LMFDB - Embedded newform 252.2.bf.f.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(19,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("252.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bf (of order $6$, degree $2$, 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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.562828176.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 $ x^8 - 2x^7 + x^6 + 2x^5 - 6x^4 + 4x^3 + 4x^2 - 16x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.2
Root			$1.40376 + 0.171630i$ of defining polynomial
Character	$\chi$	$=$	252.199
Dual form			252.2.bf.f.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.553244 - 1.30151i) q^{2} +(-1.38784 + 1.44010i) q^{4} +(-0.834598 + 0.481855i) q^{5} +(1.20103 + 2.35744i) q^{7} +(2.64212 + 1.00956i) q^{8} +O(q^{10})$	\(q+(-0.553244 - 1.30151i) q^{2} +(-1.38784 + 1.44010i) q^{4} +(-0.834598 + 0.481855i) q^{5} +(1.20103 + 2.35744i) q^{7} +(2.64212 + 1.00956i) q^{8} +(1.08887 + 0.819652i) q^{10} +(4.74861 + 2.74161i) q^{11} -3.75117i q^{13} +(2.40376 - 2.86739i) q^{14} +(-0.147789 - 3.99727i) q^{16} +(0.594545 + 0.343260i) q^{17} +(2.44109 + 4.22809i) q^{19} +(0.464369 - 1.87065i) q^{20} +(0.941086 - 7.69713i) q^{22} +(-1.07465 + 0.620450i) q^{23} +(-2.03563 + 3.52582i) q^{25} +(-4.88217 + 2.07531i) q^{26} +(-5.06180 - 1.54214i) q^{28} +2.48011 q^{29} +(2.41401 - 4.18119i) q^{31} +(-5.12071 + 2.40381i) q^{32} +(0.117828 - 0.963711i) q^{34} +(-2.13832 - 1.38879i) q^{35} +(1.36643 + 2.36673i) q^{37} +(4.15237 - 5.51625i) q^{38} +(-2.69157 + 0.430544i) q^{40} -9.42976i q^{41} +5.97437i q^{43} +(-10.5385 + 3.03356i) q^{44} +(1.40207 + 1.05541i) q^{46} +(-1.80752 - 3.13072i) q^{47} +(-4.11504 + 5.66272i) q^{49} +(5.71508 + 0.698752i) q^{50} +(5.40207 + 5.20603i) q^{52} +(-2.04757 + 3.54650i) q^{53} -5.28424 q^{55} +(0.793298 + 7.44115i) q^{56} +(-1.37210 - 3.22788i) q^{58} +(-6.34315 + 10.9867i) q^{59} +(9.01711 - 5.20603i) q^{61} +(-6.77738 - 0.828634i) q^{62} +(5.96158 + 5.33475i) q^{64} +(1.80752 + 3.13072i) q^{65} +(-8.17396 - 4.71924i) q^{67} +(-1.31946 + 0.379814i) q^{68} +(-0.624505 + 3.55138i) q^{70} -10.1163i q^{71} +(-5.76850 - 3.33044i) q^{73} +(2.32435 - 3.08781i) q^{74} +(-9.47672 - 2.35250i) q^{76} +(-0.759946 + 14.4873i) q^{77} +(-1.22492 + 0.707208i) q^{79} +(2.04945 + 3.26490i) q^{80} +(-12.2729 + 5.21696i) q^{82} +0.543780 q^{83} -0.661608 q^{85} +(7.77568 - 3.30528i) q^{86} +(9.77857 + 12.0377i) q^{88} +(-0.480107 + 0.277190i) q^{89} +(8.84315 - 4.50528i) q^{91} +(0.597935 - 2.40870i) q^{92} +(-3.07465 + 4.08455i) q^{94} +(-4.07465 - 2.35250i) q^{95} -10.8747i q^{97} +(9.64670 + 2.22289i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - q^{4} - 2 q^{7} - 4 q^{8}+O(q^{10}) $ 8 * q - q^2 - q^4 - 2 * q^7 - 4 * q^8	$ 8 q - q^{2} - q^{4} - 2 q^{7} - 4 q^{8} - 13 q^{10} + 6 q^{11} + 10 q^{14} + 7 q^{16} + 6 q^{19} + 22 q^{20} - 6 q^{22} + 2 q^{25} - 12 q^{26} - 7 q^{28} + 16 q^{29} - 6 q^{31} - 21 q^{32} + 28 q^{34} - 12 q^{35} + 6 q^{37} - 8 q^{38} - 13 q^{40} - 19 q^{44} - 12 q^{46} + 4 q^{47} + 4 q^{49} - 2 q^{50} + 20 q^{52} + 4 q^{53} + 8 q^{55} + q^{56} - 23 q^{58} - 14 q^{59} + 12 q^{61} - 48 q^{62} + 2 q^{64} - 4 q^{65} - 42 q^{67} + 10 q^{68} + 35 q^{70} - 18 q^{73} + 28 q^{74} - 44 q^{76} - 8 q^{77} + 6 q^{79} + 33 q^{80} - 14 q^{82} + 4 q^{83} - 32 q^{85} + 42 q^{86} + 11 q^{88} + 34 q^{91} + 28 q^{92} - 16 q^{94} - 24 q^{95} + 19 q^{98}+O(q^{100}) $ 8 * q - q^2 - q^4 - 2 * q^7 - 4 * q^8 - 13 * q^10 + 6 * q^11 + 10 * q^14 + 7 * q^16 + 6 * q^19 + 22 * q^20 - 6 * q^22 + 2 * q^25 - 12 * q^26 - 7 * q^28 + 16 * q^29 - 6 * q^31 - 21 * q^32 + 28 * q^34 - 12 * q^35 + 6 * q^37 - 8 * q^38 - 13 * q^40 - 19 * q^44 - 12 * q^46 + 4 * q^47 + 4 * q^49 - 2 * q^50 + 20 * q^52 + 4 * q^53 + 8 * q^55 + q^56 - 23 * q^58 - 14 * q^59 + 12 * q^61 - 48 * q^62 + 2 * q^64 - 4 * q^65 - 42 * q^67 + 10 * q^68 + 35 * q^70 - 18 * q^73 + 28 * q^74 - 44 * q^76 - 8 * q^77 + 6 * q^79 + 33 * q^80 - 14 * q^82 + 4 * q^83 - 32 * q^85 + 42 * q^86 + 11 * q^88 + 34 * q^91 + 28 * q^92 - 16 * q^94 - 24 * q^95 + 19 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.553244	−	1.30151i	−0.391203	−	0.920305i
$2$	−0.553244	−	1.30151i	−0.391203	−	0.920305i
$3$		0			0
$3$		0			0
$4$	−1.38784	+	1.44010i	−0.693921	+	0.720051i
$5$	−0.834598	+	0.481855i	−0.373244	+	0.215492i	−0.674875	−	0.737932i	$-0.735802\pi$
$5$	−0.834598	+	0.481855i	−0.373244	+	0.215492i	0.301631	+	0.953425i	$0.402469\pi$
$6$		0			0
$7$	1.20103	+	2.35744i	0.453948	+	0.891028i
$7$	1.20103	+	2.35744i	0.453948	+	0.891028i
$8$	2.64212	+	1.00956i	0.934130	+	0.356933i
$9$		0			0
$10$	1.08887	+	0.819652i	0.344332	+	0.259197i
$11$	4.74861	+	2.74161i	1.43176	+	0.826626i	0.997255	−	0.0740437i	$-0.0235904\pi$
$11$	4.74861	+	2.74161i	1.43176	+	0.826626i	0.434504	+	0.900670i	$0.356924\pi$
$12$		0			0
$13$		−	3.75117i		−	1.04039i	−0.854048	−	0.520193i	$-0.825860\pi$
$13$		−	3.75117i		−	1.04039i	0.854048	−	0.520193i	$-0.174140\pi$
$14$	2.40376	−	2.86739i	0.642432	−	0.766343i
$15$		0			0
$16$	−0.147789	−	3.99727i	−0.0369471	−	0.999317i
$17$	0.594545	+	0.343260i	0.144198	+	0.0832529i	0.570363	−	0.821393i	$-0.306802\pi$
$17$	0.594545	+	0.343260i	0.144198	+	0.0832529i	−0.426165	+	0.904645i	$0.640136\pi$
$18$		0			0
$19$	2.44109	+	4.22809i	0.560024	+	0.969989i	0.997494	+	0.0707563i	$0.0225413\pi$
$19$	2.44109	+	4.22809i	0.560024	+	0.969989i	−0.437470	+	0.899233i	$0.644125\pi$
$20$	0.464369	−	1.87065i	0.103836	−	0.418289i
$21$		0			0
$22$	0.941086	−	7.69713i	0.200640	−	1.64103i
$23$	−1.07465	+	0.620450i	−0.224080	+	0.129373i	−0.607838	−	0.794061i	$-0.707963\pi$
$23$	−1.07465	+	0.620450i	−0.224080	+	0.129373i	0.383758	+	0.923434i	$0.374630\pi$
$24$		0			0
$25$	−2.03563	+	3.52582i	−0.407126	+	0.705163i
$26$	−4.88217	+	2.07531i	−0.957473	+	0.407002i
$27$		0			0
$28$	−5.06180	−	1.54214i	−0.956590	−	0.291438i
$29$	2.48011			0.460544			0.230272	−	0.973126i	$-0.426038\pi$
$29$	2.48011			0.460544			0.230272	+	0.973126i	$0.426038\pi$
$30$		0			0
$31$	2.41401	−	4.18119i	0.433569	−	0.750963i	−0.563609	−	0.826042i	$-0.690587\pi$
$31$	2.41401	−	4.18119i	0.433569	−	0.750963i	0.997178	+	0.0750787i	$0.0239208\pi$
$32$	−5.12071	+	2.40381i	−0.905222	+	0.424938i
$33$		0			0
$34$	0.117828	−	0.963711i	0.0202073	−	0.165275i
$35$	−2.13832	−	1.38879i	−0.361443	−	0.234748i
$36$		0			0
$37$	1.36643	+	2.36673i	0.224640	+	0.389089i	0.956212	−	0.292677i	$-0.0945459\pi$
$37$	1.36643	+	2.36673i	0.224640	+	0.389089i	−0.731571	+	0.681765i	$0.761213\pi$
$38$	4.15237	−	5.51625i	0.673603	−	0.894855i
$39$		0			0
$40$	−2.69157	+	0.430544i	−0.425574	+	0.0680749i
$41$		−	9.42976i		−	1.47268i	−0.676611	−	0.736340i	$-0.736552\pi$
$41$		−	9.42976i		−	1.47268i	0.676611	−	0.736340i	$-0.263448\pi$
$42$		0			0
$43$			5.97437i			0.911083i	0.890215	+	0.455541i	$0.150554\pi$
$43$			5.97437i			0.911083i	−0.890215	+	0.455541i	$0.849446\pi$
$44$	−10.5385	+	3.03356i	−1.58874	+	0.457326i
$45$		0			0
$46$	1.40207	+	1.05541i	0.206723	+	0.155611i
$47$	−1.80752	−	3.13072i	−0.263654	−	0.456662i	0.703556	−	0.710640i	$-0.251594\pi$
$47$	−1.80752	−	3.13072i	−0.263654	−	0.456662i	−0.967210	+	0.253978i	$0.918261\pi$
$48$		0			0
$49$	−4.11504	+	5.66272i	−0.587863	+	0.808960i
$50$	5.71508	+	0.698752i	0.808234	+	0.0988184i
$51$		0			0
$52$	5.40207	+	5.20603i	0.749132	+	0.721946i
$53$	−2.04757	+	3.54650i	−0.281256	+	0.487150i	−0.971694	−	0.236242i	$-0.924084\pi$
$53$	−2.04757	+	3.54650i	−0.281256	+	0.487150i	0.690438	+	0.723391i	$0.257418\pi$
$54$		0			0
$55$	−5.28424			−0.712526
$56$	0.793298	+	7.44115i	0.106009	+	0.994365i
$57$		0			0
$58$	−1.37210	−	3.22788i	−0.180166	−	0.423841i
$59$	−6.34315	+	10.9867i	−0.825808	+	1.43034i	0.0754923	+	0.997146i	$0.475947\pi$
$59$	−6.34315	+	10.9867i	−0.825808	+	1.43034i	−0.901300	+	0.433195i	$0.857386\pi$
