LMFDB - Embedded newform 432.2.y.e.37.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(37,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("432.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.y (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.4
Character	$\chi$	$=$	432.37
Dual form			432.2.y.e.397.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.10904 + 0.877514i) q^{2} +(0.459938 - 1.94640i) q^{4} +(1.98415 - 0.531653i) q^{5} +(-1.54969 + 0.894715i) q^{7} +(1.19790 + 2.56223i) q^{8} +O(q^{10})$	\(q+(-1.10904 + 0.877514i) q^{2} +(0.459938 - 1.94640i) q^{4} +(1.98415 - 0.531653i) q^{5} +(-1.54969 + 0.894715i) q^{7} +(1.19790 + 2.56223i) q^{8} +(-1.73397 + 2.33075i) q^{10} +(0.693015 - 2.58637i) q^{11} +(1.24314 + 4.63944i) q^{13} +(0.933545 - 2.35215i) q^{14} +(-3.57691 - 1.79044i) q^{16} +3.58889 q^{17} +(4.85244 - 4.85244i) q^{19} +(-0.122219 - 4.10648i) q^{20} +(1.50099 + 3.47651i) q^{22} +(-0.446082 - 0.257545i) q^{23} +(-0.675912 + 0.390238i) q^{25} +(-5.44986 - 4.05446i) q^{26} +(1.02871 + 3.42783i) q^{28} +(6.44956 + 1.72815i) q^{29} +(4.05128 - 7.01703i) q^{31} +(5.53808 - 1.15312i) q^{32} +(-3.98022 + 3.14930i) q^{34} +(-2.59915 + 2.59915i) q^{35} +(1.25948 + 1.25948i) q^{37} +(-1.12346 + 9.63963i) q^{38} +(3.73904 + 4.44700i) q^{40} +(4.07959 + 2.35535i) q^{41} +(-1.76222 + 6.57670i) q^{43} +(-4.71535 - 2.53845i) q^{44} +(0.720722 - 0.105815i) q^{46} +(3.48945 + 6.04391i) q^{47} +(-1.89897 + 3.28911i) q^{49} +(0.407174 - 1.02591i) q^{50} +(9.60196 - 0.285778i) q^{52} +(-5.26302 - 5.26302i) q^{53} -5.50019i q^{55} +(-4.14885 - 2.89889i) q^{56} +(-8.66930 + 3.74299i) q^{58} +(-6.76946 + 1.81387i) q^{59} +(5.78773 + 1.55082i) q^{61} +(1.66451 + 11.3372i) q^{62} +(-5.13007 + 6.13860i) q^{64} +(4.93314 + 8.54446i) q^{65} +(-0.453328 - 1.69184i) q^{67} +(1.65067 - 6.98540i) q^{68} +(0.601770 - 5.16335i) q^{70} +7.58339i q^{71} -12.5473i q^{73} +(-2.50202 - 0.291601i) q^{74} +(-7.21295 - 11.6766i) q^{76} +(1.24010 + 4.62812i) q^{77} +(-4.01735 - 6.95825i) q^{79} +(-8.04904 - 1.65084i) q^{80} +(-6.59129 + 0.967720i) q^{82} +(-7.99826 - 2.14313i) q^{83} +(7.12091 - 1.90804i) q^{85} +(-3.81677 - 8.84019i) q^{86} +(7.45703 - 1.32255i) q^{88} -16.5414i q^{89} +(-6.07746 - 6.07746i) q^{91} +(-0.706455 + 0.749797i) q^{92} +(-9.17356 - 3.64089i) q^{94} +(7.04818 - 12.2078i) q^{95} +(-4.15739 - 7.20082i) q^{97} +(-0.780209 - 5.31413i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8}+O(q^{10}) $ 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8	$ 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8} - 20 q^{10} + 2 q^{11} - 16 q^{13} + 4 q^{14} - 10 q^{16} + 16 q^{17} + 28 q^{19} - 12 q^{20} - 8 q^{22} + 4 q^{26} - 16 q^{28} - 4 q^{29} + 28 q^{31} + 46 q^{32} - 14 q^{34} + 16 q^{35} + 16 q^{37} - 2 q^{38} - 10 q^{40} - 10 q^{43} - 60 q^{44} + 20 q^{46} + 56 q^{47} + 4 q^{49} + 36 q^{50} + 6 q^{52} + 8 q^{53} - 52 q^{56} - 14 q^{58} + 14 q^{59} - 32 q^{61} - 16 q^{62} - 44 q^{64} + 64 q^{65} - 18 q^{67} - 16 q^{68} + 14 q^{70} - 38 q^{74} + 10 q^{76} + 36 q^{77} + 44 q^{79} - 144 q^{80} - 88 q^{82} - 20 q^{83} - 8 q^{85} - 76 q^{86} - 42 q^{88} - 80 q^{91} + 68 q^{92} + 20 q^{94} - 48 q^{95} + 40 q^{97} - 88 q^{98}+O(q^{100}) $ 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8 - 20 * q^10 + 2 * q^11 - 16 * q^13 + 4 * q^14 - 10 * q^16 + 16 * q^17 + 28 * q^19 - 12 * q^20 - 8 * q^22 + 4 * q^26 - 16 * q^28 - 4 * q^29 + 28 * q^31 + 46 * q^32 - 14 * q^34 + 16 * q^35 + 16 * q^37 - 2 * q^38 - 10 * q^40 - 10 * q^43 - 60 * q^44 + 20 * q^46 + 56 * q^47 + 4 * q^49 + 36 * q^50 + 6 * q^52 + 8 * q^53 - 52 * q^56 - 14 * q^58 + 14 * q^59 - 32 * q^61 - 16 * q^62 - 44 * q^64 + 64 * q^65 - 18 * q^67 - 16 * q^68 + 14 * q^70 - 38 * q^74 + 10 * q^76 + 36 * q^77 + 44 * q^79 - 144 * q^80 - 88 * q^82 - 20 * q^83 - 8 * q^85 - 76 * q^86 - 42 * q^88 - 80 * q^91 + 68 * q^92 + 20 * q^94 - 48 * q^95 + 40 * q^97 - 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.10904	+	0.877514i	−0.784209	+	0.620496i
$2$	−1.10904	+	0.877514i	−0.784209	+	0.620496i
$3$		0			0
$3$		0			0
$4$	0.459938	−	1.94640i	0.229969	−	0.973198i
$5$	1.98415	−	0.531653i	0.887341	−	0.237762i	0.213769	−	0.976884i	$-0.431426\pi$
$5$	1.98415	−	0.531653i	0.887341	−	0.237762i	0.673572	+	0.739122i	$0.264759\pi$
$6$		0			0
$7$	−1.54969	+	0.894715i	−0.585729	+	0.338171i	−0.763407	−	0.645918i	$-0.776475\pi$
$7$	−1.54969	+	0.894715i	−0.585729	+	0.338171i	0.177678	+	0.984089i	$0.443141\pi$
$8$	1.19790	+	2.56223i	0.423522	+	0.905886i
$9$		0			0
$10$	−1.73397	+	2.33075i	−0.548331	+	0.737047i
$11$	0.693015	−	2.58637i	0.208952	−	0.779819i	−0.779257	−	0.626705i	$-0.784403\pi$
$11$	0.693015	−	2.58637i	0.208952	−	0.779819i	0.988209	−	0.153114i	$-0.0489301\pi$
$12$		0			0
$13$	1.24314	+	4.63944i	0.344784	+	1.28675i	0.892865	+	0.450325i	$0.148692\pi$
$13$	1.24314	+	4.63944i	0.344784	+	1.28675i	−0.548081	+	0.836425i	$0.684641\pi$
$14$	0.933545	−	2.35215i	0.249500	−	0.628639i
$15$		0			0
$16$	−3.57691	−	1.79044i	−0.894229	−	0.447611i
$17$	3.58889			0.870434			0.435217	−	0.900326i	$-0.356672\pi$
$17$	3.58889			0.870434			0.435217	+	0.900326i	$0.356672\pi$
$18$		0			0
$19$	4.85244	−	4.85244i	1.11323	−	1.11323i	0.120514	−	0.992712i	$-0.461546\pi$
$19$	4.85244	−	4.85244i	1.11323	−	1.11323i	0.992712	−	0.120514i	$-0.0384543\pi$
$20$	−0.122219	−	4.10648i	−0.0273290	−	0.918236i
$21$		0			0
$22$	1.50099	+	3.47651i	0.320013	+	0.741195i
$23$	−0.446082	−	0.257545i	−0.0930145	−	0.0537019i	0.452771	−	0.891627i	$-0.350435\pi$
$23$	−0.446082	−	0.257545i	−0.0930145	−	0.0537019i	−0.545786	+	0.837925i	$0.683769\pi$
$24$		0			0
$25$	−0.675912	+	0.390238i	−0.135182	+	0.0780476i
$26$	−5.44986	−	4.05446i	−1.06881	−	0.795145i
$27$		0			0
$28$	1.02871	+	3.42783i	0.194408	+	0.647799i
$29$	6.44956	+	1.72815i	1.19765	+	0.320910i	0.801906	−	0.597450i	$-0.203819\pi$
$29$	6.44956	+	1.72815i	1.19765	+	0.320910i	0.395746	+	0.918360i	$0.370486\pi$
$30$		0			0
$31$	4.05128	−	7.01703i	0.727632	−	1.26030i	−0.230249	−	0.973132i	$-0.573954\pi$
$31$	4.05128	−	7.01703i	0.727632	−	1.26030i	0.957881	−	0.287164i	$-0.0927125\pi$
$32$	5.53808	−	1.15312i	0.979003	−	0.203845i
$33$		0			0
$34$	−3.98022	+	3.14930i	−0.682602	+	0.540101i
$35$	−2.59915	+	2.59915i	−0.439337	+	0.439337i
$36$		0			0
$37$	1.25948	+	1.25948i	0.207057	+	0.207057i	0.803015	−	0.595959i	$-0.203228\pi$
$37$	1.25948	+	1.25948i	0.207057	+	0.207057i	−0.595959	+	0.803015i	$0.703228\pi$
$38$	−1.12346	+	9.63963i	−0.182250	+	1.56375i
$39$		0			0
$40$	3.73904	+	4.44700i	0.591194	+	0.703132i
$41$	4.07959	+	2.35535i	0.637126	+	0.367845i	0.783506	−	0.621384i	$-0.213429\pi$
$41$	4.07959	+	2.35535i	0.637126	+	0.367845i	−0.146381	+	0.989228i	$0.546762\pi$
$42$		0			0
$43$	−1.76222	+	6.57670i	−0.268736	+	1.00294i	0.691187	+	0.722676i	$0.257088\pi$
$43$	−1.76222	+	6.57670i	−0.268736	+	1.00294i	−0.959924	+	0.280262i	$0.909579\pi$
$44$	−4.71535	−	2.53845i	−0.710865	−	0.382685i
$45$		0			0
$46$	0.720722	−	0.105815i	0.106265	−	0.0156016i
$47$	3.48945	+	6.04391i	0.508989	+	0.881595i	0.999946	+	0.0104109i	$0.00331395\pi$
$47$	3.48945	+	6.04391i	0.508989	+	0.881595i	−0.490957	+	0.871184i	$0.663353\pi$
$48$		0			0
$49$	−1.89897	+	3.28911i	−0.271281	+	0.469873i
$50$	0.407174	−	1.02591i	0.0575831	−	0.145086i
$51$		0			0
$52$	9.60196	−	0.285778i	1.33155	−	0.0396303i
$53$	−5.26302	−	5.26302i	−0.722932	−	0.722932i	0.246269	−	0.969201i	$-0.420795\pi$
$53$	−5.26302	−	5.26302i	−0.722932	−	0.722932i	−0.969201	+	0.246269i	$0.920795\pi$
$54$		0			0
$55$		−	5.50019i		−	0.741646i
$56$	−4.14885	−	2.89889i	−0.554413	−	0.387381i
$57$		0			0
$58$	−8.66930	+	3.74299i	−1.13833	+	0.491478i
$59$	−6.76946	+	1.81387i	−0.881308	+	0.236146i	−0.670972	−	0.741483i	$-0.734123\pi$
$59$	−6.76946	+	1.81387i	−0.881308	+	0.236146i	−0.210337	+	0.977629i	$0.567456\pi$
$60$		0			0
$61$	5.78773	+	1.55082i	0.741042	+	0.198562i	0.609541	−	0.792754i	$-0.291354\pi$
