LMFDB - Embedded newform 891.2.u.e.215.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(107,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 9]))

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

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

chi := DirichletCharacter("891.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.u (of order $30$, degree $8$, 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 297)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			215.5
Character	$\chi$	$=$	891.215
Dual form			891.2.u.e.431.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415331 - 0.461272i) q^{2} +(0.168785 + 1.60588i) q^{4} +(-2.77455 + 2.49822i) q^{5} +(-0.902304 + 2.02661i) q^{7} +(1.81517 + 1.31880i) q^{8} +O(q^{10})$	\(q+(0.415331 - 0.461272i) q^{2} +(0.168785 + 1.60588i) q^{4} +(-2.77455 + 2.49822i) q^{5} +(-0.902304 + 2.02661i) q^{7} +(1.81517 + 1.31880i) q^{8} +2.31741i q^{10} +(-2.46299 + 2.22119i) q^{11} +(1.28259 - 6.03412i) q^{13} +(0.560062 + 1.25792i) q^{14} +(-1.79666 + 0.381893i) q^{16} +(-0.0962825 + 0.296327i) q^{17} +(1.44540 - 1.98943i) q^{19} +(-4.48015 - 4.03394i) q^{20} +(0.00161348 + 2.05864i) q^{22} +(-7.72848 - 4.46204i) q^{23} +(0.934405 - 8.89027i) q^{25} +(-2.25067 - 3.09778i) q^{26} +(-3.40679 - 1.10693i) q^{28} +(6.03070 + 2.68504i) q^{29} +(1.05467 + 0.224178i) q^{31} +(-2.81373 + 4.87352i) q^{32} +(0.0966983 + 0.167486i) q^{34} +(-2.55942 - 7.87708i) q^{35} +(-3.01593 + 2.19120i) q^{37} +(-0.317346 - 1.49300i) q^{38} +(-8.33093 + 0.875616i) q^{40} +(-3.81695 + 1.69941i) q^{41} +(-4.12066 + 2.37906i) q^{43} +(-3.98268 - 3.58037i) q^{44} +(-5.26809 + 1.71171i) q^{46} +(1.43283 + 0.150597i) q^{47} +(1.39093 + 1.54478i) q^{49} +(-3.71275 - 4.12342i) q^{50} +(9.90657 + 1.04122i) q^{52} +(-5.61052 + 1.82297i) q^{53} +(1.28469 - 12.3159i) q^{55} +(-4.31052 + 2.48868i) q^{56} +(3.74327 - 1.66661i) q^{58} +(5.56375 - 0.584774i) q^{59} +(0.312919 + 1.47217i) q^{61} +(0.541446 - 0.393383i) q^{62} +(-0.0558176 - 0.171789i) q^{64} +(11.5159 + 19.9462i) q^{65} +(-1.39875 + 2.42271i) q^{67} +(-0.492117 - 0.104603i) q^{68} +(-4.69648 - 2.09101i) q^{70} +(-6.47873 - 2.10507i) q^{71} +(5.66251 + 7.79378i) q^{73} +(-0.241870 + 2.30124i) q^{74} +(3.43875 + 1.98536i) q^{76} +(-2.27911 - 6.99570i) q^{77} +(3.69731 + 3.32908i) q^{79} +(4.03089 - 5.54804i) q^{80} +(-0.801405 + 2.46647i) q^{82} +(-13.1020 + 2.78492i) q^{83} +(-0.473149 - 1.06271i) q^{85} +(-0.614042 + 2.88884i) q^{86} +(-7.40004 + 0.783640i) q^{88} +3.05090i q^{89} +(11.0715 + 8.04392i) q^{91} +(5.86106 - 13.1641i) q^{92} +(0.664567 - 0.598379i) q^{94} +(0.959676 + 9.13071i) q^{95} +(-9.84786 + 10.9372i) q^{97} +1.29026 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 8 q^{4}+O(q^{10}) $ 64 * q + 8 * q^4	$ 64 q + 8 q^{4} + 4 q^{16} - 36 q^{22} - 8 q^{25} - 200 q^{28} - 8 q^{31} + 64 q^{34} - 24 q^{37} + 60 q^{40} - 40 q^{46} - 100 q^{52} + 16 q^{55} - 24 q^{58} - 60 q^{61} + 72 q^{64} + 24 q^{67} - 8 q^{70} + 160 q^{73} + 60 q^{79} + 144 q^{82} + 20 q^{85} + 24 q^{88} + 48 q^{91} - 20 q^{94} + 24 q^{97}+O(q^{100}) $ 64 * q + 8 * q^4 + 4 * q^16 - 36 * q^22 - 8 * q^25 - 200 * q^28 - 8 * q^31 + 64 * q^34 - 24 * q^37 + 60 * q^40 - 40 * q^46 - 100 * q^52 + 16 * q^55 - 24 * q^58 - 60 * q^61 + 72 * q^64 + 24 * q^67 - 8 * q^70 + 160 * q^73 + 60 * q^79 + 144 * q^82 + 20 * q^85 + 24 * q^88 + 48 * q^91 - 20 * q^94 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.415331	−	0.461272i	0.293684	−	0.326169i	−0.578188	−	0.815904i	$-0.696240\pi$
$2$	0.415331	−	0.461272i	0.293684	−	0.326169i	0.871871	+	0.489735i	$0.162907\pi$
$3$		0			0
$3$		0			0
$4$	0.168785	+	1.60588i	0.0843925	+	0.802941i
$5$	−2.77455	+	2.49822i	−1.24082	+	1.11724i	−0.252060	+	0.967712i	$0.581108\pi$
$5$	−2.77455	+	2.49822i	−1.24082	+	1.11724i	−0.988758	+	0.149526i	$0.952225\pi$
$6$		0			0
$7$	−0.902304	+	2.02661i	−0.341039	+	0.765986i	0.658867	+	0.752259i	$0.271036\pi$
$7$	−0.902304	+	2.02661i	−0.341039	+	0.765986i	−0.999906	+	0.0137262i	$0.995631\pi$
$8$	1.81517	+	1.31880i	0.641759	+	0.466265i
$9$		0			0
$10$			2.31741i			0.732830i
$11$	−2.46299	+	2.22119i	−0.742620	+	0.669713i
$11$	−2.46299	+	2.22119i	−0.742620	+	0.669713i
$12$		0			0
$13$	1.28259	−	6.03412i	0.355727	−	1.67356i	−0.328663	−	0.944447i	$-0.606598\pi$
$13$	1.28259	−	6.03412i	0.355727	−	1.67356i	0.684390	−	0.729116i	$-0.260069\pi$
$14$	0.560062	+	1.25792i	0.149683	+	0.336193i
$15$		0			0
$16$	−1.79666	+	0.381893i	−0.449166	+	0.0954732i
$17$	−0.0962825	+	0.296327i	−0.0233519	+	0.0718699i	−0.962053	−	0.272861i	$-0.912030\pi$
$17$	−0.0962825	+	0.296327i	−0.0233519	+	0.0718699i	0.938701	+	0.344731i	$0.112030\pi$
$18$		0			0
$19$	1.44540	−	1.98943i	0.331598	−	0.456406i	−0.610366	−	0.792120i	$-0.708977\pi$
$19$	1.44540	−	1.98943i	0.331598	−	0.456406i	0.941964	+	0.335714i	$0.108977\pi$
$20$	−4.48015	−	4.03394i	−1.00179	−	0.902017i
$21$		0			0
$22$	0.00161348	+	2.05864i	0.000343995	+	0.438903i
$23$	−7.72848	−	4.46204i	−1.61150	−	0.930399i	−0.989023	−	0.147760i	$-0.952794\pi$
$23$	−7.72848	−	4.46204i	−1.61150	−	0.930399i	−0.622475	−	0.782639i	$-0.713873\pi$
$24$		0			0
$25$	0.934405	−	8.89027i	0.186881	−	1.77805i
$26$	−2.25067	−	3.09778i	−0.441393	−	0.607525i
$27$		0			0
$28$	−3.40679	−	1.10693i	−0.643822	−	0.209191i
$29$	6.03070	+	2.68504i	1.11987	+	0.498599i	0.881315	−	0.472529i	$-0.156659\pi$
$29$	6.03070	+	2.68504i	1.11987	+	0.498599i	0.238557	+	0.971128i	$0.423326\pi$
$30$		0			0
$31$	1.05467	+	0.224178i	0.189425	+	0.0402635i	0.301647	−	0.953420i	$-0.402464\pi$
$31$	1.05467	+	0.224178i	0.189425	+	0.0402635i	−0.112222	+	0.993683i	$0.535797\pi$
$32$	−2.81373	+	4.87352i	−0.497401	+	0.861524i
$33$		0			0
$34$	0.0966983	+	0.167486i	0.0165836	+	0.0287237i
$35$	−2.55942	−	7.87708i	−0.432621	−	1.33147i
$36$		0			0
$37$	−3.01593	+	2.19120i	−0.495815	+	0.360231i	−0.807416	−	0.589982i	$-0.799135\pi$
$37$	−3.01593	+	2.19120i	−0.495815	+	0.360231i	0.311601	+	0.950213i	$0.399135\pi$
$38$	−0.317346	−	1.49300i	−0.0514803	−	0.242196i
$39$		0			0
$40$	−8.33093	+	0.875616i	−1.31724	+	0.138447i
$41$	−3.81695	+	1.69941i	−0.596107	+	0.265404i	−0.682534	−	0.730854i	$-0.739122\pi$
$41$	−3.81695	+	1.69941i	−0.596107	+	0.265404i	0.0864265	+	0.996258i	$0.472455\pi$
$42$		0			0
$43$	−4.12066	+	2.37906i	−0.628394	+	0.362803i	−0.780130	−	0.625618i	$-0.784847\pi$
$43$	−4.12066	+	2.37906i	−0.628394	+	0.362803i	0.151736	+	0.988421i	$0.451514\pi$
$44$	−3.98268	−	3.58037i	−0.600412	−	0.539762i
$45$		0			0
$46$	−5.26809	+	1.71171i	−0.776738	+	0.252377i
$47$	1.43283	+	0.150597i	0.209000	+	0.0219668i	0.208450	−	0.978033i	$-0.433158\pi$
$47$	1.43283	+	0.150597i	0.209000	+	0.0219668i	0.000550354		1.00000i	$0.499825\pi$
$48$		0			0
$49$	1.39093	+	1.54478i	0.198704	+	0.220683i
$50$	−3.71275	−	4.12342i	−0.525062	−	0.583140i
$51$		0			0
$52$	9.90657	+	1.04122i	1.37379	+	0.144392i
$53$	−5.61052	+	1.82297i	−0.770664	+	0.250404i	−0.667849	−	0.744297i	$-0.732785\pi$
$53$	−5.61052	+	1.82297i	−0.770664	+	0.250404i	−0.102815	+	0.994701i	$0.532785\pi$
$54$		0			0
$55$	1.28469	−	12.3159i	0.173228	−	1.66067i
$56$	−4.31052	+	2.48868i	−0.576017	+	0.332564i
$57$		0			0
$58$	3.74327	−	1.66661i	0.491515	−	0.218837i
$59$	5.56375	−	0.584774i	0.724339	−	0.0761311i	0.264818	−	0.964298i	$-0.414688\pi$
$59$	5.56375	−	0.584774i	0.724339	−	0.0761311i	0.459520	+	0.888167i	$0.348021\pi$
$60$		0			0
$61$	0.312919	+	1.47217i	0.0400651	+	0.188492i	0.993629	−	0.112699i	$-0.0359495\pi$
$61$	0.312919	+	1.47217i	0.0400651	+	0.188492i	−0.953564	+	0.301190i	$0.902616\pi$
$62$	0.541446	−	0.393383i	0.0687637	−	0.0499597i
$63$		0			0
$64$	−0.0558176	−	0.171789i	−0.00697720	−	0.0214736i
$65$	11.5159	+	19.9462i	1.42838	+	2.47402i
$66$		0			0
$67$	−1.39875	+	2.42271i	−0.170885	+	0.295981i	−0.938729	−	0.344655i	$-0.887996\pi$