$60$		0			0
$61$	9.01711	−	5.20603i	1.15452	−	0.666564i	0.204537	−	0.978859i	$-0.434431\pi$
$61$	9.01711	−	5.20603i	1.15452	−	0.666564i	0.949985	+	0.312295i	$0.101098\pi$
$62$	−6.77738	−	0.828634i	−0.860728	−	0.105237i
$63$		0			0
$64$	5.96158	+	5.33475i	0.745198	+	0.666843i
$65$	1.80752	+	3.13072i	0.224195	+	0.388318i
$66$		0			0
$67$	−8.17396	−	4.71924i	−0.998608	−	0.576546i	−0.0907716	−	0.995872i	$-0.528933\pi$
$67$	−8.17396	−	4.71924i	−0.998608	−	0.576546i	−0.907836	+	0.419325i	$0.862267\pi$
$68$	−1.31946	+	0.379814i	−0.160009	+	0.0460592i
$69$		0			0
$70$	−0.624505	+	3.55138i	−0.0746427	+	0.424472i
$71$		−	10.1163i		−	1.20058i	−0.799782	−	0.600291i	$-0.795052\pi$
$71$		−	10.1163i		−	1.20058i	0.799782	−	0.600291i	$-0.204948\pi$
$72$		0			0
$73$	−5.76850	−	3.33044i	−0.675152	−	0.389799i	0.122874	−	0.992422i	$-0.460789\pi$
$73$	−5.76850	−	3.33044i	−0.675152	−	0.389799i	−0.798026	+	0.602623i	$0.794122\pi$
$74$	2.32435	−	3.08781i	0.270200	−	0.358950i
$75$		0			0
$76$	−9.47672	−	2.35250i	−1.08705	−	0.269850i
$77$	−0.759946	+	14.4873i	−0.0866039	+	1.65098i
$78$		0			0
$79$	−1.22492	+	0.707208i	−0.137814	+	0.0795671i	−0.567322	−	0.823496i	$-0.692020\pi$
$79$	−1.22492	+	0.707208i	−0.137814	+	0.0795671i	0.429508	+	0.903063i	$0.358687\pi$
$80$	2.04945	+	3.26490i	0.229135	+	0.365027i
$81$		0			0
$82$	−12.2729	+	5.21696i	−1.35531	+	0.576117i
$83$	0.543780			0.0596876			0.0298438	−	0.999555i	$-0.490499\pi$
$83$	0.543780			0.0596876			0.0298438	+	0.999555i	$0.490499\pi$
$84$		0			0
$85$	−0.661608			−0.0717614
$86$	7.77568	−	3.30528i	0.838474	−	0.356418i
$87$		0			0
$88$	9.77857	+	12.0377i	1.04240	+	1.28322i
$89$	−0.480107	+	0.277190i	−0.0508912	+	0.0293821i	−0.525230	−	0.850960i	$-0.676021\pi$
$89$	−0.480107	+	0.277190i	−0.0508912	+	0.0293821i	0.474339	+	0.880343i	$0.342687\pi$
$90$		0			0
$91$	8.84315	−	4.50528i	0.927014	−	0.472281i
$92$	0.597935	−	2.40870i	0.0623390	−	0.251124i
$93$		0			0
$94$	−3.07465	+	4.08455i	−0.317126	+	0.421289i
$95$	−4.07465	−	2.35250i	−0.418050	−	0.241362i
$96$		0			0
$97$		−	10.8747i		−	1.10416i	−0.833790	−	0.552081i	$-0.813834\pi$
$97$		−	10.8747i		−	1.10416i	0.833790	−	0.552081i	$-0.186166\pi$
$98$	9.64670	+	2.22289i	0.974464	+	0.224546i
$99$		0			0
$100$	−2.25240	−	7.82479i	−0.225240	−	0.782479i
$101$	−12.4972	−	7.21527i	−1.24352	−	0.717946i	−0.273710	−	0.961812i	$-0.588251\pi$
$101$	−12.4972	−	7.21527i	−1.24352	−	0.717946i	−0.969809	+	0.243866i	$0.921584\pi$
$102$		0			0
$103$	−7.51235	−	13.0118i	−0.740214	−	1.28209i	−0.952398	−	0.304858i	$-0.901391\pi$
$103$	−7.51235	−	13.0118i	−0.740214	−	1.28209i	0.212184	−	0.977230i	$-0.431942\pi$
$104$	3.78702	−	9.91103i	0.371348	−	0.971857i
$105$		0			0
$106$	5.74861	+	0.702851i	0.558354	+	0.0682669i
$107$	10.4925	−	6.05782i	1.01434	−	0.585632i	0.101883	−	0.994796i	$-0.467513\pi$
$107$	10.4925	−	6.05782i	1.01434	−	0.585632i	0.912461	+	0.409165i	$0.134180\pi$
$108$		0			0
$109$	3.03563	−	5.25787i	0.290761	−	0.503612i	−0.683229	−	0.730204i	$-0.739425\pi$
$109$	3.03563	−	5.25787i	0.290761	−	0.503612i	0.973990	+	0.226592i	$0.0727583\pi$
$110$	2.92347	+	6.87747i	0.278742	+	0.655741i
$111$		0			0
$112$	9.24582	−	5.14925i	0.873648	−	0.486559i
$113$	7.37939			0.694194			0.347097	−	0.937829i	$-0.387167\pi$
$113$	7.37939			0.694194			0.347097	+	0.937829i	$0.387167\pi$
$114$		0			0
$115$	0.597935	−	1.03565i	0.0557577	−	0.0965752i
$116$	−3.44200	+	3.57161i	−0.319581	+	0.331615i
$117$		0			0
$118$	17.8085	+	2.17735i	1.63941	+	0.200442i
$119$	−0.0951483	+	1.81387i	−0.00872223	+	0.166277i
$120$		0			0
$121$	9.53284	+	16.5114i	0.866622	+	1.50103i
$122$	−11.7643	−	8.85562i	−1.06509	−	0.801751i
$123$		0			0
$124$	2.67107	+	9.27924i	0.239869	+	0.833301i
$125$		−	8.74207i		−	0.781915i
$126$		0			0
$127$		−	11.6431i		−	1.03316i	−0.856240	−	0.516578i	$-0.827206\pi$
$127$		−	11.6431i		−	1.03316i	0.856240	−	0.516578i	$-0.172794\pi$
$128$	3.64500	−	10.7105i	0.322176	−	0.946680i
$129$		0			0
$130$	3.07465	−	4.08455i	0.269665	−	0.358239i
$131$	4.63078	+	8.02074i	0.404593	+	0.700776i	0.994274	−	0.106861i	$-0.0340798\pi$
$131$	4.63078	+	8.02074i	0.404593	+	0.700776i	−0.589681	+	0.807636i	$0.700747\pi$
$132$		0			0
$133$	−7.03563	+	10.8328i	−0.610067	+	0.939321i
$134$	−1.61993	+	13.2494i	−0.139940	+	1.14457i
$135$		0			0
$136$	1.22432	+	1.50716i	0.104984	+	0.129238i
$137$	3.61504	−	6.26144i	0.308854	−	0.534951i	−0.669258	−	0.743030i	$-0.733388\pi$
$137$	3.61504	−	6.26144i	0.308854	−	0.534951i	0.978112	+	0.208080i	$0.0667213\pi$
$138$		0			0
$139$	5.30812			0.450229			0.225115	−	0.974332i	$-0.427724\pi$
$139$	5.30812			0.450229			0.225115	+	0.974332i	$0.427724\pi$
$140$	4.96766	−	1.15198i	0.419844	−	0.0973604i
$141$		0			0
$142$	−13.1664	+	5.59677i	−1.10490	+	0.469671i
$143$	10.2842	−	17.8128i	0.860011	−	1.48958i
$144$		0			0
$145$	−2.06989	+	1.19505i	−0.171895	+	0.0992438i
$146$	−1.14321	+	9.35029i	−0.0946127	+	0.773836i
$147$		0			0
$148$	−5.30473	−	1.31685i	−0.436046	−	0.108244i
$149$	2.33080	+	4.03707i	0.190947	+	0.330730i	0.945564	−	0.325435i	$-0.105511\pi$
$149$	2.33080	+	4.03707i	0.190947	+	0.330730i	−0.754617	+	0.656165i	$0.772178\pi$
$150$		0			0
$151$	10.5709	+	6.10309i	0.860244	+	0.496662i	0.864094	−	0.503330i	$-0.167892\pi$
$151$	10.5709	+	6.10309i	0.860244	+	0.496662i	−0.00384988	+	0.999993i	$0.501225\pi$
$152$	2.18114	+	13.6355i	0.176914	+	1.10599i
$153$		0			0
$154$	19.2758	−	7.02594i	1.55329	−	0.566167i
$155$			4.65281i			0.373723i
$156$		0			0
$157$	−18.9944	−	10.9664i	−1.51592	−	0.875217i	−0.999825	−	0.0186856i	$-0.994052\pi$
$157$	−18.9944	−	10.9664i	−1.51592	−	0.875217i	−0.516095	−	0.856531i	$-0.672615\pi$
$158$	1.59812	+	1.20298i	0.127139	+	0.0957042i
$159$		0			0
$160$	3.11545	−	4.47366i	0.246298	−	0.353674i
$161$	−2.75337	−	1.78824i	−0.216996	−	0.140933i
$162$		0			0
$163$	−3.48011	+	2.00924i	−0.272583	+	0.157376i	−0.630061	−	0.776546i	$-0.716970\pi$
$163$	−3.48011	+	2.00924i	−0.272583	+	0.157376i	0.357478	+	0.933922i	$0.383637\pi$
$164$	13.5798	+	13.0870i	1.06041	+	1.02192i
$165$		0			0
$166$	−0.300843	−	0.707734i	−0.0233499	−	0.0549308i
$167$	−14.7178			−1.13890			−0.569448	−	0.822027i	$-0.692843\pi$
$167$	−14.7178			−1.13890			−0.569448	+	0.822027i	$0.692843\pi$
$168$		0			0
$169$	−1.07126			−0.0824047
$170$	0.366030	+	0.861087i	0.0280733	+	0.0660424i
$171$		0			0
$172$	−8.60370	−	8.29148i	−0.656026	−	0.632219i
$173$	10.0918	−	5.82648i	0.767262	−	0.442979i	−0.0646349	−	0.997909i	$-0.520588\pi$
$173$	10.0918	−	5.82648i	0.767262	−	0.442979i	0.831897	+	0.554930i	$0.187255\pi$
$174$		0			0
$175$	−10.7568	−	0.564256i	−0.813134	−	0.0426538i
$176$	10.2572	−	19.3866i	0.773163	−	1.46132i
$177$		0			0
$178$	0.626381	+	0.471509i	0.0469492	+	0.0353411i
$179$	2.24663	+	1.29709i	0.167921	+	0.0969494i	0.581605	−	0.813471i	$-0.302425\pi$
$179$	2.24663	+	1.29709i	0.167921	+	0.0969494i	−0.413684	+	0.910421i	$0.635758\pi$
$180$		0			0
$181$			9.53343i			0.708615i	0.935129	+	0.354307i	$0.115283\pi$
$181$			9.53343i			0.708615i	−0.935129	+	0.354307i	$0.884717\pi$
$182$	−10.7561	−	9.01691i	−0.797293	−	0.668378i
$183$		0			0
$184$	−3.46574	+	0.554380i	−0.255498	+	0.0408694i
$185$	−2.28085	−	1.31685i	−0.167691	−	0.0968166i
$186$		0			0
$187$	1.88217	+	3.26002i	0.137638	+	0.238396i
$188$	7.01711	+	1.74193i	0.511775	+	0.127043i
$189$		0			0
$190$	−0.807521	+	6.60470i	−0.0585837	+	0.479155i
$191$	−7.21637	+	4.16637i	−0.522158	+	0.301468i	−0.737817	−	0.675001i	$-0.764143\pi$
$191$	−7.21637	+	4.16637i	−0.522158	+	0.301468i	0.215659	+	0.976469i	$0.430810\pi$
$192$		0			0
$193$	6.18630	−	10.7150i	0.445300	−	0.771282i	−0.552773	−	0.833332i	$-0.686430\pi$
$193$	6.18630	−	10.7150i	0.445300	−	0.771282i	0.998073	+	0.0620498i	$0.0197638\pi$
$194$	−14.1536	+	6.01639i	−1.01617	+	0.431951i
$195$		0			0
$196$	−2.44387	−	13.7850i	−0.174562	−	0.984646i
