	2.48578i	0.307249	+	0.223229i
$125$	−0.809017	+	0.587785i	−0.0723607	+	0.0525731i
$126$		0			0
$127$	−0.0235677	+	0.0725340i	−0.00209130	+	0.00643635i	−0.952097	−	0.305797i	$-0.901077\pi$
$127$	−0.0235677	+	0.0725340i	−0.00209130	+	0.00643635i	0.950005	+	0.312233i	$0.101077\pi$
$128$	−9.07350	+	6.59228i	−0.801992	+	0.582681i
$129$		0			0
$130$	0.688421	+	2.11874i	0.0603785	+	0.185826i
$131$	11.4831			1.00328			0.501642	−	0.865075i	$-0.332730\pi$
$131$	11.4831			1.00328			0.501642	+	0.865075i	$0.332730\pi$
$132$		0			0
$133$	−11.6550			−1.01062
$134$	−1.07954	−	3.32248i	−0.0932580	−	0.287019i
$135$		0			0
$136$	−6.73823	+	4.89561i	−0.577799	+	0.419795i
$137$	5.66406	−	17.4322i	0.483914	−	1.48933i	−0.349635	−	0.936886i	$-0.613694\pi$
$137$	5.66406	−	17.4322i	0.483914	−	1.48933i	0.833548	−	0.552447i	$-0.186306\pi$
$138$		0			0
$139$	18.7590	−	13.6292i	1.59111	−	1.15601i	0.688785	−	0.724966i	$-0.258145\pi$
$139$	18.7590	−	13.6292i	1.59111	−	1.15601i	0.902330	−	0.431046i	$-0.141855\pi$
$140$	3.84996	+	2.79716i	0.325381	+	0.236403i
$141$		0			0
$142$	0.570666			0.0478892
$143$	−11.9832	−	9.80199i	−1.00209	−	0.819683i
$144$		0			0
$145$	0.931196	+	2.86593i	0.0773317	+	0.238002i
$146$	0.394492	+	0.286615i	0.0326484	+	0.0237205i
$147$		0			0
$148$	5.82856	−	17.9385i	0.479104	−	1.47453i
$149$	−4.53161	+	13.9469i	−0.371244	+	1.14257i	0.574733	+	0.818341i	$0.305106\pi$
$149$	−4.53161	+	13.9469i	−0.371244	+	1.14257i	−0.945978	+	0.324232i	$0.894894\pi$
$150$		0			0
$151$	6.08301	+	4.41957i	0.495028	+	0.359659i	0.807115	−	0.590394i	$-0.201028\pi$
$151$	6.08301	+	4.41957i	0.495028	+	0.359659i	−0.312086	+	0.950054i	$0.601028\pi$
$152$	−2.41473	−	7.43178i	−0.195861	−	0.602797i
$153$		0			0
$154$	4.24344	+	0.243361i	0.341946	+	0.0196106i
$155$	2.38630			0.191672
$156$		0			0
$157$	10.8262	+	7.86568i	0.864023	+	0.627750i	0.928977	−	0.370139i	$-0.120690\pi$
$157$	10.8262	+	7.86568i	0.864023	+	0.627750i	−0.0649531	+	0.997888i	$0.520690\pi$
$158$	1.35221	−	0.982441i	0.107576	−	0.0781588i
$159$		0			0
$160$	−1.50869	+	4.64326i	−0.119272	+	0.367082i
$161$	6.02234	−	4.37549i	0.474627	−	0.344837i
$162$		0			0
$163$	−0.238558	−	0.734206i	−0.0186853	−	0.0575075i	0.941279	−	0.337629i	$-0.109625\pi$
$163$	−0.238558	−	0.734206i	−0.0186853	−	0.0575075i	−0.959964	+	0.280122i	$0.909625\pi$
$164$	−3.91733			−0.305892
$165$		0			0
$166$	5.30514			0.411759
$167$	2.62118	+	8.06716i	0.202833	+	0.624256i	0.999795	+	0.0202268i	$0.00643884\pi$
$167$	2.62118	+	8.06716i	0.202833	+	0.624256i	−0.796962	+	0.604029i	$0.793561\pi$
$168$		0			0
$169$	−7.11029	+	5.16593i	−0.546946	+	0.397379i
$170$	−0.682297	+	2.09989i	−0.0523298	+	0.161055i
$171$		0			0
$172$	−10.1326	+	7.36179i	−0.772606	+	0.561331i
$173$	4.10876	+	2.98519i	0.312384	+	0.226960i	0.732919	−	0.680316i	$-0.238158\pi$
$173$	4.10876	+	2.98519i	0.312384	+	0.226960i	−0.420535	+	0.907276i	$0.638158\pi$
$174$		0			0
$175$	2.68522			0.202984
$176$	−2.26259	−	8.61366i	−0.170549	−	0.649279i
$177$		0			0
$178$	0.408491	+	1.25721i	0.0306177	+	0.0942315i
$179$	−9.15568	−	6.65199i	−0.684328	−	0.497193i	0.190463	−	0.981694i	$-0.439001\pi$
$179$	−9.15568	−	6.65199i	−0.684328	−	0.497193i	−0.874791	+	0.484501i	$0.839001\pi$
$180$		0			0
$181$	2.28674	−	7.03787i	0.169972	−	0.523121i	−0.829396	−	0.558661i	$-0.811315\pi$
$181$	2.28674	−	7.03787i	0.169972	−	0.523121i	0.999368	+	0.0355402i	$0.0113152\pi$
$182$	1.84856	−	5.68929i	0.137025	−	0.421718i
$183$		0			0
$184$	4.03774	+	2.93359i	0.297666	+	0.216267i
$185$	−3.28884	−	10.1220i	−0.241800	−	0.744185i
$186$		0			0
$187$	−3.89819	−	14.8403i	−0.285064	−	1.08523i
$188$	7.73070			0.563819
$189$		0			0
$190$	−1.67589	−	1.21761i	−0.121582	−	0.0883346i
$191$	−4.17135	+	3.03067i	−0.301829	+	0.219291i	−0.728382	−	0.685171i	$-0.759728\pi$
$191$	−4.17135	+	3.03067i	−0.301829	+	0.219291i	0.426554	+	0.904462i	$0.359728\pi$
$192$		0			0
$193$	−1.24605	+	3.83494i	−0.0896925	+	0.276045i	−0.985834	−	0.167723i	$-0.946359\pi$
$193$	−1.24605	+	3.83494i	−0.0896925	+	0.276045i	0.896142	+	0.443768i	$0.146359\pi$
$194$	7.15627	−	5.19933i	0.513790	−	0.373290i
$195$		0			0
$196$	−0.115228	−	0.354635i	−0.00823056	−	0.0253311i
$197$	−11.4176			−0.813469			−0.406734	−	0.913547i	$-0.633333\pi$
$197$	−11.4176			−0.813469			−0.406734	+	0.913547i	$0.633333\pi$
$198$		0			0
$199$	−7.16644			−0.508015			−0.254008	−	0.967202i	$-0.581749\pi$
$199$	−7.16644			−0.508015			−0.254008	+	0.967202i	$0.581749\pi$
$200$	0.556333	+	1.71222i	0.0393387	+	0.121072i
$201$		0			0
$202$	2.74701	−	1.99582i	0.193279	−	0.140425i
$203$	2.50047	−	7.69565i	0.175498	−	0.540128i
$204$		0			0
$205$	−1.78826	+	1.29924i	−0.124897	+	0.0907431i
$206$	2.90678	+	2.11190i	0.202525	+	0.147143i
$207$		0			0
$208$	−12.5342			−0.869090
$209$	14.3720	+	0.824235i	0.994132	+	0.0570135i
$210$		0			0
$211$	1.07649	+	3.31309i	0.0741086	+	0.228083i	0.981249	−	0.192746i	$-0.0617393\pi$
$211$	1.07649	+	3.31309i	0.0741086	+	0.228083i	−0.907140	+	0.420829i	$0.861739\pi$
$212$	9.08148	+	6.59808i	0.623719	+	0.453158i
$213$		0			0
$214$	2.65897	−	8.18348i	0.181764	−	0.559411i
$215$	−2.18388	+	6.72129i	−0.148939	+	0.458388i
$216$		0			0
$217$	−5.18397	−	3.76638i	−0.351911	−	0.255678i
$218$	2.41358	+	7.42824i	0.163468	+	0.503104i
$219$		0			0
$220$	−4.54963	−	3.72148i	−0.306736	−	0.250902i
$221$	−21.5950			−1.45264
$222$		0			0
$223$	−8.53103	−	6.19816i	−0.571280	−	0.415059i	0.264290	−	0.964443i	$-0.414862\pi$
$223$	−8.53103	−	6.19816i	−0.571280	−	0.415059i	−0.835570	+	0.549384i	$0.814862\pi$
$224$	10.6061	−	7.70575i	0.708647	−	0.514862i
$225$		0			0
$226$	−0.302893	+	0.932209i	−0.0201481	+	0.0620096i
$227$	0.174762	−	0.126972i	0.0115994	−	0.00842743i	−0.581970	−	0.813210i	$-0.697718\pi$
$227$	0.174762	−	0.126972i	0.0115994	−	0.00842743i	0.593570	+	0.804782i	$0.297718\pi$
$228$		0			0
$229$	−0.0233956	−	0.0720042i	−0.00154602	−	0.00475817i	0.950281	−	0.311395i	$-0.100796\pi$
$229$	−0.0233956	−	0.0720042i	−0.00154602	−	0.00475817i	−0.951827	+	0.306637i	$0.900796\pi$
$230$	1.32307			0.0872407
$231$		0			0
$232$	5.42514			0.356178
$233$	−4.67235	−	14.3800i	−0.306096	−	0.942067i	−0.979266	−	0.202579i	$-0.935068\pi$
$233$	−4.67235	−	14.3800i	−0.306096	−	0.942067i	0.673170	−	0.739488i	$-0.264932\pi$
