LMFDB - Embedded newform 432.2.y.e.181.1

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			181.1
Character	$\chi$	$=$	432.181
Dual form			432.2.y.e.253.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41328 - 0.0512684i) q^{2} +(1.99474 + 0.144914i) q^{4} +(-0.430214 + 1.60558i) q^{5} +(-3.62762 - 2.09441i) q^{7} +(-2.81171 - 0.307071i) q^{8} +O(q^{10})$	\(q+(-1.41328 - 0.0512684i) q^{2} +(1.99474 + 0.144914i) q^{4} +(-0.430214 + 1.60558i) q^{5} +(-3.62762 - 2.09441i) q^{7} +(-2.81171 - 0.307071i) q^{8} +(0.690330 - 2.24708i) q^{10} +(4.63241 - 1.24125i) q^{11} +(3.28323 + 0.879738i) q^{13} +(5.01948 + 3.14597i) q^{14} +(3.95800 + 0.578131i) q^{16} +2.14142 q^{17} +(1.03156 - 1.03156i) q^{19} +(-1.09084 + 3.14037i) q^{20} +(-6.61055 + 1.51674i) q^{22} +(-0.405884 + 0.234337i) q^{23} +(1.93733 + 1.11852i) q^{25} +(-4.59503 - 1.41164i) q^{26} +(-6.93266 - 4.70349i) q^{28} +(1.75557 + 6.55186i) q^{29} +(3.18054 + 5.50886i) q^{31} +(-5.56414 - 1.01998i) q^{32} +(-3.02643 - 0.109787i) q^{34} +(4.92339 - 4.92339i) q^{35} +(-0.728237 - 0.728237i) q^{37} +(-1.51077 + 1.40500i) q^{38} +(1.70266 - 4.38232i) q^{40} +(2.52351 - 1.45695i) q^{41} +(10.6289 - 2.84802i) q^{43} +(9.42035 - 1.80468i) q^{44} +(0.585644 - 0.310376i) q^{46} +(4.61716 - 7.99715i) q^{47} +(5.27308 + 9.13324i) q^{49} +(-2.68065 - 1.68010i) q^{50} +(6.42171 + 2.23063i) q^{52} +(-1.17892 - 1.17892i) q^{53} +7.97171i q^{55} +(9.55667 + 7.00280i) q^{56} +(-2.14521 - 9.34965i) q^{58} +(-0.397061 + 1.48185i) q^{59} +(-2.01826 - 7.53224i) q^{61} +(-4.21258 - 7.94865i) q^{62} +(7.81141 + 1.72679i) q^{64} +(-2.82498 + 4.89300i) q^{65} +(-9.82470 - 2.63252i) q^{67} +(4.27158 + 0.310320i) q^{68} +(-7.21056 + 6.70573i) q^{70} +8.27863i q^{71} +8.16641i q^{73} +(0.991870 + 1.06654i) q^{74} +(2.20718 - 1.90821i) q^{76} +(-19.4043 - 5.19937i) q^{77} +(3.63065 - 6.28847i) q^{79} +(-2.63102 + 6.10616i) q^{80} +(-3.64113 + 1.92970i) q^{82} +(-2.03413 - 7.59149i) q^{83} +(-0.921267 + 3.43821i) q^{85} +(-15.1677 + 3.48013i) q^{86} +(-13.4062 + 2.06756i) q^{88} -11.1968i q^{89} +(-10.0678 - 10.0678i) q^{91} +(-0.843594 + 0.408625i) q^{92} +(-6.93535 + 11.0655i) q^{94} +(1.21246 + 2.10004i) q^{95} +(-5.67759 + 9.83387i) q^{97} +(-6.98411 - 13.1782i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.41328	−	0.0512684i	−0.999343	−	0.0362522i
$2$	−1.41328	−	0.0512684i	−0.999343	−	0.0362522i
$3$		0			0
$3$		0			0
$4$	1.99474	+	0.144914i	0.997372	+	0.0724568i
$5$	−0.430214	+	1.60558i	−0.192397	+	0.718037i	0.800528	+	0.599296i	$0.204553\pi$
$5$	−0.430214	+	1.60558i	−0.192397	+	0.718037i	−0.992925	+	0.118741i	$0.962114\pi$
$6$		0			0
$7$	−3.62762	−	2.09441i	−1.37111	−	0.791611i	−0.380043	−	0.924969i	$-0.624091\pi$
$7$	−3.62762	−	2.09441i	−1.37111	−	0.791611i	−0.991068	+	0.133358i	$0.957424\pi$
$8$	−2.81171	−	0.307071i	−0.994089	−	0.108566i
$9$		0			0
$10$	0.690330	−	2.24708i	0.218301	−	0.710590i
$11$	4.63241	−	1.24125i	1.39673	−	0.374251i	0.519557	−	0.854436i	$-0.326097\pi$
$11$	4.63241	−	1.24125i	1.39673	−	0.374251i	0.877168	+	0.480184i	$0.159430\pi$
$12$		0			0
$13$	3.28323	+	0.879738i	0.910603	+	0.243995i	0.683564	−	0.729890i	$-0.260429\pi$
$13$	3.28323	+	0.879738i	0.910603	+	0.243995i	0.227039	+	0.973886i	$0.427096\pi$
$14$	5.01948	+	3.14597i	1.34151	+	0.840797i
$15$		0			0
$16$	3.95800	+	0.578131i	0.989500	+	0.144533i
$17$	2.14142			0.519370			0.259685	−	0.965693i	$-0.416381\pi$
$17$	2.14142			0.519370			0.259685	+	0.965693i	$0.416381\pi$
$18$		0			0
$19$	1.03156	−	1.03156i	0.236656	−	0.236656i	−0.578808	−	0.815464i	$-0.696482\pi$
$19$	1.03156	−	1.03156i	0.236656	−	0.236656i	0.815464	+	0.578808i	$0.196482\pi$
$20$	−1.09084	+	3.14037i	−0.243918	+	0.702209i
$21$		0			0
$22$	−6.61055	+	1.51674i	−1.40937	+	0.323371i
$23$	−0.405884	+	0.234337i	−0.0846327	+	0.0488627i	−0.541719	−	0.840560i	$-0.682226\pi$
$23$	−0.405884	+	0.234337i	−0.0846327	+	0.0488627i	0.457086	+	0.889422i	$0.348893\pi$
$24$		0			0
$25$	1.93733	+	1.11852i	0.387465	+	0.223703i
$26$	−4.59503	−	1.41164i	−0.901159	−	0.276846i
$27$		0			0
$28$	−6.93266	−	4.70349i	−1.31015	−	0.888877i
$29$	1.75557	+	6.55186i	0.326000	+	1.21665i	0.913302	+	0.407282i	$0.133523\pi$
$29$	1.75557	+	6.55186i	0.326000	+	1.21665i	−0.587302	+	0.809368i	$0.699810\pi$
$30$		0			0
$31$	3.18054	+	5.50886i	0.571242	+	0.989421i	0.996439	+	0.0843198i	$0.0268717\pi$
$31$	3.18054	+	5.50886i	0.571242	+	0.989421i	−0.425196	+	0.905101i	$0.639795\pi$
$32$	−5.56414	−	1.01998i	−0.983610	−	0.180309i
$33$		0			0
$34$	−3.02643	−	0.109787i	−0.519028	−	0.0188283i
$35$	4.92339	−	4.92339i	0.832204	−	0.832204i
$36$		0			0
$37$	−0.728237	−	0.728237i	−0.119721	−	0.119721i	0.644708	−	0.764429i	$-0.276979\pi$
$37$	−0.728237	−	0.728237i	−0.119721	−	0.119721i	−0.764429	+	0.644708i	$0.776979\pi$
$38$	−1.51077	+	1.40500i	−0.245080	+	0.227921i
$39$		0			0
$40$	1.70266	−	4.38232i	0.269215	−	0.692905i
$41$	2.52351	−	1.45695i	0.394105	−	0.227537i	−0.289832	−	0.957078i	$-0.593599\pi$
$41$	2.52351	−	1.45695i	0.394105	−	0.227537i	0.683937	+	0.729541i	$0.260266\pi$
$42$		0			0
$43$	10.6289	−	2.84802i	1.62090	−	0.434318i	0.669633	−	0.742692i	$-0.266451\pi$
$43$	10.6289	−	2.84802i	1.62090	−	0.434318i	0.951265	+	0.308374i	$0.0997848\pi$
$44$	9.42035	−	1.80468i	1.42017	−	0.272066i
$45$		0			0
$46$	0.585644	−	0.310376i	0.0863485	−	0.0457625i
$47$	4.61716	−	7.99715i	0.673482	−	1.16650i	−0.303429	−	0.952854i	$-0.598131\pi$
$47$	4.61716	−	7.99715i	0.673482	−	1.16650i	0.976910	−	0.213650i	$-0.0685352\pi$
$48$		0			0
$49$	5.27308	+	9.13324i	0.753297	+	1.30475i
$50$	−2.68065	−	1.68010i	−0.379101	−	0.237603i
$51$		0			0
$52$	6.42171	+	2.23063i	0.890530	+	0.309333i
$53$	−1.17892	−	1.17892i	−0.161937	−	0.161937i	0.621487	−	0.783424i	$-0.286529\pi$
$53$	−1.17892	−	1.17892i	−0.161937	−	0.161937i	−0.783424	+	0.621487i	$0.786529\pi$
$54$		0			0
$55$			7.97171i			1.07491i
$56$	9.55667	+	7.00280i	1.27706	+	0.935788i
$57$		0			0
$58$	−2.14521	−	9.34965i	−0.281680	−	1.22767i
$59$	−0.397061	+	1.48185i	−0.0516930	+	0.192921i	−0.986944	−	0.161065i	$-0.948507\pi$
$59$	−0.397061	+	1.48185i	−0.0516930	+	0.192921i	0.935251	+	0.353986i	$0.115174\pi$
$60$		0			0
$61$	−2.01826	−	7.53224i	−0.258411	−	0.964404i	−0.966161	−	0.257941i	$-0.916956\pi$
$61$	−2.01826	−	7.53224i	−0.258411	−	0.964404i	0.707749	−	0.706464i	$-0.249711\pi$
$62$	−4.21258	−	7.94865i	−0.534998	−	1.00948i
$63$		0			0
$64$	7.81141	+	1.72679i	0.976427	+	0.215849i
$65$	−2.82498	+	4.89300i	−0.350395	+	0.606902i
$66$		0			0
$67$	−9.82470	−	2.63252i	−1.20028	−	0.321614i	−0.397338	−	0.917673i	$-0.630066\pi$
$67$	−9.82470	−	2.63252i	−1.20028	−	0.321614i	−0.802941	+	0.596059i	$0.796732\pi$
$68$	4.27158	+	0.310320i	0.518005	+	0.0376319i
$69$		0			0
$70$	−7.21056	+	6.70573i	−0.861826	+	0.801488i
$71$			8.27863i			0.982493i	0.871021	+	0.491246i	$0.163458\pi$
$71$			8.27863i			0.982493i	−0.871021	+	0.491246i	$0.836542\pi$
$72$		0			0
$73$			8.16641i			0.955806i	0.878413	+	0.477903i	$0.158603\pi$
$73$			8.16641i			0.955806i	−0.878413	+	0.477903i	$0.841397\pi$
$74$	0.991870	+	1.06654i	0.115303	+	0.123983i
$75$		0			0
$76$	2.20718	−	1.90821i	0.253181	−	0.218887i
$77$	−19.4043	−	5.19937i	−2.21133	−	0.592523i
$78$		0			0
$79$	3.63065	−	6.28847i	0.408480	−	0.707508i	−0.586240	−	0.810138i	$-0.699392\pi$
$79$	3.63065	−	6.28847i	0.408480	−	0.707508i	0.994720	+	0.102630i	$0.0327257\pi$
$80$	−2.63102	+	6.10616i	−0.294157	+	0.682690i
$81$		0			0
$82$	−3.64113	+	1.92970i	−0.402095	+	0.213100i
$83$	−2.03413	−	7.59149i	−0.223275	−	0.833274i	−0.983088	−	0.183133i	$-0.941376\pi$
