LMFDB - Embedded newform 819.2.et.b.271.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(136,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("819.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.et (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			271.3
Character	$\chi$	$=$	819.271
Dual form			819.2.et.b.136.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.490988 - 0.490988i) q^{2} -1.51786i q^{4} +(0.00962681 + 0.0359277i) q^{5} +(-0.176775 - 2.63984i) q^{7} +(-1.72723 + 1.72723i) q^{8} +O(q^{10})$	\(q+(-0.490988 - 0.490988i) q^{2} -1.51786i q^{4} +(0.00962681 + 0.0359277i) q^{5} +(-0.176775 - 2.63984i) q^{7} +(-1.72723 + 1.72723i) q^{8} +(0.0129135 - 0.0223668i) q^{10} +(-0.292106 - 1.09015i) q^{11} +(-3.58326 + 0.400306i) q^{13} +(-1.20934 + 1.38292i) q^{14} -1.33962 q^{16} -6.40192 q^{17} +(3.56070 + 0.954087i) q^{19} +(0.0545333 - 0.0146122i) q^{20} +(-0.391832 + 0.678673i) q^{22} +2.79435i q^{23} +(4.32893 - 2.49931i) q^{25} +(1.95588 + 1.56279i) q^{26} +(-4.00691 + 0.268320i) q^{28} +(-1.84998 - 3.20426i) q^{29} +(-2.63716 - 0.706626i) q^{31} +(4.11220 + 4.11220i) q^{32} +(3.14327 + 3.14327i) q^{34} +(0.0931417 - 0.0317644i) q^{35} +(-3.94724 + 3.94724i) q^{37} +(-1.27982 - 2.21671i) q^{38} +(-0.0786831 - 0.0454277i) q^{40} +(0.188789 + 0.0505859i) q^{41} +(1.84817 + 1.06704i) q^{43} +(-1.65470 + 0.443376i) q^{44} +(1.37199 - 1.37199i) q^{46} +(-5.43116 + 1.45527i) q^{47} +(-6.93750 + 0.933315i) q^{49} +(-3.35258 - 0.898322i) q^{50} +(0.607609 + 5.43889i) q^{52} +(0.295822 + 0.512378i) q^{53} +(0.0363547 - 0.0209894i) q^{55} +(4.86494 + 4.25427i) q^{56} +(-0.664935 + 2.48157i) q^{58} +(-7.97051 - 7.97051i) q^{59} +(-1.18838 + 0.686113i) q^{61} +(0.947871 + 1.64176i) q^{62} -1.35883i q^{64} +(-0.0488775 - 0.124885i) q^{65} +(-7.28639 + 1.95238i) q^{67} +9.71723i q^{68} +(-0.0613274 - 0.0301356i) q^{70} +(9.88214 - 2.64791i) q^{71} +(0.707590 - 2.64076i) q^{73} +3.87610 q^{74} +(1.44817 - 5.40465i) q^{76} +(-2.82619 + 0.963824i) q^{77} +(-1.63129 + 2.82548i) q^{79} +(-0.0128963 - 0.0481297i) q^{80} +(-0.0678562 - 0.117530i) q^{82} +(4.92754 - 4.92754i) q^{83} +(-0.0616301 - 0.230007i) q^{85} +(-0.383525 - 1.43133i) q^{86} +(2.38748 + 1.37841i) q^{88} +(-11.9122 - 11.9122i) q^{89} +(1.69017 + 9.38847i) q^{91} +4.24143 q^{92} +(3.38116 + 1.95211i) q^{94} +0.137113i q^{95} +(-0.663884 - 2.47765i) q^{97} +(3.86448 + 2.94799i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8}+O(q^{10}) $ 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8	$ 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8} - 6 q^{10} - 2 q^{11} + 20 q^{14} + 4 q^{16} + 12 q^{17} + 14 q^{19} - 36 q^{20} - 8 q^{22} - 24 q^{26} + 2 q^{28} + 8 q^{29} - 4 q^{31} - 10 q^{32} - 12 q^{34} + 20 q^{35} - 10 q^{37} + 48 q^{40} + 18 q^{41} + 48 q^{43} + 6 q^{44} + 24 q^{46} + 6 q^{47} - 50 q^{49} - 10 q^{50} - 26 q^{52} - 12 q^{53} + 6 q^{55} - 54 q^{56} - 46 q^{58} - 42 q^{59} + 30 q^{61} - 36 q^{62} - 28 q^{65} - 10 q^{67} - 88 q^{70} + 42 q^{71} + 40 q^{73} - 12 q^{74} - 52 q^{76} + 4 q^{79} - 30 q^{80} - 54 q^{82} - 66 q^{83} - 54 q^{85} + 18 q^{86} - 6 q^{88} + 26 q^{91} + 156 q^{92} - 18 q^{94} - 62 q^{97} + 56 q^{98}+O(q^{100}) $ 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8 - 6 * q^10 - 2 * q^11 + 20 * q^14 + 4 * q^16 + 12 * q^17 + 14 * q^19 - 36 * q^20 - 8 * q^22 - 24 * q^26 + 2 * q^28 + 8 * q^29 - 4 * q^31 - 10 * q^32 - 12 * q^34 + 20 * q^35 - 10 * q^37 + 48 * q^40 + 18 * q^41 + 48 * q^43 + 6 * q^44 + 24 * q^46 + 6 * q^47 - 50 * q^49 - 10 * q^50 - 26 * q^52 - 12 * q^53 + 6 * q^55 - 54 * q^56 - 46 * q^58 - 42 * q^59 + 30 * q^61 - 36 * q^62 - 28 * q^65 - 10 * q^67 - 88 * q^70 + 42 * q^71 + 40 * q^73 - 12 * q^74 - 52 * q^76 + 4 * q^79 - 30 * q^80 - 54 * q^82 - 66 * q^83 - 54 * q^85 + 18 * q^86 - 6 * q^88 + 26 * q^91 + 156 * q^92 - 18 * q^94 - 62 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.490988	−	0.490988i	−0.347181	−	0.347181i	0.511877	−	0.859059i	$-0.328950\pi$
$2$	−0.490988	−	0.490988i	−0.347181	−	0.347181i	−0.859059	+	0.511877i	$0.828950\pi$
$3$		0			0
$3$		0			0
$4$		−	1.51786i		−	0.758931i
$5$	0.00962681	+	0.0359277i	0.00430524	+	0.0160674i	0.968045	−	0.250776i	$-0.0806859\pi$
$5$	0.00962681	+	0.0359277i	0.00430524	+	0.0160674i	−0.963740	+	0.266844i	$0.914019\pi$
$6$		0			0
$7$	−0.176775	−	2.63984i	−0.0668147	−	0.997765i
$7$	−0.176775	−	2.63984i	−0.0668147	−	0.997765i
$8$	−1.72723	+	1.72723i	−0.610667	+	0.610667i
$9$		0			0
$10$	0.0129135	−	0.0223668i	0.00408359	−	0.00707299i
$11$	−0.292106	−	1.09015i	−0.0880732	−	0.328694i	0.907805	−	0.419392i	$-0.137757\pi$
$11$	−0.292106	−	1.09015i	−0.0880732	−	0.328694i	−0.995878	+	0.0906984i	$0.971090\pi$
$12$		0			0
$13$	−3.58326	+	0.400306i	−0.993818	+	0.111025i
$13$	−3.58326	+	0.400306i	−0.993818	+	0.111025i
$14$	−1.20934	+	1.38292i	−0.323209	+	0.369602i
$15$		0			0
$16$	−1.33962			−0.334906
$17$	−6.40192			−1.55269			−0.776347	−	0.630306i	$-0.782930\pi$
$17$	−6.40192			−1.55269			−0.776347	+	0.630306i	$0.782930\pi$
$18$		0			0
$19$	3.56070	+	0.954087i	0.816881	+	0.218883i	0.642982	−	0.765881i	$-0.277697\pi$
$19$	3.56070	+	0.954087i	0.816881	+	0.218883i	0.173899	+	0.984764i	$0.444363\pi$
$20$	0.0545333	−	0.0146122i	0.0121940	−	0.00326738i
$21$		0			0
$22$	−0.391832	+	0.678673i	−0.0835389	+	0.144694i
$23$			2.79435i			0.582661i	0.956622	+	0.291331i	$0.0940980\pi$
$23$			2.79435i			0.582661i	−0.956622	+	0.291331i	$0.905902\pi$
$24$		0			0
$25$	4.32893	−	2.49931i	0.865786	−	0.499862i
$26$	1.95588	+	1.56279i	0.383580	+	0.306489i
$27$		0			0
$28$	−4.00691	+	0.268320i	−0.757235	+	0.0507077i
$29$	−1.84998	−	3.20426i	−0.343532	−	0.595015i	0.641554	−	0.767078i	$-0.278290\pi$
$29$	−1.84998	−	3.20426i	−0.343532	−	0.595015i	−0.985086	+	0.172063i	$0.944957\pi$
$30$		0			0
$31$	−2.63716	−	0.706626i	−0.473648	−	0.126914i	0.0140952	−	0.999901i	$-0.495513\pi$
$31$	−2.63716	−	0.706626i	−0.473648	−	0.126914i	−0.487744	+	0.872987i	$0.662180\pi$
$32$	4.11220	+	4.11220i	0.726941	+	0.726941i
$33$		0			0
$34$	3.14327	+	3.14327i	0.539066	+	0.539066i
$35$	0.0931417	−	0.0317644i	0.0157438	−	0.00536916i
$36$		0			0
$37$	−3.94724	+	3.94724i	−0.648923	+	0.648923i	−0.952733	−	0.303810i	$-0.901741\pi$
$37$	−3.94724	+	3.94724i	−0.648923	+	0.648923i	0.303810	+	0.952733i	$0.401741\pi$
$38$	−1.27982	−	2.21671i	−0.207614	−	0.359598i
$39$		0			0
$40$	−0.0786831	−	0.0454277i	−0.0124409	−	0.00718275i
$41$	0.188789	+	0.0505859i	0.0294839	+	0.00790020i	0.273531	−	0.961863i	$-0.411808\pi$
$41$	0.188789	+	0.0505859i	0.0294839	+	0.00790020i	−0.244047	+	0.969763i	$0.578475\pi$
$42$		0			0
$43$	1.84817	+	1.06704i	0.281843	+	0.162722i	0.634258	−	0.773122i	$-0.281306\pi$
$43$	1.84817	+	1.06704i	0.281843	+	0.162722i	−0.352414	+	0.935844i	$0.614639\pi$
$44$	−1.65470	+	0.443376i	−0.249456	+	0.0668414i
$45$		0			0
$46$	1.37199	−	1.37199i	0.202289	−	0.202289i
$47$	−5.43116	+	1.45527i	−0.792215	+	0.212273i	−0.632163	−	0.774835i	$-0.717833\pi$
$47$	−5.43116	+	1.45527i	−0.792215	+	0.212273i	−0.160052	+	0.987109i	$0.551166\pi$
$48$		0			0
$49$	−6.93750	+	0.933315i	−0.991072	+	0.133331i
$50$	−3.35258	−	0.898322i	−0.474127	−	0.127042i
$51$		0			0
$52$	0.607609	+	5.43889i	0.0842602	+	0.754239i
$53$	0.295822	+	0.512378i	0.0406342	+	0.0703805i	0.885627	−	0.464397i	$-0.153729\pi$
$53$	0.295822	+	0.512378i	0.0406342	+	0.0703805i	−0.844993	+	0.534777i	$0.820395\pi$
$54$		0			0
$55$	0.0363547	−	0.0209894i	0.00490207	−	0.00283021i
$56$	4.86494	+	4.25427i	0.650104	+	0.568501i
$57$		0			0
$58$	−0.664935	+	2.48157i	−0.0873102	+	0.325846i
$59$	−7.97051	−	7.97051i	−1.03767	−	1.03767i	−0.999262	−	0.0384097i	$-0.987771\pi$
$59$	−7.97051	−	7.97051i	−1.03767	−	1.03767i	−0.0384097	−	0.999262i	$-0.512229\pi$
$60$		0			0
$61$	−1.18838	+	0.686113i	−0.152157	+	0.0878478i	−0.574145	−	0.818753i	$-0.694666\pi$
$61$	−1.18838	+	0.686113i	−0.152157	+	0.0878478i	0.421989	+	0.906601i	$0.361332\pi$
