LMFDB - Embedded newform 441.2.bb.f.100.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

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

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

chi := DirichletCharacter("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			100.2
Character	$\chi$	$=$	441.100
Dual form			441.2.bb.f.172.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.02995 - 0.626155i) q^{2} +(2.07613 + 1.41548i) q^{4} +(0.321603 - 0.0484738i) q^{5} +(2.57904 + 0.590375i) q^{7} +(-0.679131 - 0.851603i) q^{8} +O(q^{10})$	\(q+(-2.02995 - 0.626155i) q^{2} +(2.07613 + 1.41548i) q^{4} +(0.321603 - 0.0484738i) q^{5} +(2.57904 + 0.590375i) q^{7} +(-0.679131 - 0.851603i) q^{8} +(-0.683188 - 0.102974i) q^{10} +(-2.08594 + 1.93547i) q^{11} +(0.730204 + 3.19923i) q^{13} +(-4.86565 - 2.81331i) q^{14} +(-0.990657 - 2.52415i) q^{16} +(-0.182224 - 2.43161i) q^{17} +(-1.91818 + 3.32239i) q^{19} +(0.736303 + 0.354585i) q^{20} +(5.44624 - 2.62277i) q^{22} +(-0.259545 + 3.46339i) q^{23} +(-4.67679 + 1.44260i) q^{25} +(0.520942 - 6.95149i) q^{26} +(4.51876 + 4.87628i) q^{28} +(5.81416 + 2.79995i) q^{29} +(-0.0430144 - 0.0745032i) q^{31} +(0.593266 + 7.91659i) q^{32} +(-1.15266 + 5.05014i) q^{34} +(0.858045 + 0.0648502i) q^{35} +(2.28743 - 1.55954i) q^{37} +(5.97413 - 5.54319i) q^{38} +(-0.259691 - 0.240958i) q^{40} +(7.20887 + 9.03964i) q^{41} +(2.10877 - 2.64431i) q^{43} +(-7.07029 + 1.06567i) q^{44} +(2.69548 - 6.86798i) q^{46} +(-1.29973 - 0.400913i) q^{47} +(6.30291 + 3.04520i) q^{49} +10.3969 q^{50} +(-3.01246 + 7.67561i) q^{52} +(-0.722552 - 0.492628i) q^{53} +(-0.577023 + 0.723564i) q^{55} +(-1.24874 - 2.59726i) q^{56} +(-10.0492 - 9.32432i) q^{58} +(9.48687 + 1.42992i) q^{59} +(4.25839 - 2.90332i) q^{61} +(0.0406664 + 0.178171i) q^{62} +(2.54594 - 11.1545i) q^{64} +(0.389915 + 0.993486i) q^{65} +(4.12197 + 7.13946i) q^{67} +(3.06358 - 5.30628i) q^{68} +(-1.70118 - 0.668911i) q^{70} +(7.26245 - 3.49741i) q^{71} +(-9.18963 + 2.83463i) q^{73} +(-5.61986 + 1.73350i) q^{74} +(-8.68517 + 4.18256i) q^{76} +(-6.52237 + 3.76016i) q^{77} +(-1.61319 + 2.79413i) q^{79} +(-0.440953 - 0.763753i) q^{80} +(-8.97340 - 22.8638i) q^{82} +(-2.83326 + 12.4133i) q^{83} +(-0.176473 - 0.773180i) q^{85} +(-5.93643 + 4.04739i) q^{86} +(3.06487 + 0.461955i) q^{88} +(-11.4751 - 10.6474i) q^{89} +(-0.00552043 + 8.68205i) q^{91} +(-5.44121 + 6.82307i) q^{92} +(2.38734 + 1.62766i) q^{94} +(-0.455844 + 1.16147i) q^{95} -2.79937 q^{97} +(-10.8878 - 10.1282i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 14 q^{4} - 28 q^{7}+O(q^{10}) $ 72 * q + 14 * q^4 - 28 * q^7	$ 72 q + 14 q^{4} - 28 q^{7} + 42 q^{13} - 26 q^{16} + 28 q^{19} + 8 q^{22} - 24 q^{25} - 28 q^{28} + 28 q^{31} + 28 q^{34} - 106 q^{37} + 70 q^{40} - 2 q^{43} + 60 q^{46} + 28 q^{49} + 70 q^{52} - 42 q^{55} + 56 q^{58} + 112 q^{61} + 38 q^{64} - 36 q^{67} - 14 q^{70} - 28 q^{73} + 56 q^{76} + 62 q^{79} - 70 q^{82} - 100 q^{85} - 262 q^{88} - 154 q^{91} - 294 q^{94} + 56 q^{97}+O(q^{100}) $ 72 * q + 14 * q^4 - 28 * q^7 + 42 * q^13 - 26 * q^16 + 28 * q^19 + 8 * q^22 - 24 * q^25 - 28 * q^28 + 28 * q^31 + 28 * q^34 - 106 * q^37 + 70 * q^40 - 2 * q^43 + 60 * q^46 + 28 * q^49 + 70 * q^52 - 42 * q^55 + 56 * q^58 + 112 * q^61 + 38 * q^64 - 36 * q^67 - 14 * q^70 - 28 * q^73 + 56 * q^76 + 62 * q^79 - 70 * q^82 - 100 * q^85 - 262 * q^88 - 154 * q^91 - 294 * q^94 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{13}{21}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.02995	−	0.626155i	−1.43539	−	0.442759i	−0.523087	−	0.852279i	$-0.675220\pi$
$2$	−2.02995	−	0.626155i	−1.43539	−	0.442759i	−0.912301	+	0.409521i	$0.865696\pi$
$3$		0			0
$3$		0			0
$4$	2.07613	+	1.41548i	1.03806	+	0.707741i
$5$	0.321603	−	0.0484738i	0.143825	−	0.0216781i	−0.0767351	−	0.997052i	$-0.524450\pi$
$5$	0.321603	−	0.0484738i	0.143825	−	0.0216781i	0.220560	+	0.975373i	$0.429211\pi$
$6$		0			0
$7$	2.57904	+	0.590375i	0.974786	+	0.223141i
$7$	2.57904	+	0.590375i	0.974786	+	0.223141i
$8$	−0.679131	−	0.851603i	−0.240109	−	0.301087i
$9$		0			0
$10$	−0.683188	−	0.102974i	−0.216043	−	0.0325632i
$11$	−2.08594	+	1.93547i	−0.628933	+	0.583565i	−0.928875	−	0.370393i	$-0.879223\pi$
$11$	−2.08594	+	1.93547i	−0.628933	+	0.583565i	0.299942	+	0.953957i	$0.403033\pi$
$12$		0			0
$13$	0.730204	+	3.19923i	0.202522	+	0.887307i	0.969395	+	0.245508i	$0.0789547\pi$
$13$	0.730204	+	3.19923i	0.202522	+	0.887307i	−0.766872	+	0.641800i	$0.778188\pi$
$14$	−4.86565	−	2.81331i	−1.30040	−	0.751889i
$15$		0			0
$16$	−0.990657	−	2.52415i	−0.247664	−	0.631038i
$17$	−0.182224	−	2.43161i	−0.0441959	−	0.589753i	−0.974707	−	0.223488i	$-0.928256\pi$
$17$	−0.182224	−	2.43161i	−0.0441959	−	0.589753i	0.930511	−	0.366265i	$-0.119363\pi$
$18$		0			0
$19$	−1.91818	+	3.32239i	−0.440061	+	0.762208i	−0.997694	−	0.0678798i	$-0.978377\pi$
$19$	−1.91818	+	3.32239i	−0.440061	+	0.762208i	0.557632	+	0.830088i	$0.311710\pi$
$20$	0.736303	+	0.354585i	0.164642	+	0.0792875i
$21$		0			0
$22$	5.44624	−	2.62277i	1.16114	−	0.559176i
$23$	−0.259545	+	3.46339i	−0.0541189	+	0.722167i	0.902475	+	0.430742i	$0.141748\pi$
$23$	−0.259545	+	3.46339i	−0.0541189	+	0.722167i	−0.956594	+	0.291424i	$0.905871\pi$
$24$		0			0
$25$	−4.67679	+	1.44260i	−0.935357	+	0.288519i
$26$	0.520942	−	6.95149i	0.102165	−	1.36330i
$27$		0			0
$28$	4.51876	+	4.87628i	0.853965	+	0.921530i
$29$	5.81416	+	2.79995i	1.07966	+	0.519938i	0.887209	−	0.461368i	$-0.152641\pi$
$29$	5.81416	+	2.79995i	1.07966	+	0.519938i	0.192454	+	0.981306i	$0.438355\pi$
$30$		0			0
$31$	−0.0430144	−	0.0745032i	−0.00772562	−	0.0133812i	0.862137	−	0.506676i	$-0.169126\pi$
$31$	−0.0430144	−	0.0745032i	−0.00772562	−	0.0133812i	−0.869862	+	0.493294i	$0.835792\pi$
$32$	0.593266	+	7.91659i	0.104876	+	1.39947i
$33$		0			0
$34$	−1.15266	+	5.05014i	−0.197680	+	0.866092i
$35$	0.858045	+	0.0648502i	0.145036	+	0.0109617i
$36$		0			0
$37$	2.28743	−	1.55954i	0.376050	−	0.256387i	−0.360515	−	0.932754i	$-0.617399\pi$
$37$	2.28743	−	1.55954i	0.376050	−	0.256387i	0.736565	+	0.676367i	$0.236447\pi$
$38$	5.97413	−	5.54319i	0.969133	−	0.899224i
$39$		0			0
$40$	−0.259691	−	0.240958i	−0.0410607	−	0.0380988i
$41$	7.20887	+	9.03964i	1.12584	+	1.41175i	0.899070	+	0.437805i	$0.144244\pi$
$41$	7.20887	+	9.03964i	1.12584	+	1.41175i	0.226767	+	0.973949i	$0.427185\pi$
$42$		0			0
$43$	2.10877	−	2.64431i	0.321584	−	0.403253i	−0.594594	−	0.804026i	$-0.702687\pi$
$43$	2.10877	−	2.64431i	0.321584	−	0.403253i	0.916177	+	0.400773i	$0.131258\pi$
$44$	−7.07029	+	1.06567i	−1.06589	+	0.160656i
$45$		0			0
$46$	2.69548	−	6.86798i	0.397427	−	1.01263i
$47$	−1.29973	−	0.400913i	−0.189585	−	0.0584791i	0.198509	−	0.980099i	$-0.436390\pi$
$47$	−1.29973	−	0.400913i	−0.189585	−	0.0584791i	−0.388094	+	0.921620i	$0.626866\pi$
$48$		0			0
$49$	6.30291	+	3.04520i	0.900416	+	0.435029i
$50$	10.3969			1.47034
$51$		0			0
$52$	−3.01246	+	7.67561i	−0.417752	+	1.06442i
$53$	−0.722552	−	0.492628i	−0.0992502	−	0.0676676i	0.512678	−	0.858581i	$-0.328653\pi$
$53$	−0.722552	−	0.492628i	−0.0992502	−	0.0676676i	−0.611928	+	0.790913i	$0.709606\pi$
$54$		0			0
$55$	−0.577023	+	0.723564i	−0.0778058	+	0.0975654i
$56$	−1.24874	−	2.59726i	−0.166870	−	0.347074i
$57$		0			0
$58$	−10.0492	−	9.32432i	−1.31953	−	1.22434i
$59$	9.48687	+	1.42992i	1.23509	+	0.186159i	0.733946	−	0.679207i	$-0.237676\pi$
$59$	9.48687	+	1.42992i	1.23509	+	0.186159i	0.501139	+	0.865367i	$0.332914\pi$
$60$		0			0
$61$	4.25839	−	2.90332i	0.545230	−	0.371732i	−0.259159	−	0.965835i	$-0.583445\pi$
$61$	4.25839	−	2.90332i	0.545230	−	0.371732i	0.804389	+	0.594103i	$0.202493\pi$
$62$	0.0406664	+	0.178171i	0.00516464	+	0.0226278i
$63$		0			0
$64$	2.54594	−	11.1545i	0.318243	−	1.39431i
$65$	0.389915	+	0.993486i	0.0483629	+	0.123227i
$66$		0			0
$67$	4.12197	+	7.13946i	0.503578	+	0.872223i	0.999991	+	0.00413699i	$0.00131685\pi$