$83$	−2.03413	−	7.59149i	−0.223275	−	0.833274i	0.759813	−	0.650142i	$-0.225290\pi$
$84$		0			0
$85$	−0.921267	+	3.43821i	−0.0999254	+	0.372927i
$86$	−15.1677	+	3.48013i	−1.63558	+	0.375272i
$87$		0			0
$88$	−13.4062	+	2.06756i	−1.42910	+	0.220402i
$89$		−	11.1968i		−	1.18686i	−0.804886	−	0.593429i	$-0.797774\pi$
$89$		−	11.1968i		−	1.18686i	0.804886	−	0.593429i	$-0.202226\pi$
$90$		0			0
$91$	−10.0678	−	10.0678i	−1.05539	−	1.05539i
$92$	−0.843594	+	0.408625i	−0.0879507	+	0.0426021i
$93$		0			0
$94$	−6.93535	+	11.0655i	−0.715327	+	1.14132i
$95$	1.21246	+	2.10004i	0.124396	+	0.215460i
$96$		0			0
$97$	−5.67759	+	9.83387i	−0.576472	+	0.998479i	0.419408	+	0.907798i	$0.362238\pi$
$97$	−5.67759	+	9.83387i	−0.576472	+	0.998479i	−0.995880	+	0.0906808i	$0.971096\pi$
$98$	−6.98411	−	13.1782i	−0.705501	−	1.33120i
$99$		0			0
$100$	3.70238	+	2.51190i	0.370238	+	0.251190i
$101$	2.90189	−	0.777558i	0.288749	−	0.0773699i	−0.111537	−	0.993760i	$-0.535577\pi$
$101$	2.90189	−	0.777558i	0.288749	−	0.0773699i	0.400286	+	0.916390i	$0.368911\pi$
$102$		0			0
$103$	1.24824	−	0.720669i	0.122992	−	0.0710096i	−0.437242	−	0.899344i	$-0.644045\pi$
$103$	1.24824	−	0.720669i	0.122992	−	0.0710096i	0.560234	+	0.828334i	$0.310711\pi$
$104$	−8.96133	−	3.48175i	−0.878731	−	0.341414i
$105$		0			0
$106$	1.60570	+	1.72658i	0.155960	+	0.167701i
$107$	−5.85602	−	5.85602i	−0.566123	−	0.566123i	0.364917	−	0.931040i	$-0.381097\pi$
$107$	−5.85602	−	5.85602i	−0.566123	−	0.566123i	−0.931040	+	0.364917i	$0.881097\pi$
$108$		0			0
$109$	−2.05249	+	2.05249i	−0.196593	+	0.196593i	−0.798538	−	0.601945i	$-0.794393\pi$
$109$	−2.05249	+	2.05249i	−0.196593	+	0.196593i	0.601945	+	0.798538i	$0.294393\pi$
$110$	0.408697	−	11.2663i	0.0389677	−	1.07420i
$111$		0			0
$112$	−13.1473	−	10.3869i	−1.24230	−	0.981470i
$113$	4.12726	+	7.14862i	0.388260	+	0.672486i	0.992216	−	0.124532i	$-0.0397430\pi$
$113$	4.12726	+	7.14862i	0.388260	+	0.672486i	−0.603956	+	0.797018i	$0.706410\pi$
$114$		0			0
$115$	−0.201630	−	0.752495i	−0.0188021	−	0.0701705i
$116$	2.55245	+	13.3237i	0.236989	+	1.23707i
$117$		0			0
$118$	0.637132	−	2.07392i	0.0586528	−	0.190920i
$119$	−7.76824	−	4.48500i	−0.712114	−	0.411139i
$120$		0			0
$121$	10.3923	−	5.99998i	0.944752	−	0.545453i
$122$	2.46621	+	10.7487i	0.223280	+	0.973138i
$123$		0			0
$124$	5.54606	+	11.4497i	0.498051	+	1.02821i
$125$	−8.50616	+	8.50616i	−0.760814	+	0.760814i
$126$		0			0
$127$	−1.68483			−0.149504			−0.0747521	−	0.997202i	$-0.523817\pi$
$127$	−1.68483			−0.149504			−0.0747521	+	0.997202i	$0.523817\pi$
$128$	−10.9512	−	2.84092i	−0.967960	−	0.251104i
$129$		0			0
$130$	4.24335	−	6.77037i	0.372167	−	0.593801i
$131$	7.36461	+	1.97334i	0.643449	+	0.172412i	0.565765	−	0.824566i	$-0.308581\pi$
$131$	7.36461	+	1.97334i	0.643449	+	0.172412i	0.0776838	+	0.996978i	$0.475248\pi$
$132$		0			0
$133$	−5.90261	+	1.58160i	−0.511821	+	0.137142i
$134$	13.7501	+	4.22420i	1.18783	+	0.364915i
$135$		0			0
$136$	−6.02104	−	0.657567i	−0.516300	−	0.0563859i
$137$	8.26806	+	4.77357i	0.706388	+	0.407833i	0.809722	−	0.586813i	$-0.199618\pi$
$137$	8.26806	+	4.77357i	0.706388	+	0.407833i	−0.103334	+	0.994647i	$0.532951\pi$
$138$		0			0
$139$	3.74281	−	13.9684i	0.317461	−	1.18478i	−0.604215	−	0.796821i	$-0.706513\pi$
$139$	3.74281	−	13.9684i	0.317461	−	1.18478i	0.921676	−	0.387960i	$-0.126820\pi$
$140$	10.5344	−	9.10743i	0.890316	−	0.769718i
$141$		0			0
$142$	0.424432	−	11.7001i	0.0356175	−	0.981847i
$143$	16.3012			1.36318
$144$		0			0
$145$	−11.2748			−0.936321
$146$	0.418679	−	11.5415i	0.0346501	−	0.955178i
$147$		0			0
$148$	−1.34711	−	1.55818i	−0.110732	−	0.128081i
$149$	−0.445462	+	1.66249i	−0.0364937	+	0.136196i	−0.981769	−	0.190077i	$-0.939126\pi$
$149$	−0.445462	+	1.66249i	−0.0364937	+	0.136196i	0.945276	+	0.326273i	$0.105793\pi$
$150$		0			0
$151$	−18.5071	−	10.6851i	−1.50609	−	0.869542i	−0.999975	−	0.00707596i	$-0.997748\pi$
$151$	−18.5071	−	10.6851i	−1.50609	−	0.869542i	−0.506115	−	0.862466i	$-0.668919\pi$
$152$	−3.21721	+	2.58368i	−0.260950	+	0.209564i
$153$		0			0
$154$	27.1572	+	8.34301i	2.18839	+	0.672299i
$155$	−10.2132	+	2.73663i	−0.820346	+	0.219811i
$156$		0			0
$157$	−10.2463	−	2.74550i	−0.817746	−	0.219114i	−0.174385	−	0.984677i	$-0.555794\pi$
$157$	−10.2463	−	2.74550i	−0.817746	−	0.219114i	−0.643361	+	0.765563i	$0.722461\pi$
$158$	−5.45354	+	8.70125i	−0.433860	+	0.692234i
$159$		0			0
$160$	4.03143	−	8.49485i	0.318713	−	0.671577i
$161$	1.96319			0.154721
$162$		0			0
$163$	−3.47621	+	3.47621i	−0.272278	+	0.272278i	−0.830017	−	0.557739i	$-0.811669\pi$
$163$	−3.47621	+	3.47621i	−0.272278	+	0.272278i	0.557739	+	0.830017i	$0.311669\pi$
$164$	5.24488	−	2.54054i	0.409556	−	0.198383i
$165$		0			0
$166$	2.48560	+	10.8332i	0.192920	+	0.840821i
$167$	0.277442	−	0.160181i	0.0214691	−	0.0123952i	−0.489227	−	0.872156i	$-0.662721\pi$
$167$	0.277442	−	0.160181i	0.0214691	−	0.0123952i	0.510696	+	0.859761i	$0.329388\pi$
$168$		0			0
$169$	−1.25270	−	0.723245i	−0.0963613	−	0.0556342i
$170$	1.47828	−	4.81194i	0.113379	−	0.369059i
$171$		0			0
$172$	21.6147	−	4.14078i	1.64811	−	0.315732i
$173$	3.13236	+	11.6901i	0.238149	+	0.888784i	0.976704	+	0.214591i	$0.0688419\pi$
$173$	3.13236	+	11.6901i	0.238149	+	0.888784i	−0.738555	+	0.674193i	$0.764491\pi$
$174$		0			0
$175$	−4.68525	−	8.11510i	−0.354172	−	0.613444i
$176$	19.0527	−	2.23473i	1.43615	−	0.168449i
$177$		0			0
$178$	−0.574041	+	15.8243i	−0.0430262	+	1.18608i
$179$	−18.6780	+	18.6780i	−1.39606	+	1.39606i	−0.585104	+	0.810958i	$0.698946\pi$
$179$	−18.6780	+	18.6780i	−1.39606	+	1.39606i	−0.810958	+	0.585104i	$0.801054\pi$
$180$		0			0
$181$	4.10527	+	4.10527i	0.305143	+	0.305143i	0.843022	−	0.537879i	$-0.180774\pi$
$181$	4.10527	+	4.10527i	0.305143	+	0.305143i	−0.537879	+	0.843022i	$0.680774\pi$
$182$	13.7124	+	14.7448i	1.01643	+	1.09295i
$183$		0			0
$184$	1.21319	−	0.534253i	0.0894373	−	0.0393857i
$185$	1.48254	−	0.855945i	0.108998	−	0.0629303i
$186$		0			0
$187$	9.91993	−	2.65804i	0.725417	−	0.194375i
$188$	10.3689	−	15.2832i	0.756232	−	1.11464i
$189$		0			0
$190$	−1.60588	−	3.03012i	−0.116503	−	0.219828i
$191$	−8.60099	+	14.8974i	−0.622346	+	1.07793i	0.366702	+	0.930338i	$0.380487\pi$
$191$	−8.60099	+	14.8974i	−0.622346	+	1.07793i	−0.989048	+	0.147596i	$0.952846\pi$
$192$		0			0
$193$	9.17459	+	15.8909i	0.660402	+	1.14385i	0.980510	+	0.196468i	$0.0629473\pi$
$193$	9.17459	+	15.8909i	0.660402	+	1.14385i	−0.320108	+	0.947381i	$0.603719\pi$
$194$	8.52821	−	13.6070i	0.612290	−	0.976924i
$195$		0			0
$196$	9.19490	+	18.9826i	0.656779	+	1.35590i
$197$	−8.80431	−	8.80431i	−0.627281	−	0.627281i	0.320102	−	0.947383i	$-0.396283\pi$
$197$	−8.80431	−	8.80431i	−0.627281	−	0.627281i	−0.947383	+	0.320102i	$0.896283\pi$
$198$		0			0
$199$			10.0277i			0.710847i	0.934705	+	0.355423i	$0.115663\pi$
$199$			10.0277i			0.710847i	−0.934705	+	0.355423i	$0.884337\pi$
$200$	−5.10373	−	3.73984i	−0.360888	−	0.264446i
$201$		0			0
$202$	−4.14105	+	0.950136i	−0.291364	+	0.0668513i
$203$	7.35374	−	27.4445i	0.516131	−	1.92623i
$204$		0			0
$205$	1.25360	+	4.67849i	0.0875550	+	0.326760i
$206$	−1.80106	+	0.954515i	−0.125486	+	0.0665042i
$207$		0			0
$208$	12.4864	+	5.38014i	0.865776	+	0.373045i
$209$	3.49819	−	6.05904i	0.241975	−	0.419112i
$210$		0			0
$211$	19.2080	+	5.14678i	1.32234	+	0.354319i	0.849852	−	0.527021i	$-0.176691\pi$
$211$	19.2080	+	5.14678i	1.32234	+	0.354319i	0.472483	+	0.881340i	$0.343358\pi$
$212$	−2.18079	−	2.52248i	−0.149778	−	0.173244i
$213$		0			0
$214$	7.97600	+	8.57645i	0.545228	+	0.586274i
$215$			18.2909i			1.24743i
$216$		0			0