$67$	−1.39875	+	2.42271i	−0.170885	+	0.295981i	0.767845	+	0.640636i	$0.221329\pi$
$68$	−0.492117	−	0.104603i	−0.0596780	−	0.0126849i
$69$		0			0
$70$	−4.69648	−	2.09101i	−0.561337	−	0.249923i
$71$	−6.47873	−	2.10507i	−0.768884	−	0.249826i	−0.101797	−	0.994805i	$-0.532459\pi$
$71$	−6.47873	−	2.10507i	−0.768884	−	0.249826i	−0.667087	+	0.744980i	$0.732459\pi$
$72$		0			0
$73$	5.66251	+	7.79378i	0.662747	+	0.912193i	0.999568	−	0.0293753i	$-0.00935180\pi$
$73$	5.66251	+	7.79378i	0.662747	+	0.912193i	−0.336821	+	0.941569i	$0.609352\pi$
$74$	−0.241870	+	2.30124i	−0.0281168	+	0.267513i
$75$		0			0
$76$	3.43875	+	1.98536i	0.394452	+	0.227737i
$77$	−2.27911	−	6.99570i	−0.259728	−	0.797234i
$78$		0			0
$79$	3.69731	+	3.32908i	0.415980	+	0.374550i	0.850379	−	0.526170i	$-0.176373\pi$
$79$	3.69731	+	3.32908i	0.415980	+	0.374550i	−0.434399	+	0.900721i	$0.643039\pi$
$80$	4.03089	−	5.54804i	0.450667	−	0.620290i
$81$		0			0
$82$	−0.801405	+	2.46647i	−0.0885004	+	0.272376i
$83$	−13.1020	+	2.78492i	−1.43814	+	0.305685i	−0.860016	−	0.510267i	$-0.829547\pi$
$83$	−13.1020	+	2.78492i	−1.43814	+	0.305685i	−0.578119	+	0.815952i	$0.696213\pi$
$84$		0			0
$85$	−0.473149	−	1.06271i	−0.0513202	−	0.115267i
$86$	−0.614042	+	2.88884i	−0.0662139	+	0.311512i
$87$		0			0
$88$	−7.40004	+	0.783640i	−0.788847	+	0.0835363i
$89$			3.05090i			0.323394i	0.986840	+	0.161697i	$0.0516968\pi$
$89$			3.05090i			0.323394i	−0.986840	+	0.161697i	$0.948303\pi$
$90$		0			0
$91$	11.0715	+	8.04392i	1.16061	+	0.843231i
$92$	5.86106	−	13.1641i	0.611057	−	1.37246i
$93$		0			0
$94$	0.664567	−	0.598379i	0.0685448	−	0.0617181i
$95$	0.959676	+	9.13071i	0.0984607	+	0.936791i
$96$		0			0
$97$	−9.84786	+	10.9372i	−0.999898	+	1.11050i	−0.00602425	+	0.999982i	$0.501918\pi$
$97$	−9.84786	+	10.9372i	−0.999898	+	1.11050i	−0.993874	+	0.110518i	$0.964749\pi$
$98$	1.29026			0.130336
$99$		0			0
$100$	14.4344			1.44344
$101$	4.38534	−	4.87041i	0.436357	−	0.484624i	−0.484352	−	0.874873i	$-0.660944\pi$
$101$	4.38534	−	4.87041i	0.436357	−	0.484624i	0.920709	+	0.390249i	$0.127611\pi$
$102$		0			0
$103$	0.915875	+	8.71397i	0.0902438	+	0.858613i	0.942212	+	0.335018i	$0.108743\pi$
$103$	0.915875	+	8.71397i	0.0902438	+	0.858613i	−0.851968	+	0.523594i	$0.824591\pi$
$104$	10.2859	−	9.26146i	1.00862	−	0.908161i
$105$		0			0
$106$	−1.48934	+	3.34511i	−0.144657	+	0.324906i
$107$	0.618545	+	0.449399i	0.0597970	+	0.0434451i	0.617282	−	0.786742i	$-0.288234\pi$
$107$	0.618545	+	0.449399i	0.0597970	+	0.0434451i	−0.557485	+	0.830187i	$0.688234\pi$
$108$		0			0
$109$		−	4.39272i		−	0.420746i	−0.977621	−	0.210373i	$-0.932532\pi$
$109$		−	4.39272i		−	0.420746i	0.977621	−	0.210373i	$-0.0674678\pi$
$110$	−5.14740	−	5.70777i	−0.490786	−	0.544214i
$111$		0			0
$112$	0.847190	−	3.98572i	0.0800519	−	0.376615i
$113$	−2.44649	−	5.49492i	−0.230147	−	0.516918i	0.761148	−	0.648578i	$-0.224636\pi$
$113$	−2.44649	−	5.49492i	−0.230147	−	0.516918i	−0.991295	+	0.131660i	$0.957969\pi$
$114$		0			0
$115$	32.5902	−	6.92726i	3.03905	−	0.645971i
$116$	−3.29397	+	10.1378i	−0.305837	+	0.941269i
$117$		0			0
$118$	2.04106	−	2.80928i	0.187895	−	0.258615i
$119$	−0.513662	−	0.462504i	−0.0470874	−	0.0423976i
$120$		0			0
$121$	1.13266	−	10.9415i	0.102969	−	0.994685i
$122$	0.809034	+	0.467096i	0.0732465	+	0.0422889i
$123$		0			0
$124$	−0.181990	+	1.73152i	−0.0163432	+	0.155495i
$125$	8.64472	+	11.8984i	0.773207	+	1.06423i
$126$		0			0
$127$	−10.7264	−	3.48521i	−0.951811	−	0.309262i	−0.208360	−	0.978052i	$-0.566813\pi$
$127$	−10.7264	−	3.48521i	−0.951811	−	0.309262i	−0.743451	+	0.668790i	$0.766813\pi$
$128$	−10.3843	−	4.62338i	−0.917850	−	0.408653i
$129$		0			0
$130$	13.9835	+	2.97229i	1.22644	+	0.260687i
$131$	−8.59104	+	14.8801i	−0.750603	+	1.30008i	0.196928	+	0.980418i	$0.436903\pi$
$131$	−8.59104	+	14.8801i	−0.750603	+	1.30008i	−0.947531	+	0.319664i	$0.896430\pi$
$132$		0			0
$133$	2.72760	+	4.72433i	0.236513	+	0.409652i
$134$	0.536583	+	1.65143i	0.0463537	+	0.142662i
$135$		0			0
$136$	−0.565564	+	0.410906i	−0.0484967	+	0.0352349i
$137$	−0.282663	−	1.32982i	−0.0241495	−	0.113615i	0.964422	−	0.264368i	$-0.0851634\pi$
$137$	−0.282663	−	1.32982i	−0.0241495	−	0.113615i	−0.988571	+	0.150753i	$0.951830\pi$
$138$		0			0
$139$	−11.9976	+	1.26100i	−1.01762	+	0.106956i	−0.598623	−	0.801031i	$-0.704285\pi$
$139$	−11.9976	+	1.26100i	−1.01762	+	0.106956i	−0.418998	+	0.907987i	$0.637618\pi$
$140$	12.2177	−	5.43966i	1.03258	−	0.459735i
$141$		0			0
$142$	−3.66183	+	2.11416i	−0.307294	+	0.177416i
$143$	10.2439	+	17.7109i	0.856637	+	1.48106i
$144$		0			0
$145$	−23.4403	+	7.61622i	−1.94661	+	0.632492i
$146$	5.94687	+	0.625042i	0.492167	+	0.0517288i
$147$		0			0
$148$	−4.02785	−	4.47338i	−0.331087	−	0.367710i
$149$	9.78245	+	10.8645i	0.801410	+	0.890056i	0.995864	−	0.0908559i	$-0.0289603\pi$
$149$	9.78245	+	10.8645i	0.801410	+	0.890056i	−0.194454	+	0.980912i	$0.562294\pi$
$150$		0			0
$151$	2.76658	+	0.290779i	0.225141	+	0.0236633i	0.216427	−	0.976299i	$-0.430560\pi$
$151$	2.76658	+	0.290779i	0.225141	+	0.0236633i	0.00871382	+	0.999962i	$0.497226\pi$
$152$	5.24730	−	1.70495i	0.425613	−	0.138290i
$153$		0			0
$154$	−4.17351	−	1.85425i	−0.336311	−	0.149419i
$155$	−3.48629	+	2.01281i	−0.280026	+	0.161673i
$156$		0			0
$157$	−16.1730	+	7.20067i	−1.29074	+	0.574676i	−0.933246	−	0.359238i	$-0.883037\pi$
$157$	−16.1730	+	7.20067i	−1.29074	+	0.574676i	−0.357498	+	0.933914i	$0.616370\pi$
$158$	3.07122	−	0.322798i	0.244333	−	0.0256804i
$159$		0			0
$160$	−4.36828	−	20.5511i	−0.345343	−	1.62471i
$161$	16.0162	−	11.6365i	1.26226	−	0.917083i
$162$		0			0
$163$	0.454189	+	1.39785i	0.0355748	+	0.109488i	0.967267	−	0.253761i	$-0.0816675\pi$
$163$	0.454189	+	1.39785i	0.0355748	+	0.109488i	−0.931692	+	0.363249i	$0.881668\pi$
$164$	−3.37330	−	5.84273i	−0.263411	−	0.456241i
$165$		0			0
$166$	−4.15708	+	7.20027i	−0.322652	+	0.558849i
$167$	8.78864	+	1.86808i	0.680086	+	0.144557i	0.534987	−	0.844860i	$-0.320317\pi$
$167$	8.78864	+	1.86808i	0.680086	+	0.144557i	0.145099	+	0.989417i	$0.453650\pi$
$168$		0			0
$169$	−22.8894	−	10.1910i	−1.76073	−	0.783926i
$170$	−0.686712	−	0.223126i	−0.0526684	−	0.0171130i
$171$		0			0
$172$	−4.51600	−	6.21574i	−0.344342	−	0.473946i
$173$	0.689297	−	6.55822i	0.0524063	−	0.498612i	−0.936564	−	0.350497i	$-0.886013\pi$
$173$	0.689297	−	6.55822i	0.0524063	−	0.498612i	0.988970	−	0.148115i	$-0.0473207\pi$
$174$		0			0
$175$	17.1740	+	9.91540i	1.29823	+	0.749534i
$176$	3.57692	−	4.93132i	0.269620	−	0.371713i
$177$		0			0
$178$	1.40729	+	1.26713i	0.105481	+	0.0949756i
$179$	−0.750385	+	1.03282i	−0.0560864	+	0.0771963i	−0.836139	−	0.548518i	$-0.815192\pi$
$179$	−0.750385	+	1.03282i	−0.0560864	+	0.0771963i	0.780053	+	0.625714i	$0.215192\pi$
$180$		0			0
$181$	6.39068	−	19.6685i	0.475016	−	1.46195i	−0.370921	−	0.928664i	$-0.620958\pi$
$181$	6.39068	−	19.6685i	0.475016	−	1.46195i	0.845937	−	0.533283i	$-0.179042\pi$
$182$	8.30877	−	1.76608i	0.615887	−	0.130911i
$183$		0			0
$184$	−8.14396	−	18.2916i	−0.600381	−	1.34848i
$185$	2.89375	−	13.6140i	0.212753	−	1.00092i
$186$		0			0
$187$	−0.421054	−	0.943712i	−0.0307906	−	0.0690111i
$188$			2.32638i			0.169669i
$189$		0			0
$190$	4.61032	+	3.34960i	0.334468	+	0.243005i
$191$	2.73730	−	6.14809i	0.198064	−	0.444860i	−0.787021	−	0.616926i	$-0.788378\pi$
$191$	2.73730	−	6.14809i	0.198064	−	0.444860i	0.985085	+	0.172066i	$0.0550443\pi$
$192$		0			0
$193$	−11.7345	+	10.5658i	−0.844668	+	0.760542i	−0.972906	−	0.231201i	$-0.925734\pi$
$193$	−11.7345	+	10.5658i	−0.844668	+	0.760542i	0.128238	+	0.991743i	$0.459068\pi$
$194$	0.954881	+	9.08508i	0.0685564	+	0.652271i
$195$		0			0
$196$	−2.24597	+	2.49440i	−0.160427	+	0.178172i
$197$	2.09103			0.148980			0.0744900	−	0.997222i	$-0.476267\pi$
$197$	2.09103			0.148980			0.0744900	+	0.997222i	$0.476267\pi$
$198$		0			0
$199$	−3.76773			−0.267087			−0.133544	−	0.991043i	$-0.542636\pi$