$67$	4.12197	+	7.13946i	0.503578	+	0.872223i	−0.496413	+	0.868086i	$0.665350\pi$
$68$	3.06358	−	5.30628i	0.371514	−	0.643481i
$69$		0			0
$70$	−1.70118	−	0.668911i	−0.203330	−	0.0799502i
$71$	7.26245	−	3.49741i	0.861895	−	0.415067i	0.0499158	−	0.998753i	$-0.484105\pi$
$71$	7.26245	−	3.49741i	0.861895	−	0.415067i	0.811979	+	0.583687i	$0.198390\pi$
$72$		0			0
$73$	−9.18963	+	2.83463i	−1.07557	+	0.331768i	−0.781428	−	0.623995i	$-0.785508\pi$
$73$	−9.18963	+	2.83463i	−1.07557	+	0.331768i	−0.294137	+	0.955763i	$0.595032\pi$
$74$	−5.61986	+	1.73350i	−0.653296	+	0.201515i
$75$		0			0
$76$	−8.68517	+	4.18256i	−0.996258	+	0.479772i
$77$	−6.52237	+	3.76016i	−0.743293	+	0.428510i
$78$		0			0
$79$	−1.61319	+	2.79413i	−0.181499	+	0.314365i	−0.942391	−	0.334513i	$-0.891428\pi$
$79$	−1.61319	+	2.79413i	−0.181499	+	0.314365i	0.760893	+	0.648878i	$0.224761\pi$
$80$	−0.440953	−	0.763753i	−0.0493001	−	0.0853902i
$81$		0			0
$82$	−8.97340	−	22.8638i	−0.990946	−	2.52489i
$83$	−2.83326	+	12.4133i	−0.310991	+	1.36254i	0.541897	+	0.840445i	$0.317706\pi$
$83$	−2.83326	+	12.4133i	−0.310991	+	1.36254i	−0.852888	+	0.522094i	$0.825151\pi$
$84$		0			0
$85$	−0.176473	−	0.773180i	−0.0191412	−	0.0838632i
$86$	−5.93643	+	4.04739i	−0.640141	+	0.436441i
$87$		0			0
$88$	3.06487	+	0.461955i	0.326717	+	0.0492446i
$89$	−11.4751	−	10.6474i	−1.21636	−	1.12862i	−0.987904	−	0.155067i	$-0.950441\pi$
$89$	−11.4751	−	10.6474i	−1.21636	−	1.12862i	−0.228459	−	0.973553i	$-0.573369\pi$
$90$		0			0
$91$	−0.00552043	+	8.68205i	−0.000578699	+	0.910126i
$92$	−5.44121	+	6.82307i	−0.567286	+	0.711354i
$93$		0			0
$94$	2.38734	+	1.62766i	0.246235	+	0.167880i
$95$	−0.455844	+	1.16147i	−0.0467686	+	0.119164i
$96$		0			0
$97$	−2.79937			−0.284233			−0.142116	−	0.989850i	$-0.545391\pi$
$97$	−2.79937			−0.284233			−0.142116	+	0.989850i	$0.545391\pi$
$98$	−10.8878	−	10.1282i	−1.09983	−	1.02310i
$99$		0			0
$100$	−11.7516	−	3.62488i	−1.17516	−	0.362488i
$101$	6.30012	−	16.0524i	0.626885	−	1.59728i	−0.164786	−	0.986329i	$-0.552693\pi$
$101$	6.30012	−	16.0524i	0.626885	−	1.59728i	0.791671	−	0.610947i	$-0.209211\pi$
$102$		0			0
$103$	−9.83950	+	1.48307i	−0.969515	+	0.146131i	−0.614661	−	0.788791i	$-0.710707\pi$
$103$	−9.83950	+	1.48307i	−0.969515	+	0.146131i	−0.354853	+	0.934922i	$0.615469\pi$
$104$	2.22857	−	2.79454i	0.218530	−	0.274027i
$105$		0			0
$106$	1.15828	+	1.45244i	0.112502	+	0.141073i
$107$	−9.15996	−	8.49920i	−0.885526	−	0.821648i	0.0993238	−	0.995055i	$-0.468332\pi$
$107$	−9.15996	−	8.49920i	−0.885526	−	0.821648i	−0.984850	+	0.173407i	$0.944523\pi$
$108$		0			0
$109$	10.9955	−	10.2023i	1.05317	−	0.977202i	0.0534020	−	0.998573i	$-0.482994\pi$
$109$	10.9955	−	10.2023i	1.05317	−	0.977202i	0.999772	+	0.0213708i	$0.00680307\pi$
$110$	1.62439	−	1.10749i	0.154879	−	0.105595i
$111$		0			0
$112$	−1.06475	−	7.09475i	−0.100609	−	0.670391i
$113$	−1.18087	+	5.17373i	−0.111087	+	0.486704i	0.888524	+	0.458829i	$0.151731\pi$
$113$	−1.18087	+	5.17373i	−0.111087	+	0.486704i	−0.999611	+	0.0278747i	$0.991126\pi$
$114$		0			0
$115$	0.0844133	+	1.12642i	0.00787158	+	0.105039i
$116$	8.10768	+	14.0429i	0.752779	+	1.30385i
$117$		0			0
$118$	−18.3625	−	8.84291i	−1.69040	−	0.814056i
$119$	0.965600	−	6.37881i	0.0885164	−	0.584745i
$120$		0			0
$121$	−0.216930	+	2.89473i	−0.0197209	+	0.263157i
$122$	−10.4622	+	3.22717i	−0.947205	+	0.292174i
$123$		0			0
$124$	0.0161543	−	0.215564i	0.00145070	−	0.0193583i
$125$	−2.89927	+	1.39622i	−0.259319	+	0.124881i
$126$		0			0
$127$	−8.69169	−	4.18570i	−0.771263	−	0.371421i	0.00649949	−	0.999979i	$-0.497931\pi$
$127$	−8.69169	−	4.18570i	−0.771263	−	0.371421i	−0.777763	+	0.628558i	$0.783645\pi$
$128$	−4.21378	+	7.29848i	−0.372449	+	0.645101i
$129$		0			0
$130$	−0.169429	−	2.26087i	−0.0148599	−	0.198291i
$131$	0.247954	+	0.631778i	0.0216639	+	0.0551987i	0.941296	−	0.337581i	$-0.109609\pi$
$131$	0.247954	+	0.631778i	0.0216639	+	0.0551987i	−0.919633	+	0.392780i	$0.871513\pi$
$132$		0			0
$133$	−6.90853	+	7.43613i	−0.599045	+	0.644794i
$134$	−3.89696	−	17.0737i	−0.336646	−	1.47494i
$135$		0			0
$136$	−1.94702	+	1.80657i	−0.166955	+	0.154912i
$137$	−12.4948	−	1.88329i	−1.06750	−	0.160900i	−0.408288	−	0.912853i	$-0.633874\pi$
$137$	−12.4948	−	1.88329i	−1.06750	−	0.160900i	−0.659217	+	0.751953i	$0.729112\pi$
$138$		0			0
$139$	−1.26708	−	1.58887i	−0.107472	−	0.134766i	0.725186	−	0.688553i	$-0.241754\pi$
$139$	−1.26708	−	1.58887i	−0.107472	−	0.134766i	−0.832658	+	0.553787i	$0.813182\pi$
$140$	1.68962	+	1.34918i	0.142799	+	0.114027i
$141$		0			0
$142$	−16.9323	+	2.55213i	−1.42093	+	0.214170i
$143$	−7.71516	−	5.26011i	−0.645174	−	0.439872i
$144$		0			0
$145$	2.00558	+	0.618638i	0.166554	+	0.0513751i
$146$	20.4294			1.69075
$147$		0			0
$148$	6.95649			0.571820
$149$	−0.998384	−	0.307961i	−0.0817908	−	0.0252291i	0.253590	−	0.967312i	$-0.418389\pi$
$149$	−0.998384	−	0.307961i	−0.0817908	−	0.0252291i	−0.335381	+	0.942083i	$0.608865\pi$
$150$		0			0
$151$	17.2464	+	11.7584i	1.40349	+	0.956885i	0.999105	+	0.0422974i	$0.0134677\pi$
$151$	17.2464	+	11.7584i	1.40349	+	0.956885i	0.404388	+	0.914588i	$0.367485\pi$
$152$	4.13205	−	0.622807i	0.335154	−	0.0505163i
$153$		0			0
$154$	15.5945	−	3.54891i	1.25664	−	0.285979i
$155$	−0.0174450	−	0.0218754i	−0.00140122	−	0.00175707i
$156$		0			0
$157$	15.3420	+	2.31243i	1.22442	+	0.184552i	0.729252	−	0.684245i	$-0.239868\pi$
$157$	15.3420	+	2.31243i	1.22442	+	0.184552i	0.495169	+	0.868797i	$0.335106\pi$
$158$	5.02426	−	4.66183i	0.399708	−	0.370875i
$159$		0			0
$160$	0.574543	+	2.51724i	0.0454216	+	0.199005i
$161$	−2.71408	+	8.77900i	−0.213899	+	0.691882i
$162$		0			0
$163$	3.85704	+	9.82758i	0.302107	+	0.769756i	0.998635	+	0.0522266i	$0.0166318\pi$
$163$	3.85704	+	9.82758i	0.302107	+	0.769756i	−0.696528	+	0.717529i	$0.745273\pi$
$164$	2.17111	+	28.9715i	0.169535	+	2.26229i
$165$		0			0
$166$	13.5240	−	23.4243i	1.04967	−	1.81808i
$167$	−12.4011	−	5.97205i	−0.959626	−	0.462131i	−0.112575	−	0.993643i	$-0.535910\pi$
$167$	−12.4011	−	5.97205i	−0.959626	−	0.462131i	−0.847051	+	0.531512i	$0.821624\pi$
$168$		0			0
$169$	2.01071	−	0.968305i	0.154670	−	0.0744850i
$170$	−0.125900	+	1.68001i	−0.00965606	+	0.128851i
$171$		0			0
$172$	8.12104	−	2.50501i	0.619223	−	0.191005i
$173$	−0.658540	+	8.78760i	−0.0500679	+	0.668109i	0.914553	+	0.404467i	$0.132543\pi$
$173$	−0.658540	+	8.78760i	−0.0500679	+	0.668109i	−0.964621	+	0.263642i	$0.915076\pi$
$174$		0			0
$175$	−12.9133	+	0.959461i	−0.976154	+	0.0725285i
$176$	6.95185	+	3.34784i	0.524016	+	0.252353i
$177$		0			0
$178$	16.6270	+	28.7988i	1.24625	+	2.15856i
$179$	−0.349820	−	4.66802i	−0.0261468	−	0.348904i	−0.994899	−	0.100875i	$-0.967836\pi$
$179$	−0.349820	−	4.66802i	−0.0261468	−	0.348904i	0.968752	−	0.248030i	$-0.0797831\pi$
$180$		0			0
$181$	4.84272	−	21.2173i	0.359957	−	1.57707i	−0.393341	−	0.919393i	$-0.628681\pi$
$181$	4.84272	−	21.2173i	0.359957	−	1.57707i	0.753298	−	0.657680i	$-0.228462\pi$
$182$	5.44752	−	17.6206i	0.403797	−	1.30613i
$183$		0			0
$184$	3.12570	−	2.13107i	0.230430	−	0.157104i
$185$	0.660045	−	0.612433i	0.0485275	−	0.0450269i
$186$		0			0
$187$	5.08641	+	4.71950i	0.371955	+	0.345124i
$188$	−2.13092	−	2.67209i	−0.155413	−	0.194882i
$189$		0			0
$190$	1.65260	−	2.07229i	0.119892	−	0.150340i
$191$	18.7829	−	2.83107i	1.35908	−	0.204849i	0.571269	−	0.820763i	$-0.306451\pi$
$191$	18.7829	−	2.83107i	1.35908	−	0.204849i	0.787813	+	0.615914i	$0.211213\pi$
$192$		0			0
$193$	7.79130	−	19.8519i	0.560830	−	1.42897i	−0.316273	−	0.948668i	$-0.602431\pi$
$193$	7.79130	−	19.8519i	0.560830	−	1.42897i	0.877103	−	0.480303i	$-0.159473\pi$
$194$	5.68257	+	1.75284i	0.407984	+	0.125847i
$195$		0			0
$196$	8.77524	+	15.2439i	0.626803	+	1.08885i
$197$	21.9083			1.56090			0.780450	−	0.625218i	$-0.214990\pi$
$197$	21.9083			1.56090			0.780450	+	0.625218i	$0.214990\pi$