$234$		0			0
$235$	3.52905	−	2.56401i	0.230210	−	0.167257i
$236$	6.43336	−	19.7999i	0.418776	−	1.28886i
$237$		0			0
$238$	4.79655	−	3.48489i	0.310914	−	0.225892i
$239$	−18.7406	−	13.6158i	−1.21223	−	0.880734i	−0.216796	−	0.976217i	$-0.569561\pi$
$239$	−18.7406	−	13.6158i	−1.21223	−	0.880734i	−0.995431	+	0.0954825i	$0.969561\pi$
$240$		0			0
$241$	−21.3349			−1.37430			−0.687151	−	0.726515i	$-0.741139\pi$
$241$	−21.3349			−1.37430			−0.687151	+	0.726515i	$0.741139\pi$
$242$	−5.21544	−	0.600185i	−0.335261	−	0.0385814i
$243$		0			0
$244$	2.18107	+	6.71266i	0.139629	+	0.429734i
$245$	−0.170221	−	0.123673i	−0.0108750	−	0.00790119i
$246$		0			0
$247$	6.26085	−	19.2689i	0.398368	−	1.22605i
$248$	1.32758	−	4.08586i	0.0843012	−	0.259453i
$249$		0			0
$250$	0.386111	+	0.280526i	0.0244198	+	0.0177420i
$251$	1.92266	+	5.91734i	0.121357	+	0.373499i	0.993220	−	0.116251i	$-0.0370878\pi$
$251$	1.92266	+	5.91734i	0.121357	+	0.373499i	−0.871863	+	0.489751i	$0.837088\pi$
$252$		0			0
$253$	−7.73567	+	4.96959i	−0.486338	+	0.312435i
$254$	0.0363991			0.00228388
$255$		0			0
$256$	−0.588982	−	0.427920i	−0.0368113	−	0.0267450i
$257$	−11.5611	+	8.39964i	−0.721163	+	0.523955i	−0.886755	−	0.462239i	$-0.847046\pi$
$257$	−11.5611	+	8.39964i	−0.721163	+	0.523955i	0.165593	+	0.986194i	$0.447046\pi$
$258$		0			0
$259$	−8.83126	+	27.1798i	−0.548748	+	1.68887i
$260$	−6.69257	+	4.86243i	−0.415055	+	0.301555i
$261$		0			0
$262$	−1.69355	−	5.21220i	−0.104628	−	0.322011i
$263$	−4.13132			−0.254748			−0.127374	−	0.991855i	$-0.540655\pi$
$263$	−4.13132			−0.254748			−0.127374	+	0.991855i	$0.540655\pi$
$264$		0			0
$265$	6.33404			0.389097
$266$	1.71890	+	5.29024i	0.105393	+	0.324365i
$267$		0			0
$268$	10.4949	−	7.62497i	0.641077	−	0.465769i
$269$	0.520367	−	1.60152i	0.0317273	−	0.0976466i	−0.933939	−	0.357433i	$-0.883652\pi$
$269$	0.520367	−	1.60152i	0.0317273	−	0.0976466i	0.965666	+	0.259786i	$0.0836521\pi$
$270$		0			0
$271$	14.9110	−	10.8335i	0.905778	−	0.658086i	−0.0341657	−	0.999416i	$-0.510877\pi$
$271$	14.9110	−	10.8335i	0.905778	−	0.658086i	0.939943	+	0.341330i	$0.110877\pi$
$272$	−10.0502	−	7.30188i	−0.609381	−	0.442741i
$273$		0			0
$274$	−8.74784			−0.528476
$275$	−3.31118	−	0.189896i	−0.199672	−	0.0114512i
$276$		0			0
$277$	−1.05914	−	3.25969i	−0.0636375	−	0.195856i	0.914183	−	0.405303i	$-0.132834\pi$
$277$	−1.05914	−	3.25969i	−0.0636375	−	0.195856i	−0.977820	+	0.209446i	$0.932834\pi$
$278$	−8.95290	−	6.50466i	−0.536959	−	0.390124i
$279$		0			0
$280$	1.49388	−	4.59768i	0.0892762	−	0.274764i
$281$	7.05230	−	21.7048i	0.420705	−	1.29480i	−0.486342	−	0.873769i	$-0.661669\pi$
$281$	7.05230	−	21.7048i	0.420705	−	1.29480i	0.907047	−	0.421029i	$-0.138331\pi$
$282$		0			0
$283$	23.5416	+	17.1040i	1.39941	+	1.01673i	0.994758	+	0.102255i	$0.0326057\pi$
$283$	23.5416	+	17.1040i	1.39941	+	1.01673i	0.404647	+	0.914473i	$0.367394\pi$
$284$	0.654828	+	2.01535i	0.0388569	+	0.119589i
$285$		0			0
$286$	−2.68183	+	6.88482i	−0.158580	+	0.407108i
$287$	5.93542			0.350357
$288$		0			0
$289$	−3.56201	−	2.58795i	−0.209530	−	0.152232i
$290$	1.16351	−	0.845342i	0.0683239	−	0.0496402i
$291$		0			0
$292$	−0.559534	+	1.72207i	−0.0327443	+	0.100776i
$293$	17.1621	−	12.4690i	1.00262	−	0.728448i	0.0399740	−	0.999201i	$-0.487273\pi$
$293$	17.1621	−	12.4690i	1.00262	−	0.728448i	0.962649	+	0.270753i	$0.0872725\pi$
$294$		0			0
$295$	−3.63011	−	11.1723i	−0.211353	−	0.650478i
$296$	−19.1608			−1.11370
$297$		0			0
$298$	6.99883			0.405432
$299$	3.99878	+	12.3070i	0.231255	+	0.711731i
$300$		0			0
$301$	15.3527	−	11.1544i	0.884913	−	0.642927i
$302$	1.10892	−	3.41289i	0.0638109	−	0.196390i
$303$		0			0
$304$	9.42913	−	6.85066i	0.540798	−	0.392912i
$305$	3.22201	+	2.34093i	0.184492	+	0.134041i
$306$		0			0
$307$	−6.87520			−0.392388			−0.196194	−	0.980565i	$-0.562858\pi$
$307$	−6.87520			−0.392388			−0.196194	+	0.980565i	$0.562858\pi$
$308$	4.00982	+	15.2653i	0.228481	+	0.869823i
$309$		0			0
$310$	−0.351935	−	1.08314i	−0.0199886	−	0.0615185i
$311$	20.3530	+	14.7873i	1.15411	+	0.838511i	0.989022	−	0.147768i	$-0.0472087\pi$
$311$	20.3530	+	14.7873i	1.15411	+	0.838511i	0.165089	+	0.986279i	$0.447209\pi$
$312$		0			0
$313$	−3.57821	+	11.0126i	−0.202252	+	0.622469i	0.797563	+	0.603236i	$0.206122\pi$
$313$	−3.57821	+	11.0126i	−0.202252	+	0.622469i	−0.999815	+	0.0192328i	$0.993878\pi$
$314$	1.97358	−	6.07406i	0.111376	−	0.342779i
$315$		0			0
$316$	5.02121	+	3.64812i	0.282465	+	0.205223i
$317$	−6.40940	−	19.7261i	−0.359988	−	1.10793i	−0.953061	−	0.302780i	$-0.902085\pi$
$317$	−6.40940	−	19.7261i	−0.359988	−	1.10793i	0.593073	−	0.805149i	$-0.297915\pi$
$318$		0			0
$319$	−3.62759	+	9.31278i	−0.203106	+	0.521416i
$320$	−3.04036			−0.169961
$321$		0			0
$322$	−2.87422	−	2.08825i	−0.160174	−	0.116373i
$323$	16.2453	−	11.8029i	0.903913	−	0.656731i
$324$		0			0
$325$	−1.44244	+	4.43939i	−0.0800124	+	0.246253i
$326$	−0.298074	+	0.216564i	−0.0165088	+	0.0119943i
$327$		0			0
$328$	1.22972	+	3.78469i	0.0679000	+	0.208975i
$329$	−11.7133			−0.645777
$330$		0			0
$331$	−32.1415			−1.76665			−0.883327	−	0.468757i	$-0.844702\pi$
$331$	−32.1415			−1.76665			−0.883327	+	0.468757i	$0.844702\pi$
$332$	6.08755	+	18.7356i	0.334098	+	1.02825i
$333$		0			0
$334$	3.27512	−	2.37951i	0.179207	−	0.130201i
$335$	2.26195	−	6.96158i	0.123584	−	0.380352i
$336$		0			0
$337$	14.5594	−	10.5780i	0.793100	−	0.576221i	−0.115782	−	0.993275i	$-0.536937\pi$
$337$	14.5594	−	10.5780i	0.793100	−	0.576221i	0.908882	+	0.417054i	$0.136937\pi$
$338$	3.39346	+	2.46549i	0.184580	+	0.134105i
$339$		0			0
$340$	−8.19888			−0.444647
$341$	6.12608	+	5.01098i	0.331746	+	0.271360i
$342$		0			0
$343$	−5.63386	−	17.3392i	−0.304200	−	0.936231i
$344$	10.2933	+	7.47855i	0.554980	+	0.403217i
$345$		0			0
$346$	0.749016	−	2.30523i	0.0402673	−	0.123930i
$347$	2.48753	−	7.65583i	0.133538	−	0.410986i	−0.861822	−	0.507211i	$-0.830677\pi$
$347$	2.48753	−	7.65583i	0.133538	−	0.410986i	0.995360	+	0.0962243i	$0.0306766\pi$
$348$		0			0
$349$	−15.5569	−	11.3027i	−0.832741	−	0.605022i	0.0875926	−	0.996156i	$-0.472083\pi$
$349$	−15.5569	−	11.3027i	−0.832741	−	0.605022i	−0.920333	+	0.391135i	$0.872083\pi$
$350$	−0.396020	−	1.21882i	−0.0211682	−	0.0651489i
$351$		0			0
$352$	−13.6234	+	8.75202i	−0.726131	+	0.466484i