$62$	0.947871	+	1.64176i	0.120380	+	0.208504i
$63$		0			0
$64$		−	1.35883i		−	0.169854i
$65$	−0.0488775	−	0.124885i	−0.00606250	−	0.0154901i
$66$		0			0
$67$	−7.28639	+	1.95238i	−0.890174	+	0.238522i	−0.674792	−	0.738008i	$-0.735767\pi$
$67$	−7.28639	+	1.95238i	−0.890174	+	0.238522i	−0.215383	+	0.976530i	$0.569100\pi$
$68$			9.71723i			1.17839i
$69$		0			0
$70$	−0.0613274	−	0.0301356i	−0.00733003	−	0.00360189i
$71$	9.88214	−	2.64791i	1.17279	−	0.314249i	0.380729	−	0.924686i	$-0.375673\pi$
$71$	9.88214	−	2.64791i	1.17279	−	0.314249i	0.792065	+	0.610437i	$0.209006\pi$
$72$		0			0
$73$	0.707590	−	2.64076i	0.0828171	−	0.309078i	−0.912075	−	0.410024i	$-0.865520\pi$
$73$	0.707590	−	2.64076i	0.0828171	−	0.309078i	0.994892	+	0.100946i	$0.0321870\pi$
$74$	3.87610			0.450588
$75$		0			0
$76$	1.44817	−	5.40465i	0.166117	−	0.619956i
$77$	−2.82619	+	0.963824i	−0.322075	+	0.109838i
$78$		0			0
$79$	−1.63129	+	2.82548i	−0.183535	+	0.317891i	−0.943082	−	0.332561i	$-0.892087\pi$
$79$	−1.63129	+	2.82548i	−0.183535	+	0.317891i	0.759547	+	0.650452i	$0.225421\pi$
$80$	−0.0128963	−	0.0481297i	−0.00144185	−	0.00538106i
$81$		0			0
$82$	−0.0678562	−	0.117530i	−0.00749347	−	0.0129791i
$83$	4.92754	−	4.92754i	0.540868	−	0.540868i	−0.382915	−	0.923783i	$-0.625080\pi$
$83$	4.92754	−	4.92754i	0.540868	−	0.540868i	0.923783	+	0.382915i	$0.125080\pi$
$84$		0			0
$85$	−0.0616301	−	0.230007i	−0.00668472	−	0.0249477i
$86$	−0.383525	−	1.43133i	−0.0413565	−	0.154345i
$87$		0			0
$88$	2.38748	+	1.37841i	0.254506	+	0.146939i
$89$	−11.9122	−	11.9122i	−1.26269	−	1.26269i	−0.949785	−	0.312903i	$-0.898699\pi$
$89$	−11.9122	−	11.9122i	−1.26269	−	1.26269i	−0.312903	−	0.949785i	$-0.601301\pi$
$90$		0			0
$91$	1.69017	+	9.38847i	0.177178	+	0.984179i
$92$	4.24143			0.442199
$93$		0			0
$94$	3.38116	+	1.95211i	0.348740	+	0.201345i
$95$			0.137113i			0.0140675i
$96$		0			0
$97$	−0.663884	−	2.47765i	−0.0674072	−	0.251567i	0.923997	−	0.382399i	$-0.124902\pi$
$97$	−0.663884	−	2.47765i	−0.0674072	−	0.251567i	−0.991405	+	0.130832i	$0.958235\pi$
$98$	3.86448	+	2.94799i	0.390371	+	0.297791i
$99$		0			0
$100$	−3.79360	−	6.57071i	−0.379360	−	0.657071i
$101$	−2.30855	+	3.99852i	−0.229709	+	0.397868i	−0.957722	−	0.287696i	$-0.907111\pi$
$101$	−2.30855	+	3.99852i	−0.229709	+	0.397868i	0.728013	+	0.685564i	$0.240444\pi$
$102$		0			0
$103$	−5.86837	+	10.1643i	−0.578227	+	1.00152i	0.417455	+	0.908697i	$0.362922\pi$
$103$	−5.86837	+	10.1643i	−0.578227	+	1.00152i	−0.995683	+	0.0928218i	$0.970411\pi$
$104$	5.49769	−	6.88053i	0.539093	−	0.674691i
$105$		0			0
$106$	0.106327	−	0.396817i	0.0103274	−	0.0385422i
$107$	−13.0733			−1.26385			−0.631923	−	0.775031i	$-0.717734\pi$
$107$	−13.0733			−1.26385			−0.631923	+	0.775031i	$0.717734\pi$
$108$		0			0
$109$	3.37504	−	12.5958i	0.323270	−	1.20646i	−0.592770	−	0.805372i	$-0.701966\pi$
$109$	3.37504	−	12.5958i	0.323270	−	1.20646i	0.916040	−	0.401087i	$-0.131368\pi$
$110$	−0.0281553	−	0.00754419i	−0.00268450	−	0.000719310i
$111$		0			0
$112$	0.236812	+	3.53639i	0.0223766	+	0.334158i
$113$	−1.85773	+	3.21769i	−0.174761	+	0.302694i	−0.940078	−	0.340958i	$-0.889249\pi$
$113$	−1.85773	+	3.21769i	−0.174761	+	0.302694i	0.765318	+	0.643653i	$0.222582\pi$
$114$		0			0
$115$	−0.100395	+	0.0269006i	−0.00936184	+	0.00250850i
$116$	−4.86362	+	2.80801i	−0.451575	+	0.260717i
$117$		0			0
$118$			7.82685i			0.720520i
$119$	1.13170	+	16.9000i	0.103743	+	1.54922i
$120$		0			0
$121$	8.42317	−	4.86312i	0.765743	−	0.442102i
$122$	0.920356	+	0.246609i	0.0833251	+	0.0223269i
$123$		0			0
$124$	−1.07256	+	4.00285i	−0.0963187	+	0.359466i
$125$	0.262973	+	0.262973i	0.0235210	+	0.0235210i
$126$		0			0
$127$	2.47692	−	1.43005i	0.219791	−	0.126897i	−0.386062	−	0.922473i	$-0.626165\pi$
$127$	2.47692	−	1.43005i	0.219791	−	0.126897i	0.605854	+	0.795576i	$0.292832\pi$
$128$	7.55722	−	7.55722i	0.667970	−	0.667970i
$129$		0			0
$130$	−0.0373187	+	0.0853152i	−0.00327307	+	0.00748264i
$131$	−0.119788	−	0.0691595i	−0.0104659	−	0.00604249i	0.494758	−	0.869031i	$-0.335257\pi$
$131$	−0.119788	−	0.0691595i	−0.0104659	−	0.00604249i	−0.505224	+	0.862988i	$0.668590\pi$
$132$		0			0
$133$	1.88919	−	9.56834i	0.163814	−	0.829680i
$134$	4.53613	+	2.61894i	0.391862	+	0.226242i
$135$		0			0
$136$	11.0576	−	11.0576i	0.948180	−	0.948180i
$137$	12.0623	−	12.0623i	1.03055	−	1.03055i	0.0310355	−	0.999518i	$-0.490120\pi$
$137$	12.0623	−	12.0623i	1.03055	−	1.03055i	0.999518	−	0.0310355i	$-0.00988049\pi$
$138$		0			0
$139$	−13.3885	−	7.72988i	−1.13560	−	0.655640i	−0.190264	−	0.981733i	$-0.560934\pi$
$139$	−13.3885	−	7.72988i	−1.13560	−	0.655640i	−0.945338	+	0.326093i	$0.894268\pi$
$140$	−0.0482139	−	0.141376i	−0.00407482	−	0.0119485i
$141$		0			0
$142$	−6.15211	−	3.55192i	−0.516273	−	0.298071i
$143$	1.48309	+	3.78937i	0.124022	+	0.316883i
$144$		0			0
$145$	0.0973123	−	0.0973123i	0.00808135	−	0.00808135i
$146$	−1.64400	+	0.949165i	−0.136059	+	0.0785534i
$147$		0			0
$148$	5.99137	+	5.99137i	0.492487	+	0.492487i
$149$	1.47392	−	5.50075i	0.120748	−	0.450639i	−0.878904	−	0.476998i	$-0.841725\pi$
$149$	1.47392	−	5.50075i	0.120748	−	0.450639i	0.999653	+	0.0263595i	$0.00839147\pi$
$150$		0			0
$151$	19.9927	+	5.35703i	1.62698	+	0.435949i	0.953042	−	0.302838i	$-0.0979340\pi$
$151$	19.9927	+	5.35703i	1.62698	+	0.435949i	0.673940	+	0.738786i	$0.264601\pi$
$152$	−7.79807	+	4.50222i	−0.632507	+	0.365178i
$153$		0			0
$154$	1.86085	+	0.914401i	0.149952	+	0.0736846i
$155$		−	0.101550i		−	0.00815668i
$156$		0			0
$157$	8.02263	−	4.63187i	0.640275	−	0.369663i	−0.144445	−	0.989513i	$-0.546140\pi$
$157$	8.02263	−	4.63187i	0.640275	−	0.369663i	0.784721	+	0.619850i	$0.212806\pi$
$158$	2.18822	−	0.586332i	0.174086	−	0.0466461i
$159$		0			0
$160$	−0.108155	+	0.187329i	−0.00855037	+	0.0148097i
$161$	7.37662	−	0.493970i	0.581359	−	0.0389303i
$162$		0			0
$163$	−3.97880	−	1.06612i	−0.311644	−	0.0835047i	0.0996072	−	0.995027i	$-0.468241\pi$
$163$	−3.97880	−	1.06612i	−0.311644	−	0.0835047i	−0.411251	+	0.911522i	$0.634908\pi$
$164$	0.0767824	−	0.286556i	0.00599570	−	0.0223763i
$165$		0			0
$166$	−4.83873			−0.375558
$167$	4.15955	−	15.5237i	0.321876	−	1.20126i	−0.595540	−	0.803326i	$-0.703062\pi$
$167$	4.15955	−	15.5237i	0.321876	−	1.20126i	0.917415	−	0.397931i	$-0.130272\pi$
$168$		0			0
$169$	12.6795	−	2.86880i	0.975347	−	0.220677i
$170$	−0.0826709	+	0.143190i	−0.00634057	+	0.0109822i
$171$		0			0
$172$	1.61962	−	2.80526i	0.123495	−	0.213899i
$173$	10.5332	+	18.2440i	0.800821	+	1.38706i	0.919076	+	0.394080i	$0.128937\pi$
$173$	10.5332	+	18.2440i	0.800821	+	1.38706i	−0.118255	+	0.992983i	$0.537730\pi$
$174$		0			0
$175$	−7.36302	−	10.9859i	−0.556592	−	0.830453i
$176$	0.391312	+	1.46040i	0.0294963	+	0.110082i
$177$		0			0
$178$			11.6975i			0.876763i
$179$	7.89629	+	4.55893i	0.590196	+	0.340750i	0.765175	−	0.643822i	$-0.222652\pi$
$179$	7.89629	+	4.55893i	0.590196	+	0.340750i	−0.174979	+	0.984572i	$0.555986\pi$
$180$		0			0
$181$	15.7169			1.16823			0.584113	−	0.811672i	$-0.301443\pi$
$181$	15.7169			1.16823			0.584113	+	0.811672i	$0.301443\pi$
$182$	3.77977	−	5.43948i	0.280175	−	0.403201i
$183$		0			0
$184$	−4.82647	−	4.82647i	−0.355812	−	0.355812i
$185$	−0.179815	−	0.103816i	−0.0132203	−	0.00763272i
$186$		0			0
$187$	1.87004	+	6.97908i	0.136751	+	0.510361i
$188$	2.20890	+	8.24374i	0.161101	+	0.601236i
$189$		0			0
$190$	0.0673208	−	0.0673208i	0.00488396	−	0.00488396i
$191$	−8.65358	−	14.9884i	−0.626151	−	1.08453i	−0.988317	−	0.152412i	$-0.951296\pi$
$191$	−8.65358	−	14.9884i	−0.626151	−	1.08453i	0.362166	−	0.932114i	$-0.382037\pi$
$192$		0			0
$193$	−3.25813	−	12.1595i	−0.234525	−	0.875260i	−0.978362	−	0.206899i	$-0.933663\pi$
$193$	−3.25813	−	12.1595i	−0.234525	−	0.875260i	0.743837	−	0.668361i	$-0.233004\pi$
$194$	−0.890537	+	1.54245i	−0.0639368	+	0.110742i
$195$		0			0
$196$	1.41664	+	10.5302i	0.101189	+	0.752154i
$197$	6.43206	−	24.0048i	0.458265	−	1.71027i	−0.220042	−	0.975490i	$-0.570619\pi$