$217$		−	26.6454i		−	1.80881i
$218$	3.00598	−	2.79552i	0.203591	−	0.189337i
$219$		0			0
$220$	−1.15521	+	15.9015i	−0.0778842	+	1.07208i
$221$	7.03076	+	1.88389i	0.472940	+	0.126724i
$222$		0			0
$223$	−6.96587	+	12.0652i	−0.466469	+	0.807948i	−0.999266	−	0.0382947i	$-0.987807\pi$
$223$	−6.96587	+	12.0652i	−0.466469	+	0.807948i	0.532797	+	0.846243i	$0.321141\pi$
$224$	18.0483	+	15.3537i	1.20590	+	1.02586i
$225$		0			0
$226$	−5.46649	−	10.3146i	−0.363625	−	0.686119i
$227$	−1.96164	−	7.32092i	−0.130198	−	0.485907i	0.869773	−	0.493452i	$-0.164265\pi$
$227$	−1.96164	−	7.32092i	−0.130198	−	0.485907i	−0.999972	+	0.00754492i	$0.997598\pi$
$228$		0			0
$229$	4.94734	−	18.4637i	0.326930	−	1.22012i	−0.585428	−	0.810724i	$-0.699074\pi$
$229$	4.94734	−	18.4637i	0.326930	−	1.22012i	0.912358	−	0.409394i	$-0.134260\pi$
$230$	0.246382	+	1.07383i	0.0162459	+	0.0708060i
$231$		0			0
$232$	−2.92425	−	18.9610i	−0.191987	−	1.24485i
$233$		−	10.7647i		−	0.705216i	−0.935771	−	0.352608i	$-0.885295\pi$
$233$		−	10.7647i		−	0.705216i	0.935771	−	0.352608i	$-0.114705\pi$
$234$		0			0
$235$	10.8537	+	10.8537i	0.708017	+	0.708017i
$236$	−1.00678	+	2.89838i	−0.0655355	+	0.188668i
$237$		0			0
$238$	10.7488	+	6.73684i	0.696741	+	0.436684i
$239$	11.1429	+	19.3001i	0.720774	+	1.24842i	0.960690	+	0.277624i	$0.0895469\pi$
$239$	11.1429	+	19.3001i	0.720774	+	1.24842i	−0.239916	+	0.970794i	$0.577120\pi$
$240$		0			0
$241$	13.7285	−	23.7785i	0.884332	−	1.53171i	0.0378540	−	0.999283i	$-0.487948\pi$
$241$	13.7285	−	23.7785i	0.884332	−	1.53171i	0.846478	−	0.532424i	$-0.178719\pi$
$242$	−14.9948	+	7.94688i	−0.963905	+	0.510845i
$243$		0			0
$244$	−2.93438	−	15.3174i	−0.187855	−	0.980593i
$245$	−16.9327	+	4.53710i	−1.08179	+	0.289865i
$246$		0			0
$247$	4.29435	−	2.47934i	0.273243	−	0.157757i
$248$	−7.25115	−	16.4660i	−0.460448	−	1.04559i
$249$		0			0
$250$	12.4577	−	11.5855i	0.787895	−	0.732733i
$251$	−11.4125	−	11.4125i	−0.720350	−	0.720350i	0.248326	−	0.968676i	$-0.420119\pi$
$251$	−11.4125	−	11.4125i	−0.720350	−	0.720350i	−0.968676	+	0.248326i	$0.920119\pi$
$252$		0			0
$253$	−1.58935	+	1.58935i	−0.0999217	+	0.0999217i
$254$	2.38114	+	0.0863784i	0.149406	+	0.00541986i
$255$		0			0
$256$	15.3315	+	4.57648i	0.958221	+	0.286030i
$257$	0.930384	+	1.61147i	0.0580357	+	0.100521i	0.893584	−	0.448897i	$-0.148183\pi$
$257$	0.930384	+	1.61147i	0.0580357	+	0.100521i	−0.835548	+	0.549418i	$0.814850\pi$
$258$		0			0
$259$	1.11654	+	4.16699i	0.0693785	+	0.258924i
$260$	−6.34417	+	9.35091i	−0.393449	+	0.579919i
$261$		0			0
$262$	−10.3071	−	3.16646i	−0.636776	−	0.195625i
$263$	0.0414842	+	0.0239509i	0.00255802	+	0.00147687i	0.501278	−	0.865286i	$-0.332863\pi$
$263$	0.0414842	+	0.0239509i	0.00255802	+	0.00147687i	−0.498720	+	0.866763i	$0.666197\pi$
$264$		0			0
$265$	2.40003	−	1.38566i	0.147433	−	0.0851203i
$266$	8.42315	−	1.93263i	0.516457	−	0.118497i
$267$		0			0
$268$	−19.2163	−	6.67493i	−1.17382	−	0.407737i
$269$	14.5681	−	14.5681i	0.888235	−	0.888235i	−0.106118	−	0.994354i	$-0.533842\pi$
$269$	14.5681	−	14.5681i	0.888235	−	0.888235i	0.994354	+	0.106118i	$0.0338421\pi$
$270$		0			0
$271$	−15.7807			−0.958607			−0.479304	−	0.877649i	$-0.659111\pi$
$271$	−15.7807			−0.958607			−0.479304	+	0.877649i	$0.659111\pi$
$272$	8.47573	+	1.23802i	0.513917	+	0.0750659i
$273$		0			0
$274$	−11.4404	−	7.17030i	−0.691139	−	0.433174i
$275$	10.3629	+	2.77672i	0.624904	+	0.167442i
$276$		0			0
$277$	7.21383	−	1.93294i	0.433437	−	0.116139i	−0.0355022	−	0.999370i	$-0.511303\pi$
$277$	7.21383	−	1.93294i	0.433437	−	0.116139i	0.468939	+	0.883231i	$0.344636\pi$
$278$	−6.00579	+	19.5494i	−0.360203	+	1.17249i
$279$		0			0
$280$	−15.3550	+	12.3313i	−0.917634	+	0.736936i
$281$	−5.84440	−	3.37427i	−0.348648	−	0.201292i	0.315442	−	0.948945i	$-0.397847\pi$
$281$	−5.84440	−	3.37427i	−0.348648	−	0.201292i	−0.664089	+	0.747653i	$0.731181\pi$
$282$		0			0
$283$	−3.33366	+	12.4414i	−0.198165	+	0.739563i	0.793259	+	0.608884i	$0.208383\pi$
$283$	−3.33366	+	12.4414i	−0.198165	+	0.739563i	−0.991425	+	0.130679i	$0.958284\pi$
$284$	−1.19969	+	16.5137i	−0.0711882	+	0.979910i
$285$		0			0
$286$	−23.0383	−	0.835738i	−1.36228	−	0.0494182i
$287$	−12.2058			−0.720483
$288$		0			0
$289$	−12.4143			−0.730255
$290$	15.9345	+	0.578041i	0.935706	+	0.0339437i
$291$		0			0
$292$	−1.18342	+	16.2899i	−0.0692546	+	0.953294i
$293$	3.71874	−	13.8785i	0.217251	−	0.810792i	−0.768111	−	0.640317i	$-0.778803\pi$
$293$	3.71874	−	13.8785i	0.217251	−	0.810792i	0.985362	−	0.170475i	$-0.0545303\pi$
$294$		0			0
$295$	−2.20841	−	1.27503i	−0.128579	−	0.0742349i
$296$	1.82397	+	2.27121i	0.106016	+	0.132011i
$297$		0			0
$298$	0.714797	−	2.32673i	0.0414071	−	0.134784i
$299$	−1.53877	+	0.412311i	−0.0889891	+	0.0238446i
$300$		0			0
$301$	−44.5226	−	11.9298i	−2.56624	−	0.687622i
$302$	25.6080	+	16.0499i	1.47358	+	0.923569i
$303$		0			0
$304$	4.67929	−	3.48654i	0.268376	−	0.199967i
$305$	12.9619			0.742196
$306$		0			0
$307$	12.2394	−	12.2394i	0.698539	−	0.698539i	−0.265556	−	0.964095i	$-0.585556\pi$
$307$	12.2394	−	12.2394i	0.698539	−	0.698539i	0.964095	+	0.265556i	$0.0855556\pi$
$308$	−37.9532	−	13.1834i	−2.16258	−	0.751191i
$309$		0			0
$310$	14.5745	−	3.34401i	0.827776	−	0.189927i
$311$	−0.742777	+	0.428842i	−0.0421190	+	0.0243174i	−0.520912	−	0.853611i	$-0.674408\pi$
$311$	−0.742777	+	0.428842i	−0.0421190	+	0.0243174i	0.478793	+	0.877928i	$0.341075\pi$
$312$		0			0
$313$	15.8984	+	9.17895i	0.898631	+	0.518825i	0.876756	−	0.480936i	$-0.159703\pi$
$313$	15.8984	+	9.17895i	0.898631	+	0.518825i	0.0218755	+	0.999761i	$0.493036\pi$
$314$	14.3402	+	4.40548i	0.809265	+	0.248616i
$315$		0			0
$316$	8.15349	−	12.0177i	0.458670	−	0.676051i
$317$	−1.07887	−	4.02641i	−0.0605956	−	0.226146i	0.928987	−	0.370112i	$-0.120681\pi$
$317$	−1.07887	−	4.02641i	−0.0605956	−	0.226146i	−0.989583	+	0.143967i	$0.954014\pi$
$318$		0			0
$319$	16.2650	+	28.1718i	0.910666	+	1.57732i
$320$	−6.13308	+	11.7990i	−0.342849	+	0.659582i
$321$		0			0
$322$	−2.77455	−	0.100650i	−0.154619	−	0.00560898i
$323$	2.20900	−	2.20900i	0.122912	−	0.122912i
$324$		0			0
$325$	5.37668	+	5.37668i	0.298244	+	0.298244i
$326$	5.09109	−	4.73465i	0.281969	−	0.262228i
$327$		0			0
$328$	−7.54275	+	3.32161i	−0.416479	+	0.183405i
$329$	−33.4986	+	19.3404i	−1.84684	+	1.06627i
$330$		0			0
$331$	−4.99103	+	1.33734i	−0.274332	+	0.0735070i	−0.393362	−	0.919384i	$-0.628688\pi$
$331$	−4.99103	+	1.33734i	−0.274332	+	0.0735070i	0.119030	+	0.992891i	$0.462021\pi$
$332$	−2.95746	−	15.4378i	−0.162312	−	0.847262i
$333$		0			0
$334$	−0.400317	+	0.212158i	−0.0219044	+	0.0116088i
$335$	8.45344	−	14.6418i	0.461861	−	0.799966i
$336$		0			0
$337$	1.94762	+	3.37338i	0.106094	+	0.183760i	0.914185	−	0.405298i	$-0.132832\pi$
$337$	1.94762	+	3.37338i	0.106094	+	0.183760i	−0.808091	+	0.589058i	$0.799499\pi$
$338$	1.73334	+	1.08637i	0.0942811	+	0.0590910i
$339$		0			0
$340$	−2.33593	+	6.72485i	−0.126684	+	0.364706i
$341$	21.5715	+	21.5715i	1.16816	+	1.16816i
$342$		0			0
$343$		−	14.8542i		−	0.802049i
$344$	−30.7600	+	4.74395i	−1.65847	+	0.255777i
$345$		0			0
$346$	−3.82758	−	16.6821i	−0.205772	−	0.896834i
$347$	−0.816741	+	3.04812i	−0.0438449	+	0.163632i	−0.984377	−	0.176073i	$-0.943660\pi$
$347$	−0.816741	+	3.04812i	−0.0438449	+	0.163632i	0.940532	+	0.339705i	$0.110327\pi$
$348$		0			0
$349$	−0.374843	−	1.39893i	−0.0200649	−	0.0748831i	0.955167	−	0.296066i	$-0.0956749\pi$
$349$	−0.374843	−	1.39893i	−0.0200649	−	0.0748831i	−0.975232	+	0.221183i	$0.929008\pi$
$350$	6.20554	+	11.7091i	0.331700	+	0.625880i
$351$		0			0