$353$	−14.8497			−0.790371			−0.395186	−	0.918601i	$-0.629320\pi$
$353$	−14.8497			−0.790371			−0.395186	+	0.918601i	$0.629320\pi$
$354$		0			0
$355$	0.967351	+	0.702822i	0.0513417	+	0.0373019i
$356$	−3.97119	+	2.88524i	−0.210473	+	0.152917i
$357$		0			0
$358$	−1.66905	+	5.13682i	−0.0882123	+	0.271489i
$359$	8.27079	−	6.00908i	0.436516	−	0.317147i	−0.347733	−	0.937594i	$-0.613048\pi$
$359$	8.27079	−	6.00908i	0.436516	−	0.317147i	0.784249	+	0.620446i	$0.213048\pi$
$360$		0			0
$361$	−0.0496143	−	0.152697i	−0.00261128	−	0.00803670i
$362$	−3.53175			−0.185625
$363$		0			0
$364$	22.2134			1.16430
$365$	0.315724	+	0.971700i	0.0165258	+	0.0508611i
$366$		0			0
$367$	−11.4422	+	8.31327i	−0.597280	+	0.433949i	−0.844912	−	0.534905i	$-0.820347\pi$
$367$	−11.4422	+	8.31327i	−0.597280	+	0.433949i	0.247632	+	0.968854i	$0.420347\pi$
$368$	−2.30033	+	7.07969i	−0.119913	+	0.369054i
$369$		0			0
$370$	−4.10935	+	2.98562i	−0.213635	+	0.155215i
$371$	−13.7600	−	9.99722i	−0.714383	−	0.519030i
$372$		0			0
$373$	12.4600			0.645154			0.322577	−	0.946543i	$-0.395451\pi$
$373$	12.4600			0.645154			0.322577	+	0.946543i	$0.395451\pi$
$374$	−6.16114	+	3.95807i	−0.318585	+	0.204667i
$375$		0			0
$376$	−2.42681	−	7.46894i	−0.125153	−	0.385181i
$377$	11.3798	+	8.26788i	0.586088	+	0.425818i
$378$		0			0
$379$	5.04840	−	15.5374i	0.259319	−	0.798102i	−0.733629	−	0.679550i	$-0.762175\pi$
$379$	5.04840	−	15.5374i	0.259319	−	0.798102i	0.992948	−	0.118552i	$-0.0378251\pi$
$380$	2.37703	−	7.31575i	0.121939	−	0.375290i
$381$		0			0
$382$	1.99082	+	1.44642i	0.101859	+	0.0740051i
$383$	0.251122	+	0.772874i	0.0128317	+	0.0394920i	0.957267	−	0.289204i	$-0.0933907\pi$
$383$	0.251122	+	0.772874i	0.0128317	+	0.0394920i	−0.944436	+	0.328696i	$0.893391\pi$
$384$		0			0
$385$	6.89346	+	5.63868i	0.351323	+	0.287374i
$386$	1.92445			0.0979522
$387$		0			0
$388$	26.5736	+	19.3068i	1.34907	+	0.980155i
$389$	−24.5894	+	17.8652i	−1.24673	+	0.905802i	−0.998028	−	0.0627780i	$-0.980004\pi$
$389$	−24.5894	+	17.8652i	−1.24673	+	0.905802i	−0.248702	+	0.968580i	$0.580004\pi$
$390$		0			0
$391$	−3.96321	+	12.1975i	−0.200428	+	0.616854i
$392$	−0.306455	+	0.222653i	−0.0154783	+	0.0112457i
$393$		0			0
$394$	1.68388	+	5.18245i	0.0848327	+	0.261088i
$395$	3.50213			0.176211
$396$		0			0
$397$	−14.8996			−0.747789			−0.373894	−	0.927471i	$-0.621978\pi$
$397$	−14.8996			−0.747789			−0.373894	+	0.927471i	$0.621978\pi$
$398$	1.05692	+	3.25285i	0.0529784	+	0.163051i
$399$		0			0
$400$	−2.17239	+	1.57833i	−0.108619	+	0.0789166i
$401$	−3.76049	+	11.5736i	−0.187790	+	0.577957i	−0.999985	−	0.00542792i	$-0.998272\pi$
$401$	−3.76049	+	11.5736i	−0.187790	+	0.577957i	0.812196	+	0.583385i	$0.198272\pi$
$402$		0			0
$403$	9.01155	−	6.54727i	0.448897	−	0.326143i
$404$	10.2006	+	7.41114i	0.507496	+	0.368718i
$405$		0			0
$406$	−3.86184			−0.191660
$407$	12.8121	−	32.8913i	0.635071	−	1.63036i
$408$		0			0
$409$	−0.0809957	−	0.249279i	−0.00400498	−	0.0123261i	0.949034	−	0.315174i	$-0.102063\pi$
$409$	−0.0809957	−	0.249279i	−0.00400498	−	0.0123261i	−0.953039	+	0.302847i	$0.902063\pi$
$410$	0.853463	+	0.620077i	0.0421495	+	0.0306234i
$411$		0			0
$412$	−4.12288	+	12.6889i	−0.203120	+	0.625138i
$413$	−9.74764	+	30.0002i	−0.479650	+	1.47621i
$414$		0			0
$415$	8.99290	+	6.53372i	0.441444	+	0.320728i
$416$	7.04232	+	21.6740i	0.345278	+	1.06266i
$417$		0			0
$418$	−1.74548	−	6.64503i	−0.0853744	−	0.325019i
$419$	1.26916			0.0620023			0.0310012	−	0.999519i	$-0.490130\pi$
$419$	1.26916			0.0620023			0.0310012	+	0.999519i	$0.490130\pi$
$420$		0			0
$421$	23.9999	+	17.4369i	1.16968	+	0.849824i	0.990971	−	0.134078i	$-0.0428071\pi$
$421$	23.9999	+	17.4369i	1.16968	+	0.849824i	0.178712	+	0.983902i	$0.442807\pi$
$422$	1.34506	−	0.977240i	0.0654763	−	0.0475713i
$423$		0			0
$424$	3.52384	−	10.8452i	0.171133	−	0.526692i
$425$	−3.74278	+	2.71929i	−0.181551	+	0.131905i
$426$		0			0
$427$	−3.30470	−	10.1708i	−0.159926	−	0.492200i
$428$	31.9518			1.54445
$429$		0			0
$430$	3.37289			0.162655
$431$	−9.68919	−	29.8203i	−0.466712	−	1.43639i	−0.856817	−	0.515621i	$-0.827561\pi$
$431$	−9.68919	−	29.8203i	−0.466712	−	1.43639i	0.390105	−	0.920771i	$-0.372439\pi$
$432$		0			0
$433$	21.0607	−	15.3015i	1.01212	−	0.735345i	0.0474634	−	0.998873i	$-0.484886\pi$
$433$	21.0607	−	15.3015i	1.01212	−	0.735345i	0.964652	+	0.263528i	$0.0848863\pi$
$434$	−0.945023	+	2.90848i	−0.0453625	+	0.139612i
$435$		0			0
$436$	−23.4639	+	17.0475i	−1.12372	+	0.816429i
$437$	−9.73464	−	7.07263i	−0.465671	−	0.338330i
$438$		0			0
$439$	14.4191			0.688185			0.344093	−	0.938936i	$-0.388187\pi$
$439$	14.4191			0.688185			0.344093	+	0.938936i	$0.388187\pi$
$440$	−2.16726	+	5.56382i	−0.103320	+	0.265245i
$441$		0			0
$442$	3.18486	+	9.80199i	0.151488	+	0.466233i
$443$	−0.267467	−	0.194326i	−0.0127078	−	0.00923273i	0.581413	−	0.813608i	$-0.302500\pi$
$443$	−0.267467	−	0.194326i	−0.0127078	−	0.00923273i	−0.594121	+	0.804376i	$0.702500\pi$
$444$		0			0
$445$	−0.855908	+	2.63421i	−0.0405739	+	0.124874i
$446$	−1.55518	+	4.78636i	−0.0736400	+	0.226641i
$447$		0			0
$448$	6.60483	+	4.79869i	0.312049	+	0.226717i
$449$	−2.62920	−	8.09185i	−0.124080	−	0.381878i	0.869653	−	0.493664i	$-0.164343\pi$
$449$	−2.62920	−	8.09185i	−0.124080	−	0.381878i	−0.993732	+	0.111786i	$0.964343\pi$
$450$		0			0
$451$	−7.31906	−	0.419748i	−0.344641	−	0.0197652i
$452$	−3.63974			−0.171199
$453$		0			0
$454$	−0.0834069	−	0.0605986i	−0.00391448	−	0.00284404i
$455$	10.1404	−	7.36742i	0.475388	−	0.345390i
$456$		0			0
$457$	0.351807	−	1.08275i	0.0164569	−	0.0506490i	−0.942491	−	0.334232i	$-0.891523\pi$
$457$	0.351807	−	1.08275i	0.0164569	−	0.0506490i	0.958948	+	0.283583i	$0.0915231\pi$
$458$	−0.0292324	+	0.0212386i	−0.00136594	+	0.000992413i
$459$		0			0
$460$	1.51820	+	4.67254i	0.0707864	+	0.217858i
$461$	−14.5073			−0.675670			−0.337835	−	0.941205i	$-0.609695\pi$
$461$	−14.5073			−0.675670			−0.337835	+	0.941205i	$0.609695\pi$
$462$		0			0
$463$	−4.89739			−0.227601			−0.113801	−	0.993504i	$-0.536302\pi$
$463$	−4.89739			−0.227601			−0.113801	+	0.993504i	$0.536302\pi$
$464$	2.50047	+	7.69565i	0.116081	+	0.357261i
$465$		0			0
$466$	−5.83803	+	4.24157i	−0.270441	+	0.196487i
$467$	−10.0193	+	30.8361i	−0.463637	+	1.42693i	0.397053	+	0.917796i	$0.370033\pi$