$61$	5.78773	+	1.55082i	0.741042	+	0.198562i	0.131501	+	0.991316i	$0.458020\pi$
$62$	1.66451	+	11.3372i	0.211393	+	1.43983i
$63$		0			0
$64$	−5.13007	+	6.13860i	−0.641258	+	0.767325i
$65$	4.93314	+	8.54446i	0.611881	+	1.05981i
$66$		0			0
$67$	−0.453328	−	1.69184i	−0.0553829	−	0.206692i	0.932690	−	0.360679i	$-0.117455\pi$
$67$	−0.453328	−	1.69184i	−0.0553829	−	0.206692i	−0.988073	+	0.153988i	$0.950788\pi$
$68$	1.65067	−	6.98540i	0.200173	−	0.847104i
$69$		0			0
$70$	0.601770	−	5.16335i	0.0719252	−	0.617139i
$71$			7.58339i			0.899983i	0.893033	+	0.449992i	$0.148573\pi$
$71$			7.58339i			0.899983i	−0.893033	+	0.449992i	$0.851427\pi$
$72$		0			0
$73$		−	12.5473i		−	1.46855i	−0.678854	−	0.734273i	$-0.737523\pi$
$73$		−	12.5473i		−	1.46855i	0.678854	−	0.734273i	$-0.262477\pi$
$74$	−2.50202	−	0.291601i	−0.290854	−	0.0338979i
$75$		0			0
$76$	−7.21295	−	11.6766i	−0.827382	−	1.33940i
$77$	1.24010	+	4.62812i	0.141323	+	0.527423i
$78$		0			0
$79$	−4.01735	−	6.95825i	−0.451987	−	0.782864i	0.546523	−	0.837444i	$-0.315951\pi$
$79$	−4.01735	−	6.95825i	−0.451987	−	0.782864i	−0.998509	+	0.0545802i	$0.982618\pi$
$80$	−8.04904	−	1.65084i	−0.899911	−	0.184569i
$81$		0			0
$82$	−6.59129	+	0.967720i	−0.727886	+	0.106867i
$83$	−7.99826	−	2.14313i	−0.877923	−	0.235239i	−0.208412	−	0.978041i	$-0.566829\pi$
$83$	−7.99826	−	2.14313i	−0.877923	−	0.235239i	−0.669511	+	0.742802i	$0.733496\pi$
$84$		0			0
$85$	7.12091	−	1.90804i	0.772371	−	0.206956i
$86$	−3.81677	−	8.84019i	−0.411573	−	0.953263i
$87$		0			0
$88$	7.45703	−	1.32255i	0.794922	−	0.140984i
$89$		−	16.5414i		−	1.75339i	−0.481047	−	0.876695i	$-0.659743\pi$
$89$		−	16.5414i		−	1.75339i	0.481047	−	0.876695i	$-0.340257\pi$
$90$		0			0
$91$	−6.07746	−	6.07746i	−0.637091	−	0.637091i
$92$	−0.706455	+	0.749797i	−0.0736531	+	0.0781717i
$93$		0			0
$94$	−9.17356	−	3.64089i	−0.946180	−	0.375529i
$95$	7.04818	−	12.2078i	0.723128	−	1.25249i
$96$		0			0
$97$	−4.15739	−	7.20082i	−0.422119	−	0.731132i	0.574027	−	0.818836i	$-0.305380\pi$
$97$	−4.15739	−	7.20082i	−0.422119	−	0.731132i	−0.996147	+	0.0877040i	$0.972047\pi$
$98$	−0.780209	−	5.31413i	−0.0788130	−	0.536808i
$99$		0			0
$100$	0.448680	+	1.49508i	0.0448680	+	0.149508i
$101$	−1.25971	+	4.70129i	−0.125346	+	0.467796i	−0.999852	−	0.0172183i	$-0.994519\pi$
$101$	−1.25971	+	4.70129i	−0.125346	+	0.467796i	0.874506	+	0.485014i	$0.161186\pi$
$102$		0			0
$103$	6.13162	+	3.54009i	0.604166	+	0.348816i	0.770679	−	0.637224i	$-0.219917\pi$
$103$	6.13162	+	3.54009i	0.604166	+	0.348816i	−0.166512	+	0.986039i	$0.553251\pi$
$104$	−10.3982	+	8.74279i	−1.01963	+	0.857301i
$105$		0			0
$106$	10.4553	+	1.21852i	1.01551	+	0.118354i
$107$	−6.68494	−	6.68494i	−0.646258	−	0.646258i	0.305829	−	0.952087i	$-0.401066\pi$
$107$	−6.68494	−	6.68494i	−0.646258	−	0.646258i	−0.952087	+	0.305829i	$0.901066\pi$
$108$		0			0
$109$	−11.6423	+	11.6423i	−1.11513	+	1.11513i	−0.122687	+	0.992445i	$0.539151\pi$
$109$	−11.6423	+	11.6423i	−1.11513	+	1.11513i	−0.992445	+	0.122687i	$0.960849\pi$
$110$	4.82650	+	6.09993i	0.460188	+	0.581606i
$111$		0			0
$112$	7.14505	−	0.425686i	0.675144	−	0.0402235i
$113$	−0.346060	+	0.599393i	−0.0325545	+	0.0563861i	−0.881844	−	0.471542i	$-0.843698\pi$
$113$	−0.346060	+	0.599393i	−0.0325545	+	0.0563861i	0.849289	+	0.527928i	$0.177031\pi$
$114$		0			0
$115$	−1.02202	−	0.273849i	−0.0953039	−	0.0255366i
$116$	6.33007	−	11.7586i	0.587732	−	1.09175i
$117$		0			0
$118$	5.91590	−	7.95195i	0.544603	−	0.732036i
$119$	−5.56168	+	3.21104i	−0.509838	+	0.294355i
$120$		0			0
$121$	3.31726	+	1.91522i	0.301569	+	0.174111i
$122$	−7.77968	+	3.35889i	−0.704339	+	0.304100i
$123$		0			0
$124$	−11.7946	−	11.1128i	−1.05918	−	0.997959i
$125$	−8.39615	+	8.39615i	−0.750975	+	0.750975i
$126$		0			0
$127$	5.71585			0.507200			0.253600	−	0.967309i	$-0.418385\pi$
$127$	5.71585			0.507200			0.253600	+	0.967309i	$0.418385\pi$
$128$	0.302740	−	11.3097i	0.0267587	−	0.999642i
$129$		0			0
$130$	−12.9689	−	5.14724i	−1.13745	−	0.451443i
$131$	−2.36823	−	8.83835i	−0.206913	−	0.772210i	−0.988858	−	0.148863i	$-0.952439\pi$
$131$	−2.36823	−	8.83835i	−0.206913	−	0.772210i	0.781945	−	0.623348i	$-0.214228\pi$
$132$		0			0
$133$	−3.17824	+	11.8613i	−0.275588	+	1.02851i
$134$	1.98738	+	1.47852i	0.171683	+	0.127725i
$135$		0			0
$136$	4.29913	+	9.19557i	0.368648	+	0.788514i
$137$	−0.535518	+	0.309181i	−0.0457524	+	0.0264151i	−0.522702	−	0.852516i	$-0.675076\pi$
$137$	−0.535518	+	0.309181i	−0.0457524	+	0.0264151i	0.476949	+	0.878931i	$0.341743\pi$
$138$		0			0
$139$	−18.4588	+	4.94601i	−1.56565	+	0.419515i	−0.934447	−	0.356101i	$-0.884106\pi$
$139$	−18.4588	+	4.94601i	−1.56565	+	0.419515i	−0.631205	+	0.775616i	$0.717439\pi$
$140$	3.86353	+	6.25443i	0.326528	+	0.528595i
$141$		0			0
$142$	−6.65453	−	8.41028i	−0.558436	−	0.705775i
$143$	12.8608			1.07547
$144$		0			0
$145$	13.7157			1.13903
$146$	11.0104	+	13.9154i	0.911227	+	1.15165i
$147$		0			0
$148$	3.03072	−	1.87216i	0.249124	−	0.153890i
$149$	5.06509	−	1.35719i	0.414948	−	0.111185i	−0.0453039	−	0.998973i	$-0.514426\pi$
$149$	5.06509	−	1.35719i	0.414948	−	0.111185i	0.460252	+	0.887788i	$0.347759\pi$
$150$		0			0
$151$	−7.80108	+	4.50395i	−0.634843	+	0.366527i	−0.782625	−	0.622493i	$-0.786120\pi$
$151$	−7.80108	+	4.50395i	−0.634843	+	0.366527i	0.147782	+	0.989020i	$0.452786\pi$
$152$	18.2458	+	6.62033i	1.47993	+	0.536980i
$153$		0			0
$154$	−5.43656	−	4.04456i	−0.438091	−	0.325920i
$155$	4.30775	−	16.0767i	0.346007	−	1.29132i
$156$		0			0
$157$	2.93223	+	10.9432i	0.234017	+	0.873364i	0.978589	+	0.205822i	$0.0659868\pi$
$157$	2.93223	+	10.9432i	0.234017	+	0.873364i	−0.744572	+	0.667542i	$0.767347\pi$
$158$	10.5614	+	4.19170i	0.840217	+	0.333473i
$159$		0			0
$160$	10.3753	−	5.23231i	0.820243	−	0.413650i
$161$	0.921720			0.0726417
$162$		0			0
$163$	−11.9073	+	11.9073i	−0.932649	+	0.932649i	−0.997871	−	0.0652222i	$-0.979224\pi$
$163$	−11.9073	+	11.9073i	−0.932649	+	0.932649i	0.0652222	+	0.997871i	$0.479224\pi$
$164$	6.46081	−	6.85719i	0.504505	−	0.535457i
$165$		0			0
$166$	10.7510	−	4.64177i	0.834440	−	0.360271i
$167$	−8.19418	−	4.73091i	−0.634085	−	0.366089i	0.148248	−	0.988950i	$-0.452637\pi$
$167$	−8.19418	−	4.73091i	−0.634085	−	0.366089i	−0.782332	+	0.622861i	$0.785970\pi$
$168$		0			0
$169$	−8.72072	+	5.03491i	−0.670825	+	0.387301i
$170$	−6.22304	+	8.36480i	−0.477285	+	0.641551i
$171$		0			0
$172$	11.9903	+	6.45485i	0.914255	+	0.492178i
$173$	−23.1112	−	6.19263i	−1.75711	−	0.470817i	−0.770991	−	0.636846i	$-0.780239\pi$
$173$	−23.1112	−	6.19263i	−1.75711	−	0.470817i	−0.986121	+	0.166030i	$0.946905\pi$
$174$		0			0
$175$	0.698304	−	1.20950i	0.0527868	−	0.0914295i
$176$	−7.10959	+	8.01041i	−0.535906	+	0.603807i
$177$		0			0
$178$	14.5154	+	18.3451i	1.08797	+	1.37502i
$179$	−11.6334	+	11.6334i	−0.869521	+	0.869521i	−0.992419	−	0.122898i	$-0.960781\pi$
$179$	−11.6334	+	11.6334i	−0.869521	+	0.869521i	0.122898	+	0.992419i	$0.460781\pi$
$180$		0			0
$181$	−10.9379	−	10.9379i	−0.813010	−	0.813010i	0.172074	−	0.985084i	$-0.444953\pi$
$181$	−10.9379	−	10.9379i	−0.813010	−	0.813010i	−0.985084	+	0.172074i	$0.944953\pi$
$182$	12.0732	+	1.40709i	0.894925	+	0.104300i
$183$		0			0
$184$	0.125529	−	1.45148i	0.00925416	−	0.107004i
$185$	3.16860	+	1.82939i	0.232960	+	0.134500i
$186$		0			0
$187$	2.48715	−	9.28218i	0.181879	−	0.678780i
$188$	13.3688	−	4.01203i	0.975018	−	0.292608i
$189$		0			0
$190$	2.89581	+	19.7238i	0.210084	+	1.43092i
$191$	−3.34360	−	5.79129i	−0.241934	−	0.419043i	0.719331	−	0.694668i	$-0.244449\pi$
$191$	−3.34360	−	5.79129i	−0.241934	−	0.419043i	−0.961265	+	0.275625i	$0.911115\pi$
$192$		0			0
$193$	−0.468469	+	0.811411i	−0.0337211	+	0.0584067i	−0.882393	−	0.470512i	$-0.844069\pi$
$193$	−0.468469	+	0.811411i	−0.0337211	+	0.0584067i	0.848672	+	0.528919i	$0.177402\pi$
$194$	10.9295	+	4.33782i	0.784695	+	0.311437i
$195$		0			0
$196$	5.52850	+	5.20893i	0.394893	+	0.372067i
$197$	14.7962	+	14.7962i	1.05419	+	1.05419i	0.998445	+	0.0557400i	$0.0177518\pi$
