LMFDB - Embedded newform 252.2.bf.g.19.2

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			19.2
Root			$1.40376 + 0.171630i$ of defining polynomial
Character	$\chi$	$=$	252.19
Dual form			252.2.bf.g.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.850516 + 1.12988i) q^{2} +(-0.553244 - 1.92196i) q^{4} +(-0.834598 - 0.481855i) q^{5} +(-1.20103 + 2.35744i) q^{7} +(2.64212 + 1.00956i) q^{8} +O(q^{10})$	\(q+(-0.850516 + 1.12988i) q^{2} +(-0.553244 - 1.92196i) q^{4} +(-0.834598 - 0.481855i) q^{5} +(-1.20103 + 2.35744i) q^{7} +(2.64212 + 1.00956i) q^{8} +(1.25428 - 0.533167i) q^{10} +(-4.74861 + 2.74161i) q^{11} +3.75117i q^{13} +(-1.64212 - 3.36206i) q^{14} +(-3.38784 + 2.12662i) q^{16} +(0.594545 - 0.343260i) q^{17} +(-2.44109 + 4.22809i) q^{19} +(-0.464369 + 1.87065i) q^{20} +(0.941086 - 7.69713i) q^{22} +(1.07465 + 0.620450i) q^{23} +(-2.03563 - 3.52582i) q^{25} +(-4.23836 - 3.19043i) q^{26} +(5.19536 + 1.00409i) q^{28} +2.48011 q^{29} +(-2.41401 - 4.18119i) q^{31} +(0.478592 - 5.63657i) q^{32} +(-0.117828 + 0.963711i) q^{34} +(2.13832 - 1.38879i) q^{35} +(1.36643 - 2.36673i) q^{37} +(-2.70103 - 6.35418i) q^{38} +(-1.71865 - 2.11569i) q^{40} +9.42976i q^{41} +5.97437i q^{43} +(7.89640 + 7.60984i) q^{44} +(-1.61504 + 0.686521i) q^{46} +(1.80752 - 3.13072i) q^{47} +(-4.11504 - 5.66272i) q^{49} +(5.71508 + 0.698752i) q^{50} +(7.20959 - 2.07531i) q^{52} +(-2.04757 - 3.54650i) q^{53} +5.28424 q^{55} +(-5.55324 + 5.01612i) q^{56} +(-2.10937 + 2.80222i) q^{58} +(6.34315 + 10.9867i) q^{59} +(9.01711 + 5.20603i) q^{61} +(6.77738 + 0.828634i) q^{62} +(5.96158 + 5.33475i) q^{64} +(1.80752 - 3.13072i) q^{65} +(8.17396 - 4.71924i) q^{67} +(-0.988660 - 0.952783i) q^{68} +(-0.249518 + 3.59723i) q^{70} -10.1163i q^{71} +(-5.76850 + 3.33044i) q^{73} +(1.51194 + 3.55685i) q^{74} +(9.47672 + 2.35250i) q^{76} +(-0.759946 - 14.4873i) q^{77} +(1.22492 + 0.707208i) q^{79} +(3.85221 - 0.142425i) q^{80} +(-10.6545 - 8.02016i) q^{82} -0.543780 q^{83} -0.661608 q^{85} +(-6.75030 - 5.08130i) q^{86} +(-15.3142 + 2.44966i) q^{88} +(-0.480107 - 0.277190i) q^{89} +(-8.84315 - 4.50528i) q^{91} +(0.597935 - 2.40870i) q^{92} +(2.00000 + 4.70500i) q^{94} +(4.07465 - 2.35250i) q^{95} +10.8747i q^{97} +(9.89809 + 0.166748i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 5 q^{10} - 6 q^{11} + 12 q^{14} - 17 q^{16} - 6 q^{19} - 22 q^{20} - 6 q^{22} + 2 q^{25} - 18 q^{26} + 13 q^{28} + 16 q^{29} + 6 q^{31} + 9 q^{32} - 28 q^{34} + 12 q^{35} + 6 q^{37} - 10 q^{38} - 17 q^{40} + 23 q^{44} + 24 q^{46} - 4 q^{47} + 4 q^{49} - 2 q^{50} + 16 q^{52} + 4 q^{53} - 8 q^{55} - 41 q^{56} + 37 q^{58} + 14 q^{59} + 12 q^{61} + 48 q^{62} + 2 q^{64} - 4 q^{65} + 42 q^{67} + 26 q^{68} + 3 q^{70} - 18 q^{73} + 10 q^{74} + 44 q^{76} - 8 q^{77} - 6 q^{79} + 39 q^{80} - 10 q^{82} - 4 q^{83} - 32 q^{85} - 36 q^{86} - 37 q^{88} - 34 q^{91} + 28 q^{92} + 16 q^{94} + 24 q^{95} + 53 q^{98}+O(q^{100}) $ 8 * q - q^2 - q^4 + 2 * q^7 - 4 * q^8 - 5 * q^10 - 6 * q^11 + 12 * q^14 - 17 * q^16 - 6 * q^19 - 22 * q^20 - 6 * q^22 + 2 * q^25 - 18 * q^26 + 13 * q^28 + 16 * q^29 + 6 * q^31 + 9 * q^32 - 28 * q^34 + 12 * q^35 + 6 * q^37 - 10 * q^38 - 17 * q^40 + 23 * q^44 + 24 * q^46 - 4 * q^47 + 4 * q^49 - 2 * q^50 + 16 * q^52 + 4 * q^53 - 8 * q^55 - 41 * q^56 + 37 * q^58 + 14 * q^59 + 12 * q^61 + 48 * q^62 + 2 * q^64 - 4 * q^65 + 42 * q^67 + 26 * q^68 + 3 * q^70 - 18 * q^73 + 10 * q^74 + 44 * q^76 - 8 * q^77 - 6 * q^79 + 39 * q^80 - 10 * q^82 - 4 * q^83 - 32 * q^85 - 36 * q^86 - 37 * q^88 - 34 * q^91 + 28 * q^92 + 16 * q^94 + 24 * q^95 + 53 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.850516	+	1.12988i	−0.601406	+	0.798944i
$2$	−0.850516	+	1.12988i	−0.601406	+	0.798944i
$3$		0			0
$3$		0			0
$4$	−0.553244	−	1.92196i	−0.276622	−	0.960979i
$5$	−0.834598	−	0.481855i	−0.373244	−	0.215492i	0.301631	−	0.953425i	$-0.402469\pi$
$5$	−0.834598	−	0.481855i	−0.373244	−	0.215492i	−0.674875	+	0.737932i	$0.735802\pi$
$6$		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
$10$	1.25428	−	0.533167i	0.396637	−	0.168602i
$11$	−4.74861	+	2.74161i	−1.43176	+	0.826626i	−0.997255	−	0.0740437i	$-0.976410\pi$
$11$	−4.74861	+	2.74161i	−1.43176	+	0.826626i	−0.434504	+	0.900670i	$0.643076\pi$
$12$		0			0
$13$			3.75117i			1.04039i	0.854048	+	0.520193i	$0.174140\pi$
$13$			3.75117i			1.04039i	−0.854048	+	0.520193i	$0.825860\pi$
$14$	−1.64212	−	3.36206i	−0.438875	−	0.898548i
$15$		0			0
$16$	−3.38784	+	2.12662i	−0.846961	+	0.531656i
$17$	0.594545	−	0.343260i	0.144198	−	0.0832529i	−0.426165	−	0.904645i	$-0.640136\pi$
$17$	0.594545	−	0.343260i	0.144198	−	0.0832529i	0.570363	+	0.821393i	$0.306802\pi$
$18$		0			0
$19$	−2.44109	+	4.22809i	−0.560024	+	0.969989i	0.437470	+	0.899233i	$0.355875\pi$
$19$	−2.44109	+	4.22809i	−0.560024	+	0.969989i	−0.997494	+	0.0707563i	$0.977459\pi$
$20$	−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	$-0.292037\pi$
$23$	1.07465	+	0.620450i	0.224080	+	0.129373i	−0.383758	+	0.923434i	$0.625370\pi$
$24$		0			0
$25$	−2.03563	−	3.52582i	−0.407126	−	0.705163i
$26$	−4.23836	−	3.19043i	−0.831210	−	0.625695i
$27$		0			0
$28$	5.19536	+	1.00409i	0.981831	+	0.189756i
$29$	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	$-0.309413\pi$
$31$	−2.41401	−	4.18119i	−0.433569	−	0.750963i	−0.997178	+	0.0750787i	$0.976079\pi$
$32$	0.478592	−	5.63657i	0.0846040	−	0.996415i
$33$		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	−0.731571	−	0.681765i	$-0.761213\pi$
$37$	1.36643	−	2.36673i	0.224640	−	0.389089i	0.956212	+	0.292677i	$0.0945459\pi$
$38$	−2.70103	−	6.35418i	−0.438165	−	1.03078i
$39$		0			0
$40$	−1.71865	−	2.11569i	−0.271742	−	0.334521i
$41$			9.42976i			1.47268i	0.676611	+	0.736340i	$0.263448\pi$
$41$			9.42976i			1.47268i	−0.676611	+	0.736340i	$0.736552\pi$
$42$		0			0
$43$			5.97437i			0.911083i	0.890215	+	0.455541i	$0.150554\pi$
$43$			5.97437i			0.911083i	−0.890215	+	0.455541i	$0.849446\pi$
$44$	7.89640	+	7.60984i	1.19043	+	1.14723i
$45$		0			0
$46$	−1.61504	+	0.686521i	−0.238125	+	0.101222i
$47$	1.80752	−	3.13072i	0.263654	−	0.456662i	−0.703556	−	0.710640i	$-0.748406\pi$
$47$	1.80752	−	3.13072i	0.263654	−	0.456662i	0.967210	+	0.253978i	$0.0817390\pi$
$48$		0			0
$49$	−4.11504	−	5.66272i	−0.587863	−	0.808960i
$50$	5.71508	+	0.698752i	0.808234	+	0.0988184i
$51$		0			0
$52$	7.20959	−	2.07531i	0.999790	−	0.287794i