$198$		0			0
$199$	−8.94240	+	22.7849i	−0.633910	+	1.61518i	0.146001	+	0.989285i	$0.453360\pi$
$199$	−8.94240	+	22.7849i	−0.633910	+	1.61518i	−0.779910	+	0.625891i	$0.784735\pi$
$200$	4.40467	+	3.00305i	0.311457	+	0.212348i
$201$		0			0
$202$	−22.8402	+	28.6407i	−1.60703	+	2.01515i
$203$	13.3420	+	10.6537i	0.936421	+	0.747746i
$204$		0			0
$205$	2.75658	+	2.55773i	0.192528	+	0.178640i
$206$	20.9023	+	3.15051i	1.45633	+	0.219507i
$207$		0			0
$208$	7.35197	−	5.01249i	0.509767	−	0.347553i
$209$	−2.42916	−	10.6429i	−0.168029	−	0.736182i
$210$		0			0
$211$	−1.12843	+	4.94397i	−0.0776842	+	0.340357i	−0.998802	−	0.0489263i	$-0.984420\pi$
$211$	−1.12843	+	4.94397i	−0.0776842	+	0.340357i	0.921118	+	0.389283i	$0.127277\pi$
$212$	−0.802807	−	2.04552i	−0.0551370	−	0.140487i
$213$		0			0
$214$	13.2724	+	22.9885i	0.907282	+	1.57146i
$215$	0.550005	−	0.952637i	0.0375100	−	0.0649693i
$216$		0			0
$217$	−0.0669512	−	0.217542i	−0.00454495	−	0.0147677i
$218$	−28.7084	+	13.8252i	−1.94438	+	0.936363i
$219$		0			0
$220$	−2.22217	+	0.685448i	−0.149818	+	0.0462129i
$221$	7.64624	−	2.35855i	0.514341	−	0.158653i
$222$		0			0
$223$	−1.19391	+	0.574958i	−0.0799503	+	0.0385020i	−0.473432	−	0.880831i	$-0.656985\pi$
$223$	−1.19391	+	0.574958i	−0.0799503	+	0.0385020i	0.393481	+	0.919333i	$0.371271\pi$
$224$	−3.14370	+	20.7675i	−0.210047	+	1.38758i
$225$		0			0
$226$	5.63666	−	9.76299i	0.374945	−	0.649424i
$227$	−11.8681	−	20.5561i	−0.787712	−	1.36436i	−0.927366	−	0.374156i	$-0.877932\pi$
$227$	−11.8681	−	20.5561i	−0.787712	−	1.36436i	0.139654	−	0.990200i	$-0.455401\pi$
$228$		0			0
$229$	−10.1645	−	25.8988i	−0.671692	−	1.71144i	−0.702270	−	0.711911i	$-0.747830\pi$
$229$	−10.1645	−	25.8988i	−0.671692	−	1.71144i	0.0305779	−	0.999532i	$-0.490265\pi$
$230$	0.533958	−	2.33942i	0.0352081	−	0.154257i
$231$		0			0
$232$	−1.56413	−	6.85290i	−0.102690	−	0.449915i
$233$	17.8105	−	12.1430i	1.16680	−	0.795514i	0.184505	−	0.982831i	$-0.440932\pi$
$233$	17.8105	−	12.1430i	1.16680	−	0.795514i	0.982299	+	0.187317i	$0.0599793\pi$
$234$		0			0
$235$	−0.437430	−	0.0659319i	−0.0285348	−	0.00430092i
$236$	17.6720	+	16.3972i	1.15035	+	1.06737i
$237$		0			0
$238$	−5.95424	+	12.3440i	−0.385956	+	0.800144i
$239$	−12.5834	+	15.7790i	−0.813950	+	1.02066i	0.185329	+	0.982677i	$0.440665\pi$
$239$	−12.5834	+	15.7790i	−0.813950	+	1.02066i	−0.999278	+	0.0379840i	$0.987906\pi$
$240$		0			0
$241$	−14.4265	−	9.83581i	−0.929291	−	0.633580i	0.00115850	−	0.999999i	$-0.499631\pi$
$241$	−14.4265	−	9.83581i	−0.929291	−	0.633580i	−0.930450	+	0.366419i	$0.880584\pi$
$242$	2.25291	−	5.74031i	0.144822	−	0.369001i
$243$		0			0
$244$	12.9506			0.829074
$245$	2.17465	+	0.673820i	0.138933	+	0.0430488i
$246$		0			0
$247$	−12.0298	−	3.71069i	−0.765435	−	0.236105i
$248$	−0.0342347	+	0.0872287i	−0.00217391	+	0.00553903i
$249$		0			0
$250$	6.75961	−	1.01885i	0.427516	−	0.0644376i
$251$	1.30856	−	1.64088i	0.0825955	−	0.103572i	−0.738817	−	0.673906i	$-0.764615\pi$
$251$	1.30856	−	1.64088i	0.0825955	−	0.103572i	0.821412	+	0.570335i	$0.193187\pi$
$252$		0			0
$253$	−6.16188	−	7.72675i	−0.387394	−	0.485777i
$254$	15.0228	+	13.9391i	0.942612	+	0.874616i
$255$		0			0
$256$	−3.65049	+	3.38716i	−0.228155	+	0.211697i
$257$	−15.6330	+	10.6584i	−0.975161	+	0.664853i	−0.942357	−	0.334608i	$-0.891396\pi$
$257$	−15.6330	+	10.6584i	−0.975161	+	0.664853i	−0.0328036	+	0.999462i	$0.510444\pi$
$258$		0			0
$259$	6.82008	−	2.67168i	0.423779	−	0.166010i
$260$	−0.596748	+	2.61452i	−0.0370087	+	0.162146i
$261$		0			0
$262$	−0.107743	−	1.43773i	−0.00665639	−	0.0888234i
$263$	−13.5392	−	23.4505i	−0.834862	−	1.44602i	−0.894143	−	0.447781i	$-0.852214\pi$
$263$	−13.5392	−	23.4505i	−0.834862	−	1.44602i	0.0592815	−	0.998241i	$-0.481119\pi$
$264$		0			0
$265$	−0.256254	−	0.123406i	−0.0157416	−	0.00758074i
$266$	18.6801	−	10.7691i	1.14535	−	0.660298i
$267$		0			0
$268$	−1.54803	+	20.6570i	−0.0945609	+	1.26183i
$269$	−30.7280	+	9.47835i	−1.87352	+	0.577905i	−0.878563	+	0.477627i	$0.841497\pi$
$269$	−30.7280	+	9.47835i	−1.87352	+	0.577905i	−0.994959	+	0.100278i	$0.968027\pi$
$270$		0			0
$271$	−2.30996	+	30.8242i	−0.140320	+	1.87244i	0.273218	+	0.961952i	$0.411912\pi$
$271$	−2.30996	+	30.8242i	−0.140320	+	1.87244i	−0.413538	+	0.910487i	$0.635707\pi$
$272$	−5.95724	+	2.86886i	−0.361211	+	0.173950i
$273$		0			0
$274$	24.1846	+	11.6467i	1.46104	+	0.703602i
$275$	6.96338	−	12.0609i	0.419907	−	0.727301i
$276$		0			0
$277$	−0.809073	−	10.7963i	−0.0486125	−	0.648689i	−0.967289	−	0.253678i	$-0.918360\pi$
$277$	−0.809073	−	10.7963i	−0.0486125	−	0.648689i	0.918676	−	0.395011i	$-0.129259\pi$
$278$	1.57722	+	4.01870i	0.0945955	+	0.241026i
$279$		0			0
$280$	−0.527498	−	0.774756i	−0.0315240	−	0.0463005i
$281$	−5.01550	−	21.9743i	−0.299199	−	1.31088i	−0.871323	−	0.490711i	$-0.836737\pi$
$281$	−5.01550	−	21.9743i	−0.299199	−	1.31088i	0.572123	−	0.820168i	$-0.306120\pi$
$282$		0			0
$283$	8.85464	−	8.21590i	0.526354	−	0.488385i	−0.371650	−	0.928373i	$-0.621208\pi$
$283$	8.85464	−	8.21590i	0.526354	−	0.488385i	0.898004	+	0.439988i	$0.145017\pi$
$284$	20.0283	+	3.01878i	1.18846	+	0.179132i
$285$		0			0
$286$	12.3677	+	15.5086i	0.731318	+	0.917044i
$287$	13.2552	+	27.5695i	0.782430	+	1.62738i
$288$		0			0
$289$	10.9306	−	1.64752i	0.642976	−	0.0969130i
$290$	−3.68384	−	2.51160i	−0.216323	−	0.147486i
$291$		0			0
$292$	−23.0912	−	7.12270i	−1.35131	−	0.416824i
$293$	−7.64250			−0.446479			−0.223240	−	0.974764i	$-0.571663\pi$
$293$	−7.64250			−0.446479			−0.223240	+	0.974764i	$0.571663\pi$
$294$		0			0
$295$	3.12032			0.181672
$296$	−2.88157	−	0.888847i	−0.167488	−	0.0516632i
$297$		0			0
$298$	1.83383	+	1.25029i	0.106231	+	0.0724272i
$299$	−11.2697	+	1.69864i	−0.651744	+	0.0982347i
$300$		0			0
$301$	6.99973	−	5.57482i	0.403458	−	0.321327i
$302$	−27.6467	−	34.6678i	−1.59089	−	1.99491i
$303$		0			0
$304$	10.2865	+	1.55044i	0.589970	+	0.0889236i
$305$	1.22877	−	1.14014i	0.0703594	−	0.0652840i
$306$		0			0
$307$	0.324756	+	1.42285i	0.0185348	+	0.0812064i	0.983349	−	0.181725i	$-0.0581680\pi$
$307$	0.324756	+	1.42285i	0.0185348	+	0.0812064i	−0.964815	+	0.262931i	$0.915311\pi$
$308$	−18.8637	−	1.42570i	−1.07486	−	0.0812369i
$309$		0			0
$310$	0.0217151	+	0.0553291i	0.00123333	+	0.00314248i
$311$	1.33080	+	17.7583i	0.0754628	+	1.00698i	0.898494	+	0.438985i	$0.144662\pi$
$311$	1.33080	+	17.7583i	0.0754628	+	1.00698i	−0.823031	+	0.567996i	$0.807719\pi$
$312$		0			0
$313$	−1.80231	+	3.12170i	−0.101873	+	0.176449i	−0.912456	−	0.409174i	$-0.865817\pi$
$313$	−1.80231	+	3.12170i	−0.101873	+	0.176449i	0.810583	+	0.585623i	$0.199150\pi$
$314$	−29.6954	−	14.3005i	−1.67581	−	0.807026i
$315$		0			0
$316$	−7.30424	+	3.51754i	−0.410896	+	0.197877i
$317$	0.468518	−	6.25194i	0.0263146	−	0.351144i	−0.968469	−	0.249135i	$-0.919854\pi$
$317$	0.468518	−	6.25194i	0.0263146	−	0.351144i	0.994783	−	0.102009i	$-0.0325271\pi$
$318$		0			0
$319$	−17.5472	+	5.41259i	−0.982454	+	0.303047i
$320$	0.278081	−	3.71073i	0.0155452	−	0.207436i
$321$		0			0
$322$	11.0064	−	16.1215i	0.613365	−	0.898414i
$323$	8.42830	+	4.05886i	0.468963	+	0.225841i
$324$		0			0
$325$	−8.03021	−	13.9087i	−0.445436	−	0.771518i
$326$	−1.67599	−	22.3646i	−0.0928246	−	1.23866i
$327$		0			0
$328$	2.80242	−	12.2782i	0.154738	−	0.677950i
$329$	−3.11536	−	1.80130i	−0.171755	−	0.0993087i
$330$		0			0
$331$	11.0155	−	7.51026i	0.605468	−	0.412801i	−0.221411	−	0.975181i	$-0.571066\pi$
$331$	11.0155	−	7.51026i	0.605468	−	0.412801i	0.826879	+	0.562379i	$0.190114\pi$
$332$	−23.4530	+	21.7612i	−1.28715	+	1.19430i
$333$		0			0
$334$	21.4341	+	19.8880i	1.17282	+	1.08822i
$335$	1.67171	+	2.09626i	0.0913354	+	0.114531i
$336$		0			0
$337$	8.56488	−	10.7400i	0.466559	−	0.585046i	−0.491766	−	0.870727i	$-0.663648\pi$
$337$	8.56488	−	10.7400i	0.466559	−	0.585046i	0.958325	+	0.285681i	$0.0922199\pi$
$338$	−4.68793	+	0.706592i	−0.254990	+	0.0384335i