$197$	6.43206	−	24.0048i	0.458265	−	1.71027i	0.678307	−	0.734778i	$-0.262714\pi$
$198$		0			0
$199$	−10.5978			−0.751257			−0.375629	−	0.926770i	$-0.622573\pi$
$199$	−10.5978			−0.751257			−0.375629	+	0.926770i	$0.622573\pi$
$200$	−3.16017	+	11.7939i	−0.223458	+	0.833956i
$201$		0			0
$202$	3.09670	−	0.829758i	0.217883	−	0.0583815i
$203$	−8.13169	+	5.45008i	−0.570733	+	0.382520i
$204$		0			0
$205$			0.00726976i			0.000507742i
$206$	7.87186	−	2.10926i	0.548458	−	0.146959i
$207$		0			0
$208$	4.80022	−	0.536260i	0.332836	−	0.0371829i
$209$		−	4.16041i		−	0.287781i
$210$		0			0
$211$	−10.3404	−	17.9102i	−0.711865	−	1.23299i	−0.964156	−	0.265335i	$-0.914518\pi$
$211$	−10.3404	−	17.9102i	−0.711865	−	1.23299i	0.252292	−	0.967651i	$-0.418816\pi$
$212$	0.777719	−	0.449016i	0.0534139	−	0.0308386i
$213$		0			0
$214$	6.41885	+	6.41885i	0.438784	+	0.438784i
$215$	−0.0205444	+	0.0766728i	−0.00140112	+	0.00522904i
$216$		0			0
$217$	−1.39919	+	7.08660i	−0.0949834	+	0.481070i
$218$	−7.84149	+	4.52729i	−0.531093	+	0.306627i
$219$		0			0
$220$	−0.0318590	−	0.0551814i	−0.00214793	−	0.00372033i
$221$	22.9398	−	2.56273i	1.54309	−	0.172388i
$222$		0			0
$223$	−3.17269	−	0.850119i	−0.212459	−	0.0569282i	0.151020	−	0.988531i	$-0.451744\pi$
$223$	−3.17269	−	0.850119i	−0.212459	−	0.0569282i	−0.363479	+	0.931603i	$0.618411\pi$
$224$	10.1286	−	11.5825i	0.676746	−	0.773886i
$225$		0			0
$226$	2.49197	−	0.667721i	0.165763	−	0.0444162i
$227$	13.0106	−	13.0106i	0.863541	−	0.863541i	−0.128207	−	0.991747i	$-0.540922\pi$
$227$	13.0106	−	13.0106i	0.863541	−	0.863541i	0.991747	+	0.128207i	$0.0409220\pi$
$228$		0			0
$229$	−10.5951	+	2.83894i	−0.700142	+	0.187603i	−0.591294	−	0.806456i	$-0.701383\pi$
$229$	−10.5951	+	2.83894i	−0.700142	+	0.187603i	−0.108848	+	0.994058i	$0.534716\pi$
$230$	0.0625004	+	0.0360846i	0.00412116	+	0.00237935i
$231$		0			0
$232$	8.72982	+	2.33915i	0.573141	+	0.153573i
$233$	−7.46970	−	4.31263i	−0.489356	−	0.282530i	0.234951	−	0.972007i	$-0.424507\pi$
$233$	−7.46970	−	4.31263i	−0.489356	−	0.282530i	−0.724307	+	0.689477i	$0.757840\pi$
$234$		0			0
$235$	−0.104569	−	0.181120i	−0.00682136	−	0.0118149i
$236$	−12.0981	+	12.0981i	−0.787521	+	0.787521i
$237$		0			0
$238$	7.74207	−	8.85337i	0.501844	−	0.573879i
$239$	5.82164	+	5.82164i	0.376571	+	0.376571i	0.869863	−	0.493293i	$-0.164207\pi$
$239$	5.82164	+	5.82164i	0.376571	+	0.376571i	−0.493293	+	0.869863i	$0.664207\pi$
$240$		0			0
$241$	−4.44250	−	4.44250i	−0.286166	−	0.286166i	0.549396	−	0.835562i	$-0.314858\pi$
$241$	−4.44250	−	4.44250i	−0.286166	−	0.286166i	−0.835562	+	0.549396i	$0.814858\pi$
$242$	−6.52341	−	1.74794i	−0.419341	−	0.112362i
$243$		0			0
$244$	1.04142	+	1.80380i	0.0666704	+	0.115476i
$245$	−0.100318	−	0.240264i	−0.00640908	−	0.0153499i
$246$		0			0
$247$	−13.1409	−	1.99337i	−0.836132	−	0.126835i
$248$	5.77549	−	3.33448i	0.366744	−	0.211740i
$249$		0			0
$250$		−	0.258233i		−	0.0163321i
$251$	−5.23454	+	9.06650i	−0.330402	+	0.572272i	−0.982591	−	0.185784i	$-0.940517\pi$
$251$	−5.23454	+	9.06650i	−0.330402	+	0.572272i	0.652189	+	0.758056i	$0.273851\pi$
$252$		0			0
$253$	3.04627	−	0.816245i	0.191517	−	0.0513169i
$254$	−1.91828	−	0.514001i	−0.120364	−	0.0322513i
$255$		0			0
$256$	−10.1387			−0.633667
$257$	5.35020			0.333737			0.166868	−	0.985979i	$-0.446635\pi$
$257$	5.35020			0.333737			0.166868	+	0.985979i	$0.446635\pi$
$258$		0			0
$259$	11.1179	+	9.72232i	0.690830	+	0.604115i
$260$	−0.189558	+	0.0741892i	−0.0117559	+	0.00460102i
$261$		0			0
$262$	0.0248579	+	0.0927709i	0.00153573	+	0.00573140i
$263$	3.08129	−	5.33695i	0.190000	−	0.329090i	−0.755250	−	0.655437i	$-0.772484\pi$
$263$	3.08129	−	5.33695i	0.190000	−	0.329090i	0.945250	+	0.326347i	$0.105818\pi$
$264$		0			0
$265$	−0.0155608	+	0.0155608i	−0.000955891	+	0.000955891i
$266$	−5.62551	+	3.77037i	−0.344922	+	0.231176i
$267$		0			0
$268$	2.96345	+	11.0597i	0.181021	+	0.675581i
$269$			20.5507i			1.25300i	0.779422	+	0.626500i	$0.215513\pi$
$269$			20.5507i			1.25300i	−0.779422	+	0.626500i	$0.784487\pi$
$270$		0			0
$271$	−7.18504	−	7.18504i	−0.436460	−	0.436460i	0.454359	−	0.890819i	$-0.349868\pi$
$271$	−7.18504	−	7.18504i	−0.436460	−	0.436460i	−0.890819	+	0.454359i	$0.849868\pi$
$272$	8.57617			0.520007
$273$		0			0
$274$	−11.8449			−0.715578
$275$	−3.98914	−	3.98914i	−0.240554	−	0.240554i
$276$		0			0
$277$			20.4254i			1.22725i	0.789599	+	0.613623i	$0.210288\pi$
$277$			20.4254i			1.22725i	−0.789599	+	0.613623i	$0.789712\pi$
$278$	2.77834	+	10.3689i	0.166634	+	0.621885i
$279$		0			0
$280$	−0.106013	+	0.215741i	−0.00633547	+	0.0128930i
$281$	13.0423	−	13.0423i	0.778037	−	0.778037i	−0.201460	−	0.979497i	$-0.564569\pi$
$281$	13.0423	−	13.0423i	0.778037	−	0.778037i	0.979497	+	0.201460i	$0.0645686\pi$
$282$		0			0
$283$	−1.00784	+	1.74563i	−0.0599100	+	0.103767i	−0.894425	−	0.447218i	$-0.852415\pi$
$283$	−1.00784	+	1.74563i	−0.0599100	+	0.103767i	0.834515	+	0.550986i	$0.185748\pi$
$284$	−4.01916	−	14.9997i	−0.238493	−	0.890069i
$285$		0			0
$286$	1.13236	−	2.58872i	0.0669578	−	0.153074i
$287$	0.100166	−	0.507316i	0.00591258	−	0.0299459i
$288$		0			0
$289$	23.9846			1.41086
$290$	−0.0955584			−0.00561138
$291$		0			0
$292$	−4.00831	−	1.07402i	−0.234569	−	0.0628525i
$293$	11.4688	−	3.07306i	0.670016	−	0.179530i	0.0922540	−	0.995736i	$-0.470593\pi$
$293$	11.4688	−	3.07306i	0.670016	−	0.179530i	0.577762	+	0.816205i	$0.303926\pi$
$294$		0			0
$295$	0.209632	−	0.363093i	0.0122052	−	0.0211401i
$296$		−	13.6356i		−	0.792552i
$297$		0			0
$298$	−3.42448	+	1.97712i	−0.198375	+	0.114532i
$299$	−1.11859	−	10.0129i	−0.0646899	−	0.579059i
$300$		0			0
$301$	2.49011	−	5.06750i	0.143527	−	0.292086i
$302$	−7.18594	−	12.4464i	−0.413504	−	0.716211i
$303$		0			0
$304$	−4.77000	−	1.27812i	−0.273578	−	0.0733051i
$305$	−0.0360908	−	0.0360908i	−0.00206656	−	0.00206656i
$306$		0			0
$307$	1.46571	+	1.46571i	0.0836528	+	0.0836528i	0.747695	−	0.664042i	$-0.231161\pi$
$307$	1.46571	+	1.46571i	0.0836528	+	0.0836528i	−0.664042	+	0.747695i	$0.731161\pi$
$308$	1.46295	+	4.28977i	0.0833594	+	0.244432i
$309$		0			0
$310$	−0.0498598	+	0.0498598i	−0.00283185	+	0.00283185i
$311$	1.37387	+	2.37961i	0.0779051	+	0.134936i	0.902346	−	0.431013i	$-0.141844\pi$
$311$	1.37387	+	2.37961i	0.0779051	+	0.134936i	−0.824441	+	0.565948i	$0.808510\pi$
$312$		0			0
$313$	6.57410	+	3.79556i	0.371590	+	0.214538i	0.674153	−	0.738592i	$-0.264509\pi$
$313$	6.57410	+	3.79556i	0.371590	+	0.214538i	−0.302563	+	0.953129i	$0.597842\pi$
$314$	−6.21321	−	1.66482i	−0.350632	−	0.0939514i
$315$		0			0
$316$	4.28869	+	2.47607i	0.241257	+	0.139290i
$317$	−9.63370	+	2.58134i	−0.541083	+	0.144983i	−0.519001	−	0.854774i	$-0.673696\pi$
$317$	−9.63370	+	2.58134i	−0.541083	+	0.144983i	−0.0220814	+	0.999756i	$0.507029\pi$
$318$		0			0
$319$	−2.95274	+	2.95274i	−0.165322	+	0.165322i
$320$	0.0488198	−	0.0130812i	0.00272911	−	0.000731262i
$321$		0			0
$322$	−3.86437	−	3.37930i	−0.215353	−	0.188321i
$323$	−22.7953	−	6.10799i	−1.26837	−	0.339858i
$324$		0			0
$325$	−14.5112	+	10.6886i	−0.804936	+	0.592895i
$326$	1.43009	+	2.47700i	0.0792056	+	0.137188i
$327$		0			0
$328$	−0.413456	+	0.238709i	−0.0228293	+	0.0131805i
$329$	4.80178	+	14.0801i	0.264731	+	0.776262i
$330$		0			0
$331$	−4.37748	+	16.3370i	−0.240608	+	0.897962i	0.734932	+	0.678141i	$0.237214\pi$
$331$	−4.37748	+	16.3370i	−0.240608	+	0.897962i	−0.975540	+	0.219821i	$0.929453\pi$
$332$	−7.47932	−	7.47932i	−0.410481	−	0.410481i
$333$		0			0
$334$	−9.66423	+	5.57964i	−0.528803	+	0.305305i
$335$	−0.140289	−	0.242988i	−0.00766483	−	0.0132759i
$336$		0			0
$337$		−	7.92125i		−	0.431498i	−0.976449	−	0.215749i	$-0.930781\pi$
$337$		−	7.92125i		−	0.431498i	0.976449	−	0.215749i	$-0.0692193\pi$
$338$	−7.63404	−	4.81694i	−0.415237	−	0.262007i
$339$		0			0
$340$	−0.349118	+	0.0935459i	−0.0189336	+	0.00507324i
$341$			3.08132i			0.166863i
$342$		0			0
$343$	3.69018	+	18.1489i	0.199251	+	0.979949i
$344$	−5.03523	+	1.34919i	−0.271482	+	0.0727433i