$467$	−10.0193	+	30.8361i	−0.463637	+	1.42693i	−0.860689	+	0.509131i	$0.829967\pi$
$468$		0			0
$469$	−15.9015	+	11.5531i	−0.734264	+	0.533474i
$470$	−1.68428	−	1.22370i	−0.0776898	−	0.0564450i
$471$		0			0
$472$	−21.1490			−0.973461
$473$	−19.7204	+	12.6689i	−0.906747	+	0.582516i
$474$		0			0
$475$	−1.34127	−	4.12801i	−0.0615417	−	0.189406i
$476$	17.8111	+	12.9406i	0.816373	+	0.593129i
$477$		0			0
$478$	−3.41635	+	10.5145i	−0.156260	+	0.480920i
$479$	−5.48054	+	16.8674i	−0.250412	+	0.770690i	0.744287	+	0.667860i	$0.232790\pi$
$479$	−5.48054	+	16.8674i	−0.250412	+	0.770690i	−0.994699	+	0.102830i	$0.967210\pi$
$480$		0			0
$481$	−40.1915	−	29.2009i	−1.83258	−	1.33144i
$482$	3.14650	+	9.68394i	0.143319	+	0.441091i
$483$		0			0
$484$	−3.86502	−	19.1075i	−0.175683	−	0.868521i
$485$	18.5342			0.841595
$486$		0			0
$487$	14.9347	+	10.8507i	0.676754	+	0.491691i	0.872279	−	0.489008i	$-0.162641\pi$
$487$	14.9347	+	10.8507i	0.676754	+	0.491691i	−0.195525	+	0.980699i	$0.562641\pi$
$488$	5.80069	−	4.21445i	0.262585	−	0.190779i
$489$		0			0
$490$	−0.0310309	+	0.0955032i	−0.00140183	+	0.00431440i
$491$	−9.25018	+	6.72065i	−0.417455	+	0.303299i	−0.776613	−	0.629978i	$-0.783064\pi$
$491$	−9.25018	+	6.72065i	−0.417455	+	0.303299i	0.359158	+	0.933277i	$0.383064\pi$
$492$		0			0
$493$	4.30802	+	13.2587i	0.194023	+	0.597142i
$494$	−9.66954			−0.435053
$495$		0			0
$496$	6.40774			0.287716
$497$	−0.992176	−	3.05360i	−0.0445052	−	0.136973i
$498$		0			0
$499$	−8.80335	+	6.39601i	−0.394092	+	0.286325i	−0.767130	−	0.641491i	$-0.778316\pi$
$499$	−8.80335	+	6.39601i	−0.394092	+	0.286325i	0.373038	+	0.927816i	$0.378316\pi$
$500$	−0.547647	+	1.68548i	−0.0244915	+	0.0753771i
$501$		0			0
$502$	2.40233	−	1.74540i	0.107221	−	0.0779009i
$503$	36.1830	+	26.2885i	1.61332	+	1.17215i	0.851490	+	0.524371i	$0.175699\pi$
$503$	36.1830	+	26.2885i	1.61332	+	1.17215i	0.761831	+	0.647776i	$0.224301\pi$
$504$		0			0
$505$	7.11455			0.316594
$506$	3.39657	+	2.77831i	0.150996	+	0.123511i
$507$		0			0
$508$	0.0417673	+	0.128546i	0.00185312	+	0.00570332i
$509$	−11.1720	−	8.11693i	−0.495190	−	0.359777i	0.311987	−	0.950086i	$-0.399006\pi$
$509$	−11.1720	−	8.11693i	−0.495190	−	0.359777i	−0.807177	+	0.590310i	$0.799006\pi$
$510$		0			0
$511$	0.847790	−	2.60923i	0.0375040	−	0.115425i
$512$	−7.03891	+	21.6635i	−0.311079	+	0.957402i
$513$		0			0
$514$	5.51766	+	4.00881i	0.243374	+	0.176821i
$515$	2.32639	+	7.15989i	0.102513	+	0.315502i
$516$		0			0
$517$	14.4439	+	0.828356i	0.635241	+	0.0364311i
$518$	13.6394			0.599281
$519$		0			0
$520$	6.79871	+	4.93955i	0.298143	+	0.216614i
$521$	−2.95269	+	2.14525i	−0.129360	+	0.0939852i	−0.650584	−	0.759435i	$-0.725476\pi$
$521$	−2.95269	+	2.14525i	−0.129360	+	0.0939852i	0.521224	+	0.853420i	$0.325476\pi$
$522$		0			0
$523$	−1.54109	+	4.74299i	−0.0673872	+	0.207396i	−0.979080	−	0.203476i	$-0.934776\pi$
$523$	−1.54109	+	4.74299i	−0.0673872	+	0.207396i	0.911693	+	0.410873i	$0.134776\pi$
$524$	16.4640	−	11.9618i	0.719233	−	0.522553i
$525$		0			0
$526$	0.609292	+	1.87521i	0.0265664	+	0.0817630i
$527$	11.0398			0.480901
$528$		0			0
$529$	−15.3148			−0.665860
$530$	−0.934153	−	2.87503i	−0.0405770	−	0.124883i
$531$		0			0
$532$	−16.7105	+	12.1409i	−0.724493	+	0.526375i
$533$	−3.18839	+	9.81284i	−0.138104	+	0.425041i
$534$		0			0
$535$	14.5859	−	10.5973i	0.630605	−	0.458161i
$536$	−10.6613	−	7.74591i	−0.460499	−	0.334572i
$537$		0			0
$538$	−0.803678			−0.0346490
$539$	−0.177290	−	0.674939i	−0.00763640	−	0.0290717i
$540$		0			0
$541$	0.0765109	+	0.235476i	0.00328946	+	0.0101239i	0.952688	−	0.303951i	$-0.0983058\pi$
$541$	0.0765109	+	0.235476i	0.00328946	+	0.0101239i	−0.949398	+	0.314075i	$0.898306\pi$
$542$	−7.11642	−	5.17038i	−0.305676	−	0.222087i
$543$		0			0
$544$	−6.97967	+	21.4812i	−0.299251	+	0.921000i
$545$	−5.05716	+	15.5643i	−0.216625	+	0.666703i
$546$		0			0
$547$	20.4779	+	14.8780i	0.875570	+	0.636139i	0.932076	−	0.362263i	$-0.117996\pi$
$547$	20.4779	+	14.8780i	0.875570	+	0.636139i	−0.0565056	+	0.998402i	$0.517996\pi$
$548$	−10.0380	−	30.8937i	−0.428801	−	1.31971i
$549$		0			0
$550$	0.402144	+	1.53096i	0.0171475	+	0.0652802i
$551$	−13.0796			−0.557208
$552$		0			0
$553$	−7.60799	−	5.52753i	−0.323525	−	0.235054i
$554$	−1.32338	+	0.961489i	−0.0562249	+	0.0408498i
$555$		0			0
$556$	12.6985	−	39.0819i	0.538536	−	1.65744i
$557$	−31.2824	+	22.7280i	−1.32548	+	0.963015i	−0.325630	+	0.945497i	$0.605576\pi$
$557$	−31.2824	+	22.7280i	−1.32548	+	0.963015i	−0.999847	+	0.0175177i	$0.994424\pi$
$558$		0			0
$559$	10.1940	+	31.3740i	0.431161	+	1.32698i
$560$	7.21041			0.304695
$561$		0			0
$562$	−10.8919			−0.459447
$563$	−4.30653	−	13.2541i	−0.181498	−	0.558595i	0.818372	−	0.574689i	$-0.194877\pi$
$563$	−4.30653	−	13.2541i	−0.181498	−	0.558595i	−0.999870	+	0.0160940i	$0.994877\pi$
$564$		0			0
$565$	−1.66154	+	1.20718i	−0.0699013	+	0.0507863i
$566$	4.29157	−	13.2081i	0.180388	−	0.555178i
$567$		0			0
$568$	1.74155	−	1.26531i	0.0730739	−	0.0530913i
$569$	22.5817	+	16.4065i	0.946672	+	0.687798i	0.950017	−	0.312197i	$-0.101065\pi$
$569$	22.5817	+	16.4065i	0.946672	+	0.687798i	−0.00334520	+	0.999994i	$0.501065\pi$
$570$		0			0
$571$	−31.4113			−1.31452			−0.657261	−	0.753663i	$-0.728285\pi$
$571$	−31.4113			−1.31452			−0.657261	+	0.753663i	$0.728285\pi$
$572$	−27.3917	−	1.57091i	−1.14530	−	0.0656831i
$573$		0			0
$574$	−0.875365	−	2.69410i	−0.0365370	−	0.112449i
$575$	2.24278	+	1.62947i	0.0935302	+	0.0679537i
$576$		0			0
$577$	6.40744	−	19.7201i	0.266745	−	0.820958i	−0.724541	−	0.689232i	$-0.757948\pi$
$577$	6.40744	−	19.7201i	0.266745	−	0.820958i	0.991286	−	0.131726i	$-0.0420519\pi$
$578$	−0.649343	+	1.99847i	−0.0270091	+	0.0831255i
$579$		0			0
$580$	4.32051	+	3.13903i	0.179399	+	0.130341i
$581$	−9.22368	−	28.3876i	−0.382663	−	1.17771i
$582$		0			0
$583$	16.2607	+	13.3008i	0.673448	+	0.550864i
$584$	1.83941			0.0761153
$585$		0			0
$586$	−8.19080	−	5.95097i	−0.338359	−	0.245832i
$587$	12.3267	−	8.95591i	0.508779	−	0.369650i	−0.303581	−	0.952806i	$-0.598182\pi$
$587$	12.3267	−	8.95591i	0.508779	−	0.369650i	0.812360	+	0.583156i	$0.198182\pi$
$588$		0			0
$589$	−3.20067	+	9.85066i	−0.131881	+	0.405889i
$590$	−4.53576	+	3.29542i	−0.186734	+	0.135670i
$591$		0			0