$197$	14.7962	+	14.7962i	1.05419	+	1.05419i	0.0557400	+	0.998445i	$0.482248\pi$
$198$		0			0
$199$		−	2.36977i		−	0.167988i	−0.996466	−	0.0839942i	$-0.973232\pi$
$199$		−	2.36977i		−	0.167988i	0.996466	−	0.0839942i	$-0.0267677\pi$
$200$	−1.80956	−	1.26438i	−0.127955	−	0.0894050i
$201$		0			0
$202$	−2.72838	−	6.31933i	−0.191968	−	0.444627i
$203$	−11.5410	+	3.09241i	−0.810022	+	0.217045i
$204$		0			0
$205$	9.34678	+	2.50446i	0.652807	+	0.174919i
$206$	−9.90669	+	1.45448i	−0.690232	+	0.101338i
$207$		0			0
$208$	3.86007	−	18.8207i	0.267647	−	1.30498i
$209$	−9.18737	−	15.9130i	−0.635504	−	1.10072i
$210$		0			0
$211$	−0.521927	−	1.94786i	−0.0359309	−	0.134096i	0.945631	−	0.325243i	$-0.105446\pi$
$211$	−0.521927	−	1.94786i	−0.0359309	−	0.134096i	−0.981561	+	0.191147i	$0.938779\pi$
$212$	−12.6646	+	7.82327i	−0.869808	+	0.537304i
$213$		0			0
$214$	13.2800	+	1.54773i	0.907802	+	0.105801i
$215$			13.9861i			0.953842i
$216$		0			0
$217$			14.4990i			0.984255i
$218$	2.69549	−	23.1281i	0.182562	−	1.56643i
$219$		0			0
$220$	−10.7056	−	2.52975i	−0.721768	−	0.170555i
$221$	4.46148	+	16.6505i	0.300111	+	1.12003i
$222$		0			0
$223$	5.55008	+	9.61302i	0.371661	+	0.643735i	0.989821	−	0.142317i	$-0.0454551\pi$
$223$	5.55008	+	9.61302i	0.371661	+	0.643735i	−0.618160	+	0.786052i	$0.712122\pi$
$224$	−7.55060	+	6.74199i	−0.504496	+	0.450468i
$225$		0			0
$226$	−0.142182	−	0.968422i	−0.00945780	−	0.0644185i
$227$	16.7860	+	4.49779i	1.11412	+	0.298529i	0.768504	−	0.639845i	$-0.221002\pi$
$227$	16.7860	+	4.49779i	1.11412	+	0.298529i	0.345621	+	0.938374i	$0.387668\pi$
$228$		0			0
$229$	15.4674	−	4.14447i	1.02211	−	0.273874i	0.291430	−	0.956592i	$-0.405869\pi$
$229$	15.4674	−	4.14447i	1.02211	−	0.273874i	0.730682	+	0.682718i	$0.239202\pi$
$230$	1.37377	−	0.593127i	0.0905835	−	0.0391096i
$231$		0			0
$232$	3.29800	+	18.5954i	0.216524	+	1.22085i
$233$		−	25.2041i		−	1.65118i	−0.564273	−	0.825588i	$-0.690844\pi$
$233$		−	25.2041i		−	1.65118i	0.564273	−	0.825588i	$-0.309156\pi$
$234$		0			0
$235$	10.1369	+	10.1369i	0.661257	+	0.661257i
$236$	0.416981	+	14.0103i	0.0271432	+	0.911994i
$237$		0			0
$238$	3.35039	−	8.44162i	0.217174	−	0.547189i
$239$	−4.14085	+	7.17217i	−0.267850	+	0.463929i	−0.968306	−	0.249766i	$-0.919646\pi$
$239$	−4.14085	+	7.17217i	−0.267850	+	0.463929i	0.700457	+	0.713695i	$0.252980\pi$
$240$		0			0
$241$	−6.40038	−	11.0858i	−0.412285	−	0.714098i	0.582854	−	0.812577i	$-0.301936\pi$
$241$	−6.40038	−	11.0858i	−0.412285	−	0.714098i	−0.995139	+	0.0984784i	$0.968602\pi$
$242$	−5.35961	+	0.786887i	−0.344529	+	0.0505830i
$243$		0			0
$244$	5.68050	−	10.5519i	0.363657	−	0.675518i
$245$	−2.01918	+	7.53570i	−0.129001	+	0.481438i
$246$		0			0
$247$	28.5449	+	16.4804i	1.81627	+	1.04862i
$248$	22.8323	+	1.97462i	1.44985	+	0.125389i
$249$		0			0
$250$	1.94392	−	16.6794i	0.122944	−	1.05490i
$251$	13.9414	+	13.9414i	0.879976	+	0.879976i	0.993532	−	0.113556i	$-0.0362241\pi$
$251$	13.9414	+	13.9414i	0.879976	+	0.879976i	−0.113556	+	0.993532i	$0.536224\pi$
$252$		0			0
$253$	−0.975248	+	0.975248i	−0.0613133	+	0.0613133i
$254$	−6.33911	+	5.01574i	−0.397751	+	0.314716i
$255$		0			0
$256$	9.58863	+	12.8085i	0.599290	+	0.800532i
$257$	3.51445	−	6.08720i	0.219225	−	0.379709i	−0.735346	−	0.677692i	$-0.762980\pi$
$257$	3.51445	−	6.08720i	0.219225	−	0.379709i	0.954571	+	0.297983i	$0.0963137\pi$
$258$		0			0
$259$	−3.07867	−	0.824928i	−0.191299	−	0.0512585i
$260$	18.8998	−	5.67193i	1.17212	−	0.351758i
$261$		0			0
$262$	10.3822	+	7.72393i	0.641417	+	0.477186i
$263$	15.1779	−	8.76296i	0.935909	−	0.540348i	0.0472338	−	0.998884i	$-0.484959\pi$
$263$	15.1779	−	8.76296i	0.935909	−	0.540348i	0.888676	+	0.458536i	$0.151626\pi$
$264$		0			0
$265$	−13.2408	−	7.64455i	−0.813373	−	0.469601i
$266$	−6.88370	−	15.9436i	−0.422067	−	0.977568i
$267$		0			0
$268$	−3.50150	+	0.104213i	−0.213888	+	0.00636584i
$269$	0.311911	−	0.311911i	0.0190176	−	0.0190176i	−0.697534	−	0.716552i	$-0.745719\pi$
$269$	0.311911	−	0.311911i	0.0190176	−	0.0190176i	0.716552	+	0.697534i	$0.245719\pi$
$270$		0			0
$271$	7.46993			0.453766			0.226883	−	0.973922i	$-0.427147\pi$
$271$	7.46993			0.453766			0.226883	+	0.973922i	$0.427147\pi$
$272$	−12.8372	−	6.42570i	−0.778367	−	0.389615i
$273$		0			0
$274$	0.322599	−	0.812819i	0.0194889	−	0.0491042i
$275$	0.540881	+	2.01860i	0.0326164	+	0.121726i
$276$		0			0
$277$	2.71916	−	10.1481i	0.163379	−	0.609737i	−0.834863	−	0.550458i	$-0.814453\pi$
$277$	2.71916	−	10.1481i	0.163379	−	0.609737i	0.998241	−	0.0592792i	$-0.0188802\pi$
$278$	16.1313	−	21.6831i	0.967491	−	1.30047i
$279$		0			0
$280$	−9.77316	−	3.54610i	−0.584058	−	0.211920i
$281$	−5.76358	+	3.32761i	−0.343826	+	0.198508i	−0.661963	−	0.749537i	$-0.730276\pi$
$281$	−5.76358	+	3.32761i	−0.343826	+	0.198508i	0.318136	+	0.948045i	$0.396943\pi$
$282$		0			0
$283$	−10.6365	+	2.85005i	−0.632275	+	0.169418i	−0.560702	−	0.828018i	$-0.689469\pi$
$283$	−10.6365	+	2.85005i	−0.632275	+	0.169418i	−0.0715734	+	0.997435i	$0.522802\pi$
$284$	14.7603	+	3.48789i	0.875862	+	0.206968i
$285$		0			0
$286$	−14.2631	+	11.2855i	−0.843397	+	0.667328i
$287$	−8.42949			−0.497577
$288$		0			0
$289$	−4.11987			−0.242345
$290$	−15.2113	+	12.0357i	−0.893236	+	0.706762i
$291$		0			0
$292$	−24.4219	−	5.77096i	−1.42919	−	0.337720i
$293$	2.75926	−	0.739342i	0.161198	−	0.0431928i	−0.177318	−	0.984154i	$-0.556742\pi$
$293$	2.75926	−	0.739342i	0.161198	−	0.0431928i	0.338515	+	0.940961i	$0.390075\pi$
$294$		0			0
$295$	−12.4673	+	7.19800i	−0.725874	+	0.419084i
$296$	−1.71834	+	4.73580i	−0.0998766	+	0.275263i
$297$		0			0
$298$	−4.42644	+	5.94986i	−0.256416	+	0.344666i
$299$	0.640328	−	2.38974i	0.0370311	−	0.138202i
$300$		0			0
$301$	−3.15337	−	11.7685i	−0.181757	−	0.678328i
$302$	4.69942	−	11.8406i	0.270421	−	0.681351i
$303$		0			0
$304$	−26.0448	+	8.66875i	−1.49377	+	0.497187i
$305$	12.3082			0.704768
$306$		0			0
$307$	−8.15691	+	8.15691i	−0.465540	+	0.465540i	−0.900466	−	0.434926i	$-0.856774\pi$
$307$	−8.15691	+	8.15691i	−0.465540	+	0.465540i	0.434926	+	0.900466i	$0.356774\pi$
$308$	9.57853	−	0.285080i	0.545787	−	0.0162440i
$309$		0			0
$310$	9.33011	+	21.6099i	0.529914	+	1.22736i
$311$	8.33416	+	4.81173i	0.472587	+	0.272848i	0.717322	−	0.696742i	$-0.245368\pi$
$311$	8.33416	+	4.81173i	0.472587	+	0.272848i	−0.244735	+	0.969590i	$0.578701\pi$
$312$		0			0
$313$	−22.2531	+	12.8478i	−1.25782	+	0.726202i	−0.972650	−	0.232276i	$-0.925383\pi$
$313$	−22.2531	+	12.8478i	−1.25782	+	0.726202i	−0.285168	+	0.958477i	$0.592049\pi$
$314$	−12.8548	−	9.56339i	−0.725437	−	0.539693i
$315$		0			0
$316$	−15.3912	+	4.61899i	−0.865825	+	0.259838i
$317$	−15.6062	−	4.18167i	−0.876532	−	0.234866i	−0.207622	−	0.978209i	$-0.566572\pi$
$317$	−15.6062	−	4.18167i	−0.876532	−	0.234866i	−0.668910	+	0.743343i	$0.733239\pi$
$318$		0			0
$319$	8.93928	−	15.4833i	0.500503	−	0.866897i
$320$	−6.91524	+	14.9073i	−0.386574	+	0.833346i
$321$		0			0
$322$	−1.02222	+	0.808822i	−0.0569663	+	0.0450739i
$323$	17.4149	−	17.4149i	0.968989	−	0.968989i
$324$		0			0
$325$	−2.65074	−	2.65074i	−0.147036	−	0.147036i
$326$	2.75683	−	23.6544i	0.152687	−	1.31010i
$327$		0			0
$328$	−1.14802	+	13.2743i	−0.0633886	+	0.732953i
$329$	−10.8152	−	6.24413i	−0.596259	−	0.344250i
$330$		0			0
$331$	5.25422	−	19.6090i	0.288798	−	1.07781i	−0.657221	−	0.753698i	$-0.728268\pi$
$331$	5.25422	−	19.6090i	0.288798	−	1.07781i	0.946019	−	0.324111i	$-0.105065\pi$
$332$	−7.85007	+	14.5821i	−0.430829	+	0.800295i
$333$		0			0
$334$	13.2391	−	1.94374i	0.724412	−	0.106357i
$335$	−1.79895	−	3.11587i	−0.0982870	−	0.170238i
$336$		0			0
$337$	1.04249	−	1.80564i	0.0567879	−	0.0983595i	−0.836234	−	0.548373i	$-0.815247\pi$
$337$	1.04249	−	1.80564i	0.0567879	−	0.0983595i	0.893022	+	0.450013i	$0.148581\pi$
$338$	5.25342	−	13.2365i	0.285748	−	0.719969i
$339$		0			0
$340$	−0.438630	−	14.7377i	−0.0237881	−	0.799264i
$341$	−15.3410	−	15.3410i	−0.830762	−	0.830762i
$342$		0			0
$343$		−	19.3222i		−	1.04330i