$352$	−27.0414	+	2.18151i	−1.44131	+	0.116275i
$353$	−7.73892	+	13.4042i	−0.411901	+	0.713434i	−0.995098	−	0.0988971i	$-0.968469\pi$
$353$	−7.73892	+	13.4042i	−0.411901	+	0.713434i	0.583196	+	0.812331i	$0.301802\pi$
$354$		0			0
$355$	−13.2920	−	3.56158i	−0.705466	−	0.189029i
$356$	1.62257	−	22.3347i	0.0859959	−	1.18374i
$357$		0			0
$358$	27.3550	−	25.4398i	1.44576	−	1.34453i
$359$		−	4.78775i		−	0.252688i	−0.991987	−	0.126344i	$-0.959676\pi$
$359$		−	4.78775i		−	0.252688i	0.991987	−	0.126344i	$-0.0403242\pi$
$360$		0			0
$361$			16.8718i			0.887988i
$362$	−5.59145	−	6.01239i	−0.293880	−	0.316004i
$363$		0			0
$364$	−18.6236	−	21.5416i	−0.976144	−	1.12908i
$365$	−13.1118	−	3.51330i	−0.686304	−	0.183895i
$366$		0			0
$367$	−9.93807	+	17.2133i	−0.518763	+	0.898524i	0.480999	+	0.876721i	$0.340274\pi$
$367$	−9.93807	+	17.2133i	−0.518763	+	0.898524i	−0.999762	+	0.0218032i	$0.993059\pi$
$368$	−1.74197	+	0.692854i	−0.0908064	+	0.0361175i
$369$		0			0
$370$	−2.13913	+	1.13369i	−0.111208	+	0.0589375i
$371$	1.80753	+	6.74579i	0.0938422	+	0.350224i
$372$		0			0
$373$	0.114573	−	0.427591i	0.00593235	−	0.0221398i	−0.962896	−	0.269872i	$-0.913019\pi$
$373$	0.114573	−	0.427591i	0.00593235	−	0.0221398i	0.968829	+	0.247732i	$0.0796853\pi$
$374$	−14.1559	+	3.24798i	−0.731987	+	0.167949i
$375$		0			0
$376$	−15.4378	+	21.0679i	−0.796144	+	1.08649i
$377$			23.0557i			1.18743i
$378$		0			0
$379$	−6.18132	−	6.18132i	−0.317513	−	0.317513i	0.530298	−	0.847811i	$-0.322080\pi$
$379$	−6.18132	−	6.18132i	−0.317513	−	0.317513i	−0.847811	+	0.530298i	$0.822080\pi$
$380$	2.11422	+	4.36475i	0.108457	+	0.223907i
$381$		0			0
$382$	12.9194	−	20.6132i	0.661014	−	1.05466i
$383$	−6.46708	−	11.2013i	−0.330452	−	0.572360i	0.652148	−	0.758091i	$-0.273868\pi$
$383$	−6.46708	−	11.2013i	−0.330452	−	0.572360i	−0.982601	+	0.185731i	$0.940535\pi$
$384$		0			0
$385$	16.6960	−	28.9183i	0.850907	−	1.47381i
$386$	−12.1516	−	22.9287i	−0.618501	−	1.16704i
$387$		0			0
$388$	−12.7504	+	18.7933i	−0.647303	+	0.954085i
$389$	26.4265	−	7.08096i	1.33988	−	0.359019i	0.483489	−	0.875351i	$-0.339369\pi$
$389$	26.4265	−	7.08096i	1.33988	−	0.359019i	0.856389	+	0.516331i	$0.172703\pi$
$390$		0			0
$391$	−0.869168	+	0.501814i	−0.0439557	+	0.0253778i
$392$	−12.0218	−	27.2992i	−0.607193	−	1.37882i
$393$		0			0
$394$	11.9916	+	12.8944i	0.604128	+	0.649609i
$395$	8.53468	+	8.53468i	0.429426	+	0.429426i
$396$		0			0
$397$	21.9741	−	21.9741i	1.10285	−	1.10285i	0.108781	−	0.994066i	$-0.465305\pi$
$397$	21.9741	−	21.9741i	1.10285	−	1.10285i	0.994066	−	0.108781i	$-0.0346948\pi$
$398$	0.514105	−	14.1720i	0.0257698	−	0.710380i
$399$		0			0
$400$	7.02129	+	5.54711i	0.351064	+	0.277356i
$401$	−13.4970	−	23.3775i	−0.674009	−	1.16742i	−0.976758	−	0.214347i	$-0.931238\pi$
$401$	−13.4970	−	23.3775i	−0.674009	−	1.16742i	0.302749	−	0.953070i	$-0.402096\pi$
$402$		0			0
$403$	5.59609	+	20.8849i	0.278761	+	1.04035i
$404$	5.90120	−	1.13051i	0.293596	−	0.0562448i
$405$		0			0
$406$	−11.8000	+	38.4099i	−0.585622	+	1.90625i
$407$	−4.27742	−	2.46957i	−0.212024	−	0.122412i
$408$		0			0
$409$	−11.1537	+	6.43957i	−0.551513	+	0.318416i	−0.749732	−	0.661741i	$-0.769818\pi$
$409$	−11.1537	+	6.43957i	−0.551513	+	0.318416i	0.198219	+	0.980158i	$0.436484\pi$
$410$	−1.53183	−	6.67630i	−0.0756517	−	0.329719i
$411$		0			0
$412$	2.59434	−	1.25666i	0.127814	−	0.0619113i
$413$	4.54399	−	4.54399i	0.223595	−	0.223595i
$414$		0			0
$415$	13.0638			0.641279
$416$	−17.3710	−	8.24382i	−0.851684	−	0.404186i
$417$		0			0
$418$	−5.25457	+	8.38379i	−0.257009	+	0.410065i
$419$	−0.203434	−	0.0545100i	−0.00993841	−	0.00266299i	0.253846	−	0.967245i	$-0.418304\pi$
$419$	−0.203434	−	0.0545100i	−0.00993841	−	0.00266299i	−0.263785	+	0.964582i	$0.584971\pi$
$420$		0			0
$421$	−34.2301	+	9.17194i	−1.66827	+	0.447013i	−0.964645	−	0.263554i	$-0.915105\pi$
$421$	−34.2301	+	9.17194i	−1.66827	+	0.447013i	−0.703630	+	0.710567i	$0.748439\pi$
$422$	−26.8825	−	8.25862i	−1.30862	−	0.402023i
$423$		0			0
$424$	2.95276	+	3.67678i	0.143399	+	0.178560i
$425$	4.14862	+	2.39521i	0.201238	+	0.116185i
$426$		0			0
$427$	−8.45410	+	31.5511i	−0.409123	+	1.52687i
$428$	−10.8326	−	12.5299i	−0.523616	−	0.605655i
$429$		0			0
$430$	0.937743	−	25.8502i	0.0452220	−	1.24661i
$431$	−33.5339			−1.61527			−0.807635	−	0.589683i	$-0.799253\pi$
$431$	−33.5339			−1.61527			−0.807635	+	0.589683i	$0.799253\pi$
$432$		0			0
$433$	−28.9691			−1.39217			−0.696083	−	0.717962i	$-0.745075\pi$
$433$	−28.9691			−1.39217			−0.696083	+	0.717962i	$0.745075\pi$
$434$	−1.36607	+	37.6575i	−0.0655733	+	1.80762i
$435$		0			0
$436$	−4.39162	+	3.79676i	−0.210321	+	0.181832i
$437$	−0.176961	+	0.660427i	−0.00846519	+	0.0315925i
$438$		0			0
$439$	14.6656	+	8.46718i	0.699950	+	0.404116i	0.807329	−	0.590102i	$-0.200912\pi$
$439$	14.6656	+	8.46718i	0.699950	+	0.404116i	−0.107379	+	0.994218i	$0.534246\pi$
$440$	2.44788	−	22.4141i	0.116698	−	1.06855i
$441$		0			0
$442$	−9.83987	−	3.02292i	−0.468035	−	0.143786i
$443$	3.08511	−	0.826654i	0.146578	−	0.0392755i	−0.184784	−	0.982779i	$-0.559159\pi$
$443$	3.08511	−	0.826654i	0.146578	−	0.0392755i	0.331362	+	0.943504i	$0.392492\pi$
$444$		0			0
$445$	17.9773	+	4.81702i	0.852208	+	0.228348i
$446$	10.4633	−	16.6945i	0.495452	−	0.790506i
$447$		0			0
$448$	−24.7202	−	22.6244i	−1.16792	−	1.06890i
$449$	41.9192			1.97829			0.989145	−	0.146944i	$-0.0469436\pi$
$449$	41.9192			1.97829			0.989145	+	0.146944i	$0.0469436\pi$
$450$		0			0
$451$	9.88149	−	9.88149i	0.465301	−	0.465301i
$452$	7.19689	+	14.8578i	0.338513	+	0.698850i
$453$		0			0
$454$	2.39702	+	10.4471i	0.112498	+	0.490307i
$455$	20.4959	−	11.8333i	0.960862	−	0.554754i
$456$		0			0
$457$	−4.93980	−	2.85199i	−0.231074	−	0.133411i	0.379993	−	0.924989i	$-0.375926\pi$
$457$	−4.93980	−	2.85199i	−0.231074	−	0.133411i	−0.611067	+	0.791579i	$0.709260\pi$
$458$	−7.93860	+	25.8409i	−0.370947	+	1.20746i
$459$		0			0
$460$	−0.293154	−	1.53025i	−0.0136684	−	0.0713484i
$461$	−10.2715	−	38.3338i	−0.478392	−	1.78538i	−0.608135	−	0.793834i	$-0.708082\pi$
$461$	−10.2715	−	38.3338i	−0.478392	−	1.78538i	0.129743	−	0.991548i	$-0.458585\pi$
$462$		0			0
$463$	−6.28293	−	10.8824i	−0.291992	−	0.505746i	0.682288	−	0.731083i	$-0.260985\pi$
$463$	−6.28293	−	10.8824i	−0.291992	−	0.505746i	−0.974281	+	0.225337i	$0.927652\pi$
$464$	3.16070	+	26.9472i	0.146732	+	1.25099i
$465$		0			0
$466$	−0.551886	+	15.2135i	−0.0255656	+	0.704753i
$467$	−12.1784	+	12.1784i	−0.563550	+	0.563550i	−0.930314	−	0.366764i	$-0.880466\pi$
$467$	−12.1784	+	12.1784i	−0.563550	+	0.563550i	0.366764	+	0.930314i	$0.380466\pi$
$468$		0			0
$469$	30.1267	+	30.1267i	1.39112	+	1.39112i
$470$	−14.7829	−	15.8958i	−0.681884	−	0.733219i
$471$		0			0
$472$	1.57145	−	4.04461i	0.0723321	−	0.186168i
$473$	45.7025	−	26.3864i	2.10140	−	1.21325i
$474$		0			0
$475$	3.15228	−	0.844652i	0.144637	−	0.0387553i
$476$	−14.8457	−	10.0721i	−0.680452	−	0.461656i
$477$		0			0
$478$	−14.7586	−	27.8478i	−0.675043	−	1.27373i
$479$	10.6864	−	18.5094i	0.488275	−	0.845717i	−0.511634	−	0.859204i	$-0.670960\pi$
$479$	10.6864	−	18.5094i	0.488275	−	0.845717i	0.999909	+	0.0134862i	$0.00429292\pi$
$480$		0			0
$481$	−1.75031	−	3.03162i	−0.0798072	−	0.138230i
$482$	−20.6214	+	32.9019i	−0.939278	+	1.49864i
$483$		0			0
$484$	21.5994	−	10.4624i	0.981790	−	0.475565i
$485$	−13.3465	−	13.3465i	−0.606033	−	0.606033i
$486$		0			0
$487$			39.3716i			1.78410i	0.451939	+	0.892049i	$0.350732\pi$
$487$			39.3716i			1.78410i	−0.451939	+	0.892049i	$0.649268\pi$
$488$	3.36182	+	21.7982i	0.152182	+	0.986759i
$489$		0			0
$490$	24.1633	−	5.54410i	1.09159	−	0.250457i