$345$		0			0
$346$	3.78592	−	14.1292i	0.203532	−	0.759592i
$347$	−24.3383			−1.30655			−0.653274	−	0.757122i	$-0.726605\pi$
$347$	−24.3383			−1.30655			−0.653274	+	0.757122i	$0.726605\pi$
$348$		0			0
$349$	4.20514	−	15.6938i	0.225096	−	0.840070i	−0.757270	−	0.653102i	$-0.773467\pi$
$349$	4.20514	−	15.6938i	0.225096	−	0.840070i	0.982366	−	0.186968i	$-0.0598660\pi$
$350$	−1.77877	+	9.00908i	−0.0950794	+	0.481556i
$351$		0			0
$352$	3.28173	−	5.68412i	0.174917	−	0.302965i
$353$	4.23848	+	15.8182i	0.225591	+	0.841919i	0.982167	+	0.188012i	$0.0602044\pi$
$353$	4.23848	+	15.8182i	0.225591	+	0.841919i	−0.756575	+	0.653907i	$0.773129\pi$
$354$		0			0
$355$	0.190267	+	0.329552i	0.0100983	+	0.0174908i
$356$	−18.0810	+	18.0810i	−0.958292	+	0.958292i
$357$		0			0
$358$	−1.63861	−	6.11536i	−0.0866031	−	0.323207i
$359$	−1.78847	−	6.67467i	−0.0943920	−	0.352276i	0.902535	−	0.430617i	$-0.141704\pi$
$359$	−1.78847	−	6.67467i	−0.0943920	−	0.352276i	−0.996927	+	0.0783418i	$0.975037\pi$
$360$		0			0
$361$	−4.68617	−	2.70556i	−0.246640	−	0.142398i
$362$	−7.71680	−	7.71680i	−0.405586	−	0.405586i
$363$		0			0
$364$	14.2504	−	2.56545i	0.746923	−	0.134466i
$365$	0.101688			0.00532262
$366$		0			0
$367$	−12.3820	−	7.14874i	−0.646335	−	0.373161i	0.140716	−	0.990050i	$-0.455060\pi$
$367$	−12.3820	−	7.14874i	−0.646335	−	0.373161i	−0.787050	+	0.616889i	$0.788393\pi$
$368$		−	3.74337i		−	0.195137i
$369$		0			0
$370$	0.0373145	+	0.139260i	0.00193989	+	0.00723976i
$371$	1.30030	−	0.871497i	0.0675083	−	0.0452459i
$372$		0			0
$373$	−11.3326	−	19.6286i	−0.586780	−	1.01633i	−0.994651	−	0.103293i	$-0.967062\pi$
$373$	−11.3326	−	19.6286i	−0.586780	−	1.01633i	0.407871	−	0.913039i	$-0.366271\pi$
$374$	2.50848	−	4.34481i	0.129710	−	0.224665i
$375$		0			0
$376$	6.86726	−	11.8944i	0.354152	−	0.613409i
$377$	7.91164	+	10.7411i	0.407470	+	0.553196i
$378$		0			0
$379$	−3.37163	+	12.5831i	−0.173189	+	0.646349i	0.823664	+	0.567078i	$0.191926\pi$
$379$	−3.37163	+	12.5831i	−0.173189	+	0.646349i	−0.996853	+	0.0792716i	$0.974741\pi$
$380$	0.208118			0.0106762
$381$		0			0
$382$	−3.11034	+	11.6080i	−0.159139	+	0.593914i
$383$	−2.21834	−	0.594401i	−0.113352	−	0.0303725i	0.201697	−	0.979448i	$-0.435354\pi$
$383$	−2.21834	−	0.594401i	−0.113352	−	0.0303725i	−0.315049	+	0.949075i	$0.602021\pi$
$384$		0			0
$385$	−0.0618353	−	0.0922602i	−0.00315142	−	0.00470202i
$386$	−4.37047	+	7.56988i	−0.222451	+	0.385297i
$387$		0			0
$388$	−3.76072	+	1.00768i	−0.190922	+	0.0511574i
$389$	10.9179	−	6.30348i	0.553562	−	0.319599i	−0.196996	−	0.980404i	$-0.563118\pi$
$389$	10.9179	−	6.30348i	0.553562	−	0.319599i	0.750557	+	0.660805i	$0.229785\pi$
$390$		0			0
$391$		−	17.8892i		−	0.904695i
$392$	10.3706	−	13.5947i	0.523794	−	0.686636i
$393$		0			0
$394$	−14.9441	+	8.62799i	−0.752874	+	0.434672i
$395$	−0.117217	−	0.0314083i	−0.00589784	−	0.00158032i
$396$		0			0
$397$	−0.580104	+	2.16498i	−0.0291146	+	0.108657i	−0.978954	−	0.204081i	$-0.934579\pi$
$397$	−0.580104	+	2.16498i	−0.0291146	+	0.108657i	0.949839	+	0.312738i	$0.101246\pi$
$398$	5.20339	+	5.20339i	0.260822	+	0.260822i
$399$		0			0
$400$	−5.79914	+	3.34813i	−0.289957	+	0.167407i
$401$	−25.4962	+	25.4962i	−1.27322	+	1.27322i	−0.328828	+	0.944390i	$0.606654\pi$
$401$	−25.4962	+	25.4962i	−1.27322	+	1.27322i	−0.944390	+	0.328828i	$0.893346\pi$
$402$		0			0
$403$	9.73251	+	1.47635i	0.484811	+	0.0735423i
$404$	6.06920	+	3.50405i	0.301954	+	0.174333i
$405$		0			0
$406$	6.66849	+	1.31664i	0.330952	+	0.0653438i
$407$	5.45612	+	3.15009i	0.270450	+	0.156144i
$408$		0			0
$409$	−6.52622	+	6.52622i	−0.322701	+	0.322701i	−0.849802	−	0.527102i	$-0.823279\pi$
$409$	−6.52622	+	6.52622i	−0.322701	+	0.322701i	0.527102	+	0.849802i	$0.323279\pi$
$410$	0.00356936	−	0.00356936i	0.000176278	−	0.000176278i
$411$		0			0
$412$	15.4280	+	8.90737i	0.760084	+	0.438834i
$413$	−19.6319	+	22.4498i	−0.966021	+	1.10468i
$414$		0			0
$415$	0.224472	+	0.129599i	0.0110189	+	0.00636176i
$416$	−16.3812	−	13.0889i	−0.803155	−	0.641738i
$417$		0			0
$418$	−2.04271	+	2.04271i	−0.0999123	+	0.0999123i
$419$	−15.4156	+	8.90022i	−0.753103	+	0.434804i	−0.826814	−	0.562475i	$-0.809849\pi$
$419$	−15.4156	+	8.90022i	−0.753103	+	0.434804i	0.0737108	+	0.997280i	$0.476516\pi$
$420$		0			0
$421$	−5.59661	−	5.59661i	−0.272762	−	0.272762i	0.557449	−	0.830211i	$-0.311780\pi$
$421$	−5.59661	−	5.59661i	−0.272762	−	0.272762i	−0.830211	+	0.557449i	$0.811780\pi$
$422$	−3.71664	+	13.8707i	−0.180923	+	0.675215i
$423$		0			0
$424$	−1.39595	−	0.374042i	−0.0677931	−	0.0181651i
$425$	−27.7135	+	16.0004i	−1.34430	+	0.776132i
$426$		0			0
$427$	2.02131	+	3.01585i	0.0978178	+	0.145947i
$428$			19.8435i			0.959172i
$429$		0			0
$430$	0.0477325	−	0.0275584i	0.00230186	−	0.00132898i
$431$	11.2196	−	3.00628i	0.540428	−	0.144807i	0.0217286	−	0.999764i	$-0.493083\pi$
$431$	11.2196	−	3.00628i	0.540428	−	0.144807i	0.518699	+	0.854957i	$0.326416\pi$
$432$		0			0
$433$	−14.5052	+	25.1237i	−0.697073	+	1.20737i	0.272403	+	0.962183i	$0.412181\pi$
$433$	−14.5052	+	25.1237i	−0.697073	+	1.20737i	−0.969477	+	0.245183i	$0.921152\pi$
$434$	4.16642	−	2.79245i	0.199995	−	0.134042i
$435$		0			0
$436$	−19.1187	−	5.12283i	−0.915619	−	0.245339i
$437$	−2.66605	+	9.94983i	−0.127534	+	0.475965i
$438$		0			0
$439$	16.8557			0.804480			0.402240	−	0.915534i	$-0.368232\pi$
$439$	16.8557			0.804480			0.402240	+	0.915534i	$0.368232\pi$
$440$	−0.0265394	+	0.0990464i	−0.00126522	+	0.00472185i
$441$		0			0
$442$	−12.5214	−	10.0049i	−0.595583	−	0.475884i
$443$	−16.1369	+	27.9499i	−0.766685	+	1.32794i	0.172666	+	0.984980i	$0.444762\pi$
$443$	−16.1369	+	27.9499i	−0.766685	+	1.32794i	−0.939351	+	0.342957i	$0.888571\pi$
$444$		0			0
$445$	0.313301	−	0.542654i	0.0148519	−	0.0257243i
$446$	1.14035	+	1.97515i	0.0539973	+	0.0935261i
$447$		0			0
$448$	−3.58710	+	0.240207i	−0.169474	+	0.0113487i
$449$	−4.40700	−	16.4471i	−0.207979	−	0.776188i	−0.988521	−	0.151085i	$-0.951723\pi$
$449$	−4.40700	−	16.4471i	−0.207979	−	0.776188i	0.780542	−	0.625103i	$-0.214943\pi$
$450$		0			0
$451$		−	0.220586i		−	0.0103870i
$452$	4.88400	+	2.81978i	0.229724	+	0.132631i
$453$		0			0
$454$	−12.7761			−0.599610
$455$	−0.321035	+	0.151105i	−0.0150504	+	0.00708392i
$456$		0			0
$457$	−4.03922	−	4.03922i	−0.188947	−	0.188947i	0.606294	−	0.795241i	$-0.292656\pi$
$457$	−4.03922	−	4.03922i	−0.188947	−	0.188947i	−0.795241	+	0.606294i	$0.792656\pi$
$458$	6.59594	+	3.80817i	0.308208	+	0.177944i
$459$		0			0
$460$	0.0408314	+	0.152385i	0.00190378	+	0.00710499i
$461$	7.08521	+	26.4424i	0.329991	+	1.23154i	0.909198	+	0.416363i	$0.136695\pi$
$461$	7.08521	+	26.4424i	0.329991	+	1.23154i	−0.579207	+	0.815180i	$0.696638\pi$
$462$		0			0
$463$	−13.6953	+	13.6953i	−0.636477	+	0.636477i	−0.949685	−	0.313208i	$-0.898596\pi$
$463$	−13.6953	+	13.6953i	−0.636477	+	0.636477i	0.313208	+	0.949685i	$0.398596\pi$
$464$	2.47828	+	4.29250i	0.115051	+	0.199274i
$465$		0			0
$466$	1.55008	+	5.78499i	0.0718062	+	0.267984i
$467$	−8.36822	+	14.4942i	−0.387235	+	0.670711i	−0.992077	−	0.125635i	$-0.959903\pi$
$467$	−8.36822	+	14.4942i	−0.387235	+	0.670711i	0.604841	+	0.796346i	$0.293236\pi$
$468$		0			0
$469$	6.44203	+	18.8898i	0.297465	+	0.872248i
$470$	−0.0375852	+	0.140270i	−0.00173368	+	0.00647017i
$471$		0			0
$472$	27.5338			1.26734
$473$	0.623378	−	2.32648i	0.0286629	−	0.106972i
$474$		0			0
$475$	17.7986	−	4.76912i	0.816655	−	0.218822i
$476$	25.6519	−	1.71776i	1.17575	−	0.0787335i
$477$		0			0
$478$		−	5.71671i		−	0.261476i
$479$	21.7606	−	5.83074i	0.994267	−	0.266413i	0.275225	−	0.961380i	$-0.411248\pi$
$479$	21.7606	−	5.83074i	0.994267	−	0.266413i	0.719042	+	0.694967i	$0.244581\pi$
$480$		0			0
$481$	12.5639	−	15.7241i	0.572864	−	0.716958i
$482$			4.36243i			0.198703i
$483$		0			0
$484$	−7.38154	−	12.7852i	−0.335525	−	0.581146i
$485$	0.0826252	−	0.0477037i	0.00375182	−	0.00216611i
$486$		0			0
$487$	−4.93594	−	4.93594i	−0.223669	−	0.223669i	0.586373	−	0.810042i	$-0.300555\pi$
