LMFDB - Embedded newform 504.2.cj.c.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(37,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))

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

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

chi := DirichletCharacter("504.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cj (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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.951588245534976.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 2 x^{10} - 9 x^{9} + 8 x^{8} - 13 x^{7} + 35 x^{6} - 26 x^{5} + 32 x^{4} - 72 x^{3} + \cdots + 64 $ x^12 - x^11 + 2x^10 - 9x^9 + 8x^8 - 13x^7 + 35x^6 - 26x^5 + 32x^4 - 72x^3 + 32x^2 - 32x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.3
Root			$1.41417 - 0.0105323i$ of defining polynomial
Character	$\chi$	$=$	504.37
Dual form			504.2.cj.c.109.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.242117 - 1.39333i) q^{2} +(-1.88276 - 0.674701i) q^{4} +(-1.28690 - 0.742990i) q^{5} +(0.129755 + 2.64257i) q^{7} +(-1.39593 + 2.45995i) q^{8} +O(q^{10})$	\(q+(0.242117 - 1.39333i) q^{2} +(-1.88276 - 0.674701i) q^{4} +(-1.28690 - 0.742990i) q^{5} +(0.129755 + 2.64257i) q^{7} +(-1.39593 + 2.45995i) q^{8} +(-1.34681 + 1.61319i) q^{10} +(-4.37021 + 2.52314i) q^{11} +2.58633i q^{13} +(3.71339 + 0.459019i) q^{14} +(3.08956 + 2.54060i) q^{16} +(0.629755 + 1.09077i) q^{17} +(-2.68324 - 1.54917i) q^{19} +(1.92162 + 2.26714i) q^{20} +(2.45748 + 6.70006i) q^{22} +(-0.697966 + 1.20891i) q^{23} +(-1.39593 - 2.41782i) q^{25} +(3.60362 + 0.626196i) q^{26} +(1.53864 - 5.06286i) q^{28} +0.638384i q^{29} +(1.82772 + 3.16571i) q^{31} +(4.28794 - 3.68966i) q^{32} +(1.67228 - 0.613365i) q^{34} +(1.79642 - 3.49712i) q^{35} +(5.21370 + 3.01013i) q^{37} +(-2.80817 + 3.36357i) q^{38} +(3.62414 - 2.12854i) q^{40} -6.36226 q^{41} +1.02401i q^{43} +(9.93042 - 1.80188i) q^{44} +(1.51543 + 1.26520i) q^{46} +(-5.48316 + 9.49712i) q^{47} +(-6.96633 + 0.685774i) q^{49} +(-3.70682 + 1.35960i) q^{50} +(1.74500 - 4.86944i) q^{52} +(4.99481 - 2.88375i) q^{53} +7.49868 q^{55} +(-6.68172 - 3.36965i) q^{56} +(0.889482 + 0.154564i) q^{58} +(-3.01720 + 1.74198i) q^{59} +(-11.1614 - 6.44406i) q^{61} +(4.85341 - 1.78015i) q^{62} +(-4.10275 - 6.86786i) q^{64} +(1.92162 - 3.32834i) q^{65} +(-0.443410 + 0.256003i) q^{67} +(-0.449735 - 2.47855i) q^{68} +(-4.43771 - 3.34973i) q^{70} +7.41363 q^{71} +(-4.94731 - 8.56899i) q^{73} +(5.45644 - 6.53562i) q^{74} +(4.00667 + 4.72709i) q^{76} +(-7.23463 - 11.2212i) q^{77} +(-4.35341 + 7.54032i) q^{79} +(-2.08830 - 5.56500i) q^{80} +(-1.54041 + 8.86475i) q^{82} -2.97196i q^{83} -1.87161i q^{85} +(1.42679 + 0.247931i) q^{86} +(-0.106298 - 14.2727i) q^{88} +(-1.29186 + 2.23757i) q^{89} +(-6.83456 + 0.335590i) q^{91} +(2.12976 - 1.80517i) q^{92} +(11.9051 + 9.93929i) q^{94} +(2.30203 + 3.98724i) q^{95} -1.57040 q^{97} +(-0.731157 + 9.87246i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 4 q^{7} - 4 q^{8}+O(q^{10}) $ 12 * q + 2 * q^2 - 4 * q^7 - 4 * q^8	$ 12 q + 2 q^{2} - 4 q^{7} - 4 q^{8} - 8 q^{10} + 16 q^{14} + 8 q^{16} + 2 q^{17} - 8 q^{20} + 12 q^{22} - 2 q^{23} - 4 q^{25} + 2 q^{26} + 26 q^{28} + 10 q^{31} + 12 q^{32} + 32 q^{34} - 18 q^{38} + 10 q^{40} + 8 q^{41} + 30 q^{44} - 4 q^{46} - 30 q^{47} - 12 q^{49} + 16 q^{50} - 32 q^{52} + 4 q^{55} + 40 q^{56} - 22 q^{58} + 28 q^{62} + 24 q^{64} - 8 q^{65} - 4 q^{68} - 48 q^{70} - 32 q^{71} - 10 q^{73} - 18 q^{74} + 52 q^{76} - 22 q^{79} - 36 q^{80} - 26 q^{82} - 40 q^{86} - 14 q^{88} + 10 q^{89} + 20 q^{92} + 42 q^{94} + 34 q^{95} + 40 q^{97} - 52 q^{98}+O(q^{100}) $ 12 * q + 2 * q^2 - 4 * q^7 - 4 * q^8 - 8 * q^10 + 16 * q^14 + 8 * q^16 + 2 * q^17 - 8 * q^20 + 12 * q^22 - 2 * q^23 - 4 * q^25 + 2 * q^26 + 26 * q^28 + 10 * q^31 + 12 * q^32 + 32 * q^34 - 18 * q^38 + 10 * q^40 + 8 * q^41 + 30 * q^44 - 4 * q^46 - 30 * q^47 - 12 * q^49 + 16 * q^50 - 32 * q^52 + 4 * q^55 + 40 * q^56 - 22 * q^58 + 28 * q^62 + 24 * q^64 - 8 * q^65 - 4 * q^68 - 48 * q^70 - 32 * q^71 - 10 * q^73 - 18 * q^74 + 52 * q^76 - 22 * q^79 - 36 * q^80 - 26 * q^82 - 40 * q^86 - 14 * q^88 + 10 * q^89 + 20 * q^92 + 42 * q^94 + 34 * q^95 + 40 * q^97 - 52 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$1$

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 $

$2$	0.242117	−	1.39333i	0.171203	−	0.985236i
$2$	0.242117	−	1.39333i	0.171203	−	0.985236i
$3$		0			0
$3$		0			0
$4$	−1.88276	−	0.674701i	−0.941379	−	0.337350i
$5$	−1.28690	−	0.742990i	−0.575518	−	0.332275i	0.183832	−	0.982958i	$-0.441150\pi$
$5$	−1.28690	−	0.742990i	−0.575518	−	0.332275i	−0.759350	+	0.650682i	$0.774483\pi$
$6$		0			0
$7$	0.129755	+	2.64257i	0.0490429	+	0.998797i
$7$	0.129755	+	2.64257i	0.0490429	+	0.998797i
$8$	−1.39593	+	2.45995i	−0.493536	+	0.869725i
$9$		0			0
$10$	−1.34681	+	1.61319i	−0.425900	+	0.510134i
$11$	−4.37021	+	2.52314i	−1.31767	+	0.760756i	−0.983353	−	0.181705i	$-0.941838\pi$
$11$	−4.37021	+	2.52314i	−1.31767	+	0.760756i	−0.334315	+	0.942461i	$0.608505\pi$
$12$		0			0
$13$			2.58633i			0.717320i	0.933468	+	0.358660i	$0.116766\pi$
$13$			2.58633i			0.717320i	−0.933468	+	0.358660i	$0.883234\pi$
$14$	3.71339	+	0.459019i	0.992447	+	0.122678i
$15$		0			0
$16$	3.08956	+	2.54060i	0.772389	+	0.635149i
$17$	0.629755	+	1.09077i	0.152738	+	0.264550i	0.932233	−	0.361858i	$-0.117858\pi$
$17$	0.629755	+	1.09077i	0.152738	+	0.264550i	−0.779495	+	0.626408i	$0.784524\pi$
$18$		0			0
$19$	−2.68324	−	1.54917i	−0.615577	−	0.355404i	0.159568	−	0.987187i	$-0.448990\pi$
$19$	−2.68324	−	1.54917i	−0.615577	−	0.355404i	−0.775145	+	0.631783i	$0.782323\pi$
$20$	1.92162	+	2.26714i	0.429687	+	0.506948i
$21$		0			0
$22$	2.45748	+	6.70006i	0.523936	+	1.42846i
$23$	−0.697966	+	1.20891i	−0.145536	+	0.252076i	−0.929573	−	0.368639i	$-0.879824\pi$
$23$	−0.697966	+	1.20891i	−0.145536	+	0.252076i	0.784037	+	0.620714i	$0.213157\pi$
$24$		0			0
$25$	−1.39593	−	2.41782i	−0.279186	−	0.483565i
$26$	3.60362	+	0.626196i	0.706729	+	0.122807i
$27$		0			0
$28$	1.53864	−	5.06286i	0.290776	−	0.956791i
$29$			0.638384i			0.118545i	0.998242	+	0.0592725i	$0.0188781\pi$