$197$	−3.23686			−0.230617			−0.115308	−	0.993330i	$-0.536786\pi$
$197$	−3.23686			−0.230617			−0.115308	+	0.993330i	$0.536786\pi$
$198$		0			0
$199$	−9.61504	+	16.6537i	−0.681592	+	1.18055i	0.292903	+	0.956142i	$0.405379\pi$
$199$	−9.61504	+	16.6537i	−0.681592	+	1.18055i	−0.974495	+	0.224410i	$0.927955\pi$
$200$	−8.93790	+	7.26054i	−0.632005	+	0.513397i
$201$		0			0
$202$	−2.47672	+	20.2570i	−0.174261	+	1.42528i
$203$	2.97869	+	5.84670i	0.209063	+	0.410358i
$204$		0			0
$205$	4.54378	+	7.87006i	0.317351	+	0.549669i
$206$	−12.7787	+	16.9761i	−0.890338	+	1.18278i
$207$		0			0
$208$	−14.9944	+	0.554380i	−1.03968	+	0.0384393i
$209$			26.7700i			1.85172i
$210$		0			0
$211$			9.24637i			0.636546i	0.947999	+	0.318273i	$0.103103\pi$
$211$			9.24637i			0.636546i	−0.947999	+	0.318273i	$0.896897\pi$
$212$	−2.26562	−	7.87070i	−0.155603	−	0.540562i
$213$		0			0
$214$	−13.6892	−	10.3046i	−0.935773	−	0.704405i
$215$	−2.87878	−	4.98620i	−0.196331	−	0.340056i
$216$		0			0
$217$	12.7562	+	0.669139i	0.865947	+	0.0454241i
$218$	−8.52260	−	1.04201i	−0.577223	−	0.0705740i
$219$		0			0
$220$	7.33369	−	7.60984i	0.494437	−	0.513055i
$221$	1.28763	−	2.23024i	0.0866152	−	0.150022i
$222$		0			0
$223$	1.94585			0.130303			0.0651517	−	0.997875i	$-0.479247\pi$
$223$	1.94585			0.130303			0.0651517	+	0.997875i	$0.479247\pi$
$224$	−11.8170	−	9.18471i	−0.789556	−	0.613679i
$225$		0			0
$226$	−4.08260	−	9.60432i	−0.271571	−	0.638870i
$227$	−4.32265	+	7.48706i	−0.286905	+	0.496933i	−0.973069	−	0.230513i	$-0.925960\pi$
$227$	−4.32265	+	7.48706i	−0.286905	+	0.496933i	0.686165	+	0.727446i	$0.259293\pi$
$228$		0			0
$229$	14.5396	−	8.39446i	0.960805	−	0.554721i	0.0643846	−	0.997925i	$-0.479492\pi$
$229$	14.5396	−	8.39446i	0.960805	−	0.554721i	0.896421	+	0.443204i	$0.146158\pi$
$230$	−1.67871	−	0.205247i	−0.110691	−	0.0135336i
$231$		0			0
$232$	6.55274	+	2.50381i	0.430208	+	0.164383i
$233$	−0.523283	−	0.906353i	−0.0342814	−	0.0593772i	0.848376	−	0.529395i	$-0.177581\pi$
$233$	−0.523283	−	0.906353i	−0.0342814	−	0.0593772i	−0.882657	+	0.470018i	$0.844248\pi$
$234$		0			0
$235$	3.01711	+	1.74193i	0.196814	+	0.113631i
$236$	−7.01862	−	24.3825i	−0.456873	−	1.58717i
$237$		0			0
$238$	2.41340	−	0.879676i	0.156438	−	0.0570210i
$239$			19.2479i			1.24505i	0.782602	+	0.622523i	$0.213892\pi$
$239$			19.2479i			1.24505i	−0.782602	+	0.622523i	$0.786108\pi$
$240$		0			0
$241$	−2.38754	−	1.37844i	−0.153795	−	0.0887934i	0.421128	−	0.907001i	$-0.361634\pi$
$241$	−2.38754	−	1.37844i	−0.153795	−	0.0887934i	−0.574922	+	0.818208i	$0.694968\pi$
$242$	16.2157	−	21.5419i	1.04238	−	1.38476i
$243$		0			0
$244$	−5.01711	+	20.2107i	−0.321187	+	1.29386i
$245$	0.705792	−	6.70895i	0.0450914	−	0.428619i
$246$		0			0
$247$	15.8603	−	9.15692i	1.00916	−	0.582641i
$248$	10.5992	−	8.61011i	0.673053	−	0.546742i
$249$		0			0
$250$	−11.3779	+	4.83650i	−0.719600	+	0.305887i
$251$	20.7493			1.30968			0.654841	−	0.755767i	$-0.272736\pi$
$251$	20.7493			1.30968			0.654841	+	0.755767i	$0.272736\pi$
$252$		0			0
$253$	−6.80413			−0.427772
$254$	−15.1536	+	6.44147i	−0.950819	+	0.404173i
$255$		0			0
$256$	−15.9563	+	1.18150i	−0.997270	+	0.0738438i
$257$	−6.45283	+	3.72554i	−0.402516	+	0.232393i	−0.687569	−	0.726119i	$-0.741322\pi$
$257$	−6.45283	+	3.72554i	−0.402516	+	0.232393i	0.285053	+	0.958512i	$0.407989\pi$
$258$		0			0
$259$	−3.93830	+	6.06381i	−0.244714	+	0.376787i
$260$	−7.01711	−	1.74193i	−0.435182	−	0.108030i
$261$		0			0
$262$	7.87711	−	10.4644i	0.486649	−	0.646494i
$263$	−25.7034	−	14.8399i	−1.58494	−	0.915066i	−0.994123	−	0.108260i	$-0.965472\pi$
$263$	−25.7034	−	14.8399i	−1.58494	−	0.915066i	−0.590818	−	0.806805i	$-0.701195\pi$
$264$		0			0
$265$		−	3.94654i		−	0.242434i
$266$	17.9914	+	3.16375i	1.10312	+	0.193982i
$267$		0			0
$268$	18.1403	−	5.22178i	1.10810	−	0.318971i
$269$	3.73727	+	2.15771i	0.227865	+	0.131558i	0.609587	−	0.792719i	$-0.291335\pi$
$269$	3.73727	+	2.15771i	0.227865	+	0.131558i	−0.381722	+	0.924277i	$0.624669\pi$
$270$		0			0
$271$	6.79142	+	11.7631i	0.412550	+	0.714557i	0.995168	−	0.0981892i	$-0.0313050\pi$
$271$	6.79142	+	11.7631i	0.412550	+	0.714557i	−0.582618	+	0.812746i	$0.697972\pi$
$272$	1.28424	−	2.42728i	0.0778683	−	0.147176i
$273$		0			0
$274$	−10.1493	−	1.24090i	−0.613142	−	0.0749656i
$275$	−19.3328	+	11.1618i	−1.16581	+	0.673082i
$276$		0			0
$277$	−1.03563	+	1.79376i	−0.0622250	+	0.107777i	−0.895460	−	0.445143i	$-0.853153\pi$
$277$	−1.03563	+	1.79376i	−0.0622250	+	0.107777i	0.833235	+	0.552920i	$0.186486\pi$
$278$	−2.93669	−	6.90856i	−0.176131	−	0.414348i
$279$		0			0
$280$	−4.24764	−	5.82811i	−0.253845	−	0.348296i
$281$	−23.7122			−1.41455			−0.707276	−	0.706938i	$-0.750076\pi$
$281$	−23.7122			−1.41455			−0.707276	+	0.706938i	$0.750076\pi$
$282$		0			0
$283$	−6.12739	+	10.6129i	−0.364235	+	0.630874i	−0.988653	−	0.150216i	$-0.952003\pi$
$283$	−6.12739	+	10.6129i	−0.364235	+	0.630874i	0.624418	+	0.781091i	$0.285336\pi$
$284$	14.5685	+	14.0398i	0.864480	+	0.833109i
$285$		0			0
$286$	−28.8732	−	3.53017i	−1.70731	−	0.208743i
$287$	22.2301	−	11.3254i	1.31220	−	0.668520i
$288$		0			0
$289$	−8.26434	−	14.3143i	−0.486138	−	0.842016i
$290$	2.70053	+	2.03282i	0.158580	+	0.119372i
$291$		0			0
$292$	12.8019	−	3.68510i	0.749177	−	0.215654i
$293$		−	10.7090i		−	0.625626i	−0.949815	−	0.312813i	$-0.898729\pi$
$293$		−	10.7090i		−	0.625626i	0.949815	−	0.312813i	$-0.101271\pi$
$294$		0			0
$295$		−	12.2259i		−	0.711821i
$296$	1.22093	+	7.63269i	0.0709649	+	0.443641i
$297$		0			0
$298$	3.96477	−	5.26704i	0.229673	−	0.305112i
$299$	2.32741	+	4.03120i	0.134598	+	0.233130i
$300$		0			0
$301$	−14.0842	+	7.17541i	−0.811801	+	0.413584i
$302$	2.09495	−	17.1345i	0.120551	−	0.985982i
$303$		0			0
$304$	16.5400	−	10.3825i	0.948636	−	0.595480i
$305$	−5.01711	+	8.68988i	−0.287279	+	0.497581i
$306$		0			0
$307$	4.22056			0.240880			0.120440	−	0.992721i	$-0.461569\pi$
$307$	4.22056			0.240880			0.120440	+	0.992721i	$0.461569\pi$
$308$	−19.8085	−	21.2005i	−1.12870	−	1.20801i
$309$		0			0
$310$	6.05567	−	2.57414i	0.343939	−	0.146201i
$311$	4.85070	−	8.40165i	0.275058	−	0.476414i	−0.695092	−	0.718921i	$-0.744636\pi$
$311$	4.85070	−	8.40165i	0.275058	−	0.476414i	0.970150	+	0.242507i	$0.0779697\pi$
$312$		0			0
$313$	11.8328	−	6.83168i	0.668831	−	0.386149i	−0.126803	−	0.991928i	$-0.540472\pi$
$313$	11.8328	−	6.83168i	0.668831	−	0.386149i	0.795633	+	0.605778i	$0.207138\pi$
$314$	−3.76434	+	30.7885i	−0.212434	+	1.73750i
$315$		0			0
$316$	0.681544	−	2.74550i	0.0383398	−	0.154447i
$317$	10.0442	+	17.3970i	0.564138	+	0.977115i	0.997129	+	0.0757171i	$0.0241246\pi$
$317$	10.0442	+	17.3970i	0.564138	+	0.977115i	−0.432992	+	0.901398i	$0.642542\pi$
$318$		0			0
$319$	11.7771	+	6.79948i	0.659388	+	0.380698i
$320$	−7.54610	−	1.57975i	−0.421840	−	0.0883106i
$321$		0			0
$322$	−0.804130	+	4.57286i	−0.0448124	+	0.254836i
$323$			3.35171i			0.186494i
$324$		0			0
$325$	13.2259	+	7.63599i	0.733642	+	0.423569i
$326$	4.54039	+	3.41778i	0.251469	+	0.189294i
$327$		0			0
$328$	9.51989	−	24.9145i	0.525648	−	1.37568i
$329$	5.20959	−	8.02121i	0.287214	−	0.442224i
$330$		0			0
$331$	8.15886	−	4.71052i	0.448452	−	0.258914i	−0.258724	−	0.965951i	$-0.583302\pi$
$331$	8.15886	−	4.71052i	0.448452	−	0.258914i	0.707176	+	0.707037i	$0.249969\pi$
$332$	−0.754681	+	0.783099i	−0.0414185	+	0.0429781i
$333$		0			0
$334$	8.14252	+	19.1553i	0.445539	+	1.04813i
$335$	9.09596			0.496965
$336$		0			0
$337$	−13.4411			−0.732185			−0.366092	−	0.930578i	$-0.619305\pi$
$337$	−13.4411			−0.732185			−0.366092	+	0.930578i	$0.619305\pi$
$338$	0.592669	+	1.39425i	0.0322369	+	0.0758374i
$339$		0			0
$340$	0.918207	−	0.952783i	0.0497968	−	0.0516719i
$341$	22.9264	−	13.2365i	1.24153	−	0.716799i
$342$		0			0
$343$	−18.2918	−	2.89985i	−0.987666	−	0.156577i
$344$	−6.03148	+	15.7850i	−0.325195	+	0.851070i
$345$		0			0
$346$	−13.1664	−	9.91103i	−0.707831	−	0.532820i