$491$	−9.08087	+	33.8903i	−0.409814	+	1.52945i	0.385187	+	0.922839i	$0.374137\pi$
$491$	−9.08087	+	33.8903i	−0.409814	+	1.52945i	−0.795001	+	0.606608i	$0.792530\pi$
$492$		0			0
$493$	3.75940	+	14.0303i	0.169315	+	0.631891i
$494$	−6.19624	+	3.28385i	−0.278782	+	0.147747i
$495$		0			0
$496$	9.40375	+	23.6428i	0.422241	+	1.06160i
$497$	17.3388	−	30.0317i	0.777752	−	1.34711i
$498$		0			0
$499$	−12.6475	−	3.38889i	−0.566181	−	0.151708i	−0.0356364	−	0.999365i	$-0.511346\pi$
$499$	−12.6475	−	3.38889i	−0.566181	−	0.151708i	−0.530544	+	0.847657i	$0.678012\pi$
$500$	−18.2003	+	15.7349i	−0.813940	+	0.703688i
$501$		0			0
$502$	15.5440	+	16.7142i	0.693762	+	0.745991i
$503$			2.93881i			0.131035i	0.997851	+	0.0655175i	$0.0208698\pi$
$503$			2.93881i			0.131035i	−0.997851	+	0.0655175i	$0.979130\pi$
$504$		0			0
$505$			4.99373i			0.222218i
$506$	2.32769	−	2.16472i	0.103478	−	0.0962337i
$507$		0			0
$508$	−3.36080	−	0.244154i	−0.149111	−	0.0108326i
$509$	15.3559	+	4.11461i	0.680640	+	0.182377i	0.582543	−	0.812800i	$-0.302058\pi$
$509$	15.3559	+	4.11461i	0.680640	+	0.182377i	0.0980972	+	0.995177i	$0.468724\pi$
$510$		0			0
$511$	17.1038	−	29.6246i	0.756627	−	1.31052i
$512$	−21.4332	−	7.25389i	−0.947222	−	0.320580i
$513$		0			0
$514$	−1.23228	−	2.32517i	−0.0543535	−	0.102559i
$515$	0.620083	+	2.31418i	0.0273241	+	0.101975i
$516$		0			0
$517$	11.4621	−	42.7772i	0.504103	−	1.88134i
$518$	−1.36436	−	5.94638i	−0.0599463	−	0.261269i
$519$		0			0
$520$	9.44551	−	12.8902i	0.414213	−	0.565274i
$521$		−	19.2119i		−	0.841689i	−0.907133	−	0.420844i	$-0.861734\pi$
$521$		−	19.2119i		−	0.841689i	0.907133	−	0.420844i	$-0.138266\pi$
$522$		0			0
$523$	−10.0495	−	10.0495i	−0.439436	−	0.439436i	0.452386	−	0.891822i	$-0.350573\pi$
$523$	−10.0495	−	10.0495i	−0.439436	−	0.439436i	−0.891822	+	0.452386i	$0.850573\pi$
$524$	14.4045	+	5.00354i	0.629265	+	0.218581i
$525$		0			0
$526$	−0.0574010	−	0.0359762i	−0.00250280	−	0.00156864i
$527$	6.81087	+	11.7968i	0.296686	+	0.513875i
$528$		0			0
$529$	−11.3902	+	19.7284i	−0.495225	+	0.857755i
$530$	−3.46296	+	1.83528i	−0.150422	+	0.0797196i
$531$		0			0
$532$	−12.0034	+	2.29952i	−0.520413	+	0.0996967i
$533$	9.56697	−	2.56346i	0.414392	−	0.111036i
$534$		0			0
$535$	11.9217	−	6.88297i	0.515418	−	0.297577i
$536$	26.8158	+	10.4188i	1.15827	+	0.450022i
$537$		0			0
$538$	−21.3358	+	19.8420i	−0.919852	+	0.855451i
$539$	35.7637	+	35.7637i	1.54045	+	1.54045i
$540$		0			0
$541$	15.3802	−	15.3802i	0.661246	−	0.661246i	−0.294428	−	0.955674i	$-0.595129\pi$
$541$	15.3802	−	15.3802i	0.661246	−	0.661246i	0.955674	+	0.294428i	$0.0951290\pi$
$542$	22.3026	+	0.809049i	0.957977	+	0.0347516i
$543$		0			0
$544$	−11.9151	−	2.18421i	−0.510857	−	0.0936472i
$545$	−2.41243	−	4.17844i	−0.103337	−	0.178985i
$546$		0			0
$547$	6.19933	+	23.1362i	0.265064	+	0.989233i	0.962211	+	0.272304i	$0.0877858\pi$
$547$	6.19933	+	23.1362i	0.265064	+	0.989233i	−0.697147	+	0.716928i	$0.745548\pi$
$548$	15.8009	+	10.7202i	0.674981	+	0.457944i
$549$		0			0
$550$	−14.5033	−	4.45558i	−0.618423	−	0.189986i
$551$	8.56961	+	4.94767i	0.365078	+	0.210778i
$552$		0			0
$553$	−26.3412	+	15.2081i	−1.12014	+	0.646714i
$554$	−10.2943	+	2.36195i	−0.437362	+	0.100350i
$555$		0			0
$556$	9.49015	−	27.3209i	0.402472	−	1.15866i
$557$	−0.932077	+	0.932077i	−0.0394934	+	0.0394934i	−0.726578	−	0.687084i	$-0.758890\pi$
$557$	−0.932077	+	0.932077i	−0.0394934	+	0.0394934i	0.687084	+	0.726578i	$0.258890\pi$
$558$		0			0
$559$	37.4027			1.58197
$560$	22.3331	−	16.6404i	0.943747	−	0.703185i
$561$		0			0
$562$	8.08680	+	5.06843i	0.341121	+	0.213799i
$563$	−6.39635	−	1.71390i	−0.269574	−	0.0722321i	0.121500	−	0.992591i	$-0.461230\pi$
$563$	−6.39635	−	1.71390i	−0.269574	−	0.0722321i	−0.391074	+	0.920359i	$0.627896\pi$
$564$		0			0
$565$	−13.2533	+	3.55121i	−0.557570	+	0.149400i
$566$	5.34926	−	17.4123i	0.224846	−	0.731893i
$567$		0			0
$568$	2.54213	−	23.2771i	0.106665	−	0.976685i
$569$	7.84553	+	4.52962i	0.328902	+	0.189892i	0.655353	−	0.755322i	$-0.272520\pi$
$569$	7.84553	+	4.52962i	0.328902	+	0.189892i	−0.326452	+	0.945214i	$0.605853\pi$
$570$		0			0
$571$	4.79838	−	17.9078i	0.200806	−	0.749417i	−0.789881	−	0.613260i	$-0.789858\pi$
$571$	4.79838	−	17.9078i	0.200806	−	0.749417i	0.990687	−	0.136158i	$-0.0434754\pi$
$572$	32.5168	+	2.36227i	1.35959	+	0.0987714i
$573$		0			0
$574$	17.2502	+	0.625769i	0.720009	+	0.0261191i
$575$	−1.04844			−0.0437230
$576$		0			0
$577$	43.3455			1.80450			0.902248	−	0.431217i	$-0.141916\pi$
$577$	43.3455			1.80450			0.902248	+	0.431217i	$0.141916\pi$
$578$	17.5450	+	0.636463i	0.729775	+	0.0264734i
$579$		0			0
$580$	−22.4903	−	1.63387i	−0.933860	−	0.0678428i
$581$	−8.52060	+	31.7993i	−0.353494	+	1.31926i
$582$		0			0
$583$	−6.92456	−	3.99790i	−0.286786	−	0.165576i
$584$	2.50767	−	22.9616i	0.103768	−	0.950156i
$585$		0			0
$586$	−5.96717	+	19.4236i	−0.246501	+	0.802383i
$587$	−25.4359	+	6.81553i	−1.04985	+	0.281307i	−0.742191	−	0.670189i	$-0.766213\pi$
$587$	−25.4359	+	6.81553i	−1.04985	+	0.281307i	−0.307662	+	0.951496i	$0.599547\pi$
$588$		0			0
$589$	8.96364	+	2.40180i	0.369341	+	0.0989645i
$590$	3.05574	+	1.91520i	0.125803	+	0.0788474i
$591$		0			0
$592$	−2.46135	−	3.30338i	−0.101161	−	0.135768i
$593$	−41.9274			−1.72175			−0.860876	−	0.508814i	$-0.830084\pi$
$593$	−41.9274			−1.72175			−0.860876	+	0.508814i	$0.830084\pi$
$594$		0			0
$595$	10.5430	−	10.5430i	0.432222	−	0.432222i
$596$	−1.12950	+	3.25168i	−0.0462661	+	0.133194i
$597$		0			0
$598$	2.19585	−	0.503823i	0.0897950	−	0.0206028i
$599$	−21.1742	+	12.2249i	−0.865154	+	0.499497i	−0.865735	−	0.500503i	$-0.833148\pi$
$599$	−21.1742	+	12.2249i	−0.865154	+	0.499497i	0.000580933		1.00000i	$0.499815\pi$
$600$		0			0
$601$	−24.7521	−	14.2906i	−1.00966	−	0.582928i	−0.0985682	−	0.995130i	$-0.531426\pi$
$601$	−24.7521	−	14.2906i	−1.00966	−	0.582928i	−0.911092	+	0.412203i	$0.864760\pi$
$602$	62.3115	+	19.1428i	2.53963	+	0.780202i
$603$		0			0
$604$	−35.3686	−	23.9960i	−1.43913	−	0.976383i
$605$	5.16255	+	19.2669i	0.209887	+	0.783310i
$606$		0			0
$607$	−9.32245	−	16.1470i	−0.378387	−	0.655385i	0.612441	−	0.790516i	$-0.290188\pi$
$607$	−9.32245	−	16.1470i	−0.378387	−	0.655385i	−0.990828	+	0.135131i	$0.956854\pi$
$608$	−6.79192	+	4.68757i	−0.275449	+	0.190106i
$609$		0			0
$610$	−18.3188	−	0.664535i	−0.741708	−	0.0269062i
$611$	22.1946	−	22.1946i	0.897896	−	0.897896i
$612$		0			0
$613$	−13.3177	−	13.3177i	−0.537896	−	0.537896i	0.385014	−	0.922911i	$-0.374196\pi$
$613$	−13.3177	−	13.3177i	−0.537896	−	0.537896i	−0.922911	+	0.385014i	$0.874196\pi$
$614$	−17.9252	+	16.6702i	−0.723404	+	0.672757i
$615$		0			0
$616$	52.9627	+	20.5776i	2.13393	+	0.829096i
$617$	−15.1035	+	8.72003i	−0.608045	+	0.351055i	−0.772200	−	0.635379i	$-0.780844\pi$
$617$	−15.1035	+	8.72003i	−0.608045	+	0.351055i	0.164155	+	0.986435i	$0.447510\pi$
$618$		0			0
$619$	−21.8310	+	5.84959i	−0.877461	+	0.235115i	−0.669311	−	0.742982i	$-0.733411\pi$
$619$	−21.8310	+	5.84959i	−0.877461	+	0.235115i	−0.208150	+	0.978097i	$0.566744\pi$
$620$	−20.7693	+	3.97883i	−0.834117	+	0.159794i
$621$		0			0
$622$	1.07174	−	0.567995i	0.0429729	−	0.0227745i
$623$	−23.4506	+	40.6177i	−0.939530	+	1.62731i
$624$		0			0
$625$	−4.40527	−	7.63015i	−0.176211	−	0.305206i
$626$	−21.9984	−	13.7876i	−0.879232	−	0.551061i
$627$		0			0
$628$	−20.0409	−	6.96139i	−0.799720	−	0.277790i
$629$	−1.55946	−	1.55946i	−0.0621797	−	0.0621797i
$630$		0			0
$631$		−	19.8510i		−	0.790254i	−0.918627	−	0.395127i	$-0.870701\pi$
$631$		−	19.8510i		−	0.790254i	0.918627	−	0.395127i	$-0.129299\pi$