$29$			0.638384i			0.118545i	−0.998242	+	0.0592725i	$0.981122\pi$
$30$		0			0
$31$	1.82772	+	3.16571i	0.328268	+	0.568578i	0.982168	−	0.188003i	$-0.0602016\pi$
$31$	1.82772	+	3.16571i	0.328268	+	0.568578i	−0.653900	+	0.756581i	$0.726868\pi$
$32$	4.28794	−	3.68966i	0.758007	−	0.652246i
$33$		0			0
$34$	1.67228	−	0.613365i	0.286793	−	0.105191i
$35$	1.79642	−	3.49712i	0.303650	−	0.591121i
$36$		0			0
$37$	5.21370	+	3.01013i	0.857127	+	0.494862i	0.863049	−	0.505120i	$-0.168552\pi$
$37$	5.21370	+	3.01013i	0.857127	+	0.494862i	−0.00592229	+	0.999982i	$0.501885\pi$
$38$	−2.80817	+	3.36357i	−0.455545	+	0.545643i
$39$		0			0
$40$	3.62414	−	2.12854i	0.573027	−	0.336552i
$41$	−6.36226			−0.993618			−0.496809	−	0.867860i	$-0.665495\pi$
$41$	−6.36226			−0.993618			−0.496809	+	0.867860i	$0.665495\pi$
$42$		0			0
$43$			1.02401i			0.156160i	0.996947	+	0.0780801i	$0.0248790\pi$
$43$			1.02401i			0.156160i	−0.996947	+	0.0780801i	$0.975121\pi$
$44$	9.93042	−	1.80188i	1.49707	−	0.271644i
$45$		0			0
$46$	1.51543	+	1.26520i	0.223438	+	0.186543i
$47$	−5.48316	+	9.49712i	−0.799802	+	1.38530i	0.119943	+	0.992781i	$0.461729\pi$
$47$	−5.48316	+	9.49712i	−0.799802	+	1.38530i	−0.919745	+	0.392516i	$0.871605\pi$
$48$		0			0
$49$	−6.96633	+	0.685774i	−0.995190	+	0.0979677i
$50$	−3.70682	+	1.35960i	−0.524223	+	0.192277i
$51$		0			0
$52$	1.74500	−	4.86944i	0.241988	−	0.675270i
$53$	4.99481	−	2.88375i	0.686089	−	0.396114i	−0.116056	−	0.993243i	$-0.537025\pi$
$53$	4.99481	−	2.88375i	0.686089	−	0.396114i	0.802145	+	0.597129i	$0.203692\pi$
$54$		0			0
$55$	7.49868			1.01112
$56$	−6.68172	−	3.36965i	−0.892883	−	0.450289i
$57$		0			0
$58$	0.889482	+	0.154564i	0.116795	+	0.0202952i
$59$	−3.01720	+	1.74198i	−0.392806	+	0.226787i	−0.683375	−	0.730067i	$-0.739489\pi$
$59$	−3.01720	+	1.74198i	−0.392806	+	0.226787i	0.290569	+	0.956854i	$0.406155\pi$
$60$		0			0
$61$	−11.1614	−	6.44406i	−1.42908	−	0.825077i	−0.432028	−	0.901860i	$-0.642202\pi$
$61$	−11.1614	−	6.44406i	−1.42908	−	0.825077i	−0.997048	+	0.0767831i	$0.975535\pi$
$62$	4.85341	−	1.78015i	0.616383	−	0.226080i
$63$		0			0
$64$	−4.10275	−	6.86786i	−0.512844	−	0.858482i
$65$	1.92162	−	3.32834i	0.238348	−	0.412830i
$66$		0			0
$67$	−0.443410	+	0.256003i	−0.0541711	+	0.0312757i	−0.526841	−	0.849964i	$-0.676624\pi$
$67$	−0.443410	+	0.256003i	−0.0541711	+	0.0312757i	0.472670	+	0.881240i	$0.343290\pi$
$68$	−0.449735	−	2.47855i	−0.0545384	−	0.300568i
$69$		0			0
$70$	−4.43771	−	3.34973i	−0.530408	−	0.400369i
$71$	7.41363			0.879836			0.439918	−	0.898038i	$-0.355007\pi$
$71$	7.41363			0.879836			0.439918	+	0.898038i	$0.355007\pi$
$72$		0			0
$73$	−4.94731	−	8.56899i	−0.579038	−	1.00292i	−0.995590	−	0.0938118i	$-0.970095\pi$
$73$	−4.94731	−	8.56899i	−0.579038	−	1.00292i	0.416552	−	0.909112i	$-0.363239\pi$
$74$	5.45644	−	6.53562i	0.634299	−	0.759750i
$75$		0			0
$76$	4.00667	+	4.72709i	0.459596	+	0.542235i
$77$	−7.23463	−	11.2212i	−0.824463	−	1.27877i
$78$		0			0
$79$	−4.35341	+	7.54032i	−0.489797	+	0.848353i	−0.999931	−	0.0117420i	$-0.996262\pi$
$79$	−4.35341	+	7.54032i	−0.489797	+	0.848353i	0.510134	+	0.860095i	$0.329596\pi$
$80$	−2.08830	−	5.56500i	−0.233479	−	0.622185i
$81$		0			0
$82$	−1.54041	+	8.86475i	−0.170110	+	0.978948i
$83$		−	2.97196i		−	0.326215i	−0.986608	−	0.163107i	$-0.947848\pi$
$83$		−	2.97196i		−	0.326215i	0.986608	−	0.163107i	$-0.0521517\pi$
$84$		0			0
$85$		−	1.87161i		−	0.203004i
$86$	1.42679	+	0.247931i	0.153855	+	0.0267351i
$87$		0			0
$88$	−0.106298	−	14.2727i	−0.0113314	−	1.52147i
$89$	−1.29186	+	2.23757i	−0.136937	+	0.237182i	−0.926336	−	0.376699i	$-0.877059\pi$
$89$	−1.29186	+	2.23757i	−0.136937	+	0.237182i	0.789399	+	0.613881i	$0.210393\pi$
$90$		0			0
$91$	−6.83456	+	0.335590i	−0.716456	+	0.0351794i
$92$	2.12976	−	1.80517i	0.222042	−	0.188202i
$93$		0			0
$94$	11.9051	+	9.93929i	1.22792	+	1.02516i
$95$	2.30203	+	3.98724i	0.236184	+	0.409082i
$96$		0			0
$97$	−1.57040			−0.159449			−0.0797247	−	0.996817i	$-0.525404\pi$
$97$	−1.57040			−0.159449			−0.0797247	+	0.996817i	$0.525404\pi$
$98$	−0.731157	+	9.87246i	−0.0738580	+	0.997269i
$99$		0			0
$100$	0.996894	+	5.49402i	0.0996894	+	0.549402i
$101$	−0.181183	+	0.104606i	−0.0180284	+	0.0104087i	−0.508987	−	0.860774i	$-0.669980\pi$
$101$	−0.181183	+	0.104606i	−0.0180284	+	0.0104087i	0.490959	+	0.871183i	$0.336647\pi$
$102$		0			0
$103$	−3.43846	+	5.95558i	−0.338801	+	0.586821i	−0.984207	−	0.177019i	$-0.943355\pi$
$103$	−3.43846	+	5.95558i	−0.338801	+	0.586821i	0.645406	+	0.763839i	$0.276688\pi$
$104$	−6.36226	−	3.61034i	−0.623871	−	0.354023i
$105$		0			0
$106$	−2.80870	−	7.65764i	−0.272805	−	0.743776i
$107$	11.2048	+	6.46908i	1.08321	+	0.625389i	0.931759	−	0.363076i	$-0.118274\pi$
$107$	11.2048	+	6.46908i	1.08321	+	0.625389i	0.151447	+	0.988465i	$0.451607\pi$
$108$		0			0
$109$	16.6430	−	9.60883i	1.59411	−	0.920359i	0.601517	−	0.798860i	$-0.294563\pi$
$109$	16.6430	−	9.60883i	1.59411	−	0.920359i	0.992591	−	0.121500i	$-0.0387703\pi$
$110$	1.81556	−	10.4482i	0.173107	−	0.996193i
$111$		0			0
$112$	−6.31281	+	8.49402i	−0.596505	+	0.802610i
$113$	1.05137			0.0989050			0.0494525	−	0.998776i	$-0.484252\pi$
$113$	1.05137			0.0989050			0.0494525	+	0.998776i	$0.484252\pi$
$114$		0			0
$115$	1.79642	−	1.03716i	0.167517	−	0.0967160i
$116$	0.430718	−	1.20192i	0.0399912	−	0.111596i
$117$		0			0
$118$	1.69665	+	4.62573i	0.156189	+	0.425833i
$119$	−2.80071	+	1.80570i	−0.256741	+	0.165529i
$120$		0			0
$121$	7.23250	−	12.5271i	0.657500	−	1.13882i
$122$	−11.6811	+	13.9914i	−1.05756	+	1.26672i
$123$		0			0
$124$	−1.30525	−	7.19342i	−0.117215	−	0.645989i
$125$			11.5786i			1.03562i
$126$		0			0
$127$	−7.20814			−0.639619			−0.319809	−	0.947482i	$-0.603619\pi$
$127$	−7.20814			−0.639619			−0.319809	+	0.947482i	$0.603619\pi$
$128$	−10.5626	+	4.05367i	−0.933608	+	0.358297i
$129$		0			0
$130$	−4.17223	−	3.48331i	−0.365929	−	0.305506i
$131$	−12.7767	−	7.37662i	−1.11630	−	0.644498i	−0.175849	−	0.984417i	$-0.556267\pi$
$131$	−12.7767	−	7.37662i	−1.11630	−	0.644498i	−0.940455	+	0.339919i	$0.889600\pi$
$132$		0			0
$133$	3.74562	−	7.29165i	0.324786	−	0.632267i