$592$	−8.83126	−	27.1798i	−0.362962	−	1.11708i
$593$	−27.5413			−1.13098			−0.565492	−	0.824754i	$-0.691314\pi$
$593$	−27.5413			−1.13098			−0.565492	+	0.824754i	$0.691314\pi$
$594$		0			0
$595$	12.4227			0.509281
$596$	8.03103	+	24.7170i	0.328964	+	1.01245i
$597$		0			0
$598$	4.99640	−	3.63010i	0.204318	−	0.148446i
$599$	8.26097	−	25.4247i	0.337534	−	1.03882i	−0.627926	−	0.778273i	$-0.716096\pi$
$599$	8.26097	−	25.4247i	0.337534	−	1.03882i	0.965460	−	0.260551i	$-0.0839041\pi$
$600$		0			0
$601$	−1.94714	+	1.41468i	−0.0794255	+	0.0577060i	−0.626789	−	0.779189i	$-0.715631\pi$
$601$	−1.94714	+	1.41468i	−0.0794255	+	0.0577060i	0.547364	+	0.836895i	$0.315631\pi$
$602$	−7.32722	−	5.32353i	−0.298635	−	0.216971i
$603$		0			0
$604$	13.3254			0.542202
$605$	−8.10166	−	7.44064i	−0.329379	−	0.302505i
$606$		0			0
$607$	3.18067	+	9.78909i	0.129099	+	0.397327i	0.994626	−	0.103536i	$-0.0330159\pi$
$607$	3.18067	+	9.78909i	0.129099	+	0.397327i	−0.865526	+	0.500864i	$0.833016\pi$
$608$	−17.1438	−	12.4557i	−0.695275	−	0.505147i
$609$		0			0
$610$	0.587364	−	1.80772i	0.0237817	−	0.0731924i
$611$	6.29216	−	19.3653i	0.254553	−	0.783435i
$612$		0			0
$613$	−22.5519	−	16.3849i	−0.910861	−	0.661779i	0.0303715	−	0.999539i	$-0.490331\pi$
$613$	−22.5519	−	16.3849i	−0.910861	−	0.661779i	−0.941232	+	0.337759i	$0.890331\pi$
$614$	1.01396	+	3.12066i	0.0409203	+	0.125940i
$615$		0			0
$616$	13.4897	−	8.66611i	0.543515	−	0.349168i
$617$	28.7216			1.15629			0.578143	−	0.815935i	$-0.303778\pi$
$617$	28.7216			1.15629			0.578143	+	0.815935i	$0.303778\pi$
$618$		0			0
$619$	−18.3621	−	13.3408i	−0.738035	−	0.536214i	0.154060	−	0.988061i	$-0.450765\pi$
$619$	−18.3621	−	13.3408i	−0.738035	−	0.536214i	−0.892095	+	0.451848i	$0.850765\pi$
$620$	3.42138	−	2.48578i	0.137406	−	0.0998312i
$621$		0			0
$622$	3.71029	−	11.4191i	0.148769	−	0.457864i
$623$	6.01703	−	4.37163i	0.241067	−	0.175146i
$624$		0			0
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	5.52635			0.220877
$627$		0			0
$628$	23.7157			0.946360
$629$	−15.2152	−	46.8277i	−0.606671	−	1.86714i
$630$		0			0
$631$	−23.0864	+	16.7733i	−0.919056	+	0.667733i	−0.943289	−	0.331973i	$-0.892286\pi$
$631$	−23.0864	+	16.7733i	−0.919056	+	0.667733i	0.0242327	+	0.999706i	$0.492286\pi$
$632$	1.94835	−	5.99641i	0.0775013	−	0.238524i
$633$		0			0
$634$	−8.00844	+	5.81847i	−0.318056	+	0.231081i
$635$	0.0617011	+	0.0448285i	0.00244853	+	0.00177896i
$636$		0			0
$637$	−0.982140			−0.0389138
$638$	4.76209	+	0.273106i	0.188533	+	0.0108124i
$639$		0			0
$640$	3.46577	+	10.6665i	0.136997	+	0.421632i
$641$	1.92040	+	1.39526i	0.0758514	+	0.0551093i	0.625065	−	0.780573i	$-0.285073\pi$
$641$	1.92040	+	1.39526i	0.0758514	+	0.0551093i	−0.549213	+	0.835682i	$0.685073\pi$
$642$		0			0
$643$	3.51053	−	10.8043i	0.138442	−	0.426080i	−0.857668	−	0.514204i	$-0.828087\pi$
$643$	3.51053	−	10.8043i	0.138442	−	0.426080i	0.996109	+	0.0881244i	$0.0280873\pi$
$644$	4.07670	−	12.5468i	0.160644	−	0.494413i
$645$		0			0
$646$	−7.75323	−	5.63305i	−0.305047	−	0.221630i
$647$	14.9632	+	46.0520i	0.588264	+	1.81049i	0.585746	+	0.810495i	$0.300802\pi$
$647$	14.9632	+	46.0520i	0.588264	+	1.81049i	0.00251822	+	0.999997i	$0.499198\pi$
$648$		0			0
$649$	14.1415	−	36.3043i	0.555104	−	1.42507i
$650$	2.22778			0.0873806
$651$		0			0
$652$	−1.10685	−	0.804171i	−0.0433475	−	0.0314938i
$653$	24.0722	−	17.4894i	0.942016	−	0.684415i	−0.00688905	−	0.999976i	$-0.502193\pi$
$653$	24.0722	−	17.4894i	0.942016	−	0.684415i	0.948905	+	0.315562i	$0.102193\pi$
$654$		0			0
$655$	3.54847	−	10.9211i	0.138650	−	0.426722i
$656$	−4.80186	+	3.48875i	−0.187481	+	0.136213i
$657$		0			0
$658$	1.72750	+	5.31669i	0.0673449	+	0.207266i
$659$	28.4931			1.10993			0.554966	−	0.831873i	$-0.312731\pi$
$659$	28.4931			1.10993			0.554966	+	0.831873i	$0.312731\pi$
$660$		0			0
$661$	−1.02875			−0.0400139			−0.0200070	−	0.999800i	$-0.506369\pi$
$661$	−1.02875			−0.0400139			−0.0200070	+	0.999800i	$0.506369\pi$
$662$	4.74027	+	14.5890i	0.184236	+	0.567019i
$663$		0			0
$664$	16.1902	−	11.7629i	0.628301	−	0.456488i
$665$	−3.60161	+	11.0846i	−0.139664	+	0.429843i
$666$		0			0
$667$	6.75841	−	4.91027i	0.261687	−	0.190127i
$668$	12.1616	+	8.83591i	0.470546	+	0.341872i
$669$		0			0
$670$	−3.49346			−0.134964
$671$	3.35580	+	12.7755i	0.129549	+	0.493192i
$672$		0			0
$673$	4.02863	+	12.3988i	0.155292	+	0.477940i	0.998190	−	0.0601327i	$-0.0191524\pi$
$673$	4.02863	+	12.3988i	0.155292	+	0.477940i	−0.842898	+	0.538073i	$0.819152\pi$
$674$	−6.94861	−	5.04846i	−0.267651	−	0.194459i
$675$		0			0
$676$	−4.81316	+	14.8134i	−0.185122	+	0.569746i
$677$	11.4665	−	35.2903i	0.440694	−	1.35632i	−0.446444	−	0.894812i	$-0.647310\pi$
$677$	11.4665	−	35.2903i	0.440694	−	1.35632i	0.887138	−	0.461505i	$-0.152690\pi$
$678$		0			0
$679$	−40.2635	−	29.2531i	−1.54517	−	1.12263i
$680$	2.57378	+	7.92127i	0.0986998	+	0.303767i
$681$		0			0
$682$	1.37101	−	3.51966i	0.0524986	−	0.134775i
$683$	32.8992			1.25885			0.629426	−	0.777061i	$-0.283290\pi$
$683$	32.8992			1.25885			0.629426	+	0.777061i	$0.283290\pi$
$684$		0			0
$685$	−14.8287	−	10.7737i	−0.566576	−	0.411641i
$686$	−7.03941	+	5.11443i	−0.268766	+	0.195270i
$687$		0			0
$688$	−5.86420	+	18.0481i	−0.223570	+	0.688079i
$689$	23.9197	−	17.3787i	0.911267	−	0.662074i
$690$		0			0
$691$	11.3409	+	34.9036i	0.431427	+	1.32780i	0.896704	+	0.442631i	$0.145955\pi$
$691$	11.3409	+	34.9036i	0.431427	+	1.32780i	−0.465277	+	0.885165i	$0.654045\pi$
$692$	9.00061			0.342152
$693$		0			0
$694$	−3.84185			−0.145835
$695$	−7.16529	−	22.0525i	−0.271795	−	0.836498i
$696$		0			0
$697$	−8.27305	+	6.01072i	−0.313364	+	0.227672i
$698$	−2.83597	+	8.72823i	−0.107343	+	0.330368i
$699$		0			0
$700$	3.84996	−	2.79716i	0.145515	−	0.105723i
$701$	−29.3266	−	21.3070i	−1.10765	−	0.804755i	−0.125359	−	0.992111i	$-0.540008\pi$
$701$	−29.3266	−	21.3070i	−1.10765	−	0.804755i	−0.982292	+	0.187356i	$0.940008\pi$
$702$		0			0
$703$	46.1949			1.74227
$704$	−7.80516	−	6.38443i	−0.294168	−	0.240622i
$705$		0			0
$706$	2.19006	+	6.74031i	0.0824240	+	0.253675i
$707$	−15.4556	−	11.2291i	−0.581267	−	0.422315i
$708$		0			0
$709$	−5.74811	+	17.6909i	−0.215875	+	0.664394i	0.783216	+	0.621750i	$0.213578\pi$
$709$	−5.74811	+	17.6909i	−0.215875	+	0.664394i	−0.999090	+	0.0426440i	$0.986422\pi$