$632$	−12.1393	+	16.5665i	−0.482877	+	0.658979i
$633$		0			0
$634$	1.31833	+	5.74578i	0.0523575	+	0.228194i
$635$	0.724836	−	2.70512i	0.0287642	−	0.107350i
$636$		0			0
$637$	9.27785	+	34.6254i	0.367602	+	1.37191i
$638$	−21.5428	−	40.6487i	−0.852886	−	1.60930i
$639$		0			0
$640$	9.27269	−	16.3608i	0.366535	−	0.646719i
$641$	−20.5842	+	35.6529i	−0.813026	+	1.40820i	0.0977099	+	0.995215i	$0.468848\pi$
$641$	−20.5842	+	35.6529i	−0.813026	+	1.40820i	−0.910736	+	0.412988i	$0.864485\pi$
$642$		0			0
$643$	−25.1215	−	6.73128i	−0.990694	−	0.265456i	−0.273152	−	0.961971i	$-0.588066\pi$
$643$	−25.1215	−	6.73128i	−0.990694	−	0.265456i	−0.717542	+	0.696515i	$0.754733\pi$
$644$	3.91606	+	0.284493i	0.154314	+	0.0112106i
$645$		0			0
$646$	−3.23520	+	3.00869i	−0.127287	+	0.118375i
$647$		−	40.3426i		−	1.58603i	−0.609201	−	0.793016i	$-0.708510\pi$
$647$		−	40.3426i		−	1.58603i	0.609201	−	0.793016i	$-0.291490\pi$
$648$		0			0
$649$			7.35741i			0.288803i
$650$	−7.32312	−	7.87443i	−0.287236	−	0.308860i
$651$		0			0
$652$	−7.43789	+	6.43039i	−0.291290	+	0.251834i
$653$	6.29024	+	1.68547i	0.246156	+	0.0659574i	0.379787	−	0.925074i	$-0.375997\pi$
$653$	6.29024	+	1.68547i	0.246156	+	0.0659574i	−0.133631	+	0.991031i	$0.542664\pi$
$654$		0			0
$655$	−6.33671	+	10.9755i	−0.247596	+	0.428849i
$656$	10.8303	−	4.30768i	0.422854	−	0.168187i
$657$		0			0
$658$	48.3345	−	25.6161i	1.88428	−	0.998618i
$659$	0.0237696	+	0.0887093i	0.000925932	+	0.00345562i	0.966387	−	0.257091i	$-0.0827640\pi$
$659$	0.0237696	+	0.0887093i	0.000925932	+	0.00345562i	−0.965461	+	0.260546i	$0.916097\pi$
$660$		0			0
$661$	−7.23883	+	27.0157i	−0.281558	+	1.05079i	0.669760	+	0.742578i	$0.266397\pi$
$661$	−7.23883	+	27.0157i	−0.281558	+	1.05079i	−0.951318	+	0.308211i	$0.900270\pi$
$662$	7.12231	−	1.63416i	0.276816	−	0.0635136i
$663$		0			0
$664$	3.38826	+	21.9697i	0.131490	+	0.852589i
$665$		−	10.1575i		−	0.393892i
$666$		0			0
$667$	−2.24790	−	2.24790i	−0.0870392	−	0.0870392i
$668$	0.576639	−	0.279316i	0.0223108	−	0.0108070i
$669$		0			0
$670$	−12.6978	+	20.2596i	−0.490558	+	0.782697i
$671$	−18.6988	−	32.3873i	−0.721859	−	1.25030i
$672$		0			0
$673$	2.48158	−	4.29822i	0.0956578	−	0.165684i	−0.814225	−	0.580549i	$-0.802838\pi$
$673$	2.48158	−	4.29822i	0.0956578	−	0.165684i	0.909883	+	0.414865i	$0.136171\pi$
$674$	−2.57959	−	4.86739i	−0.0993622	−	0.187485i
$675$		0			0
$676$	−2.39400	−	1.62422i	−0.0920769	−	0.0624700i
$677$	6.63841	−	1.77876i	0.255135	−	0.0683632i	−0.128985	−	0.991647i	$-0.541172\pi$
$677$	6.63841	−	1.77876i	0.255135	−	0.0683632i	0.384119	+	0.923283i	$0.374505\pi$
$678$		0			0
$679$	41.1923	−	23.7824i	1.58081	−	0.912683i
$680$	3.64611	−	9.38436i	0.139822	−	0.359874i
$681$		0			0
$682$	−29.3807	−	31.5926i	−1.12504	−	1.20974i
$683$	−20.7192	−	20.7192i	−0.792797	−	0.792797i	0.189151	−	0.981948i	$-0.439426\pi$
$683$	−20.7192	−	20.7192i	−0.792797	−	0.792797i	−0.981948	+	0.189151i	$0.939426\pi$
$684$		0			0
$685$	−11.2214	+	11.2214i	−0.428747	+	0.428747i
$686$	−0.761549	+	20.9932i	−0.0290761	+	0.801522i
$687$		0			0
$688$	43.7159	−	5.12753i	1.66665	−	0.195485i
$689$	−2.83351	−	4.90779i	−0.107948	−	0.186972i
$690$		0			0
$691$	1.42402	+	5.31450i	0.0541721	+	0.202173i	0.987708	−	0.156311i	$-0.0499603\pi$
$691$	1.42402	+	5.31450i	0.0541721	+	0.202173i	−0.933536	+	0.358484i	$0.883294\pi$
$692$	4.55420	+	23.7727i	0.173125	+	0.903704i
$693$		0			0
$694$	1.31056	−	4.26598i	0.0497481	−	0.161934i
$695$	20.8171	+	12.0188i	0.789638	+	0.455898i
$696$		0			0
$697$	5.40388	−	3.11993i	0.204687	−	0.118176i
$698$	0.458038	+	1.99631i	0.0173370	+	0.0755613i
$699$		0			0
$700$	−8.16989	−	16.8665i	−0.308793	−	0.637493i
$701$	1.06232	−	1.06232i	0.0401233	−	0.0401233i	−0.686760	−	0.726884i	$-0.740968\pi$
$701$	1.06232	−	1.06232i	0.0401233	−	0.0401233i	0.726884	+	0.686760i	$0.240968\pi$
$702$		0			0
$703$	−1.50244			−0.0566656
$704$	38.3291	−	1.69673i	1.44458	−	0.0639478i
$705$		0			0
$706$	11.6245	−	18.5472i	0.437494	−	0.698033i
$707$	−12.1555	−	3.25705i	−0.457153	−	0.122494i
$708$		0			0
$709$	35.4604	−	9.50159i	1.33174	−	0.356840i	0.478379	−	0.878153i	$-0.341224\pi$
$709$	35.4604	−	9.50159i	1.33174	−	0.356840i	0.853365	+	0.521314i	$0.174558\pi$
$710$	18.6028	+	5.71498i	0.698149	+	0.214479i
$711$		0			0
$712$	−3.43821	+	31.4821i	−0.128853	+	1.17984i
$713$	−2.58187	−	1.49064i	−0.0966916	−	0.0558249i
$714$		0			0
$715$	−7.01301	+	26.1729i	−0.262272	+	0.978812i
$716$	−39.9646	+	34.5512i	−1.49355	+	1.29124i
$717$		0			0
$718$	−0.245460	+	6.76644i	−0.00916048	+	0.252521i
$719$	7.37513			0.275046			0.137523	−	0.990499i	$-0.456086\pi$
$719$	7.37513			0.275046			0.137523	+	0.990499i	$0.456086\pi$
$720$		0			0
$721$	−6.03749			−0.224848
$722$	0.864988	−	23.8446i	0.0321915	−	0.887404i
$723$		0			0
$724$	7.59406	+	8.78388i	0.282231	+	0.326450i
$725$	−3.92726	+	14.6567i	−0.145855	+	0.544337i
$726$		0			0
$727$	−5.80127	−	3.34936i	−0.215157	−	0.124221i	0.388549	−	0.921428i	$-0.372977\pi$
$727$	−5.80127	−	3.34936i	−0.215157	−	0.124221i	−0.603706	+	0.797207i	$0.706310\pi$
$728$	25.2161	+	31.3991i	0.934571	+	1.16373i
$729$		0			0
$730$	18.3506	+	5.63751i	0.679186	+	0.208654i
$731$	22.7610	−	6.09879i	0.841846	−	0.225572i
$732$		0			0
$733$	34.6439	+	9.28281i	1.27960	+	0.342868i	0.833702	−	0.552214i	$-0.186217\pi$
$733$	34.6439	+	9.28281i	1.27960	+	0.342868i	0.445900	+	0.895083i	$0.352884\pi$
$734$	14.9278	−	23.8177i	0.550996	−	0.879127i
$735$		0			0
$736$	2.49742	−	0.889891i	0.0920560	−	0.0328018i
$737$	−48.7797			−1.79682
$738$		0			0
$739$	4.01107	−	4.01107i	0.147549	−	0.147549i	−0.629473	−	0.777022i	$-0.716729\pi$
$739$	4.01107	−	4.01107i	0.147549	−	0.147549i	0.777022	+	0.629473i	$0.216729\pi$
$740$	3.08132	−	1.49255i	0.113272	−	0.0548672i
$741$		0			0
$742$	−2.20871	−	9.62638i	−0.0810841	−	0.353396i
$743$	19.1551	−	11.0592i	0.702734	−	0.405724i	−0.105631	−	0.994405i	$-0.533686\pi$
$743$	19.1551	−	11.0592i	0.702734	−	0.405724i	0.808365	+	0.588682i	$0.200353\pi$
$744$		0			0
$745$	−2.47761	−	1.43045i	−0.0907726	−	0.0524076i
$746$	−0.183846	+	0.598434i	−0.00673107	+	0.0219102i
$747$		0			0
$748$	20.1729	−	3.86457i	0.737594	−	0.141303i
$749$	8.97853	+	33.5083i	0.328068	+	1.22437i
$750$		0			0
$751$	−6.05672	−	10.4905i	−0.221013	−	0.382805i	0.734103	−	0.679038i	$-0.237603\pi$
$751$	−6.05672	−	10.4905i	−0.221013	−	0.382805i	−0.955116	+	0.296233i	$0.904270\pi$
$752$	22.8981	−	28.9834i	0.835008	−	1.05692i
$753$		0			0
$754$	1.18203	−	32.5842i	0.0430469	−	1.18665i
$755$	25.1178	−	25.1178i	0.914131	−	0.914131i
$756$		0			0
$757$	−19.9365	−	19.9365i	−0.724604	−	0.724604i	0.244935	−	0.969539i	$-0.421233\pi$
$757$	−19.9365	−	19.9365i	−0.724604	−	0.724604i	−0.969539	+	0.244935i	$0.921233\pi$
$758$	8.41906	+	9.05287i	0.305794	+	0.328815i
$759$		0			0
$760$	−2.76422	−	6.27702i	−0.100269	−	0.227691i
$761$	−37.1681	+	21.4590i	−1.34734	+	0.777889i	−0.987873	−	0.155267i	$-0.950376\pi$
$761$	−37.1681	+	21.4590i	−1.34734	+	0.777889i	−0.359471	+	0.933156i	$0.617043\pi$
$762$		0			0
$763$	11.7444	−	3.14690i	0.425176	−	0.113925i
$764$	−19.3156	+	28.4700i	−0.698814	+	1.03001i
$765$		0			0
$766$	8.56555	+	16.1622i	0.309486	+	0.583964i
$767$	−2.60728	+	4.51595i	−0.0941435	+	0.163061i
$768$		0			0
$769$	−13.7618	−	23.8361i	−0.496263	−	0.859553i	0.503728	−	0.863863i	$-0.331962\pi$
$769$	−13.7618	−	23.8361i	−0.496263	−	0.859553i	−0.999991	+	0.00430961i	$0.998628\pi$
$770$	−25.0788	+	40.0138i	−0.903777	+	1.44200i
$771$		0			0
$772$	15.9982	+	33.0277i	0.575786	+	1.18869i
$773$	11.4688	+	11.4688i	0.412504	+	0.412504i	0.882610	−	0.470106i	$-0.155784\pi$