$53$	−2.04757	−	3.54650i	−0.281256	−	0.487150i	0.690438	−	0.723391i	$-0.257418\pi$
$53$	−2.04757	−	3.54650i	−0.281256	−	0.487150i	−0.971694	+	0.236242i	$0.924084\pi$
$54$		0			0
$55$	5.28424			0.712526
$56$	−5.55324	+	5.01612i	−0.742083	+	0.670308i
$57$		0			0
$58$	−2.10937	+	2.80222i	−0.276974	+	0.367949i
$59$	6.34315	+	10.9867i	0.825808	+	1.43034i	0.901300	+	0.433195i	$0.142614\pi$
$59$	6.34315	+	10.9867i	0.825808	+	1.43034i	−0.0754923	+	0.997146i	$0.524053\pi$
$60$		0			0
$61$	9.01711	+	5.20603i	1.15452	+	0.666564i	0.949985	−	0.312295i	$-0.101098\pi$
$61$	9.01711	+	5.20603i	1.15452	+	0.666564i	0.204537	+	0.978859i	$0.434431\pi$
$62$	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	$-0.471067\pi$
$67$	8.17396	−	4.71924i	0.998608	−	0.576546i	0.907836	+	0.419325i	$0.137733\pi$
$68$	−0.988660	−	0.952783i	−0.119893	−	0.115542i
$69$		0			0
$70$	−0.249518	+	3.59723i	−0.0298231	+	0.429952i
$71$		−	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	−0.798026	−	0.602623i	$-0.794122\pi$
$73$	−5.76850	+	3.33044i	−0.675152	+	0.389799i	0.122874	+	0.992422i	$0.460789\pi$
$74$	1.51194	+	3.55685i	0.175760	+	0.413475i
$75$		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	$-0.307980\pi$
$79$	1.22492	+	0.707208i	0.137814	+	0.0795671i	−0.429508	+	0.903063i	$0.641313\pi$
$80$	3.85221	−	0.142425i	0.430690	−	0.0159237i
$81$		0			0
$82$	−10.6545	−	8.02016i	−1.17659	−	0.885679i
$83$	−0.543780			−0.0596876			−0.0298438	−	0.999555i	$-0.509501\pi$
$83$	−0.543780			−0.0596876			−0.0298438	+	0.999555i	$0.509501\pi$
$84$		0			0
$85$	−0.661608			−0.0717614
$86$	−6.75030	−	5.08130i	−0.727904	−	0.547930i
$87$		0			0
$88$	−15.3142	+	2.44966i	−1.63250	+	0.261135i
$89$	−0.480107	−	0.277190i	−0.0508912	−	0.0293821i	0.474339	−	0.880343i	$-0.342687\pi$
$89$	−0.480107	−	0.277190i	−0.0508912	−	0.0293821i	−0.525230	+	0.850960i	$0.676021\pi$
$90$		0			0
$91$	−8.84315	−	4.50528i	−0.927014	−	0.472281i
$92$	0.597935	−	2.40870i	0.0623390	−	0.251124i
$93$		0			0
$94$	2.00000	+	4.70500i	0.206284	+	0.485284i
$95$	4.07465	−	2.35250i	0.418050	−	0.241362i
$96$		0			0
$97$			10.8747i			1.10416i	0.833790	+	0.552081i	$0.186166\pi$
$97$			10.8747i			1.10416i	−0.833790	+	0.552081i	$0.813834\pi$
$98$	9.89809	+	0.166748i	0.999858	+	0.0168441i
$99$		0			0
$100$	−5.65027	+	5.86303i	−0.565027	+	0.586303i
$101$	−12.4972	+	7.21527i	−1.24352	+	0.717946i	−0.969809	−	0.243866i	$-0.921584\pi$
$101$	−12.4972	+	7.21527i	−1.24352	+	0.717946i	−0.273710	+	0.961812i	$0.588251\pi$
$102$		0			0
$103$	7.51235	−	13.0118i	0.740214	−	1.28209i	−0.212184	−	0.977230i	$-0.568058\pi$
$103$	7.51235	−	13.0118i	0.740214	−	1.28209i	0.952398	−	0.304858i	$-0.0986090\pi$
$104$	−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	$-0.532487\pi$
$107$	−10.4925	−	6.05782i	−1.01434	−	0.585632i	−0.912461	+	0.409165i	$0.865820\pi$
$108$		0			0
$109$	3.03563	+	5.25787i	0.290761	+	0.503612i	0.973990	−	0.226592i	$-0.0727583\pi$
$109$	3.03563	+	5.25787i	0.290761	+	0.503612i	−0.683229	+	0.730204i	$0.739425\pi$
$110$	−4.49433	+	5.97054i	−0.428518	+	0.569268i
$111$		0			0
$112$	−0.944476	−	10.5408i	−0.0892446	−	0.996010i
$113$	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
$116$	−1.37210	−	4.76666i	−0.127397	−	0.442573i
$117$		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
$122$	−13.5514	+	5.76041i	−1.22688	+	0.521523i
$123$		0			0
$124$	−6.70053	+	6.95284i	−0.601725	+	0.624383i
$125$			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	$-0.172794\pi$
$128$	−11.0980	+	2.19857i	−0.980937	+	0.194328i
$129$		0			0
$130$	2.00000	+	4.70500i	0.175412	+	0.412656i
$131$	−4.63078	+	8.02074i	−0.404593	+	0.700776i	−0.994274	−	0.106861i	$-0.965920\pi$
$131$	−4.63078	+	8.02074i	−0.404593	+	0.700776i	0.589681	+	0.807636i	$0.299253\pi$
$132$		0			0
$133$	−7.03563	−	10.8328i	−0.610067	−	0.939321i
$134$	−1.61993	+	13.2494i	−0.139940	+	1.14457i
$135$		0			0
$136$	1.91740	−	0.306707i	0.164416	−	0.0262999i
$137$	3.61504	+	6.26144i	0.308854	+	0.534951i	0.978112	−	0.208080i	$-0.0667213\pi$
$137$	3.61504	+	6.26144i	0.308854	+	0.534951i	−0.669258	+	0.743030i	$0.733388\pi$
$138$		0			0
$139$	−5.30812			−0.450229			−0.225115	−	0.974332i	$-0.572276\pi$
$139$	−5.30812			−0.450229			−0.225115	+	0.974332i	$0.572276\pi$
$140$	−3.85221	−	3.34143i	−0.325571	−	0.282402i
$141$		0			0
$142$	11.4302	+	8.60406i	0.959197	+	0.722037i
$143$	−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	−0.754617	−	0.656165i	$-0.772178\pi$
$149$	2.33080	−	4.03707i	0.190947	−	0.330730i	0.945564	+	0.325435i	$0.105511\pi$
$150$		0			0
$151$	−10.5709	+	6.10309i	−0.860244	+	0.496662i	−0.864094	−	0.503330i	$-0.832108\pi$
$151$	−10.5709	+	6.10309i	−0.860244	+	0.496662i	0.00384988	+	0.999993i	$0.498775\pi$
$152$	−10.7181	+	8.70668i	−0.869356	+	0.706205i
$153$		0			0
$154$	17.0152	+	11.4631i	1.37113	+	0.923719i
$155$			4.65281i			0.373723i
$156$		0			0
$157$	−18.9944	+	10.9664i	−1.51592	+	0.875217i	−0.516095	+	0.856531i	$0.672615\pi$
$157$	−18.9944	+	10.9664i	−1.51592	+	0.875217i	−0.999825	+	0.0186856i	$0.994052\pi$
$158$	−1.84087	+	0.782517i	−0.146452	+	0.0622537i
$159$		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	$-0.283030\pi$
$163$	3.48011	+	2.00924i	0.272583	+	0.157376i	−0.357478	+	0.933922i	$0.616363\pi$
$164$	18.1236	−	5.21696i	1.41521	−	0.407376i
$165$		0			0
$166$	0.462494	−	0.614404i	0.0358965	−	0.0476870i
$167$	14.7178			1.13890			0.569448	−	0.822027i	$-0.307157\pi$
$167$	14.7178			1.13890			0.569448	+	0.822027i	$0.307157\pi$
$168$		0			0
$169$	−1.07126			−0.0824047
$170$	0.562708	−	0.747535i	0.0431577	−	0.0573333i
$171$		0			0
$172$	11.4825	−	3.30528i	0.875531	−	0.252026i
$173$	10.0918	+	5.82648i	0.767262	+	0.442979i	0.831897	−	0.554930i	$-0.187255\pi$
$173$	10.0918	+	5.82648i	0.767262	+	0.442979i	−0.0646349	+	0.997909i	$0.520588\pi$
$174$		0			0
$175$	10.7568	−	0.564256i	0.813134	−	0.0426538i
$176$	10.2572	−	19.3866i	0.773163	−	1.46132i
$177$		0			0
$178$	0.721529	−	0.306707i	0.0540809	−	0.0229887i
$179$	−2.24663	+	1.29709i	−0.167921	+	0.0969494i	−0.581605	−	0.813471i	$-0.697575\pi$
$179$	−2.24663	+	1.29709i	−0.167921	+	0.0969494i	0.413684	+	0.910421i	$0.364242\pi$
$180$		0			0
$181$		−	9.53343i		−	0.708615i	−0.935129	−	0.354307i	$-0.884717\pi$
$181$		−	9.53343i		−	0.708615i	0.935129	−	0.354307i	$-0.115283\pi$
$182$	12.6117	−	6.15986i	0.934838	−	0.456599i
$183$		0			0