$487$	−4.93594	−	4.93594i	−0.223669	−	0.223669i	−0.810042	+	0.586373i	$0.800555\pi$
$488$	0.867535	−	3.23768i	0.0392714	−	0.146563i
$489$		0			0
$490$	−0.0687119	+	0.167222i	−0.00310409	+	0.00755431i
$491$	2.12954	−	1.22949i	0.0961048	−	0.0554861i	−0.451177	−	0.892434i	$-0.648996\pi$
$491$	2.12954	−	1.22949i	0.0961048	−	0.0554861i	0.547282	+	0.836948i	$0.315662\pi$
$492$		0			0
$493$	11.8434	+	20.5134i	0.533401	+	0.923877i
$494$	5.47328	+	7.43073i	0.246255	+	0.334324i
$495$		0			0
$496$	3.53281	+	0.946613i	0.158628	+	0.0425042i
$497$	−8.73697	−	25.6192i	−0.391907	−	1.14918i
$498$		0			0
$499$	18.0154	−	4.82722i	0.806481	−	0.216096i	0.168054	−	0.985778i	$-0.446252\pi$
$499$	18.0154	−	4.82722i	0.806481	−	0.216096i	0.638428	+	0.769682i	$0.279585\pi$
$500$	0.399156	−	0.399156i	0.0178508	−	0.0178508i
$501$		0			0
$502$	7.02164	−	1.88144i	0.313391	−	0.0839729i
$503$	−29.6335	−	17.1089i	−1.32129	−	0.762849i	−0.337359	−	0.941376i	$-0.609533\pi$
$503$	−29.6335	−	17.1089i	−1.32129	−	0.762849i	−0.983935	+	0.178527i	$0.942867\pi$
$504$		0			0
$505$	−0.165882	−	0.0444479i	−0.00738165	−	0.00197791i
$506$	−1.89645	−	1.09491i	−0.0843074	−	0.0486749i
$507$		0			0
$508$	−2.17062	−	3.75963i	−0.0963057	−	0.166806i
$509$	−6.06864	+	6.06864i	−0.268988	+	0.268988i	−0.828692	−	0.559705i	$-0.810915\pi$
$509$	−6.06864	+	6.06864i	−0.268988	+	0.268988i	0.559705	+	0.828692i	$0.310915\pi$
$510$		0			0
$511$	−7.09627	−	1.40110i	−0.313920	−	0.0619811i
$512$	−10.1365	−	10.1365i	−0.447973	−	0.447973i
$513$		0			0
$514$	−2.62689	−	2.62689i	−0.115867	−	0.115867i
$515$	−0.421674	−	0.112987i	−0.0185812	−	0.00497882i
$516$		0			0
$517$	3.17294	+	5.49570i	0.139546	+	0.241701i
$518$	−0.685198	−	10.2323i	−0.0301059	−	0.449581i
$519$		0			0
$520$	0.300127	+	0.131282i	0.0131614	+	0.00575710i
$521$	19.8996	−	11.4890i	0.871817	−	0.503344i	0.00386537	−	0.999993i	$-0.498770\pi$
$521$	19.8996	−	11.4890i	0.871817	−	0.503344i	0.867952	+	0.496649i	$0.165436\pi$
$522$		0			0
$523$			29.8987i			1.30738i	0.756762	+	0.653690i	$0.226780\pi$
$523$			29.8987i			1.30738i	−0.756762	+	0.653690i	$0.773220\pi$
$524$	−0.104975	+	0.181821i	−0.00458583	+	0.00794289i
$525$		0			0
$526$	−4.13326	+	1.10750i	−0.180218	+	0.0482894i
$527$	16.8829	+	4.52376i	0.735431	+	0.197058i
$528$		0			0
$529$	15.1916			0.660506
$530$	0.0152803			0.000663734
$531$		0			0
$532$	−14.5234	−	2.86753i	−0.629670	−	0.124323i
$533$	−0.696731	−	0.105689i	−0.0301788	−	0.00457790i
$534$		0			0
$535$	−0.125854	−	0.469695i	−0.00544116	−	0.0203067i
$536$	9.21305	−	15.9575i	0.397943	−	0.689258i
$537$		0			0
$538$	10.0902	−	10.0902i	0.435018	−	0.435018i
$539$	3.04394	+	7.29032i	0.131112	+	0.314016i
$540$		0			0
$541$	3.31979	+	12.3896i	0.142729	+	0.532672i	0.999846	+	0.0175501i	$0.00558667\pi$
$541$	3.31979	+	12.3896i	0.142729	+	0.532672i	−0.857117	+	0.515122i	$0.827747\pi$
$542$			7.05554i			0.303062i
$543$		0			0
$544$	−26.3260	−	26.3260i	−1.12872	−	1.12872i
$545$	0.485030			0.0207764
$546$		0			0
$547$	33.5639			1.43509			0.717543	−	0.696514i	$-0.245267\pi$
$547$	33.5639			1.43509			0.717543	+	0.696514i	$0.245267\pi$
$548$	−18.3089	−	18.3089i	−0.782119	−	0.782119i
$549$		0			0
$550$			3.91724i			0.167032i
$551$	−3.53008	−	13.1744i	−0.150387	−	0.561250i
$552$		0			0
$553$	7.74718	+	3.80687i	0.329444	+	0.161885i
$554$	10.0286	−	10.0286i	0.426076	−	0.426076i
$555$		0			0
$556$	−11.7329	+	20.3219i	−0.497585	+	0.861842i
$557$	−6.14230	−	22.9234i	−0.260257	−	0.971294i	−0.965090	−	0.261920i	$-0.915644\pi$
$557$	−6.14230	−	22.9234i	−0.260257	−	0.971294i	0.704832	−	0.709374i	$-0.251022\pi$
$558$		0			0
$559$	−7.04961	−	3.08365i	−0.298167	−	0.130425i
$560$	−0.124775	+	0.0425523i	−0.00527270	+	0.00179816i
$561$		0			0
$562$	−12.8072			−0.540239
$563$	−24.7532			−1.04322			−0.521611	−	0.853183i	$-0.674669\pi$
$563$	−24.7532			−1.04322			−0.521611	+	0.853183i	$0.674669\pi$
$564$		0			0
$565$	−0.133488	−	0.0357681i	−0.00561589	−	0.00150477i
$566$	1.35193	−	0.362247i	0.0568257	−	0.0152264i
$567$		0			0
$568$	−12.4952	+	21.6423i	−0.524285	+	0.908089i
$569$		−	38.5792i		−	1.61733i	−0.588273	−	0.808663i	$-0.700192\pi$
$569$		−	38.5792i		−	1.61733i	0.588273	−	0.808663i	$-0.299808\pi$
$570$		0			0
$571$	−25.3815	+	14.6540i	−1.06218	+	0.613252i	−0.926035	−	0.377437i	$-0.876806\pi$
$571$	−25.3815	+	14.6540i	−1.06218	+	0.613252i	−0.136148	+	0.990689i	$0.543472\pi$
$572$	5.75174	−	2.25112i	0.240492	−	0.0941240i
$573$		0			0
$574$	−0.298266	+	0.199906i	−0.0124494	+	0.00834391i
$575$	6.98393	+	12.0965i	0.291250	+	0.504460i
$576$		0			0
$577$	−38.5387	−	10.3264i	−1.60439	−	0.429894i	−0.658024	−	0.752997i	$-0.728607\pi$
$577$	−38.5387	−	10.3264i	−1.60439	−	0.429894i	−0.946364	+	0.323103i	$0.895274\pi$
$578$	−11.7762	−	11.7762i	−0.489824	−	0.489824i
$579$		0			0
$580$	−0.147707	−	0.147707i	−0.00613318	−	0.00613318i
$581$	−13.8790	−	12.1368i	−0.575797	−	0.503521i
$582$		0			0
$583$	0.472160	−	0.472160i	0.0195549	−	0.0195549i
$584$	3.33903	+	5.78337i	0.138170	+	0.239317i
$585$		0			0
$586$	−7.13990	−	4.12222i	−0.294946	−	0.170287i
$587$	−31.6109	−	8.47012i	−1.30472	−	0.349599i	−0.461489	−	0.887146i	$-0.652684\pi$
$587$	−31.6109	−	8.47012i	−1.30472	−	0.349599i	−0.843234	+	0.537547i	$0.819351\pi$
$588$		0			0
$589$	−8.71597	−	5.03217i	−0.359135	−	0.207347i
$590$	−0.281201	+	0.0753476i	−0.0115769	+	0.00310201i
$591$		0			0
$592$	5.28782	−	5.28782i	0.217328	−	0.217328i
$593$	21.0102	−	5.62965i	0.862784	−	0.231182i	0.199819	−	0.979833i	$-0.435965\pi$
$593$	21.0102	−	5.62965i	0.862784	−	0.231182i	0.662965	+	0.748651i	$0.269298\pi$
$594$		0			0
$595$	−0.596286	+	0.203353i	−0.0244453	+	0.00833666i
$596$	−8.34937	−	2.23721i	−0.342003	−	0.0916396i
$597$		0			0
$598$	−4.36698	+	5.46542i	−0.178579	+	0.223498i
$599$	15.0536	+	26.0736i	0.615073	+	1.06534i	0.990372	+	0.138434i	$0.0442069\pi$
$599$	15.0536	+	26.0736i	0.615073	+	1.06534i	−0.375299	+	0.926904i	$0.622460\pi$
$600$		0			0
$601$	−16.4105	+	9.47460i	−0.669398	+	0.386477i	−0.795849	−	0.605496i	$-0.792975\pi$
$601$	−16.4105	+	9.47460i	−0.669398	+	0.386477i	0.126450	+	0.991973i	$0.459642\pi$
$602$	−3.71069	+	1.26547i	−0.151237	+	0.0515766i
$603$		0			0
$604$	8.13122	−	30.3461i	0.330855	−	1.23477i
$605$	0.255809	+	0.255809i	0.0104001	+	0.0104001i
$606$		0			0
$607$	−18.4475	+	10.6507i	−0.748763	+	0.432298i	−0.825247	−	0.564772i	$-0.808964\pi$
$607$	−18.4475	+	10.6507i	−0.748763	+	0.432298i	0.0764838	+	0.997071i	$0.475631\pi$
$608$	10.7189	+	18.5657i	0.434709	+	0.752939i
$609$		0			0
$610$			0.0354404i			0.00143494i
$611$	18.8787	−	7.38875i	0.763750	−	0.298917i
$612$		0			0
$613$	24.1774	−	6.47832i	0.976518	−	0.261657i	0.264940	−	0.964265i	$-0.414648\pi$
$613$	24.1774	−	6.47832i	0.976518	−	0.261657i	0.711577	+	0.702608i	$0.247981\pi$
$614$		−	1.43930i		−	0.0580853i
$615$		0			0
$616$	3.21674	−	6.54623i	0.129606	−	0.263755i
$617$	29.1852	−	7.82015i	1.17495	−	0.314827i	0.382029	−	0.924150i	$-0.375225\pi$
$617$	29.1852	−	7.82015i	1.17495	−	0.314827i	0.792922	+	0.609323i	$0.208559\pi$
$618$		0			0
$619$	10.9864	−	41.0017i	0.441580	−	1.64800i	−0.283232	−	0.959052i	$-0.591407\pi$
$619$	10.9864	−	41.0017i	0.441580	−	1.64800i	0.724812	−	0.688947i	$-0.241927\pi$
$620$	−0.154139			−0.00619035
$621$		0			0
$622$	0.493808	−	1.84292i	0.0197999	−	0.0738942i
$623$	−29.3404	+	33.5520i	−1.17550	+	1.34423i
$624$		0			0
$625$	12.4896	−	21.6327i	0.499585	−	0.865307i
$626$	−1.36423	−	5.09138i	−0.0545257	−	0.203493i
$627$		0			0
$628$	−7.03053	−	12.1772i	−0.280549	−	0.485924i
$629$	25.2700	−	25.2700i	1.00758	−	1.00758i
$630$		0			0
$631$	−9.55956	−	35.6768i	−0.380560	−	1.42027i	−0.845048	−	0.534690i	$-0.820428\pi$
$631$	−9.55956	−	35.6768i	−0.380560	−	1.42027i	0.464488	−	0.885579i	$-0.346238\pi$
$632$	−2.06264	−	7.69786i	−0.0820473	−	0.306205i
$633$		0			0
$634$	5.99744	+	3.46263i	0.238189	+	0.137518i
$635$	0.0752234	+	0.0752234i	0.00298515	+	0.00298515i
$636$		0			0
$637$	24.4853	−	6.12143i	0.970141	−	0.242540i