$773$	11.4688	+	11.4688i	0.412504	+	0.412504i	−0.470106	+	0.882610i	$0.655784\pi$
$774$		0			0
$775$			14.2300i			0.511155i
$776$	18.9834	−	25.9066i	0.681465	−	0.929992i
$777$		0			0
$778$	−37.7112	+	8.65257i	−1.35201	+	0.310210i
$779$	1.10022	−	4.10608i	0.0394195	−	0.147115i
$780$		0			0
$781$	10.2759	+	38.3500i	0.367699	+	1.37227i
$782$	1.25411	−	0.664645i	0.0448468	−	0.0237677i
$783$		0			0
$784$	15.5906	+	39.1979i	0.556808	+	1.39992i
$785$	8.81622	−	15.2701i	0.314664	−	0.545015i
$786$		0			0
$787$	−42.8263	−	11.4753i	−1.52659	−	0.409049i	−0.604687	−	0.796463i	$-0.706702\pi$
$787$	−42.8263	−	11.4753i	−1.52659	−	0.409049i	−0.921906	+	0.387414i	$0.873368\pi$
$788$	−16.2865	−	18.8382i	−0.580181	−	0.671083i
$789$		0			0
$790$	−11.6244	−	12.4995i	−0.413576	−	0.444712i
$791$		−	34.5766i		−	1.22940i
$792$		0			0
$793$		−	26.5056i		−	0.941241i
$794$	−32.1822	+	29.9290i	−1.14210	+	1.06214i
$795$		0			0
$796$	−1.45315	+	20.0027i	−0.0515057	+	0.708978i
$797$	28.6863	+	7.68647i	1.01612	+	0.272269i	0.728185	−	0.685381i	$-0.240364\pi$
$797$	28.6863	+	7.68647i	1.01612	+	0.272269i	0.287936	+	0.957650i	$0.407031\pi$
$798$		0			0
$799$	9.88726	−	17.1252i	0.349786	−	0.605847i
$800$	−9.63868	−	8.19961i	−0.340779	−	0.289900i
$801$		0			0
$802$	17.8766	+	33.7310i	0.631244	+	1.19108i
$803$	10.1366	+	37.8302i	0.357712	+	1.33500i
$804$		0			0
$805$	−0.844592	+	3.15206i	−0.0297679	+	0.111096i
$806$	−6.83813	−	29.8032i	−0.240863	−	1.04977i
$807$		0			0
$808$	−8.39803	+	1.29518i	−0.295442	+	0.0455643i
$809$			16.7474i			0.588806i	0.955681	+	0.294403i	$0.0951209\pi$
$809$			16.7474i			0.588806i	−0.955681	+	0.294403i	$0.904879\pi$
$810$		0			0
$811$	−7.60619	−	7.60619i	−0.267090	−	0.267090i	0.560837	−	0.827926i	$-0.310480\pi$
$811$	−7.60619	−	7.60619i	−0.267090	−	0.267090i	−0.827926	+	0.560837i	$0.810480\pi$
$812$	18.6459	−	53.6791i	0.654343	−	1.88377i
$813$		0			0
$814$	5.91860	+	3.70950i	0.207447	+	0.130018i
$815$	−4.08582	−	7.07684i	−0.143120	−	0.247891i
$816$		0			0
$817$	8.02649	−	13.9023i	0.280811	−	0.486379i
$818$	16.0934	−	8.52912i	0.562694	−	0.298214i
$819$		0			0
$820$	1.82263	+	9.51404i	0.0636489	+	0.332245i
$821$	−37.2860	+	9.99074i	−1.30129	+	0.348679i	−0.841937	−	0.539575i	$-0.818585\pi$
$821$	−37.2860	+	9.99074i	−1.30129	+	0.348679i	−0.459351	+	0.888255i	$0.651918\pi$
$822$		0			0
$823$	23.9783	−	13.8439i	0.835831	−	0.482567i	−0.0200141	−	0.999800i	$-0.506371\pi$
$823$	23.9783	−	13.8439i	0.835831	−	0.482567i	0.855845	+	0.517233i	$0.173038\pi$
$824$	−3.73097	+	1.64301i	−0.129975	+	0.0572371i
$825$		0			0
$826$	−6.65491	+	6.18898i	−0.231554	+	0.215342i
$827$	27.6025	+	27.6025i	0.959833	+	0.959833i	0.999224	−	0.0393907i	$-0.0125417\pi$
$827$	27.6025	+	27.6025i	0.959833	+	0.959833i	−0.0393907	+	0.999224i	$0.512542\pi$
$828$		0			0
$829$	14.8542	−	14.8542i	0.515908	−	0.515908i	−0.400423	−	0.916330i	$-0.631137\pi$
$829$	14.8542	−	14.8542i	0.515908	−	0.515908i	0.916330	+	0.400423i	$0.131137\pi$
$830$	−18.4629	−	0.669762i	−0.640858	−	0.0232478i
$831$		0			0
$832$	24.1275	+	12.5414i	0.836471	+	0.434796i
$833$	11.2919	+	19.5581i	0.391240	+	0.677647i
$834$		0			0
$835$	0.137824	+	0.514368i	0.00476961	+	0.0178004i
$836$	7.85602	−	11.5793i	0.271706	−	0.400478i
$837$		0			0
$838$	0.284716	+	0.0874679i	0.00983534	+	0.00302153i
$839$	−44.0413	−	25.4272i	−1.52047	−	0.877846i	−0.999708	−	0.0241463i	$-0.992313\pi$
$839$	−44.0413	−	25.4272i	−1.52047	−	0.877846i	−0.520766	−	0.853700i	$-0.674353\pi$
$840$		0			0
$841$	−14.7301	+	8.50445i	−0.507936	+	0.293257i
$842$	48.8471	−	11.2076i	1.68338	−	0.386240i
$843$		0			0
$844$	37.5693	+	13.0500i	1.29319	+	0.449200i
$845$	1.70015	−	1.70015i	0.0584871	−	0.0584871i
$846$		0			0
$847$	−50.2656			−1.72715
$848$	−3.98458	−	5.34772i	−0.136831	−	0.183641i
$849$		0			0
$850$	−5.74038	−	3.59780i	−0.196894	−	0.123404i
$851$	0.466233	+	0.124927i	0.0159823	+	0.00428244i
$852$		0			0
$853$	−13.6365	+	3.65390i	−0.466906	+	0.125107i	−0.484599	−	0.874736i	$-0.661034\pi$
$853$	−13.6365	+	3.65390i	−0.466906	+	0.125107i	0.0176931	+	0.999843i	$0.494368\pi$
$854$	13.5656	−	44.1573i	0.464206	−	1.51103i
$855$		0			0
$856$	14.6672	+	18.2637i	0.501315	+	0.624239i
$857$	14.7618	+	8.52275i	0.504255	+	0.291132i	0.730469	−	0.682946i	$-0.239302\pi$
$857$	14.7618	+	8.52275i	0.504255	+	0.291132i	−0.226214	+	0.974078i	$0.572635\pi$
$858$		0			0
$859$	−6.67877	+	24.9255i	−0.227877	+	0.850448i	0.753355	+	0.657614i	$0.228434\pi$
$859$	−6.67877	+	24.9255i	−0.227877	+	0.850448i	−0.981232	+	0.192833i	$0.938232\pi$
$860$	−2.65059	+	36.4856i	−0.0903845	+	1.24415i
$861$		0			0
$862$	47.3929	+	1.71923i	1.61421	+	0.0585571i
$863$	18.8217			0.640698			0.320349	−	0.947300i	$-0.396200\pi$
$863$	18.8217			0.640698			0.320349	+	0.947300i	$0.396200\pi$
$864$		0			0
$865$	−20.1170			−0.683999
$866$	40.9415	+	1.48520i	1.39125	+	0.0504691i
$867$		0			0
$868$	3.86128	−	53.1507i	0.131060	−	1.80405i
$869$	9.01309	−	33.6373i	0.305748	−	1.14107i
$870$		0			0
$871$	−29.9408	−	17.2863i	−1.01450	−	0.585725i
$872$	6.40126	−	5.14074i	0.216774	−	0.174088i
$873$		0			0
$874$	0.283955	−	0.924299i	0.00960492	−	0.0312649i
$875$	48.6724	−	13.0417i	1.64543	−	0.440891i
$876$		0			0
$877$	−10.4503	−	2.80014i	−0.352880	−	0.0945540i	0.0780244	−	0.996951i	$-0.475139\pi$
$877$	−10.4503	−	2.80014i	−0.352880	−	0.0945540i	−0.430905	+	0.902397i	$0.641805\pi$
$878$	−20.2925	−	12.7184i	−0.684840	−	0.429225i
$879$		0			0
$880$	−4.60869	+	31.5520i	−0.155359	+	1.06362i
$881$	−40.1658			−1.35322			−0.676610	−	0.736342i	$-0.736552\pi$
$881$	−40.1658			−1.35322			−0.676610	+	0.736342i	$0.736552\pi$
$882$		0			0
$883$	−16.5617	+	16.5617i	−0.557346	+	0.557346i	−0.928551	−	0.371205i	$-0.878945\pi$
$883$	−16.5617	+	16.5617i	−0.557346	+	0.557346i	0.371205	+	0.928551i	$0.378945\pi$
$884$	13.7516	+	4.77672i	0.462515	+	0.160658i
$885$		0			0
$886$	−4.40252	+	1.01013i	−0.147906	+	0.0339359i
$887$	−13.1259	+	7.57822i	−0.440723	+	0.254452i	−0.703904	−	0.710295i	$-0.748562\pi$
$887$	−13.1259	+	7.57822i	−0.440723	+	0.254452i	0.263181	+	0.964746i	$0.415228\pi$
$888$		0			0
$889$	6.11191	+	3.52871i	0.204987	+	0.118349i
$890$	−25.1601	−	7.72948i	−0.843370	−	0.259093i
$891$		0			0
$892$	−15.6435	+	23.0576i	−0.523784	+	0.772026i
$893$	−3.48667	−	13.0124i	−0.116677	−	0.435444i
$894$		0			0
$895$	−21.9535	−	38.0246i	−0.733826	−	1.27102i
$896$	33.7768	+	33.2421i	1.12840	+	1.11054i
$897$		0			0
$898$	−59.2437	−	2.14913i	−1.97699	−	0.0717174i
$899$	−30.5097	+	30.5097i	−1.01755	+	1.01755i
$900$		0			0
$901$	−2.52455	−	2.52455i	−0.0841050	−	0.0841050i
$902$	−14.4720	+	13.4587i	−0.481863	+	0.448127i
$903$		0			0
$904$	−9.40951	−	21.3672i	−0.312956	−	0.710663i
$905$	−8.35749	+	4.82520i	−0.277812	+	0.160395i
$906$		0			0
$907$	9.75684	−	2.61434i	0.323971	−	0.0868077i	−0.0931683	−	0.995650i	$-0.529699\pi$
$907$	9.75684	−	2.61434i	0.323971	−	0.0868077i	0.417139	+	0.908843i	$0.363033\pi$
$908$	−2.85206	−	14.8876i	−0.0946489	−	0.494063i
$909$		0			0
$910$	−29.5732	+	15.6730i	−0.980341	+	0.519556i
$911$	25.2358	−	43.7097i	0.836099	−	1.44817i	−0.0570332	−	0.998372i	$-0.518164\pi$
$911$	25.2358	−	43.7097i	0.836099	−	1.44817i	0.893132	−	0.449794i	$-0.148503\pi$
$912$		0			0
$913$	−18.8459	−	32.6420i	−0.623708	−	1.08029i
$914$	6.83512	+	4.28393i	0.226086	+	0.141700i
$915$		0			0
$916$	12.5443	−	36.1135i	0.414476	−	1.19322i
$917$	−22.5830	−	22.5830i	−0.745757	−	0.745757i
$918$		0			0
$919$			16.7422i			0.552274i	0.961118	+	0.276137i	$0.0890544\pi$
$919$			16.7422i			0.552274i	−0.961118	+	0.276137i	$0.910946\pi$