$134$	0.249340	+	0.679801i	0.0215397	+	0.0587258i
$135$		0			0
$136$	−3.56233	+	0.0265311i	−0.305468	+	0.00227502i
$137$	−4.68113	−	8.10795i	−0.399936	−	0.692709i	0.593782	−	0.804626i	$-0.297634\pi$
$137$	−4.68113	−	8.10795i	−0.399936	−	0.692709i	−0.993718	+	0.111917i	$0.964301\pi$
$138$		0			0
$139$			1.69519i			0.143784i	0.997412	+	0.0718921i	$0.0229037\pi$
$139$			1.69519i			0.143784i	−0.997412	+	0.0718921i	$0.977096\pi$
$140$	−5.74173	+	5.37218i	−0.485265	+	0.454032i
$141$		0			0
$142$	1.79497	−	10.3297i	0.150630	−	0.866846i
$143$	−6.52569	−	11.3028i	−0.545705	−	0.945189i
$144$		0			0
$145$	0.474313	−	0.821534i	0.0393895	−	0.0682247i
$146$	−13.1373	+	4.81855i	−1.08725	+	0.398786i
$147$		0			0
$148$	−7.78520	−	9.18503i	−0.639939	−	0.755005i
$149$	3.19276	+	1.84334i	0.261561	+	0.151012i	0.625047	−	0.780587i	$-0.285080\pi$
$149$	3.19276	+	1.84334i	0.261561	+	0.151012i	−0.363485	+	0.931600i	$0.618413\pi$
$150$		0			0
$151$	7.13861	+	12.3644i	0.580932	+	1.00620i	0.995369	+	0.0961252i	$0.0306449\pi$
$151$	7.13861	+	12.3644i	0.580932	+	1.00620i	−0.414438	+	0.910078i	$0.636022\pi$
$152$	7.55650	−	4.43811i	0.612913	−	0.359978i
$153$		0			0
$154$	−17.3865	+	7.36342i	−1.40104	+	0.593361i
$155$		−	5.43191i		−	0.436302i
$156$		0			0
$157$	−11.1614	+	6.44406i	−0.890780	+	0.514292i	−0.874197	−	0.485571i	$-0.838612\pi$
$157$	−11.1614	+	6.44406i	−0.890780	+	0.514292i	−0.0165822	+	0.999863i	$0.505279\pi$
$158$	9.45215	+	7.89139i	0.751973	+	0.627806i
$159$		0			0
$160$	−8.25951	+	1.56232i	−0.652972	+	0.123512i
$161$	−3.28520	−	1.68756i	−0.258910	−	0.132998i
$162$		0			0
$163$	2.79831	+	1.61560i	0.219180	+	0.126544i	0.605571	−	0.795791i	$-0.292945\pi$
$163$	2.79831	+	1.61560i	0.219180	+	0.126544i	−0.386390	+	0.922335i	$0.626278\pi$
$164$	11.9786	+	4.29262i	0.935371	+	0.335197i
$165$		0			0
$166$	−4.14093	−	0.719563i	−0.321399	−	0.0558489i
$167$	14.0487			1.08712			0.543562	−	0.839369i	$-0.317075\pi$
$167$	14.0487			1.08712			0.543562	+	0.839369i	$0.317075\pi$
$168$		0			0
$169$	6.31088			0.485453
$170$	−2.60777	−	0.453149i	−0.200007	−	0.0347549i
$171$		0			0
$172$	0.690901	−	1.92797i	0.0526807	−	0.147006i
$173$	5.66273	+	3.26938i	0.430529	+	0.248566i	0.699572	−	0.714562i	$-0.253374\pi$
$173$	5.66273	+	3.26938i	0.430529	+	0.248566i	−0.269043	+	0.963128i	$0.586707\pi$
$174$		0			0
$175$	6.20814	−	4.00257i	0.469291	−	0.302566i
$176$	−19.9123	−	3.30755i	−1.50095	−	0.249316i
$177$		0			0
$178$	2.80490	+	2.34175i	0.210236	+	0.175522i
$179$	0.109447	−	0.0631891i	0.00818044	−	0.00472298i	−0.495904	−	0.868377i	$-0.665163\pi$
$179$	0.109447	−	0.0631891i	0.00818044	−	0.00472298i	0.504085	+	0.863654i	$0.331830\pi$
$180$		0			0
$181$			2.71920i			0.202117i	0.994880	+	0.101058i	$0.0322229\pi$
$181$			2.71920i			0.202117i	−0.994880	+	0.101058i	$0.967777\pi$
$182$	−1.18718	+	9.60407i	−0.0879994	+	0.711901i
$183$		0			0
$184$	−1.99956	−	3.40452i	−0.147409	−	0.250985i
$185$	−4.47299	−	7.74745i	−0.328861	−	0.569604i
$186$		0			0
$187$	−5.50433	−	3.17793i	−0.402516	−	0.232393i
$188$	16.7312	−	14.1813i	1.22025	−	1.03428i
$189$		0			0
$190$	6.11292	−	2.24212i	0.443478	−	0.162661i
$191$	−1.22365	+	2.11943i	−0.0885404	+	0.153357i	−0.906894	−	0.421358i	$-0.861554\pi$
$191$	−1.22365	+	2.11943i	−0.0885404	+	0.153357i	0.818354	+	0.574715i	$0.194887\pi$
$192$		0			0
$193$	−1.97431	−	3.41961i	−0.142114	−	0.246149i	0.786178	−	0.618000i	$-0.212057\pi$
$193$	−1.97431	−	3.41961i	−0.142114	−	0.246149i	−0.928293	+	0.371851i	$0.878723\pi$
$194$	−0.380220	+	2.18808i	−0.0272982	+	0.157095i
$195$		0			0
$196$	13.5786	+	3.40904i	0.969900	+	0.243503i
$197$			19.5468i			1.39265i	0.717727	+	0.696325i	$0.245183\pi$
$197$			19.5468i			1.39265i	−0.717727	+	0.696325i	$0.754817\pi$
$198$		0			0
$199$	−10.3981	−	18.0101i	−0.737103	−	1.27670i	−0.953795	−	0.300460i	$-0.902860\pi$
$199$	−10.3981	−	18.0101i	−0.737103	−	1.27670i	0.216692	−	0.976240i	$-0.430473\pi$
$200$	7.89636	−	0.0588095i	0.558357	−	0.00415846i
$201$		0			0
$202$	0.101884	+	0.277775i	0.00716850	+	0.0195442i
$203$	−1.68697	+	0.0828337i	−0.118402	+	0.00581378i
$204$		0			0
$205$	8.18757	+	4.72709i	0.571845	+	0.330155i
$206$	7.46560	+	6.23287i	0.520153	+	0.434264i
$207$		0			0
$208$	−6.57083	+	7.99062i	−0.455605	+	0.554050i
$209$	15.6351			1.08150
$210$		0			0
$211$			17.2132i			1.18500i	0.805569	+	0.592502i	$0.201860\pi$
$211$			17.2132i			1.18500i	−0.805569	+	0.592502i	$0.798140\pi$
$212$	−11.3497	+	2.05941i	−0.779499	+	0.141441i
$213$		0			0
$214$	11.7265	−	14.0457i	0.801604	−	0.960145i
$215$	0.760830	−	1.31780i	0.0518882	−	0.0898730i
$216$		0			0
$217$	−8.12844	+	5.24064i	−0.551794	+	0.355758i
$218$	−9.35875	−	25.5157i	−0.633855	−	1.72814i
$219$		0			0
$220$	−14.1182	−	5.05936i	−0.951849	−	0.341102i
$221$	−2.82109	+	1.62876i	−0.189767	+	0.109562i
$222$		0			0
$223$	17.5164			1.17298			0.586492	−	0.809955i	$-0.300509\pi$
$223$	17.5164			1.17298			0.586492	+	0.809955i	$0.300509\pi$
$224$	10.3066	+	10.8524i	0.688636	+	0.725107i
$225$		0			0
$226$	0.254556	−	1.46492i	0.0169328	−	0.0974447i
$227$	11.4237	−	6.59546i	0.758215	−	0.437756i	−0.0704394	−	0.997516i	$-0.522440\pi$
$227$	11.4237	−	6.59546i	0.758215	−	0.437756i	0.828655	+	0.559760i	$0.189107\pi$
$228$		0			0
$229$	14.8693	+	8.58482i	0.982594	+	0.567301i	0.903052	−	0.429531i	$-0.141321\pi$
$229$	14.8693	+	8.58482i	0.982594	+	0.567301i	0.0795417	+	0.996832i	$0.474654\pi$
$230$	−1.01017	−	2.75413i	−0.0666087	−	0.181602i
$231$		0			0
$232$	−1.57040	−	0.891141i	−0.103102	−	0.0585062i
$233$	12.4393	−	21.5455i	0.814927	−	1.41149i	−0.0944534	−	0.995529i	$-0.530110\pi$
$233$	12.4393	−	21.5455i	0.814927	−	1.41149i	0.909380	−	0.415966i	$-0.136556\pi$
$234$		0			0
$235$	14.1125	−	8.14787i	0.920600	−	0.531508i
$236$	6.85598	−	1.24402i	0.446286	−	0.0809791i
$237$		0			0
$238$	1.83785	+	4.33952i	0.119130	+	0.281289i
$239$	13.3242			0.861872			0.430936	−	0.902383i	$-0.358183\pi$
$239$	13.3242			0.861872			0.430936	+	0.902383i	$0.358183\pi$
$240$		0			0
$241$	11.1218	+	19.2635i	0.716416	+	1.24087i	0.962411	+	0.271598i	$0.0875521\pi$
$241$	11.1218	+	19.2635i	0.716416	+	1.24087i	−0.245995	+	0.969271i	$0.579115\pi$