$184$	2.21298	+	2.72423i	0.163143	+	0.200833i
$185$	−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	$-0.235857\pi$
$191$	7.21637	+	4.16637i	0.522158	+	0.301468i	−0.215659	+	0.976469i	$0.569190\pi$
$192$		0			0
$193$	6.18630	+	10.7150i	0.445300	+	0.771282i	0.998073	−	0.0620498i	$-0.0197638\pi$
$193$	6.18630	+	10.7150i	0.445300	+	0.771282i	−0.552773	+	0.833332i	$0.686430\pi$
$194$	−12.2871	−	9.24915i	−0.882164	−	0.664050i
$195$		0			0
$196$	−8.60689	+	11.0418i	−0.614778	+	0.788700i
$197$	−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	0.974495	+	0.224410i	$0.0720455\pi$
$199$	9.61504	+	16.6537i	0.681592	+	1.18055i	−0.292903	+	0.956142i	$0.594621\pi$
$200$	−1.81886	−	11.3707i	−0.128613	−	0.804031i
$201$		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
$206$	8.31232	+	19.5547i	0.579147	+	1.36244i
$207$		0			0
$208$	−7.97732	−	12.7084i	−0.553128	−	0.881167i
$209$		−	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	$0.896897\pi$
$212$	−5.68342	+	5.89743i	−0.390339	+	0.405037i
$213$		0			0
$214$	15.7686	−	6.70291i	1.07792	−	0.458201i
$215$	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
$220$	−2.92347	−	10.1561i	−0.197100	−	0.684723i
$221$	1.28763	+	2.23024i	0.0866152	+	0.150022i
$222$		0			0
$223$	−1.94585			−0.130303			−0.0651517	−	0.997875i	$-0.520753\pi$
$223$	−1.94585			−0.130303			−0.0651517	+	0.997875i	$0.520753\pi$
$224$	12.7131	+	7.89796i	0.849428	+	0.527705i
$225$		0			0
$226$	−6.27629	+	8.33780i	−0.417492	+	0.554622i
$227$	4.32265	+	7.48706i	0.286905	+	0.496933i	0.973069	−	0.230513i	$-0.0740404\pi$
$227$	4.32265	+	7.48706i	0.286905	+	0.496933i	−0.686165	+	0.727446i	$0.740707\pi$
$228$		0			0
$229$	14.5396	+	8.39446i	0.960805	+	0.554721i	0.896421	−	0.443204i	$-0.146158\pi$
$229$	14.5396	+	8.39446i	0.960805	+	0.554721i	0.0643846	+	0.997925i	$0.479492\pi$
$230$	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	−0.882657	−	0.470018i	$-0.844248\pi$
$233$	−0.523283	+	0.906353i	−0.0342814	+	0.0593772i	0.848376	+	0.529395i	$0.177581\pi$
$234$		0			0
$235$	−3.01711	+	1.74193i	−0.196814	+	0.113631i
$236$	17.6066	−	18.2696i	1.14609	−	1.18925i
$237$		0			0
$238$	−2.13037	−	1.43522i	−0.138092	−	0.0930315i
$239$			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	−0.574922	−	0.818208i	$-0.694968\pi$
$241$	−2.38754	+	1.37844i	−0.153795	+	0.0887934i	0.421128	+	0.907001i	$0.361634\pi$
$242$	10.5480	+	24.8141i	0.678050	+	1.59511i
$243$		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
$248$	−2.15695	−	13.4843i	−0.136966	−	0.856252i
$249$		0			0
$250$	−9.87747	−	7.43528i	−0.624706	−	0.470248i
$251$	−20.7493			−1.30968			−0.654841	−	0.755767i	$-0.727264\pi$
$251$	−20.7493			−1.30968			−0.654841	+	0.755767i	$0.727264\pi$
$252$		0			0
$253$	−6.80413			−0.427772
$254$	13.1553	+	9.90263i	0.825434	+	0.621346i
$255$		0			0
$256$	6.95495	−	14.4093i	0.434684	−	0.900583i
$257$	−6.45283	−	3.72554i	−0.402516	−	0.232393i	0.285053	−	0.958512i	$-0.407989\pi$
$257$	−6.45283	−	3.72554i	−0.402516	−	0.232393i	−0.687569	+	0.726119i	$0.741322\pi$
$258$		0			0
$259$	3.93830	+	6.06381i	0.244714	+	0.376787i
$260$	−7.01711	−	1.74193i	−0.435182	−	0.108030i
$261$		0			0
$262$	−5.12390	−	12.0540i	−0.316556	−	0.744698i
$263$	25.7034	−	14.8399i	1.58494	−	0.915066i	0.590818	−	0.806805i	$-0.298805\pi$
$263$	25.7034	−	14.8399i	1.58494	−	0.915066i	0.994123	−	0.108260i	$-0.0345280\pi$
$264$		0			0
$265$			3.94654i			0.242434i
$266$	18.2236	+	1.26406i	1.11736	+	0.0775045i
$267$		0			0
$268$	−13.5924	−	13.0991i	−0.830286	−	0.800155i
$269$	3.73727	−	2.15771i	0.227865	−	0.131558i	−0.381722	−	0.924277i	$-0.624669\pi$
$269$	3.73727	−	2.15771i	0.227865	−	0.131558i	0.609587	+	0.792719i	$0.291335\pi$
$270$		0			0
$271$	−6.79142	+	11.7631i	−0.412550	+	0.714557i	−0.995168	−	0.0981892i	$-0.968695\pi$
$271$	−6.79142	+	11.7631i	−0.412550	+	0.714557i	0.582618	+	0.812746i	$0.302028\pi$
$272$	−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	0.833235	−	0.552920i	$-0.186486\pi$
$277$	−1.03563	−	1.79376i	−0.0622250	−	0.107777i	−0.895460	+	0.445143i	$0.853153\pi$
$278$	4.51465	−	5.99753i	0.270770	−	0.359708i
$279$		0			0
$280$	7.05177	−	1.51059i	0.421424	−	0.0902747i
$281$	−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	$-0.0479970\pi$
$283$	6.12739	+	10.6129i	0.364235	+	0.630874i	−0.624418	+	0.781091i	$0.714664\pi$
$284$	−19.4431	+	5.59677i	−1.15373	+	0.332107i
$285$		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
$290$	3.11074	−	1.32231i	0.182669	−	0.0776488i
$291$		0			0
$292$	9.59236	+	9.24426i	0.561351	+	0.540980i
$293$			10.7090i			0.625626i	0.949815	+	0.312813i	$0.101271\pi$
$293$			10.7090i			0.625626i	−0.949815	+	0.312813i	$0.898729\pi$
$294$		0			0
$295$		−	12.2259i		−	0.711821i
$296$	5.99964	−	4.87370i	0.348722	−	0.283278i
$297$		0			0
$298$	2.57901	+	6.06712i	0.149398	+	0.351459i
$299$	−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
$304$	−0.721529	−	19.5154i	−0.0413825	−	1.11928i
$305$	−5.01711	−	8.68988i	−0.287279	−	0.497581i
$306$		0			0
$307$	−4.22056			−0.240880			−0.120440	−	0.992721i	$-0.538431\pi$
$307$	−4.22056			−0.240880			−0.120440	+	0.992721i	$0.538431\pi$
$308$	−27.4236	+	9.47561i	−1.56260	+	0.539923i
$309$		0			0
$310$	−5.25711	−	3.95729i	−0.298584	−	0.224759i
$311$	−4.85070	−	8.40165i	−0.275058	−	0.476414i	0.695092	−	0.718921i	$-0.255364\pi$
$311$	−4.85070	−	8.40165i	−0.275058	−	0.476414i	−0.970150	+	0.242507i	$0.922030\pi$
$312$		0			0
$313$	11.8328	+	6.83168i	0.668831	+	0.386149i	0.795633	−	0.605778i	$-0.207138\pi$
$313$	11.8328	+	6.83168i	0.668831	+	0.386149i	−0.126803	+	0.991928i	$0.540472\pi$
$314$	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	−0.432992	−	0.901398i	$-0.642542\pi$
$317$	10.0442	−	17.3970i	0.564138	−	0.977115i	0.997129	−	0.0757171i	$-0.0241246\pi$
$318$		0			0
$319$	−11.7771	+	6.79948i	−0.659388	+	0.380698i
$320$	−2.40495	−	7.32499i	−0.134441	−	0.409479i
$321$		0			0
$322$	0.321286	−	4.63190i	0.0179046	−	0.258125i
$323$			3.35171i			0.186494i
$324$		0			0
$325$	13.2259	−	7.63599i	0.733642	−	0.423569i
$326$	−5.23008	+	2.22320i	−0.289667	+	0.123132i
$327$		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	$-0.416698\pi$
$331$	−8.15886	−	4.71052i	−0.448452	−	0.258914i	−0.707176	+	0.707037i	$0.750031\pi$
$332$	0.300843	+	1.04512i	0.0165109	+	0.0573585i
$333$		0			0
$334$	−12.5177	+	16.6293i	−0.684939	+	0.909914i