$344$	−18.9620	+	3.36301i	−1.02236	+	0.181322i
$345$		0			0
$346$	31.0653	−	13.4125i	1.67008	−	0.721062i
$347$	−8.16281	+	2.18722i	−0.438203	+	0.117416i	−0.471174	−	0.882040i	$-0.656170\pi$
$347$	−8.16281	+	2.18722i	−0.438203	+	0.117416i	0.0329715	+	0.999456i	$0.489503\pi$
$348$		0			0
$349$	−1.50715	−	0.403839i	−0.0806758	−	0.0216170i	0.218255	−	0.975892i	$-0.429963\pi$
$349$	−1.50715	−	0.403839i	−0.0806758	−	0.0216170i	−0.298931	+	0.954275i	$0.596630\pi$
$350$	0.286905	+	1.95415i	0.0153357	+	0.104454i
$351$		0			0
$352$	0.855574	−	15.1226i	0.0456023	−	0.806039i
$353$	8.13441	+	14.0892i	0.432951	+	0.749893i	0.997126	−	0.0757623i	$-0.0241390\pi$
$353$	8.13441	+	14.0892i	0.432951	+	0.749893i	−0.564175	+	0.825655i	$0.690806\pi$
$354$		0			0
$355$	4.03173	+	15.0466i	0.213982	+	0.798592i
$356$	−32.1962	−	7.60803i	−1.70640	−	0.403225i
$357$		0			0
$358$	2.69343	−	23.1104i	0.142352	−	1.22142i
$359$			3.08148i			0.162634i	0.996688	+	0.0813172i	$0.0259127\pi$
$359$			3.08148i			0.162634i	−0.996688	+	0.0813172i	$0.974087\pi$
$360$		0			0
$361$		−	28.0923i		−	1.47854i
$362$	21.7288	+	2.53241i	1.14204	+	0.133100i
$363$		0			0
$364$	−14.6244	+	9.03389i	−0.766527	+	0.473504i
$365$	−6.67079	−	24.8957i	−0.349165	−	1.30310i
$366$		0			0
$367$	−1.38231	−	2.39424i	−0.0721562	−	0.124978i	0.827690	−	0.561186i	$-0.189655\pi$
$367$	−1.38231	−	2.39424i	−0.0721562	−	0.124978i	−0.899846	+	0.436208i	$0.856321\pi$
$368$	1.13448	+	1.71990i	0.0591387	+	0.0896561i
$369$		0			0
$370$	−5.11942	+	0.751623i	−0.266146	+	0.0390750i
$371$	12.8650	+	3.44716i	0.667916	+	0.178968i
$372$		0			0
$373$	−22.6202	+	6.06106i	−1.17123	+	0.313830i	−0.791442	−	0.611244i	$-0.790669\pi$
$373$	−22.6202	+	6.06106i	−1.17123	+	0.313830i	−0.379787	+	0.925074i	$0.624003\pi$
$374$	5.38689	+	12.4768i	0.278550	+	0.645161i
$375$		0			0
$376$	−11.3059	+	16.1808i	−0.583056	+	0.834461i
$377$			32.0707i			1.65172i
$378$		0			0
$379$	4.70551	+	4.70551i	0.241706	+	0.241706i	0.817555	−	0.575850i	$-0.195329\pi$
$379$	4.70551	+	4.70551i	0.241706	+	0.241706i	−0.575850	+	0.817555i	$0.695329\pi$
$380$	−20.5195	−	19.3334i	−1.05263	−	0.991781i
$381$		0			0
$382$	8.79012	+	3.48871i	0.449742	+	0.178498i
$383$	−18.3311	+	31.7505i	−0.936678	+	1.62237i	−0.165063	+	0.986283i	$0.552783\pi$
$383$	−18.3311	+	31.7505i	−0.936678	+	1.62237i	−0.771614	+	0.636091i	$0.780550\pi$
$384$		0			0
$385$	4.92111	+	8.52361i	0.250803	+	0.434403i
$386$	−0.192475	−	1.31098i	−0.00979671	−	0.0667269i
$387$		0			0
$388$	−15.9278	+	4.78001i	−0.808611	+	0.242668i
$389$	0.757647	−	2.82758i	0.0384142	−	0.143364i	−0.944055	−	0.329787i	$-0.893023\pi$
$389$	0.757647	−	2.82758i	0.0384142	−	0.143364i	0.982469	+	0.186423i	$0.0596896\pi$
$390$		0			0
$391$	−1.60094	−	0.924302i	−0.0809630	−	0.0467440i
$392$	−10.7022	−	0.925571i	−0.540545	−	0.0467484i
$393$		0			0
$394$	−29.3934	−	3.42570i	−1.48082	−	0.172584i
$395$	−11.6704	−	11.6704i	−0.587202	−	0.587202i
$396$		0			0
$397$	13.3392	−	13.3392i	0.669474	−	0.669474i	−0.288120	−	0.957594i	$-0.593030\pi$
$397$	13.3392	−	13.3392i	0.669474	−	0.669474i	0.957594	+	0.288120i	$0.0930302\pi$
$398$	2.07951	+	2.62817i	0.104236	+	0.131738i
$399$		0			0
$400$	3.11638	−	0.185667i	0.155819	−	0.00928333i
$401$	4.84547	−	8.39261i	0.241971	−	0.419107i	−0.719304	−	0.694695i	$-0.755539\pi$
$401$	4.84547	−	8.39261i	0.241971	−	0.419107i	0.961276	+	0.275588i	$0.0888726\pi$
$402$		0			0
$403$	37.5914	+	10.0726i	1.87256	+	0.501751i
$404$	8.57119	+	4.61419i	0.426433	+	0.229565i
$405$		0			0
$406$	10.0858	−	13.5570i	0.500551	−	0.672824i
$407$	4.13030	−	2.38463i	0.204731	−	0.118202i
$408$		0			0
$409$	−6.19403	−	3.57613i	−0.306275	−	0.176828i	0.338983	−	0.940792i	$-0.389917\pi$
$409$	−6.19403	−	3.57613i	−0.306275	−	0.176828i	−0.645258	+	0.763964i	$0.723250\pi$
$410$	−12.5636	+	5.42438i	−0.620474	+	0.267891i
$411$		0			0
$412$	9.71059	−	10.3063i	0.478406	−	0.507757i
$413$	8.86768	−	8.86768i	0.436350	−	0.436350i
$414$		0			0
$415$	−17.0092			−0.834948
$416$	12.2344	+	24.2601i	0.599842	+	1.18945i
$417$		0			0
$418$	24.1530	+	9.58609i	1.18136	+	0.468871i
$419$	4.80711	+	17.9404i	0.234843	+	0.876445i	0.978220	+	0.207572i	$0.0665562\pi$
$419$	4.80711	+	17.9404i	0.234843	+	0.876445i	−0.743377	+	0.668873i	$0.766777\pi$
$420$		0			0
$421$	−0.527873	+	1.97005i	−0.0257270	+	0.0960144i	−0.977596	−	0.210492i	$-0.932493\pi$
$421$	−0.527873	+	1.97005i	−0.0257270	+	0.0960144i	0.951869	+	0.306506i	$0.0991601\pi$
$422$	2.28811	+	1.70225i	0.111383	+	0.0828644i
$423$		0			0
$424$	7.18051	−	19.7897i	0.348716	−	0.961071i
$425$	−2.42577	+	1.40052i	−0.117667	+	0.0679353i
$426$		0			0
$427$	−10.3567	+	2.77508i	−0.501198	+	0.134295i
$428$	−16.0862	+	9.93689i	−0.777556	+	0.480317i
$429$		0			0
$430$	−12.2730	−	15.5111i	−0.591856	−	0.748012i
$431$	19.8202			0.954707			0.477354	−	0.878711i	$-0.341596\pi$
$431$	19.8202			0.954707			0.477354	+	0.878711i	$0.341596\pi$
$432$		0			0
$433$	23.7342			1.14060			0.570298	−	0.821438i	$-0.306828\pi$
$433$	23.7342			1.14060			0.570298	+	0.821438i	$0.306828\pi$
$434$	−12.7231	−	16.0799i	−0.610727	−	0.771862i
$435$		0			0
$436$	17.3058	+	28.0153i	0.828799	+	1.34169i
$437$	−3.41431	+	0.914861i	−0.163329	+	0.0437637i
$438$		0			0
$439$	19.0949	−	11.0245i	0.911350	−	0.526168i	0.0304850	−	0.999535i	$-0.490295\pi$
$439$	19.0949	−	11.0245i	0.911350	−	0.526168i	0.880865	+	0.473367i	$0.156961\pi$
$440$	14.0928	−	6.58868i	0.671846	−	0.314103i
$441$		0			0
$442$	−19.5590	−	14.5510i	−0.930325	−	0.692121i
$443$	−2.60232	+	9.71199i	−0.123640	+	0.461431i	−0.999788	−	0.0206123i	$-0.993438\pi$
$443$	−2.60232	+	9.71199i	−0.123640	+	0.461431i	0.876148	+	0.482043i	$0.160105\pi$
$444$		0			0
$445$	−8.79430	−	32.8208i	−0.416890	−	1.55585i
$446$	−14.5908	−	5.79094i	−0.690895	−	0.274209i
$447$		0			0
$448$	2.45773	−	14.1029i	0.116117	−	0.666299i
$449$	−24.6980			−1.16557			−0.582786	−	0.812626i	$-0.698037\pi$
$449$	−24.6980			−1.16557			−0.582786	+	0.812626i	$0.698037\pi$
$450$		0			0
$451$	8.91903	−	8.91903i	0.419981	−	0.419981i
$452$	1.00749	+	0.949252i	0.0473883	+	0.0446491i
$453$		0			0
$454$	−22.5632	+	9.74171i	−1.05894	+	0.457201i
$455$	−15.2897	−	8.82752i	−0.716793	−	0.413841i
$456$		0			0
$457$	27.1171	−	15.6561i	1.26849	−	0.732360i	0.293784	−	0.955872i	$-0.405085\pi$
$457$	27.1171	−	15.6561i	1.26849	−	0.732360i	0.974701	+	0.223511i	$0.0717520\pi$
$458$	−13.5171	+	18.1692i	−0.631612	+	0.848992i
$459$		0			0
$460$	−1.00309	+	1.86330i	−0.0467691	+	0.0868769i
$461$	11.8344	+	3.17103i	0.551185	+	0.147689i	0.523653	−	0.851931i	$-0.324569\pi$
$461$	11.8344	+	3.17103i	0.551185	+	0.147689i	0.0275314	+	0.999621i	$0.491235\pi$
$462$		0			0
$463$	−12.7250	+	22.0403i	−0.591379	+	1.02430i	0.402668	+	0.915346i	$0.368083\pi$
$463$	−12.7250	+	22.0403i	−0.591379	+	1.02430i	−0.994047	+	0.108953i	$0.965250\pi$
$464$	−19.9754	−	17.7290i	−0.927333	−	0.823049i
$465$		0			0
$466$	22.1170	+	27.9524i	1.02455	+	1.29487i
$467$	6.28473	−	6.28473i	0.290822	−	0.290822i	−0.546583	−	0.837405i	$-0.684072\pi$
$467$	6.28473	−	6.28473i	0.290822	−	0.290822i	0.837405	+	0.546583i	$0.184072\pi$
$468$		0			0
$469$	2.21624	+	2.21624i	0.102336	+	0.102336i
$470$	−20.1374	−	2.34694i	−0.928871	−	0.108256i
$471$		0			0
$472$	−12.7567	−	15.1721i	−0.587175	−	0.698352i
$473$	15.7885	+	9.11550i	0.725956	+	0.419131i
$474$		0			0
$475$	−1.38622	+	5.17343i	−0.0636040	+	0.237373i
$476$	3.69192	+	12.3021i	0.169219	+	0.563866i
$477$		0			0
$478$	−1.70131	−	11.5879i	−0.0778161	−	0.530017i
$479$	1.61178	+	2.79169i	0.0736442	+	0.127555i	0.900496	−	0.434865i	$-0.143204\pi$
$479$	1.61178	+	2.79169i	0.0736442	+	0.127555i	−0.826852	+	0.562420i	$0.809870\pi$
$480$		0			0
$481$	−4.27757	+	7.40897i	−0.195040	+	0.337820i
$482$	16.8262	+	6.67815i	0.766413	+	0.304181i
$483$		0			0
$484$	5.25351	−	5.57582i	0.238796	−	0.253446i
$485$	−12.0772	−	12.0772i	−0.548399	−	0.548399i
$486$		0			0
$487$			11.2953i			0.511838i	0.966698	+	0.255919i	$0.0823780\pi$
$487$			11.2953i			0.511838i	−0.966698	+	0.255919i	$0.917622\pi$