$347$	19.5890	+	11.3097i	1.05159	+	0.607136i	0.923094	−	0.384574i	$-0.125651\pi$
$347$	19.5890	+	11.3097i	1.05159	+	0.607136i	0.128497	+	0.991710i	$0.458985\pi$
$348$		0			0
$349$			2.48180i			0.132848i	0.997791	+	0.0664239i	$0.0211590\pi$
$349$			2.48180i			0.132848i	−0.997791	+	0.0664239i	$0.978841\pi$
$350$	5.21673	+	14.3122i	0.278846	+	0.765018i
$351$		0			0
$352$	−30.9066	−	2.62423i	−1.64733	−	0.139872i
$353$	7.89315	+	4.55711i	0.420110	+	0.242551i	0.695124	−	0.718889i	$-0.255349\pi$
$353$	7.89315	+	4.55711i	0.420110	+	0.242551i	−0.275014	+	0.961440i	$0.588683\pi$
$354$		0			0
$355$	4.87458	+	8.44303i	0.258716	+	0.448109i
$356$	0.267131	−	1.07610i	0.0141579	−	0.0570331i
$357$		0			0
$358$	0.445241	−	3.64162i	0.0235317	−	0.192466i
$359$	6.00000	−	3.46410i	0.316668	−	0.182828i	−0.333238	−	0.942843i	$-0.608141\pi$
$359$	6.00000	−	3.46410i	0.316668	−	0.182828i	0.649906	+	0.760014i	$0.274808\pi$
$360$		0			0
$361$	−2.41780	+	4.18776i	−0.127253	+	0.220408i
$362$	12.4078	−	5.27431i	0.652141	−	0.277212i
$363$		0			0
$364$	−5.78484	+	18.9877i	−0.303208	+	0.995223i
$365$	6.41917			0.335995
$366$		0			0
$367$	−1.91680	+	3.31999i	−0.100056	+	0.173302i	−0.911707	−	0.410840i	$-0.865235\pi$
$367$	−1.91680	+	3.31999i	−0.100056	+	0.173302i	0.811652	+	0.584142i	$0.198569\pi$
$368$	2.63893	+	4.20398i	0.137564	+	0.219147i
$369$		0			0
$370$	−0.452022	+	3.69708i	−0.0234995	+	0.192202i
$371$	−10.8199	−	0.567567i	−0.561740	−	0.0294666i
$372$		0			0
$373$	13.4150	+	23.2355i	0.694603	+	1.20309i	0.970314	+	0.241848i	$0.0777534\pi$
$373$	13.4150	+	23.2355i	0.694603	+	1.20309i	−0.275711	+	0.961241i	$0.588913\pi$
$374$	3.20164	−	4.25325i	0.165553	−	0.219930i
$375$		0			0
$376$	−1.61504	−	10.0965i	−0.0832894	−	0.520689i
$377$		−	9.30330i		−	0.479144i
$378$		0			0
$379$			6.93692i			0.356325i	0.984001	+	0.178163i	$0.0570153\pi$
$379$			6.93692i			0.356325i	−0.984001	+	0.178163i	$0.942985\pi$
$380$	9.04282	−	2.60301i	0.463887	−	0.133532i
$381$		0			0
$382$	9.41497	+	7.08713i	0.481712	+	0.362609i
$383$	−1.12881	−	1.95515i	−0.0576793	−	0.0999035i	0.835744	−	0.549119i	$-0.185037\pi$
$383$	−1.12881	−	1.95515i	−0.0576793	−	0.0999035i	−0.893423	+	0.449216i	$0.851703\pi$
$384$		0			0
$385$	−6.34654	−	12.4573i	−0.323450	−	0.634881i
$386$	−17.3682	−	2.12351i	−0.884017	−	0.108084i
$387$		0			0
$388$	15.6607	+	15.0924i	0.795054	+	0.766202i
$389$	15.3047	−	26.5086i	0.775981	−	1.34404i	−0.158261	−	0.987397i	$-0.550589\pi$
$389$	15.3047	−	26.5086i	0.775981	−	1.34404i	0.934242	−	0.356641i	$-0.116078\pi$
$390$		0			0
$391$	−0.851904			−0.0430827
$392$	−16.5893	+	10.8072i	−0.837885	+	0.545847i
$393$		0			0
$394$	1.79078	+	4.21280i	0.0902179	+	0.212238i
$395$	0.681544	−	1.18047i	0.0342922	−	0.0593958i
$396$		0			0
$397$	−12.0368	+	6.94947i	−0.604112	+	0.348784i	−0.770657	−	0.637250i	$-0.780072\pi$
$397$	−12.0368	+	6.94947i	−0.604112	+	0.348784i	0.166546	+	0.986034i	$0.446739\pi$
$398$	26.9944	+	3.30046i	1.35311	+	0.165437i
$399$		0			0
$400$	14.3945	+	7.61589i	0.719724	+	0.380794i
$401$	−5.13832	−	8.89984i	−0.256596	−	0.444437i	0.708732	−	0.705478i	$-0.249268\pi$
$401$	−5.13832	−	8.89984i	−0.256596	−	0.444437i	−0.965328	+	0.261041i	$0.915934\pi$
$402$		0			0
$403$	−15.6843	−	9.05535i	−0.781292	−	0.451079i
$404$	27.7349	−	7.98361i	1.37986	−	0.397199i
$405$		0			0
$406$	5.96158	−	7.11144i	0.295868	−	0.352935i
$407$			14.9849i			0.742775i
$408$		0			0
$409$	10.5342	+	6.08193i	0.520883	+	0.300732i	0.737296	−	0.675570i	$-0.236102\pi$
$409$	10.5342	+	6.08193i	0.520883	+	0.300732i	−0.216413	+	0.976302i	$0.569436\pi$
$410$	7.72912	−	10.2678i	0.381714	−	0.507092i
$411$		0			0
$412$	29.1642	+	7.23973i	1.43682	+	0.356676i
$413$	−33.5187	−	1.75826i	−1.64935	−	0.0865182i
$414$		0			0
$415$	−0.453838	+	0.262023i	−0.0222780	+	0.0128622i
$416$	9.01711	+	19.2086i	0.442100	+	0.941781i
$417$		0			0
$418$	34.8414	−	14.8104i	1.70415	−	0.724398i
$419$	−16.2245			−0.792619			−0.396310	−	0.918117i	$-0.629709\pi$
$419$	−16.2245			−0.792619			−0.396310	+	0.918117i	$0.629709\pi$
$420$		0			0
$421$	−9.58477			−0.467133			−0.233567	−	0.972341i	$-0.575040\pi$
$421$	−9.58477			−0.467133			−0.233567	+	0.972341i	$0.575040\pi$
$422$	12.0342	−	5.11550i	0.585816	−	0.249019i
$423$		0			0
$424$	−8.99034	+	7.30313i	−0.436609	+	0.354672i
$425$	−2.42055	+	1.39750i	−0.117414	+	0.0677889i
$426$		0			0
$427$	23.1027	+	15.0047i	1.11802	+	0.726127i
$428$	−5.83799	+	23.5175i	−0.282190	+	1.13676i
$429$		0			0
$430$	−4.89690	+	6.50534i	−0.236150	+	0.313715i
$431$	0.131544	+	0.0759470i	0.00633626	+	0.00365824i	0.503165	−	0.864190i	$-0.332169\pi$
$431$	0.131544	+	0.0759470i	0.00633626	+	0.00365824i	−0.496829	+	0.867849i	$0.665502\pi$
$432$		0			0
$433$			9.46997i			0.455098i	0.973767	+	0.227549i	$0.0730711\pi$
$433$			9.46997i			0.455098i	−0.973767	+	0.227549i	$0.926929\pi$
$434$	−6.18640	−	16.9725i	−0.296957	−	0.814705i
$435$		0			0
$436$	3.35889	+	11.6687i	0.160862	+	0.558830i
$437$	−5.24663	−	3.02915i	−0.250981	−	0.144904i
$438$		0			0
$439$	−16.7373	−	28.9898i	−0.798826	−	1.38361i	−0.920381	−	0.391023i	$-0.872121\pi$
$439$	−16.7373	−	28.9898i	−0.798826	−	1.38361i	0.121555	−	0.992585i	$-0.461212\pi$
$440$	−13.9616	−	5.33475i	−0.665592	−	0.254324i
$441$		0			0
$442$	−3.61504	−	0.441992i	−0.171950	−	0.0210234i
$443$	22.6513	−	13.0777i	1.07619	−	0.621341i	0.146327	−	0.989236i	$-0.453255\pi$
$443$	22.6513	−	13.0777i	1.07619	−	0.621341i	0.929867	+	0.367895i	$0.119921\pi$
$444$		0			0
$445$	0.267131	−	0.462684i	0.0126632	−	0.0219333i
$446$	−1.07653	−	2.53253i	−0.0509750	−	0.119919i
$447$		0			0
$448$	−5.41629	+	20.4613i	−0.255896	+	0.966704i
$449$	−10.2918			−0.485701			−0.242851	−	0.970064i	$-0.578082\pi$
$449$	−10.2918			−0.485701			−0.242851	+	0.970064i	$0.578082\pi$
$450$		0			0
$451$	25.8527	−	44.7782i	1.21736	−	2.10852i
$452$	−10.2414	+	10.6271i	−0.481716	+	0.499855i
$453$		0			0
$454$	12.1359	+	1.48380i	0.569568	+	0.0696380i
$455$	−5.20959	+	8.02121i	−0.244229	+	0.376040i
$456$		0			0
$457$	−5.96574	−	10.3330i	−0.279065	−	0.483356i	0.692087	−	0.721814i	$-0.256691\pi$
$457$	−5.96574	−	10.3330i	−0.279065	−	0.483356i	−0.971153	+	0.238458i	$0.923358\pi$
$458$	−18.9694	−	14.2792i	−0.886382	−	0.667225i
$459$		0			0
$460$	0.661608	+	2.29841i	0.0308476	+	0.107164i
$461$			30.0093i			1.39767i	0.715281	+	0.698837i	$0.246299\pi$
$461$			30.0093i			1.39767i	−0.715281	+	0.698837i	$0.753701\pi$
$462$		0			0
$463$		−	13.2736i		−	0.616875i	−0.951245	−	0.308437i	$-0.900194\pi$
$463$		−	13.2736i		−	0.616875i	0.951245	−	0.308437i	$-0.0998060\pi$
$464$	−0.366532	−	9.91365i	−0.0170158	−	0.460230i
$465$		0			0
$466$	−0.890122	+	1.18249i	−0.0412341	+	0.0547778i
$467$	−14.8246	−	25.6770i	−0.686002	−	1.18819i	−0.973121	−	0.230295i	$-0.926031\pi$
$467$	−14.8246	−	25.6770i	−0.686002	−	1.18819i	0.287119	−	0.957895i	$-0.407303\pi$
$468$		0			0
$469$	1.30812	−	24.9376i	0.0604036	−	1.15151i
$470$	0.597935	−	4.89050i	0.0275807	−	0.225582i
$471$		0			0
$472$	−27.8510	+	22.6243i	−1.28195	+	1.04137i
$473$	−16.3794	+	28.3699i	−0.753125	+	1.30445i
$474$		0			0
$475$	−19.8766			−0.912001
$476$	−2.48011	−	2.65439i	−0.113676	−	0.121664i
$477$		0			0
$478$	25.0513	−	10.6488i	1.14582	−	0.487065i
$479$	5.76773	−	9.99001i	0.263535	−	0.456455i	−0.703644	−	0.710553i	$-0.748445\pi$
$479$	5.76773	−	9.99001i	0.263535	−	0.456455i	0.967179	+	0.254097i	$0.0817784\pi$
$480$		0			0
$481$	8.87802	−	5.12573i	0.404803	−	0.233713i
$482$	−0.473165	+	3.87001i	−0.0215521	+	0.176274i
$483$		0			0
$484$	−37.0081	−	9.18691i	−1.68219	−	0.417587i
$485$	5.24005	+	9.07604i	0.237939	+	0.412122i
$486$		0			0
$487$	−8.44822	−	4.87758i	−0.382825	−	0.221024i	0.296221	−	0.955119i	$-0.404273\pi$
$487$	−8.44822	−	4.87758i	−0.382825	−	0.221024i	−0.679047	+	0.734095i	$0.737607\pi$
$488$	29.0801	−	4.65165i	1.31639	−	0.210570i
$489$		0			0