$335$	−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	$0.619305\pi$
$338$	0.911125	−	1.21039i	0.0495587	−	0.0658367i
$339$		0			0
$340$	0.366030	+	1.27158i	0.0198508	+	0.0689612i
$341$	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
$346$	−15.1664	+	6.44693i	−0.815351	+	0.346589i
$347$	−19.5890	+	11.3097i	−1.05159	+	0.607136i	−0.923094	−	0.384574i	$-0.874349\pi$
$347$	−19.5890	+	11.3097i	−1.05159	+	0.607136i	−0.128497	+	0.991710i	$0.541015\pi$
$348$		0			0
$349$		−	2.48180i		−	0.132848i	−0.997791	−	0.0664239i	$-0.978841\pi$
$349$		−	2.48180i		−	0.132848i	0.997791	−	0.0664239i	$-0.0211590\pi$
$350$	−8.51126	+	12.6337i	−0.454946	+	0.675301i
$351$		0			0
$352$	13.1806	+	28.0780i	0.702530	+	1.49656i
$353$	7.89315	−	4.55711i	0.420110	−	0.242551i	−0.275014	−	0.961440i	$-0.588683\pi$
$353$	7.89315	−	4.55711i	0.420110	−	0.242551i	0.695124	+	0.718889i	$0.255349\pi$
$354$		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	$-0.391859\pi$
$359$	−6.00000	−	3.46410i	−0.316668	−	0.182828i	−0.649906	+	0.760014i	$0.725192\pi$
$360$		0			0
$361$	−2.41780	−	4.18776i	−0.127253	−	0.220408i
$362$	10.7716	+	8.10834i	0.566143	+	0.426165i
$363$		0			0
$364$	−3.76653	+	19.4887i	−0.197420	+	1.02148i
$365$	6.41917			0.335995
$366$		0			0
$367$	1.91680	+	3.31999i	0.100056	+	0.173302i	0.911707	−	0.410840i	$-0.134765\pi$
$367$	1.91680	+	3.31999i	0.100056	+	0.173302i	−0.811652	+	0.584142i	$0.801431\pi$
$368$	−4.96021	+	0.183391i	−0.258569	+	0.00955992i
$369$		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	−0.275711	−	0.961241i	$-0.588913\pi$
$373$	13.4150	−	23.2355i	0.694603	−	1.20309i	0.970314	−	0.241848i	$-0.0777534\pi$
$374$	−2.08260	−	4.89932i	−0.107689	−	0.253338i
$375$		0			0
$376$	7.93633	−	6.44693i	0.409285	−	0.332475i
$377$			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	$0.942985\pi$
$380$	−6.77568	−	6.52980i	−0.347585	−	0.334972i
$381$		0			0
$382$	−10.8451	+	4.61004i	−0.554885	+	0.235870i
$383$	1.12881	−	1.95515i	0.0576793	−	0.0999035i	−0.835744	−	0.549119i	$-0.814963\pi$
$383$	1.12881	−	1.95515i	0.0576793	−	0.0999035i	0.893423	+	0.449216i	$0.148297\pi$
$384$		0			0
$385$	−6.34654	+	12.4573i	−0.323450	+	0.634881i
$386$	−17.3682	−	2.12351i	−0.884017	−	0.108084i
$387$		0			0
$388$	20.9008	−	6.01639i	1.06108	−	0.305436i
$389$	15.3047	+	26.5086i	0.775981	+	1.34404i	0.934242	+	0.356641i	$0.116078\pi$
$389$	15.3047	+	26.5086i	0.775981	+	1.34404i	−0.158261	+	0.987397i	$0.550589\pi$
$390$		0			0
$391$	0.851904			0.0430827
$392$	−5.15558	−	19.1160i	−0.260396	−	0.965502i
$393$		0			0
$394$	2.75300	−	3.65726i	0.138694	−	0.184250i
$395$	−0.681544	−	1.18047i	−0.0342922	−	0.0593958i
$396$		0			0
$397$	−12.0368	−	6.94947i	−0.604112	−	0.348784i	0.166546	−	0.986034i	$-0.446739\pi$
$397$	−12.0368	−	6.94947i	−0.604112	−	0.348784i	−0.770657	+	0.637250i	$0.780072\pi$
$398$	−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	−0.965328	−	0.261041i	$-0.915934\pi$
$401$	−5.13832	+	8.89984i	−0.256596	+	0.444437i	0.708732	+	0.705478i	$0.249268\pi$
$402$		0			0
$403$	15.6843	−	9.05535i	0.781292	−	0.451079i
$404$	20.7815	+	20.0273i	1.03392	+	0.996396i
$405$		0			0
$406$	−4.07263	−	8.33827i	−0.202121	−	0.413821i
$407$			14.9849i			0.742775i
$408$		0			0
$409$	10.5342	−	6.08193i	0.520883	−	0.300732i	−0.216413	−	0.976302i	$-0.569436\pi$
$409$	10.5342	−	6.08193i	0.520883	−	0.300732i	0.737296	+	0.675570i	$0.236102\pi$
$410$	5.02764	+	11.8275i	0.248297	+	0.584120i
$411$		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
$416$	21.1437	+	1.79528i	1.03666	+	0.0880209i
$417$		0			0
$418$	30.2468	+	22.7683i	1.47942	+	1.11364i
$419$	16.2245			0.792619			0.396310	−	0.918117i	$-0.370291\pi$
$419$	16.2245			0.792619			0.396310	+	0.918117i	$0.370291\pi$
$420$		0			0
$421$	−9.58477			−0.467133			−0.233567	−	0.972341i	$-0.575040\pi$
$421$	−9.58477			−0.467133			−0.233567	+	0.972341i	$0.575040\pi$
$422$	−10.4473	−	7.86419i	−0.508565	−	0.382823i
$423$		0			0
$424$	−1.82953	−	11.4374i	−0.0888499	−	0.555451i
$425$	−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
$430$	3.18534	+	7.49351i	0.153611	+	0.361369i
$431$	−0.131544	+	0.0759470i	−0.00633626	+	0.00365824i	−0.503165	−	0.864190i	$-0.667831\pi$
$431$	−0.131544	+	0.0759470i	−0.00633626	+	0.00365824i	0.496829	+	0.867849i	$0.334498\pi$
$432$		0			0
$433$		−	9.46997i		−	0.455098i	−0.973767	−	0.227549i	$-0.926929\pi$
$433$		−	9.46997i		−	0.455098i	0.973767	−	0.227549i	$-0.0730711\pi$
$434$	−10.0933	+	14.9820i	−0.484494	+	0.719161i
$435$		0			0
$436$	8.42595	−	8.74324i	0.403530	−	0.418725i
$437$	−5.24663	+	3.02915i	−0.250981	+	0.144904i
$438$		0			0
$439$	16.7373	−	28.9898i	0.798826	−	1.38361i	−0.121555	−	0.992585i	$-0.538788\pi$
$439$	16.7373	−	28.9898i	0.798826	−	1.38361i	0.920381	−	0.391023i	$-0.127879\pi$
$440$	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	$-0.546745\pi$
$443$	−22.6513	−	13.0777i	−1.07619	−	0.621341i	−0.929867	+	0.367895i	$0.880079\pi$
$444$		0			0
$445$	0.267131	+	0.462684i	0.0126632	+	0.0219333i
$446$	1.65497	−	2.19857i	0.0783652	−	0.104105i
$447$		0			0
$448$	−19.7364	+	7.64686i	−0.932457	+	0.361280i
$449$	−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
$452$	−4.08260	−	14.1829i	−0.192029	−	0.667106i
$453$		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	−0.971153	−	0.238458i	$-0.923358\pi$
$457$	−5.96574	+	10.3330i	−0.279065	+	0.483356i	0.692087	+	0.721814i	$0.256691\pi$
$458$	−21.8509	+	9.28837i	−1.02103	+	0.434017i
$459$		0			0
$460$	−1.65968	+	1.72217i	−0.0773829	+	0.0802968i
$461$		−	30.0093i		−	1.39767i	−0.715281	−	0.698837i	$-0.753701\pi$
$461$		−	30.0093i		−	1.39767i	0.715281	−	0.698837i	$-0.246299\pi$
$462$		0			0
$463$		−	13.2736i		−	0.616875i	−0.951245	−	0.308437i	$-0.900194\pi$
$463$		−	13.2736i		−	0.616875i	0.951245	−	0.308437i	$-0.0998060\pi$
$464$	−8.40221	+	5.27425i	−0.390063	+	0.244851i
$465$		0			0
$466$	−0.579007	−	1.36211i	−0.0268220	−	0.0630987i
$467$	14.8246	−	25.6770i	0.686002	−	1.18819i	−0.287119	−	0.957895i	$-0.592697\pi$
$467$	14.8246	−	25.6770i	0.686002	−	1.18819i	0.973121	−	0.230295i	$-0.0739692\pi$
$468$		0			0
$469$	1.30812	+	24.9376i	0.0604036	+	1.15151i
$470$	0.597935	−	4.89050i	0.0275807	−	0.225582i
$471$		0			0
$472$	5.66768	+	35.4318i	0.260876	+	1.63088i
$473$	−16.3794	−	28.3699i	−0.753125	−	1.30445i
$474$		0			0
$475$	19.8766			0.912001
$476$	3.43354	−	1.18638i	0.157376	−	0.0543778i
$477$		0			0