$488$	2.95957	+	16.6872i	0.133973	+	0.755395i
$489$		0			0
$490$	−4.37332	−	10.1292i	−0.197567	−	0.457593i
$491$	27.3357	−	7.32459i	1.23364	−	0.330554i	0.417647	−	0.908609i	$-0.362855\pi$
$491$	27.3357	−	7.32459i	1.23364	−	0.330554i	0.815998	+	0.578055i	$0.196188\pi$
$492$		0			0
$493$	23.1468	+	6.20215i	1.04248	+	0.279331i
$494$	−46.1191	+	6.77112i	−2.07500	+	0.304647i
$495$		0			0
$496$	−27.0547	+	17.8457i	−1.21479	+	0.801297i
$497$	−6.78498	−	11.7519i	−0.304348	−	0.527146i
$498$		0			0
$499$	−4.52377	−	16.8830i	−0.202512	−	0.755785i	−0.990194	−	0.139702i	$-0.955385\pi$
$499$	−4.52377	−	16.8830i	−0.202512	−	0.755785i	0.787682	−	0.616082i	$-0.211281\pi$
$500$	12.4805	+	20.2039i	0.558146	+	0.903548i
$501$		0			0
$502$	−27.6954	−	3.22780i	−1.23611	−	0.144064i
$503$		−	14.1184i		−	0.629509i	−0.949173	−	0.314754i	$-0.898078\pi$
$503$		−	14.1184i		−	0.629509i	0.949173	−	0.314754i	$-0.101922\pi$
$504$		0			0
$505$			9.99782i			0.444897i
$506$	0.225795	−	1.93738i	0.0100378	−	0.0861272i
$507$		0			0
$508$	2.62894	−	11.1253i	0.116640	−	0.493606i
$509$	7.88327	+	29.4208i	0.349420	+	1.30405i	0.887363	+	0.461072i	$0.152535\pi$
$509$	7.88327	+	29.4208i	0.349420	+	1.30405i	−0.537943	+	0.842981i	$0.680798\pi$
$510$		0			0
$511$	11.2262	+	19.4444i	0.496619	+	0.860170i
$512$	−21.8738	−	5.79099i	−0.966696	−	0.255928i
$513$		0			0
$514$	1.44394	+	9.83492i	0.0636896	+	0.433800i
$515$	14.0482	+	3.76420i	0.619037	+	0.165870i
$516$		0			0
$517$	18.0500	−	4.83648i	0.793838	−	0.212708i
$518$	4.13826	−	1.78670i	0.181825	−	0.0785032i
$519$		0			0
$520$	−15.9835	+	22.8753i	−0.700921	+	1.00315i
$521$			8.75761i			0.383678i	0.981426	+	0.191839i	$0.0614451\pi$
$521$			8.75761i			0.383678i	−0.981426	+	0.191839i	$0.938555\pi$
$522$		0			0
$523$	21.3424	+	21.3424i	0.933236	+	0.933236i	0.997907	−	0.0646706i	$-0.0205997\pi$
$523$	21.3424	+	21.3424i	0.933236	+	0.933236i	−0.0646706	+	0.997907i	$0.520600\pi$
$524$	−18.2922	+	0.544420i	−0.799097	+	0.0237831i
$525$		0			0
$526$	−9.14327	+	23.0373i	−0.398665	+	1.00447i
$527$	14.5396	−	25.1834i	0.633356	−	1.09700i
$528$		0			0
$529$	−11.3673	−	19.6888i	−0.494232	−	0.856035i
$530$	21.3927	−	3.14084i	0.929241	−	0.136429i
$531$		0			0
$532$	21.6251	+	11.6416i	0.937566	+	0.504727i
$533$	−5.85605	+	21.8551i	−0.253654	+	0.946648i
$534$		0			0
$535$	−16.8180	−	9.70989i	−0.727107	−	0.419795i
$536$	3.79186	−	3.18819i	0.163783	−	0.137709i
$537$		0			0
$538$	−0.0722154	+	0.619628i	−0.00311342	+	0.0267141i
$539$	7.19083	+	7.19083i	0.309731	+	0.309731i
$540$		0			0
$541$	−25.1121	+	25.1121i	−1.07965	+	1.07965i	−0.0831121	+	0.996540i	$0.526486\pi$
$541$	−25.1121	+	25.1121i	−1.07965	+	1.07965i	−0.996540	+	0.0831121i	$0.973514\pi$
$542$	−8.28445	+	6.55497i	−0.355848	+	0.281560i
$543$		0			0
$544$	19.8756	−	4.13843i	0.852157	−	0.177434i
$545$	−16.9105	+	29.2898i	−0.724366	+	1.25464i
$546$		0			0
$547$	−5.32802	−	1.42764i	−0.227810	−	0.0610414i	0.143108	−	0.989707i	$-0.454290\pi$
$547$	−5.32802	−	1.42764i	−0.227810	−	0.0610414i	−0.370918	+	0.928666i	$0.620957\pi$
$548$	0.355484	+	1.18453i	0.0151855	+	0.0506008i
$549$		0			0
$550$	−2.37121	−	1.76407i	−0.101109	−	0.0752203i
$551$	39.6818	−	22.9103i	1.69050	−	0.976013i
$552$		0			0
$553$	12.4513	+	7.18876i	0.529483	+	0.305697i
$554$	5.88940	+	13.6407i	0.250217	+	0.579538i
$555$		0			0
$556$	1.13701	+	38.2029i	0.0482201	+	1.62016i
$557$	15.4160	−	15.4160i	0.653197	−	0.653197i	−0.300565	−	0.953761i	$-0.597175\pi$
$557$	15.4160	−	15.4160i	0.653197	−	0.653197i	0.953761	+	0.300565i	$0.0971751\pi$
$558$		0			0
$559$	−32.7029			−1.38319
$560$	13.9506	−	4.64331i	0.589519	−	0.196216i
$561$		0			0
$562$	3.47202	−	8.74807i	0.146458	−	0.369015i
$563$	−4.27894	−	15.9692i	−0.180336	−	0.673022i	−0.995581	−	0.0939062i	$-0.970065\pi$
$563$	−4.27894	−	15.9692i	−0.180336	−	0.673022i	0.815245	−	0.579116i	$-0.196602\pi$
$564$		0			0
$565$	−0.367967	+	1.37327i	−0.0154805	+	0.0577740i
$566$	9.29536	−	12.4945i	0.390713	−	0.525183i
$567$		0			0
$568$	−19.4304	+	9.08415i	−0.815282	+	0.381163i
$569$	−9.85656	+	5.69069i	−0.413208	+	0.238566i	−0.692167	−	0.721737i	$-0.743344\pi$
$569$	−9.85656	+	5.69069i	−0.413208	+	0.238566i	0.278959	+	0.960303i	$0.410011\pi$
$570$		0			0
$571$	11.8982	−	3.18813i	0.497926	−	0.133419i	−0.00111115	−	0.999999i	$-0.500354\pi$
$571$	11.8982	−	3.18813i	0.497926	−	0.133419i	0.499037	+	0.866580i	$0.333687\pi$
$572$	5.91517	−	25.0322i	0.247326	−	1.04665i
$573$		0			0
$574$	9.34864	−	7.39700i	0.390205	−	0.308745i
$575$	0.402016			0.0167652
$576$		0			0
$577$	21.7471			0.905342			0.452671	−	0.891678i	$-0.350471\pi$
$577$	21.7471			0.905342			0.452671	+	0.891678i	$0.350471\pi$
$578$	4.56910	−	3.61524i	0.190049	−	0.150374i
$579$		0			0
$580$	6.30837	−	26.6962i	0.261941	−	1.10850i
$581$	14.3123	−	3.83498i	0.593775	−	0.159102i
$582$		0			0
$583$	−17.2595	+	9.96475i	−0.714814	+	0.412698i
$584$	32.1490	−	15.0304i	1.33034	−	0.621961i
$585$		0			0
$586$	−2.41135	+	3.24125i	−0.0996118	+	0.133895i
$587$	−4.07718	+	15.2163i	−0.168283	+	0.628042i	0.829315	+	0.558781i	$0.188731\pi$
$587$	−4.07718	+	15.2163i	−0.168283	+	0.628042i	−0.997599	+	0.0692610i	$0.977936\pi$
$588$		0			0
$589$	−14.3911	−	53.7083i	−0.592975	−	2.21301i
$590$	7.51039	−	18.9231i	0.309198	−	0.779052i
$591$		0			0
$592$	−2.25002	−	6.76006i	−0.0924752	−	0.277837i
$593$	−10.1125			−0.415270			−0.207635	−	0.978206i	$-0.566577\pi$
$593$	−10.1125			−0.415270			−0.207635	+	0.978206i	$0.566577\pi$
$594$		0			0
$595$	−9.32807	+	9.32807i	−0.382414	+	0.382414i
$596$	−0.311997	−	10.4829i	−0.0127799	−	0.429396i
$597$		0			0
$598$	1.38688	+	3.21221i	0.0567137	+	0.131357i
$599$	4.23917	+	2.44748i	0.173208	+	0.100002i	0.584097	−	0.811684i	$-0.301449\pi$
$599$	4.23917	+	2.44748i	0.173208	+	0.100002i	−0.410890	+	0.911685i	$0.634782\pi$
$600$		0			0
$601$	25.8322	−	14.9142i	1.05372	−	0.608364i	0.130030	−	0.991510i	$-0.458493\pi$
$601$	25.8322	−	14.9142i	1.05372	−	0.608364i	0.923688	+	0.383146i	$0.125159\pi$
$602$	13.8243	+	10.2847i	0.563436	+	0.419171i
$603$		0			0
$604$	5.17847	+	17.2555i	0.210709	+	0.702117i
$605$	7.60019	+	2.03647i	0.308992	+	0.0827941i
$606$		0			0
$607$	−8.48425	+	14.6952i	−0.344365	+	0.596458i	−0.985238	−	0.171189i	$-0.945239\pi$
$607$	−8.48425	+	14.6952i	−0.344365	+	0.596458i	0.640873	+	0.767647i	$0.278572\pi$
$608$	21.2777	−	32.4686i	0.862926	−	1.31678i
$609$		0			0
$610$	−13.6503	+	10.8007i	−0.552685	+	0.437306i
$611$	−23.7025	+	23.7025i	−0.958901	+	0.958901i
$612$		0			0
$613$	30.2781	+	30.2781i	1.22292	+	1.22292i	0.966589	+	0.256332i	$0.0825140\pi$
$613$	30.2781	+	30.2781i	1.22292	+	1.22292i	0.256332	+	0.966589i	$0.417486\pi$
$614$	1.88853	−	16.2041i	0.0762150	−	0.653946i
$615$		0			0
$616$	−10.3728	+	8.72146i	−0.417932	+	0.351398i
$617$	−14.9377	−	8.62428i	−0.601368	−	0.347200i	0.168211	−	0.985751i	$-0.446201\pi$
$617$	−14.9377	−	8.62428i	−0.601368	−	0.347200i	−0.769580	+	0.638551i	$0.779534\pi$
$618$		0			0
$619$	4.48369	−	16.7334i	0.180215	−	0.672570i	−0.815390	−	0.578912i	$-0.803477\pi$
$619$	4.48369	−	16.7334i	0.180215	−	0.672570i	0.995604	−	0.0936580i	$-0.0298560\pi$
$620$	−29.3104	−	15.7789i	−1.17713	−	0.633696i
$621$		0			0
$622$	−13.4653	+	1.97694i	−0.539908	+	0.0792682i
$623$	14.7999	+	25.6341i	0.592945	+	1.02701i
$624$		0			0
$625$	−10.2442	+	17.7435i	−0.409770	+	0.709742i
$626$	13.4054	−	33.7761i	0.535787	−	1.34997i
$627$		0			0
$628$	22.6485	−	0.674074i	0.903773	−	0.0268985i
$629$	4.52012	+	4.52012i	0.180229	+	0.180229i
$630$		0			0
$631$		−	11.6246i		−	0.462766i	−0.972863	−	0.231383i	$-0.925675\pi$
$631$		−	11.6246i		−	0.462766i	0.972863	−	0.231383i	$-0.0743251\pi$
$632$	13.0163	−	18.6287i	0.517759	−	0.741009i
$633$		0			0
$634$	20.9774	−	9.05703i	0.833118	−	0.359701i
$635$	11.3411	−	3.03885i	0.450059	−	0.120593i
$636$		0			0
$637$	−17.6203	−	4.72135i	−0.698142	−	0.187067i
$638$	3.67279	+	25.0159i	0.145407	+	0.990389i
$639$		0			0
$640$	−5.41213	−	22.6011i	−0.213933	−	0.893385i