$490$	−9.12223	+	2.79310i	−0.412100	+	0.126179i
$491$		−	40.4736i		−	1.82655i	−0.407346	−	0.913274i	$-0.633546\pi$
$491$		−	40.4736i		−	1.82655i	0.407346	−	0.913274i	$-0.366454\pi$
$492$		0			0
$493$	1.47453	+	0.851323i	0.0664097	+	0.0383416i
$494$	−20.6924	−	15.5762i	−0.930995	−	0.700808i
$495$		0			0
$496$	−17.0701	−	9.03151i	−0.766470	−	0.405527i
$497$	23.8485	−	12.1500i	1.06975	−	0.545001i
$498$		0			0
$499$	−27.6827	+	15.9826i	−1.23925	+	0.715480i	−0.968941	−	0.247294i	$-0.920459\pi$
$499$	−27.6827	+	15.9826i	−1.23925	+	0.715480i	−0.270307	+	0.962774i	$0.587125\pi$
$500$	12.5895	+	12.1326i	0.563019	+	0.542587i
$501$		0			0
$502$	−11.4794	−	27.0053i	−0.512351	−	1.20531i
$503$	−22.7110			−1.01263			−0.506317	−	0.862348i	$-0.668993\pi$
$503$	−22.7110			−1.01263			−0.506317	+	0.862348i	$0.668993\pi$
$504$		0			0
$505$	13.9069			0.618847
$506$	3.76434	+	8.85562i	0.167346	+	0.393681i
$507$		0			0
$508$	16.7672	+	16.1588i	0.743925	+	0.716929i
$509$	1.98947	−	1.14862i	0.0881819	−	0.0509118i	−0.455261	−	0.890358i	$-0.650454\pi$
$509$	1.98947	−	1.14862i	0.0881819	−	0.0509118i	0.543443	+	0.839446i	$0.317121\pi$
$510$		0			0
$511$	0.923166	−	17.5989i	0.0408384	−	0.778528i
$512$	10.3655	+	20.1136i	0.458093	+	0.888904i
$513$		0			0
$514$	8.41881	+	6.33727i	0.371338	+	0.279525i
$515$	12.5396	+	7.23973i	0.552560	+	0.319021i
$516$		0			0
$517$		−	19.8221i		−	0.871773i
$518$	10.0709	+	1.77096i	0.442491	+	0.0778114i
$519$		0			0
$520$	1.61504	+	10.0965i	0.0708242	+	0.442762i
$521$	32.5712	+	18.8050i	1.42697	+	0.823862i	0.996881	−	0.0789240i	$-0.0251485\pi$
$521$	32.5712	+	18.8050i	1.42697	+	0.823862i	0.430090	+	0.902786i	$0.358482\pi$
$522$		0			0
$523$	−17.8444	−	30.9073i	−0.780279	−	1.35148i	−0.931779	−	0.363026i	$-0.881744\pi$
$523$	−17.8444	−	30.9073i	−0.780279	−	1.35148i	0.151500	−	0.988457i	$-0.451590\pi$
$524$	−17.9775	−	4.46273i	−0.785350	−	0.194955i
$525$		0			0
$526$	−5.09394	+	41.6632i	−0.222106	+	1.81660i
$527$	2.87047	−	1.65727i	0.125040	−	0.0721917i
$528$		0			0
$529$	−10.7301	+	18.5850i	−0.466525	+	0.808046i
$530$	−5.13645	+	2.18340i	−0.223113	+	0.0948408i
$531$		0			0
$532$	−5.83597	−	25.1662i	−0.253021	−	1.09109i
$533$	−35.3726			−1.53216
$534$		0			0
$535$	−5.83799	+	10.1117i	−0.252398	+	0.437167i
$536$	−16.8322	−	20.7209i	−0.727041	−	0.895005i
$537$		0			0
$538$	0.740657	−	6.05782i	0.0319320	−	0.261171i
$539$	−35.0657	+	15.6082i	−1.51039	+	0.672293i
$540$		0			0
$541$	−18.5102	−	32.0605i	−0.795814	−	1.37839i	−0.922321	−	0.386425i	$-0.873710\pi$
$541$	−18.5102	−	32.0605i	−0.795814	−	1.37839i	0.126507	−	0.991966i	$-0.459623\pi$
$542$	11.5524	−	15.3469i	0.496219	−	0.659208i
$543$		0			0
$544$	−3.86963	−	0.328564i	−0.165909	−	0.0140871i
$545$			5.85094i			0.250627i
$546$		0			0
$547$			2.09106i			0.0894073i	0.999000	+	0.0447036i	$0.0142344\pi$
$547$			2.09106i			0.0894073i	−0.999000	+	0.0447036i	$0.985766\pi$
$548$	4.00000	+	13.8959i	0.170872	+	0.593604i
$549$		0			0
$550$	25.2229	+	18.9866i	1.07551	+	0.809591i
$551$	6.05415	+	10.4861i	0.257916	+	0.446723i
$552$		0			0
$553$	−3.13837	−	2.03829i	−0.133457	−	0.0866771i
$554$	2.90755	+	0.355491i	0.123530	+	0.0151034i
$555$		0			0
$556$	−7.36684	+	7.64424i	−0.312424	+	0.324188i
$557$	−8.39887	+	14.5473i	−0.355872	+	0.616388i	−0.987267	−	0.159073i	$-0.949149\pi$
$557$	−8.39887	+	14.5473i	−0.355872	+	0.616388i	0.631395	+	0.775461i	$0.282483\pi$
$558$		0			0
$559$	22.4109			0.947878
$560$	−5.23535	+	8.75271i	−0.221234	+	0.369869i
$561$		0			0
$562$	13.1186	+	30.8616i	0.553376	+	1.30182i
$563$	−8.69784	+	15.0651i	−0.366570	+	0.634918i	−0.989027	−	0.147736i	$-0.952801\pi$
$563$	−8.69784	+	15.0651i	−0.366570	+	0.634918i	0.622456	+	0.782654i	$0.286135\pi$
$564$		0			0
$565$	−6.15882	+	3.55580i	−0.259104	+	0.149594i
$566$	17.2028	+	2.10329i	0.723086	+	0.0884079i
$567$		0			0
$568$	10.2130	−	26.7284i	0.428527	−	1.12150i
$569$	−17.1425	−	29.6917i	−0.718652	−	1.24474i	−0.961534	−	0.274686i	$-0.911426\pi$
$569$	−17.1425	−	29.6917i	−0.718652	−	1.24474i	0.242882	−	0.970056i	$-0.421907\pi$
$570$		0			0
$571$	5.14176	+	2.96860i	0.215176	+	0.124232i	0.603715	−	0.797201i	$-0.293687\pi$
$571$	5.14176	+	2.96860i	0.215176	+	0.124232i	−0.388539	+	0.921432i	$0.627020\pi$
$572$	11.3794	+	39.5317i	0.475796	+	1.65290i
$573$		0			0
$574$	−27.0388	−	22.6669i	−1.12858	−	0.946097i
$575$		−	5.05203i		−	0.210684i
$576$		0			0
$577$	33.7930	+	19.5104i	1.40682	+	0.812229i	0.995080	−	0.0990712i	$-0.0315871\pi$
$577$	33.7930	+	19.5104i	1.40682	+	0.812229i	0.411742	+	0.911300i	$0.364920\pi$
$578$	−14.0579	+	18.6754i	−0.584732	+	0.776794i
$579$		0			0
$580$	1.15169	−	4.63940i	0.0478211	−	0.192641i
$581$	0.653097	+	1.28193i	0.0270950	+	0.0531833i
$582$		0			0
$583$	−19.4462	+	11.2273i	−0.805381	+	0.464987i
$584$	−11.8788	−	14.6231i	−0.491547	−	0.605107i
$585$		0			0
$586$	−13.9378	+	5.92469i	−0.575767	+	0.244747i
$587$	7.71931			0.318610			0.159305	−	0.987229i	$-0.449075\pi$
$587$	7.71931			0.318610			0.159305	+	0.987229i	$0.449075\pi$
$588$		0			0
$589$	23.5712			0.971235
$590$	−15.9121	+	6.76392i	−0.655092	+	0.278466i
$591$		0			0
$592$	9.25853	−	5.81178i	0.380523	−	0.238863i
$593$	−0.336377	+	0.194207i	−0.0138133	+	0.00797513i	−0.506891	−	0.862010i	$-0.669205\pi$
$593$	−0.336377	+	0.194207i	−0.0138133	+	0.00797513i	0.493077	+	0.869985i	$0.335872\pi$
$594$		0			0
$595$	−0.794612	−	1.55970i	−0.0325759	−	0.0639415i
$596$	−9.04858	−	2.24622i	−0.370644	−	0.0920088i
$597$		0			0
$598$	3.95901	−	5.25938i	0.161896	−	0.215072i
$599$	−18.0000	−	10.3923i	−0.735460	−	0.424618i	0.0849563	−	0.996385i	$-0.472925\pi$
$599$	−18.0000	−	10.3923i	−0.735460	−	0.424618i	−0.820416	+	0.571767i	$0.806258\pi$
$600$		0			0
$601$			26.4110i			1.07733i	0.842521	+	0.538664i	$0.181071\pi$
$601$			26.4110i			1.07733i	−0.842521	+	0.538664i	$0.818929\pi$
$602$	17.1309	+	14.3610i	0.698202	+	0.585309i
$603$		0			0
$604$	−23.4598	+	6.75299i	−0.954564	+	0.274775i
$605$	−15.9122	−	9.18691i	−0.646922	−	0.373501i
$606$		0			0
$607$	20.3531	+	35.2526i	0.826106	+	1.43086i	0.901071	+	0.433671i	$0.142782\pi$
$607$	20.3531	+	35.2526i	0.826106	+	1.43086i	−0.0749655	+	0.997186i	$0.523885\pi$
$608$	−22.6636	−	15.7829i	−0.919131	−	0.640081i
$609$		0			0
$610$	14.0856	+	1.72217i	0.570310	+	0.0697288i
$611$	−11.7438	+	6.78031i	−0.475105	+	0.274302i
$612$		0			0
$613$	−8.66920	+	15.0155i	−0.350146	+	0.606470i	−0.986275	−	0.165113i	$-0.947201\pi$
$613$	−8.66920	+	15.0155i	−0.350146	+	0.606470i	0.636129	+	0.771583i	$0.280535\pi$
$614$	−2.33500	−	5.49310i	−0.0942330	−	0.221683i
$615$		0			0
$616$	−16.6337	+	37.5100i	−0.670189	+	1.51132i
$617$	46.4753			1.87103			0.935513	−	0.353291i	$-0.114938\pi$
$617$	46.4753			1.87103			0.935513	+	0.353291i	$0.114938\pi$
$618$		0			0
$619$	13.1911	−	22.8476i	0.530194	−	0.918322i	−0.469186	−	0.883099i	$-0.655453\pi$
$619$	13.1911	−	22.8476i	0.530194	−	0.918322i	0.999379	−	0.0352227i	$-0.0112141\pi$
$620$	−6.70053	−	6.45737i	−0.269100	−	0.259334i
$621$		0			0
$622$	−13.6184	−	1.66505i	−0.546049	−	0.0667625i
$623$	−1.23008	−	0.798909i	−0.0492822	−	0.0320076i
$624$		0			0
$625$	−5.96574	−	10.3330i	−0.238630	−	0.413318i
$626$	−15.4379	−	11.6209i	−0.617023	−	0.464465i
$627$		0			0
$628$	42.1541	−	12.1342i	1.68213	−	0.484209i
$629$			1.87617i			0.0748079i
$630$		0			0
$631$			41.0696i			1.63495i	0.575961	+	0.817477i	$0.304628\pi$
$631$			41.0696i			1.63495i	−0.575961	+	0.817477i	$0.695372\pi$
$632$	−3.95035	+	0.631898i	−0.157137	+	0.0251356i
$633$		0			0
$634$	17.0855	−	22.6974i	0.678551	−	0.901428i
$635$	5.61028	+	9.71729i	0.222637	+	0.385619i
$636$		0			0
$637$	21.2418	+	15.4362i	0.841632	+	0.611605i
$638$	2.33399	−	19.0897i	0.0924037	−	0.755768i
$639$		0			0
$640$	2.11878	+	10.6953i	0.0837522	+	0.422769i
$641$	22.7239	−	39.3590i	0.897540	−	1.55459i	0.0669115	−	0.997759i	$-0.478685\pi$