$339$		0			0
$340$	0.728041	−	1.85502i	0.0394835	−	0.100602i
$341$	0.233924	+	0.0721559i	0.0126677	+	0.00390746i
$342$		0			0
$343$	14.4577	+	11.5748i	0.780641	+	0.624980i
$344$	−3.68403			−0.198630
$345$		0			0
$346$	6.83920	−	17.4260i	0.367678	−	0.936828i
$347$	−20.8072	−	14.1861i	−1.11699	−	0.761550i	−0.143356	−	0.989671i	$-0.545790\pi$
$347$	−20.8072	−	14.1861i	−1.11699	−	0.761550i	−0.973633	+	0.228121i	$0.926742\pi$
$348$		0			0
$349$	2.07941	−	2.60750i	0.111308	−	0.139576i	−0.723056	−	0.690789i	$-0.757263\pi$
$349$	2.07941	−	2.60750i	0.111308	−	0.139576i	0.834365	+	0.551213i	$0.185835\pi$
$350$	26.8141	+	6.13807i	1.43327	+	0.328094i
$351$		0			0
$352$	−16.5598	−	15.3652i	−0.882640	−	0.818970i
$353$	29.0588	+	4.37991i	1.54664	+	0.233119i	0.866206	−	0.499688i	$-0.166552\pi$
$353$	29.0588	+	4.37991i	1.54664	+	0.233119i	0.680437	+	0.732807i	$0.261790\pi$
$354$		0			0
$355$	2.16609	−	1.47682i	0.114964	−	0.0783813i
$356$	−8.75273	−	38.3482i	−0.463894	−	2.03245i
$357$		0			0
$358$	−2.21279	+	9.69487i	−0.116950	+	0.512390i
$359$	−1.25636	−	3.20114i	−0.0663079	−	0.168950i	0.893879	−	0.448309i	$-0.147973\pi$
$359$	−1.25636	−	3.20114i	−0.0663079	−	0.168950i	−0.960187	+	0.279359i	$0.909878\pi$
$360$		0			0
$361$	2.14116	+	3.70859i	0.112692	+	0.195189i
$362$	−23.1158	+	40.0377i	−1.21494	+	2.10434i
$363$		0			0
$364$	−12.3007	+	18.0172i	−0.644734	+	0.944360i
$365$	−2.81801	+	1.35708i	−0.147501	+	0.0710328i
$366$		0			0
$367$	−24.5910	+	7.58532i	−1.28364	+	0.395950i	−0.860192	−	0.509970i	$-0.829656\pi$
$367$	−24.5910	+	7.58532i	−1.28364	+	0.395950i	−0.423448	+	0.905921i	$0.639180\pi$
$368$	8.99925	−	2.77590i	0.469118	−	0.144704i
$369$		0			0
$370$	−1.72333	+	0.829914i	−0.0895919	+	0.0431452i
$371$	−1.57266	−	1.69708i	−0.0816483	−	0.0881082i
$372$		0			0
$373$	5.25110	−	9.09518i	0.271892	−	0.470930i	−0.697454	−	0.716629i	$-0.745684\pi$
$373$	5.25110	−	9.09518i	0.271892	−	0.470930i	0.969346	+	0.245699i	$0.0790174\pi$
$374$	−7.37000	−	12.7652i	−0.381093	−	0.660073i
$375$		0			0
$376$	0.541266	+	1.37912i	0.0279137	+	0.0711229i
$377$	−4.71218	+	20.6454i	−0.242690	+	1.06329i
$378$		0			0
$379$	−6.08541	−	26.6619i	−0.312587	−	1.36953i	−0.850253	−	0.526374i	$-0.823551\pi$
$379$	−6.08541	−	26.6619i	−0.312587	−	1.36953i	0.537667	−	0.843157i	$-0.319306\pi$
$380$	−2.59043	+	1.76613i	−0.132886	+	0.0906003i
$381$		0			0
$382$	−39.9009	−	6.01410i	−2.04151	−	0.307708i
$383$	6.42620	+	5.96264i	0.328363	+	0.304677i	0.827075	−	0.562091i	$-0.190003\pi$
$383$	6.42620	+	5.96264i	0.328363	+	0.304677i	−0.498712	+	0.866768i	$0.666193\pi$
$384$		0			0
$385$	−1.91534	+	1.52544i	−0.0976148	+	0.0777437i
$386$	−28.2463	+	35.4197i	−1.43770	+	1.80282i
$387$		0			0
$388$	−5.81185	−	3.96245i	−0.295052	−	0.201163i
$389$	1.79795	−	4.58110i	0.0911596	−	0.232271i	−0.878021	−	0.478622i	$-0.841136\pi$
$389$	1.79795	−	4.58110i	0.0911596	−	0.232271i	0.969181	+	0.246351i	$0.0792317\pi$
$390$		0			0
$391$	8.46892			0.428292
$392$	−1.68720	−	7.43568i	−0.0852164	−	0.375558i
$393$		0			0
$394$	−44.4726	−	13.7180i	−2.24050	−	0.691102i
$395$	−0.383365	+	0.976799i	−0.0192892	+	0.0491481i
$396$		0			0
$397$	−30.8660	+	4.65230i	−1.54912	+	0.233492i	−0.867209	−	0.497944i	$-0.834089\pi$
$397$	−30.8660	+	4.65230i	−1.54912	+	0.233492i	−0.681910	+	0.731436i	$0.738851\pi$
$398$	32.4194	−	40.6527i	1.62504	−	2.03773i
$399$		0			0
$400$	8.27442	+	10.3758i	0.413721	+	0.518790i
$401$	10.7563	+	9.98041i	0.537145	+	0.498398i	0.901451	−	0.432882i	$-0.142503\pi$
$401$	10.7563	+	9.98041i	0.537145	+	0.498398i	−0.364306	+	0.931279i	$0.618694\pi$
$402$		0			0
$403$	0.206944	−	0.192016i	0.0103086	−	0.00956498i
$404$	35.8018	−	24.4092i	1.78120	−	1.21440i
$405$		0			0
$406$	−20.4125	−	29.9806i	−1.01306	−	1.48791i
$407$	−1.75299	+	7.68033i	−0.0868923	+	0.380700i
$408$		0			0
$409$	−1.42350	−	18.9953i	−0.0703874	−	0.939255i	−0.914890	−	0.403703i	$-0.867723\pi$
$409$	−1.42350	−	18.9953i	−0.0703874	−	0.939255i	0.844502	−	0.535552i	$-0.179896\pi$
$410$	−3.99417	−	6.91810i	−0.197258	−	0.341661i
$411$		0			0
$412$	−22.5273	−	10.8486i	−1.10984	−	0.534472i
$413$	23.6229	+	9.28863i	1.16240	+	0.457063i
$414$		0			0
$415$	−0.309463	+	4.12950i	−0.0151909	+	0.202709i
$416$	−24.8938	+	7.67872i	−1.22052	+	0.376480i
$417$		0			0
$418$	−1.73301	+	23.1255i	−0.0847645	+	1.13110i
$419$	−25.8926	+	12.4692i	−1.26494	+	0.609162i	−0.941476	−	0.337080i	$-0.890561\pi$
$419$	−25.8926	+	12.4692i	−1.26494	+	0.609162i	−0.323461	+	0.946241i	$0.604846\pi$
$420$		0			0
$421$	−3.72907	−	1.79583i	−0.181744	−	0.0875233i	0.340799	−	0.940136i	$-0.389302\pi$
$421$	−3.72907	−	1.79583i	−0.181744	−	0.0875233i	−0.522543	+	0.852613i	$0.675017\pi$
$422$	5.38634	−	9.32941i	0.262203	−	0.454149i
$423$		0			0
$424$	0.0711842	+	0.949887i	0.00345701	+	0.0461306i
$425$	4.36006	+	11.1093i	0.211494	+	0.538878i
$426$		0			0
$427$	12.6966	−	4.97373i	0.614432	−	0.240696i
$428$	−6.98680	−	30.6112i	−0.337720	−	1.47965i
$429$		0			0
$430$	−1.71298	+	1.58941i	−0.0826071	+	0.0766482i
$431$	29.1457	+	4.39300i	1.40390	+	0.211604i	0.806923	−	0.590657i	$-0.201131\pi$
$431$	29.1457	+	4.39300i	1.40390	+	0.211604i	0.596975	+	0.802260i	$0.296369\pi$
$432$		0			0
$433$	−6.84546	−	8.58393i	−0.328972	−	0.412517i	0.589648	−	0.807660i	$-0.299266\pi$
$433$	−6.84546	−	8.58393i	−0.328972	−	0.412517i	−0.918620	+	0.395143i	$0.870695\pi$
$434$	−0.000307443		0.483519i	−1.47577e−5		0.0232097i
$435$		0			0
$436$	37.2691	−	5.61742i	1.78487	−	0.269026i
$437$	−11.0089	−	7.50572i	−0.526626	−	0.359047i
$438$		0			0
$439$	−6.27318	−	1.93502i	−0.299403	−	0.0923534i	0.141414	−	0.989950i	$-0.454835\pi$
$439$	−6.27318	−	1.93502i	−0.299403	−	0.0923534i	−0.440817	+	0.897597i	$0.645311\pi$
$440$	1.00806			0.0480576
$441$		0			0
$442$	−16.9983			−0.808525
$443$	25.5339	+	7.87616i	1.21315	+	0.374208i	0.834332	−	0.551262i	$-0.185854\pi$
$443$	25.5339	+	7.87616i	1.21315	+	0.374208i	0.378820	+	0.925470i	$0.376330\pi$
$444$		0			0
$445$	−4.20656	−	2.86798i	−0.199410	−	0.135955i
$446$	2.78359	−	0.419558i	0.131807	−	0.0198667i
$447$		0			0
$448$	13.1514	−	27.2649i	0.621346	−	1.28814i
$449$	−10.4932	−	13.1580i	−0.495203	−	0.620965i	0.469937	−	0.882700i	$-0.344277\pi$
$449$	−10.4932	−	13.1580i	−0.495203	−	0.620965i	−0.965140	+	0.261735i	$0.915705\pi$
$450$		0			0
$451$	−32.5331	−	4.90358i	−1.53193	−	0.230901i
$452$	−9.77497	+	9.06984i	−0.459776	+	0.426610i
$453$		0			0
$454$	11.2202	+	49.1590i	0.526591	+	2.30715i
$455$	0.419077	+	2.79244i	0.0196466	+	0.130912i
$456$		0			0
$457$	1.90401	+	4.85134i	0.0890659	+	0.226936i	0.968465	−	0.249149i	$-0.0801508\pi$
$457$	1.90401	+	4.85134i	0.0890659	+	0.226936i	−0.879399	+	0.476085i	$0.842056\pi$
$458$	4.41678	+	58.9378i	0.206382	+	2.75398i
$459$		0			0
$460$	−1.41917	+	2.45807i	−0.0661691	+	0.114608i
$461$	10.3996	+	5.00820i	0.484359	+	0.233255i	0.660095	−	0.751182i	$-0.270516\pi$
$461$	10.3996	+	5.00820i	0.484359	+	0.233255i	−0.175736	+	0.984437i	$0.556230\pi$
$462$		0			0
$463$	1.43236	−	0.689790i	0.0665676	−	0.0320573i	−0.400304	−	0.916383i	$-0.631095\pi$
$463$	1.43236	−	0.689790i	0.0665676	−	0.0320573i	0.466871	+	0.884325i	$0.345381\pi$
$464$	1.30767	−	17.4496i	0.0607070	−	0.810079i
$465$		0			0
$466$	−43.7577	+	13.4975i	−2.02704	+	0.625259i
$467$	−1.89852	+	25.3339i	−0.0878529	+	1.17232i	0.762817	+	0.646615i	$0.223816\pi$
$467$	−1.89852	+	25.3339i	−0.0878529	+	1.17232i	−0.850670	+	0.525701i	$0.823803\pi$
$468$		0			0
$469$	6.41577	+	20.8465i	0.296253	+	0.962600i
$470$	0.846674	+	0.407737i	0.0390542	+	0.0188075i
$471$		0			0
$472$	−5.22511	−	9.05016i	−0.240505	−	0.416567i
$473$	0.719218	+	9.59730i	0.0330697	+	0.441284i
$474$		0			0
$475$	4.17806	−	18.3053i	0.191702	−	0.839903i
$476$	11.0338	−	11.8765i	0.505733	−	0.544356i
$477$		0			0
$478$	35.4236	−	24.1514i	1.62024	−	1.10466i
$479$	19.1113	−	17.7327i	0.873217	−	0.810227i	−0.109760	−	0.993958i	$-0.535008\pi$