$641$	3.04338	+	5.27129i	0.120206	+	0.208203i	0.919849	−	0.392273i	$-0.128311\pi$
$641$	3.04338	+	5.27129i	0.120206	+	0.208203i	−0.799643	+	0.600476i	$0.794978\pi$
$642$		0			0
$643$	−8.34195	−	31.1326i	−0.328974	−	1.22775i	−0.910256	−	0.414046i	$-0.864115\pi$
$643$	−8.34195	−	31.1326i	−0.328974	−	1.22775i	0.581282	−	0.813702i	$-0.302551\pi$
$644$	0.423934	−	1.79403i	0.0167053	−	0.0706947i
$645$		0			0
$646$	−4.03199	+	34.5956i	−0.158636	+	1.36114i
$647$		−	13.1882i		−	0.518482i	−0.965813	−	0.259241i	$-0.916528\pi$
$647$		−	13.1882i		−	0.518482i	0.965813	−	0.259241i	$-0.0834724\pi$
$648$		0			0
$649$			18.7653i			0.736604i
$650$	5.26583	+	0.613713i	0.206543	+	0.0240718i
$651$		0			0
$652$	17.6996	+	28.6528i	0.693172	+	1.12213i
$653$	−4.09053	−	15.2661i	−0.160075	−	0.597407i	−0.998617	−	0.0525710i	$-0.983258\pi$
$653$	−4.09053	−	15.2661i	−0.160075	−	0.597407i	0.838542	−	0.544836i	$-0.183408\pi$
$654$		0			0
$655$	−9.39787	−	16.2776i	−0.367205	−	0.636018i
$656$	−10.3752	−	15.7292i	−0.405085	−	0.614121i
$657$		0			0
$658$	17.4738	−	2.56546i	0.681198	−	0.100012i
$659$	−34.5804	−	9.26579i	−1.34706	−	0.360944i	−0.488012	−	0.872837i	$-0.662278\pi$
$659$	−34.5804	−	9.26579i	−1.34706	−	0.360944i	−0.859049	+	0.511893i	$0.828944\pi$
$660$		0			0
$661$	−24.5781	+	6.58569i	−0.955978	+	0.256153i	−0.702897	−	0.711292i	$-0.748111\pi$
$661$	−24.5781	+	6.58569i	−0.955978	+	0.256153i	−0.253081	+	0.967445i	$0.581444\pi$
$662$	11.3801	+	26.3578i	0.442298	+	1.02443i
$663$		0			0
$664$	−4.08993	−	23.0606i	−0.158720	−	0.894926i
$665$			25.2244i			0.978162i
$666$		0			0
$667$	−2.43195	−	2.43195i	−0.0941656	−	0.0941656i
$668$	−12.9770	+	13.7732i	−0.502097	+	0.532901i
$669$		0			0
$670$	4.72932	+	1.87702i	0.182710	+	0.0725156i
$671$	8.02196	−	13.8944i	0.309684	−	0.536389i
$672$		0			0
$673$	−16.8241	−	29.1402i	−0.648522	−	1.12327i	−0.983476	−	0.181039i	$-0.942054\pi$
$673$	−16.8241	−	29.1402i	−0.648522	−	1.12327i	0.334954	−	0.942235i	$-0.391279\pi$
$674$	0.428316	+	2.91732i	0.0164981	+	0.112371i
$675$		0			0
$676$	5.78894	+	19.2897i	0.222652	+	0.741912i
$677$	9.52351	−	35.5422i	0.366018	−	1.36600i	−0.500017	−	0.866015i	$-0.666673\pi$
$677$	9.52351	−	35.5422i	0.366018	−	1.36600i	0.866035	−	0.499983i	$-0.166660\pi$
$678$		0			0
$679$	12.8854	+	7.43937i	0.494495	+	0.285497i
$680$	13.4190	+	15.9598i	0.514595	+	0.612030i
$681$		0			0
$682$	30.4757	+	3.55183i	1.16698	+	0.136007i
$683$	0.339146	+	0.339146i	0.0129771	+	0.0129771i	0.713566	−	0.700588i	$-0.247079\pi$
$683$	0.339146	+	0.339146i	0.0129771	+	0.0129771i	−0.700588	+	0.713566i	$0.747079\pi$
$684$		0			0
$685$	−0.898173	+	0.898173i	−0.0343174	+	0.0343174i
$686$	16.9555	+	21.4290i	0.647363	+	0.818165i
$687$		0			0
$688$	18.0785	−	20.3691i	0.689237	−	0.776566i
$689$	17.8749	−	30.9602i	0.680978	−	1.17949i
$690$		0			0
$691$	17.3154	+	4.63964i	0.658707	+	0.176500i	0.572663	−	0.819791i	$-0.305911\pi$
$691$	17.3154	+	4.63964i	0.658707	+	0.176500i	0.0860448	+	0.996291i	$0.472577\pi$
$692$	−22.6830	+	42.1353i	−0.862279	+	1.60174i
$693$		0			0
$694$	7.13356	−	9.58869i	0.270786	−	0.363982i
$695$	−33.9955	+	19.6273i	−1.28952	+	0.744506i
$696$		0			0
$697$	14.6412	+	8.45311i	0.554576	+	0.320184i
$698$	2.02586	−	0.874671i	0.0766800	−	0.0331068i
$699$		0			0
$700$	−2.03299	−	1.91547i	−0.0768396	−	0.0723980i
$701$	14.5424	−	14.5424i	0.549258	−	0.549258i	−0.376968	−	0.926226i	$-0.623033\pi$
$701$	14.5424	−	14.5424i	0.549258	−	0.549258i	0.926226	+	0.376968i	$0.123033\pi$
$702$		0			0
$703$	12.2231			0.461001
$704$	12.3215	+	17.5224i	0.464382	+	0.660399i
$705$		0			0
$706$	−21.3849	−	8.48743i	−0.804830	−	0.319429i
$707$	−2.25416	−	8.41264i	−0.0847764	−	0.316390i
$708$		0			0
$709$	−8.65273	+	32.2924i	−0.324960	+	1.21277i	0.589392	+	0.807847i	$0.299367\pi$
$709$	−8.65273	+	32.2924i	−0.324960	+	1.21277i	−0.914352	+	0.404920i	$0.867299\pi$
$710$	−17.6750	−	13.1494i	−0.663330	−	0.493488i
$711$		0			0
$712$	42.3830	−	19.8150i	1.58837	−	0.742599i
$713$	−3.61441	+	2.08678i	−0.135361	+	0.0781505i
$714$		0			0
$715$	25.5178	−	6.83748i	0.954313	−	0.255707i
$716$	17.2926	+	27.9939i	0.646254	+	1.04618i
$717$		0			0
$718$	−2.70404	−	3.41748i	−0.100914	−	0.127539i
$719$	−38.7103			−1.44365			−0.721826	−	0.692075i	$-0.756697\pi$
$719$	−38.7103			−1.44365			−0.721826	+	0.692075i	$0.756697\pi$
$720$		0			0
$721$	−12.6695			−0.471837
$722$	24.6514	+	31.1555i	0.917431	+	1.15949i
$723$		0			0
$724$	−26.3203	+	16.2588i	−0.978187	+	0.604253i
$725$	−5.03373	+	1.34878i	−0.186948	+	0.0500925i
$726$		0			0
$727$	−24.4245	+	14.1015i	−0.905853	+	0.522994i	−0.879095	−	0.476647i	$-0.841852\pi$
$727$	−24.4245	+	14.1015i	−0.905853	+	0.522994i	−0.0267585	+	0.999642i	$0.508519\pi$
$728$	8.29167	−	22.8521i	0.307310	−	0.846953i
$729$		0			0
$730$	29.2445	+	21.7566i	1.08239	+	0.805249i
$731$	−6.32442	+	23.6031i	−0.233917	+	0.872990i
$732$		0			0
$733$	1.95090	+	7.28085i	0.0720580	+	0.268924i	0.992550	−	0.121837i	$-0.0388785\pi$
$733$	1.95090	+	7.28085i	0.0720580	+	0.268924i	−0.920492	+	0.390761i	$0.872212\pi$
$734$	3.63402	+	1.44230i	0.134134	+	0.0532364i
$735$		0			0
$736$	−2.76742	−	0.911920i	−0.102008	−	0.0336138i
$737$	−4.68989			−0.172754
$738$		0			0
$739$	−16.1043	+	16.1043i	−0.592407	+	0.592407i	−0.938281	−	0.345874i	$-0.887583\pi$
$739$	−16.1043	+	16.1043i	−0.592407	+	0.592407i	0.345874	+	0.938281i	$0.387583\pi$
$740$	5.01808	−	5.32594i	0.184468	−	0.195786i
$741$		0			0
$742$	−17.2927	+	7.46616i	−0.634835	+	0.274091i
$743$	−5.50307	−	3.17720i	−0.201888	−	0.116560i	0.395648	−	0.918402i	$-0.370520\pi$
$743$	−5.50307	−	3.17720i	−0.201888	−	0.116560i	−0.597536	+	0.801842i	$0.703853\pi$
$744$		0			0
$745$	9.32837	−	5.38574i	0.341765	−	0.197318i
$746$	19.7680	−	26.5715i	0.723759	−	0.972851i
$747$		0			0
$748$	−16.9229	−	9.11021i	−0.618761	−	0.333102i
$749$	16.3407	+	4.37848i	0.597077	+	0.159986i
$750$		0			0
$751$	7.20371	−	12.4772i	0.262867	−	0.455299i	−0.704136	−	0.710066i	$-0.748665\pi$
$751$	7.20371	−	12.4772i	0.262867	−	0.455299i	0.967003	+	0.254767i	$0.0819986\pi$
$752$	−1.66020	−	27.8662i	−0.0605414	−	1.01618i
$753$		0			0
$754$	−28.1425	−	35.5677i	−1.02489	−	1.29530i
$755$	−13.0840	+	13.0840i	−0.476176	+	0.476176i
$756$		0			0
$757$	−29.7018	−	29.7018i	−1.07953	−	1.07953i	−0.996551	−	0.0829799i	$-0.973556\pi$
$757$	−29.7018	−	29.7018i	−1.07953	−	1.07953i	−0.0829799	−	0.996551i	$-0.526444\pi$
$758$	−9.34774	−	1.08944i	−0.339525	−	0.0395704i
$759$		0			0
$760$	39.7222	+	3.43533i	1.44088	+	0.124613i
$761$	21.6542	+	12.5021i	0.784965	+	0.453200i	0.838187	−	0.545383i	$-0.183616\pi$
$761$	21.6542	+	12.5021i	0.784965	+	0.453200i	−0.0532222	+	0.998583i	$0.516949\pi$
$762$		0			0
$763$	7.62545	−	28.4586i	0.276060	−	1.03027i
$764$	−12.8100	+	3.84434i	−0.463449	+	0.139083i
$765$		0			0
$766$	−7.53153	−	51.2984i	−0.272125	−	1.85349i
$767$	−16.8307	−	29.1516i	−0.607721	−	1.05260i
$768$		0			0
$769$	−26.1481	+	45.2899i	−0.942926	+	1.63320i	−0.183076	+	0.983099i	$0.558605\pi$
$769$	−26.1481	+	45.2899i	−0.942926	+	1.63320i	−0.759851	+	0.650097i	$0.774728\pi$
$770$	−12.9373	−	5.13468i	−0.466227	−	0.185041i
$771$		0			0
$772$	1.36386	+	1.28502i	0.0490864	+	0.0462490i
$773$	−0.679496	−	0.679496i	−0.0244398	−	0.0244398i	0.694781	−	0.719221i	$-0.255501\pi$
$773$	−0.679496	−	0.679496i	−0.0244398	−	0.0244398i	−0.719221	+	0.694781i	$0.755501\pi$
$774$		0			0
$775$			6.32386i			0.227160i
$776$	13.4700	−	19.2781i	0.483546	−	0.692043i
$777$		0			0
$778$	1.64098	+	3.80074i	0.0588319	+	0.136263i
$779$	31.2252	−	8.36677i	1.11876	−	0.299771i
$780$		0			0
$781$	19.6134	+	5.25540i	0.701824	+	0.188053i
$782$	2.58659	−	0.379758i	0.0924964	−	0.0135801i
$783$		0			0
$784$	12.6814	−	8.36487i	0.452908	−	0.298745i
$785$	11.6360	+	20.1541i	0.415306	+	0.719331i
$786$		0			0
$787$	−7.58525	−	28.3085i	−0.270385	−	1.00909i	−0.958871	−	0.283841i	$-0.908391\pi$
$787$	−7.58525	−	28.3085i	−0.270385	−	1.00909i	0.688487	−	0.725249i	$-0.258275\pi$