$478$	−21.7478	−	16.3707i	−0.994721	−	0.748777i
$479$	−5.76773	−	9.99001i	−0.263535	−	0.456455i	0.703644	−	0.710553i	$-0.251555\pi$
$479$	−5.76773	−	9.99001i	−0.263535	−	0.456455i	−0.967179	+	0.254097i	$0.918222\pi$
$480$		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	$-0.595727\pi$
$487$	8.44822	−	4.87758i	0.382825	−	0.221024i	0.679047	+	0.734095i	$0.262393\pi$
$488$	18.5685	+	22.8582i	0.840555	+	1.03474i
$489$		0			0
$490$	−8.18058	−	4.90862i	−0.369561	−	0.221749i
$491$		−	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
$494$	23.8356	−	10.1320i	1.07241	−	0.455861i
$495$		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	$-0.0795413\pi$
$499$	27.6827	+	15.9826i	1.23925	+	0.715480i	0.270307	+	0.962774i	$0.412875\pi$
$500$	16.8019	−	4.83650i	0.751404	−	0.216295i
$501$		0			0
$502$	17.6476	−	23.4441i	0.787650	−	1.04636i
$503$	22.7110			1.01263			0.506317	−	0.862348i	$-0.331007\pi$
$503$	22.7110			1.01263			0.506317	+	0.862348i	$0.331007\pi$
$504$		0			0
$505$	13.9069			0.618847
$506$	5.78702	−	7.68783i	0.257265	−	0.341766i
$507$		0			0
$508$	−22.3775	+	6.44147i	−0.992841	+	0.285794i
$509$	1.98947	+	1.14862i	0.0881819	+	0.0509118i	0.543443	−	0.839446i	$-0.317121\pi$
$509$	1.98947	+	1.14862i	0.0881819	+	0.0509118i	−0.455261	+	0.890358i	$0.650454\pi$
$510$		0			0
$511$	−0.923166	−	17.5989i	−0.0408384	−	0.778528i
$512$	10.3655	+	20.1136i	0.458093	+	0.888904i
$513$		0			0
$514$	9.69764	−	4.12227i	0.427745	−	0.181825i
$515$	−12.5396	+	7.23973i	−0.552560	+	0.319021i
$516$		0			0
$517$			19.8221i			0.871773i
$518$	−10.2009	−	0.707576i	−0.448204	−	0.0310891i
$519$		0			0
$520$	7.93633	−	6.44693i	0.348031	−	0.282717i
$521$	32.5712	−	18.8050i	1.42697	−	0.823862i	0.430090	−	0.902786i	$-0.358482\pi$
$521$	32.5712	−	18.8050i	1.42697	−	0.823862i	0.996881	+	0.0789240i	$0.0251485\pi$
$522$		0			0
$523$	17.8444	−	30.9073i	0.780279	−	1.35148i	−0.151500	−	0.988457i	$-0.548410\pi$
$523$	17.8444	−	30.9073i	0.780279	−	1.35148i	0.931779	−	0.363026i	$-0.118256\pi$
$524$	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
$530$	−4.45910	−	3.35660i	−0.193691	−	0.145801i
$531$		0			0
$532$	−16.9277	+	19.5154i	−0.733910	+	0.846098i
$533$	−35.3726			−1.53216
$534$		0			0
$535$	5.83799	+	10.1117i	0.252398	+	0.437167i
$536$	26.3609	−	4.21669i	1.13862	−	0.182133i
$537$		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	0.126507	+	0.991966i	$0.459623\pi$
$541$	−18.5102	+	32.0605i	−0.795814	+	1.37839i	−0.922321	+	0.386425i	$0.873710\pi$
$542$	−7.51463	−	17.6782i	−0.322781	−	0.759342i
$543$		0			0
$544$	−1.65027	−	3.51548i	−0.0707547	−	0.150725i
$545$		−	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	$0.985766\pi$
$548$	10.0342	−	10.4121i	0.428640	−	0.444781i
$549$		0			0
$550$	−29.0543	+	12.3504i	−1.23888	+	0.526623i
$551$	−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
$556$	2.93669	+	10.2020i	0.124543	+	0.432661i
$557$	−8.39887	−	14.5473i	−0.355872	−	0.616388i	0.631395	−	0.775461i	$-0.282483\pi$
$557$	−8.39887	−	14.5473i	−0.355872	−	0.616388i	−0.987267	+	0.159073i	$0.949149\pi$
$558$		0			0
$559$	−22.4109			−0.947878
$560$	−4.29087	+	9.25241i	−0.181322	+	0.390986i
$561$		0			0
$562$	20.1676	−	26.7919i	0.850720	−	1.13015i
$563$	8.69784	+	15.0651i	0.366570	+	0.634918i	0.989027	−	0.147736i	$-0.0471986\pi$
$563$	8.69784	+	15.0651i	0.366570	+	0.634918i	−0.622456	+	0.782654i	$0.713865\pi$
$564$		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	0.242882	+	0.970056i	$0.421907\pi$
$569$	−17.1425	+	29.6917i	−0.718652	+	1.24474i	−0.961534	+	0.274686i	$0.911426\pi$
$570$		0			0
$571$	−5.14176	+	2.96860i	−0.215176	+	0.124232i	−0.603715	−	0.797201i	$-0.706313\pi$
$571$	−5.14176	+	2.96860i	−0.215176	+	0.124232i	0.388539	+	0.921432i	$0.372980\pi$
$572$	−28.5458	+	29.6207i	−1.19356	+	1.23850i
$573$		0			0
$574$	31.7034	−	15.4848i	1.32327	−	0.646322i
$575$		−	5.05203i		−	0.210684i
$576$		0			0
$577$	33.7930	−	19.5104i	1.40682	−	0.812229i	0.411742	−	0.911300i	$-0.364920\pi$
$577$	33.7930	−	19.5104i	1.40682	−	0.812229i	0.995080	+	0.0990712i	$0.0315871\pi$
$578$	−9.14440	−	21.5122i	−0.380357	−	0.894790i
$579$		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
$584$	−18.6033	+	2.97579i	−0.769812	+	0.123139i
$585$		0			0
$586$	−12.0999	−	9.10818i	−0.499840	−	0.376255i
$587$	−7.71931			−0.318610			−0.159305	−	0.987229i	$-0.550925\pi$
$587$	−7.71931			−0.318610			−0.159305	+	0.987229i	$0.550925\pi$
$588$		0			0
$589$	23.5712			0.971235
$590$	13.8138	+	10.3984i	0.568705	+	0.428093i
$591$		0			0
$592$	0.403887	+	10.9240i	0.0165996	+	0.448974i
$593$	−0.336377	−	0.194207i	−0.0138133	−	0.00797513i	0.493077	−	0.869985i	$-0.335872\pi$
$593$	−0.336377	−	0.194207i	−0.0138133	−	0.00797513i	−0.506891	+	0.862010i	$0.669205\pi$
$594$		0			0
$595$	0.794612	−	1.55970i	0.0325759	−	0.0639415i
$596$	−9.04858	−	2.24622i	−0.370644	−	0.0920088i
$597$		0			0
$598$	−2.57526	−	6.05829i	−0.105310	−	0.247742i
$599$	18.0000	−	10.3923i	0.735460	−	0.424618i	−0.0849563	−	0.996385i	$-0.527075\pi$
$599$	18.0000	−	10.3923i	0.735460	−	0.424618i	0.820416	+	0.571767i	$0.193742\pi$
$600$		0			0
$601$		−	26.4110i		−	1.07733i	−0.842521	−	0.538664i	$-0.818929\pi$
$601$		−	26.4110i		−	1.07733i	0.842521	−	0.538664i	$-0.181071\pi$
$602$	20.0862	−	9.81062i	0.818652	−	0.399851i
$603$		0			0
$604$	17.5781	+	16.9402i	0.715244	+	0.689289i
$605$	−15.9122	+	9.18691i	−0.646922	+	0.373501i
$606$		0			0
$607$	−20.3531	+	35.2526i	−0.826106	+	1.43086i	0.0749655	+	0.997186i	$0.476115\pi$
$607$	−20.3531	+	35.2526i	−0.826106	+	1.43086i	−0.901071	+	0.433671i	$0.857218\pi$
$608$	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	0.636129	−	0.771583i	$-0.280535\pi$
$613$	−8.66920	−	15.0155i	−0.350146	−	0.606470i	−0.986275	+	0.165113i	$0.947201\pi$
$614$	3.58966	−	4.76872i	0.144867	−	0.192450i
$615$		0			0
$616$	12.6179	−	39.0444i	0.508391	−	1.57314i
$617$	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	−0.999379	−	0.0352227i	$-0.988786\pi$
$619$	−13.1911	−	22.8476i	−0.530194	−	0.918322i	0.469186	−	0.883099i	$-0.344547\pi$
$620$	8.94251	−	2.57414i	0.359140	−	0.103380i
$621$		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
$626$	−17.7830	+	7.55917i	−0.710750	+	0.302125i
$627$		0			0
$628$	31.5856	+	30.4394i	1.26040	+	1.21466i
$629$		−	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	$0.695372\pi$
$632$	2.52242	+	3.10515i	0.100336	+	0.123516i