$199$	−3.76773			−0.267087			−0.133544	+	0.991043i	$0.542636\pi$
$200$	13.4206	−	14.9051i	0.948978	−	1.05395i
$201$		0			0
$202$	−0.425217	−	4.04567i	−0.0299182	−	0.284652i
$203$	−10.8830	+	9.79913i	−0.763840	+	0.687764i
$204$		0			0
$205$	6.34481	−	14.2507i	0.443141	−	0.995311i
$206$	4.39990	+	3.19671i	0.306556	+	0.222726i
$207$		0			0
$208$			11.3311i			0.785670i
$209$	0.858871	+	8.11046i	0.0594093	+	0.561012i
$210$		0			0
$211$	2.26402	−	10.6514i	0.155862	−	0.733272i	−0.828905	−	0.559390i	$-0.811035\pi$
$211$	2.26402	−	10.6514i	0.155862	−	0.733272i	0.984766	−	0.173882i	$-0.0556312\pi$
$212$	−3.87444	−	8.70214i	−0.266098	−	0.597665i
$213$		0			0
$214$	0.464197	−	0.0986680i	0.0317318	−	0.00674481i
$215$	5.48956	−	16.8951i	0.374385	−	1.15224i
$216$		0			0
$217$	−1.40596	+	1.93513i	−0.0954425	+	0.131365i
$218$	−2.02624	−	1.82443i	−0.137234	−	0.123566i
$219$		0			0
$220$	19.9947	−	0.0156711i	1.34804	−	0.00105654i
$221$	1.66458	+	0.961046i	0.111972	+	0.0646470i
$222$		0			0
$223$	−1.18712	+	11.2947i	−0.0794953	+	0.756348i	0.880067	+	0.474850i	$0.157498\pi$
$223$	−1.18712	+	11.2947i	−0.0794953	+	0.756348i	−0.959562	+	0.281497i	$0.909169\pi$
$224$	−7.33787	−	10.0997i	−0.490282	−	0.674815i
$225$		0			0
$226$	−3.55076	−	1.15371i	−0.236193	−	0.0767437i
$227$	9.78741	+	4.35764i	0.649613	+	0.289226i	0.704967	−	0.709240i	$-0.250962\pi$
$227$	9.78741	+	4.35764i	0.649613	+	0.289226i	−0.0553535	+	0.998467i	$0.517629\pi$
$228$		0			0
$229$	19.2449	+	4.09063i	1.27174	+	0.270317i	0.793855	−	0.608107i	$-0.208071\pi$
$229$	19.2449	+	4.09063i	1.27174	+	0.270317i	0.477884	+	0.878423i	$0.341404\pi$
$230$	10.3404	−	17.9101i	0.681825	−	1.18095i
$231$		0			0
$232$	7.40571	+	12.8271i	0.486209	+	0.842138i
$233$	6.22888	+	19.1705i	0.408068	+	1.25590i	0.918306	+	0.395871i	$0.129557\pi$
$233$	6.22888	+	19.1705i	0.408068	+	1.25590i	−0.510238	+	0.860033i	$0.670443\pi$
$234$		0			0
$235$	−4.35170	+	3.16169i	−0.283874	+	0.206246i
$236$	1.87816	+	8.83603i	0.122258	+	0.575176i
$237$		0			0
$238$	−0.426680	+	0.0448459i	−0.0276576	+	0.00290693i
$239$	15.7116	−	6.99526i	1.01630	−	0.452486i	0.170143	−	0.985419i	$-0.445577\pi$
$239$	15.7116	−	6.99526i	1.01630	−	0.452486i	0.846157	+	0.532933i	$0.178910\pi$
$240$		0			0
$241$	−17.7792	+	10.2648i	−1.14526	+	0.661215i	−0.947727	−	0.319081i	$-0.896626\pi$
$241$	−17.7792	+	10.2648i	−1.14526	+	0.661215i	−0.197531	+	0.980297i	$0.563292\pi$
$242$	−4.57659	−	5.06683i	−0.294194	−	0.325708i
$243$		0			0
$244$	−2.31131	+	0.750990i	−0.147966	+	0.0480772i
$245$	−7.71841	−	0.811238i	−0.493111	−	0.0518281i
$246$		0			0
$247$	−10.1506	−	11.2734i	−0.645866	−	0.717307i
$248$	1.61877	+	1.79782i	0.102792	+	0.114162i
$249$		0			0
$250$	9.07884	+	0.954224i	0.574196	+	0.0603504i
$251$	6.04667	−	1.96468i	0.381662	−	0.124010i	−0.111901	−	0.993719i	$-0.535694\pi$
$251$	6.04667	−	1.96468i	0.381662	−	0.124010i	0.493563	+	0.869710i	$0.335694\pi$
$252$		0			0
$253$	28.9462	−	6.17642i	1.81983	−	0.388308i
$254$	−6.06263	+	3.50026i	−0.380403	+	0.219626i
$255$		0			0
$256$	−6.11553	+	2.72281i	−0.382221	+	0.170176i
$257$	13.7662	−	1.44689i	0.858713	−	0.0902544i	0.335071	−	0.942193i	$-0.391240\pi$
$257$	13.7662	−	1.44689i	0.858713	−	0.0902544i	0.523642	+	0.851939i	$0.324573\pi$
$258$		0			0
$259$	−1.71942	−	8.08923i	−0.106839	−	0.502640i
$260$	−30.0875	+	21.8598i	−1.86595	+	1.35569i
$261$		0			0
$262$	3.29566	+	10.1430i	0.203606	+	0.626636i
$263$	−7.71773	−	13.3675i	−0.475896	−	0.824275i	0.523723	−	0.851889i	$-0.324543\pi$
$263$	−7.71773	−	13.3675i	−0.475896	−	0.824275i	−0.999619	+	0.0276132i	$0.991209\pi$
$264$		0			0
$265$	11.0125	−	19.0742i	0.676493	−	1.17172i
$266$	3.31206	+	0.704000i	0.203075	+	0.0431650i
$267$		0			0
$268$	−4.12668	−	1.83732i	−0.252077	−	0.112232i
$269$	5.84229	+	1.89827i	0.356211	+	0.115740i	0.481655	−	0.876361i	$-0.340036\pi$
$269$	5.84229	+	1.89827i	0.356211	+	0.115740i	−0.125445	+	0.992101i	$0.540036\pi$
$270$		0			0
$271$	11.0715	+	15.2386i	0.672546	+	0.925680i	0.999815	−	0.0192514i	$-0.00612829\pi$
$271$	11.0715	+	15.2386i	0.672546	+	0.925680i	−0.327269	+	0.944931i	$0.606128\pi$
$272$	0.0598221	−	0.569170i	0.00362725	−	0.0345110i
$273$		0			0
$274$	−0.730810	−	0.421933i	−0.0441498	−	0.0254899i
$275$	17.4455	+	23.9722i	1.05200	+	1.44558i
$276$		0			0
$277$	−4.07581	−	3.66987i	−0.244891	−	0.220501i	0.537540	−	0.843239i	$-0.319354\pi$
$277$	−4.07581	−	3.66987i	−0.244891	−	0.220501i	−0.782431	+	0.622737i	$0.786021\pi$
$278$	−4.40130	+	6.05787i	−0.263973	+	0.363327i
$279$		0			0
$280$	5.74250	−	17.6736i	0.343180	−	1.05620i
$281$	25.5289	−	5.42633i	1.52293	−	0.323708i	0.630961	−	0.775814i	$-0.282661\pi$
$281$	25.5289	−	5.42633i	1.52293	−	0.323708i	0.891964	+	0.452107i	$0.149327\pi$
$282$		0			0
$283$	7.01448	+	15.7548i	0.416968	+	0.936525i	0.992892	+	0.119022i	$0.0379758\pi$
$283$	7.01448	+	15.7548i	0.416968	+	0.936525i	−0.575924	+	0.817503i	$0.695358\pi$
$284$	2.28698	−	10.7594i	0.135707	−	0.638452i
$285$		0			0
$286$	12.4241	+	2.63065i	0.734654	+	0.155554i
$287$		−	9.26884i		−	0.547122i
$288$		0			0
$289$	13.6747	+	9.93529i	0.804397	+	0.584429i
$290$	−6.22234	+	13.9756i	−0.365388	+	0.820676i
$291$		0			0
$292$	−11.5602	+	10.4088i	−0.676507	+	0.609129i
$293$	−2.83816	−	27.0033i	−0.165807	−	1.57755i	−0.688632	−	0.725111i	$-0.741789\pi$
$293$	−2.83816	−	27.0033i	−0.165807	−	1.57755i	0.522825	−	0.852440i	$-0.324878\pi$
$294$		0			0
$295$	−13.9760	+	15.5220i	−0.813716	+	0.903723i
$296$	−8.36416			−0.486157
$297$		0			0
$298$	9.07446			0.525669
$299$	−36.8369	+	40.9116i	−2.13034	+	2.36598i
$300$		0			0
$301$	−1.10334	−	10.4976i	−0.0635955	−	0.605071i
$302$	1.28318	−	1.15538i	0.0738384	−	0.0664844i
$303$		0			0
$304$	−1.83716	+	4.12632i	−0.105368	+	0.236661i
$305$	−4.54600	−	3.30286i	−0.260303	−	0.189121i
$306$		0			0
$307$			14.5585i			0.830895i	0.909617	+	0.415448i	$0.136375\pi$
$307$			14.5585i			0.830895i	−0.909617	+	0.415448i	$0.863625\pi$
$308$	10.8496	−	4.84074i	0.618213	−	0.275827i
$309$		0			0
$310$	−0.519512	+	2.44411i	−0.0295063	+	0.138816i
$311$	1.78202	+	4.00248i	0.101049	+	0.226960i	0.956994	−	0.290106i	$-0.0936907\pi$
$311$	1.78202	+	4.00248i	0.101049	+	0.226960i	−0.855945	+	0.517066i	$0.827024\pi$
$312$		0			0
$313$	5.51498	−	1.17225i	0.311725	−	0.0662593i	−0.0493925	−	0.998779i	$-0.515729\pi$
$313$	5.51498	−	1.17225i	0.311725	−	0.0662593i	0.361118	+	0.932520i	$0.382395\pi$
$314$	−3.39567	+	10.4508i	−0.191629	+	0.589773i
$315$		0			0
$316$	−4.72205	+	6.49935i	−0.265636	+	0.365617i
$317$	11.8229	+	10.6454i	0.664042	+	0.597906i	0.930655	−	0.365898i	$-0.119238\pi$
$317$	11.8229	+	10.6454i	0.664042	+	0.597906i	−0.266613	+	0.963804i	$0.585905\pi$
$318$		0			0
$319$	−20.8175	+	6.78207i	−1.16556	+	0.379723i
$320$	0.584035	+	0.337193i	0.0326486	+	0.0188497i
$321$		0			0
$322$	1.28446	−	12.2208i	0.0715802	−	0.681040i
$323$	0.450354	+	0.619859i	0.0250584	+	0.0344899i
$324$		0			0
$325$	−52.4465	−	17.0409i	−2.90921	−	0.945259i
$326$	0.833428	+	0.371066i	0.0461593	+	0.0205515i
$327$		0			0
$328$	−9.16959	−	1.94906i	−0.506306	−	0.107619i
$329$	−1.59805	+	2.76791i	−0.0881035	+	0.152600i
$330$		0			0
$331$	−9.89275	−	17.1347i	−0.543755	−	0.941811i	−0.998684	−	0.0512832i	$-0.983669\pi$
$331$	−9.89275	−	17.1347i	−0.543755	−	0.941811i	0.454930	−	0.890527i	$-0.349664\pi$
$332$	−6.68369	−	20.5703i	−0.366815	−	1.12894i
$333$		0			0
$334$	4.51189	−	3.27808i	0.246880	−	0.179369i
$335$	−2.17155	−	10.2163i	−0.118644	−	0.558178i
$336$		0			0
$337$	23.7395	−	2.49513i	1.29318	−	0.135918i	0.567166	−	0.823603i	$-0.308040\pi$
$337$	23.7395	−	2.49513i	1.29318	−	0.135918i	0.726009	+	0.687685i	$0.241373\pi$
$338$	−14.2075	+	6.32561i	−0.772788	+	0.344068i
$339$		0			0
$340$	1.62673	−	0.939191i	0.0882216	−	0.0509348i
$341$	−3.09559	+	1.79048i	−0.167636	+	0.0969598i
$342$		0			0
$343$	−19.1545	+	6.22366i	−1.03424	+	0.336046i
$344$	−10.6172	−	1.11591i	−0.572440	−	0.0601659i