$920$	0.335856	+	2.17771i	0.0110729	+	0.0717970i
$921$		0			0
$922$	12.5512	+	54.7031i	0.413353	+	1.80155i
$923$	−7.28302	+	27.1806i	−0.239724	+	0.894661i
$924$		0			0
$925$	−0.596288	−	2.22538i	−0.0196058	−	0.0731699i
$926$	8.32164	+	15.7020i	0.273466	+	0.515999i
$927$		0			0
$928$	−3.08543	−	38.2461i	−0.101284	−	1.25549i
$929$	−9.92665	+	17.1935i	−0.325683	+	0.564099i	−0.981650	−	0.190690i	$-0.938927\pi$
$929$	−9.92665	+	17.1935i	−0.325683	+	0.564099i	0.655967	+	0.754789i	$0.272261\pi$
$930$		0			0
$931$	14.8610	+	3.98199i	0.487049	+	0.130504i
$932$	1.55994	−	21.4727i	0.0510977	−	0.703363i
$933$		0			0
$934$	17.8359	−	16.5872i	0.583609	−	0.542749i
$935$			17.0708i			0.558273i
$936$		0			0
$937$			3.05876i			0.0999253i	0.998751	+	0.0499626i	$0.0159102\pi$
$937$			3.05876i			0.0999253i	−0.998751	+	0.0499626i	$0.984090\pi$
$938$	−41.0330	−	44.1221i	−1.33978	−	1.44064i
$939$		0			0
$940$	20.0775	+	23.2232i	0.654855	+	0.757457i
$941$	11.4732	+	3.07424i	0.374016	+	0.100217i	0.440930	−	0.897541i	$-0.354649\pi$
$941$	11.4732	+	3.07424i	0.374016	+	0.100217i	−0.0669140	+	0.997759i	$0.521315\pi$
$942$		0			0
$943$	−0.682835	+	1.18270i	−0.0222362	+	0.0385141i
$944$	−2.42827	+	5.63562i	−0.0790335	+	0.183424i
$945$		0			0
$946$	−65.9434	+	34.9483i	−2.14401	+	1.13627i
$947$	−14.9176	−	55.6732i	−0.484757	−	1.80914i	−0.581153	−	0.813794i	$-0.697398\pi$
$947$	−14.9176	−	55.6732i	−0.484757	−	1.80914i	0.0963965	−	0.995343i	$-0.469268\pi$
$948$		0			0
$949$	−7.18430	+	26.8122i	−0.233212	+	0.870360i
$950$	−4.49838	+	1.03212i	−0.145947	+	0.0334864i
$951$		0			0
$952$	20.4648	+	14.9959i	0.663269	+	0.486020i
$953$			44.2546i			1.43355i	0.697306	+	0.716774i	$0.254382\pi$
$953$			44.2546i			1.43355i	−0.697306	+	0.716774i	$0.745618\pi$
$954$		0			0
$955$	−20.2186	−	20.2186i	−0.654259	−	0.654259i
$956$	19.4304	+	40.1134i	0.628423	+	1.29736i
$957$		0			0
$958$	−16.0519	+	25.6112i	−0.518613	+	0.827460i
$959$	−19.9956	−	34.6334i	−0.645691	−	1.11837i
$960$		0			0
$961$	−4.73171	+	8.19557i	−0.152636	+	0.264373i
$962$	2.31826	+	4.37428i	0.0747436	+	0.141032i
$963$		0			0
$964$	30.8307	−	45.4425i	0.992990	−	1.46361i
$965$	−29.4611	+	7.89407i	−0.948386	+	0.254119i
$966$		0			0
$967$	−36.7930	+	21.2424i	−1.18318	+	0.683110i	−0.956748	−	0.290916i	$-0.906040\pi$
$967$	−36.7930	+	21.2424i	−1.18318	+	0.683110i	−0.226433	+	0.974027i	$0.572706\pi$
$968$	−31.0625	+	13.6790i	−0.998385	+	0.439661i
$969$		0			0
$970$	18.1781	+	19.5466i	0.583664	+	0.627604i
$971$	−11.1469	−	11.1469i	−0.357720	−	0.357720i	0.505252	−	0.862972i	$-0.331400\pi$
$971$	−11.1469	−	11.1469i	−0.357720	−	0.357720i	−0.862972	+	0.505252i	$0.831400\pi$
$972$		0			0
$973$	−42.8329	+	42.8329i	−1.37316	+	1.37316i
$974$	2.01852	−	55.6432i	0.0646775	−	1.78292i
$975$		0			0
$976$	−3.63365	−	30.9794i	−0.116310	−	0.991627i
$977$	2.47430	+	4.28561i	0.0791598	+	0.137109i	0.902888	−	0.429877i	$-0.141443\pi$
$977$	2.47430	+	4.28561i	0.0791598	+	0.137109i	−0.823728	+	0.566985i	$0.808110\pi$
$978$		0			0
$979$	−13.8980	−	51.8682i	−0.444183	−	1.65771i
$980$	−34.4338	+	6.59657i	−1.09995	+	0.210720i
$981$		0			0
$982$	14.5714	−	47.4310i	0.464991	−	1.51359i
$983$	41.6831	+	24.0658i	1.32948	+	0.767578i	0.985220	−	0.171294i	$-0.0547948\pi$
$983$	41.6831	+	24.0658i	1.32948	+	0.767578i	0.344265	+	0.938873i	$0.388128\pi$
$984$		0			0
$985$	17.9237	−	10.3483i	0.571098	−	0.329724i
$986$	−4.59379	−	20.0215i	−0.146296	−	0.637614i
$987$		0			0
$988$	8.92541	−	4.32334i	0.283955	−	0.137544i
$989$	−3.64672	+	3.64672i	−0.115959	+	0.115959i
$990$		0			0
$991$	−8.90020			−0.282724			−0.141362	−	0.989958i	$-0.545148\pi$
$991$	−8.90020			−0.282724			−0.141362	+	0.989958i	$0.545148\pi$
$992$	−12.0780	−	33.8962i	−0.383478	−	1.07620i
$993$		0			0
$994$	−26.0443	+	41.5544i	−0.826076	+	1.31803i
$995$	−16.1003	−	4.31407i	−0.510414	−	0.136765i
$996$		0			0
$997$	−24.8773	+	6.66586i	−0.787873	+	0.211110i	−0.630253	−	0.776390i	$-0.717049\pi$
$997$	−24.8773	+	6.66586i	−0.787873	+	0.211110i	−0.157620	+	0.987500i	$0.550382\pi$
$998$	17.7008	+	5.43789i	0.560309	+	0.172133i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.y.e.181.1		72
3.2	odd	2		144.2.x.e.133.18	yes	72
4.3	odd	2		1728.2.bc.e.1585.6		72
9.4	even	3	inner	432.2.y.e.37.12		72
9.5	odd	6		144.2.x.e.85.7	yes	72
12.11	even	2		576.2.bb.e.241.8		72
16.3	odd	4		1728.2.bc.e.721.13		72
16.13	even	4	inner	432.2.y.e.397.12		72
36.23	even	6		576.2.bb.e.49.16		72
36.31	odd	6		1728.2.bc.e.1009.13		72
48.29	odd	4		144.2.x.e.61.7	yes	72
48.35	even	4		576.2.bb.e.529.16		72
144.13	even	12	inner	432.2.y.e.253.1		72
144.67	odd	12		1728.2.bc.e.145.6		72
144.77	odd	12		144.2.x.e.13.18	✓	72
144.131	even	12		576.2.bb.e.337.8		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.18	✓	72	144.77	odd	12
144.2.x.e.61.7	yes	72	48.29	odd	4
144.2.x.e.85.7	yes	72	9.5	odd	6
144.2.x.e.133.18	yes	72	3.2	odd	2
432.2.y.e.37.12		72	9.4	even	3	inner
432.2.y.e.181.1		72	1.1	even	1	trivial
432.2.y.e.253.1		72	144.13	even	12	inner
432.2.y.e.397.12		72	16.13	even	4	inner
576.2.bb.e.49.16		72	36.23	even	6
576.2.bb.e.241.8		72	12.11	even	2
576.2.bb.e.337.8		72	144.131	even	12
576.2.bb.e.529.16		72	48.35	even	4
1728.2.bc.e.145.6		72	144.67	odd	12
1728.2.bc.e.721.13		72	16.3	odd	4
1728.2.bc.e.1009.13		72	36.31	odd	6
1728.2.bc.e.1585.6		72	4.3	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-1.41328 - 0.0512684i) q^{2} +(1.99474 + 0.144914i) q^{4} +(-0.430214 + 1.60558i) q^{5} +(-3.62762 - 2.09441i) q^{7} +(-2.81171 - 0.307071i) q^{8} +O(q^{10})\)	\(q+(-1.41328 - 0.0512684i) q^{2} +(1.99474 + 0.144914i) q^{4} +(-0.430214 + 1.60558i) q^{5} +(-3.62762 - 2.09441i) q^{7} +(-2.81171 - 0.307071i) q^{8} +(0.690330 - 2.24708i) q^{10} +(4.63241 - 1.24125i) q^{11} +(3.28323 + 0.879738i) q^{13} +(5.01948 + 3.14597i) q^{14} +(3.95800 + 0.578131i) q^{16} +2.14142 q^{17} +(1.03156 - 1.03156i) q^{19} +(-1.09084 + 3.14037i) q^{20} +(-6.61055 + 1.51674i) q^{22} +(-0.405884 + 0.234337i) q^{23} +(1.93733 + 1.11852i) q^{25} +(-4.59503 - 1.41164i) q^{26} +(-6.93266 - 4.70349i) q^{28} +(1.75557 + 6.55186i) q^{29} +(3.18054 + 5.50886i) q^{31} +(-5.56414 - 1.01998i) q^{32} +(-3.02643 - 0.109787i) q^{34} +(4.92339 - 4.92339i) q^{35} +(-0.728237 - 0.728237i) q^{37} +(-1.51077 + 1.40500i) q^{38} +(1.70266 - 4.38232i) q^{40} +(2.52351 - 1.45695i) q^{41} +(10.6289 - 2.84802i) q^{43} +(9.42035 - 1.80468i) q^{44} +(0.585644 - 0.310376i) q^{46} +(4.61716 - 7.99715i) q^{47} +(5.27308 + 9.13324i) q^{49} +(-2.68065 - 1.68010i) q^{50} +(6.42171 + 2.23063i) q^{52} +(-1.17892 - 1.17892i) q^{53} +7.97171i q^{55} +(9.55667 + 7.00280i) q^{56} +(-2.14521 - 9.34965i) q^{58} +(-0.397061 + 1.48185i) q^{59} +(-2.01826 - 7.53224i) q^{61} +(-4.21258 - 7.94865i) q^{62} +(7.81141 + 1.72679i) q^{64} +(-2.82498 + 4.89300i) q^{65} +(-9.82470 - 2.63252i) q^{67} +(4.27158 + 0.310320i) q^{68} +(-7.21056 + 6.70573i) q^{70} +8.27863i q^{71} +8.16641i q^{73} +(0.991870 + 1.06654i) q^{74} +(2.20718 - 1.90821i) q^{76} +(-19.4043 - 5.19937i) q^{77} +(3.63065 - 6.28847i) q^{79} +(-2.63102 + 6.10616i) q^{80} +(-3.64113 + 1.92970i) q^{82} +(-2.03413 - 7.59149i) q^{83} +(-0.921267 + 3.43821i) q^{85} +(-15.1677 + 3.48013i) q^{86} +(-13.4062 + 2.06756i) q^{88} -11.1968i q^{89} +(-10.0678 - 10.0678i) q^{91} +(-0.843594 + 0.408625i) q^{92} +(-6.93535 + 11.0655i) q^{94} +(1.21246 + 2.10004i) q^{95} +(-5.67759 + 9.83387i) q^{97} +(-6.98411 - 13.1782i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8}+O(q^{10}) \) 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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