$479$	19.1113	−	17.7327i	0.873217	−	0.810227i	0.982976	+	0.183731i	$0.0588177\pi$
$480$		0			0
$481$	6.65962	+	6.17922i	0.303652	+	0.281748i
$482$	23.1262	+	28.9994i	1.05337	+	1.32089i
$483$		0			0
$484$	−4.54781	+	5.70277i	−0.206719	+	0.259217i
$485$	−0.900285	+	0.135696i	−0.0408798	+	0.00616164i
$486$		0			0
$487$	4.02357	−	10.2519i	0.182325	−	0.464557i	−0.810265	−	0.586063i	$-0.800677\pi$
$487$	4.02357	−	10.2519i	0.182325	−	0.464557i	0.992591	+	0.121506i	$0.0387723\pi$
$488$	−5.36448	−	1.65472i	−0.242839	−	0.0749058i
$489$		0			0
$490$	−3.99250	−	2.72948i	−0.180363	−	0.123305i
$491$	37.2589			1.68147			0.840735	−	0.541447i	$-0.182123\pi$
$491$	37.2589			1.68147			0.840735	+	0.541447i	$0.182123\pi$
$492$		0			0
$493$	5.74892	−	14.6480i	0.258919	−	0.659714i
$494$	22.0963	+	15.0650i	0.994159	+	0.677806i
$495$		0			0
$496$	−0.145445	+	0.182382i	−0.00653067	+	0.00818920i
$497$	20.7950	−	4.73240i	0.932781	−	0.212277i
$498$		0			0
$499$	2.70358	+	2.50856i	0.121029	+	0.112299i	0.738366	−	0.674401i	$-0.235598\pi$
$499$	2.70358	+	2.50856i	0.121029	+	0.112299i	−0.617337	+	0.786699i	$0.711788\pi$
$500$	−7.99558	−	1.20514i	−0.357573	−	0.0538955i
$501$		0			0
$502$	−3.68375	+	2.51154i	−0.164414	+	0.112095i
$503$	−3.09362	−	13.5540i	−0.137938	−	0.604344i	−0.995887	−	0.0906089i	$-0.971119\pi$
$503$	−3.09362	−	13.5540i	−0.137938	−	0.604344i	0.857949	−	0.513735i	$-0.171738\pi$
$504$		0			0
$505$	1.24801	−	5.46790i	0.0555358	−	0.243318i
$506$	7.67013	+	19.5432i	0.340979	+	0.868800i
$507$		0			0
$508$	−12.1203	−	20.9930i	−0.537752	−	0.931413i
$509$	13.1872	−	22.8409i	0.584512	−	1.01240i	−0.410424	−	0.911895i	$-0.634619\pi$
$509$	13.1872	−	22.8409i	0.584512	−	1.01240i	0.994936	−	0.100510i	$-0.0320473\pi$
$510$		0			0
$511$	−25.3739	+	1.88529i	−1.12248	+	0.0834003i
$512$	24.7171	−	11.9031i	1.09235	−	0.526049i
$513$		0			0
$514$	38.4080	−	11.8473i	1.69410	−	0.522562i
$515$	−3.09252	+	0.953916i	−0.136273	+	0.0420346i
$516$		0			0
$517$	3.48710	−	1.67930i	0.153362	−	0.0738555i
$518$	−15.5173	+	1.15294i	−0.681790	+	0.0506572i
$519$		0			0
$520$	0.581253	−	1.00676i	0.0254896	−	0.0441493i
$521$	1.56572	+	2.71191i	0.0685955	+	0.118811i	0.898283	−	0.439417i	$-0.144815\pi$
$521$	1.56572	+	2.71191i	0.0685955	+	0.118811i	−0.829688	+	0.558228i	$0.811482\pi$
$522$		0			0
$523$	4.35373	+	11.0931i	0.190375	+	0.485068i	0.993911	−	0.110189i	$-0.0351456\pi$
$523$	4.35373	+	11.0931i	0.190375	+	0.485068i	−0.803536	+	0.595257i	$0.797050\pi$
$524$	−0.379484	+	1.66263i	−0.0165778	+	0.0726322i
$525$		0			0
$526$	12.8001	+	56.0810i	0.558111	+	2.44525i
$527$	−0.173325	+	0.118171i	−0.00755014	+	0.00514760i
$528$		0			0
$529$	10.8154	+	1.63016i	0.470235	+	0.0708765i
$530$	0.442911	+	0.410962i	0.0192388	+	0.0178510i
$531$		0			0
$532$	−24.8687	+	5.65948i	−1.07819	+	0.245370i
$533$	−23.6560	+	29.6636i	−1.02465	+	1.28487i
$534$		0			0
$535$	−3.35786	−	2.28935i	−0.145173	−	0.0989771i
$536$	3.28063	−	8.35891i	0.141702	−	0.361050i
$537$		0			0
$538$	68.3112			2.94510
$539$	−19.0414	+	5.84697i	−0.820169	+	0.251847i
$540$		0			0
$541$	25.5776	+	7.88964i	1.09967	+	0.339202i	0.790906	−	0.611938i	$-0.209610\pi$
$541$	25.5776	+	7.88964i	1.09967	+	0.339202i	0.308760	+	0.951140i	$0.400086\pi$
$542$	23.9898	−	61.1251i	1.03045	−	2.62555i
$543$		0			0
$544$	19.1420	−	2.88519i	0.820705	−	0.123701i
$545$	3.04162	−	3.81408i	0.130289	−	0.163377i
$546$		0			0
$547$	−23.2165	−	29.1126i	−0.992668	−	1.24477i	−0.969514	−	0.245034i	$-0.921201\pi$
$547$	−23.2165	−	29.1126i	−0.992668	−	1.24477i	−0.0231535	−	0.999732i	$-0.507371\pi$
$548$	−23.2751	−	21.5961i	−0.994264	−	0.922542i
$549$		0			0
$550$	−21.6873	+	20.1229i	−0.924749	+	0.858041i
$551$	−20.4552	+	13.9461i	−0.871419	+	0.594123i
$552$		0			0
$553$	−5.81008	+	6.25380i	−0.247070	+	0.265939i
$554$	−5.11781	+	22.4226i	−0.217435	+	0.952644i
$555$		0			0
$556$	−0.381609	−	5.09222i	−0.0161838	−	0.215958i
$557$	−0.869283	−	1.50564i	−0.0368327	−	0.0637961i	0.847021	−	0.531559i	$-0.178394\pi$
$557$	−0.869283	−	1.50564i	−0.0368327	−	0.0637961i	−0.883854	+	0.467763i	$0.845060\pi$
$558$		0			0
$559$	9.99958	+	4.81555i	0.422937	+	0.203676i
$560$	−0.686336	−	2.23008i	−0.0290030	−	0.0942381i
$561$		0			0
$562$	−3.57815	+	47.7472i	−0.150935	+	2.01409i
$563$	−8.38147	+	2.58534i	−0.353237	+	0.108959i	−0.466295	−	0.884629i	$-0.654412\pi$
$563$	−8.38147	+	2.58534i	−0.353237	+	0.108959i	0.113058	+	0.993588i	$0.463935\pi$
$564$		0			0
$565$	−0.128981	+	1.72113i	−0.00542626	+	0.0724084i
$566$	−23.1189	+	11.1335i	−0.971758	+	0.467974i
$567$		0			0
$568$	−7.91057	−	3.80953i	−0.331920	−	0.159844i
$569$	−8.21979	+	14.2371i	−0.344591	+	0.596850i	−0.985279	−	0.170951i	$-0.945316\pi$
$569$	−8.21979	+	14.2371i	−0.344591	+	0.596850i	0.640688	+	0.767801i	$0.278649\pi$
$570$		0			0
$571$	0.942948	+	12.5828i	0.0394611	+	0.526572i	0.981550	+	0.191208i	$0.0612404\pi$
$571$	0.942948	+	12.5828i	0.0394611	+	0.526572i	−0.942088	+	0.335364i	$0.891141\pi$
$572$	−8.57209	−	21.8413i	−0.358417	−	0.913232i
$573$		0			0
$574$	−9.64452	−	64.2645i	−0.402555	−	2.68235i
$575$	−3.78244	−	16.5720i	−0.157739	−	0.691098i
$576$		0			0
$577$	5.19961	−	4.82453i	0.216463	−	0.200848i	−0.564487	−	0.825442i	$-0.690926\pi$
$577$	5.19961	−	4.82453i	0.216463	−	0.200848i	0.780950	+	0.624594i	$0.214736\pi$
$578$	−23.2201	−	3.49987i	−0.965829	−	0.145575i
$579$		0			0
$580$	3.28816	+	4.12323i	0.136534	+	0.171208i
$581$	−14.6356	+	30.3418i	−0.607187	+	1.25879i
$582$		0			0
$583$	2.46066	−	0.370885i	0.101910	−	0.0153605i
$584$	8.65494	+	5.90084i	0.358144	+	0.244178i
$585$		0			0
$586$	15.5138	+	4.78539i	0.640871	+	0.197683i
$587$	33.1857			1.36972			0.684860	−	0.728675i	$-0.259863\pi$
$587$	33.1857			1.36972			0.684860	+	0.728675i	$0.259863\pi$
$588$		0			0
$589$	0.330038			0.0135990
$590$	−6.33407	−	1.95380i	−0.260770	−	0.0804368i
$591$		0			0
$592$	−6.20257	−	4.22884i	−0.254924	−	0.173804i
$593$	−3.28072	+	0.494489i	−0.134723	+	0.0203062i	−0.216058	−	0.976381i	$-0.569320\pi$
$593$	−3.28072	+	0.494489i	−0.134723	+	0.0203062i	0.0813345	+	0.996687i	$0.474082\pi$
$594$		0			0
$595$	0.00133416	−	2.09825i	5.46953e−5	−	0.0860199i
$596$	−1.63686	−	2.05256i	−0.0670485	−	0.0840761i
$597$		0			0
$598$	23.9405	+	3.60845i	0.979000	+	0.147561i
$599$	7.22027	−	6.69943i	0.295012	−	0.273731i	−0.518754	−	0.854923i	$-0.673604\pi$
$599$	7.22027	−	6.69943i	0.295012	−	0.273731i	0.813766	+	0.581192i	$0.197414\pi$
$600$		0			0
$601$	−5.40902	−	23.6985i	−0.220639	−	0.966680i	−0.956999	−	0.290091i	$-0.906314\pi$
$601$	−5.40902	−	23.6985i	−0.220639	−	0.966680i	0.736361	−	0.676589i	$-0.236543\pi$
$602$	−17.6998	+	6.93366i	−0.721389	+	0.282595i
$603$		0			0
$604$	19.1620	+	48.8239i	0.779690	+	1.98662i
$605$	0.0705533	+	0.941468i	0.00286840	+	0.0382761i
$606$		0			0
$607$	−3.42182	+	5.92676i	−0.138887	+	0.240560i	−0.927076	−	0.374874i	$-0.877686\pi$
$607$	−3.42182	+	5.92676i	−0.138887	+	0.240560i	0.788188	+	0.615434i	$0.211019\pi$
$608$	−27.4400	−	13.2144i	−1.11284	−	0.535914i
$609$		0			0
$610$	−3.20824	+	1.54501i	−0.129898	+	0.0625556i
$611$	0.333547	−	4.45088i	0.0134939	−	0.180063i
$612$		0			0
$613$	21.1658	−	6.52878i	0.854878	−	0.263695i	0.163816	−	0.986491i	$-0.447620\pi$
$613$	21.1658	−	6.52878i	0.854878	−	0.263695i	0.691062	+	0.722796i	$0.257143\pi$
$614$	0.231688	−	3.09166i	0.00935015	−	0.124769i
$615$		0			0
$616$	7.63171	+	3.00083i	0.307490	+	0.120907i
$617$	30.2908	+	14.5873i	1.21946	+	0.587262i	0.929162	−	0.369674i	$-0.120530\pi$
$617$	30.2908	+	14.5873i	1.21946	+	0.587262i	0.290300	+	0.956936i	$0.406245\pi$
$618$		0			0
$619$	3.32660	+	5.76185i	0.133708	+	0.231588i	0.925103	−	0.379716i	$-0.123978\pi$
$619$	3.32660	+	5.76185i	0.133708	+	0.231588i	−0.791395	+	0.611305i	$0.790645\pi$
$620$	−0.00525396	−	0.0701092i	−0.000211004	−	0.00281565i
$621$		0			0
$622$	8.41800	−	36.8817i	0.337531	−	1.47882i