$345$		0			0
$346$	−2.73884	−	3.04179i	−0.147241	−	0.163528i
$347$	−11.6107	−	12.8949i	−0.623293	−	0.692236i	0.345976	−	0.938244i	$-0.387548\pi$
$347$	−11.6107	−	12.8949i	−0.623293	−	0.692236i	−0.969268	+	0.246007i	$0.920881\pi$
$348$		0			0
$349$	11.0956	+	1.16619i	0.593933	+	0.0624248i	0.396726	−	0.917937i	$-0.370146\pi$
$349$	11.0956	+	1.16619i	0.593933	+	0.0624248i	0.197207	+	0.980362i	$0.436813\pi$
$350$	11.7066	−	3.80370i	0.625743	−	0.203316i
$351$		0			0
$352$	−3.89480	−	18.2532i	−0.207594	−	0.972901i
$353$	20.3046	−	11.7228i	1.08070	−	0.623944i	0.149617	−	0.988744i	$-0.452196\pi$
$353$	20.3046	−	11.7228i	1.08070	−	0.623944i	0.931086	+	0.364800i	$0.118863\pi$
$354$		0			0
$355$	23.2345	−	10.3447i	1.23316	−	0.549038i
$356$	−4.89938	+	0.514946i	−0.259667	+	0.0272921i
$357$		0			0
$358$	0.164751	+	0.775092i	0.00870736	+	0.0409649i
$359$	−14.8582	+	10.7951i	−0.784184	+	0.569743i	−0.906232	−	0.422781i	$-0.861054\pi$
$359$	−14.8582	+	10.7951i	−0.784184	+	0.569743i	0.122048	+	0.992524i	$0.461054\pi$
$360$		0			0
$361$	4.00269	+	12.3190i	0.210668	+	0.648370i
$362$	−6.41828	−	11.1168i	−0.337337	−	0.584285i
$363$		0			0
$364$	−11.0489	+	19.1372i	−0.579119	+	1.00306i
$365$	−35.1815	−	7.47806i	−1.84149	−	0.391420i
$366$		0			0
$367$	12.3333	+	5.49114i	0.643793	+	0.286635i	0.702547	−	0.711637i	$-0.252046\pi$
$367$	12.3333	+	5.49114i	0.643793	+	0.286635i	−0.0587540	+	0.998272i	$0.518713\pi$
$368$	15.5895	+	5.06533i	0.812659	+	0.264049i
$369$		0			0
$370$	−5.07791	−	6.98915i	−0.263988	−	0.363348i
$371$	1.36795	−	13.0152i	0.0710205	−	0.675715i
$372$		0			0
$373$	−24.4937	−	14.1414i	−1.26823	−	0.732215i	−0.293581	−	0.955934i	$-0.594847\pi$
$373$	−24.4937	−	14.1414i	−1.26823	−	0.732215i	−0.974654	+	0.223719i	$0.928180\pi$
$374$	−0.610185	−	0.197733i	−0.0315519	−	0.0102245i
$375$		0			0
$376$	2.40223	+	2.16298i	0.123885	+	0.111547i
$377$	23.9368	−	32.9461i	1.23281	−	1.69681i
$378$		0			0
$379$	−0.0682032	+	0.209908i	−0.00350336	+	0.0107822i	−0.952793	−	0.303621i	$-0.901804\pi$
$379$	−0.0682032	+	0.209908i	−0.00350336	+	0.0107822i	0.949290	+	0.314403i	$0.101804\pi$
$380$	−14.5009	+	3.08225i	−0.743879	+	0.158116i
$381$		0			0
$382$	−1.69905	−	3.81613i	−0.0869311	−	0.195250i
$383$	−8.02299	+	37.7452i	−0.409956	+	1.92869i	−0.0412334	+	0.999150i	$0.513129\pi$
$383$	−8.02299	+	37.7452i	−0.409956	+	1.92869i	−0.368722	+	0.929540i	$0.620205\pi$
$384$		0			0
$385$	23.8003	+	13.7162i	1.21298	+	0.699045i
$386$			9.80110i			0.498863i
$387$		0			0
$388$	−19.2260	−	13.9685i	−0.976050	−	0.709142i
$389$	−14.7882	+	33.2148i	−0.749791	+	1.68406i	−0.0205630	+	0.999789i	$0.506546\pi$
$389$	−14.7882	+	33.2148i	−0.749791	+	1.68406i	−0.729228	+	0.684270i	$0.760121\pi$
$390$		0			0
$391$	2.06634	−	1.86054i	0.104499	−	0.0940916i
$392$	0.487515	+	4.63840i	0.0246232	+	0.234274i
$393$		0			0
$394$	0.868471	−	0.964535i	0.0437530	−	0.0485926i
$395$	−18.5752			−0.934617
$396$		0			0
$397$	22.4527			1.12687			0.563434	−	0.826161i	$-0.309480\pi$
$397$	22.4527			1.12687			0.563434	+	0.826161i	$0.309480\pi$
$398$	−1.56486	+	1.73795i	−0.0784391	+	0.0871154i
$399$		0			0
$400$	1.71632	+	16.3297i	0.0858159	+	0.816484i
$401$	−20.4559	+	18.4186i	−1.02152	+	0.919780i	−0.996802	−	0.0799145i	$-0.974535\pi$
$401$	−20.4559	+	18.4186i	−1.02152	+	0.919780i	−0.0247175	+	0.999694i	$0.507869\pi$
$402$		0			0
$403$	2.70543	−	6.07650i	0.134767	−	0.302692i
$404$	8.56149	+	6.22029i	0.425950	+	0.309471i
$405$		0			0
$406$			9.08993i			0.451126i
$407$	2.56114	−	12.0958i	0.126951	−	0.599569i
$408$		0			0
$409$	−8.30739	+	39.0832i	−0.410774	+	1.93254i	−0.0534133	+	0.998572i	$0.517010\pi$
$409$	−8.30739	+	39.0832i	−0.410774	+	1.93254i	−0.357361	+	0.933967i	$0.616323\pi$
$410$	−3.93824	−	8.84544i	−0.194496	−	0.436845i
$411$		0			0
$412$	−13.8390	+	2.94157i	−0.681799	+	0.144921i
$413$	−3.83509	+	11.8032i	−0.188712	+	0.580797i
$414$		0			0
$415$	29.3949	−	40.4587i	1.44294	−	1.98604i
$416$	25.7985	+	23.2291i	1.26488	+	1.13890i
$417$		0			0
$418$	4.09784	+	2.97235i	0.200432	+	0.145383i
$419$	21.9499	+	12.6728i	1.07232	+	0.619105i	0.928815	−	0.370544i	$-0.120829\pi$
$419$	21.9499	+	12.6728i	1.07232	+	0.619105i	0.143507	+	0.989649i	$0.454162\pi$
$420$		0			0
$421$	1.55719	−	14.8157i	0.0758927	−	0.722071i	−0.888729	−	0.458433i	$-0.848411\pi$
$421$	1.55719	−	14.8157i	0.0758927	−	0.722071i	0.964622	−	0.263638i	$-0.0849225\pi$
$422$	−3.97287	−	5.46819i	−0.193396	−	0.266187i
$423$		0			0
$424$	−12.5882	−	4.09014i	−0.611335	−	0.198635i
$425$	2.54446	+	1.13287i	0.123424	+	0.0549521i
$426$		0			0
$427$	−3.26585	−	0.694178i	−0.158046	−	0.0335936i
$428$	−0.617281	+	1.06916i	−0.0298374	+	0.0516799i
$429$		0			0
$430$	−5.51327	−	9.54926i	−0.265873	−	0.460506i
$431$	4.81473	+	14.8182i	0.231917	+	0.713768i	0.997515	+	0.0704489i	$0.0224432\pi$
$431$	4.81473	+	14.8182i	0.231917	+	0.713768i	−0.765598	+	0.643319i	$0.777557\pi$
$432$		0			0
$433$	−8.59479	+	6.24448i	−0.413039	+	0.300091i	−0.774831	−	0.632168i	$-0.782165\pi$
$433$	−8.59479	+	6.24448i	−0.413039	+	0.300091i	0.361792	+	0.932259i	$0.382165\pi$
$434$	0.308685	+	1.45225i	0.0148174	+	0.0697102i
$435$		0			0
$436$	7.05418	−	0.741425i	0.337834	−	0.0355078i
$437$	−20.0477	+	8.92580i	−0.959010	+	0.426979i
$438$		0			0
$439$	−15.4266	+	8.90653i	−0.736270	+	0.425085i	−0.820711	−	0.571343i	$-0.806423\pi$
$439$	−15.4266	+	8.90653i	−0.736270	+	0.425085i	0.0844418	+	0.996428i	$0.473089\pi$
$440$	18.5741	−	20.6612i	0.885486	−	0.984983i
$441$		0			0
$442$	1.13466	−	0.368672i	0.0539701	−	0.0175359i
$443$	−18.2172	−	1.91470i	−0.865524	−	0.0909703i	−0.338649	−	0.940913i	$-0.609970\pi$
$443$	−18.2172	−	1.91470i	−0.865524	−	0.0909703i	−0.526875	+	0.849943i	$0.676637\pi$
$444$		0			0
$445$	−7.62181	−	8.46487i	−0.361308	−	0.401273i
$446$	4.71687	+	5.23862i	0.223350	+	0.248056i
$447$		0			0
$448$	0.398513	+	0.0418854i	0.0188280	+	0.00197890i
$449$	−13.4434	+	4.36802i	−0.634433	+	0.206140i	−0.608538	−	0.793525i	$-0.708244\pi$
$449$	−13.4434	+	4.36802i	−0.634433	+	0.206140i	−0.0258953	+	0.999665i	$0.508244\pi$
$450$		0			0
$451$	5.62640	−	12.6638i	0.264937	−	0.596315i
$452$	8.41126	−	4.85624i	0.395632	−	0.228418i
$453$		0			0
$454$	6.07507	−	2.70480i	0.285117	−	0.126942i
$455$	−50.8139	+	5.34076i	−2.38219	+	0.250379i
$456$		0			0
$457$	−1.79926	−	8.46487i	−0.0841660	−	0.395970i	0.915818	−	0.401593i	$-0.131543\pi$
$457$	−1.79926	−	8.46487i	−0.0841660	−	0.395970i	−0.999984	+	0.00562314i	$0.998210\pi$
$458$	9.87990	−	7.17817i	0.461658	−	0.335414i
$459$		0			0
$460$	16.6251	+	51.1668i	0.775150	+	2.38567i
$461$	−18.1341	−	31.4092i	−0.844590	−	1.46287i	−0.885977	−	0.463729i	$-0.846511\pi$
$461$	−18.1341	−	31.4092i	−0.844590	−	1.46287i	0.0413877	−	0.999143i	$-0.486822\pi$
$462$		0			0
$463$	14.1514	−	24.5109i	0.657669	−	1.13912i	−0.323548	−	0.946212i	$-0.604876\pi$
$463$	14.1514	−	24.5109i	0.657669	−	1.13912i	0.981217	−	0.192905i	$-0.0617908\pi$
$464$	−11.8605	−	2.52103i	−0.550611	−	0.117036i
$465$		0			0
$466$	11.4299	+	5.08891i	0.529479	+	0.235739i
$467$	−26.4483	−	8.59356i	−1.22388	−	0.397662i	−0.375386	−	0.926869i	$-0.622490\pi$
$467$	−26.4483	−	8.59356i	−1.22388	−	0.397662i	−0.848493	+	0.529206i	$0.822490\pi$
$468$		0			0
$469$	−3.64778	−	5.02074i	−0.168439	−	0.231836i
$470$	−0.348995	+	3.32047i	−0.0160979	+	0.153162i
$471$		0			0
$472$	10.8703	+	6.27600i	0.500348	+	0.288876i
$473$	4.86480	−	15.0124i	0.223684	−	0.690269i
$474$		0			0
$475$	−16.3360	−	14.7090i	−0.749545	−	0.674894i
$476$	0.656028	−	0.902945i	0.0300690	−	0.0413864i
$477$		0			0
$478$	3.29881	−	10.1527i	0.150884	−	0.464373i
$479$	7.25282	−	1.54164i	0.331390	−	0.0704391i	−0.0392120	−	0.999231i	$-0.512485\pi$
$479$	7.25282	−	1.54164i	0.331390	−	0.0704391i	0.370602	+	0.928792i	$0.379151\pi$
$480$		0			0
$481$	9.35375	+	21.0089i	0.426494	+	0.957922i
$482$	−2.64938	+	12.4643i	−0.120676	+	0.567736i