$633$		0			0
$634$	11.1138	+	26.1452i	0.441384	+	1.03836i
$635$	−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
$640$	10.3218	+	3.51273i	0.408004	+	0.138853i
$641$	22.7239	+	39.3590i	0.897540	+	1.55459i	0.830629	+	0.556827i	$0.187981\pi$
$641$	22.7239	+	39.3590i	0.897540	+	1.55459i	0.0669115	+	0.997759i	$0.478685\pi$
$642$		0			0
$643$	30.5534			1.20491			0.602454	−	0.798154i	$-0.294190\pi$
$643$	30.5534			1.20491			0.602454	+	0.798154i	$0.294190\pi$
$644$	4.96021	+	4.30252i	0.195460	+	0.169543i
$645$		0			0
$646$	−3.78702	−	2.85069i	−0.148998	−	0.112159i
$647$	18.0896	+	31.3321i	0.711175	+	1.23179i	0.964417	+	0.264388i	$0.0851698\pi$
$647$	18.0896	+	31.3321i	0.711175	+	1.23179i	−0.253242	+	0.967403i	$0.581497\pi$
$648$		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	−0.935245	−	0.354000i	$-0.884821\pi$
$653$	−4.11545	+	7.12816i	−0.161050	+	0.278946i	0.774196	+	0.632946i	$0.218155\pi$
$654$		0			0
$655$	7.72968	−	4.46273i	0.302024	−	0.174373i
$656$	−20.0535	−	31.9465i	−0.782959	−	1.24730i
$657$		0			0
$658$	−13.4938	−	0.935982i	−0.526044	−	0.0364884i
$659$		−	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	−0.803340	−	0.595520i	$-0.796946\pi$
$661$	−17.7212	+	10.2313i	−0.689275	+	0.397953i	0.114065	+	0.993473i	$0.463613\pi$
$662$	12.2616	−	5.21214i	0.476559	−	0.202575i
$663$		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
$668$	−8.14252	−	28.2869i	−0.315044	−	1.09445i
$669$		0			0
$670$	7.73626	−	10.2773i	0.298878	−	0.397047i
$671$	−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	$0.474020\pi$
$674$	11.4319	−	15.1868i	0.440340	−	0.584975i
$675$		0			0
$676$	0.592669	+	2.05892i	0.0227950	+	0.0791892i
$677$	−20.7962	−	12.0067i	−0.799262	−	0.461454i	0.0439511	−	0.999034i	$-0.486005\pi$
$677$	−20.7962	−	12.0067i	−0.799262	−	0.461454i	−0.843213	+	0.537580i	$0.819339\pi$
$678$		0			0
$679$	−25.6365	−	13.0609i	−0.983840	−	0.501232i
$680$	−1.74805	−	0.667932i	−0.0670345	−	0.0256140i
$681$		0			0
$682$	−34.4549	+	14.6461i	−1.31935	+	0.560827i
$683$	−7.09951	+	4.09890i	−0.271655	+	0.156840i	−0.629640	−	0.776887i	$-0.716797\pi$
$683$	−7.09951	+	4.09890i	−0.271655	+	0.156840i	0.357984	+	0.933728i	$0.383464\pi$
$684$		0			0
$685$		−	6.96771i		−	0.266222i
$686$	−12.2810	+	23.1339i	−0.468892	+	0.883256i
$687$		0			0
$688$	−12.7052	−	20.2402i	−0.484382	−	0.771651i
$689$	13.3035	−	7.68079i	0.506824	−	0.292615i
$690$		0			0
$691$	−17.9925	+	31.1638i	−0.684465	+	1.18553i	0.289139	+	0.957287i	$0.406631\pi$
$691$	−17.9925	+	31.1638i	−0.684465	+	1.18553i	−0.973605	+	0.228242i	$0.926702\pi$
$692$	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
$698$	2.80413	+	2.11081i	0.106138	+	0.0798954i
$699$		0			0
$700$	−7.03559	−	20.3619i	−0.265920	−	0.769606i
$701$	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
$704$	−42.9350	−	8.98829i	−1.61817	−	0.338759i
$705$		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	−0.963518	−	0.267644i	$-0.913755\pi$
$709$	−6.65603	+	11.5286i	−0.249973	+	0.432965i	0.713545	+	0.700609i	$0.247088\pi$
$710$	−5.39367	−	12.6886i	−0.202421	−	0.476195i
$711$		0			0
$712$	−0.988660	−	1.21706i	−0.0370516	−	0.0456114i
$713$		−	5.99109i		−	0.224368i
$714$		0			0
$715$			19.8221i			0.741303i
$716$	3.73590	+	3.60033i	0.139617	+	0.134550i
$717$		0			0
$718$	9.01711	−	3.83299i	0.336515	−	0.143046i
$719$	−23.7520	+	41.1397i	−0.885800	+	1.53425i	−0.0410056	+	0.999159i	$0.513056\pi$
$719$	−23.7520	+	41.1397i	−0.885800	+	1.53425i	−0.844794	+	0.535091i	$0.820277\pi$
$720$		0			0
$721$	21.6519	+	33.3375i	0.806358	+	1.24155i
$722$	6.78803	+	0.829936i	0.252624	+	0.0308870i
$723$		0			0
$724$	−18.3229	+	5.27431i	−0.680964	+	0.196018i
$725$	−5.04858	−	8.74440i	−0.187500	−	0.324759i
$726$		0			0
$727$	−24.3567			−0.903340			−0.451670	−	0.892185i	$-0.649172\pi$
$727$	−24.3567			−0.903340			−0.451670	+	0.892185i	$0.649172\pi$
$728$	−18.8163	−	20.8312i	−0.697379	−	0.772054i
$729$		0			0
$730$	−5.45961	+	7.25287i	−0.202069	+	0.268441i
$731$	2.05076	+	3.55203i	0.0758503	+	0.131377i
$732$		0			0
$733$	3.35812	+	1.93881i	0.124035	+	0.0716117i	0.560734	−	0.827996i	$-0.310519\pi$
$733$	3.35812	+	1.93881i	0.124035	+	0.0716117i	−0.436699	+	0.899608i	$0.643852\pi$
$734$	−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	$-0.615987\pi$
$739$	7.46497	−	4.30990i	0.274603	−	0.158542i	0.630978	+	0.775801i	$0.282654\pi$
$740$	3.79279	+	3.65515i	0.139426	+	0.134366i
$741$		0			0
$742$	−8.56119	+	12.7078i	−0.314291	+	0.466520i
$743$			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
$746$	14.8436	+	34.9195i	0.543461	+	1.27849i
$747$		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	$-0.557348\pi$
$751$	−30.7146	−	17.7331i	−1.12079	−	0.647090i	−0.941603	+	0.336725i	$0.890681\pi$
$752$	0.534262	+	14.4503i	0.0194825	+	0.526948i
$753$		0			0
$754$	−10.5116	−	7.91261i	−0.382809	−	0.288160i
$755$	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	$0.320443\pi$
$758$	−7.83786	−	5.89996i	−0.284684	−	0.214296i
$759$		0			0
$760$	13.1407	−	2.10199i	0.476663	−	0.0762471i
$761$	−43.5568	−	25.1475i	−1.57893	−	0.911597i	−0.995009	−	0.0997877i	$-0.968184\pi$
$761$	−43.5568	−	25.1475i	−1.57893	−	0.911597i	−0.583923	−	0.811809i	$-0.698483\pi$
$762$		0			0
$763$	−16.0410	+	0.841446i	−0.580723	+	0.0304624i
$764$	4.01518	−	16.1746i	0.145264	−	0.585175i
$765$		0			0
$766$	1.24901	+	2.93830i	0.0451286	+	0.106165i
$767$	−41.2128	+	23.7942i	−1.48811	+	0.859160i
$768$		0			0
$769$		−	20.2817i		−	0.731377i	−0.930737	−	0.365689i	$-0.880833\pi$
$769$		−	20.2817i		−	0.731377i	0.930737	−	0.365689i	$-0.119167\pi$
$770$	−8.67735	−	17.7659i	−0.312710	−	0.640239i
$771$		0			0
$772$	17.1712	−	17.8178i	0.618006	−	0.641277i
$773$	18.8149	−	10.8628i	0.676723	−	0.390706i	−0.121896	−	0.992543i	$-0.538897\pi$
$773$	18.8149	−	10.8628i	0.676723	−	0.390706i	0.798619	+	0.601836i	$0.205564\pi$
$774$		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
$782$	−0.724559	+	0.962547i	−0.0259102	+	0.0344206i
$783$		0			0
$784$	25.9836	+	10.4333i	0.927985	+	0.372617i
$785$	21.1369			0.754410
$786$		0			0
$787$	−0.299328	−	0.518452i	−0.0106699	−	0.0184808i	0.860641	−	0.509212i	$-0.170063\pi$
$787$	−0.299328	−	0.518452i	−0.0106699	−	0.0184808i	−0.871311	+	0.490731i	$0.836730\pi$
$788$	1.79078	+	6.22111i	0.0637937	+	0.221618i
$789$		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