$710$	0.176345	−	0.542735i	0.00661812	−	0.0203685i
$711$		0			0
$712$	4.03418	+	2.93100i	0.151187	+	0.109844i
$713$	−2.04426	−	6.29158i	−0.0765580	−	0.235621i
$714$		0			0
$715$	−13.0253	+	8.36775i	−0.487117	+	0.312936i
$716$	−20.0563			−0.749540
$717$		0			0
$718$	−3.94732	−	2.86790i	−0.147313	−	0.107029i
$719$	−30.2799	+	21.9996i	−1.12925	+	0.820447i	−0.985585	−	0.169179i	$-0.945888\pi$
$719$	−30.2799	+	21.9996i	−1.12925	+	0.820447i	−0.143664	+	0.989627i	$0.545888\pi$
$720$		0			0
$721$	6.24687	−	19.2259i	0.232645	−	0.716009i
$722$	−0.0619923	+	0.0450400i	−0.00230711	+	0.00167622i
$723$		0			0
$724$	−4.05262	−	12.4727i	−0.150614	−	0.463544i
$725$	3.01341			0.111915
$726$		0			0
$727$	14.6011			0.541526			0.270763	−	0.962646i	$-0.412724\pi$
$727$	14.6011			0.541526			0.270763	+	0.962646i	$0.412724\pi$
$728$	−6.97319	−	21.4613i	−0.258443	−	0.795407i
$729$		0			0
$730$	0.394492	−	0.286615i	0.0146008	−	0.0106081i
$731$	−10.1033	+	31.0949i	−0.373686	+	1.15009i
$732$		0			0
$733$	−33.8468	+	24.5911i	−1.25016	+	0.908293i	−0.998231	−	0.0594528i	$-0.981064\pi$
$733$	−33.8468	+	24.5911i	−1.25016	+	0.908293i	−0.251927	+	0.967746i	$0.581064\pi$
$734$	5.46092	+	3.96759i	0.201566	+	0.146447i
$735$		0			0
$736$	13.5346			0.498891
$737$	20.4254	−	13.1218i	0.752381	−	0.483348i
$738$		0			0
$739$	−3.68654	−	11.3460i	−0.135612	−	0.417370i	0.860073	−	0.510171i	$-0.170418\pi$
$739$	−3.68654	−	11.3460i	−0.135612	−	0.417370i	−0.995685	+	0.0928012i	$0.970418\pi$
$740$	−15.2594	−	11.0866i	−0.560945	−	0.407550i
$741$		0			0
$742$	−2.50841	+	7.72008i	−0.0920865	+	0.283413i
$743$	−14.4250	+	44.3956i	−0.529202	+	1.62872i	0.226652	+	0.973976i	$0.427222\pi$
$743$	−14.4250	+	44.3956i	−0.529202	+	1.62872i	−0.755854	+	0.654740i	$0.772778\pi$
$744$		0			0
$745$	11.8639	+	8.61964i	0.434660	+	0.315799i
$746$	−1.83762	−	5.65561i	−0.0672800	−	0.207067i
$747$		0			0
$748$	−21.0480	−	17.2168i	−0.769593	−	0.629508i
$749$	−48.4124			−1.76895
$750$		0			0
$751$	−11.6530	−	8.46642i	−0.425225	−	0.308944i	0.354512	−	0.935052i	$-0.384647\pi$
$751$	−11.6530	−	8.46642i	−0.425225	−	0.308944i	−0.779737	+	0.626108i	$0.784647\pi$
$752$	9.47628	−	6.88492i	0.345564	−	0.251067i
$753$		0			0
$754$	2.07450	−	6.38465i	0.0755488	−	0.232515i
$755$	6.08301	−	4.41957i	0.221383	−	0.160845i
$756$		0			0
$757$	−4.96330	−	15.2755i	−0.180394	−	0.555196i	0.819444	−	0.573159i	$-0.194282\pi$
$757$	−4.96330	−	15.2755i	−0.180394	−	0.555196i	−0.999839	+	0.0179624i	$0.994282\pi$
$758$	−7.79698			−0.283199
$759$		0			0
$760$	−7.81423			−0.283452
$761$	12.0158	+	36.9809i	0.435573	+	1.34056i	0.892498	+	0.451051i	$0.148951\pi$
$761$	12.0158	+	36.9809i	0.435573	+	1.34056i	−0.456925	+	0.889505i	$0.651049\pi$
$762$		0			0
$763$	35.5518	−	25.8299i	1.28706	−	0.935106i
$764$	−2.82371	+	8.69049i	−0.102158	+	0.314411i
$765$		0			0
$766$	0.313773	−	0.227969i	0.0113371	−	0.00823686i
$767$	−44.3621	−	32.2309i	−1.60182	−	1.16379i
$768$		0			0
$769$	43.0017			1.55068			0.775341	−	0.631543i	$-0.217578\pi$
$769$	43.0017			1.55068			0.775341	+	0.631543i	$0.217578\pi$
$770$	1.54275	−	3.96055i	0.0555967	−	0.142728i
$771$		0			0
$772$	2.20828	+	6.79637i	0.0794776	+	0.244607i
$773$	−6.35452	−	4.61683i	−0.228556	−	0.166056i	0.467613	−	0.883933i	$-0.345114\pi$
$773$	−6.35452	−	4.61683i	−0.228556	−	0.166056i	−0.696170	+	0.717877i	$0.745114\pi$
$774$		0			0
$775$	0.737407	−	2.26951i	0.0264885	−	0.0815231i
$776$	10.3112	−	31.7346i	0.370150	−	1.13920i
$777$		0			0
$778$	11.7355	+	8.52635i	0.420739	+	0.305684i
$779$	−2.96475	−	9.12457i	−0.106223	−	0.326922i
$780$		0			0
$781$	1.00752	+	3.83561i	0.0360519	+	0.137249i
$782$	6.12096			0.218885
$783$		0			0
$784$	−0.457082	−	0.332090i	−0.0163244	−	0.0118603i
$785$	10.8262	−	7.86568i	0.386403	−	0.280738i
$786$		0			0
$787$	−3.53048	+	10.8657i	−0.125848	+	0.387321i	−0.994055	−	0.108882i	$-0.965273\pi$
$787$	−3.53048	+	10.8657i	−0.125848	+	0.387321i	0.868206	+	0.496203i	$0.165273\pi$
$788$	−16.3700	+	11.8935i	−0.583159	+	0.423690i
$789$		0			0
$790$	−0.516500	−	1.58962i	−0.0183762	−	0.0565562i
$791$	5.51483			0.196085
$792$		0			0
$793$	18.5903			0.660161
$794$	2.19741	+	6.76294i	0.0779832	+	0.240008i
$795$		0			0
$796$	−10.2749	+	7.46518i	−0.364186	+	0.264596i
$797$	1.32414	−	4.07529i	0.0469035	−	0.144354i	−0.924862	−	0.380303i	$-0.875820\pi$
$797$	1.32414	−	4.07529i	0.0469035	−	0.144354i	0.971766	+	0.235949i	$0.0758197\pi$
$798$		0			0
$799$	16.3265	−	11.8619i	0.577592	−	0.419645i
$800$	3.94979	+	2.86969i	0.139646	+	0.101459i
$801$		0			0
$802$	5.80787			0.205083
$803$	−1.22994	+	3.15752i	−0.0434038	+	0.111427i
$804$		0			0
$805$	−2.30033	−	7.07969i	−0.0810760	−	0.249526i
$806$	−4.30085	−	3.12475i	−0.151491	−	0.110065i
$807$		0			0
$808$	3.95806	−	12.1817i	0.139244	−	0.428549i
$809$	6.13350	−	18.8770i	0.215642	−	0.663679i	−0.783465	−	0.621436i	$-0.786550\pi$
$809$	6.13350	−	18.8770i	0.215642	−	0.663679i	0.999107	−	0.0422430i	$-0.0134504\pi$
$810$		0			0
$811$	2.53899	+	1.84468i	0.0891559	+	0.0647756i	0.631470	−	0.775400i	$-0.282452\pi$
$811$	2.53899	+	1.84468i	0.0891559	+	0.0647756i	−0.542314	+	0.840176i	$0.682452\pi$
$812$	−4.43138	−	13.6384i	−0.155511	−	0.478614i
$813$		0			0
$814$	−16.8189	−	0.964566i	−0.589504	−	0.0338080i
$815$	−0.771990			−0.0270416
$816$		0			0
$817$	−24.8164	−	18.0301i	−0.868215	−	0.630795i
$818$	−0.101203	+	0.0735281i	−0.00353847	+	0.00257085i
$819$		0			0
$820$	−1.21052	+	3.72560i	−0.0422733	+	0.130104i
$821$	19.0118	−	13.8129i	0.663516	−	0.482073i	−0.204332	−	0.978902i	$-0.565502\pi$
$821$	19.0118	−	13.8129i	0.663516	−	0.482073i	0.867849	+	0.496829i	$0.165502\pi$
$822$		0			0
$823$	−3.91103	−	12.0369i	−0.136330	−	0.419580i	0.859465	−	0.511195i	$-0.170797\pi$
$823$	−3.91103	−	12.0369i	−0.136330	−	0.419580i	−0.995795	+	0.0916150i	$0.970797\pi$
$824$	13.5535			0.472159
$825$		0			0
$826$	15.0547			0.523820
$827$	−9.33959	−	28.7443i	−0.324770	−	0.999538i	−0.971545	−	0.236857i	$-0.923883\pi$
$827$	−9.33959	−	28.7443i	−0.324770	−	0.999538i	0.646775	−	0.762681i	$-0.276117\pi$
$828$		0			0
$829$	−1.61937	+	1.17654i	−0.0562432	+	0.0408630i	−0.615552	−	0.788097i	$-0.711067\pi$
$829$	−1.61937	+	1.17654i	−0.0562432	+	0.0408630i	0.559308	+	0.828960i	$0.311067\pi$