$641$	22.7239	−	39.3590i	0.897540	−	1.55459i	0.830629	−	0.556827i	$-0.187981\pi$
$642$		0			0
$643$	−30.5534			−1.20491			−0.602454	−	0.798154i	$-0.705810\pi$
$643$	−30.5534			−1.20491			−0.602454	+	0.798154i	$0.705810\pi$
$644$	6.39649	−	1.48333i	0.252057	−	0.0584513i
$645$		0			0
$646$	4.36228	−	1.85432i	0.171632	−	0.0729571i
$647$	−18.0896	+	31.3321i	−0.711175	+	1.23179i	0.253242	+	0.967403i	$0.418503\pi$
$647$	−18.0896	+	31.3321i	−0.711175	+	1.23179i	−0.964417	+	0.264388i	$0.914830\pi$
$648$		0			0
$649$	−60.2423	+	34.7809i	−2.36472	+	1.36527i
$650$	2.62113	−	21.4382i	0.102809	−	0.840876i
$651$		0			0
$652$	1.93633	−	7.80022i	0.0758324	−	0.305480i
$653$	−4.11545	−	7.12816i	−0.161050	−	0.278946i	0.774196	−	0.632946i	$-0.218155\pi$
$653$	−4.11545	−	7.12816i	−0.161050	−	0.278946i	−0.935245	+	0.354000i	$0.884821\pi$
$654$		0			0
$655$	−7.72968	−	4.46273i	−0.302024	−	0.174373i
$656$	−37.6933	+	1.39361i	−1.47168	+	0.0544114i
$657$		0			0
$658$	−13.3218	−	2.34262i	−0.519339	−	0.0913250i
$659$		−	22.8837i		−	0.891422i	−0.895177	−	0.445711i	$-0.852951\pi$
$659$		−	22.8837i		−	0.891422i	0.895177	−	0.445711i	$-0.147049\pi$
$660$		0			0
$661$	−17.7212	−	10.2313i	−0.689275	−	0.397953i	0.114065	−	0.993473i	$-0.463613\pi$
$661$	−17.7212	−	10.2313i	−0.689275	−	0.397953i	−0.803340	+	0.595520i	$0.796946\pi$
$662$	−10.6446	−	8.01275i	−0.413715	−	0.311424i
$663$		0			0
$664$	1.43673	+	0.548978i	0.0557560	+	0.0213045i
$665$	0.652090	−	12.4312i	0.0252870	−	0.482060i
$666$		0			0
$667$	−2.66525	+	1.53878i	−0.103199	+	0.0595819i
$668$	20.4260	−	21.1951i	0.790304	−	0.820063i
$669$		0			0
$670$	−5.03228	−	11.8385i	−0.194414	−	0.457359i
$671$	57.0916			2.20400
$672$		0			0
$673$	4.23008			0.163058			0.0815289	−	0.996671i	$-0.474020\pi$
$673$	4.23008			0.163058			0.0815289	+	0.996671i	$0.474020\pi$
$674$	7.43622	+	17.4937i	0.286433	+	0.673833i
$675$		0			0
$676$	1.48674	−	1.54273i	0.0571824	−	0.0593356i
$677$	−20.7962	+	12.0067i	−0.799262	+	0.461454i	−0.843213	−	0.537580i	$-0.819339\pi$
$677$	−20.7962	+	12.0067i	−0.799262	+	0.461454i	0.0439511	+	0.999034i	$0.486005\pi$
$678$		0			0
$679$	25.6365	−	13.0609i	0.983840	−	0.501232i
$680$	−1.74805	−	0.667932i	−0.0670345	−	0.0256140i
$681$		0			0
$682$	−29.9113	−	22.5158i	−1.14536	−	0.862174i
$683$	7.09951	+	4.09890i	0.271655	+	0.156840i	0.629640	−	0.776887i	$-0.283203\pi$
$683$	7.09951	+	4.09890i	0.271655	+	0.156840i	−0.357984	+	0.933728i	$0.616536\pi$
$684$		0			0
$685$			6.96771i			0.266222i
$686$	6.34567	+	25.4113i	0.242279	+	0.970207i
$687$		0			0
$688$	23.8812	−	0.882944i	0.910461	−	0.0336619i
$689$	13.3035	+	7.68079i	0.506824	+	0.292615i
$690$		0			0
$691$	17.9925	+	31.1638i	0.684465	+	1.18553i	0.973605	+	0.228242i	$0.0732976\pi$
$691$	17.9925	+	31.1638i	0.684465	+	1.18553i	−0.289139	+	0.957287i	$0.593369\pi$
$692$	−5.61504	+	22.6194i	−0.213452	+	0.859860i
$693$		0			0
$694$	3.88217	−	31.7522i	0.147365	−	1.20530i
$695$	−4.43015	+	2.55775i	−0.168045	+	0.0970209i
$696$		0			0
$697$	3.23686	−	5.60641i	0.122605	−	0.212358i
$698$	3.23008	−	1.37304i	0.122260	−	0.0519704i
$699$		0			0
$700$	15.7413	−	14.7077i	0.594964	−	0.555900i
$701$	12.9471			0.489003			0.244502	−	0.969649i	$-0.421376\pi$
$701$	12.9471			0.489003			0.244502	+	0.969649i	$0.421376\pi$
$702$		0			0
$703$	−6.67117	+	11.5548i	−0.251608	+	0.435798i
$704$	13.6834	+	41.6769i	0.515713	+	1.57076i
$705$		0			0
$706$	1.56428	−	12.7942i	0.0588723	−	0.481516i
$707$	2.00000	−	38.1272i	0.0752177	−	1.43392i
$708$		0			0
$709$	−6.65603	−	11.5286i	−0.249973	−	0.432965i	0.713545	−	0.700609i	$-0.247088\pi$
$709$	−6.65603	−	11.5286i	−0.249973	−	0.432965i	−0.963518	+	0.267644i	$0.913755\pi$
$710$	8.29183	−	11.0154i	0.311187	−	0.413399i
$711$		0			0
$712$	−1.54834	+	0.247673i	−0.0580265	+	0.00928192i
$713$			5.99109i			0.224368i
$714$		0			0
$715$			19.8221i			0.741303i
$716$	−4.98592	+	1.43522i	−0.186333	+	0.0536367i
$717$		0			0
$718$	−7.82802	−	5.89255i	−0.292139	−	0.219908i
$719$	23.7520	+	41.1397i	0.885800	+	1.53425i	0.844794	+	0.535091i	$0.179723\pi$
$719$	23.7520	+	41.1397i	0.885800	+	1.53425i	0.0410056	+	0.999159i	$0.486944\pi$
$720$		0			0
$721$	21.6519	−	33.3375i	0.806358	−	1.24155i
$722$	6.78803	+	0.829936i	0.252624	+	0.0308870i
$723$		0			0
$724$	−13.7291	−	13.2309i	−0.510239	−	0.491723i
$725$	−5.04858	+	8.74440i	−0.187500	+	0.324759i
$726$		0			0
$727$	24.3567			0.903340			0.451670	−	0.892185i	$-0.350828\pi$
$727$	24.3567			0.903340			0.451670	+	0.892185i	$0.350828\pi$
$728$	27.9130	−	2.97579i	1.03452	−	0.110290i
$729$		0			0
$730$	−3.55137	−	8.35460i	−0.131442	−	0.309218i
$731$	−2.05076	+	3.55203i	−0.0758503	+	0.131377i
$732$		0			0
$733$	3.35812	−	1.93881i	0.124035	−	0.0716117i	−0.436699	−	0.899608i	$-0.643852\pi$
$733$	3.35812	−	1.93881i	0.124035	−	0.0716117i	0.560734	+	0.827996i	$0.310519\pi$
$734$	5.38144	+	0.657960i	0.198633	+	0.0242857i
$735$		0			0
$736$	4.01153	−	5.76041i	0.147867	−	0.212331i
$737$	−25.8766	−	44.8196i	−0.953177	−	1.65095i
$738$		0			0
$739$	−7.46497	−	4.30990i	−0.274603	−	0.158542i	0.356374	−	0.934343i	$-0.384013\pi$
$739$	−7.46497	−	4.30990i	−0.274603	−	0.158542i	−0.630978	+	0.775801i	$0.717346\pi$
$740$	5.06185	−	1.45708i	0.186077	−	0.0535632i
$741$		0			0
$742$	5.24733	+	14.3961i	0.192636	+	0.528499i
$743$			6.12929i			0.224862i	0.993660	+	0.112431i	$0.0358637\pi$
$743$			6.12929i			0.224862i	−0.993660	+	0.112431i	$0.964136\pi$
$744$		0			0
$745$	−3.89057	−	2.24622i	−0.142539	−	0.0822952i
$746$	22.8194	−	30.3146i	0.835477	−	1.10990i
$747$		0			0
$748$	−7.30692	−	1.81387i	−0.267167	−	0.0663216i
$749$	26.8827	+	17.4597i	0.982273	+	0.637963i
$750$		0			0
$751$	30.7146	−	17.7331i	1.12079	−	0.647090i	0.179190	−	0.983815i	$-0.442652\pi$
$751$	30.7146	−	17.7331i	1.12079	−	0.647090i	0.941603	+	0.336725i	$0.109319\pi$
$752$	−12.2472	+	7.68783i	−0.446609	+	0.280346i
$753$		0			0
$754$	−12.1083	+	5.14699i	−0.440959	+	0.187442i
$755$	−11.7632			−0.428108
$756$		0			0
$757$	29.4204			1.06930			0.534651	−	0.845073i	$-0.320443\pi$
$757$	29.4204			1.06930			0.534651	+	0.845073i	$0.320443\pi$
$758$	9.02845	−	3.83781i	0.327928	−	0.139395i
$759$		0			0
$760$	−8.39073	−	10.3292i	−0.304364	−	0.374679i
$761$	−43.5568	+	25.1475i	−1.57893	+	0.911597i	−0.583923	+	0.811809i	$0.698483\pi$
$761$	−43.5568	+	25.1475i	−1.57893	+	0.911597i	−0.995009	+	0.0997877i	$0.968184\pi$
$762$		0			0
$763$	16.0410	+	0.841446i	0.580723	+	0.0304624i
$764$	4.01518	−	16.1746i	0.145264	−	0.585175i
$765$		0			0
$766$	−1.92014	+	2.55082i	−0.0693774	+	0.0921650i
$767$	41.2128	+	23.7942i	1.48811	+	0.859160i
$768$		0			0
$769$			20.2817i			0.731377i	0.930737	+	0.365689i	$0.119167\pi$
$769$			20.2817i			0.731377i	−0.930737	+	0.365689i	$0.880833\pi$
$770$	−12.7020	+	15.1520i	−0.457750	+	0.546039i
$771$		0			0
$772$	6.84507	+	23.7796i	0.246359	+	0.855847i
$773$	18.8149	+	10.8628i	0.676723	+	0.390706i	0.798619	−	0.601836i	$-0.205564\pi$
$773$	18.8149	+	10.8628i	0.676723	+	0.390706i	−0.121896	+	0.992543i	$0.538897\pi$
$774$		0			0
$775$	9.82806	+	17.0227i	0.353034	+	0.611473i
$776$	10.9787	−	28.7324i	0.394112	−	1.03143i
$777$		0			0
$778$	−42.9684	−	5.25351i	−1.54049	−	0.188347i
$779$	39.8698	−	23.0189i	1.42848	−	0.824736i
$780$		0			0
$781$	27.7349	−	48.0382i	0.992432	−	1.71894i
$782$	0.471311	+	1.10876i	0.0168540	+	0.0396492i
$783$		0			0
$784$	23.2436	+	15.6120i	0.830128	+	0.557573i
$785$	21.1369			0.754410
$786$		0			0
$787$	0.299328	−	0.518452i	0.0106699	−	0.0184808i	−0.860641	−	0.509212i	$-0.829937\pi$
$787$	0.299328	−	0.518452i	0.0106699	−	0.0184808i	0.871311	+	0.490731i	$0.163270\pi$
$788$	4.49225	−	4.66141i	0.160030	−	0.166056i
$789$		0			0
$790$	−1.91345	−	0.233947i	−0.0680774	−	0.00832346i
$791$	8.86288	+	17.3965i	0.315128	+	0.618547i
$792$		0			0
$793$	−19.5287	−	33.8247i	−0.693484	−	1.20115i
$794$	15.7041	+	11.8213i	0.557318	+	0.419521i
$795$		0			0