$794$	18.0896	−	7.68951i	0.641975	−	0.272890i
$795$		0			0
$796$	26.6883	−	27.6933i	0.945942	−	0.981562i
$797$			36.1789i			1.28152i	0.767741	+	0.640760i	$0.221381\pi$
$797$			36.1789i			1.28152i	−0.767741	+	0.640760i	$0.778619\pi$
$798$		0			0
$799$		−	2.48180i		−	0.0877998i
$800$	−20.8478	+	9.78655i	−0.737079	+	0.346007i
$801$		0			0
$802$	−5.68549	−	13.3751i	−0.200762	−	0.472292i
$803$	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
$808$	−40.3034	+	6.44693i	−1.41787	+	0.226802i
$809$	−15.0603	−	26.0852i	−0.529491	−	0.917106i	−0.999408	−	0.0343953i	$-0.989049\pi$
$809$	−15.0603	−	26.0852i	−0.529491	−	0.917106i	0.469917	−	0.882711i	$-0.344284\pi$
$810$		0			0
$811$	−21.5947			−0.758292			−0.379146	−	0.925337i	$-0.623782\pi$
$811$	−21.5947			−0.758292			−0.379146	+	0.925337i	$0.623782\pi$
$812$	12.8851	+	2.49026i	0.452177	+	0.0873911i
$813$		0			0
$814$	−16.9311	−	12.7449i	−0.593435	−	0.446709i
$815$	−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	0.0222131	−	0.999753i	$-0.492929\pi$
$821$	25.1264	−	43.5202i	0.876918	−	1.51887i	0.854705	−	0.519114i	$-0.173738\pi$
$822$		0			0
$823$	−2.87338	+	1.65894i	−0.100160	+	0.0578272i	−0.549243	−	0.835663i	$-0.685084\pi$
$823$	−2.87338	+	1.65894i	−0.100160	+	0.0578272i	0.449084	+	0.893490i	$0.351751\pi$
$824$	32.9847	−	26.7945i	1.14907	−	0.933430i
$825$		0			0
$826$	26.5216	−	39.3675i	0.922805	−	1.36977i
$827$			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	0.0797067	−	0.996818i	$-0.474602\pi$
$829$	28.2980	−	16.3379i	0.982830	−	0.567437i	0.903123	+	0.429381i	$0.141268\pi$
$830$	−0.682050	+	0.289926i	−0.0236743	+	0.0100635i
$831$		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
$836$	−51.4508	+	14.8104i	−1.77946	+	0.512227i
$837$		0			0
$838$	−13.7992	+	18.3317i	−0.476686	+	0.633258i
$839$	8.66161			0.299032			0.149516	−	0.988759i	$-0.452228\pi$
$839$	8.66161			0.299032			0.149516	+	0.988759i	$0.452228\pi$
$840$		0			0
$841$	−22.8491			−0.787899
$842$	8.15201	−	10.8296i	0.280937	−	0.373213i
$843$		0			0
$844$	17.7711	−	5.11550i	0.611707	−	0.176083i
$845$	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
$850$	3.63772	−	1.54632i	0.124773	−	0.0530384i
$851$	2.93688	−	1.69561i	0.100675	−	0.0581248i
$852$		0			0
$853$			7.17809i			0.245773i	0.992421	+	0.122887i	$0.0392151\pi$
$853$			7.17809i			0.245773i	−0.992421	+	0.122887i	$0.960785\pi$
$854$	2.69582	−	38.8650i	0.0922491	−	1.32993i
$855$		0			0
$856$	−21.6066	−	26.5982i	−0.738498	−	0.909109i
$857$	−39.5334	+	22.8246i	−1.35044	+	0.779675i	−0.988311	−	0.152454i	$-0.951282\pi$
$857$	−39.5334	+	22.8246i	−1.35044	+	0.779675i	−0.362126	+	0.932129i	$0.617949\pi$
$858$		0			0
$859$	6.77944	−	11.7423i	0.231311	−	0.400643i	−0.726883	−	0.686761i	$-0.759032\pi$
$859$	6.77944	−	11.7423i	0.231311	−	0.400643i	0.958194	+	0.286118i	$0.0923651\pi$
$860$	−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	$-0.0826620\pi$
$863$	36.0550	+	20.8163i	1.22733	+	0.708597i	0.260856	+	0.965378i	$0.415995\pi$
$864$		0			0
$865$	−5.61504	−	9.72554i	−0.190917	−	0.330678i
$866$	10.6999	+	8.05436i	0.363597	+	0.273698i
$867$		0			0
$868$	−8.34335	−	24.1467i	−0.283192	−	0.819591i
$869$	−7.75555			−0.263089
$870$		0			0
$871$	17.7026	+	30.6619i	0.599831	+	1.03894i
$872$	2.71237	+	16.9566i	0.0918525	+	0.574221i
$873$		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	−0.650619	−	0.759404i	$-0.725491\pi$
$877$	9.84239	−	17.0475i	0.332354	−	0.575654i	0.982973	+	0.183751i	$0.0588239\pi$
$878$	18.5196	+	43.5673i	0.625006	+	1.47033i
$879$		0			0
$880$	−17.9022	+	11.2376i	−0.603482	+	0.378819i
$881$			7.24606i			0.244126i	0.992522	+	0.122063i	$0.0389510\pi$
$881$			7.24606i			0.244126i	−0.992522	+	0.122063i	$0.961049\pi$
$882$		0			0
$883$		−	35.4533i		−	1.19310i	−0.802577	−	0.596549i	$-0.796538\pi$
$883$		−	35.4533i		−	1.19310i	0.802577	−	0.596549i	$-0.203462\pi$
$884$	3.57405	−	3.70863i	0.120208	−	0.124735i
$885$		0			0
$886$	34.0415	−	14.4703i	1.14365	−	0.486141i
$887$	8.98684	−	15.5657i	0.301749	−	0.522644i	−0.674784	−	0.738016i	$-0.735763\pi$
$887$	8.98684	−	15.5657i	0.301749	−	0.522644i	0.976532	+	0.215372i	$0.0690964\pi$
$888$		0			0
$889$	27.4479	+	13.9837i	0.920572	+	0.468999i
$890$	−0.749976	−	0.0916955i	−0.0251392	−	0.00307364i
$891$		0			0
$892$	1.07653	+	3.73983i	0.0360448	+	0.125219i
$893$	8.82463	+	15.2847i	0.295305	+	0.511483i
$894$		0			0
$895$	2.50005			0.0835674
$896$	8.14611	−	28.8035i	0.272143	−	0.962257i
$897$		0			0
$898$	8.75337	−	11.6285i	0.292104	−	0.388048i
$899$	−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	$-0.620071\pi$
$907$	7.60870	−	4.39289i	0.252643	−	0.145863i	0.620974	+	0.783831i	$0.286737\pi$
$908$	11.9983	−	12.4501i	0.398178	−	0.413172i
$909$		0			0
$910$	−13.4938	−	0.935982i	−0.447316	−	0.0310275i
$911$			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
$914$	−6.60102	−	15.5289i	−0.218342	−	0.513650i
$915$		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	$-0.157201\pi$
$919$	27.5939	+	15.9314i	0.910240	+	0.525527i	0.0297316	+	0.999558i	$0.490535\pi$
$920$	−0.534262	−	3.33997i	−0.0176141	−	0.110116i
$921$		0			0
$922$	33.9069	+	25.5234i	1.11666	+	0.840570i
$923$	37.9479			1.24907
$924$		0			0
$925$	−11.1262			−0.365828
$926$	14.9975	+	11.2894i	0.492848	+	0.370992i
$927$		0			0
$928$	1.18696	−	13.9793i	0.0389639	−	0.458893i
$929$	−44.1750	−	25.5044i	−1.44933	−	0.836773i	−0.450892	−	0.892579i	$-0.648894\pi$
$929$	−44.1750	−	25.5044i	−1.44933	−	0.836773i	−0.998442	+	0.0558058i	$0.982227\pi$
$930$		0			0
$931$	33.9876	−	3.57555i	1.11390	−	0.117184i
$932$	2.03148	+	0.504294i	0.0665432	+	0.0165187i
$933$		0			0
$934$	16.4033	+	38.5887i	0.536731	+	1.26266i
$935$	3.14171	−	1.81387i	0.102745	−	0.0593199i
$936$		0			0
$937$		−	2.65742i		−	0.0868141i	−0.999057	−	0.0434071i	$-0.986179\pi$
$937$		−	2.65742i		−	0.0868141i	0.999057	−	0.0434071i	$-0.0138212\pi$
$938$	−29.2890	−	19.7318i	−0.956318	−	0.644266i
$939$		0			0
$940$	5.01711	+	4.83504i	0.163640	+	0.157702i
$941$	−26.2920	+	15.1797i	−0.857096	+	0.494844i	−0.863039	−	0.505138i	$-0.831442\pi$
$941$	−26.2920	+	15.1797i	−0.857096	+	0.494844i	0.00594304	+	0.999982i	$0.498108\pi$
$942$		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	$-0.0836630\pi$
$947$	37.6505	+	21.7375i	1.22348	+	0.706374i	0.257818	+	0.966193i	$0.416996\pi$
$948$		0			0
$949$	−12.4931	−	21.6386i	−0.405542	−	0.702419i