$788$	35.6046	−	21.9939i	1.26836	−	0.783501i
$789$		0			0
$790$	23.1839	+	2.70200i	0.824846	+	0.0961327i
$791$		−	1.23850i		−	0.0440360i
$792$		0			0
$793$			28.7797i			1.02200i
$794$	−3.08836	+	26.4990i	−0.109602	+	0.940414i
$795$		0			0
$796$	−4.61251	−	1.08995i	−0.163486	−	0.0386321i
$797$	−5.63071	−	21.0141i	−0.199450	−	0.744357i	−0.991070	−	0.133343i	$-0.957429\pi$
$797$	−5.63071	−	21.0141i	−0.199450	−	0.744357i	0.791620	−	0.611014i	$-0.209238\pi$
$798$		0			0
$799$	12.5233	+	21.6909i	0.443041	+	0.767370i
$800$	−3.29326	+	2.94058i	−0.116434	+	0.103965i
$801$		0			0
$802$	1.99081	+	13.5597i	0.0702979	+	0.478810i
$803$	−32.4518	−	8.69544i	−1.14520	−	0.306855i
$804$		0			0
$805$	1.82883	−	0.490035i	0.0644579	−	0.0172714i
$806$	−50.5292	+	21.8161i	−1.77982	+	0.768439i
$807$		0			0
$808$	−13.5548	+	2.40402i	−0.476856	+	0.0845731i
$809$			12.5804i			0.442303i	0.975240	+	0.221151i	$0.0709815\pi$
$809$			12.5804i			0.442303i	−0.975240	+	0.221151i	$0.929019\pi$
$810$		0			0
$811$	30.5378	+	30.5378i	1.07233	+	1.07233i	0.997172	+	0.0751549i	$0.0239451\pi$
$811$	30.5378	+	30.5378i	1.07233	+	1.07233i	0.0751549	+	0.997172i	$0.476055\pi$
$812$	0.710898	+	23.8857i	0.0249476	+	0.838225i
$813$		0			0
$814$	−2.48812	+	6.26905i	−0.0872086	+	0.219730i
$815$	−17.2953	+	29.9564i	−0.605829	+	1.04933i
$816$		0			0
$817$	23.3620	+	40.4641i	0.817331	+	1.41566i
$818$	10.0075	−	1.46929i	0.349905	−	0.0513723i
$819$		0			0
$820$	9.17361	−	17.0406i	0.320356	−	0.595085i
$821$	4.88097	−	18.2160i	0.170347	−	0.635744i	−0.826951	−	0.562275i	$-0.809926\pi$
$821$	4.88097	−	18.2160i	0.170347	−	0.635744i	0.997298	−	0.0734689i	$-0.0234070\pi$
$822$		0			0
$823$	−11.5958	−	6.69486i	−0.404206	−	0.233368i	0.284091	−	0.958797i	$-0.408308\pi$
$823$	−11.5958	−	6.69486i	−0.404206	−	0.233368i	−0.688297	+	0.725429i	$0.741641\pi$
$824$	−1.72547	+	19.9513i	−0.0601095	+	0.695037i
$825$		0			0
$826$	−2.05309	+	17.6161i	−0.0714363	+	0.612943i
$827$	7.23348	+	7.23348i	0.251533	+	0.251533i	0.821599	−	0.570066i	$-0.193082\pi$
$827$	7.23348	+	7.23348i	0.251533	+	0.251533i	−0.570066	+	0.821599i	$0.693082\pi$
$828$		0			0
$829$	−25.9641	+	25.9641i	−0.901769	+	0.901769i	−0.995589	−	0.0938197i	$-0.970092\pi$
$829$	−25.9641	+	25.9641i	−0.901769	+	0.901769i	0.0938197	+	0.995589i	$0.470092\pi$
$830$	18.8638	−	14.9258i	0.654774	−	0.518082i
$831$		0			0
$832$	−34.8571	−	16.1695i	−1.20845	−	0.560578i
$833$	−6.81519	+	11.8043i	−0.236132	+	0.408993i
$834$		0			0
$835$	−18.7737	−	5.03040i	−0.649691	−	0.174084i
$836$	−35.1986	+	10.5633i	−1.21737	+	0.365338i
$837$		0			0
$838$	−21.0742	−	15.6783i	−0.727996	−	0.541597i
$839$	−41.1955	+	23.7842i	−1.42223	+	0.821123i	−0.996489	−	0.0837230i	$-0.973319\pi$
$839$	−41.1955	+	23.7842i	−1.42223	+	0.821123i	−0.425738	+	0.904846i	$0.639986\pi$
$840$		0			0
$841$	13.4955	+	7.79166i	0.465364	+	0.268678i
$842$	−1.14331	−	2.64808i	−0.0394012	−	0.0912588i
$843$		0			0
$844$	−4.03136	+	0.119983i	−0.138765	+	0.00412999i
$845$	−14.6264	+	14.6264i	−0.503165	+	0.503165i
$846$		0			0
$847$	−6.85431			−0.235517
$848$	9.40225	+	28.2485i	0.322874	+	0.970058i
$849$		0			0
$850$	1.46130	−	3.68189i	0.0501223	−	0.126288i
$851$	−0.237457	−	0.886202i	−0.00813992	−	0.0303786i
$852$		0			0
$853$	0.0729011	−	0.272071i	0.00249609	−	0.00931552i	−0.964667	−	0.263474i	$-0.915132\pi$
$853$	0.0729011	−	0.272071i	0.00249609	−	0.00931552i	0.967163	+	0.254158i	$0.0817984\pi$
$854$	9.05086	−	12.1659i	0.309714	−	0.416307i
$855$		0			0
$856$	9.12048	−	25.1363i	0.311731	−	0.859140i
$857$	24.7820	−	14.3079i	0.846538	−	0.488749i	−0.0129433	−	0.999916i	$-0.504120\pi$
$857$	24.7820	−	14.3079i	0.846538	−	0.488749i	0.859481	+	0.511167i	$0.170787\pi$
$858$		0			0
$859$	1.05613	−	0.282990i	0.0360347	−	0.00965548i	−0.240757	−	0.970586i	$-0.577396\pi$
$859$	1.05613	−	0.282990i	0.0360347	−	0.00965548i	0.276791	+	0.960930i	$0.410729\pi$
$860$	27.2224	+	6.43272i	0.928278	+	0.219354i
$861$		0			0
$862$	−21.9814	+	17.3925i	−0.748690	+	0.592392i
$863$	−30.2887			−1.03104			−0.515520	−	0.856878i	$-0.672401\pi$
$863$	−30.2887			−1.03104			−0.515520	+	0.856878i	$0.672401\pi$
$864$		0			0
$865$	−49.1485			−1.67110
$866$	−26.3222	+	20.8271i	−0.894465	+	0.707735i
$867$		0			0
$868$	28.2208	+	6.66863i	0.957875	+	0.226348i
$869$	−20.7807	+	5.56816i	−0.704935	+	0.188887i
$870$		0			0
$871$	7.28567	−	4.20638i	0.246865	−	0.142528i
$872$	−43.7767	−	15.8840i	−1.48247	−	0.537900i
$873$		0			0
$874$	2.98380	−	4.01072i	0.100929	−	0.135665i
$875$	5.49929	−	20.5236i	0.185910	−	0.693825i
$876$		0			0
$877$	6.25984	+	23.3620i	0.211380	+	0.788880i	0.987410	+	0.158184i	$0.0505639\pi$
$877$	6.25984	+	23.3620i	0.211380	+	0.788880i	−0.776030	+	0.630696i	$0.782769\pi$
$878$	−11.5029	+	28.9826i	−0.388204	+	0.978116i
$879$		0			0
$880$	−9.84778	+	19.6737i	−0.331968	+	0.663201i
$881$	10.3324			0.348108			0.174054	−	0.984736i	$-0.444313\pi$
$881$	10.3324			0.348108			0.174054	+	0.984736i	$0.444313\pi$
$882$		0			0
$883$	13.2455	−	13.2455i	0.445745	−	0.445745i	−0.448192	−	0.893937i	$-0.647932\pi$
$883$	13.2455	−	13.2455i	0.445745	−	0.445745i	0.893937	+	0.448192i	$0.147932\pi$
$884$	34.4604	−	1.02563i	1.15903	−	0.0344955i
$885$		0			0
$886$	−5.63633	−	13.0546i	−0.189356	−	0.438576i
$887$	4.21020	+	2.43076i	0.141365	+	0.0816170i	0.569014	−	0.822328i	$-0.307325\pi$
$887$	4.21020	+	2.43076i	0.141365	+	0.0816170i	−0.427650	+	0.903945i	$0.640658\pi$
$888$		0			0
$889$	−8.85782	+	5.11406i	−0.297082	+	0.171520i
$890$	38.5539	+	28.6824i	1.29233	+	0.961437i
$891$		0			0
$892$	21.2634	−	6.38126i	0.711952	−	0.213660i
$893$	46.2601	+	12.3953i	1.54803	+	0.414794i
$894$		0			0
$895$	−16.8975	+	29.2674i	−0.564822	+	0.978301i
$896$	9.64977	+	17.7974i	0.322376	+	0.594568i
$897$		0			0
$898$	27.3911	−	21.6729i	0.914052	−	0.723233i
$899$	38.2555	−	38.2555i	1.27589	−	1.27589i
$900$		0			0
$901$	−18.8884	−	18.8884i	−0.629264	−	0.629264i
$902$	−2.06498	+	17.7181i	−0.0687564	+	0.589949i
$903$		0			0
$904$	−1.95033	−	0.168672i	−0.0648670	−	0.00560994i
$905$	−27.5177	−	15.8874i	−0.914720	−	0.528114i
$906$		0			0
$907$	0.989509	−	3.69290i	0.0328561	−	0.122621i	−0.947550	−	0.319608i	$-0.896449\pi$
$907$	0.989509	−	3.69290i	0.0328561	−	0.122621i	0.980406	+	0.196987i	$0.0631156\pi$
$908$	16.4750	−	30.6035i	0.546742	−	1.01561i
$909$		0			0
$910$	24.7032	−	3.62687i	0.818902	−	0.120230i
$911$	−24.1877	−	41.8944i	−0.801376	−	1.38802i	−0.918711	−	0.394931i	$-0.870769\pi$
$911$	−24.1877	−	41.8944i	−0.801376	−	1.38802i	0.117335	−	0.993092i	$-0.462565\pi$
$912$		0			0
$913$	−11.0858	+	19.2012i	−0.366887	+	0.635467i
$914$	−16.3355	+	41.1589i	−0.540331	+	1.36141i
$915$		0			0
$916$	−0.952750	−	32.0118i	−0.0314798	−	1.05770i
$917$	11.5778	+	11.5778i	0.382334	+	0.382334i
$918$		0			0
$919$		−	44.5150i		−	1.46841i	−0.678926	−	0.734206i	$-0.737554\pi$
$919$		−	44.5150i		−	1.46841i	0.678926	−	0.734206i	$-0.262446\pi$
$920$	−0.522613	−	2.94670i	−0.0172300	−	0.0971497i
$921$		0			0
$922$	−15.9075	+	6.86809i	−0.523885	+	0.226189i
$923$	−35.1827	+	9.42718i	−1.15805	+	0.310299i
$924$		0			0
$925$	−1.34279	−	0.359800i	−0.0441507	−	0.0118301i
$926$	−5.22817	−	35.6099i	−0.171808	−	1.17021i
$927$		0			0
$928$	37.7109	+	2.13353i	1.23792	+	0.0700364i
$929$	−26.5718	−	46.0236i	−0.871791	−	1.50999i	−0.860142	−	0.510054i	$-0.829625\pi$
$929$	−26.5718	−	46.0236i	−0.871791	−	1.50999i	−0.0116490	−	0.999932i	$-0.503708\pi$
$930$		0			0
$931$	6.74558	+	25.1748i	0.221077	+	0.825072i
$932$	−49.0572	−	11.5923i	−1.60692	−	0.379719i
$933$		0			0
$934$	−1.45507	+	12.4849i	−0.0476115	+	0.408520i
$935$		−	19.7396i		−	0.645553i
$936$		0			0
$937$		−	2.96531i		−	0.0968724i	−0.998826	−	0.0484362i	$-0.984576\pi$
$937$		−	2.96531i		−	0.0968724i	0.998826	−	0.0484362i	$-0.0154238\pi$
$938$	−4.40268	−	0.513116i	−0.143752	−	0.0167538i
$939$		0			0
$940$	24.3927	−	15.0680i	0.795602	−	0.491465i
$941$	−12.2347	−	45.6603i	−0.398838	−	1.48848i	−0.815143	−	0.579260i	$-0.803342\pi$