$483$		0			0
$484$	17.7620	−	0.0278423i	0.807363	−	0.00126556i
$485$		−	54.9478i		−	2.49505i
$486$		0			0
$487$	15.0683	+	10.9477i	0.682808	+	0.496089i	0.874288	−	0.485408i	$-0.161329\pi$
$487$	15.0683	+	10.9477i	0.682808	+	0.496089i	−0.191480	+	0.981496i	$0.561329\pi$
$488$	−1.37349	+	3.08491i	−0.0621749	+	0.139647i
$489$		0			0
$490$	−3.57990	+	3.22336i	−0.161723	+	0.145616i
$491$	−2.23296	−	21.2452i	−0.100772	−	0.958783i	−0.921740	−	0.387808i	$-0.873232\pi$
$491$	−2.23296	−	21.2452i	−0.100772	−	0.958783i	0.820968	−	0.570974i	$-0.193434\pi$
$492$		0			0
$493$	−1.37630	+	1.52854i	−0.0619854	+	0.0688418i
$494$	−9.41594			−0.423643
$495$		0			0
$496$	−1.98051			−0.0889273
$497$	10.1119	−	11.2304i	0.453582	−	0.503754i
$498$		0			0
$499$	−1.24894	−	11.8829i	−0.0559102	−	0.531950i	−0.986251	−	0.165254i	$-0.947156\pi$
$499$	−1.24894	−	11.8829i	−0.0559102	−	0.531950i	0.930341	−	0.366696i	$-0.119511\pi$
$500$	−17.6484	+	15.8907i	−0.789260	+	0.710653i
$501$		0			0
$502$	1.60512	−	3.60515i	0.0716399	−	0.160906i
$503$	−21.5801	−	15.6789i	−0.962210	−	0.699087i	−0.00854739	−	0.999963i	$-0.502721\pi$
$503$	−21.5801	−	15.6789i	−0.962210	−	0.699087i	−0.953663	+	0.300877i	$0.902721\pi$
$504$		0			0
$505$			24.4688i			1.08885i
$506$	9.17325	−	15.9173i	0.407801	−	0.707612i
$507$		0			0
$508$	3.78638	−	17.8135i	0.167994	−	0.790348i
$509$	−10.5196	−	23.6274i	−0.466273	−	1.04727i	−0.981717	−	0.190344i	$-0.939040\pi$
$509$	−10.5196	−	23.6274i	−0.466273	−	1.04727i	0.515444	−	0.856923i	$-0.327627\pi$
$510$		0			0
$511$	−20.9042	+	4.44333i	−0.924749	+	0.196562i
$512$	5.74119	−	17.6696i	0.253727	−	0.780892i
$513$		0			0
$514$	5.05013	−	6.95091i	0.222752	−	0.306591i
$515$	−24.3105	−	21.8893i	−1.07125	−	0.964558i
$516$		0			0
$517$	−3.86356	+	2.81167i	−0.169919	+	0.123657i
$518$	−4.44546	−	2.56659i	−0.195322	−	0.112769i
$519$		0			0
$520$	−5.40161	+	51.3928i	−0.236876	+	2.25373i
$521$	13.0853	+	18.0103i	0.573276	+	0.789047i	0.992938	−	0.118634i	$-0.0378514\pi$
$521$	13.0853	+	18.0103i	0.573276	+	0.789047i	−0.419662	+	0.907680i	$0.637851\pi$
$522$		0			0
$523$	−27.2570	−	8.85633i	−1.19186	−	0.387260i	−0.355103	−	0.934827i	$-0.615554\pi$
$523$	−27.2570	−	8.85633i	−1.19186	−	0.387260i	−0.836762	+	0.547567i	$0.815554\pi$
$524$	−25.3458	−	11.2847i	−1.10723	−	0.492973i
$525$		0			0
$526$	−9.37147	−	1.99197i	−0.408616	−	0.0868539i
$527$	−0.167977	+	0.290944i	−0.00731717	+	0.0126737i
$528$		0			0
$529$	28.3196	+	49.0509i	1.23129	+	2.13265i
$530$	−4.22457	−	13.0019i	−0.183503	−	0.564766i
$531$		0			0
$532$	−7.12635	+	5.17759i	−0.308966	+	0.224477i
$533$	5.35888	+	25.2116i	0.232119	+	1.09203i
$534$		0			0
$535$	−2.83888	+	0.298379i	−0.122736	+	0.0129000i
$536$	−5.73404	+	2.55296i	−0.247673	+	0.110271i
$537$		0			0
$538$	3.30211	−	1.90647i	0.142364	−	0.0821938i
$539$	−6.85710	−	0.715277i	−0.295356	−	0.0308092i
$540$		0			0
$541$	27.0426	−	8.78666i	1.16265	−	0.377768i	0.336755	−	0.941592i	$-0.390670\pi$
$541$	27.0426	−	8.78666i	1.16265	−	0.377768i	0.825895	+	0.563824i	$0.190670\pi$
$542$	11.6275	+	1.22210i	0.499443	+	0.0524936i
$543$		0			0
$544$	−1.17324	−	1.30302i	−0.0503023	−	0.0558664i
$545$	10.9740	+	12.1878i	0.470073	+	0.522069i
$546$		0			0
$547$	−17.7675	−	1.86744i	−0.759685	−	0.0798461i	−0.283238	−	0.959050i	$-0.591409\pi$
$547$	−17.7675	−	1.86744i	−0.759685	−	0.0798461i	−0.476447	+	0.879203i	$0.658075\pi$
$548$	2.08783	−	0.678378i	0.0891878	−	0.0289789i
$549$		0			0
$550$	18.3034	+	1.90926i	0.780458	+	0.0814110i
$551$	14.0585	−	8.11667i	0.598911	−	0.345782i
$552$		0			0
$553$	−10.0828	+	4.48916i	−0.428766	+	0.190899i
$554$	−3.38562	+	0.355843i	−0.143841	+	0.0151183i
$555$		0			0
$556$	−4.05002	−	19.0538i	−0.171759	−	0.808063i
$557$	27.7784	−	20.1822i	1.17701	−	0.855148i	0.185179	−	0.982705i	$-0.440713\pi$
$557$	27.7784	−	20.1822i	1.17701	−	0.855148i	0.991831	+	0.127556i	$0.0407134\pi$
$558$		0			0
$559$	9.07042	+	27.9159i	0.383638	+	1.18072i
$560$	7.60662	+	13.1750i	0.321438	+	0.556747i
$561$		0			0
$562$	8.09993	−	14.0295i	0.341675	−	0.591798i
$563$	0.0961862	+	0.0204450i	0.00405377	+	0.000861654i	0.209938	−	0.977715i	$-0.432674\pi$
$563$	0.0961862	+	0.0204450i	0.00405377	+	0.000861654i	−0.205884	+	0.978576i	$0.566007\pi$
$564$		0			0
$565$	20.5154	+	9.13406i	0.863091	+	0.384273i
$566$	10.1806	+	3.30787i	0.427922	+	0.139040i
$567$		0			0
$568$	−8.98384	−	12.3652i	−0.376953	−	0.518832i
$569$	−3.65319	+	34.7578i	−0.153150	+	1.45712i	0.600383	+	0.799713i	$0.295015\pi$
$569$	−3.65319	+	34.7578i	−0.153150	+	1.45712i	−0.753533	+	0.657410i	$0.771652\pi$
$570$		0			0
$571$	7.73170	+	4.46390i	0.323562	+	0.186808i	0.652979	−	0.757376i	$-0.273519\pi$
$571$	7.73170	+	4.46390i	0.323562	+	0.186808i	−0.329417	+	0.944184i	$0.606852\pi$
$572$	−26.7125	+	19.4398i	−1.11691	+	0.812819i
$573$		0			0
$574$	−4.27546	−	3.84964i	−0.178454	−	0.160681i
$575$	−46.8903	+	64.5389i	−1.95546	+	2.69146i
$576$		0			0
$577$	−1.57214	+	4.83854i	−0.0654489	+	0.201431i	−0.978433	−	0.206564i	$-0.933772\pi$
$577$	−1.57214	+	4.83854i	−0.0654489	+	0.201431i	0.912984	+	0.407995i	$0.133772\pi$
$578$	10.2624	−	2.18135i	0.426860	−	0.0907320i
$579$		0			0
$580$	−16.1871	−	36.3569i	−0.672133	−	1.50964i
$581$	6.17807	−	29.0655i	0.256310	−	1.20584i
$582$		0			0
$583$	9.76951	−	16.9520i	0.404612	−	0.702078i
$584$			21.6147i			0.894424i
$585$		0			0
$586$	−13.6347	−	9.90616i	−0.563242	−	0.409220i
$587$	1.39311	−	3.12898i	0.0574999	−	0.129147i	−0.882510	−	0.470293i	$-0.844148\pi$
$587$	1.39311	−	3.12898i	0.0574999	−	0.129147i	0.940010	+	0.341146i	$0.110815\pi$
$588$		0			0
$589$	1.97041	−	1.77417i	0.0811895	−	0.0731034i
$590$	1.35516	+	12.8935i	0.0557911	+	0.530817i
$591$		0			0
$592$	4.58180	−	5.08861i	0.188311	−	0.209141i
$593$	16.6897			0.685365			0.342683	−	0.939451i	$-0.388664\pi$
$593$	16.6897			0.685365			0.342683	+	0.939451i	$0.388664\pi$
$594$		0			0
$595$	2.58062			0.105795
$596$	−15.7960	+	17.5432i	−0.647029	+	0.718599i
$597$		0			0
$598$	3.57183	+	33.9837i	0.146063	+	1.38970i
$599$	35.8479	−	32.2776i	1.46470	−	1.31883i	0.618726	−	0.785607i	$-0.287649\pi$
$599$	35.8479	−	32.2776i	1.46470	−	1.31883i	0.845978	−	0.533219i	$-0.179018\pi$
$600$		0			0
$601$	7.69170	−	17.2758i	0.313751	−	0.704696i	−0.685986	−	0.727614i	$-0.740629\pi$
$601$	7.69170	−	17.2758i	0.313751	−	0.704696i	0.999737	+	0.0229181i	$0.00729568\pi$
$602$	−5.30050	−	3.85104i	−0.216032	−	0.156956i
$603$		0			0
$604$			4.49188i			0.182772i
$605$	24.1917	+	33.1875i	0.983532	+	1.34926i
$606$		0			0
$607$	−7.45061	+	35.0524i	−0.302411	+	1.42273i	0.520160	+	0.854069i	$0.325872\pi$
$607$	−7.45061	+	35.0524i	−0.302411	+	1.42273i	−0.822571	+	0.568663i	$0.807461\pi$
$608$	5.62854	+	12.6419i	0.228267	+	0.512697i
$609$		0			0
$610$	−3.41162	+	0.725161i	−0.138132	+	0.0293609i
$611$	2.74646	−	8.45274i	0.111110	−	0.341961i
$612$		0			0
$613$	−0.393669	+	0.541839i	−0.0159002	+	0.0218847i	−0.816893	−	0.576789i	$-0.804305\pi$
$613$	−0.393669	+	0.541839i	−0.0159002	+	0.0218847i	0.800993	+	0.598674i	$0.204305\pi$
$614$	6.71541	+	6.04659i	0.271012	+	0.244020i
$615$		0			0
$616$	5.08895	−	15.7041i	0.205040	−	0.632735i
$617$	−9.40017	−	5.42719i	−0.378436	−	0.218490i	0.298701	−	0.954347i	$-0.403447\pi$
$617$	−9.40017	−	5.42719i	−0.378436	−	0.218490i	−0.677138	+	0.735856i	$0.736780\pi$
$618$		0			0
$619$	−2.89953	+	27.5872i	−0.116542	+	1.10882i	0.767381	+	0.641191i	$0.221559\pi$
$619$	−2.89953	+	27.5872i	−0.116542	+	1.10882i	−0.883923	+	0.467632i	$0.845107\pi$
$620$	−3.82077	−	5.25884i	−0.153446	−	0.211200i
$621$		0			0
$622$	2.58636	+	0.840360i	0.103704	+	0.0336953i
$623$	−6.18297	−	2.75283i	−0.247715	−	0.110290i
$624$		0			0
$625$	−9.99064	−	2.12358i	−0.399626	−	0.0849430i
$626$	1.74982	−	3.03078i	0.0699369	−	0.121134i
$627$		0			0
$628$	−14.2932	−	24.7565i	−0.570360	−	0.987893i
$629$	−0.358931	−	1.10467i	−0.0143115	−	0.0440463i
$630$		0			0