$242$	−15.7033	−	13.1103i	−1.00944	−	0.842763i
$243$		0			0
$244$	16.6665	+	19.6632i	1.06696	+	1.25881i
$245$	9.47446	+	4.29339i	0.605301	+	0.274295i
$246$		0			0
$247$	4.00667	−	6.93975i	0.254938	−	0.441566i
$248$	−10.3389	+	0.0770004i	−0.656519	+	0.00488953i
$249$		0			0
$250$	16.1328	+	2.80337i	1.02033	+	0.177301i
$251$			27.4386i			1.73191i	0.500121	+	0.865955i	$0.333289\pi$
$251$			27.4386i			1.73191i	−0.500121	+	0.865955i	$0.666711\pi$
$252$		0			0
$253$		−	7.04427i		−	0.442870i
$254$	−1.74522	+	10.0433i	−0.109505	+	0.630175i
$255$		0			0
$256$	3.09074	+	15.6986i	0.193171	+	0.981165i
$257$	−12.0948	+	20.9487i	−0.754451	+	1.30675i	0.191196	+	0.981552i	$0.438763\pi$
$257$	−12.0948	+	20.9487i	−0.754451	+	1.30675i	−0.945647	+	0.325195i	$0.894570\pi$
$258$		0			0
$259$	−7.27797	+	14.1681i	−0.452231	+	0.880365i
$260$	−5.86358	+	4.96995i	−0.363644	+	0.308223i
$261$		0			0
$262$	−13.3715	+	16.0162i	−0.826097	+	0.989482i
$263$	−5.43846	−	9.41968i	−0.335350	−	0.580842i	0.648202	−	0.761468i	$-0.275521\pi$
$263$	−5.43846	−	9.41968i	−0.335350	−	0.580842i	−0.983552	+	0.180626i	$0.942188\pi$
$264$		0			0
$265$	−8.57040			−0.526475
$266$	−9.25283	−	6.98433i	−0.567327	−	0.428237i
$267$		0			0
$268$	1.00756	−	0.182822i	0.0615465	−	0.0111677i
$269$	20.7887	−	12.0024i	1.26751	−	0.731796i	0.292992	−	0.956115i	$-0.405349\pi$
$269$	20.7887	−	12.0024i	1.26751	−	0.731796i	0.974516	+	0.224319i	$0.0720156\pi$
$270$		0			0
$271$	−3.11160	+	5.38945i	−0.189016	+	0.327386i	−0.944922	−	0.327294i	$-0.893863\pi$
$271$	−3.11160	+	5.38945i	−0.189016	+	0.327386i	0.755906	+	0.654680i	$0.227197\pi$
$272$	−0.825537	+	4.96995i	−0.0500555	+	0.301347i
$273$		0			0
$274$	−12.4305	+	4.55930i	−0.750952	+	0.275437i
$275$	12.2010	+	7.04427i	0.735750	+	0.424786i
$276$		0			0
$277$	−24.2493	+	14.0003i	−1.45700	+	0.841199i	−0.998863	−	0.0476832i	$-0.984816\pi$
$277$	−24.2493	+	14.0003i	−1.45700	+	0.841199i	−0.458136	+	0.888882i	$0.651483\pi$
$278$	2.36197	+	0.410435i	0.141661	+	0.0246163i
$279$		0			0
$280$	6.09507	+	9.30085i	0.364250	+	0.555832i
$281$	16.7112			0.996906			0.498453	−	0.866917i	$-0.333902\pi$
$281$	16.7112			0.996906			0.498453	+	0.866917i	$0.333902\pi$
$282$		0			0
$283$	24.1193	−	13.9253i	1.43374	−	0.827772i	0.436339	−	0.899782i	$-0.356275\pi$
$283$	24.1193	−	13.9253i	1.43374	−	0.827772i	0.997404	+	0.0720102i	$0.0229414\pi$
$284$	−13.9581	−	5.00198i	−0.828260	−	0.296813i
$285$		0			0
$286$	−17.3286	+	6.35585i	−1.02466	+	0.375829i
$287$	−0.825537	−	16.8127i	−0.0487299	−	0.992422i
$288$		0			0
$289$	7.70682	−	13.3486i	0.453342	−	0.785212i
$290$	−1.02983	−	0.859784i	−0.0604738	−	0.0504882i
$291$		0			0
$292$	3.53308	+	19.4713i	0.206758	+	1.13947i
$293$		−	20.1851i		−	1.17923i	−0.807685	−	0.589614i	$-0.799280\pi$
$293$		−	20.1851i		−	1.17923i	0.807685	−	0.589614i	$-0.200720\pi$
$294$		0			0
$295$	5.17710			0.301423
$296$	−14.6828	+	8.62352i	−0.853418	+	0.501232i
$297$		0			0
$298$	3.34141	−	4.00228i	0.193563	−	0.231846i
$299$	−3.12665	−	1.80517i	−0.180819	−	0.104396i
$300$		0			0
$301$	−2.70602	+	0.132871i	−0.155972	+	0.00765855i
$302$	18.9562	−	6.95282i	1.09080	−	0.400090i
$303$		0			0
$304$	−4.35421	−	11.6033i	−0.249731	−	0.665494i
$305$	9.57574	+	16.5857i	0.548305	+	0.949693i
$306$		0			0
$307$			17.8844i			1.02071i	0.859962	+	0.510357i	$0.170487\pi$
$307$			17.8844i			1.02071i	−0.859962	+	0.510357i	$0.829513\pi$
$308$	6.05012	+	26.0080i	0.344738	+	1.48194i
$309$		0			0
$310$	−7.56847	−	1.31516i	−0.429860	−	0.0746961i
$311$	−0.715667	−	1.23957i	−0.0405818	−	0.0702897i	0.845021	−	0.534733i	$-0.179588\pi$
$311$	−0.715667	−	1.23957i	−0.0405818	−	0.0702897i	−0.885603	+	0.464443i	$0.846254\pi$
$312$		0			0
$313$	−2.42829	+	4.20591i	−0.137255	+	0.237732i	−0.926457	−	0.376402i	$-0.877161\pi$
$313$	−2.42829	+	4.20591i	−0.137255	+	0.237732i	0.789202	+	0.614134i	$0.210495\pi$
$314$	6.27635	+	17.1118i	0.354195	+	0.965676i
$315$		0			0
$316$	13.2839	−	11.2594i	0.747277	−	0.633389i
$317$	−9.78002	−	5.64650i	−0.549301	−	0.317139i	0.199539	−	0.979890i	$-0.436056\pi$
$317$	−9.78002	−	5.64650i	−0.549301	−	0.317139i	−0.748840	+	0.662751i	$0.769389\pi$
$318$		0			0
$319$	−1.61073	−	2.78987i	−0.0901838	−	0.156203i
$320$	0.177064	+	11.8865i	0.00989815	+	0.664477i
$321$		0			0
$322$	−3.14674	+	4.16879i	−0.175361	+	0.232318i
$323$		−	3.90239i		−	0.217135i
$324$		0			0
$325$	6.25330	−	3.61034i	0.346871	−	0.200266i
$326$	2.92860	−	3.50781i	0.162200	−	0.194280i
$327$		0			0
$328$	8.88128	−	15.6509i	0.490387	−	0.864174i
$329$	−25.8082	−	13.2573i	−1.42285	−	0.730900i
$330$		0			0
$331$	−20.6415	−	11.9174i	−1.13456	−	0.655039i	−0.189483	−	0.981884i	$-0.560681\pi$
$331$	−20.6415	−	11.9174i	−1.13456	−	0.655039i	−0.945078	+	0.326845i	$0.894014\pi$
$332$	−2.00518	+	5.59548i	−0.110049	+	0.307092i
$333$		0			0
$334$	3.40144	−	19.5746i	0.186119	−	1.07107i
$335$	0.760830			0.0415686
$336$		0			0
$337$	16.4650			0.896906			0.448453	−	0.893806i	$-0.351975\pi$
$337$	16.4650			0.896906			0.448453	+	0.893806i	$0.351975\pi$
$338$	1.52797	−	8.79317i	0.0831109	−	0.478285i
$339$		0			0
$340$	−1.26277	+	3.52378i	−0.0684836	+	0.191104i
$341$	−15.9751	−	9.22320i	−0.865098	−	0.499465i
$342$		0			0
$343$	−2.71612	−	18.3200i	−0.146657	−	0.989187i
$344$	−2.51902	−	1.42945i	−0.135817	−	0.0770708i
$345$		0			0
$346$	5.92638	−	7.09850i	0.318604	−	0.381618i
$347$	−2.78706	+	1.60911i	−0.149617	+	0.0863817i	−0.572940	−	0.819597i	$-0.694197\pi$
$347$	−2.78706	+	1.60911i	−0.149617	+	0.0863817i	0.423322	+	0.905979i	$0.360864\pi$
$348$		0			0
$349$			22.8716i			1.22429i	0.790747	+	0.612143i	$0.209692\pi$
$349$			22.8716i			1.22429i	−0.790747	+	0.612143i	$0.790308\pi$
$350$	−4.07382	−	9.61910i	−0.217755	−	0.514162i
$351$		0			0
$352$	−9.42964	+	26.9437i	−0.502601	+	1.43610i
$353$	11.6608	+	20.1971i	0.620641	+	1.07498i	0.989367	+	0.145444i	$0.0464609\pi$
$353$	11.6608	+	20.1971i	0.620641	+	1.07498i	−0.368725	+	0.929538i	$0.620206\pi$
$354$		0			0
$355$	−9.54058	−	5.50826i	−0.506361	−	0.292348i
$356$	3.94196	−	3.34119i	0.208923	−	0.177083i
$357$		0			0
$358$	−0.0615446	−	0.167795i	−0.00325273	−	0.00886825i