$638$	2.89952			0.114793
$639$		0			0
$640$	0.344266	+	0.198762i	0.0136083	+	0.00785676i
$641$		−	8.28328i		−	0.327170i	−0.986529	−	0.163585i	$-0.947694\pi$
$641$		−	8.28328i		−	0.327170i	0.986529	−	0.163585i	$-0.0523058\pi$
$642$		0			0
$643$	8.56893	+	31.9797i	0.337926	+	1.26116i	0.900663	+	0.434519i	$0.143082\pi$
$643$	8.56893	+	31.9797i	0.337926	+	1.26116i	−0.562737	+	0.826636i	$0.690252\pi$
$644$	−0.749778	−	11.1967i	−0.0295454	−	0.441211i
$645$		0			0
$646$	8.19329	+	14.1912i	0.322361	+	0.558345i
$647$	6.58281	−	11.4018i	0.258797	−	0.448250i	−0.707123	−	0.707091i	$-0.750007\pi$
$647$	6.58281	−	11.4018i	0.258797	−	0.448250i	0.965920	+	0.258841i	$0.0833406\pi$
$648$		0			0
$649$	−6.36085	+	11.0173i	−0.249685	+	0.432467i
$650$	12.3728	+	1.87686i	0.485301	+	0.0736166i
$651$		0			0
$652$	−1.61822	+	6.03927i	−0.0633743	+	0.236516i
$653$	47.3352			1.85237			0.926184	−	0.377071i	$-0.123069\pi$
$653$	47.3352			1.85237			0.926184	+	0.377071i	$0.123069\pi$
$654$		0			0
$655$	0.00133157	−	0.00496949i	5.20288e−5	−	0.000194174i
$656$	−0.252907	−	0.0677662i	−0.00987435	−	0.00264582i
$657$		0			0
$658$	4.55556	−	9.27079i	0.177594	−	0.361413i
$659$	2.76562	−	4.79019i	0.107733	−	0.186599i	−0.807118	−	0.590390i	$-0.798974\pi$
$659$	2.76562	−	4.79019i	0.107733	−	0.186599i	0.914852	+	0.403790i	$0.132307\pi$
$660$		0			0
$661$	17.5567	−	4.70431i	0.682877	−	0.182976i	0.0993289	−	0.995055i	$-0.468330\pi$
$661$	17.5567	−	4.70431i	0.682877	−	0.182976i	0.583549	+	0.812078i	$0.301664\pi$
$662$	10.1706	−	5.87198i	0.395290	−	0.228221i
$663$		0			0
$664$			17.0220i			0.660581i
$665$	0.361956	−	0.0242381i	0.0140360	−	0.000939914i
$666$		0			0
$667$	8.95380	−	5.16948i	0.346692	−	0.200163i
$668$	−23.5628	−	6.31362i	−0.911671	−	0.244281i
$669$		0			0
$670$	−0.0504240	+	0.188185i	−0.00194805	+	0.00727022i
$671$	1.09510	+	1.09510i	0.0422760	+	0.0422760i
$672$		0			0
$673$	−3.86827	+	2.23334i	−0.149111	+	0.0860891i	−0.572699	−	0.819766i	$-0.694104\pi$
$673$	−3.86827	+	2.23334i	−0.149111	+	0.0860891i	0.423588	+	0.905855i	$0.360770\pi$
$674$	−3.88924	+	3.88924i	−0.149808	+	0.149808i
$675$		0			0
$676$	−4.35444	−	19.2457i	−0.167479	−	0.740221i
$677$	20.1346	+	11.6247i	0.773836	+	0.446775i	0.834241	−	0.551399i	$-0.185906\pi$
$677$	20.1346	+	11.6247i	0.773836	+	0.446775i	−0.0604051	+	0.998174i	$0.519239\pi$
$678$		0			0
$679$	−6.42323	+	2.19053i	−0.246501	+	0.0840649i
$680$	0.503723	+	0.290825i	0.0193169	+	0.0111526i
$681$		0			0
$682$	1.51289	−	1.51289i	0.0579317	−	0.0579317i
$683$	−5.61092	+	5.61092i	−0.214696	+	0.214696i	−0.806259	−	0.591563i	$-0.798511\pi$
$683$	−5.61092	+	5.61092i	−0.214696	+	0.214696i	0.591563	+	0.806259i	$0.298511\pi$
$684$		0			0
$685$	0.549494	+	0.317250i	0.0209951	+	0.0121215i
$686$	7.09906	−	10.7227i	0.271043	−	0.409396i
$687$		0			0
$688$	−2.47585	−	1.42943i	−0.0943910	−	0.0544967i
$689$	−1.26511	−	1.71756i	−0.0481970	−	0.0654340i
$690$		0			0
$691$	−8.15837	+	8.15837i	−0.310359	+	0.310359i	−0.845049	−	0.534690i	$-0.820429\pi$
$691$	−8.15837	+	8.15837i	−0.310359	+	0.310359i	0.534690	+	0.845049i	$0.320429\pi$
$692$	27.6918	−	15.9879i	1.05268	−	0.607768i
$693$		0			0
$694$	11.9498	+	11.9498i	0.453609	+	0.453609i
$695$	0.148828	−	0.555434i	0.00564537	−	0.0210688i
$696$		0			0
$697$	−1.20861	−	0.323847i	−0.0457795	−	0.0122666i
$698$	−9.77014	+	5.64079i	−0.369805	+	0.213507i
$699$		0			0
$700$	−16.6750	+	11.1760i	−0.630256	+	0.422415i
$701$			11.0088i			0.415797i	0.978150	+	0.207898i	$0.0666624\pi$
$701$			11.0088i			0.415797i	−0.978150	+	0.207898i	$0.933338\pi$
$702$		0			0
$703$	−17.8210	+	10.2889i	−0.672131	+	0.388055i
$704$	−1.48134	+	0.396923i	−0.0558299	+	0.0149596i
$705$		0			0
$706$	5.68552	−	9.84760i	0.213977	−	0.370619i
$707$	10.9635	+	5.38736i	0.412327	+	0.202612i
$708$		0			0
$709$	28.7098	+	7.69277i	1.07822	+	0.288908i	0.753866	−	0.657028i	$-0.228187\pi$
$709$	28.7098	+	7.69277i	1.07822	+	0.288908i	0.324353	+	0.945936i	$0.394853\pi$
$710$	0.0683873	−	0.255225i	0.00256653	−	0.00957842i
$711$		0			0
$712$	41.1501			1.54216
$713$	1.97456	−	7.36914i	0.0739477	−	0.275977i
$714$		0			0
$715$	−0.121866	+	0.0897635i	−0.00455754	+	0.00335697i
$716$	6.91982	−	11.9855i	0.258606	−	0.447918i
$717$		0			0
$718$	−2.39907	+	4.15530i	−0.0895323	+	0.155075i
$719$	12.1922	+	21.1175i	0.454693	+	0.787552i	0.998671	−	0.0515483i	$-0.0164156\pi$
$719$	12.1922	+	21.1175i	0.454693	+	0.787552i	−0.543977	+	0.839100i	$0.683082\pi$
$720$		0			0
$721$	27.8695	+	13.6947i	1.03792	+	0.510019i
$722$	0.972454	+	3.62925i	0.0361910	+	0.135067i
$723$		0			0
$724$		−	23.8560i		−	0.886602i
$725$	−16.0168	−	9.24733i	−0.594851	−	0.343437i
$726$		0			0
$727$	20.3008			0.752915			0.376458	−	0.926434i	$-0.377142\pi$
$727$	20.3008			0.752915			0.376458	+	0.926434i	$0.377142\pi$
$728$	−19.1353	−	13.2967i	−0.709203	−	0.492809i
$729$		0			0
$730$	−0.0499278	−	0.0499278i	−0.00184791	−	0.00184791i
$731$	−11.8318	−	6.83111i	−0.437616	−	0.252658i
$732$		0			0
$733$	−4.25111	−	15.8654i	−0.157019	−	0.586001i	−0.998924	−	0.0463761i	$-0.985233\pi$
$733$	−4.25111	−	15.8654i	−0.157019	−	0.586001i	0.841906	−	0.539625i	$-0.181434\pi$
$734$	2.56946	+	9.58936i	0.0948406	+	0.353950i
$735$		0			0
$736$	−11.4909	+	11.4909i	−0.423560	+	0.423560i
$737$	4.25679	+	7.37298i	0.156801	+	0.271587i
$738$		0			0
$739$	−11.0872	−	41.3778i	−0.407847	−	1.52211i	−0.798743	−	0.601672i	$-0.794501\pi$
$739$	−11.0872	−	41.3778i	−0.407847	−	1.52211i	0.390896	−	0.920435i	$-0.372165\pi$
$740$	−0.157579	+	0.272934i	−0.00579270	+	0.0100333i
$741$		0			0
$742$	−1.06633	−	0.210538i	−0.0391461	−	0.00772910i
$743$	−12.7481	+	47.5766i	−0.467683	+	1.74542i	0.180155	+	0.983638i	$0.442340\pi$
$743$	−12.7481	+	47.5766i	−0.467683	+	1.74542i	−0.647838	+	0.761778i	$0.724327\pi$
$744$		0			0
$745$	0.211819			0.00776043
$746$	−4.07326	+	15.2016i	−0.149133	+	0.556570i
$747$		0			0
$748$	10.5933	−	2.83846i	0.387328	−	0.103784i
$749$	2.31104	+	34.5115i	0.0844435	+	1.26102i
$750$		0			0
$751$		−	23.0508i		−	0.841135i	−0.907261	−	0.420567i	$-0.861831\pi$
$751$		−	23.0508i		−	0.841135i	0.907261	−	0.420567i	$-0.138169\pi$
$752$	7.27571	−	1.94952i	0.265318	−	0.0710917i
$753$		0			0
$754$	1.38925	−	9.15829i	0.0505934	−	0.333525i
$755$			0.769863i			0.0280182i
$756$		0			0
$757$	24.1858	+	41.8911i	0.879049	+	1.52256i	0.852387	+	0.522912i	$0.175154\pi$
$757$	24.1858	+	41.8911i	0.879049	+	1.52256i	0.0266620	+	0.999645i	$0.491512\pi$
$758$	7.83357	−	4.52272i	0.284528	−	0.164272i
$759$		0			0
$760$	−0.236825	−	0.236825i	−0.00859055	−	0.00859055i
$761$	7.56647	−	28.2385i	0.274284	−	1.02364i	−0.682035	−	0.731320i	$-0.738905\pi$
$761$	7.56647	−	28.2385i	0.274284	−	1.02364i	0.956319	−	0.292324i	$-0.0944285\pi$
$762$		0			0
$763$	−33.8475	−	6.68293i	−1.22536	−	0.241938i
$764$	−22.7504	+	13.1349i	−0.823079	+	0.475205i
$765$		0			0
$766$	0.797333	+	1.38102i	0.0288088	+	0.0498983i
$767$	31.7510	+	25.3698i	1.14646	+	0.916049i
$768$		0			0
$769$	1.87337	+	0.501968i	0.0675554	+	0.0181014i	0.292438	−	0.956284i	$-0.405533\pi$
$769$	1.87337	+	0.501968i	0.0675554	+	0.0181014i	−0.224883	+	0.974386i	$0.572200\pi$
$770$	−0.0149383	+	0.0756591i	−0.000538339	+	0.00272656i
$771$		0			0
$772$	−18.4564	+	4.94539i	−0.664262	+	0.177988i
$773$	3.60192	−	3.60192i	0.129552	−	0.129552i	−0.639358	−	0.768910i	$-0.720800\pi$
$773$	3.60192	−	3.60192i	0.129552	−	0.129552i	0.768910	+	0.639358i	$0.220800\pi$
$774$		0			0
$775$	−13.1822	+	3.53215i	−0.473517	+	0.126879i
$776$	5.42614	+	3.13278i	0.194787	+	0.112460i
$777$		0			0
$778$	−8.45552	−	2.26565i	−0.303145	−	0.0812275i
$779$	0.623959	+	0.360243i	0.0223557	+	0.0129070i
$780$		0			0
$781$	−5.77326	−	9.99958i	−0.206583	−	0.357813i
$782$	−8.78338	+	8.78338i	−0.314093	+	0.314093i
$783$		0			0
$784$	9.29365	−	1.25029i	0.331916	−	0.0446533i
$785$	0.243645	+	0.243645i	0.00869606	+	0.00869606i
$786$		0			0
$787$	21.6820	+	21.6820i	0.772878	+	0.772878i	0.978609	−	0.205730i	$-0.0659569\pi$