$623$	−23.3089	−	34.2347i	−0.933853	−	1.37158i
$624$		0			0
$625$	19.3542	−	13.1955i	0.774170	−	0.527820i
$626$	5.61326	−	5.20835i	0.224351	−	0.208167i
$627$		0			0
$628$	28.5787	+	26.5171i	1.14041	+	1.05815i
$629$	−4.20902	−	5.27795i	−0.167825	−	0.210446i
$630$		0			0
$631$	−24.1060	+	30.2280i	−0.959646	+	1.20336i	0.0194192	+	0.999811i	$0.493818\pi$
$631$	−24.1060	+	30.2280i	−0.959646	+	1.20336i	−0.979065	+	0.203547i	$0.934753\pi$
$632$	3.47506	−	0.523782i	0.138231	−	0.0208349i
$633$		0			0
$634$	−4.86575	+	12.3977i	−0.193244	+	0.492376i
$635$	−2.99817	−	0.924813i	−0.118979	−	0.0367001i
$636$		0			0
$637$	−5.13990	+	22.3881i	−0.203650	+	0.887049i
$638$	39.0089			1.54438
$639$		0			0
$640$	−1.00138	+	2.55147i	−0.0395829	+	0.100856i
$641$	−19.5601	−	13.3358i	−0.772577	−	0.526734i	0.111675	−	0.993745i	$-0.464379\pi$
$641$	−19.5601	−	13.3358i	−0.772577	−	0.526734i	−0.884252	+	0.467011i	$0.845331\pi$
$642$		0			0
$643$	9.00035	−	11.2861i	0.354939	−	0.445080i	−0.572021	−	0.820239i	$-0.693841\pi$
$643$	9.00035	−	11.2861i	0.354939	−	0.445080i	0.926960	+	0.375159i	$0.122412\pi$
$644$	−18.0613	+	14.3846i	−0.711714	+	0.566833i
$645$		0			0
$646$	−14.5675	−	13.5167i	−0.573151	−	0.531807i
$647$	10.2517	+	1.54519i	0.403035	+	0.0607477i	0.347432	−	0.937705i	$-0.387054\pi$
$647$	10.2517	+	1.54519i	0.403035	+	0.0607477i	0.0556030	+	0.998453i	$0.482292\pi$
$648$		0			0
$649$	−22.5566	+	15.3788i	−0.885423	+	0.603671i
$650$	7.59186	+	33.2621i	0.297777	+	1.30465i
$651$		0			0
$652$	−5.90304	+	25.8629i	−0.231181	+	1.01287i
$653$	−3.25186	−	8.28561i	−0.127255	−	0.324241i	0.853020	−	0.521878i	$-0.174768\pi$
$653$	−3.25186	−	8.28561i	−0.127255	−	0.324241i	−0.980275	+	0.197637i	$0.936673\pi$
$654$		0			0
$655$	0.110367	+	0.191162i	0.00431241	+	0.00746932i
$656$	15.6759	−	27.1515i	0.612041	−	1.06009i
$657$		0			0
$658$	5.19612	+	5.60723i	0.202566	+	0.218593i
$659$	−21.5138	+	10.3605i	−0.838058	+	0.403587i	−0.803131	−	0.595802i	$-0.796834\pi$
$659$	−21.5138	+	10.3605i	−0.838058	+	0.403587i	−0.0349270	+	0.999390i	$0.511120\pi$
$660$		0			0
$661$	9.02784	−	2.78472i	0.351142	−	0.108313i	−0.114166	−	0.993462i	$-0.536420\pi$
$661$	9.02784	−	2.78472i	0.351142	−	0.108313i	0.465308	+	0.885149i	$0.345943\pi$
$662$	−27.0635	+	8.34798i	−1.05185	+	0.324454i
$663$		0			0
$664$	12.4954	−	6.01746i	0.484915	−	0.233523i
$665$	−1.86134	+	2.72636i	−0.0721798	+	0.105724i
$666$		0			0
$667$	−11.2064	+	19.4100i	−0.433913	+	0.751559i
$668$	−17.2930	−	29.9523i	−0.669085	−	1.15889i
$669$		0			0
$670$	−2.08090	−	5.30205i	−0.0803922	−	0.204836i
$671$	−3.26345	+	14.2981i	−0.125984	+	0.551972i
$672$		0			0
$673$	2.50956	+	10.9951i	0.0967365	+	0.423830i	0.999986	−	0.00528540i	$-0.00168240\pi$
$673$	2.50956	+	10.9951i	0.0967365	+	0.423830i	−0.903250	+	0.429116i	$0.858825\pi$
$674$	−24.1111	+	16.4387i	−0.928727	+	0.633195i
$675$		0			0
$676$	5.54510	+	0.835790i	0.213273	+	0.0321458i
$677$	−14.0810	−	13.0653i	−0.541179	−	0.502140i	0.361549	−	0.932353i	$-0.382248\pi$
$677$	−14.0810	−	13.0653i	−0.541179	−	0.502140i	−0.902727	+	0.430213i	$0.858439\pi$
$678$		0			0
$679$	−7.21969	−	1.65268i	−0.277066	−	0.0634239i
$680$	−0.538595	+	0.675376i	−0.0206542	+	0.0258995i
$681$		0			0
$682$	−0.429672	−	0.292945i	−0.0164530	−	0.0112174i
$683$	−13.9299	+	35.4927i	−0.533011	+	1.35809i	0.370223	+	0.928943i	$0.379281\pi$
$683$	−13.9299	+	35.4927i	−0.533011	+	1.35809i	−0.903234	+	0.429147i	$0.858814\pi$
$684$		0			0
$685$	−4.10966			−0.157022
$686$	−22.1007	−	32.5489i	−0.843807	−	1.24272i
$687$		0			0
$688$	−8.76370	−	2.70324i	−0.334113	−	0.103060i
$689$	1.04842	−	2.67133i	0.0399416	−	0.101770i
$690$		0			0
$691$	51.1593	−	7.71103i	1.94619	−	0.293341i	0.946614	−	0.322369i	$-0.104479\pi$
$691$	51.1593	−	7.71103i	1.94619	−	0.293341i	0.999579	+	0.0290280i	$0.00924119\pi$
$692$	−13.8059	+	17.3121i	−0.524822	+	0.658106i
$693$		0			0
$694$	33.3548	+	41.8256i	1.26613	+	1.58768i
$695$	−0.484514	−	0.449563i	−0.0183787	−	0.0170529i
$696$		0			0
$697$	20.6673	−	19.1764i	0.782829	−	0.726359i
$698$	−5.85378	+	3.99104i	−0.221569	+	0.151063i
$699$		0			0
$700$	−28.1678	−	16.2866i	−1.06464	−	0.615574i
$701$	4.09866	−	17.9574i	0.154804	−	0.678242i	−0.836645	−	0.547746i	$-0.815486\pi$
$701$	4.09866	−	17.9574i	0.154804	−	0.678242i	0.991449	−	0.130496i	$-0.0416569\pi$
$702$		0			0
$703$	0.793701	+	10.5912i	0.0299350	+	0.399455i
$704$	16.2785	+	28.1951i	0.613518	+	1.06264i
$705$		0			0
$706$	−56.2452	−	27.0863i	−2.11682	−	1.01941i
$707$	25.7252	−	37.6805i	0.967496	−	1.41712i
$708$		0			0
$709$	−2.40155	+	32.0465i	−0.0901922	+	1.20353i	0.750073	+	0.661356i	$0.230019\pi$
$709$	−2.40155	+	32.0465i	−0.0901922	+	1.20353i	−0.840265	+	0.542176i	$0.817601\pi$
$710$	−5.32176	+	1.64155i	−0.199722	+	0.0616062i
$711$		0			0
$712$	−1.27422	+	17.0032i	−0.0477533	+	0.637223i
$713$	0.269198	−	0.129639i	0.0100815	−	0.00485501i
$714$		0			0
$715$	−2.73619	−	1.31768i	−0.102328	−	0.0492785i
$716$	5.88123	−	10.1866i	0.219792	−	0.380691i
$717$		0			0
$718$	0.545922	+	7.28482i	0.0203736	+	0.271867i
$719$	−14.3440	−	36.5479i	−0.534940	−	1.36301i	−0.901568	−	0.432638i	$-0.857583\pi$
$719$	−14.3440	−	36.5479i	−0.534940	−	1.36301i	0.366627	−	0.930368i	$-0.380512\pi$
$720$		0			0
$721$	−26.2521	−	1.98411i	−0.977677	−	0.0738920i
$722$	−2.02428	−	8.86894i	−0.0753358	−	0.330068i
$723$		0			0
$724$	40.0869	−	37.1952i	1.48982	−	1.38235i
$725$	−31.2308	−	4.70729i	−1.15988	−	0.174824i
$726$		0			0
$727$	12.2676	+	15.3830i	0.454979	+	0.570526i	0.955422	−	0.295244i	$-0.0954009\pi$
$727$	12.2676	+	15.3830i	0.454979	+	0.570526i	−0.500443	+	0.865770i	$0.666829\pi$
$728$	7.39741	−	5.89155i	0.274166	−	0.218355i
$729$		0			0
$730$	6.57014	−	0.990289i	0.243172	−	0.0366522i
$731$	−6.81420	−	4.64585i	−0.252032	−	0.171833i
$732$		0			0
$733$	−19.7377	−	6.08826i	−0.729027	−	0.224875i	−0.0920463	−	0.995755i	$-0.529341\pi$
$733$	−19.7377	−	6.08826i	−0.729027	−	0.224875i	−0.636981	+	0.770880i	$0.719817\pi$
$734$	54.6680			2.01783
$735$		0			0
$736$	−27.5722			−1.01633
$737$	−22.4163	−	6.91452i	−0.825716	−	0.254700i
$738$		0			0
$739$	0.389313	+	0.265429i	0.0143211	+	0.00976398i	0.570459	−	0.821326i	$-0.306765\pi$
$739$	0.389313	+	0.265429i	0.0143211	+	0.00976398i	−0.556138	+	0.831090i	$0.687718\pi$
$740$	2.23723	−	0.337208i	0.0822421	−	0.0123960i
$741$		0			0
$742$	2.12977	+	4.42972i	0.0781863	+	0.162620i
$743$	1.40178	+	1.75778i	0.0514265	+	0.0644868i	0.806880	−	0.590716i	$-0.201155\pi$
$743$	1.40178	+	1.75778i	0.0514265	+	0.0644868i	−0.755453	+	0.655203i	$0.772583\pi$
$744$		0			0
$745$	−0.336011	−	0.0506455i	−0.0123105	−	0.00185551i
$746$	−16.3544	+	15.1747i	−0.598779	+	0.555585i
$747$		0			0
$748$	3.87969	+	16.9980i	0.141855	+	0.621509i
$749$	−18.6062	−	27.3276i	−0.679856	−	0.998529i
$750$		0			0
$751$	10.4904	+	26.7292i	0.382802	+	0.975362i	0.984302	+	0.176490i	$0.0564744\pi$
$751$	10.4904	+	26.7292i	0.382802	+	0.975362i	−0.601501	+	0.798872i	$0.705430\pi$
$752$	0.275619	+	3.67788i	0.0100508	+	0.134118i
$753$		0			0
$754$	22.4927	−	38.9585i	0.819135	−	1.41878i
$755$	6.11647	+	2.94553i	0.222601	+	0.107199i
$756$		0			0
$757$	−33.2219	+	15.9988i	−1.20747	+	0.581487i	−0.925796	−	0.378022i	$-0.876604\pi$
$757$	−33.2219	+	15.9988i	−1.20747	+	0.581487i	−0.281675	+	0.959510i	$0.590890\pi$
$758$	−4.34145	+	57.9327i	−0.157689	+	2.10421i
$759$		0			0
$760$	1.29869	−	0.400593i	0.0471084	−	0.0145310i
$761$	1.07171	−	14.3009i	0.0388494	−	0.518409i	−0.943502	−	0.331366i	$-0.892491\pi$
$761$	1.07171	−	14.3009i	0.0388494	−	0.518409i	0.982352	−	0.187043i	$-0.0598904\pi$
$762$		0			0
$763$	34.3809	−	19.8207i	1.24467	−	0.717557i
$764$	43.0030	+	20.7092i	1.55580	+	0.749231i
$765$		0			0
$766$	−9.31129	−	16.1276i	−0.336431	−	0.582715i
$767$	2.35272	+	31.3948i	0.0849517	+	1.13360i
$768$		0			0
$769$	3.96978	−	17.3927i	0.143154	−	0.627198i	−0.851537	−	0.524294i	$-0.824329\pi$