$796$	−10.6389	−	36.9594i	−0.377087	−	1.30999i
$797$		−	36.1789i		−	1.28152i	−0.767741	−	0.640760i	$-0.778619\pi$
$797$		−	36.1789i		−	1.28152i	0.767741	−	0.640760i	$-0.221381\pi$
$798$		0			0
$799$		−	2.48180i		−	0.0877998i
$800$	1.94847	−	22.9480i	0.0688890	−	0.811333i
$801$		0			0
$802$	−8.74046	+	11.6113i	−0.308636	+	0.410011i
$803$	−18.2616	−	31.6299i	−0.644436	−	1.11620i
$804$		0			0
$805$	3.15963	+	0.165741i	0.111362	+	0.00584162i
$806$	−3.10834	+	25.4231i	−0.109487	+	0.895490i
$807$		0			0
$808$	−25.7349	−	31.6803i	−0.905350	−	1.11451i
$809$	−15.0603	+	26.0852i	−0.529491	+	0.917106i	0.469917	+	0.882711i	$0.344284\pi$
$809$	−15.0603	+	26.0852i	−0.529491	+	0.917106i	−0.999408	+	0.0343953i	$0.989049\pi$
$810$		0			0
$811$	21.5947			0.758292			0.379146	−	0.925337i	$-0.376218\pi$
$811$	21.5947			0.758292			0.379146	+	0.925337i	$0.376218\pi$
$812$	−12.5538	−	3.82468i	−0.440552	−	0.134220i
$813$		0			0
$814$	19.5030	−	8.29032i	0.683579	−	0.290575i
$815$	1.93633	−	3.35382i	0.0678266	−	0.117479i
$816$		0			0
$817$	−25.2601	+	14.5839i	−0.883740	+	0.510228i
$818$	2.08769	−	17.0751i	0.0729942	−	0.597018i
$819$		0			0
$820$	−17.6397	−	4.37889i	−0.616006	−	0.152917i
$821$	25.1264	+	43.5202i	0.876918	+	1.51887i	0.854705	+	0.519114i	$0.173738\pi$
$821$	25.1264	+	43.5202i	0.876918	+	1.51887i	0.0222131	+	0.999753i	$0.492929\pi$
$822$		0			0
$823$	2.87338	+	1.65894i	0.100160	+	0.0578272i	0.549243	−	0.835663i	$-0.314916\pi$
$823$	2.87338	+	1.65894i	0.100160	+	0.0578272i	−0.449084	+	0.893490i	$0.648249\pi$
$824$	−6.71237	−	41.9628i	−0.233837	−	1.46184i
$825$		0			0
$826$	16.2556	+	44.5976i	0.565606	+	1.55175i
$827$			29.3948i			1.02216i	0.859534	+	0.511078i	$0.170754\pi$
$827$			29.3948i			1.02216i	−0.859534	+	0.511078i	$0.829246\pi$
$828$		0			0
$829$	28.2980	+	16.3379i	0.982830	+	0.567437i	0.903123	−	0.429381i	$-0.141268\pi$
$829$	28.2980	+	16.3379i	0.982830	+	0.567437i	0.0797067	+	0.996818i	$0.474602\pi$
$830$	0.592108	+	0.445710i	0.0205524	+	0.0154708i
$831$		0			0
$832$	20.0115	−	22.3629i	0.693775	−	0.775294i
$833$	−4.39036	+	1.95421i	−0.152117	+	0.0677094i
$834$		0			0
$835$	12.2834	−	7.09184i	0.425086	−	0.245423i
$836$	−38.5516	−	37.1526i	−1.33333	−	1.28495i
$837$		0			0
$838$	8.97611	+	21.1163i	0.310075	+	0.729451i
$839$	−8.66161			−0.299032			−0.149516	−	0.988759i	$-0.547772\pi$
$839$	−8.66161			−0.299032			−0.149516	+	0.988759i	$0.547772\pi$
$840$		0			0
$841$	−22.8491			−0.787899
$842$	5.30272	+	12.4747i	0.182744	+	0.429905i
$843$		0			0
$844$	−13.3157	−	12.8325i	−0.458346	−	0.441713i
$845$	0.894073	−	0.516193i	0.0307570	−	0.0177576i
$846$		0			0
$847$	−27.4753	+	42.3038i	−0.944062	+	1.45358i
$848$	14.4789	+	7.66057i	0.497209	+	0.263065i
$849$		0			0
$850$	3.15801	+	2.37720i	0.108319	+	0.0815372i
$851$	−2.93688	−	1.69561i	−0.100675	−	0.0581248i
$852$		0			0
$853$		−	7.17809i		−	0.245773i	−0.992421	−	0.122887i	$-0.960785\pi$
$853$		−	7.17809i		−	0.245773i	0.992421	−	0.122887i	$-0.0392151\pi$
$854$	6.74724	−	38.3696i	0.230886	−	1.31298i
$855$		0			0
$856$	33.8380	−	5.41274i	1.15656	−	0.185004i
$857$	−39.5334	−	22.8246i	−1.35044	−	0.779675i	−0.362126	−	0.932129i	$-0.617949\pi$
$857$	−39.5334	−	22.8246i	−1.35044	−	0.779675i	−0.988311	+	0.152454i	$0.951282\pi$
$858$		0			0
$859$	−6.77944	−	11.7423i	−0.231311	−	0.400643i	0.726883	−	0.686761i	$-0.240968\pi$
$859$	−6.77944	−	11.7423i	−0.231311	−	0.400643i	−0.958194	+	0.286118i	$0.907635\pi$
$860$	11.1759	+	2.77431i	0.381096	+	0.0946033i
$861$		0			0
$862$	0.0260696	−	0.213223i	0.000887934	−	0.00726240i
$863$	−36.0550	+	20.8163i	−1.22733	+	0.708597i	−0.966470	−	0.256781i	$-0.917338\pi$
$863$	−36.0550	+	20.8163i	−1.22733	+	0.708597i	−0.260856	+	0.965378i	$0.584005\pi$
$864$		0			0
$865$	−5.61504	+	9.72554i	−0.190917	+	0.330678i
$866$	12.3252	−	5.23920i	0.418828	−	0.178035i
$867$		0			0
$868$	−18.6672	+	17.4416i	−0.633607	+	0.592005i
$869$	−7.75555			−0.263089
$870$		0			0
$871$	−17.7026	+	30.6619i	−0.599831	+	1.03894i
$872$	13.3286	−	10.8273i	0.451364	−	0.366657i
$873$		0			0
$874$	−1.03979	+	8.50439i	−0.0351713	+	0.287665i
$875$	20.6089	−	10.4995i	0.696708	−	0.354948i
$876$		0			0
$877$	9.84239	+	17.0475i	0.332354	+	0.575654i	0.982973	−	0.183751i	$-0.0588239\pi$
$877$	9.84239	+	17.0475i	0.332354	+	0.575654i	−0.650619	+	0.759404i	$0.725491\pi$
$878$	−28.4706	+	37.8221i	−0.960837	+	1.27643i
$879$		0			0
$880$	0.780950	+	21.1225i	0.0263258	+	0.712040i
$881$		−	7.24606i		−	0.244126i	−0.992522	−	0.122063i	$-0.961049\pi$
$881$		−	7.24606i		−	0.244126i	0.992522	−	0.122063i	$-0.0389510\pi$
$882$		0			0
$883$		−	35.4533i		−	1.19310i	−0.802577	−	0.596549i	$-0.796538\pi$
$883$		−	35.4533i		−	1.19310i	0.802577	−	0.596549i	$-0.203462\pi$
$884$	1.42474	+	4.94953i	0.0479193	+	0.166471i
$885$		0			0
$886$	−29.5524	−	22.2456i	−0.992833	−	0.747357i
$887$	−8.98684	−	15.5657i	−0.301749	−	0.522644i	0.674784	−	0.738016i	$-0.264237\pi$
$887$	−8.98684	−	15.5657i	−0.301749	−	0.522644i	−0.976532	+	0.215372i	$0.930904\pi$
$888$		0			0
$889$	27.4479	−	13.9837i	0.920572	−	0.468999i
$890$	−0.749976	−	0.0916955i	−0.0251392	−	0.00307364i
$891$		0			0
$892$	−2.70053	+	2.80222i	−0.0904203	+	0.0938251i
$893$	8.82463	−	15.2847i	0.295305	−	0.511483i
$894$		0			0
$895$	−2.50005			−0.0835674
$896$	29.6270	−	4.27074i	0.989770	−	0.142675i
$897$		0			0
$898$	5.69389	+	13.3949i	0.190008	+	0.446993i
$899$	5.98700	−	10.3698i	0.199678	−	0.345852i
$900$		0			0
$901$	−2.43475	+	1.40570i	−0.0811132	+	0.0468307i
$902$	−72.5820	−	8.87421i	−2.41672	−	0.295479i
$903$		0			0
$904$	19.4972	+	7.44992i	0.648468	+	0.247781i
$905$	−4.59374	−	7.95658i	−0.152701	−	0.264486i
$906$		0			0
$907$	−7.60870	−	4.39289i	−0.252643	−	0.145863i	0.368331	−	0.929695i	$-0.379929\pi$
$907$	−7.60870	−	4.39289i	−0.252643	−	0.145863i	−0.620974	+	0.783831i	$0.713263\pi$
$908$	−4.78297	−	16.6159i	−0.158728	−	0.551419i
$909$		0			0
$910$	13.3218	+	2.34262i	0.441615	+	0.0776573i
$911$			21.5478i			0.713911i	0.934121	+	0.356955i	$0.116185\pi$
$911$			21.5478i			0.713911i	−0.934121	+	0.356955i	$0.883815\pi$
$912$		0			0
$913$	2.58220	+	1.49083i	0.0854582	+	0.0493393i
$914$	−10.1479	+	13.4811i	−0.335663	+	0.445915i
$915$		0			0
$916$	−8.08983	+	32.5887i	−0.267295	+	1.07676i
$917$	−13.3467	+	20.5500i	−0.440747	+	0.678619i
$918$		0			0
$919$	−27.5939	+	15.9314i	−0.910240	+	0.525527i	−0.880508	−	0.474031i	$-0.842799\pi$
$919$	−27.5939	+	15.9314i	−0.910240	+	0.525527i	−0.0297316	+	0.999558i	$0.509465\pi$
$920$	2.62537	−	2.13267i	0.0865558	−	0.0703120i
$921$		0			0
$922$	39.0574	−	16.6025i	1.28629	−	0.546774i
$923$	−37.9479			−1.24907
$924$		0			0
$925$	−11.1262			−0.365828
$926$	−17.2756	+	7.34352i	−0.567713	+	0.241323i
$927$		0			0
$928$	−12.6999	+	5.96171i	−0.416895	+	0.195703i
$929$	−44.1750	+	25.5044i	−1.44933	+	0.836773i	−0.998442	−	0.0558058i	$-0.982227\pi$
$929$	−44.1750	+	25.5044i	−1.44933	+	0.836773i	−0.450892	+	0.892579i	$0.648894\pi$
$930$		0			0
$931$	−33.9876	−	3.57555i	−1.11390	−	0.117184i
$932$	2.03148	+	0.504294i	0.0665432	+	0.0165187i
$933$		0			0
$934$	−25.2172	+	33.5000i	−0.825131	+	1.09615i
$935$	−3.14171	−	1.81387i	−0.102745	−	0.0593199i
$936$		0			0
$937$			2.65742i			0.0868141i	0.999057	+	0.0434071i	$0.0138212\pi$
$937$			2.65742i			0.0868141i	−0.999057	+	0.0434071i	$0.986179\pi$
$938$	−33.1801	+	12.0940i	−1.08337	+	0.394884i
$939$		0			0
$940$	−6.69582	+	1.92742i	−0.218394	+	0.0628656i
$941$	−26.2920	−	15.1797i	−0.857096	−	0.494844i	0.00594304	−	0.999982i	$-0.498108\pi$
$941$	−26.2920	−	15.1797i	−0.857096	−	0.494844i	−0.863039	+	0.505138i	$0.831442\pi$
$942$		0			0
$943$	5.85070	+	10.1337i	0.190525	+	0.329999i
$944$	44.8541	+	23.7316i	1.45988	+	0.772397i
$945$		0			0
$946$	45.9855	+	5.62240i	1.49512	+	0.182800i
$947$	−37.6505	+	21.7375i	−1.22348	+	0.706374i	−0.965657	−	0.259819i	$-0.916337\pi$