$830$	1.63938	−	5.04549i	0.0569037	−	0.175132i
$831$		0			0
$832$	−11.4815	+	8.34180i	−0.398050	+	0.289200i
$833$	−0.787500	−	0.572152i	−0.0272852	−	0.0198239i
$834$		0			0
$835$	8.48232			0.293543
$836$	21.4646	−	13.7894i	0.742368	−	0.476915i
$837$		0			0
$838$	−0.187177	−	0.576072i	−0.00646592	−	0.0199001i
$839$	28.6185	+	20.7925i	0.988019	+	0.717838i	0.959486	−	0.281755i	$-0.0909166\pi$
$839$	28.6185	+	20.7925i	0.988019	+	0.717838i	0.0285326	+	0.999593i	$0.490917\pi$
$840$		0			0
$841$	−6.15541	+	18.9444i	−0.212256	+	0.653255i
$842$	4.37511	−	13.4652i	0.150776	−	0.464041i
$843$		0			0
$844$	4.99463	+	3.62881i	0.171922	+	0.124909i
$845$	2.71589	+	8.35865i	0.0934295	+	0.287546i
$846$		0			0
$847$	5.85616	+	28.9511i	0.201220	+	0.994771i
$848$	17.0083			0.584067
$849$		0			0
$850$	1.78628	+	1.29781i	0.0612688	+	0.0445144i
$851$	−23.8696	+	17.3423i	−0.818241	+	0.594487i
$852$		0			0
$853$	−5.62515	+	17.3124i	−0.192602	+	0.592767i	0.807395	+	0.590012i	$0.200877\pi$
$853$	−5.62515	+	17.3124i	−0.192602	+	0.592767i	−0.999996	+	0.00275489i	$0.999123\pi$
$854$	−4.12917	+	3.00001i	−0.141297	+	0.102658i
$855$		0			0
$856$	−10.0302	−	30.8699i	−0.342827	−	1.05511i
$857$	29.2837			1.00031			0.500156	−	0.865935i	$-0.333276\pi$
$857$	29.2837			1.00031			0.500156	+	0.865935i	$0.333276\pi$
$858$		0			0
$859$	8.44030			0.287979			0.143990	−	0.989579i	$-0.454007\pi$
$859$	8.44030			0.287979			0.143990	+	0.989579i	$0.454007\pi$
$860$	3.87032	+	11.9116i	0.131977	+	0.406183i
$861$		0			0
$862$	−12.1065	+	8.79587i	−0.412348	+	0.299589i
$863$	5.97907	−	18.4017i	0.203530	−	0.626400i	−0.796241	−	0.604980i	$-0.793181\pi$
$863$	5.97907	−	18.4017i	0.203530	−	0.626400i	0.999771	−	0.0214204i	$-0.00681885\pi$
$864$		0			0
$865$	4.10876	−	2.98519i	0.139702	−	0.101500i
$866$	−10.0515	−	7.30281i	−0.341562	−	0.248160i
$867$		0			0
$868$	−11.3559			−0.385446
$869$	8.99063	+	7.35411i	0.304986	+	0.249471i
$870$		0			0
$871$	−10.5585	−	32.4956i	−0.357760	−	1.10107i
$872$	23.8361	+	17.3179i	0.807191	+	0.586458i
$873$		0			0
$874$	−1.77460	+	5.46165i	−0.0600266	+	0.184743i
$875$	0.829779	−	2.55380i	0.0280516	−	0.0863341i
$876$		0			0
$877$	−14.1691	−	10.2945i	−0.478456	−	0.347619i	0.322271	−	0.946647i	$-0.395554\pi$
$877$	−14.1691	−	10.2945i	−0.478456	−	0.347619i	−0.800728	+	0.599028i	$0.795554\pi$
$878$	−2.12655	−	6.54484i	−0.0717675	−	0.220878i
$879$		0			0
$880$	−8.89126	−	0.509914i	−0.299724	−	0.0171892i
$881$	20.0575			0.675754			0.337877	−	0.941190i	$-0.390291\pi$
$881$	20.0575			0.675754			0.337877	+	0.941190i	$0.390291\pi$
$882$		0			0
$883$	−21.7609	−	15.8102i	−0.732313	−	0.532057i	0.157981	−	0.987442i	$-0.449501\pi$
$883$	−21.7609	−	15.8102i	−0.732313	−	0.532057i	−0.890294	+	0.455386i	$0.849501\pi$
$884$	−30.9620	+	22.4952i	−1.04136	+	0.756595i
$885$		0			0
$886$	−0.0487585	+	0.150063i	−0.00163807	+	0.00504148i
$887$	5.50591	−	4.00028i	0.184870	−	0.134316i	−0.491501	−	0.870877i	$-0.663552\pi$
$887$	5.50591	−	4.00028i	0.184870	−	0.134316i	0.676371	+	0.736561i	$0.263552\pi$
$888$		0			0
$889$	−0.0632845	−	0.194770i	−0.00212249	−	0.00653237i
$890$	1.32190			0.0443103
$891$		0			0
$892$	−18.6880			−0.625720
$893$	5.85082	+	18.0070i	0.195790	+	0.602581i
$894$		0			0
$895$	−9.15568	+	6.65199i	−0.306041	+	0.222352i
$896$	9.30635	−	28.6420i	0.310903	−	0.956862i
$897$		0			0
$898$	−3.28514	+	2.38680i	−0.109627	+	0.0796484i
$899$	−5.81757	−	4.22671i	−0.194027	−	0.140969i
$900$		0			0
$901$	29.3033			0.976235
$902$	0.888901	+	3.38403i	0.0295972	+	0.112676i
$903$		0			0
$904$	1.14258	+	3.51650i	0.0380017	+	0.116957i
$905$	−5.98677	−	4.34965i	−0.199007	−	0.144587i
$906$		0			0
$907$	−6.59174	+	20.2873i	−0.218875	+	0.673629i	0.779981	+	0.625804i	$0.215229\pi$
$907$	−6.59174	+	20.2873i	−0.218875	+	0.673629i	−0.998856	+	0.0478248i	$0.984771\pi$
$908$	0.118301	−	0.364094i	0.00392597	−	0.0120829i
$909$		0			0
$910$	−4.83960	−	3.51617i	−0.160431	−	0.116560i
$911$	8.52542	+	26.2385i	0.282460	+	0.869322i	0.987149	+	0.159805i	$0.0510866\pi$
$911$	8.52542	+	26.2385i	0.282460	+	0.869322i	−0.704689	+	0.709516i	$0.748913\pi$
$912$		0			0
$913$	9.36631	+	35.6574i	0.309980	+	1.18009i
$914$	−0.543347			−0.0179723
$915$		0			0
$916$	−0.108549	−	0.0788658i	−0.00358657	−	0.00260580i
$917$	−24.9458	+	18.1242i	−0.823782	+	0.598512i
$918$		0			0
$919$	−1.85685	+	5.71479i	−0.0612518	+	0.188514i	−0.977000	−	0.213239i	$-0.931599\pi$
$919$	−1.85685	+	5.71479i	−0.0612518	+	0.188514i	0.915748	+	0.401752i	$0.131599\pi$
$920$	4.03774	−	2.93359i	0.133120	−	0.0967176i
$921$		0			0
$922$	2.13955	+	6.58486i	0.0704624	+	0.216861i
$923$	5.58140			0.183714
$924$		0			0
$925$	−10.6429			−0.349937
$926$	0.722274	+	2.22293i	0.0237354	+	0.0730501i
$927$		0			0
$928$	11.9024	−	8.64757i	0.390714	−	0.283870i
$929$	−2.96576	+	9.12766i	−0.0973034	+	0.299469i	−0.987847	−	0.155429i	$-0.950324\pi$
$929$	−2.96576	+	9.12766i	−0.0973034	+	0.299469i	0.890544	+	0.454898i	$0.150324\pi$
$930$		0			0
$931$	0.738836	−	0.536796i	0.0242144	−	0.0175928i
$932$	−21.6785	−	15.7504i	−0.710103	−	0.515920i
$933$		0			0
$934$	15.4742			0.506332
$935$	−15.3186	−	0.878523i	−0.500972	−	0.0287308i
$936$		0			0
$937$	−11.9255	−	36.7029i	−0.389589	−	1.19903i	−0.933096	−	0.359628i	$-0.882904\pi$
$937$	−11.9255	−	36.7029i	−0.389589	−	1.19903i	0.543507	−	0.839405i	$-0.317096\pi$
$938$	7.58916	+	5.51385i	0.247795	+	0.180034i
$939$		0			0
$940$	2.38892	−	7.35233i	0.0779179	−	0.239807i
$941$	9.01854	−	27.7562i	0.293996	−	0.904826i	−0.689561	−	0.724228i	$-0.742196\pi$
$941$	9.01854	−	27.7562i	0.293996	−	0.904826i	0.983557	−	0.180599i	$-0.0578035\pi$
$942$		0			0
$943$	4.95744	+	3.60179i	0.161437	+	0.117291i
$944$	−9.74764	−	30.0002i	−0.317259	−	0.976422i
$945$		0			0
$946$	8.65882	+	7.08270i	0.281523	+	0.230279i
$947$	−46.7623			−1.51957			−0.759785	−	0.650174i	$-0.774696\pi$
$947$	−46.7623			−1.51957			−0.759785	+	0.650174i	$0.774696\pi$
$948$		0			0
$949$	3.85834	+	2.80325i	0.125247	+	0.0909972i
$950$	−1.67589	+	1.21761i	−0.0543732	+	0.0395044i
$951$		0			0
$952$	6.91116	−	21.2704i	0.223992	−	0.689376i
$953$	−4.97738	+	3.61628i	−0.161233	+	0.117143i	−0.665476	−	0.746419i	$-0.731772\pi$
$953$	−4.97738	+	3.61628i	−0.161233	+	0.117143i	0.504243	+	0.863562i	$0.331772\pi$
$954$		0			0