$769$	3.96978	−	17.3927i	0.143154	−	0.627198i	0.994691	−	0.102904i	$-0.0328136\pi$
$770$	4.84320	−	1.89726i	0.174537	−	0.0683726i
$771$		0			0
$772$	44.2757	−	30.1867i	1.59352	−	1.08644i
$773$	19.1327	−	17.7525i	0.688155	−	0.638514i	−0.256514	−	0.966541i	$-0.582574\pi$
$773$	19.1327	−	17.7525i	0.688155	−	0.638514i	0.944669	+	0.328026i	$0.106383\pi$
$774$		0			0
$775$	0.308647	+	0.286383i	0.0110869	+	0.0102872i
$776$	1.90114	+	2.38395i	0.0682469	+	0.0855789i
$777$		0			0
$778$	−6.51821	+	8.17358i	−0.233689	+	0.293037i
$779$	−43.8611	+	6.61100i	−1.57149	+	0.236864i
$780$		0			0
$781$	−8.37989	+	21.3516i	−0.299856	+	0.764021i
$782$	−17.1914	−	5.30286i	−0.614765	−	0.189630i
$783$		0			0
$784$	1.44253	−	18.9263i	0.0515190	−	0.675938i
$785$	5.04611			0.180103
$786$		0			0
$787$	−3.01445	+	7.68069i	−0.107454	+	0.273787i	−0.974480	−	0.224475i	$-0.927933\pi$
$787$	−3.01445	+	7.68069i	−0.107454	+	0.273787i	0.867026	+	0.498262i	$0.166028\pi$
$788$	45.4844	+	31.0107i	1.62032	+	1.10471i
$789$		0			0
$790$	1.38984	−	1.74280i	0.0494482	−	0.0620061i
$791$	−6.09996	+	12.6461i	−0.216890	+	0.449644i
$792$		0			0
$793$	12.3979	+	11.5036i	0.440262	+	0.408503i
$794$	65.5693	+	9.88299i	2.32697	+	0.350734i
$795$		0			0
$796$	−50.8171	+	34.6465i	−1.80116	+	1.22801i
$797$	3.41202	+	14.9491i	0.120860	+	0.529523i	0.998719	+	0.0506031i	$0.0161143\pi$
$797$	3.41202	+	14.9491i	0.120860	+	0.529523i	−0.877859	+	0.478920i	$0.841029\pi$
$798$		0			0
$799$	−0.738023	+	3.23349i	−0.0261094	+	0.114393i
$800$	−14.1950	−	36.1683i	−0.501870	−	1.27874i
$801$		0			0
$802$	−15.5855	−	26.9948i	−0.550342	−	0.953220i
$803$	13.6827	−	23.6991i	0.482851	−	0.836322i
$804$		0			0
$805$	−0.447303	+	2.95491i	−0.0157654	+	0.104147i
$806$	−0.540316	+	0.260203i	−0.0190318	+	0.00916524i
$807$		0			0
$808$	−17.9489	+	5.53651i	−0.631440	+	0.194774i
$809$	39.2060	−	12.0934i	1.37841	−	0.425183i	0.485035	−	0.874495i	$-0.338807\pi$
$809$	39.2060	−	12.0934i	1.37841	−	0.425183i	0.893375	+	0.449312i	$0.148331\pi$
$810$		0			0
$811$	36.8525	−	17.7472i	1.29407	−	0.623189i	0.345099	−	0.938566i	$-0.387845\pi$
$811$	36.8525	−	17.7472i	1.29407	−	0.623189i	0.948967	+	0.315377i	$0.102131\pi$
$812$	12.6195	+	41.0038i	0.442856	+	1.43895i
$813$		0			0
$814$	8.36755	−	14.4930i	0.293282	−	0.507980i
$815$	1.71682	+	2.97361i	0.0601374	+	0.104161i
$816$		0			0
$817$	4.74042	+	12.0784i	0.165846	+	0.422570i
$818$	−9.00436	+	39.4507i	−0.314830	+	1.37936i
$819$		0			0
$820$	2.10259	+	9.21206i	0.0734258	+	0.321699i
$821$	−15.7043	+	10.7070i	−0.548084	+	0.373677i	−0.805475	−	0.592630i	$-0.798090\pi$
$821$	−15.7043	+	10.7070i	−0.548084	+	0.373677i	0.257391	+	0.966307i	$0.417137\pi$
$822$		0			0
$823$	5.37034	+	0.809449i	0.187198	+	0.0282156i	0.241972	−	0.970283i	$-0.422206\pi$
$823$	5.37034	+	0.809449i	0.187198	+	0.0282156i	−0.0547739	+	0.998499i	$0.517444\pi$
$824$	7.94530	+	7.37216i	0.276787	+	0.256821i
$825$		0			0
$826$	−42.1370	−	33.6470i	−1.46613	−	1.17073i
$827$	25.6457	−	32.1586i	0.891787	−	1.11827i	−0.100578	−	0.994929i	$-0.532069\pi$
$827$	25.6457	−	32.1586i	0.891787	−	1.11827i	0.992365	−	0.123336i	$-0.0393593\pi$
$828$		0			0
$829$	45.9019	+	31.2954i	1.59424	+	1.08693i	0.945354	+	0.326047i	$0.105717\pi$
$829$	45.9019	+	31.2954i	1.59424	+	1.08693i	0.648885	+	0.760887i	$0.275236\pi$
$830$	3.21390	−	8.18888i	0.111556	−	0.284240i
$831$		0			0
$832$	37.5449			1.30163
$833$	6.25621	−	15.8812i	0.216765	−	0.550250i
$834$		0			0
$835$	−4.27771	−	1.31950i	−0.148036	−	0.0456632i
$836$	10.0215	−	25.5344i	0.346601	−	0.883126i
$837$		0			0
$838$	60.3683	−	9.09905i	2.08539	−	0.314322i
$839$	16.4697	−	20.6524i	0.568597	−	0.712999i	−0.411524	−	0.911399i	$-0.635003\pi$
$839$	16.4697	−	20.6524i	0.568597	−	0.712999i	0.980121	+	0.198400i	$0.0635747\pi$
$840$		0			0
$841$	7.88356	+	9.88567i	0.271847	+	0.340885i
$842$	6.44535	+	5.98041i	0.222121	+	0.206099i
$843$		0			0
$844$	−9.34086	+	8.66705i	−0.321526	+	0.298332i
$845$	0.599711	−	0.408876i	0.0206307	−	0.0140658i
$846$		0			0
$847$	−2.26845	+	7.33756i	−0.0779448	+	0.252122i
$848$	−0.527666	+	2.31186i	−0.0181201	+	0.0793895i
$849$		0			0
$850$	−1.89457	−	25.2813i	−0.0649832	−	0.867140i
$851$	4.80761	+	8.32702i	0.164803	+	0.285447i
$852$		0			0
$853$	−29.7401	−	14.3221i	−1.01828	−	0.490378i	−0.151178	−	0.988507i	$-0.548307\pi$
$853$	−29.7401	−	14.3221i	−1.01828	−	0.490378i	−0.867103	+	0.498128i	$0.834021\pi$
$854$	−28.8877	+	2.14637i	−0.988518	+	0.0734471i
$855$		0			0
$856$	−1.01713	+	13.5727i	−0.0347650	+	0.463906i
$857$	−4.88246	+	1.50604i	−0.166782	+	0.0514453i	−0.377021	−	0.926205i	$-0.623052\pi$
$857$	−4.88246	+	1.50604i	−0.166782	+	0.0514453i	0.210240	+	0.977650i	$0.432576\pi$
$858$		0			0
$859$	−0.401674	+	5.35997i	−0.0137050	+	0.182880i	0.986150	+	0.165855i	$0.0530384\pi$
$859$	−0.401674	+	5.35997i	−0.0137050	+	0.182880i	−0.999855	+	0.0170247i	$0.994581\pi$
$860$	2.49032	−	1.19928i	0.0849192	−	0.0408949i
$861$		0			0
$862$	−56.4134	−	27.1673i	−1.92145	−	0.925321i
$863$	−19.7520	+	34.2116i	−0.672368	+	1.16457i	0.304863	+	0.952396i	$0.401389\pi$
$863$	−19.7520	+	34.2116i	−0.672368	+	1.16457i	−0.977231	+	0.212179i	$0.931944\pi$
$864$		0			0
$865$	0.214180	+	2.85804i	0.00728235	+	0.0971762i
$866$	8.52103	+	21.7112i	0.289556	+	0.737778i
$867$		0			0
$868$	0.168927	−	0.546413i	0.00573374	−	0.0185465i
$869$	−2.04293	−	8.95067i	−0.0693017	−	0.303631i
$870$		0			0
$871$	−19.8309	+	18.4004i	−0.671945	+	0.623473i
$872$	−16.1557	−	2.43507i	−0.547100	−	0.0824620i
$873$		0			0
$874$	17.6477	+	22.1295i	0.596941	+	0.748541i
$875$	−8.30164	+	1.88924i	−0.280647	+	0.0638680i
$876$		0			0
$877$	17.5832	−	2.65024i	0.593742	−	0.0894922i	0.154704	−	0.987961i	$-0.450558\pi$
$877$	17.5832	−	2.65024i	0.593742	−	0.0894922i	0.439038	+	0.898469i	$0.355319\pi$
$878$	11.5226	+	7.85597i	0.388868	+	0.265126i
$879$		0			0
$880$	2.39802	+	0.739691i	0.0808372	+	0.0249350i
$881$	−11.7955			−0.397399			−0.198700	−	0.980060i	$-0.563672\pi$
$881$	−11.7955			−0.397399			−0.198700	+	0.980060i	$0.563672\pi$
$882$		0			0
$883$	8.35689			0.281232			0.140616	−	0.990064i	$-0.455092\pi$
$883$	8.35689			0.281232			0.140616	+	0.990064i	$0.455092\pi$
$884$	19.2131	+	5.92644i	0.646205	+	0.199328i
$885$		0			0
$886$	−46.9007	−	31.9764i	−1.57566	−	1.07427i
$887$	22.5503	−	3.39890i	0.757163	−	0.114124i	0.240895	−	0.970551i	$-0.422559\pi$
$887$	22.5503	−	3.39890i	0.757163	−	0.114124i	0.516268	+	0.856427i	$0.327321\pi$
$888$		0			0
$889$	−19.9451	−	15.9265i	−0.668938	−	0.534156i
$890$	6.74328	+	8.45581i	0.226035	+	0.283439i
$891$		0			0
$892$	−3.29256	−	0.496273i	−0.110243	−	0.0166165i
$893$	3.82510	−	3.54917i	0.128002	−	0.118769i
$894$		0			0
$895$	−0.338780	−	1.48429i	−0.0113242	−	0.0496144i
$896$	−15.1764	+	16.3354i	−0.507007	+	0.545727i
$897$		0			0
$898$	13.0616	+	33.2804i	0.435871	+	1.11058i
$899$	−0.0414875	−	0.553612i	−0.00138369	−	0.0184640i
$900$		0			0
$901$	−1.06621	+	1.84674i	−0.0355207	+	0.0615237i
$902$	62.9701	+	30.3248i	2.09668	+	1.00971i
$903$		0			0
$904$	5.20794	−	2.50801i	0.173213	−	0.0834152i
$905$	0.528946	−	7.05830i	0.0175828	−	0.234626i
$906$		0			0
$907$	44.4113	−	13.6991i	1.47465	−	0.454870i	0.549832	−	0.835275i	$-0.314692\pi$
$907$	44.4113	−	13.6991i	1.47465	−	0.454870i	0.924820	+	0.380406i	$0.124216\pi$
$908$	4.45712	−	59.4762i	0.147915	−	1.97379i
$909$		0			0
$910$	0.897797	−	5.93090i	0.0297617	−	0.196608i
$911$	−4.50081	−	2.16748i	−0.149119	−	0.0718117i	0.357836	−	0.933784i	$-0.383515\pi$
$911$	−4.50081	−	2.16748i	−0.149119	−	0.0718117i	−0.506955	+	0.861973i	$0.669229\pi$
$912$		0			0
$913$	−18.1156	−	31.3771i	−0.599537	−	1.03843i
$914$	−0.827346	−	11.0402i	−0.0273662	−	0.365176i
$915$		0			0
$916$	15.5564	−	68.1571i	0.513998	−	2.25197i
$917$	0.266499	+	1.77577i	0.00880058	+	0.0586410i
$918$		0			0
$919$	−21.9031	+	14.9333i	−0.722516	+	0.492603i	−0.867879	−	0.496775i	$-0.834517\pi$