$359$	−2.55488	+	4.42518i	−0.134841	+	0.233552i	−0.925537	−	0.378658i	$-0.876386\pi$
$359$	−2.55488	+	4.42518i	−0.134841	+	0.233552i	0.790696	+	0.612210i	$0.209719\pi$
$360$		0			0
$361$	−4.70015	−	8.14090i	−0.247376	−	0.428468i
$362$	3.78876	+	0.658366i	0.199133	+	0.0346030i
$363$		0			0
$364$	13.0942	+	3.97945i	0.686325	+	0.208580i
$365$			14.7032i			0.769600i
$366$		0			0
$367$	−14.0779	−	24.3837i	−0.734862	−	1.27282i	−0.954784	−	0.297301i	$-0.903914\pi$
$367$	−14.0779	−	24.3837i	−0.734862	−	1.27282i	0.219922	−	0.975517i	$-0.429420\pi$
$368$	−5.22777	+	1.96176i	−0.272516	+	0.102264i
$369$		0			0
$370$	−11.8778	+	4.35658i	−0.617496	+	0.226488i
$371$	8.26861	+	12.8249i	0.429285	+	0.665837i
$372$		0			0
$373$	−6.10052	−	3.52214i	−0.315873	−	0.182369i	0.333679	−	0.942687i	$-0.391710\pi$
$373$	−6.10052	−	3.52214i	−0.315873	−	0.182369i	−0.649551	+	0.760318i	$0.725043\pi$
$374$	−5.76060	+	6.89994i	−0.297874	+	0.356787i
$375$		0			0
$376$	−15.7084	−	26.7457i	−0.810096	−	1.37930i
$377$	−1.65107			−0.0850346
$378$		0			0
$379$		−	13.1974i		−	0.677905i	−0.940803	−	0.338953i	$-0.889927\pi$
$379$		−	13.1974i		−	0.677905i	0.940803	−	0.338953i	$-0.110073\pi$
$380$	−1.64398	−	9.06019i	−0.0843344	−	0.464778i
$381$		0			0
$382$	2.65680	+	2.21811i	0.135934	+	0.113488i
$383$	−2.46546	+	4.27031i	−0.125979	+	0.218202i	−0.922115	−	0.386915i	$-0.873541\pi$
$383$	−2.46546	+	4.27031i	−0.125979	+	0.218202i	0.796136	+	0.605118i	$0.206874\pi$
$384$		0			0
$385$	0.972993	+	19.8158i	0.0495883	+	1.00991i
$386$	−5.24267	+	1.92293i	−0.266845	+	0.0978746i
$387$		0			0
$388$	2.95667	+	1.05955i	0.150102	+	0.0537903i
$389$	−19.8735	+	11.4739i	−1.00762	+	0.581752i	−0.910495	−	0.413520i	$-0.864299\pi$
$389$	−19.8735	+	11.4739i	−1.00762	+	0.581752i	−0.0971291	+	0.995272i	$0.530966\pi$
$390$		0			0
$391$	−1.75819			−0.0889155
$392$	8.03755	−	18.0941i	0.405957	−	0.913892i
$393$		0			0
$394$	27.2352	+	4.73261i	1.37209	+	0.238426i
$395$	11.2048	−	6.46908i	0.563773	−	0.325495i
$396$		0			0
$397$	−25.9079	−	14.9579i	−1.30028	−	0.750716i	−0.319827	−	0.947476i	$-0.603625\pi$
$397$	−25.9079	−	14.9579i	−1.30028	−	0.750716i	−0.980452	+	0.196760i	$0.936958\pi$
$398$	−27.6116	+	10.1275i	−1.38404	+	0.507646i
$399$		0			0
$400$	1.82991	−	11.0165i	0.0914953	−	0.550826i
$401$	−7.83525	+	13.5711i	−0.391274	+	0.677706i	−0.992618	−	0.121284i	$-0.961299\pi$
$401$	−7.83525	+	13.5711i	−0.391274	+	0.677706i	0.601344	+	0.798990i	$0.294632\pi$
$402$		0			0
$403$	−8.18757	+	4.72709i	−0.407852	+	0.235473i
$404$	0.411701	−	0.0747036i	0.0204829	−	0.00371664i
$405$		0			0
$406$	−0.293030	+	2.37057i	−0.0145429	+	0.117650i
$407$	−30.3800			−1.50588
$408$		0			0
$409$	13.0434	+	22.5918i	0.644954	+	1.11709i	0.984312	+	0.176436i	$0.0564568\pi$
$409$	13.0434	+	22.5918i	0.644954	+	1.11709i	−0.339358	+	0.940657i	$0.610210\pi$
$410$	8.56877	−	10.2635i	0.423182	−	0.506878i
$411$		0			0
$412$	10.4920	−	8.89299i	0.516904	−	0.438126i
$413$	−4.99481	−	7.74713i	−0.245778	−	0.381211i
$414$		0			0
$415$	−2.20814	+	3.82460i	−0.108393	+	0.187742i
$416$	9.54269	+	11.0900i	0.467869	+	0.543733i
$417$		0			0
$418$	3.78553	−	21.7849i	0.185156	−	1.06554i
$419$		−	0.252757i		−	0.0123480i	−0.999981	−	0.00617398i	$-0.998035\pi$
$419$		−	0.252757i		−	0.0123480i	0.999981	−	0.00617398i	$-0.00196525\pi$
$420$		0			0
$421$			18.3701i			0.895302i	0.894208	+	0.447651i	$0.147739\pi$
$421$			18.3701i			0.895302i	−0.894208	+	0.447651i	$0.852261\pi$
$422$	23.9837	+	4.16761i	1.16751	+	0.202876i
$423$		0			0
$424$	0.121490	+	16.3125i	0.00590009	+	0.792206i
$425$	1.75819	−	3.04528i	0.0852848	−	0.147718i
$426$		0			0
$427$	15.5806	−	30.3310i	0.753998	−	1.46782i
$428$	−16.7312	−	19.7396i	−0.808732	−	0.954148i
$429$		0			0
$430$	−1.65192	−	1.37915i	−0.0796627	−	0.0665086i
$431$	13.7223	+	23.7678i	0.660982	+	1.14485i	0.980358	+	0.197226i	$0.0631932\pi$
$431$	13.7223	+	23.7678i	0.660982	+	1.14485i	−0.319377	+	0.947628i	$0.603473\pi$
$432$		0			0
$433$	−7.26215			−0.348997			−0.174498	−	0.984657i	$-0.555830\pi$
$433$	−7.26215			−0.348997			−0.174498	+	0.984657i	$0.555830\pi$
$434$	5.33393	+	12.5945i	0.256037	+	0.604554i
$435$		0			0
$436$	−37.8178	+	6.86207i	−1.81114	+	0.328634i
$437$	3.74562	−	2.16253i	0.179177	−	0.103448i
$438$		0			0
$439$	−15.0022	+	25.9845i	−0.716015	+	1.24017i	0.246551	+	0.969130i	$0.420703\pi$
$439$	−15.0022	+	25.9845i	−0.716015	+	1.24017i	−0.962567	+	0.271045i	$0.912631\pi$
$440$	−10.4676	+	18.4464i	−0.499025	+	0.879398i
$441$		0			0
$442$	1.58637	+	4.32507i	0.0754558	+	0.205723i
$443$	−30.3838	−	17.5421i	−1.44358	−	0.833451i	−0.445493	−	0.895285i	$-0.646972\pi$
$443$	−30.3838	−	17.5421i	−1.44358	−	0.833451i	−0.998086	+	0.0618342i	$0.980305\pi$
$444$		0			0
$445$	3.32499	−	1.91968i	0.157620	−	0.0910017i
$446$	4.24102	−	24.4062i	0.200818	−	1.15567i
$447$		0			0
$448$	17.6164	−	11.7329i	0.832298	−	0.554329i
$449$	21.0107			0.991556			0.495778	−	0.868449i	$-0.334883\pi$
$449$	21.0107			0.991556			0.495778	+	0.868449i	$0.334883\pi$
$450$		0			0
$451$	27.8044	−	16.0529i	1.30926	−	0.755901i
$452$	−1.97948	−	0.709363i	−0.0931071	−	0.0333656i
$453$		0			0
$454$	−6.42380	−	17.5139i	−0.301484	−	0.821966i
$455$	9.04471	+	4.64614i	0.424022	+	0.217814i
$456$		0			0
$457$	−6.68780	+	11.5836i	−0.312842	+	0.541858i	−0.978976	−	0.203974i	$-0.934614\pi$
$457$	−6.68780	+	11.5836i	−0.312842	+	0.541858i	0.666135	+	0.745832i	$0.267948\pi$
$458$	15.5616	−	18.6394i	0.727148	−	0.870963i
$459$		0			0
$460$	−4.08200	+	0.740682i	−0.190324	+	0.0345345i
$461$			2.68641i			0.125118i	0.998041	+	0.0625592i	$0.0199262\pi$
$461$			2.68641i			0.125118i	−0.998041	+	0.0625592i	$0.980074\pi$
$462$		0			0
$463$	−21.0380			−0.977721			−0.488860	−	0.872362i	$-0.662587\pi$
$463$	−21.0380			−0.977721			−0.488860	+	0.872362i	$0.662587\pi$
$464$	−1.62188	+	1.97232i	−0.0752937	+	0.0915629i
$465$		0			0
$466$	−27.0083	−	22.5487i	−1.25114	−	1.04455i
$467$	−21.3849	−	12.3466i	−0.989574	−	0.571331i	−0.0844270	−	0.996430i	$-0.526906\pi$
$467$	−21.3849	−	12.3466i	−0.989574	−	0.571331i	−0.905147	+	0.425099i	$0.860239\pi$
$468$		0			0
$469$	−0.734040	−	1.13852i	−0.0338948	−	0.0525721i