$947$	−37.6505	+	21.7375i	−1.22348	+	0.706374i	−0.257818	+	0.966193i	$0.583004\pi$
$948$		0			0
$949$	−12.4931	+	21.6386i	−0.405542	+	0.702419i
$950$	10.9966	+	25.8695i	0.356777	+	0.839319i
$951$		0			0
$952$	−2.08260	+	4.69640i	−0.0674975	+	0.152211i
$953$	53.8683			1.74497			0.872483	−	0.488645i	$-0.162509\pi$
$953$	53.8683			1.74497			0.872483	+	0.488645i	$0.162509\pi$
$954$		0			0
$955$	4.01518	−	6.95449i	0.129928	−	0.225042i
$956$	−27.7190	−	26.7131i	−0.896496	−	0.863963i
$957$		0			0
$958$	−16.1930	−	1.97984i	−0.523173	−	0.0639656i
$959$	19.1027	+	1.00205i	0.616860	+	0.0323580i
$960$		0			0
$961$	3.84512	+	6.65995i	0.124036	+	0.214837i
$962$	−11.5829	−	8.71903i	−0.373447	−	0.281113i
$963$		0			0
$964$	5.29862	−	1.52523i	0.170657	−	0.0491244i
$965$			11.9236i			0.383835i
$966$		0			0
$967$		−	44.9529i		−	1.44559i	−0.691064	−	0.722794i	$-0.742858\pi$
$967$		−	44.9529i		−	1.44559i	0.691064	−	0.722794i	$-0.257142\pi$
$968$	8.51771	+	53.2490i	0.273770	+	1.71149i
$969$		0			0
$970$	8.91350	−	11.8412i	0.286195	−	0.380199i
$971$	−0.641758	−	1.11156i	−0.0205950	−	0.0356716i	0.855544	−	0.517730i	$-0.173223\pi$
$971$	−0.641758	−	1.11156i	−0.0205950	−	0.0356716i	−0.876139	+	0.482058i	$0.839889\pi$
$972$		0			0
$973$	6.37523	+	12.5136i	0.204381	+	0.401167i
$974$	−1.67428	+	13.6939i	−0.0536474	+	0.438781i
$975$		0			0
$976$	−22.1425	−	35.2744i	−0.708765	−	1.12911i
$977$	9.67678	−	16.7607i	0.309588	−	0.536222i	−0.668684	−	0.743546i	$-0.733142\pi$
$977$	9.67678	−	16.7607i	0.309588	−	0.536222i	0.978272	+	0.207325i	$0.0664756\pi$
$978$		0			0
$979$	−3.03979			−0.0971520
$980$	8.68205	+	10.3274i	0.277338	+	0.329896i
$981$		0			0
$982$	−52.6767	+	22.3918i	−1.68098	+	0.714550i
$983$	4.21637	−	7.30296i	0.134481	−	0.232928i	−0.790918	−	0.611922i	$-0.790397\pi$
$983$	4.21637	−	7.30296i	0.134481	−	0.232928i	0.925399	+	0.378994i	$0.123730\pi$
$984$		0			0
$985$	2.70148	−	1.55970i	0.0860763	−	0.0496962i
$986$	0.292225	−	2.39011i	0.00930635	−	0.0761165i
$987$		0			0
$988$	−8.82463	+	35.5488i	−0.280749	+	1.13096i
$989$	−3.70680	−	6.42036i	−0.117869	−	0.204156i
$990$		0			0
$991$	21.1967	+	12.2379i	0.673334	+	0.388750i	0.797339	−	0.603532i	$-0.206240\pi$
$991$	21.1967	+	12.2379i	0.673334	+	0.388750i	−0.124005	+	0.992282i	$0.539574\pi$
$992$	−2.31065	+	27.2135i	−0.0733633	+	0.864029i
$993$		0			0
$994$	−29.0073	−	24.3171i	−0.920057	−	0.771292i
$995$		−	18.5322i		−	0.587511i
$996$		0			0
$997$	−29.0273	−	16.7589i	−0.919304	−	0.530761i	−0.0358914	−	0.999356i	$-0.511427\pi$
$997$	−29.0273	−	16.7589i	−0.919304	−	0.530761i	−0.883413	+	0.468595i	$0.844760\pi$
$998$	36.1168	+	27.1870i	1.14326	+	0.860588i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bf.f.199.2		8
3.2	odd	2		84.2.o.b.31.3	yes	8
4.3	odd	2		252.2.bf.g.199.2		8
7.3	odd	6		1764.2.b.i.1567.8		8
7.4	even	3		1764.2.b.j.1567.8		8
7.5	odd	6		252.2.bf.g.19.2		8
12.11	even	2		84.2.o.a.31.3	yes	8
21.2	odd	6		588.2.o.d.19.3		8
21.5	even	6		84.2.o.a.19.3	✓	8
21.11	odd	6		588.2.b.a.391.1		8
21.17	even	6		588.2.b.b.391.1		8
21.20	even	2		588.2.o.b.31.3		8
24.5	odd	2		1344.2.bl.i.703.2		8
24.11	even	2		1344.2.bl.j.703.2		8
28.3	even	6		1764.2.b.j.1567.7		8
28.11	odd	6		1764.2.b.i.1567.7		8
28.19	even	6	inner	252.2.bf.f.19.2		8
84.11	even	6		588.2.b.b.391.2		8
84.23	even	6		588.2.o.b.19.3		8
84.47	odd	6		84.2.o.b.19.3	yes	8
84.59	odd	6		588.2.b.a.391.2		8
84.83	odd	2		588.2.o.d.31.3		8
168.5	even	6		1344.2.bl.j.1279.2		8
168.131	odd	6		1344.2.bl.i.1279.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.o.a.19.3	✓	8	21.5	even	6
84.2.o.a.31.3	yes	8	12.11	even	2
84.2.o.b.19.3	yes	8	84.47	odd	6
84.2.o.b.31.3	yes	8	3.2	odd	2
252.2.bf.f.19.2		8	28.19	even	6	inner
252.2.bf.f.199.2		8	1.1	even	1	trivial
252.2.bf.g.19.2		8	7.5	odd	6
252.2.bf.g.199.2		8	4.3	odd	2
588.2.b.a.391.1		8	21.11	odd	6
588.2.b.a.391.2		8	84.59	odd	6
588.2.b.b.391.1		8	21.17	even	6
588.2.b.b.391.2		8	84.11	even	6
588.2.o.b.19.3		8	84.23	even	6
588.2.o.b.31.3		8	21.20	even	2
588.2.o.d.19.3		8	21.2	odd	6
588.2.o.d.31.3		8	84.83	odd	2
1344.2.bl.i.703.2		8	24.5	odd	2
1344.2.bl.i.1279.2		8	168.131	odd	6
1344.2.bl.j.703.2		8	24.11	even	2
1344.2.bl.j.1279.2		8	168.5	even	6
1764.2.b.i.1567.7		8	28.11	odd	6
1764.2.b.i.1567.8		8	7.3	odd	6
1764.2.b.j.1567.7		8	28.3	even	6
1764.2.b.j.1567.8		8	7.4	even	3

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.553244 - 1.30151i) q^{2} +(-1.38784 + 1.44010i) q^{4} +(-0.834598 + 0.481855i) q^{5} +(1.20103 + 2.35744i) q^{7} +(2.64212 + 1.00956i) q^{8} +O(q^{10})\)	\(q+(-0.553244 - 1.30151i) q^{2} +(-1.38784 + 1.44010i) q^{4} +(-0.834598 + 0.481855i) q^{5} +(1.20103 + 2.35744i) q^{7} +(2.64212 + 1.00956i) q^{8} +(1.08887 + 0.819652i) q^{10} +(4.74861 + 2.74161i) q^{11} -3.75117i q^{13} +(2.40376 - 2.86739i) q^{14} +(-0.147789 - 3.99727i) q^{16} +(0.594545 + 0.343260i) q^{17} +(2.44109 + 4.22809i) q^{19} +(0.464369 - 1.87065i) q^{20} +(0.941086 - 7.69713i) q^{22} +(-1.07465 + 0.620450i) q^{23} +(-2.03563 + 3.52582i) q^{25} +(-4.88217 + 2.07531i) q^{26} +(-5.06180 - 1.54214i) q^{28} +2.48011 q^{29} +(2.41401 - 4.18119i) q^{31} +(-5.12071 + 2.40381i) q^{32} +(0.117828 - 0.963711i) q^{34} +(-2.13832 - 1.38879i) q^{35} +(1.36643 + 2.36673i) q^{37} +(4.15237 - 5.51625i) q^{38} +(-2.69157 + 0.430544i) q^{40} -9.42976i q^{41} +5.97437i q^{43} +(-10.5385 + 3.03356i) q^{44} +(1.40207 + 1.05541i) q^{46} +(-1.80752 - 3.13072i) q^{47} +(-4.11504 + 5.66272i) q^{49} +(5.71508 + 0.698752i) q^{50} +(5.40207 + 5.20603i) q^{52} +(-2.04757 + 3.54650i) q^{53} -5.28424 q^{55} +(0.793298 + 7.44115i) q^{56} +(-1.37210 - 3.22788i) q^{58} +(-6.34315 + 10.9867i) q^{59} +(9.01711 - 5.20603i) q^{61} +(-6.77738 - 0.828634i) q^{62} +(5.96158 + 5.33475i) q^{64} +(1.80752 + 3.13072i) q^{65} +(-8.17396 - 4.71924i) q^{67} +(-1.31946 + 0.379814i) q^{68} +(-0.624505 + 3.55138i) q^{70} -10.1163i q^{71} +(-5.76850 - 3.33044i) q^{73} +(2.32435 - 3.08781i) q^{74} +(-9.47672 - 2.35250i) q^{76} +(-0.759946 + 14.4873i) q^{77} +(-1.22492 + 0.707208i) q^{79} +(2.04945 + 3.26490i) q^{80} +(-12.2729 + 5.21696i) q^{82} +0.543780 q^{83} -0.661608 q^{85} +(7.77568 - 3.30528i) q^{86} +(9.77857 + 12.0377i) q^{88} +(-0.480107 + 0.277190i) q^{89} +(8.84315 - 4.50528i) q^{91} +(0.597935 - 2.40870i) q^{92} +(-3.07465 + 4.08455i) q^{94} +(-4.07465 - 2.35250i) q^{95} -10.8747i q^{97} +(9.64670 + 2.22289i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - q^{4} - 2 q^{7} - 4 q^{8}+O(q^{10}) \) 8 * q - q^2 - q^4 - 2 * q^7 - 4 * q^8	\( 8 q - q^{2} - q^{4} - 2 q^{7} - 4 q^{8} - 13 q^{10} + 6 q^{11} + 10 q^{14} + 7 q^{16} + 6 q^{19} + 22 q^{20} - 6 q^{22} + 2 q^{25} - 12 q^{26} - 7 q^{28} + 16 q^{29} - 6 q^{31} - 21 q^{32} + 28 q^{34} - 12 q^{35} + 6 q^{37} - 8 q^{38} - 13 q^{40} - 19 q^{44} - 12 q^{46} + 4 q^{47} + 4 q^{49} - 2 q^{50} + 20 q^{52} + 4 q^{53} + 8 q^{55} + q^{56} - 23 q^{58} - 14 q^{59} + 12 q^{61} - 48 q^{62} + 2 q^{64} - 4 q^{65} - 42 q^{67} + 10 q^{68} + 35 q^{70} - 18 q^{73} + 28 q^{74} - 44 q^{76} - 8 q^{77} + 6 q^{79} + 33 q^{80} - 14 q^{82} + 4 q^{83} - 32 q^{85} + 42 q^{86} + 11 q^{88} + 34 q^{91} + 28 q^{92} - 16 q^{94} - 24 q^{95} + 19 q^{98}+O(q^{100}) \) 8 * q - q^2 - q^4 - 2 * q^7 - 4 * q^8 - 13 * q^10 + 6 * q^11 + 10 * q^14 + 7 * q^16 + 6 * q^19 + 22 * q^20 - 6 * q^22 + 2 * q^25 - 12 * q^26 - 7 * q^28 + 16 * q^29 - 6 * q^31 - 21 * q^32 + 28 * q^34 - 12 * q^35 + 6 * q^37 - 8 * q^38 - 13 * q^40 - 19 * q^44 - 12 * q^46 + 4 * q^47 + 4 * q^49 - 2 * q^50 + 20 * q^52 + 4 * q^53 + 8 * q^55 + q^56 - 23 * q^58 - 14 * q^59 + 12 * q^61 - 48 * q^62 + 2 * q^64 - 4 * q^65 - 42 * q^67 + 10 * q^68 + 35 * q^70 - 18 * q^73 + 28 * q^74 - 44 * q^76 - 8 * q^77 + 6 * q^79 + 33 * q^80 - 14 * q^82 + 4 * q^83 - 32 * q^85 + 42 * q^86 + 11 * q^88 + 34 * q^91 + 28 * q^92 - 16 * q^94 - 24 * q^95 + 19 * q^98

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