$919$	−21.9031	+	14.9333i	−0.722516	+	0.492603i	0.145363	+	0.989378i	$0.453565\pi$
$920$	0.901933	−	0.836871i	0.0297358	−	0.0275908i
$921$		0			0
$922$	−17.9748	−	16.6781i	−0.591967	−	0.549266i
$923$	16.4921	+	20.6805i	0.542844	+	0.680705i
$924$		0			0
$925$	−8.44801	+	10.5935i	−0.277769	+	0.348311i
$926$	−3.33954	+	0.503354i	−0.109744	+	0.0165412i
$927$		0			0
$928$	−18.7167	+	47.6895i	−0.614407	+	1.56548i
$929$	43.9184	+	13.5470i	1.44092	+	0.444464i	0.914091	−	0.405510i	$-0.132906\pi$
$929$	43.9184	+	13.5470i	1.44092	+	0.444464i	0.526825	+	0.849974i	$0.323382\pi$
$930$		0			0
$931$	−22.2075	+	15.0995i	−0.727821	+	0.494865i
$932$	54.1651			1.77424
$933$		0			0
$934$	19.7169	−	50.2378i	0.645156	−	1.64383i
$935$	1.86458	+	1.27125i	0.0609782	+	0.0415742i
$936$		0			0
$937$	−37.1156	+	46.5415i	−1.21251	+	1.52044i	−0.423713	+	0.905797i	$0.639273\pi$
$937$	−37.1156	+	46.5415i	−1.21251	+	1.52044i	−0.788801	+	0.614648i	$0.789298\pi$
$938$	0.0294615	−	46.3344i	0.000961952	−	1.51287i
$939$		0			0
$940$	−0.814835	−	0.756056i	−0.0265770	−	0.0246598i
$941$	38.5011	+	5.80310i	1.25510	+	0.189176i	0.742731	−	0.669590i	$-0.233530\pi$
$941$	38.5011	+	5.80310i	1.25510	+	0.189176i	0.512368	+	0.858766i	$0.328768\pi$
$942$		0			0
$943$	−33.1788	+	22.6209i	−1.08045	+	0.736639i
$944$	−5.78891	−	25.3629i	−0.188413	−	0.825491i
$945$		0			0
$946$	4.54942	−	19.9323i	0.147915	−	0.648056i
$947$	−4.67880	−	11.9214i	−0.152041	−	0.387393i	0.834478	−	0.551041i	$-0.185769\pi$
$947$	−4.67880	−	11.9214i	−0.152041	−	0.387393i	−0.986519	+	0.163648i	$0.947674\pi$
$948$		0			0
$949$	−15.7789	−	27.3299i	−0.512206	−	0.887166i
$950$	−19.9432	+	34.5426i	−0.647042	+	1.12071i
$951$		0			0
$952$	−6.08799	+	3.50974i	−0.197313	+	0.113751i
$953$	−1.53491	+	0.739176i	−0.0497208	+	0.0239443i	−0.458579	−	0.888654i	$-0.651641\pi$
$953$	−1.53491	+	0.739176i	−0.0497208	+	0.0239443i	0.408858	+	0.912598i	$0.365927\pi$
$954$		0			0
$955$	5.90340	−	1.82096i	0.191029	−	0.0589248i
$956$	−48.4596	+	14.9478i	−1.56730	+	0.483447i
$957$		0			0
$958$	−49.8983	+	24.0297i	−1.61214	+	0.776365i
$959$	−31.1128	−	12.2337i	−1.00469	−	0.395047i
$960$		0			0
$961$	15.4963	−	26.8404i	0.499881	−	0.865819i
$962$	−9.64951	−	16.7134i	−0.311113	−	0.538863i
$963$		0			0
$964$	−16.0288	−	40.8408i	−0.516254	−	1.31539i
$965$	1.54341	−	6.76210i	0.0496840	−	0.217680i
$966$		0			0
$967$	−9.29266	−	40.7138i	−0.298832	−	1.30927i	−0.871869	−	0.489739i	$-0.837092\pi$
$967$	−9.29266	−	40.7138i	−0.298832	−	1.30927i	0.573037	−	0.819529i	$-0.305765\pi$
$968$	2.61249	−	1.78116i	0.0839685	−	0.0572487i
$969$		0			0
$970$	1.91250	+	0.288262i	0.0614065	+	0.00925554i
$971$	−24.4835	−	22.7173i	−0.785712	−	0.729034i	0.181393	−	0.983411i	$-0.441939\pi$
$971$	−24.4835	−	22.7173i	−0.785712	−	0.729034i	−0.967105	+	0.254377i	$0.918130\pi$
$972$		0			0
$973$	−2.32982	−	4.84580i	−0.0746906	−	0.155349i
$974$	−14.5869	+	18.2914i	−0.467394	+	0.586094i
$975$		0			0
$976$	−11.5470	−	7.87262i	−0.369611	−	0.251996i
$977$	−18.9870	+	48.3782i	−0.607449	+	1.54775i	0.213615	+	0.976918i	$0.431476\pi$
$977$	−18.9870	+	48.3782i	−0.607449	+	1.54775i	−0.821064	+	0.570837i	$0.806619\pi$
$978$		0			0
$979$	44.5441			1.42363
$980$	3.56107	+	4.47711i	0.113754	+	0.143016i
$981$		0			0
$982$	−75.6335	−	23.3298i	−2.41356	−	0.744485i
$983$	−4.52781	+	11.5367i	−0.144415	+	0.367963i	−0.984719	−	0.174153i	$-0.944281\pi$
$983$	−4.52781	+	11.5367i	−0.144415	+	0.367963i	0.840304	+	0.542116i	$0.182377\pi$
$984$		0			0
$985$	7.04576	−	1.06198i	0.224497	−	0.0338374i
$986$	−20.8419	+	26.1350i	−0.663742	+	0.832307i
$987$		0			0
$988$	−19.7229	−	24.7318i	−0.627470	−	0.786822i
$989$	8.61095	+	7.98980i	0.273812	+	0.254061i
$990$		0			0
$991$	−36.5400	+	33.9041i	−1.16073	+	1.07700i	−0.164850	+	0.986319i	$0.552714\pi$
$991$	−36.5400	+	33.9041i	−1.16073	+	1.07700i	−0.995880	+	0.0906813i	$0.971096\pi$
$992$	0.564292	−	0.384728i	0.0179163	−	0.0122151i
$993$		0			0
$994$	−45.1758	−	3.41435i	−1.43289	−	0.108297i
$995$	−1.77143	+	7.76114i	−0.0561581	+	0.246045i
$996$		0			0
$997$	1.76076	+	23.4957i	0.0557638	+	0.744116i	0.953078	+	0.302724i	$0.0978961\pi$
$997$	1.76076	+	23.4957i	0.0557638	+	0.744116i	−0.897314	+	0.441392i	$0.854485\pi$
$998$	−3.91738	−	6.78510i	−0.124002	−	0.214779i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.f.100.2	✓	72
3.2	odd	2	inner	441.2.bb.f.100.5	yes	72
49.25	even	21	inner	441.2.bb.f.172.2	yes	72
147.74	odd	42	inner	441.2.bb.f.172.5	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.bb.f.100.2	✓	72	1.1	even	1	trivial
441.2.bb.f.100.5	yes	72	3.2	odd	2	inner
441.2.bb.f.172.2	yes	72	49.25	even	21	inner
441.2.bb.f.172.5	yes	72	147.74	odd	42	inner

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.02995 - 0.626155i) q^{2} +(2.07613 + 1.41548i) q^{4} +(0.321603 - 0.0484738i) q^{5} +(2.57904 + 0.590375i) q^{7} +(-0.679131 - 0.851603i) q^{8} +O(q^{10})\)	\(q+(-2.02995 - 0.626155i) q^{2} +(2.07613 + 1.41548i) q^{4} +(0.321603 - 0.0484738i) q^{5} +(2.57904 + 0.590375i) q^{7} +(-0.679131 - 0.851603i) q^{8} +(-0.683188 - 0.102974i) q^{10} +(-2.08594 + 1.93547i) q^{11} +(0.730204 + 3.19923i) q^{13} +(-4.86565 - 2.81331i) q^{14} +(-0.990657 - 2.52415i) q^{16} +(-0.182224 - 2.43161i) q^{17} +(-1.91818 + 3.32239i) q^{19} +(0.736303 + 0.354585i) q^{20} +(5.44624 - 2.62277i) q^{22} +(-0.259545 + 3.46339i) q^{23} +(-4.67679 + 1.44260i) q^{25} +(0.520942 - 6.95149i) q^{26} +(4.51876 + 4.87628i) q^{28} +(5.81416 + 2.79995i) q^{29} +(-0.0430144 - 0.0745032i) q^{31} +(0.593266 + 7.91659i) q^{32} +(-1.15266 + 5.05014i) q^{34} +(0.858045 + 0.0648502i) q^{35} +(2.28743 - 1.55954i) q^{37} +(5.97413 - 5.54319i) q^{38} +(-0.259691 - 0.240958i) q^{40} +(7.20887 + 9.03964i) q^{41} +(2.10877 - 2.64431i) q^{43} +(-7.07029 + 1.06567i) q^{44} +(2.69548 - 6.86798i) q^{46} +(-1.29973 - 0.400913i) q^{47} +(6.30291 + 3.04520i) q^{49} +10.3969 q^{50} +(-3.01246 + 7.67561i) q^{52} +(-0.722552 - 0.492628i) q^{53} +(-0.577023 + 0.723564i) q^{55} +(-1.24874 - 2.59726i) q^{56} +(-10.0492 - 9.32432i) q^{58} +(9.48687 + 1.42992i) q^{59} +(4.25839 - 2.90332i) q^{61} +(0.0406664 + 0.178171i) q^{62} +(2.54594 - 11.1545i) q^{64} +(0.389915 + 0.993486i) q^{65} +(4.12197 + 7.13946i) q^{67} +(3.06358 - 5.30628i) q^{68} +(-1.70118 - 0.668911i) q^{70} +(7.26245 - 3.49741i) q^{71} +(-9.18963 + 2.83463i) q^{73} +(-5.61986 + 1.73350i) q^{74} +(-8.68517 + 4.18256i) q^{76} +(-6.52237 + 3.76016i) q^{77} +(-1.61319 + 2.79413i) q^{79} +(-0.440953 - 0.763753i) q^{80} +(-8.97340 - 22.8638i) q^{82} +(-2.83326 + 12.4133i) q^{83} +(-0.176473 - 0.773180i) q^{85} +(-5.93643 + 4.04739i) q^{86} +(3.06487 + 0.461955i) q^{88} +(-11.4751 - 10.6474i) q^{89} +(-0.00552043 + 8.68205i) q^{91} +(-5.44121 + 6.82307i) q^{92} +(2.38734 + 1.62766i) q^{94} +(-0.455844 + 1.16147i) q^{95} -2.79937 q^{97} +(-10.8878 - 10.1282i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 14 q^{4} - 28 q^{7}+O(q^{10}) \) 72 * q + 14 * q^4 - 28 * q^7	\( 72 q + 14 q^{4} - 28 q^{7} + 42 q^{13} - 26 q^{16} + 28 q^{19} + 8 q^{22} - 24 q^{25} - 28 q^{28} + 28 q^{31} + 28 q^{34} - 106 q^{37} + 70 q^{40} - 2 q^{43} + 60 q^{46} + 28 q^{49} + 70 q^{52} - 42 q^{55} + 56 q^{58} + 112 q^{61} + 38 q^{64} - 36 q^{67} - 14 q^{70} - 28 q^{73} + 56 q^{76} + 62 q^{79} - 70 q^{82} - 100 q^{85} - 262 q^{88} - 154 q^{91} - 294 q^{94} + 56 q^{97}+O(q^{100}) \) 72 * q + 14 * q^4 - 28 * q^7 + 42 * q^13 - 26 * q^16 + 28 * q^19 + 8 * q^22 - 24 * q^25 - 28 * q^28 + 28 * q^31 + 28 * q^34 - 106 * q^37 + 70 * q^40 - 2 * q^43 + 60 * q^46 + 28 * q^49 + 70 * q^52 - 42 * q^55 + 56 * q^58 + 112 * q^61 + 38 * q^64 - 36 * q^67 - 14 * q^70 - 28 * q^73 + 56 * q^76 + 62 * q^79 - 70 * q^82 - 100 * q^85 - 262 * q^88 - 154 * q^91 - 294 * q^94 + 56 * q^97

Introduction

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