$950$	−16.9054	+	22.4581i	−0.548483	+	0.728637i
$951$		0			0
$952$	−1.57981	+	4.88852i	−0.0512021	+	0.158438i
$953$	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
$956$	36.9937	−	10.6488i	1.19646	−	0.344407i
$957$		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
$962$	−13.3423	+	5.67155i	−0.430174	+	0.182858i
$963$		0			0
$964$	3.97020	+	3.82613i	0.127872	+	0.123231i
$965$		−	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	$-0.257142\pi$
$968$	41.8561	−	34.0010i	1.34531	−	1.09283i
$969$		0			0
$970$	5.79806	+	13.6399i	0.186164	+	0.437952i
$971$	0.641758	−	1.11156i	0.0205950	−	0.0356716i	−0.855544	−	0.517730i	$-0.826777\pi$
$971$	0.641758	−	1.11156i	0.0205950	−	0.0356716i	0.876139	+	0.482058i	$0.160111\pi$
$972$		0			0
$973$	6.37523	−	12.5136i	0.204381	−	0.401167i
$974$	−1.67428	+	13.6939i	−0.0536474	+	0.438781i
$975$		0			0
$976$	−41.6198	+	1.53878i	−1.33222	+	0.0492553i
$977$	9.67678	+	16.7607i	0.309588	+	0.536222i	0.978272	−	0.207325i	$-0.0664756\pi$
$977$	9.67678	+	16.7607i	0.309588	+	0.536222i	−0.668684	+	0.743546i	$0.733142\pi$
$978$		0			0
$979$	3.03979			0.0971520
$980$	12.5038	−	5.06819i	0.399421	−	0.161897i
$981$		0			0
$982$	45.7302	+	34.4234i	1.45931	+	1.09850i
$983$	−4.21637	−	7.30296i	−0.134481	−	0.232928i	0.790918	−	0.611922i	$-0.209603\pi$
$983$	−4.21637	−	7.30296i	−0.134481	−	0.232928i	−0.925399	+	0.378994i	$0.876270\pi$
$984$		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	$-0.793760\pi$
$991$	−21.1967	+	12.2379i	−0.673334	+	0.388750i	0.124005	+	0.992282i	$0.460426\pi$
$992$	−24.7229	+	11.6057i	−0.784952	+	0.368480i
$993$		0			0
$994$	−34.0115	+	16.6121i	−1.07878	+	0.526905i
$995$		−	18.5322i		−	0.587511i
$996$		0			0
$997$	−29.0273	+	16.7589i	−0.919304	+	0.530761i	−0.883413	−	0.468595i	$-0.844760\pi$
$997$	−29.0273	+	16.7589i	−0.919304	+	0.530761i	−0.0358914	+	0.999356i	$0.511427\pi$
$998$	−41.6030	+	17.6846i	−1.31692	+	0.559795i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.o.a.19.3	✓	8	3.2	odd	2
84.2.o.a.31.3	yes	8	84.59	odd	6
84.2.o.b.19.3	yes	8	12.11	even	2
84.2.o.b.31.3	yes	8	21.17	even	6
252.2.bf.f.19.2		8	4.3	odd	2
252.2.bf.f.199.2		8	7.3	odd	6
252.2.bf.g.19.2		8	1.1	even	1	trivial
252.2.bf.g.199.2		8	28.3	even	6	inner
588.2.b.a.391.1		8	21.5	even	6
588.2.b.a.391.2		8	84.23	even	6
588.2.b.b.391.1		8	21.2	odd	6
588.2.b.b.391.2		8	84.47	odd	6
588.2.o.b.19.3		8	84.83	odd	2
588.2.o.b.31.3		8	21.11	odd	6
588.2.o.d.19.3		8	21.20	even	2
588.2.o.d.31.3		8	84.11	even	6
1344.2.bl.i.703.2		8	168.101	even	6
1344.2.bl.i.1279.2		8	24.11	even	2
1344.2.bl.j.703.2		8	168.59	odd	6
1344.2.bl.j.1279.2		8	24.5	odd	2
1764.2.b.i.1567.7		8	28.19	even	6
1764.2.b.i.1567.8		8	7.2	even	3
1764.2.b.j.1567.7		8	28.23	odd	6
1764.2.b.j.1567.8		8	7.5	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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.850516 + 1.12988i) q^{2} +(-0.553244 - 1.92196i) q^{4} +(-0.834598 - 0.481855i) q^{5} +(-1.20103 + 2.35744i) q^{7} +(2.64212 + 1.00956i) q^{8} +O(q^{10})\)	\(q+(-0.850516 + 1.12988i) q^{2} +(-0.553244 - 1.92196i) q^{4} +(-0.834598 - 0.481855i) q^{5} +(-1.20103 + 2.35744i) q^{7} +(2.64212 + 1.00956i) q^{8} +(1.25428 - 0.533167i) q^{10} +(-4.74861 + 2.74161i) q^{11} +3.75117i q^{13} +(-1.64212 - 3.36206i) q^{14} +(-3.38784 + 2.12662i) q^{16} +(0.594545 - 0.343260i) q^{17} +(-2.44109 + 4.22809i) q^{19} +(-0.464369 + 1.87065i) q^{20} +(0.941086 - 7.69713i) q^{22} +(1.07465 + 0.620450i) q^{23} +(-2.03563 - 3.52582i) q^{25} +(-4.23836 - 3.19043i) q^{26} +(5.19536 + 1.00409i) q^{28} +2.48011 q^{29} +(-2.41401 - 4.18119i) q^{31} +(0.478592 - 5.63657i) q^{32} +(-0.117828 + 0.963711i) q^{34} +(2.13832 - 1.38879i) q^{35} +(1.36643 - 2.36673i) q^{37} +(-2.70103 - 6.35418i) q^{38} +(-1.71865 - 2.11569i) q^{40} +9.42976i q^{41} +5.97437i q^{43} +(7.89640 + 7.60984i) q^{44} +(-1.61504 + 0.686521i) q^{46} +(1.80752 - 3.13072i) q^{47} +(-4.11504 - 5.66272i) q^{49} +(5.71508 + 0.698752i) q^{50} +(7.20959 - 2.07531i) q^{52} +(-2.04757 - 3.54650i) q^{53} +5.28424 q^{55} +(-5.55324 + 5.01612i) q^{56} +(-2.10937 + 2.80222i) q^{58} +(6.34315 + 10.9867i) q^{59} +(9.01711 + 5.20603i) q^{61} +(6.77738 + 0.828634i) q^{62} +(5.96158 + 5.33475i) q^{64} +(1.80752 - 3.13072i) q^{65} +(8.17396 - 4.71924i) q^{67} +(-0.988660 - 0.952783i) q^{68} +(-0.249518 + 3.59723i) q^{70} -10.1163i q^{71} +(-5.76850 + 3.33044i) q^{73} +(1.51194 + 3.55685i) q^{74} +(9.47672 + 2.35250i) q^{76} +(-0.759946 - 14.4873i) q^{77} +(1.22492 + 0.707208i) q^{79} +(3.85221 - 0.142425i) q^{80} +(-10.6545 - 8.02016i) q^{82} -0.543780 q^{83} -0.661608 q^{85} +(-6.75030 - 5.08130i) q^{86} +(-15.3142 + 2.44966i) q^{88} +(-0.480107 - 0.277190i) q^{89} +(-8.84315 - 4.50528i) q^{91} +(0.597935 - 2.40870i) q^{92} +(2.00000 + 4.70500i) q^{94} +(4.07465 - 2.35250i) q^{95} +10.8747i q^{97} +(9.89809 + 0.166748i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - q^{4} + 2 q^{7} - 4 q^{8}+O(q^{10}) \) 8 * q - q^2 - q^4 + 2 * q^7 - 4 * q^8	\( 8 q - q^{2} - q^{4} + 2 q^{7} - 4 q^{8} - 5 q^{10} - 6 q^{11} + 12 q^{14} - 17 q^{16} - 6 q^{19} - 22 q^{20} - 6 q^{22} + 2 q^{25} - 18 q^{26} + 13 q^{28} + 16 q^{29} + 6 q^{31} + 9 q^{32} - 28 q^{34} + 12 q^{35} + 6 q^{37} - 10 q^{38} - 17 q^{40} + 23 q^{44} + 24 q^{46} - 4 q^{47} + 4 q^{49} - 2 q^{50} + 16 q^{52} + 4 q^{53} - 8 q^{55} - 41 q^{56} + 37 q^{58} + 14 q^{59} + 12 q^{61} + 48 q^{62} + 2 q^{64} - 4 q^{65} + 42 q^{67} + 26 q^{68} + 3 q^{70} - 18 q^{73} + 10 q^{74} + 44 q^{76} - 8 q^{77} - 6 q^{79} + 39 q^{80} - 10 q^{82} - 4 q^{83} - 32 q^{85} - 36 q^{86} - 37 q^{88} - 34 q^{91} + 28 q^{92} + 16 q^{94} + 24 q^{95} + 53 q^{98}+O(q^{100}) \) 8 * q - q^2 - q^4 + 2 * q^7 - 4 * q^8 - 5 * q^10 - 6 * q^11 + 12 * q^14 - 17 * q^16 - 6 * q^19 - 22 * q^20 - 6 * q^22 + 2 * q^25 - 18 * q^26 + 13 * q^28 + 16 * q^29 + 6 * q^31 + 9 * q^32 - 28 * q^34 + 12 * q^35 + 6 * q^37 - 10 * q^38 - 17 * q^40 + 23 * q^44 + 24 * q^46 - 4 * q^47 + 4 * q^49 - 2 * q^50 + 16 * q^52 + 4 * q^53 - 8 * q^55 - 41 * q^56 + 37 * q^58 + 14 * q^59 + 12 * q^61 + 48 * q^62 + 2 * q^64 - 4 * q^65 + 42 * q^67 + 26 * q^68 + 3 * q^70 - 18 * q^73 + 10 * q^74 + 44 * q^76 - 8 * q^77 - 6 * q^79 + 39 * q^80 - 10 * q^82 - 4 * q^83 - 32 * q^85 - 36 * q^86 - 37 * q^88 - 34 * q^91 + 28 * q^92 + 16 * q^94 + 24 * q^95 + 53 * q^98

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