$787$	21.6820	+	21.6820i	0.772878	+	0.772878i	−0.205730	+	0.978609i	$0.565957\pi$
$788$	−36.4359	−	9.76297i	−1.29798	−	0.347791i
$789$		0			0
$790$	0.0421312	+	0.0729734i	0.00149896	+	0.00259628i
$791$	8.82257	+	4.33531i	0.313695	+	0.154146i
$792$		0			0
$793$	3.98363	−	2.93424i	0.141463	−	0.104198i
$794$	1.34780	−	0.778154i	0.0478317	−	0.0276157i
$795$		0			0
$796$			16.0860i			0.570152i
$797$	15.8566	−	27.4644i	0.561669	−	0.972839i	−0.435682	−	0.900101i	$-0.643493\pi$
$797$	15.8566	−	27.4644i	0.561669	−	0.972839i	0.997351	−	0.0727386i	$-0.0231739\pi$
$798$		0			0
$799$	34.7698	−	9.31655i	1.23007	−	0.329596i
$800$	28.0791	+	7.52376i	0.992745	+	0.266005i
$801$		0			0
$802$	25.0366			0.884075
$803$	−3.08553			−0.108886
$804$		0			0
$805$	0.0887606	+	0.260270i	0.00312840	+	0.00917332i
$806$	−4.05368	−	5.50342i	−0.142785	−	0.193850i
$807$		0			0
$808$	−2.91897	−	10.8938i	−0.102689	−	0.383241i
$809$	4.55711	−	7.89315i	0.160219	−	0.277508i	−0.774728	−	0.632295i	$-0.782113\pi$
$809$	4.55711	−	7.89315i	0.160219	−	0.277508i	0.934947	+	0.354787i	$0.115446\pi$
$810$		0			0
$811$	−21.0935	+	21.0935i	−0.740695	+	0.740695i	−0.972712	−	0.232017i	$-0.925467\pi$
$811$	−21.0935	+	21.0935i	−0.740695	+	0.740695i	0.232017	+	0.972712i	$0.425467\pi$
$812$	8.27246	+	12.3428i	0.290306	+	0.433147i
$813$		0			0
$814$	−1.13223	−	4.22555i	−0.0396847	−	0.148105i
$815$		−	0.153213i		−	0.00536681i
$816$		0			0
$817$	5.56273	+	5.56273i	0.194615	+	0.194615i
$818$	6.40859			0.224071
$819$		0			0
$820$	0.0110345			0.000385341
$821$	27.6740	+	27.6740i	0.965831	+	0.965831i	0.999435	−	0.0336043i	$-0.0106986\pi$
$821$	27.6740	+	27.6740i	0.965831	+	0.965831i	−0.0336043	+	0.999435i	$0.510699\pi$
$822$		0			0
$823$			36.5955i			1.27564i	0.770187	+	0.637819i	$0.220163\pi$
$823$			36.5955i			1.27564i	−0.770187	+	0.637819i	$0.779837\pi$
$824$	−7.42007	−	27.6921i	−0.258491	−	0.964700i
$825$		0			0
$826$	20.6616	−	1.38359i	0.718910	−	0.0481413i
$827$	4.61851	−	4.61851i	0.160601	−	0.160601i	−0.622232	−	0.782833i	$-0.713774\pi$
$827$	4.61851	−	4.61851i	0.160601	−	0.160601i	0.782833	+	0.622232i	$0.213774\pi$
$828$		0			0
$829$	5.83825	−	10.1121i	0.202771	−	0.351209i	−0.746649	−	0.665218i	$-0.768339\pi$
$829$	5.83825	−	10.1121i	0.202771	−	0.351209i	0.949420	+	0.314009i	$0.101672\pi$
$830$	−0.0465815	−	0.173845i	−0.00161687	−	0.00603424i
$831$		0			0
$832$	0.543949	+	4.86905i	0.0188580	+	0.168804i
$833$	44.4133	−	5.97501i	1.53883	−	0.207022i
$834$		0			0
$835$	0.597773			0.0206868
$836$	−6.31492			−0.218406
$837$		0			0
$838$	11.9388	+	3.19899i	0.412419	+	0.110507i
$839$	−22.6006	+	6.05583i	−0.780261	+	0.209070i	−0.626900	−	0.779100i	$-0.715676\pi$
$839$	−22.6006	+	6.05583i	−0.780261	+	0.209070i	−0.153361	+	0.988170i	$0.549010\pi$
$840$		0			0
$841$	7.65516	−	13.2591i	0.263971	−	0.457211i
$842$			5.49574i			0.189396i
$843$		0			0
$844$	−27.1851	+	15.6953i	−0.935751	+	0.540256i
$845$	0.225133	+	0.427929i	0.00774480	+	0.0147212i
$846$		0			0
$847$	−14.3269	−	21.3761i	−0.492277	−	0.734493i
$848$	−0.396290	−	0.686394i	−0.0136086	−	0.0235709i
$849$		0			0
$850$	21.4630	+	5.75099i	0.736174	+	0.197257i
$851$	−11.0300	−	11.0300i	−0.378102	−	0.378102i
$852$		0			0
$853$	−34.6514	−	34.6514i	−1.18644	−	1.18644i	−0.978044	−	0.208398i	$-0.933175\pi$
$853$	−34.6514	−	34.6514i	−1.18644	−	1.18644i	−0.208398	−	0.978044i	$-0.566825\pi$
$854$	0.488311	−	2.47319i	0.0167097	−	0.0846307i
$855$		0			0
$856$	22.5806	−	22.5806i	0.771790	−	0.771790i
$857$	1.19667	+	2.07269i	0.0408775	+	0.0708019i	0.885740	−	0.464181i	$-0.153651\pi$
$857$	1.19667	+	2.07269i	0.0408775	+	0.0708019i	−0.844863	+	0.534983i	$0.820318\pi$
$858$		0			0
$859$	1.71704	+	0.991332i	0.0585846	+	0.0338238i	0.529006	−	0.848618i	$-0.322565\pi$
$859$	1.71704	+	0.991332i	0.0585846	+	0.0338238i	−0.470422	+	0.882442i	$0.655898\pi$
$860$	0.116379	+	0.0311836i	0.00396848	+	0.00106335i
$861$		0			0
$862$	−6.98473	−	4.03263i	−0.237901	−	0.137352i
$863$	13.7577	−	3.68636i	0.468317	−	0.125485i	−0.0169406	−	0.999856i	$-0.505393\pi$
$863$	13.7577	−	3.68636i	0.468317	−	0.125485i	0.485257	+	0.874371i	$0.338726\pi$
$864$		0			0
$865$	−0.554064	+	0.554064i	−0.0188387	+	0.0188387i
$866$	19.4573	−	5.21356i	0.661186	−	0.177164i
$867$		0			0
$868$	10.7565	+	2.12378i	0.365098	+	0.0720858i
$869$	3.55672	+	0.953020i	0.120653	+	0.0323290i
$870$		0			0
$871$	25.3275	−	9.91268i	0.858189	−	0.335878i
$872$	15.9264	+	27.5853i	0.539335	+	0.934156i
$873$		0			0
$874$	6.19425	−	3.57625i	0.209524	−	0.120969i
$875$	0.647719	−	0.740693i	0.0218969	−	0.0250400i
$876$		0			0
$877$	−12.7259	+	47.4938i	−0.429724	+	1.60375i	0.323660	+	0.946173i	$0.395086\pi$
$877$	−12.7259	+	47.4938i	−0.429724	+	1.60375i	−0.753385	+	0.657580i	$0.771580\pi$
$878$	−8.27596	−	8.27596i	−0.279300	−	0.279300i
$879$		0			0
$880$	−0.0487017	+	0.0281179i	−0.00164173	+	0.000947855i
$881$	−13.0843	−	22.6627i	−0.440821	−	0.763525i	0.556930	−	0.830560i	$-0.311979\pi$
$881$	−13.0843	−	22.6627i	−0.440821	−	0.763525i	−0.997751	+	0.0670352i	$0.978646\pi$
$882$		0			0
$883$		−	4.56808i		−	0.153728i	−0.997042	−	0.0768640i	$-0.975509\pi$
$883$		−	4.56808i		−	0.153728i	0.997042	−	0.0768640i	$-0.0244907\pi$
$884$	−3.88987	−	34.8194i	−0.130830	−	1.17110i
$885$		0			0
$886$	21.6461	−	5.80004i	0.727214	−	0.194856i
$887$			1.20579i			0.0404865i	0.999795	+	0.0202432i	$0.00644406\pi$
$887$			1.20579i			0.0404865i	−0.999795	+	0.0202432i	$0.993556\pi$
$888$		0			0
$889$	−4.21297	−	6.28588i	−0.141298	−	0.210822i
$890$	−0.420264	+	0.112609i	−0.0140873	+	0.00377467i
$891$		0			0
$892$	−1.29036	+	4.81570i	−0.0432045	+	0.161242i
$893$	−20.7272			−0.693609
$894$		0			0
$895$	−0.0877758	+	0.327584i	−0.00293402	+	0.0109499i
$896$	−21.2858	−	18.6139i	−0.711108	−	0.621848i
$897$		0			0
$898$	−5.91156	+	10.2391i	−0.197271	+	0.341684i
$899$	2.61448	+	9.75739i	0.0871979	+	0.325427i
$900$		0			0
$901$	−1.89383	−	3.28020i	−0.0630925	−	0.109279i
$902$	−0.108305	+	0.108305i	−0.00360616	+	0.00360616i
$903$		0			0
$904$	−2.34895	−	8.76641i	−0.0781250	−	0.291566i
$905$	0.151303	+	0.564672i	0.00502949	+	0.0187703i
$906$		0			0
$907$	−30.1251	−	17.3927i	−1.00029	−	0.577515i	−0.0919531	−	0.995763i	$-0.529311\pi$
$907$	−30.1251	−	17.3927i	−1.00029	−	0.577515i	−0.908333	+	0.418248i	$0.862644\pi$
$908$	−19.7482	−	19.7482i	−0.655368	−	0.655368i
$909$		0			0
$910$	0.231816	+	0.0834338i	0.00768461	+	0.00276580i
$911$	−10.2796			−0.340579			−0.170290	−	0.985394i	$-0.554470\pi$
$911$	−10.2796			−0.340579			−0.170290	+	0.985394i	$0.554470\pi$
$912$		0			0
$913$	−6.81114	−	3.93241i	−0.225416	−	0.130144i
$914$			3.96642i			0.131197i
$915$		0			0
$916$	4.30912	+	16.0818i	0.142377	+	0.531359i
$917$	−0.161394	+	0.328446i	−0.00532971	+	0.0108462i
$918$		0			0
$919$	10.5049	+	18.1950i	0.346525	+	0.600198i	0.985630	−	0.168921i	$-0.0540284\pi$
$919$	10.5049	+	18.1950i	0.346525	+	0.600198i	−0.639105	+	0.769120i	$0.720695\pi$
$920$	0.126941	−	0.219868i	0.00418511	−	0.00724883i
$921$		0			0
$922$	9.50413	−	16.4616i	0.313002	−	0.542135i
$923$	−34.3503	+	13.4440i	−1.13065	+	0.442516i
$924$		0			0
$925$	−7.22196	+	26.9527i	−0.237457	+	0.886200i
$926$	13.4485			0.441945
$927$		0			0
$928$	5.56906	−	20.7840i	0.182813	−	0.682268i
$929$	1.15836	+	0.310383i	0.0380047	+	0.0101833i	0.277771	−	0.960647i	$-0.410404\pi$
$929$	1.15836	+	0.310383i	0.0380047	+	0.0101833i	−0.239767	+	0.970831i	$0.577071\pi$
$930$		0			0
$931$	−25.5928	−	3.29573i	−0.838771	−	0.108013i
$932$	−6.54598	+	11.3380i	−0.214421	+	0.371387i
$933$		0			0
$934$	11.2252	−	3.00778i	0.367299	−	0.0984174i
$935$	−0.232740	+	0.134373i	−0.00761141	+	0.00439445i
$936$		0			0
$937$		−	21.5733i		−	0.704768i	−0.935855	−	0.352384i	$-0.885371\pi$
$937$		−	21.5733i		−	0.704768i	0.935855	−	0.352384i	$-0.114629\pi$
$938$	6.11169	−	12.4376i	0.199554	−	0.406103i
$939$		0			0
$940$	−0.274914	+	0.158722i	−0.00896672	+	0.00517694i
$941$	35.7815	+	9.58762i	1.16644	+	0.312548i	0.789537	−	0.613704i	$-0.210321\pi$