$470$	−7.93582	−	21.6362i	−0.366052	−	0.998004i
$471$		0			0
$472$	−0.0733884	−	9.85387i	−0.00337797	−	0.453561i
$473$	−2.58373	−	4.47515i	−0.118800	−	0.205767i
$474$		0			0
$475$			8.65014i			0.396896i
$476$	6.49138	−	1.51006i	0.297532	−	0.0692135i
$477$		0			0
$478$	3.22602	−	18.5651i	0.147555	−	0.849147i
$479$	−20.4562	−	35.4311i	−0.934666	−	1.61889i	−0.775229	−	0.631680i	$-0.782366\pi$
$479$	−20.4562	−	35.4311i	−0.934666	−	1.61889i	−0.159437	−	0.987208i	$-0.550968\pi$
$480$		0			0
$481$	−7.78520	+	13.4844i	−0.354974	+	0.614834i
$482$	29.5332	−	10.8323i	1.34520	−	0.493399i
$483$		0			0
$484$	−22.0691	+	18.7057i	−1.00314	+	0.850257i
$485$	2.02094	+	1.16679i	0.0917660	+	0.0529811i
$486$		0			0
$487$	−8.76704	−	15.1850i	−0.397273	−	0.688096i	0.596116	−	0.802898i	$-0.296710\pi$
$487$	−8.76704	−	15.1850i	−0.397273	−	0.688096i	−0.993388	+	0.114802i	$0.963377\pi$
$488$	31.4327	−	18.4612i	1.42289	−	0.835697i
$489$		0			0
$490$	8.27606	−	12.1616i	0.373874	−	0.549404i
$491$			15.7509i			0.710830i	0.934709	+	0.355415i	$0.115660\pi$
$491$			15.7509i			0.710830i	−0.934709	+	0.355415i	$0.884340\pi$
$492$		0			0
$493$	−0.696329	+	0.402026i	−0.0313611	+	0.0181063i
$494$	−8.69930	−	7.26286i	−0.391400	−	0.326771i
$495$		0			0
$496$	−2.39593	+	14.4241i	−0.107581	+	0.647663i
$497$	0.961958	+	19.5910i	0.0431497	+	0.878778i
$498$		0			0
$499$	8.82147	+	5.09308i	0.394903	+	0.227997i	0.684282	−	0.729217i	$-0.260116\pi$
$499$	8.82147	+	5.09308i	0.394903	+	0.227997i	−0.289379	+	0.957215i	$0.593449\pi$
$500$	7.81206	−	21.7996i	0.349366	−	0.974909i
$501$		0			0
$502$	38.2312	+	6.64337i	1.70634	+	0.296508i
$503$	−27.1001			−1.20833			−0.604167	−	0.796858i	$-0.706494\pi$
$503$	−27.1001			−1.20833			−0.604167	+	0.796858i	$0.706494\pi$
$504$		0			0
$505$	0.310885			0.0138342
$506$	−9.81502	−	1.70554i	−0.436331	−	0.0758205i
$507$		0			0
$508$	13.5712	+	4.86333i	0.602124	+	0.215776i
$509$	−19.4357	−	11.2212i	−0.861471	−	0.497371i	0.00303361	−	0.999995i	$-0.499034\pi$
$509$	−19.4357	−	11.2212i	−0.861471	−	0.497371i	−0.864505	+	0.502625i	$0.832368\pi$
$510$		0			0
$511$	22.0022	−	14.1855i	0.973319	−	0.627528i
$512$	22.6218	−	0.505513i	0.999750	−	0.0223407i
$513$		0			0
$514$	26.2602	+	21.9241i	1.15829	+	0.967030i
$515$	8.84987	−	5.10948i	0.389972	−	0.225150i
$516$		0			0
$517$		−	55.3392i		−	2.43382i
$518$	17.9788	+	13.5710i	0.789944	+	0.596275i
$519$		0			0
$520$	5.50512	+	9.37323i	0.241415	+	0.411043i
$521$	−5.13510	−	8.89426i	−0.224973	−	0.389664i	0.731338	−	0.682015i	$-0.238896\pi$
$521$	−5.13510	−	8.89426i	−0.224973	−	0.389664i	−0.956311	+	0.292350i	$0.905563\pi$
$522$		0			0
$523$	15.4655	+	8.92903i	0.676261	+	0.390439i	0.798445	−	0.602068i	$-0.205656\pi$
$523$	15.4655	+	8.92903i	0.676261	+	0.390439i	−0.122184	+	0.992507i	$0.538990\pi$
$524$	19.0784	+	22.5088i	0.833443	+	0.983302i
$525$		0			0
$526$	−14.4415	+	5.29692i	−0.629680	+	0.230956i
$527$	−2.30203	+	3.98724i	−0.100278	+	0.173687i
$528$		0			0
$529$	10.5257	+	18.2310i	0.457639	+	0.792653i
$530$	−2.07504	+	11.9414i	−0.0901341	+	0.518702i
$531$		0			0
$532$	−11.9718	+	11.2013i	−0.519043	+	0.485636i
$533$		−	16.4549i		−	0.712742i
$534$		0			0
$535$	−9.61292	−	16.6501i	−0.415603	−	0.719845i
$536$	−0.0107852	−	1.44813i	−0.000465850	−	0.0625497i
$537$		0			0
$538$	−11.6900	−	31.8716i	−0.503991	−	1.37408i
$539$	28.7140	−	20.5740i	1.23680	−	0.886186i
$540$		0			0
$541$	19.9303	+	11.5067i	0.856869	+	0.494714i	0.862963	−	0.505268i	$-0.168606\pi$
$541$	19.9303	+	11.5067i	0.856869	+	0.494714i	−0.00609356	+	0.999981i	$0.501940\pi$
$542$	6.75593	+	5.64038i	0.290192	+	0.242275i
$543$		0			0
$544$	6.72492	+	2.35356i	0.288328	+	0.100908i
$545$	−28.5571			−1.22325
$546$		0			0
$547$		−	9.10136i		−	0.389146i	−0.980888	−	0.194573i	$-0.937668\pi$
$547$		−	9.10136i		−	0.389146i	0.980888	−	0.194573i	$-0.0623321\pi$
$548$	3.34299	+	18.4237i	0.142806	+	0.787021i
$549$		0			0
$550$	12.7691	−	15.2946i	0.544477	−	0.652163i
$551$	0.988965	−	1.71294i	0.0421313	−	0.0729736i
$552$		0			0
$553$	−20.4907	−	10.5258i	−0.871353	−	0.447602i
$554$	13.6360	+	37.1771i	0.579337	+	1.57950i
$555$		0			0
$556$	1.14375	−	3.19164i	0.0485057	−	0.135356i
$557$	15.0016	−	8.66116i	0.635637	−	0.366985i	−0.147295	−	0.989093i	$-0.547057\pi$
$557$	15.0016	−	8.66116i	0.635637	−	0.366985i	0.782932	+	0.622107i	$0.213723\pi$
$558$		0			0
$559$	−2.64843			−0.112017
$560$	14.4349	−	6.24057i	0.609986	−	0.263712i
$561$		0			0
$562$	4.04607	−	23.2843i	0.170673	−	0.982187i
$563$	−6.91560	+	3.99272i	−0.291458	+	0.168273i	−0.638599	−	0.769540i	$-0.720486\pi$
$563$	−6.91560	+	3.99272i	−0.291458	+	0.168273i	0.347141	+	0.937813i	$0.387152\pi$
$564$		0			0
$565$	−1.35301	−	0.781160i	−0.0569215	−	0.0328637i
$566$	−13.5629	−	36.9778i	−0.570090	−	1.55429i
$567$		0			0
$568$	−10.3489	+	18.2372i	−0.434231	+	0.765216i
$569$	5.98535	−	10.3669i	0.250919	−	0.434604i	−0.712860	−	0.701306i	$-0.752601\pi$
$569$	5.98535	−	10.3669i	0.250919	−	0.434604i	0.963779	+	0.266702i	$0.0859339\pi$
$570$		0			0
$571$	−36.9016	+	21.3051i	−1.54428	+	0.891592i	−0.545722	+	0.837966i	$0.683745\pi$
$571$	−36.9016	+	21.3051i	−1.54428	+	0.891592i	−0.998561	+	0.0536265i	$0.982922\pi$
$572$	4.66027	+	25.6834i	0.194856	+	1.07388i
$573$		0			0
$574$	−23.6256	−	2.92040i	−0.986113	−	0.121895i
$575$	3.89725			0.162527
$576$		0			0
$577$	14.9650	+	25.9202i	0.623001	+	1.07907i	0.988924	+	0.148425i	$0.0474203\pi$
$577$	14.9650	+	25.9202i	0.623001	+	1.07907i	−0.365922	+	0.930645i	$0.619246\pi$
$578$	−16.7331	−	13.9701i	−0.696005	−	0.581079i
$579$		0			0
$580$	−1.44731	+	1.22673i	−0.0600961	+	0.0509372i
$581$	7.85360	−	0.385627i	0.325822	−	0.0159985i
$582$		0			0
$583$	−14.5522	+	25.2052i	−0.602692	+	1.04389i
$584$	27.9854	−	0.208426i	1.15804	−	0.00862473i
$585$		0			0
$586$	−28.1246	−	4.88717i	−1.16182	−	0.201887i
$587$		−	19.4269i		−	0.801833i	−0.916115	−	0.400916i	$-0.868692\pi$
$587$		−	19.4269i		−	0.801833i	0.916115	−	0.400916i	$-0.131308\pi$
$588$		0			0
$589$		−	11.3258i		−	0.466671i
$590$	1.25347	−	7.21343i	0.0516044	−	0.296972i
$591$		0			0
$592$	8.46050	+	22.5459i	0.347724	+	0.926630i