$631$	−35.5496	+	25.8283i	−1.41521	+	1.02821i	−0.422667	+	0.906285i	$0.638906\pi$
$631$	−35.5496	+	25.8283i	−1.41521	+	1.02821i	−0.992540	+	0.121923i	$0.961094\pi$
$632$	2.32087	+	10.9188i	0.0923193	+	0.434328i
$633$		0			0
$634$	9.82086	−	1.03221i	0.390036	−	0.0409945i
$635$	38.4677	−	17.1269i	1.52654	−	0.679661i
$636$		0			0
$637$	11.1054	−	6.41170i	0.440012	−	0.254041i
$638$	−5.51779	+	12.4193i	−0.218451	+	0.491687i
$639$		0			0
$640$	40.3620	−	13.1144i	1.59545	−	0.518392i
$641$	−14.0124	−	1.47276i	−0.553457	−	0.0581707i	−0.176328	−	0.984331i	$-0.556422\pi$
$641$	−14.0124	−	1.47276i	−0.553457	−	0.0581707i	−0.377129	+	0.926161i	$0.623089\pi$
$642$		0			0
$643$	19.5756	+	21.7409i	0.771985	+	0.857376i	0.993027	−	0.117888i	$-0.0376124\pi$
$643$	19.5756	+	21.7409i	0.771985	+	0.857376i	−0.221042	+	0.975264i	$0.570946\pi$
$644$	21.3901	+	23.7561i	0.842888	+	0.936122i
$645$		0			0
$646$	0.472970	+	0.0497111i	0.0186088	+	0.00195586i
$647$	−39.3432	+	12.7834i	−1.54674	+	0.502566i	−0.953226	−	0.302258i	$-0.902260\pi$
$647$	−39.3432	+	12.7834i	−1.54674	+	0.502566i	−0.593513	+	0.804824i	$0.702260\pi$
$648$		0			0
$649$	−12.4046	+	13.7984i	−0.486923	+	0.541635i
$650$	−29.6432	+	17.1145i	−1.16270	+	0.671285i
$651$		0			0
$652$	−2.16812	+	0.965310i	−0.0849102	+	0.0378045i
$653$	27.1642	−	2.85507i	1.06302	−	0.111728i	0.443160	−	0.896443i	$-0.353857\pi$
$653$	27.1642	−	2.85507i	1.06302	−	0.111728i	0.619857	+	0.784715i	$0.287191\pi$
$654$		0			0
$655$	−13.3375	−	62.7480i	−0.521139	−	2.45177i
$656$	6.20878	−	4.51094i	0.242412	−	0.176123i
$657$		0			0
$658$	0.613038	+	1.88674i	0.0238987	+	0.0735526i
$659$	−0.320896	−	0.555808i	−0.0125003	−	0.0216512i	0.859708	−	0.510787i	$-0.170646\pi$
$659$	−0.320896	−	0.555808i	−0.0125003	−	0.0216512i	−0.872208	+	0.489135i	$0.837312\pi$
$660$		0			0
$661$	4.12078	−	7.13740i	0.160280	−	0.277613i	−0.774689	−	0.632342i	$-0.782094\pi$
$661$	4.12078	−	7.13740i	0.160280	−	0.277613i	0.934969	+	0.354729i	$0.115427\pi$
$662$	−12.0125	−	2.55335i	−0.466881	−	0.0992386i
$663$		0			0
$664$	−27.4552	−	12.2238i	−1.06547	−	0.474376i
$665$	−19.3703	−	6.29378i	−0.751147	−	0.244063i
$666$		0			0
$667$	−34.6273	−	47.6604i	−1.34078	−	1.84542i
$668$	−1.51653	+	14.4288i	−0.0586764	+	0.558268i
$669$		0			0
$670$	−5.61442	−	3.24149i	−0.216904	−	0.125230i
$671$	−4.04067	−	2.93088i	−0.155988	−	0.113145i
$672$		0			0
$673$	−11.0142	−	9.91720i	−0.424565	−	0.382280i	0.428967	−	0.903320i	$-0.358878\pi$
$673$	−11.0142	−	9.91720i	−0.424565	−	0.382280i	−0.853532	+	0.521040i	$0.825544\pi$
$674$	8.70884	−	11.9867i	0.335452	−	0.461710i
$675$		0			0
$676$	12.5022	−	38.4778i	0.480854	−	1.47992i
$677$	6.15913	−	1.30916i	0.236714	−	0.0503152i	−0.0880268	−	0.996118i	$-0.528056\pi$
$677$	6.15913	−	1.30916i	0.236714	−	0.0503152i	0.324741	+	0.945803i	$0.394723\pi$
$678$		0			0
$679$	−13.2796	−	29.8264i	−0.509623	−	1.14463i
$680$	0.542654	−	2.55298i	0.0208098	−	0.0979025i
$681$		0			0
$682$	−0.459799	+	2.17155i	−0.0176066	+	0.0831530i
$683$			14.1497i			0.541422i	0.962661	+	0.270711i	$0.0872588\pi$
$683$			14.1497i			0.541422i	−0.962661	+	0.270711i	$0.912741\pi$
$684$		0			0
$685$	4.10646	+	2.98352i	0.156900	+	0.113994i
$686$	−5.08465	+	11.4203i	−0.194133	+	0.436029i
$687$		0			0
$688$	6.49489	−	5.84802i	0.247615	−	0.222954i
$689$	3.80400	+	36.1926i	0.144921	+	1.37883i
$690$		0			0
$691$	−17.2334	+	19.1396i	−0.655590	+	0.728106i	−0.975660	−	0.219287i	$-0.929627\pi$
$691$	−17.2334	+	19.1396i	−0.655590	+	0.728106i	0.320070	+	0.947394i	$0.396293\pi$
$692$	10.6481			0.404779
$693$		0			0
$694$	−10.7703			−0.408837
$695$	30.1376	−	33.4712i	1.14319	−	1.26964i
$696$		0			0
$697$	−0.136077	−	1.29469i	−0.00515429	−	0.0490398i
$698$	5.14627	−	4.63372i	0.194789	−	0.175389i
$699$		0			0
$700$	−13.0243	+	29.2530i	−0.492270	+	1.10566i
$701$	8.55571	+	6.21609i	0.323145	+	0.234778i	0.737516	−	0.675329i	$-0.235999\pi$
$701$	8.55571	+	6.21609i	0.323145	+	0.234778i	−0.414371	+	0.910108i	$0.635999\pi$
$702$		0			0
$703$			9.16714i			0.345745i
$704$	0.519054	+	0.299134i	0.0195626	+	0.0112740i
$705$		0			0
$706$	3.02570	−	14.2348i	0.113874	−	0.535733i
$707$	5.91351	+	13.2819i	0.222400	+	0.499519i
$708$		0			0
$709$	25.5086	−	5.42201i	0.957994	−	0.203628i	0.297720	−	0.954653i	$-0.403774\pi$
$709$	25.5086	−	5.42201i	0.957994	−	0.203628i	0.660273	+	0.751025i	$0.270440\pi$
$710$	4.87831	−	15.0139i	0.183080	−	0.563462i
$711$		0			0
$712$	−4.02351	+	5.53789i	−0.150788	+	0.207541i
$713$	−7.15073	−	6.43855i	−0.267797	−	0.241125i
$714$		0			0
$715$	−72.6678	−	23.5483i	−2.71762	−	0.880655i
$716$	−1.78523	−	1.03071i	−0.0667173	−	0.0385193i
$717$		0			0
$718$	−1.19159	+	11.3372i	−0.0444697	+	0.423101i
$719$	8.91625	+	12.2722i	0.332520	+	0.457675i	0.942238	−	0.334944i	$-0.108717\pi$
$719$	8.91625	+	12.2722i	0.332520	+	0.457675i	−0.609718	+	0.792618i	$0.708717\pi$
$720$		0			0
$721$	−18.4862	−	6.00653i	−0.688461	−	0.223695i
$722$	7.34486	+	3.27014i	0.273348	+	0.121702i
$723$		0			0
$724$	32.6639	+	6.94293i	1.21395	+	0.258032i
$725$	29.5058	−	51.1056i	1.09582	−	1.89801i
$726$		0			0
$727$	8.28230	+	14.3454i	0.307174	+	0.532040i	0.977743	−	0.209807i	$-0.0672834\pi$
$727$	8.28230	+	14.3454i	0.307174	+	0.532040i	−0.670569	+	0.741847i	$0.733950\pi$
$728$	9.48835	+	29.2021i	0.351662	+	1.08230i
$729$		0			0
$730$	−18.0614	+	13.1224i	−0.668483	+	0.485681i
$731$	−0.308233	−	1.45012i	−0.0114004	−	0.0536347i
$732$		0			0
$733$	22.5016	−	2.36502i	0.831117	−	0.0873539i	0.320593	−	0.947217i	$-0.396118\pi$
$733$	22.5016	−	2.36502i	0.831117	−	0.0873539i	0.510525	+	0.859863i	$0.329451\pi$
$734$	7.65531	−	3.40836i	0.282563	−	0.125805i
$735$		0			0
$736$	43.4916	−	25.1099i	1.60312	−	0.925563i
$737$	−1.93618	−	9.07401i	−0.0713199	−	0.334245i
$738$		0			0
$739$	−29.5613	+	9.60506i	−1.08743	+	0.353328i	−0.797253	−	0.603645i	$-0.793714\pi$
$739$	−29.5613	+	9.60506i	−1.08743	+	0.353328i	−0.290178	+	0.956973i	$0.593714\pi$
$740$	22.3510	+	2.34918i	0.821638	+	0.0863577i
$741$		0			0
$742$	−5.43539	−	6.03661i	−0.199539	−	0.221611i
$743$	−31.4842	−	34.9667i	−1.15504	−	1.28281i	−0.952844	−	0.303461i	$-0.901858\pi$
$743$	−31.4842	−	34.9667i	−1.15504	−	1.28281i	−0.202199	−	0.979344i	$-0.564809\pi$
$744$		0			0
$745$	−54.2839	−	5.70546i	−1.98881	−	0.209032i
$746$	−16.6960	+	5.42487i	−0.611285	+	0.198619i
$747$		0			0
$748$	1.44442	−	0.835448i	0.0528134	−	0.0305470i
$749$	−1.46887	+	0.848053i	−0.0536714	+	0.0309872i
$750$		0			0
$751$	33.3657	−	14.8554i	1.21753	−	0.542080i	0.305496	−	0.952193i	$-0.401178\pi$
$751$	33.3657	−	14.8554i	1.21753	−	0.542080i	0.912034	+	0.410114i	$0.134511\pi$
$752$	−2.63183	+	0.276617i	−0.0959731	+	0.0100872i
$753$		0			0
$754$	−5.25544	−	24.7249i	−0.191392	−	0.900428i
$755$	−8.40245	+	6.10474i	−0.305796	+	0.222174i
$756$		0			0
$757$	−8.52322	−	26.2318i	−0.309782	−	0.953409i	−0.977849	−	0.209309i	$-0.932878\pi$
$757$	−8.52322	−	26.2318i	−0.309782	−	0.953409i	0.668068	−	0.744100i	$-0.267122\pi$
$758$	0.0684977	+	0.118642i	0.00248795	+	0.00430925i
$759$		0			0
$760$	−10.2996	+	17.8394i	−0.373605	+	0.647103i
$761$	51.5524	+	10.9578i	1.86877	+	0.397220i	0.995879	−	0.0906909i	$-0.0289075\pi$
$761$	51.5524	+	10.9578i	1.86877	+	0.397220i	0.872894	+	0.487911i	$0.162241\pi$
$762$		0			0
$763$	8.90231	+	3.96356i	0.322285	+	0.143491i
$764$	10.3351	+	3.35808i	0.373912	+	0.121491i
$765$		0			0
$766$	14.0786	+	19.3775i	0.508681	+	0.700139i
$767$	3.60742	−	34.3224i	0.130257	−	1.23931i
$768$		0			0
$769$	15.7023	+	9.06575i	0.566241	+	0.326919i	0.755647	−	0.654980i	$-0.227323\pi$
$769$	15.7023	+	9.06575i	0.566241	+	0.326919i	−0.189406	+	0.981899i	$0.560656\pi$
$770$	16.2119	−	5.28163i	0.584237	−	0.190337i
$771$		0			0
$772$	−18.9480	−	17.0609i	−0.681954	−	0.614034i
$773$	8.15106	−	11.2190i	0.293173	−	0.403518i	−0.636868	−	0.770973i	$-0.719771\pi$
$773$	8.15106	−	11.2190i	0.293173	−	0.403518i	0.930042	+	0.367454i	$0.119771\pi$