$955$	1.59332	+	4.90372i	0.0515585	+	0.158681i
$956$	−41.0529			−1.32774
$957$		0			0
$958$	8.46440			0.273472
$959$	15.2093	+	46.8093i	0.491132	+	1.51155i
$960$		0			0
$961$	20.4726	−	14.8742i	0.660408	−	0.479814i
$962$	−7.32680	+	22.5496i	−0.236226	+	0.727027i
$963$		0			0
$964$	−30.5891	+	22.2243i	−0.985209	+	0.715796i
$965$	3.26220	+	2.37013i	0.105014	+	0.0762970i
$966$		0			0
$967$	3.39625			0.109216			0.0546080	−	0.998508i	$-0.482609\pi$
$967$	3.39625			0.109216			0.0546080	+	0.998508i	$0.482609\pi$
$968$	−17.2472	+	9.73233i	−0.554346	+	0.312809i
$969$		0			0
$970$	−2.73345	−	8.41270i	−0.0877658	−	0.270115i
$971$	−7.60072	−	5.52224i	−0.243919	−	0.177217i	0.459109	−	0.888380i	$-0.348169\pi$
$971$	−7.60072	−	5.52224i	−0.243919	−	0.177217i	−0.703027	+	0.711163i	$0.748169\pi$
$972$		0			0
$973$	−19.2404	+	59.2158i	−0.616818	+	1.89837i
$974$	2.72255	−	8.37914i	0.0872360	−	0.268485i
$975$		0			0
$976$	8.65182	+	6.28591i	0.276938	+	0.201207i
$977$	5.11585	+	15.7450i	0.163671	+	0.503726i	0.998936	−	0.0461210i	$-0.0146860\pi$
$977$	5.11585	+	15.7450i	0.163671	+	0.503726i	−0.835265	+	0.549847i	$0.814686\pi$
$978$		0			0
$979$	−7.72885	+	4.96520i	−0.247015	+	0.158689i
$980$	−0.372885			−0.0119114
$981$		0			0
$982$	4.41474	+	3.20750i	0.140880	+	0.102355i
$983$	41.1126	−	29.8701i	1.31129	−	0.952707i	0.311291	−	0.950315i	$-0.399238\pi$
$983$	41.1126	−	29.8701i	1.31129	−	0.952707i	0.999997	−	0.00239240i	$-0.000761525\pi$
$984$		0			0
$985$	−3.52822	+	10.8588i	−0.112419	+	0.345989i
$986$	5.38279	−	3.91083i	0.171423	−	0.124546i
$987$		0			0
$988$	−11.0956	−	34.1488i	−0.352999	−	1.08642i
$989$	19.5918			0.622983
$990$		0			0
$991$	11.3642			0.360996			0.180498	−	0.983575i	$-0.442229\pi$
$991$	11.3642			0.360996			0.180498	+	0.983575i	$0.442229\pi$
$992$	−3.60018	−	11.0802i	−0.114306	−	0.351797i
$993$		0			0
$994$	−1.23971	+	0.900700i	−0.0393211	+	0.0285685i
$995$	−2.21455	+	6.81569i	−0.0702060	+	0.216072i
$996$		0			0
$997$	23.5945	−	17.1424i	0.747246	−	0.542906i	−0.147726	−	0.989028i	$-0.547195\pi$
$997$	23.5945	−	17.1424i	0.747246	−	0.542906i	0.894972	+	0.446122i	$0.147195\pi$
$998$	4.20149	+	3.05256i	0.132996	+	0.0966271i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.n.e.181.1		8
3.2	odd	2		55.2.g.b.16.2	✓	8
11.3	even	5		5445.2.a.bp.1.2		4
11.8	odd	10		5445.2.a.bi.1.3		4
11.9	even	5	inner	495.2.n.e.361.1		8
12.11	even	2		880.2.bo.h.401.1		8
15.2	even	4		275.2.z.a.49.2		16
15.8	even	4		275.2.z.a.49.3		16
15.14	odd	2		275.2.h.a.126.1		8
33.2	even	10		605.2.g.k.251.1		8
33.5	odd	10		605.2.g.m.81.1		8
33.8	even	10		605.2.a.k.1.2		4
33.14	odd	10		605.2.a.j.1.3		4
33.17	even	10		605.2.g.e.81.2		8
33.20	odd	10		55.2.g.b.31.2	yes	8
33.26	odd	10		605.2.g.m.366.1		8
33.29	even	10		605.2.g.e.366.2		8
33.32	even	2		605.2.g.k.511.1		8
132.47	even	10		9680.2.a.cn.1.3		4
132.107	odd	10		9680.2.a.cm.1.3		4
132.119	even	10		880.2.bo.h.801.1		8
165.14	odd	10		3025.2.a.bd.1.2		4
165.53	even	20		275.2.z.a.174.2		16
165.74	even	10		3025.2.a.w.1.3		4
165.119	odd	10		275.2.h.a.251.1		8
165.152	even	20		275.2.z.a.174.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.16.2	✓	8	3.2	odd	2
55.2.g.b.31.2	yes	8	33.20	odd	10
275.2.h.a.126.1		8	15.14	odd	2
275.2.h.a.251.1		8	165.119	odd	10
275.2.z.a.49.2		16	15.2	even	4
275.2.z.a.49.3		16	15.8	even	4
275.2.z.a.174.2		16	165.53	even	20
275.2.z.a.174.3		16	165.152	even	20
495.2.n.e.181.1		8	1.1	even	1	trivial
495.2.n.e.361.1		8	11.9	even	5	inner
605.2.a.j.1.3		4	33.14	odd	10
605.2.a.k.1.2		4	33.8	even	10
605.2.g.e.81.2		8	33.17	even	10
605.2.g.e.366.2		8	33.29	even	10
605.2.g.k.251.1		8	33.2	even	10
605.2.g.k.511.1		8	33.32	even	2
605.2.g.m.81.1		8	33.5	odd	10
605.2.g.m.366.1		8	33.26	odd	10
880.2.bo.h.401.1		8	12.11	even	2
880.2.bo.h.801.1		8	132.119	even	10
3025.2.a.w.1.3		4	165.74	even	10
3025.2.a.bd.1.2		4	165.14	odd	10
5445.2.a.bi.1.3		4	11.8	odd	10
5445.2.a.bp.1.2		4	11.3	even	5
9680.2.a.cm.1.3		4	132.107	odd	10
9680.2.a.cn.1.3		4	132.47	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)

\(f(q)\)	\(=\)	\(q+(-0.147481 - 0.453901i) q^{2} +(1.43376 - 1.04169i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-2.17239 + 1.57833i) q^{7} +(-1.45650 - 1.05821i) q^{8} +O(q^{10})\)	\(q+(-0.147481 - 0.453901i) q^{2} +(1.43376 - 1.04169i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-2.17239 + 1.57833i) q^{7} +(-1.45650 - 1.05821i) q^{8} -0.477260 q^{10} +(2.79042 - 1.79264i) q^{11} +(-1.44244 - 4.43939i) q^{13} +(1.03679 + 0.753275i) q^{14} +(0.829779 - 2.55380i) q^{16} +(1.42961 - 4.39990i) q^{17} +(3.51149 + 2.55125i) q^{19} +(-0.547647 - 1.68548i) q^{20} +(-1.22522 - 1.00220i) q^{22} -2.77222 q^{23} +(-0.809017 - 0.587785i) q^{25} +(-1.80231 + 1.30945i) q^{26} +(-1.47055 + 4.52590i) q^{28} +(-2.43790 + 1.77124i) q^{29} +(0.737407 + 2.26951i) q^{31} -4.88221 q^{32} -2.20796 q^{34} +(0.829779 + 2.55380i) q^{35} +(8.61029 - 6.25574i) q^{37} +(0.640135 - 1.97013i) q^{38} +(-1.45650 + 1.05821i) q^{40} +(-1.78826 - 1.29924i) q^{41} -7.06719 q^{43} +(2.13343 - 5.47695i) q^{44} +(0.408851 + 1.25832i) q^{46} +(3.52905 + 2.56401i) q^{47} +(0.0650188 - 0.200107i) q^{49} +(-0.147481 + 0.453901i) q^{50} +(-6.69257 - 4.86243i) q^{52} +(1.95733 + 6.02403i) q^{53} +(-0.842610 - 3.20780i) q^{55} +4.83428 q^{56} +(1.16351 + 0.845342i) q^{58} +(9.50375 - 6.90488i) q^{59} +(-1.23070 + 3.78770i) q^{61} +(0.921378 - 0.669420i) q^{62} +(-0.939522 - 2.89155i) q^{64} -4.66785 q^{65} +7.31984 q^{67} +(-2.53359 - 7.79760i) q^{68} +(1.03679 - 0.753275i) q^{70} +(-0.369495 + 1.13719i) q^{71} +(-0.826577 + 0.600544i) q^{73} +(-4.10935 - 2.98562i) q^{74} +7.69223 q^{76} +(-3.23251 + 8.29852i) q^{77} +(1.08222 + 3.33073i) q^{79} +(-2.17239 - 1.57833i) q^{80} +(-0.325994 + 1.00331i) q^{82} +(-3.43498 + 10.5718i) q^{83} +(-3.74278 - 2.71929i) q^{85} +(1.04228 + 3.20780i) q^{86} +(-5.96123 - 0.341876i) q^{88} -2.76978 q^{89} +(10.1404 + 7.36742i) q^{91} +(-3.97470 + 2.88779i) q^{92} +(0.643336 - 1.97998i) q^{94} +(3.51149 - 2.55125i) q^{95} +(5.72738 + 17.6271i) q^{97} -0.100418 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - q^{7} - 4 q^{8}+O(q^{10}) \) 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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