$593$	−9.07706	+	15.7219i	−0.372750	+	0.645622i	−0.989988	−	0.141155i	$-0.954919\pi$
$593$	−9.07706	+	15.7219i	−0.372750	+	0.645622i	0.617237	+	0.786777i	$0.288252\pi$
$594$		0			0
$595$	4.94585	−	0.242851i	0.202760	−	0.00995592i
$596$	−4.76750	−	5.62473i	−0.195284	−	0.230398i
$597$		0			0
$598$	−3.27222	+	3.91940i	−0.133811	+	0.160276i
$599$	5.59258	+	9.68663i	0.228507	+	0.395785i	0.957366	−	0.288879i	$-0.0932824\pi$
$599$	5.59258	+	9.68663i	0.228507	+	0.395785i	−0.728859	+	0.684664i	$0.759949\pi$
$600$		0			0
$601$	−4.21883			−0.172090			−0.0860448	−	0.996291i	$-0.527423\pi$
$601$	−4.21883			−0.172090			−0.0860448	+	0.996291i	$0.527423\pi$
$602$	−0.470041	+	3.80256i	−0.0191574	+	0.154981i
$603$		0			0
$604$	−5.09798	−	28.0957i	−0.207434	−	1.14320i
$605$	−18.6150	+	10.7474i	−0.756806	+	0.436942i
$606$		0			0
$607$	13.6196	−	23.5898i	0.552802	−	0.957481i	−0.445269	−	0.895397i	$-0.646892\pi$
$607$	13.6196	−	23.5898i	0.552802	−	0.957481i	0.998071	−	0.0620841i	$-0.0197747\pi$
$608$	−17.2215	+	3.25751i	−0.698423	+	0.132110i
$609$		0			0
$610$	25.4278	−	9.32653i	1.02954	−	0.377620i
$611$	−24.5627	−	14.1813i	−0.993701	−	0.573713i
$612$		0			0
$613$	3.20401	−	1.84984i	0.129409	−	0.0747141i	−0.433898	−	0.900962i	$-0.642862\pi$
$613$	3.20401	−	1.84984i	0.129409	−	0.0747141i	0.563307	+	0.826248i	$0.309529\pi$
$614$	24.9189	+	4.33012i	1.00564	+	0.174749i
$615$		0			0
$616$	37.7027	−	2.13285i	1.51908	−	0.0859351i
$617$	−26.0487			−1.04868			−0.524341	−	0.851508i	$-0.675688\pi$
$617$	−26.0487			−1.04868			−0.524341	+	0.851508i	$0.675688\pi$
$618$		0			0
$619$	−27.7816	+	16.0397i	−1.11664	+	0.644692i	−0.940541	−	0.339681i	$-0.889681\pi$
$619$	−27.7816	+	16.0397i	−1.11664	+	0.644692i	−0.176098	+	0.984373i	$0.556348\pi$
$620$	−3.66492	+	10.2270i	−0.147187	+	0.410725i
$621$		0			0
$622$	−1.90041	+	0.697042i	−0.0761996	+	0.0279488i
$623$	−6.08057	−	3.12350i	−0.243613	−	0.125140i
$624$		0			0
$625$	1.62309	−	2.81127i	0.0649236	−	0.112451i
$626$	5.27231	+	4.40174i	0.210724	+	0.175929i
$627$		0			0
$628$	25.3621	−	4.60198i	1.01206	−	0.183639i
$629$			7.58258i			0.302337i
$630$		0			0
$631$	11.7538			0.467912			0.233956	−	0.972247i	$-0.424833\pi$
$631$	11.7538			0.467912			0.233956	+	0.972247i	$0.424833\pi$
$632$	−12.4718	−	21.2350i	−0.496101	−	0.844682i
$633$		0			0
$634$	−10.2354	+	12.2597i	−0.406499	+	0.486896i
$635$	9.27612	+	5.35557i	0.368112	+	0.212529i
$636$		0			0
$637$	−1.77364	−	18.0172i	−0.0702742	−	0.713869i
$638$	−4.27721	+	1.56881i	−0.169336	+	0.0621099i
$639$		0			0
$640$	16.6048	+	2.63122i	0.656361	+	0.104008i
$641$	20.9136	+	36.2235i	0.826039	+	1.43074i	0.901123	+	0.433564i	$0.142744\pi$
$641$	20.9136	+	36.2235i	0.826039	+	1.43074i	−0.0750839	+	0.997177i	$0.523922\pi$
$642$		0			0
$643$		−	42.9368i		−	1.69326i	−0.532180	−	0.846631i	$-0.678627\pi$
$643$		−	42.9368i		−	1.69326i	0.532180	−	0.846631i	$-0.321373\pi$
$644$	5.04664	+	5.39379i	0.198865	+	0.212545i
$645$		0			0
$646$	−5.43733	−	0.944836i	−0.213929	−	0.0371741i
$647$	−4.55891	−	7.89626i	−0.179229	−	0.310434i	0.762388	−	0.647121i	$-0.224027\pi$
$647$	−4.55891	−	7.89626i	−0.179229	−	0.310434i	−0.941617	+	0.336687i	$0.890694\pi$
$648$		0			0
$649$	8.79054	−	15.2257i	0.345059	−	0.597660i
$650$	−3.51638	−	9.58706i	−0.137924	−	0.376035i
$651$		0			0
$652$	−4.17849	−	4.92981i	−0.163642	−	0.193066i
$653$	18.8716	+	10.8955i	0.738502	+	0.426374i	0.821524	−	0.570174i	$-0.193124\pi$
$653$	18.8716	+	10.8955i	0.738502	+	0.426374i	−0.0830227	+	0.996548i	$0.526457\pi$
$654$		0			0
$655$	10.9615	+	18.9859i	0.428301	+	0.741840i
$656$	−19.6566	−	16.1639i	−0.767460	−	0.631096i
$657$		0			0
$658$	−24.7205	+	32.7497i	−0.963706	+	1.27672i
$659$			0.152682i			0.00594765i	0.999996	+	0.00297383i	$0.000946600\pi$
$659$			0.152682i			0.00594765i	−0.999996	+	0.00297383i	$0.999053\pi$
$660$		0			0
$661$	−24.6004	+	14.2031i	−0.956845	+	0.552435i	−0.895201	−	0.445663i	$-0.852968\pi$
$661$	−24.6004	+	14.2031i	−0.956845	+	0.552435i	−0.0616446	+	0.998098i	$0.519635\pi$
$662$	−21.6026	+	25.8751i	−0.839608	+	1.00567i
$663$		0			0
$664$	7.31088	+	4.14865i	0.283717	+	0.160999i
$665$	−10.2379	+	6.60065i	−0.397007	+	0.255962i
$666$		0			0
$667$	−0.771750	−	0.445570i	−0.0298823	−	0.0172525i
$668$	−26.4504	−	9.47869i	−1.02340	−	0.366742i
$669$		0			0
$670$	0.184210	−	1.06009i	0.00711666	−	0.0409549i
$671$	65.0371			2.51073
$672$		0			0
$673$	26.2542			1.01203			0.506013	−	0.862526i	$-0.331119\pi$
$673$	26.2542			1.01203			0.506013	+	0.862526i	$0.331119\pi$
$674$	3.98646	−	22.9413i	0.153553	−	0.883664i
$675$		0			0
$676$	−11.8819	−	4.25796i	−0.456995	−	0.163768i
$677$	4.00416	+	2.31180i	0.153892	+	0.0888498i	0.574969	−	0.818175i	$-0.305014\pi$
$677$	4.00416	+	2.31180i	0.153892	+	0.0888498i	−0.421076	+	0.907025i	$0.638348\pi$
$678$		0			0
$679$	−0.203767	−	4.14988i	−0.00781986	−	0.159258i
$680$	4.60407	+	2.61264i	0.176558	+	0.100190i
$681$		0			0
$682$	−16.7188	+	20.0255i	−0.640198	+	0.766816i
$683$	−16.8469	+	9.72659i	−0.644631	+	0.372178i	−0.786396	−	0.617723i	$-0.788055\pi$
$683$	−16.8469	+	9.72659i	−0.644631	+	0.372178i	0.141765	+	0.989900i	$0.454722\pi$
$684$		0			0
$685$			13.9121i			0.531555i
$686$	−26.1835	−	0.651128i	−0.999691	−	0.0248602i
$687$		0			0
$688$	−2.60160	+	3.16374i	−0.0991851	+	0.120617i
$689$	7.45834	+	12.9182i	0.284140	+	0.492145i
$690$		0			0
$691$	15.0449	+	8.68618i	0.572335	+	0.330438i	0.758081	−	0.652160i	$-0.226137\pi$
$691$	15.0449	+	8.68618i	0.572335	+	0.330438i	−0.185746	+	0.982598i	$0.559470\pi$
$692$	−8.45570	−	9.97610i	−0.321438	−	0.379234i
$693$		0			0
$694$	1.56723	+	4.27290i	0.0594914	+	0.162197i
$695$	1.25951	−	2.18154i	0.0477760	−	0.0827504i
$696$		0			0
$697$	−4.00667	−	6.93975i	−0.151763	−	0.262862i
$698$	31.8677	+	5.53760i	1.20621	+	0.209601i
$699$		0			0
$700$	−14.3890	+	3.34724i	−0.543851	+	0.126514i
$701$			25.1180i			0.948695i	0.880338	+	0.474348i	$0.157316\pi$
$701$			25.1180i			0.948695i	−0.880338	+	0.474348i	$0.842684\pi$
$702$		0			0
$703$	−9.32640	−	16.1538i	−0.351752	−	0.609252i
$704$	35.2585	+	19.6622i	1.32885	+	0.741046i
$705$		0			0
$706$	30.9646	−	11.3573i	1.16537	−	0.427438i