$774$		0			0
$775$	2.97849	−	9.16686i	0.106991	−	0.329283i
$776$	−32.2994	+	6.86545i	−1.15948	+	0.246455i
$777$		0			0
$778$	9.17908	+	20.6165i	0.329086	+	0.739139i
$779$	−2.13617	+	10.0499i	−0.0765362	+	0.360074i
$780$		0			0
$781$	20.6328	−	9.20571i	0.738300	−	0.329406i
$782$		−	1.72589i		−	0.0617175i
$783$		0			0
$784$	−3.08897	−	2.24427i	−0.110320	−	0.0801525i
$785$	26.8839	−	60.3823i	0.959528	−	2.15514i
$786$		0			0
$787$	0.499268	−	0.449543i	0.0177970	−	0.0160245i	−0.660184	−	0.751104i	$-0.729522\pi$
$787$	0.499268	−	0.449543i	0.0177970	−	0.0160245i	0.677981	+	0.735079i	$0.262855\pi$
$788$	0.352935	+	3.35795i	0.0125728	+	0.119622i
$789$		0			0
$790$	−7.71484	+	8.56820i	−0.274482	+	0.304843i
$791$	13.3435			0.474441
$792$		0			0
$793$	9.28457			0.329705
$794$	9.32531	−	10.3568i	0.330943	−	0.367549i
$795$		0			0
$796$	−0.635936	−	6.05053i	−0.0225402	−	0.214455i
$797$	3.90582	−	3.51682i	0.138351	−	0.124572i	−0.597050	−	0.802204i	$-0.703660\pi$
$797$	3.90582	−	3.51682i	0.138351	−	0.124572i	0.735401	+	0.677632i	$0.236994\pi$
$798$		0			0
$799$	−0.182583	+	0.410088i	−0.00645931	+	0.0145079i
$800$	40.6977	+	29.5686i	1.43888	+	1.04541i
$801$		0			0
$802$			17.0856i			0.603312i
$803$	−31.2582	−	6.61853i	−1.10308	−	0.233563i
$804$		0			0
$805$	−15.3674	+	72.2981i	−0.541631	+	2.54817i
$806$	−1.67927	−	3.77170i	−0.0591497	−	0.132852i
$807$		0			0
$808$	14.3832	−	3.05725i	0.506000	−	0.107554i
$809$	−8.82483	+	27.1600i	−0.310265	+	0.954896i	0.667395	+	0.744704i	$0.267409\pi$
$809$	−8.82483	+	27.1600i	−0.310265	+	0.954896i	−0.977660	+	0.210193i	$0.932591\pi$
$810$		0			0
$811$	13.6775	−	18.8255i	0.480283	−	0.661053i	−0.498276	−	0.867018i	$-0.666033\pi$
$811$	13.6775	−	18.8255i	0.480283	−	0.661053i	0.978559	+	0.205965i	$0.0660335\pi$
$812$	−17.5731	−	15.8229i	−0.616697	−	0.555276i
$813$		0			0
$814$	−4.51575	−	6.20517i	−0.158277	−	0.217491i
$815$	−4.75231	−	2.74375i	−0.166466	−	0.0961092i
$816$		0			0
$817$	−1.22304	+	11.6364i	−0.0427888	+	0.407108i
$818$	14.5777	+	20.0644i	0.509696	+	0.701536i
$819$		0			0
$820$	23.9558	+	7.78372i	0.836574	+	0.271819i
$821$	−19.6247	−	8.73748i	−0.684907	−	0.304940i	0.0346243	−	0.999400i	$-0.488977\pi$
$821$	−19.6247	−	8.73748i	−0.684907	−	0.304940i	−0.719531	+	0.694460i	$0.755643\pi$
$822$		0			0
$823$	−47.3885	−	10.0727i	−1.65186	−	0.351114i	−0.714542	−	0.699592i	$-0.753365\pi$
$823$	−47.3885	−	10.0727i	−1.65186	−	0.351114i	−0.937317	+	0.348479i	$0.886698\pi$
$824$	−9.82949	+	17.0252i	−0.342426	+	0.593100i
$825$		0			0
$826$	3.85165	+	6.67125i	0.134016	+	0.232122i
$827$	−12.2819	−	37.7998i	−0.427084	−	1.31443i	−0.900985	−	0.433851i	$-0.857155\pi$
$827$	−12.2819	−	37.7998i	−0.427084	−	1.31443i	0.473901	−	0.880578i	$-0.342845\pi$
$828$		0			0
$829$	27.8772	−	20.2540i	0.968215	−	0.703450i	0.0131712	−	0.999913i	$-0.495807\pi$
$829$	27.8772	−	20.2540i	0.968215	−	0.703450i	0.955044	+	0.296464i	$0.0958074\pi$
$830$	−6.45382	−	30.3628i	−0.224015	−	1.05391i
$831$		0			0
$832$	−1.10819	+	0.116475i	−0.0384194	+	0.00403805i
$833$	−0.591683	+	0.263434i	−0.0205006	+	0.00912746i
$834$		0			0
$835$	−29.0514	+	16.7729i	−1.00537	+	0.580449i
$836$	−12.8795	+	2.74817i	−0.445446	+	0.0950474i
$837$		0			0
$838$	14.9621	−	4.86147i	0.516856	−	0.167937i
$839$	26.1231	+	2.74565i	0.901870	+	0.0947904i	0.544101	−	0.839020i	$-0.316871\pi$
$839$	26.1231	+	2.74565i	0.901870	+	0.0947904i	0.357769	+	0.933810i	$0.383537\pi$
$840$		0			0
$841$	9.75507	+	10.8341i	0.336382	+	0.373590i
$842$	−6.18730	−	6.87170i	−0.213229	−	0.236814i
$843$		0			0
$844$	17.4870	+	1.83796i	0.601928	+	0.0632652i
$845$	88.9674	−	28.9073i	3.06057	−	0.994440i
$846$		0			0
$847$	21.1522	+	12.1680i	0.726797	+	0.418099i
$848$	9.38404	−	5.41788i	0.322249	−	0.186051i
$849$		0			0
$850$	1.57935	−	0.703174i	0.0541714	−	0.0241187i
$851$	33.0857	−	3.47745i	1.13416	−	0.119205i
$852$		0			0
$853$	8.47914	+	39.8912i	0.290320	+	1.36585i	0.845436	+	0.534077i	$0.179341\pi$
$853$	8.47914	+	39.8912i	0.290320	+	1.36585i	−0.555116	+	0.831773i	$0.687326\pi$
$854$	−1.67661	+	1.21813i	−0.0573726	+	0.0416836i
$855$		0			0
$856$	0.530097	+	1.63147i	0.0181183	+	0.0557625i
$857$	22.9703	+	39.7858i	0.784651	+	1.35906i	0.929207	+	0.369559i	$0.120491\pi$
$857$	22.9703	+	39.7858i	0.784651	+	1.35906i	−0.144556	+	0.989497i	$0.546175\pi$
$858$		0			0
$859$	9.12751	−	15.8093i	0.311427	−	0.539407i	−0.667245	−	0.744838i	$-0.732527\pi$
$859$	9.12751	−	15.8093i	0.311427	−	0.539407i	0.978671	+	0.205432i	$0.0658598\pi$
$860$	28.0581	+	5.96394i	0.956775	+	0.203369i
$861$		0			0
$862$	8.83493	+	3.93357i	0.300919	+	0.133978i
$863$	18.5553	+	6.02899i	0.631631	+	0.205229i	0.607297	−	0.794475i	$-0.292254\pi$
$863$	18.5553	+	6.02899i	0.631631	+	0.205229i	0.0243334	+	0.999704i	$0.492254\pi$
$864$		0			0
$865$	14.4714	+	19.9181i	0.492042	+	0.677237i
$866$	−0.689280	+	6.55806i	−0.0234227	+	0.222852i
$867$		0			0
$868$	−3.34490	−	1.93118i	−0.113533	−	0.0655485i
$869$	−16.5010	+	0.0129328i	−0.559756	+	0.000438715i
$870$		0			0
$871$	12.8249	+	11.5476i	0.434555	+	0.391275i
$872$	5.79310	−	7.97352i	0.196179	−	0.270017i
$873$		0			0
$874$	−4.20920	+	12.9546i	−0.142378	+	0.438196i
$875$	−31.9136	+	6.78345i	−1.07888	+	0.229322i
$876$		0			0
$877$	8.33127	+	18.7123i	0.281327	+	0.631871i	0.997839	−	0.0657038i	$-0.0209292\pi$
$877$	8.33127	+	18.7123i	0.281327	+	0.631871i	−0.716512	+	0.697575i	$0.754263\pi$
$878$	−2.29880	+	10.8150i	−0.0775807	+	0.364989i
$879$		0			0
$880$	2.39519	+	22.6181i	0.0807417	+	0.762457i
$881$			38.0577i			1.28220i	0.767459	+	0.641099i	$0.221521\pi$
$881$			38.0577i			1.28220i	−0.767459	+	0.641099i	$0.778479\pi$
$882$		0			0
$883$	17.6981	+	12.8584i	0.595590	+	0.432721i	0.844311	−	0.535854i	$-0.180010\pi$
$883$	17.6981	+	12.8584i	0.595590	+	0.432721i	−0.248721	+	0.968575i	$0.580010\pi$
$884$	−1.26237	+	2.83533i	−0.0424581	+	0.0953625i
$885$		0			0
$886$	−8.44936	+	7.60784i	−0.283862	+	0.255590i
$887$	−3.54116	−	33.6919i	−0.118900	−	1.13126i	−0.877457	−	0.479655i	$-0.840762\pi$
$887$	−3.54116	−	33.6919i	−0.118900	−	1.13126i	0.758557	−	0.651607i	$-0.225905\pi$
$888$		0			0
$889$	16.7416	−	18.5934i	0.561495	−	0.623603i
$890$	−7.07018			−0.236993
$891$		0			0
$892$	−18.3383			−0.614011
$893$	2.37063	−	2.63285i	0.0793300	−	0.0881048i
$894$		0			0
$895$	−0.498218	−	4.74023i	−0.0166536	−	0.158448i
$896$	18.7396	−	16.8732i	0.626045	−	0.563693i
$897$		0			0
$898$	−3.56862	+	8.01524i	−0.119086	+	0.267472i
$899$	5.75849	+	4.18379i	0.192056	+	0.139537i
$900$		0			0
$901$		−	1.83807i		−	0.0612349i
$902$	−3.50464	−	7.85497i	−0.116692	−	0.261542i
$903$		0			0
$904$	2.80588	−	13.2006i	0.0933222	−	0.439046i
$905$	31.4049	+	70.5366i	1.04393	+	2.34472i
$906$		0			0
$907$	15.9195	−	3.38378i	0.528597	−	0.112357i	0.0641203	−	0.997942i	$-0.479576\pi$
$907$	15.9195	−	3.38378i	0.528597	−	0.112357i	0.464476	+	0.885585i	$0.346243\pi$
$908$	−5.34588	+	16.4529i	−0.177409	+	0.546010i
$909$		0			0
$910$	−18.6411	+	25.6572i	−0.617945	+	0.850529i
$911$	−12.2976	−	11.0728i	−0.407439	−	0.366859i	0.439778	−	0.898106i	$-0.355057\pi$
$911$	−12.2976	−	11.0728i	−0.407439	−	0.366859i	−0.847217	+	0.531247i	$0.821724\pi$
$912$		0			0
$913$	26.0844	−	35.9613i	0.863267	−	1.19015i
$914$	−4.65190	−	2.68578i	−0.153871	−	0.0888376i
$915$		0			0
$916$	−3.32082	+	31.5955i	−0.109723	+	1.04394i
$917$	−22.4044	−	30.8371i	−0.739860	−	1.01833i
$918$		0			0
$919$	30.9592	+	10.0592i	1.02125	+	0.331824i	0.771325	−	0.636441i	$-0.219594\pi$
$919$	30.9592	+	10.0592i	1.02125	+	0.331824i	0.249924	+	0.968265i	$0.419594\pi$
$920$	68.2924	+	30.4057i	2.25153	+	1.00245i
$921$		0			0
$922$	−22.0198	−	4.68046i	−0.725185	−	0.154143i
$923$	−21.0118	+	36.3935i	−0.691612	+	1.19791i
$924$		0			0
$925$	16.6623	+	28.8599i	0.547852	+	0.948907i
$926$	−5.42868	−	16.7078i	−0.178397	−	0.549051i
$927$		0			0