$941$	35.7815	+	9.58762i	1.16644	+	0.312548i	0.376907	+	0.926251i	$0.376988\pi$
$942$		0			0
$943$	−0.141355	+	0.527543i	−0.00460314	+	0.0171791i
$944$	10.6775	+	10.6775i	0.347523	+	0.347523i
$945$		0			0
$946$	−1.44834	+	0.836202i	−0.0470897	+	0.0271873i
$947$	−26.3284	+	26.3284i	−0.855558	+	0.855558i	−0.990811	−	0.135253i	$-0.956815\pi$
$947$	−26.3284	+	26.3284i	−0.855558	+	0.855558i	0.135253	+	0.990811i	$0.456815\pi$
$948$		0			0
$949$	−1.47837	+	9.74579i	−0.0479898	+	0.316362i
$950$	−11.0805	−	6.39732i	−0.359498	−	0.207556i
$951$		0			0
$952$	−31.1449	−	27.2355i	−1.00941	−	0.882709i
$953$	37.3599	+	21.5697i	1.21020	+	0.698712i	0.962804	−	0.270201i	$-0.0870902\pi$
$953$	37.3599	+	21.5697i	1.21020	+	0.698712i	0.247401	+	0.968913i	$0.420424\pi$
$954$		0			0
$955$	0.455194	−	0.455194i	0.0147297	−	0.0147297i
$956$	8.83644	−	8.83644i	0.285791	−	0.285791i
$957$		0			0
$958$	−13.5470	−	7.82138i	−0.437684	−	0.252697i
$959$	−33.9749	−	29.7103i	−1.09711	−	0.959395i
$960$		0			0
$961$	−20.3915	−	11.7730i	−0.657790	−	0.379775i
$962$	−13.8891	+	1.55163i	−0.447802	+	0.0500265i
$963$		0			0
$964$	−6.74309	+	6.74309i	−0.217180	+	0.217180i
$965$	0.405498	−	0.234115i	0.0130535	−	0.00753641i
$966$		0			0
$967$	−6.54638	−	6.54638i	−0.210517	−	0.210517i	0.593970	−	0.804487i	$-0.297560\pi$
$967$	−6.54638	−	6.54638i	−0.210517	−	0.210517i	−0.804487	+	0.593970i	$0.797560\pi$
$968$	−6.14902	+	22.9485i	−0.197637	+	0.737591i
$969$		0			0
$970$	−0.0639900	−	0.0171461i	−0.00205459	−	0.000550527i
$971$	32.3192	−	18.6595i	1.03717	−	0.598812i	0.118142	−	0.992997i	$-0.462306\pi$
$971$	32.3192	−	18.6595i	1.03717	−	0.598812i	0.919031	+	0.394184i	$0.128973\pi$
$972$		0			0
$973$	−18.0389	+	36.7100i	−0.578300	+	1.17687i
$974$			4.84698i			0.155307i
$975$		0			0
$976$	1.59199	−	0.919134i	0.0509583	−	0.0294208i
$977$	−36.2796	+	9.72109i	−1.16069	+	0.311005i	−0.787240	−	0.616646i	$-0.788491\pi$
$977$	−36.2796	+	9.72109i	−1.16069	+	0.311005i	−0.373447	+	0.927651i	$0.621824\pi$
$978$		0			0
$979$	−9.50648	+	16.4657i	−0.303829	+	0.526246i
$980$	−0.364687	+	0.152269i	−0.0116495	+	0.00486404i
$981$		0			0
$982$	−1.64925	−	0.441914i	−0.0526295	−	0.0141020i
$983$	−9.02589	+	33.6851i	−0.287881	+	1.07439i	0.658827	+	0.752295i	$0.271053\pi$
$983$	−9.02589	+	33.6851i	−0.287881	+	1.07439i	−0.946708	+	0.322093i	$0.895614\pi$
$984$		0			0
$985$	0.924357			0.0294525
$986$	4.25686	−	15.8868i	0.135566	−	0.505939i
$987$		0			0
$988$	−3.02566	+	19.9460i	−0.0962591	+	0.634566i
$989$	−2.98168	+	5.16442i	−0.0948119	+	0.164219i
$990$		0			0
$991$	19.0679	−	33.0266i	0.605712	−	1.04912i	−0.386227	−	0.922404i	$-0.626222\pi$
$991$	19.0679	−	33.0266i	0.605712	−	1.04912i	0.991939	−	0.126720i	$-0.0404450\pi$
$992$	−7.93875	−	13.7503i	−0.252055	−	0.436573i
$993$		0			0
$994$	−8.28896	+	16.8685i	−0.262910	+	0.535035i
$995$	−0.102023	−	0.380755i	−0.00323434	−	0.0120707i
$996$		0			0
$997$			18.6171i			0.589610i	0.955557	+	0.294805i	$0.0952546\pi$
$997$			18.6171i			0.589610i	−0.955557	+	0.294805i	$0.904745\pi$
$998$	−11.2155	−	6.47526i	−0.355020	−	0.204971i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.et.b.271.3		28
3.2	odd	2		91.2.ba.a.89.5	yes	28
7.3	odd	6		819.2.gh.b.388.5		28
13.6	odd	12		819.2.gh.b.19.5		28
21.2	odd	6		637.2.bd.b.440.5		28
21.5	even	6		637.2.bd.a.440.5		28
21.11	odd	6		637.2.x.a.570.3		28
21.17	even	6		91.2.w.a.24.3	yes	28
21.20	even	2		637.2.bb.a.362.5		28
39.32	even	12		91.2.w.a.19.3	✓	28
91.45	even	12	inner	819.2.et.b.136.3		28
273.32	even	12		637.2.bb.a.227.5		28
273.110	odd	12		637.2.bd.b.97.5		28
273.149	even	12		637.2.bd.a.97.5		28
273.188	odd	12		637.2.x.a.19.3		28
273.227	odd	12		91.2.ba.a.45.5	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.19.3	✓	28	39.32	even	12
91.2.w.a.24.3	yes	28	21.17	even	6
91.2.ba.a.45.5	yes	28	273.227	odd	12
91.2.ba.a.89.5	yes	28	3.2	odd	2
637.2.x.a.19.3		28	273.188	odd	12
637.2.x.a.570.3		28	21.11	odd	6
637.2.bb.a.227.5		28	273.32	even	12
637.2.bb.a.362.5		28	21.20	even	2
637.2.bd.a.97.5		28	273.149	even	12
637.2.bd.a.440.5		28	21.5	even	6
637.2.bd.b.97.5		28	273.110	odd	12
637.2.bd.b.440.5		28	21.2	odd	6
819.2.et.b.136.3		28	91.45	even	12	inner
819.2.et.b.271.3		28	1.1	even	1	trivial
819.2.gh.b.19.5		28	13.6	odd	12
819.2.gh.b.388.5		28	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.et (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.490988 - 0.490988i) q^{2} -1.51786i q^{4} +(0.00962681 + 0.0359277i) q^{5} +(-0.176775 - 2.63984i) q^{7} +(-1.72723 + 1.72723i) q^{8} +O(q^{10})\)	\(q+(-0.490988 - 0.490988i) q^{2} -1.51786i q^{4} +(0.00962681 + 0.0359277i) q^{5} +(-0.176775 - 2.63984i) q^{7} +(-1.72723 + 1.72723i) q^{8} +(0.0129135 - 0.0223668i) q^{10} +(-0.292106 - 1.09015i) q^{11} +(-3.58326 + 0.400306i) q^{13} +(-1.20934 + 1.38292i) q^{14} -1.33962 q^{16} -6.40192 q^{17} +(3.56070 + 0.954087i) q^{19} +(0.0545333 - 0.0146122i) q^{20} +(-0.391832 + 0.678673i) q^{22} +2.79435i q^{23} +(4.32893 - 2.49931i) q^{25} +(1.95588 + 1.56279i) q^{26} +(-4.00691 + 0.268320i) q^{28} +(-1.84998 - 3.20426i) q^{29} +(-2.63716 - 0.706626i) q^{31} +(4.11220 + 4.11220i) q^{32} +(3.14327 + 3.14327i) q^{34} +(0.0931417 - 0.0317644i) q^{35} +(-3.94724 + 3.94724i) q^{37} +(-1.27982 - 2.21671i) q^{38} +(-0.0786831 - 0.0454277i) q^{40} +(0.188789 + 0.0505859i) q^{41} +(1.84817 + 1.06704i) q^{43} +(-1.65470 + 0.443376i) q^{44} +(1.37199 - 1.37199i) q^{46} +(-5.43116 + 1.45527i) q^{47} +(-6.93750 + 0.933315i) q^{49} +(-3.35258 - 0.898322i) q^{50} +(0.607609 + 5.43889i) q^{52} +(0.295822 + 0.512378i) q^{53} +(0.0363547 - 0.0209894i) q^{55} +(4.86494 + 4.25427i) q^{56} +(-0.664935 + 2.48157i) q^{58} +(-7.97051 - 7.97051i) q^{59} +(-1.18838 + 0.686113i) q^{61} +(0.947871 + 1.64176i) q^{62} -1.35883i q^{64} +(-0.0488775 - 0.124885i) q^{65} +(-7.28639 + 1.95238i) q^{67} +9.71723i q^{68} +(-0.0613274 - 0.0301356i) q^{70} +(9.88214 - 2.64791i) q^{71} +(0.707590 - 2.64076i) q^{73} +3.87610 q^{74} +(1.44817 - 5.40465i) q^{76} +(-2.82619 + 0.963824i) q^{77} +(-1.63129 + 2.82548i) q^{79} +(-0.0128963 - 0.0481297i) q^{80} +(-0.0678562 - 0.117530i) q^{82} +(4.92754 - 4.92754i) q^{83} +(-0.0616301 - 0.230007i) q^{85} +(-0.383525 - 1.43133i) q^{86} +(2.38748 + 1.37841i) q^{88} +(-11.9122 - 11.9122i) q^{89} +(1.69017 + 9.38847i) q^{91} +4.24143 q^{92} +(3.38116 + 1.95211i) q^{94} +0.137113i q^{95} +(-0.663884 - 2.47765i) q^{97} +(3.86448 + 2.94799i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8}+O(q^{10}) \) 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8	\( 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8} - 6 q^{10} - 2 q^{11} + 20 q^{14} + 4 q^{16} + 12 q^{17} + 14 q^{19} - 36 q^{20} - 8 q^{22} - 24 q^{26} + 2 q^{28} + 8 q^{29} - 4 q^{31} - 10 q^{32} - 12 q^{34} + 20 q^{35} - 10 q^{37} + 48 q^{40} + 18 q^{41} + 48 q^{43} + 6 q^{44} + 24 q^{46} + 6 q^{47} - 50 q^{49} - 10 q^{50} - 26 q^{52} - 12 q^{53} + 6 q^{55} - 54 q^{56} - 46 q^{58} - 42 q^{59} + 30 q^{61} - 36 q^{62} - 28 q^{65} - 10 q^{67} - 88 q^{70} + 42 q^{71} + 40 q^{73} - 12 q^{74} - 52 q^{76} + 4 q^{79} - 30 q^{80} - 54 q^{82} - 66 q^{83} - 54 q^{85} + 18 q^{86} - 6 q^{88} + 26 q^{91} + 156 q^{92} - 18 q^{94} - 62 q^{97} + 56 q^{98}+O(q^{100}) \) 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8 - 6 * q^10 - 2 * q^11 + 20 * q^14 + 4 * q^16 + 12 * q^17 + 14 * q^19 - 36 * q^20 - 8 * q^22 - 24 * q^26 + 2 * q^28 + 8 * q^29 - 4 * q^31 - 10 * q^32 - 12 * q^34 + 20 * q^35 - 10 * q^37 + 48 * q^40 + 18 * q^41 + 48 * q^43 + 6 * q^44 + 24 * q^46 + 6 * q^47 - 50 * q^49 - 10 * q^50 - 26 * q^52 - 12 * q^53 + 6 * q^55 - 54 * q^56 - 46 * q^58 - 42 * q^59 + 30 * q^61 - 36 * q^62 - 28 * q^65 - 10 * q^67 - 88 * q^70 + 42 * q^71 + 40 * q^73 - 12 * q^74 - 52 * q^76 + 4 * q^79 - 30 * q^80 - 54 * q^82 - 66 * q^83 - 54 * q^85 + 18 * q^86 - 6 * q^88 + 26 * q^91 + 156 * q^92 - 18 * q^94 - 62 * q^97 + 56 * q^98

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