$941$	−12.2347	−	45.6603i	−0.398838	−	1.48848i	0.416305	−	0.909225i	$-0.363325\pi$
$942$		0			0
$943$	−1.21322	−	2.10136i	−0.0395079	−	0.0684298i
$944$	27.4614	+	5.63226i	0.893793	+	0.183315i
$945$		0			0
$946$	−25.5091	+	3.74519i	−0.829371	+	0.121767i
$947$	31.0213	+	8.31213i	1.00806	+	0.270108i	0.724817	−	0.688942i	$-0.241924\pi$
$947$	31.0213	+	8.31213i	1.00806	+	0.270108i	0.283239	+	0.959049i	$0.408591\pi$
$948$		0			0
$949$	58.2123	−	15.5979i	1.88965	−	0.506331i
$950$	−3.00239	−	6.95396i	−0.0974104	−	0.225616i
$951$		0			0
$952$	−14.8898	−	10.4038i	−0.482580	−	0.337189i
$953$		−	14.4065i		−	0.466671i	−0.972396	−	0.233336i	$-0.925036\pi$
$953$		−	14.4065i		−	0.466671i	0.972396	−	0.233336i	$-0.0749641\pi$
$954$		0			0
$955$	−9.71317	−	9.71317i	−0.314311	−	0.314311i
$956$	12.0553	+	11.3585i	0.389898	+	0.367360i
$957$		0			0
$958$	−4.23727	−	1.68173i	−0.136900	−	0.0543342i
$959$	0.553259	−	0.958272i	0.0178656	−	0.0309442i
$960$		0			0
$961$	−17.3258	−	30.0092i	−0.558897	−	0.968038i
$962$	−1.75748	−	11.9705i	−0.0566634	−	0.385943i
$963$		0			0
$964$	−24.5211	+	7.35890i	−0.789772	+	0.237014i
$965$	−0.498125	+	1.85903i	−0.0160352	+	0.0598442i
$966$		0			0
$967$	−46.2878	−	26.7243i	−1.48852	−	0.859395i	−0.488602	−	0.872507i	$-0.662493\pi$
$967$	−46.2878	−	26.7243i	−1.48852	−	0.859395i	−0.999914	+	0.0131113i	$0.995826\pi$
$968$	−0.933493	+	10.7938i	−0.0300036	+	0.346927i
$969$		0			0
$970$	23.9921	+	2.79619i	0.770340	+	0.0897803i
$971$	18.6508	+	18.6508i	0.598532	+	0.598532i	0.939922	−	0.341389i	$-0.110898\pi$
$971$	18.6508	+	18.6508i	0.598532	+	0.598532i	−0.341389	+	0.939922i	$0.610898\pi$
$972$		0			0
$973$	24.1801	−	24.1801i	0.775180	−	0.775180i
$974$	−9.91176	−	12.5269i	−0.317593	−	0.401388i
$975$		0			0
$976$	−17.9256	−	15.9097i	−0.573783	−	0.509258i
$977$	−1.32572	+	2.29622i	−0.0424136	+	0.0734624i	−0.886453	−	0.462819i	$-0.846838\pi$
$977$	−1.32572	+	2.29622i	−0.0424136	+	0.0734624i	0.844039	+	0.536281i	$0.180171\pi$
$978$		0			0
$979$	−42.7822	−	11.4635i	−1.36733	−	0.366374i
$980$	13.7387	+	7.39608i	0.438868	+	0.236259i
$981$		0			0
$982$	−23.8890	+	32.1108i	−0.762328	+	1.02470i
$983$	−23.4130	+	13.5175i	−0.746760	+	0.431142i	−0.824522	−	0.565830i	$-0.808556\pi$
$983$	−23.4130	+	13.5175i	−0.746760	+	0.431142i	0.0777621	+	0.996972i	$0.475223\pi$
$984$		0			0
$985$	37.2244	+	21.4915i	1.18607	+	0.684776i
$986$	−31.1131	+	13.4332i	−0.990845	+	0.427799i
$987$		0			0
$988$	45.2062	−	47.9796i	1.43820	−	1.52644i
$989$	2.47989	−	2.47989i	0.0788560	−	0.0788560i
$990$		0			0
$991$	5.32341			0.169104			0.0845519	−	0.996419i	$-0.473054\pi$
$991$	5.32341			0.169104			0.0845519	+	0.996419i	$0.473054\pi$
$992$	14.3448	−	43.5325i	0.455449	−	1.38216i
$993$		0			0
$994$	17.8373	+	7.07944i	0.565765	+	0.224546i
$995$	−1.25989	−	4.70199i	−0.0399413	−	0.149063i
$996$		0			0
$997$	1.57391	−	5.87389i	0.0498461	−	0.186028i	−0.936514	−	0.350630i	$-0.885967\pi$
$997$	1.57391	−	5.87389i	0.0498461	−	0.186028i	0.986360	+	0.164602i	$0.0526340\pi$
$998$	19.8321	+	14.7542i	0.627773	+	0.467036i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.y.e.37.4		72
3.2	odd	2		144.2.x.e.85.15	yes	72
4.3	odd	2		1728.2.bc.e.1009.14		72
9.2	odd	6		144.2.x.e.133.2	yes	72
9.7	even	3	inner	432.2.y.e.181.17		72
12.11	even	2		576.2.bb.e.49.1		72
16.3	odd	4		1728.2.bc.e.145.5		72
16.13	even	4	inner	432.2.y.e.253.17		72
36.7	odd	6		1728.2.bc.e.1585.5		72
36.11	even	6		576.2.bb.e.241.10		72
48.29	odd	4		144.2.x.e.13.2	✓	72
48.35	even	4		576.2.bb.e.337.10		72
144.29	odd	12		144.2.x.e.61.15	yes	72
144.61	even	12	inner	432.2.y.e.397.4		72
144.83	even	12		576.2.bb.e.529.1		72
144.115	odd	12		1728.2.bc.e.721.14		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.2	✓	72	48.29	odd	4
144.2.x.e.61.15	yes	72	144.29	odd	12
144.2.x.e.85.15	yes	72	3.2	odd	2
144.2.x.e.133.2	yes	72	9.2	odd	6
432.2.y.e.37.4		72	1.1	even	1	trivial
432.2.y.e.181.17		72	9.7	even	3	inner
432.2.y.e.253.17		72	16.13	even	4	inner
432.2.y.e.397.4		72	144.61	even	12	inner
576.2.bb.e.49.1		72	12.11	even	2
576.2.bb.e.241.10		72	36.11	even	6
576.2.bb.e.337.10		72	48.35	even	4
576.2.bb.e.529.1		72	144.83	even	12
1728.2.bc.e.145.5		72	16.3	odd	4
1728.2.bc.e.721.14		72	144.115	odd	12
1728.2.bc.e.1009.14		72	4.3	odd	2
1728.2.bc.e.1585.5		72	36.7	odd	6

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.10904 + 0.877514i) q^{2} +(0.459938 - 1.94640i) q^{4} +(1.98415 - 0.531653i) q^{5} +(-1.54969 + 0.894715i) q^{7} +(1.19790 + 2.56223i) q^{8} +O(q^{10})\)	\(q+(-1.10904 + 0.877514i) q^{2} +(0.459938 - 1.94640i) q^{4} +(1.98415 - 0.531653i) q^{5} +(-1.54969 + 0.894715i) q^{7} +(1.19790 + 2.56223i) q^{8} +(-1.73397 + 2.33075i) q^{10} +(0.693015 - 2.58637i) q^{11} +(1.24314 + 4.63944i) q^{13} +(0.933545 - 2.35215i) q^{14} +(-3.57691 - 1.79044i) q^{16} +3.58889 q^{17} +(4.85244 - 4.85244i) q^{19} +(-0.122219 - 4.10648i) q^{20} +(1.50099 + 3.47651i) q^{22} +(-0.446082 - 0.257545i) q^{23} +(-0.675912 + 0.390238i) q^{25} +(-5.44986 - 4.05446i) q^{26} +(1.02871 + 3.42783i) q^{28} +(6.44956 + 1.72815i) q^{29} +(4.05128 - 7.01703i) q^{31} +(5.53808 - 1.15312i) q^{32} +(-3.98022 + 3.14930i) q^{34} +(-2.59915 + 2.59915i) q^{35} +(1.25948 + 1.25948i) q^{37} +(-1.12346 + 9.63963i) q^{38} +(3.73904 + 4.44700i) q^{40} +(4.07959 + 2.35535i) q^{41} +(-1.76222 + 6.57670i) q^{43} +(-4.71535 - 2.53845i) q^{44} +(0.720722 - 0.105815i) q^{46} +(3.48945 + 6.04391i) q^{47} +(-1.89897 + 3.28911i) q^{49} +(0.407174 - 1.02591i) q^{50} +(9.60196 - 0.285778i) q^{52} +(-5.26302 - 5.26302i) q^{53} -5.50019i q^{55} +(-4.14885 - 2.89889i) q^{56} +(-8.66930 + 3.74299i) q^{58} +(-6.76946 + 1.81387i) q^{59} +(5.78773 + 1.55082i) q^{61} +(1.66451 + 11.3372i) q^{62} +(-5.13007 + 6.13860i) q^{64} +(4.93314 + 8.54446i) q^{65} +(-0.453328 - 1.69184i) q^{67} +(1.65067 - 6.98540i) q^{68} +(0.601770 - 5.16335i) q^{70} +7.58339i q^{71} -12.5473i q^{73} +(-2.50202 - 0.291601i) q^{74} +(-7.21295 - 11.6766i) q^{76} +(1.24010 + 4.62812i) q^{77} +(-4.01735 - 6.95825i) q^{79} +(-8.04904 - 1.65084i) q^{80} +(-6.59129 + 0.967720i) q^{82} +(-7.99826 - 2.14313i) q^{83} +(7.12091 - 1.90804i) q^{85} +(-3.81677 - 8.84019i) q^{86} +(7.45703 - 1.32255i) q^{88} -16.5414i q^{89} +(-6.07746 - 6.07746i) q^{91} +(-0.706455 + 0.749797i) q^{92} +(-9.17356 - 3.64089i) q^{94} +(7.04818 - 12.2078i) q^{95} +(-4.15739 - 7.20082i) q^{97} +(-0.780209 - 5.31413i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8}+O(q^{10}) \) 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8	\( 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8} - 20 q^{10} + 2 q^{11} - 16 q^{13} + 4 q^{14} - 10 q^{16} + 16 q^{17} + 28 q^{19} - 12 q^{20} - 8 q^{22} + 4 q^{26} - 16 q^{28} - 4 q^{29} + 28 q^{31} + 46 q^{32} - 14 q^{34} + 16 q^{35} + 16 q^{37} - 2 q^{38} - 10 q^{40} - 10 q^{43} - 60 q^{44} + 20 q^{46} + 56 q^{47} + 4 q^{49} + 36 q^{50} + 6 q^{52} + 8 q^{53} - 52 q^{56} - 14 q^{58} + 14 q^{59} - 32 q^{61} - 16 q^{62} - 44 q^{64} + 64 q^{65} - 18 q^{67} - 16 q^{68} + 14 q^{70} - 38 q^{74} + 10 q^{76} + 36 q^{77} + 44 q^{79} - 144 q^{80} - 88 q^{82} - 20 q^{83} - 8 q^{85} - 76 q^{86} - 42 q^{88} - 80 q^{91} + 68 q^{92} + 20 q^{94} - 48 q^{95} + 40 q^{97} - 88 q^{98}+O(q^{100}) \) 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8 - 20 * q^10 + 2 * q^11 - 16 * q^13 + 4 * q^14 - 10 * q^16 + 16 * q^17 + 28 * q^19 - 12 * q^20 - 8 * q^22 + 4 * q^26 - 16 * q^28 - 4 * q^29 + 28 * q^31 + 46 * q^32 - 14 * q^34 + 16 * q^35 + 16 * q^37 - 2 * q^38 - 10 * q^40 - 10 * q^43 - 60 * q^44 + 20 * q^46 + 56 * q^47 + 4 * q^49 + 36 * q^50 + 6 * q^52 + 8 * q^53 - 52 * q^56 - 14 * q^58 + 14 * q^59 - 32 * q^61 - 16 * q^62 - 44 * q^64 + 64 * q^65 - 18 * q^67 - 16 * q^68 + 14 * q^70 - 38 * q^74 + 10 * q^76 + 36 * q^77 + 44 * q^79 - 144 * q^80 - 88 * q^82 - 20 * q^83 - 8 * q^85 - 76 * q^86 - 42 * q^88 - 80 * q^91 + 68 * q^92 + 20 * q^94 - 48 * q^95 + 40 * q^97 - 88 * q^98

Introduction

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