$928$	−30.0543	+	21.8357i	−0.986581	+	0.716793i
$929$	−10.7827	−	50.7287i	−0.353769	−	1.66435i	−0.690941	−	0.722911i	$-0.742804\pi$
$929$	−10.7827	−	50.7287i	−0.353769	−	1.66435i	0.337172	−	0.941443i	$-0.390530\pi$
$930$		0			0
$931$	5.08369	−	0.534317i	0.166611	−	0.0175115i
$932$	−29.7343	+	13.2386i	−0.973979	+	0.433643i
$933$		0			0
$934$	−14.9488	+	8.63067i	−0.489138	+	0.282404i
$935$	3.52584	+	1.56649i	0.115307	+	0.0512298i
$936$		0			0
$937$	4.46609	−	1.45112i	0.145901	−	0.0474061i	−0.235156	−	0.971958i	$-0.575560\pi$
$937$	4.46609	−	1.45112i	0.145901	−	0.0474061i	0.381057	+	0.924552i	$0.375560\pi$
$938$	−3.83097	−	0.402651i	−0.125086	−	0.0131470i
$939$		0			0
$940$	−5.81181	−	6.45467i	−0.189560	−	0.210528i
$941$	6.02987	+	6.69685i	0.196568	+	0.218311i	0.833369	−	0.552718i	$-0.186409\pi$
$941$	6.02987	+	6.69685i	0.196568	+	0.218311i	−0.636801	+	0.771029i	$0.719743\pi$
$942$		0			0
$943$	37.0820	+	3.89748i	1.20756	+	0.126919i
$944$	−9.77287	+	3.17540i	−0.318080	+	0.103350i
$945$		0			0
$946$	−4.90427	−	8.47910i	−0.159452	−	0.275679i
$947$	28.1466	−	16.2504i	0.914641	−	0.528068i	0.0327198	−	0.999465i	$-0.489583\pi$
$947$	28.1466	−	16.2504i	0.914641	−	0.528068i	0.881922	+	0.471396i	$0.156250\pi$
$948$		0			0
$949$	54.2913	−	24.1720i	1.76237	−	0.784658i
$950$	−13.5697	+	1.42623i	−0.440258	+	0.0462730i
$951$		0			0
$952$	−0.322435	−	1.51694i	−0.0104502	−	0.0491643i
$953$	−9.17192	+	6.66379i	−0.297108	+	0.215861i	−0.726345	−	0.687331i	$-0.758782\pi$
$953$	−9.17192	+	6.66379i	−0.297108	+	0.215861i	0.429237	+	0.903192i	$0.358782\pi$
$954$		0			0
$955$	7.76447	+	23.8966i	0.251252	+	0.773275i
$956$	13.8855	+	24.0503i	0.449088	+	0.777843i
$957$		0			0
$958$	2.30121	−	3.98581i	0.0743488	−	0.128776i
$959$	2.95008	+	0.627059i	0.0952631	+	0.0202488i
$960$		0			0
$961$	−27.2578	−	12.1360i	−0.879285	−	0.391483i
$962$	13.5757	+	4.41102i	0.437699	+	0.142217i
$963$		0			0
$964$	−19.4850	−	26.8187i	−0.627568	−	0.863774i
$965$	6.16233	−	58.6307i	0.198373	−	1.88739i
$966$		0			0
$967$	4.25298	+	2.45546i	0.136767	+	0.0789623i	0.566822	−	0.823840i	$-0.308173\pi$
$967$	4.25298	+	2.45546i	0.136767	+	0.0789623i	−0.430055	+	0.902802i	$0.641506\pi$
$968$	16.4856	−	18.3670i	0.529868	−	0.590337i
$969$		0			0
$970$	−25.3459	−	22.8215i	−0.813808	−	0.732756i
$971$	6.66140	−	9.16863i	0.213774	−	0.294235i	−0.688641	−	0.725103i	$-0.741792\pi$
$971$	6.66140	−	9.16863i	0.213774	−	0.294235i	0.902415	+	0.430867i	$0.141792\pi$
$972$		0			0
$973$	8.26991	−	25.4522i	0.265121	−	0.815959i
$974$	11.3082	−	2.40363i	0.362338	−	0.0770173i
$975$		0			0
$976$	−1.12442	−	2.52549i	−0.0359918	−	0.0808388i
$977$	6.20943	−	29.2131i	0.198657	−	0.934610i	−0.759973	−	0.649955i	$-0.774788\pi$
$977$	6.20943	−	29.2131i	0.198657	−	0.934610i	0.958630	−	0.284655i	$-0.0918789\pi$
$978$		0			0
$979$	−6.77661	−	7.51433i	−0.216581	−	0.240159i
$980$		−	12.5318i		−	0.400313i
$981$		0			0
$982$	−10.7272	−	7.79379i	−0.342320	−	0.248710i
$983$	−2.73519	+	6.14335i	−0.0872392	+	0.195942i	−0.951896	−	0.306420i	$-0.900869\pi$
$983$	−2.73519	+	6.14335i	−0.0872392	+	0.195942i	0.864657	+	0.502362i	$0.167536\pi$
$984$		0			0
$985$	−5.80168	+	5.22386i	−0.184857	+	0.166446i
$986$	0.133451	+	1.26970i	0.00424993	+	0.0404354i
$987$		0			0
$988$	16.3904	−	18.2034i	0.521449	−	0.579128i
$989$	42.4618			1.35021
$990$		0			0
$991$	−6.33993			−0.201395			−0.100697	−	0.994917i	$-0.532107\pi$
$991$	−6.33993			−0.201395			−0.100697	+	0.994917i	$0.532107\pi$
$992$	−4.06010	+	4.50919i	−0.128908	+	0.143167i
$993$		0			0
$994$	−0.980486	−	9.32871i	−0.0310991	−	0.295889i
$995$	10.4538	−	9.41261i	0.331406	−	0.298400i
$996$		0			0
$997$	2.74694	−	6.16972i	0.0869963	−	0.195397i	−0.864808	−	0.502103i	$-0.832560\pi$
$997$	2.74694	−	6.16972i	0.0869963	−	0.195397i	0.951804	+	0.306706i	$0.0992267\pi$
$998$	−5.99996	−	4.35922i	−0.189925	−	0.137989i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.u.e.215.5		64
3.2	odd	2	inner	891.2.u.e.215.4		64
9.2	odd	6	inner	891.2.u.e.512.5		64
9.4	even	3		297.2.k.a.215.5	yes	32
9.5	odd	6		297.2.k.a.215.4	yes	32
9.7	even	3	inner	891.2.u.e.512.4		64
11.2	odd	10	inner	891.2.u.e.134.5		64
33.2	even	10	inner	891.2.u.e.134.4		64
99.2	even	30	inner	891.2.u.e.431.5		64
99.13	odd	30		297.2.k.a.134.4	✓	32
99.68	even	30		297.2.k.a.134.5	yes	32
99.79	odd	30	inner	891.2.u.e.431.4		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.k.a.134.4	✓	32	99.13	odd	30
297.2.k.a.134.5	yes	32	99.68	even	30
297.2.k.a.215.4	yes	32	9.5	odd	6
297.2.k.a.215.5	yes	32	9.4	even	3
891.2.u.e.134.4		64	33.2	even	10	inner
891.2.u.e.134.5		64	11.2	odd	10	inner
891.2.u.e.215.4		64	3.2	odd	2	inner
891.2.u.e.215.5		64	1.1	even	1	trivial
891.2.u.e.431.4		64	99.79	odd	30	inner
891.2.u.e.431.5		64	99.2	even	30	inner
891.2.u.e.512.4		64	9.7	even	3	inner
891.2.u.e.512.5		64	9.2	odd	6	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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.u (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.415331 - 0.461272i) q^{2} +(0.168785 + 1.60588i) q^{4} +(-2.77455 + 2.49822i) q^{5} +(-0.902304 + 2.02661i) q^{7} +(1.81517 + 1.31880i) q^{8} +O(q^{10})\)	\(q+(0.415331 - 0.461272i) q^{2} +(0.168785 + 1.60588i) q^{4} +(-2.77455 + 2.49822i) q^{5} +(-0.902304 + 2.02661i) q^{7} +(1.81517 + 1.31880i) q^{8} +2.31741i q^{10} +(-2.46299 + 2.22119i) q^{11} +(1.28259 - 6.03412i) q^{13} +(0.560062 + 1.25792i) q^{14} +(-1.79666 + 0.381893i) q^{16} +(-0.0962825 + 0.296327i) q^{17} +(1.44540 - 1.98943i) q^{19} +(-4.48015 - 4.03394i) q^{20} +(0.00161348 + 2.05864i) q^{22} +(-7.72848 - 4.46204i) q^{23} +(0.934405 - 8.89027i) q^{25} +(-2.25067 - 3.09778i) q^{26} +(-3.40679 - 1.10693i) q^{28} +(6.03070 + 2.68504i) q^{29} +(1.05467 + 0.224178i) q^{31} +(-2.81373 + 4.87352i) q^{32} +(0.0966983 + 0.167486i) q^{34} +(-2.55942 - 7.87708i) q^{35} +(-3.01593 + 2.19120i) q^{37} +(-0.317346 - 1.49300i) q^{38} +(-8.33093 + 0.875616i) q^{40} +(-3.81695 + 1.69941i) q^{41} +(-4.12066 + 2.37906i) q^{43} +(-3.98268 - 3.58037i) q^{44} +(-5.26809 + 1.71171i) q^{46} +(1.43283 + 0.150597i) q^{47} +(1.39093 + 1.54478i) q^{49} +(-3.71275 - 4.12342i) q^{50} +(9.90657 + 1.04122i) q^{52} +(-5.61052 + 1.82297i) q^{53} +(1.28469 - 12.3159i) q^{55} +(-4.31052 + 2.48868i) q^{56} +(3.74327 - 1.66661i) q^{58} +(5.56375 - 0.584774i) q^{59} +(0.312919 + 1.47217i) q^{61} +(0.541446 - 0.393383i) q^{62} +(-0.0558176 - 0.171789i) q^{64} +(11.5159 + 19.9462i) q^{65} +(-1.39875 + 2.42271i) q^{67} +(-0.492117 - 0.104603i) q^{68} +(-4.69648 - 2.09101i) q^{70} +(-6.47873 - 2.10507i) q^{71} +(5.66251 + 7.79378i) q^{73} +(-0.241870 + 2.30124i) q^{74} +(3.43875 + 1.98536i) q^{76} +(-2.27911 - 6.99570i) q^{77} +(3.69731 + 3.32908i) q^{79} +(4.03089 - 5.54804i) q^{80} +(-0.801405 + 2.46647i) q^{82} +(-13.1020 + 2.78492i) q^{83} +(-0.473149 - 1.06271i) q^{85} +(-0.614042 + 2.88884i) q^{86} +(-7.40004 + 0.783640i) q^{88} +3.05090i q^{89} +(11.0715 + 8.04392i) q^{91} +(5.86106 - 13.1641i) q^{92} +(0.664567 - 0.598379i) q^{94} +(0.959676 + 9.13071i) q^{95} +(-9.84786 + 10.9372i) q^{97} +1.29026 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{4}+O(q^{10}) \) 64 * q + 8 * q^4	\( 64 q + 8 q^{4} + 4 q^{16} - 36 q^{22} - 8 q^{25} - 200 q^{28} - 8 q^{31} + 64 q^{34} - 24 q^{37} + 60 q^{40} - 40 q^{46} - 100 q^{52} + 16 q^{55} - 24 q^{58} - 60 q^{61} + 72 q^{64} + 24 q^{67} - 8 q^{70} + 160 q^{73} + 60 q^{79} + 144 q^{82} + 20 q^{85} + 24 q^{88} + 48 q^{91} - 20 q^{94} + 24 q^{97}+O(q^{100}) \) 64 * q + 8 * q^4 + 4 * q^16 - 36 * q^22 - 8 * q^25 - 200 * q^28 - 8 * q^31 + 64 * q^34 - 24 * q^37 + 60 * q^40 - 40 * q^46 - 100 * q^52 + 16 * q^55 - 24 * q^58 - 60 * q^61 + 72 * q^64 + 24 * q^67 - 8 * q^70 + 160 * q^73 + 60 * q^79 + 144 * q^82 + 20 * q^85 + 24 * q^88 + 48 * q^91 - 20 * q^94 + 24 * q^97

Introduction

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