$707$	−0.299938	−	0.465215i	−0.0112803	−	0.0174962i
$708$		0			0
$709$	−17.4147	−	10.0544i	−0.654024	−	0.377601i	0.135972	−	0.990713i	$-0.456584\pi$
$709$	−17.4147	−	10.0544i	−0.654024	−	0.377601i	−0.789996	+	0.613112i	$0.789918\pi$
$710$	−9.98478	+	11.9596i	−0.374722	+	0.448834i
$711$		0			0
$712$	−3.70097	−	6.30143i	−0.138700	−	0.236156i
$713$	−5.10275			−0.191099
$714$		0			0
$715$			19.3941i			0.725297i
$716$	−0.248696	+	0.0451260i	−0.00929419	+	0.00168644i
$717$		0			0
$718$	5.54717	+	4.63121i	0.207019	+	0.172835i
$719$	−19.1966	+	33.2496i	−0.715914	+	1.24000i	0.246692	+	0.969094i	$0.420656\pi$
$719$	−19.1966	+	33.2496i	−0.715914	+	1.24000i	−0.962606	+	0.270906i	$0.912677\pi$
$720$		0			0
$721$	−16.1842	−	8.31358i	−0.602730	−	0.309614i
$722$	−12.4810	+	4.57783i	−0.464494	+	0.170369i
$723$		0			0
$724$	1.83465	−	5.11960i	0.0681842	−	0.190269i
$725$	1.54350	−	0.891141i	0.0573242	−	0.0330961i
$726$		0			0
$727$	14.8679			0.551422			0.275711	−	0.961241i	$-0.411087\pi$
$727$	14.8679			0.551422			0.275711	+	0.961241i	$0.411087\pi$
$728$	8.71504	−	17.2812i	0.323001	−	0.640482i
$729$		0			0
$730$	20.4865	+	3.55990i	0.758238	+	0.131758i
$731$	−1.11696	+	0.644877i	−0.0413122	+	0.0238516i
$732$		0			0
$733$	36.4503	+	21.0446i	1.34632	+	0.777300i	0.987727	−	0.156192i	$-0.0499219\pi$
$733$	36.4503	+	21.0446i	1.34632	+	0.777300i	0.358597	+	0.933492i	$0.383255\pi$
$734$	−37.3831	+	13.7115i	−1.37984	+	0.506102i
$735$		0			0
$736$	1.46765	+	7.75900i	0.0540982	+	0.286000i
$737$	1.29186	−	2.23757i	0.0475864	−	0.0824221i
$738$		0			0
$739$	−10.9859	+	6.34270i	−0.404122	+	0.233320i	−0.688261	−	0.725463i	$-0.741626\pi$
$739$	−10.9859	+	6.34270i	−0.404122	+	0.233320i	0.284139	+	0.958783i	$0.408292\pi$
$740$	3.19435	+	17.6045i	0.117427	+	0.647155i
$741$		0			0
$742$	19.8714	−	8.41580i	0.729501	−	0.308954i
$743$	25.7219			0.943644			0.471822	−	0.881694i	$-0.343596\pi$
$743$	25.7219			0.943644			0.471822	+	0.881694i	$0.343596\pi$
$744$		0			0
$745$	−2.73917	−	4.74438i	−0.100355	−	0.173821i
$746$	−6.38455	+	7.64729i	−0.233755	+	0.279987i
$747$		0			0
$748$	8.21917	+	9.69704i	0.300523	+	0.354559i
$749$	−15.6411	+	30.4488i	−0.571513	+	1.11257i
$750$		0			0
$751$	−17.9305	+	31.0565i	−0.654292	+	1.13327i	0.327779	+	0.944755i	$0.393700\pi$
$751$	−17.9305	+	31.0565i	−0.654292	+	1.13327i	−0.982071	+	0.188513i	$0.939633\pi$
$752$	−41.0689	+	15.4114i	−1.49763	+	0.561995i
$753$		0			0
$754$	−0.399754	+	2.30050i	−0.0145582	+	0.0837791i
$755$		−	21.2157i		−	0.772117i
$756$		0			0
$757$			30.7289i			1.11686i	0.829551	+	0.558431i	$0.188597\pi$
$757$			30.7289i			1.11686i	−0.829551	+	0.558431i	$0.811403\pi$
$758$	−18.3884	−	3.19532i	−0.667896	−	0.116059i
$759$		0			0
$760$	−13.0219	+	0.0969829i	−0.472354	+	0.00351794i
$761$	22.5624	−	39.0792i	0.817887	−	1.41662i	−0.0893497	−	0.996000i	$-0.528479\pi$
$761$	22.5624	−	39.0792i	0.817887	−	1.41662i	0.907236	−	0.420621i	$-0.138188\pi$
$762$		0			0
$763$	27.5515	+	42.7334i	0.997431	+	1.54705i
$764$	3.73382	−	3.16477i	0.135085	−	0.114497i
$765$		0			0
$766$	5.35303	+	4.46913i	0.193413	+	0.161476i
$767$	−4.50535	−	7.80349i	−0.162679	−	0.281768i
$768$		0			0
$769$	−28.0168			−1.01031			−0.505156	−	0.863028i	$-0.668565\pi$
$769$	−28.0168			−1.01031			−0.505156	+	0.863028i	$0.668565\pi$
$770$	27.8456	+	3.44204i	1.00348	+	0.124042i
$771$		0			0
$772$	1.40994	+	7.77037i	0.0507449	+	0.279662i
$773$	−29.9953	+	17.3178i	−1.07886	+	0.622878i	−0.930588	−	0.366069i	$-0.880703\pi$
$773$	−29.9953	+	17.3178i	−1.07886	+	0.622878i	−0.148268	+	0.988947i	$0.547370\pi$
$774$		0			0
$775$	5.10275	−	8.83822i	0.183296	−	0.317478i
$776$	2.19216	−	3.86310i	0.0786941	−	0.138677i
$777$		0			0
$778$	11.1753	+	30.4684i	0.400655	+	1.09235i
$779$	17.0715	+	9.85621i	0.611649	+	0.353136i
$780$		0			0
$781$	−32.3992	+	18.7057i	−1.15933	+	0.669341i
$782$	−0.425689	+	2.44975i	−0.0152226	+	0.0876028i
$783$		0			0
$784$	−23.2651	−	15.5799i	−0.830898	−	0.556425i
$785$	19.1515			0.683546
$786$		0			0
$787$	−29.6763	+	17.1336i	−1.05784	+	0.610747i	−0.924835	−	0.380368i	$-0.875797\pi$
$787$	−29.6763	+	17.1336i	−1.05784	+	0.610747i	−0.133009	+	0.991115i	$0.542464\pi$
$788$	13.1882	−	36.8018i	0.469811	−	1.31101i
$789$		0			0
$790$	−6.30071	−	17.1783i	−0.224169	−	0.611175i
$791$	0.136421	+	2.77833i	0.00485058	+	0.0987860i
$792$		0			0
$793$	16.6665	−	28.8672i	0.591844	−	1.02510i
$794$	−27.1141	+	32.4767i	−0.962244	+	1.15256i
$795$		0			0
$796$	7.42574	+	40.9242i	0.263198	+	1.45052i
$797$		−	20.5838i		−	0.729114i	−0.931181	−	0.364557i	$-0.881220\pi$
$797$		−	20.5838i		−	0.729114i	0.931181	−	0.364557i	$-0.118780\pi$
$798$		0			0
$799$	−13.8122			−0.488641
$800$	−14.9066	−	5.21696i	−0.527029	−	0.184447i
$801$		0			0
$802$	17.0120	+	14.2029i	0.600713	+	0.501522i
$803$	43.2416	+	24.9655i	1.52596	+	0.881014i
$804$		0			0
$805$	2.97387	+	4.61258i	0.104815	+	0.162572i
$806$	4.60407	+	12.5525i	0.162171	+	0.442144i
$807$		0			0
$808$	−0.00440697	−	0.591724i	−0.000155037	−	0.0208168i
$809$	−23.4504	−	40.6172i	−0.824471	−	1.42802i	−0.902323	−	0.431060i	$-0.858140\pi$
$809$	−23.4504	−	40.6172i	−0.824471	−	1.42802i	0.0778526	−	0.996965i	$-0.475194\pi$
$810$		0			0
$811$			22.2462i			0.781168i	0.920567	+	0.390584i	$0.127727\pi$
$811$			22.2462i			0.781168i	−0.920567	+	0.390584i	$0.872273\pi$
$812$	3.23205	+	0.982246i	0.113423	+	0.0344701i
$813$		0			0
$814$	−7.35552	+	42.3294i	−0.257811	+	1.48365i
$815$	−2.40076	−	4.15823i	−0.0840948	−	0.145656i
$816$		0			0
$817$	1.58637	−	2.74767i	0.0554999	−	0.0961287i
$818$	34.6360	−	12.7039i	1.21102	−	0.444182i
$819$		0			0
$820$	−12.2258	−	14.4241i	−0.426945	−	0.503713i
$821$	28.4062	+	16.4003i	0.991384	+	0.572376i	0.905688	−	0.423945i	$-0.139355\pi$
$821$	28.4062	+	16.4003i	0.991384	+	0.572376i	0.0856966	+	0.996321i	$0.472688\pi$
$822$		0			0
$823$	6.88576	+	11.9265i	0.240023	+	0.415731i	0.960720	−	0.277518i	$-0.0895118\pi$
$823$	6.88576	+	11.9265i	0.240023	+	0.415731i	−0.720698	+	0.693249i	$0.756178\pi$
$824$	−9.85060	−	16.7720i	−0.343162	−	0.584281i
$825$		0			0
$826$	−12.0037	+	5.08372i	−0.417661	+	0.176885i
$827$			22.0460i			0.766615i	0.923621	+	0.383307i	$0.125215\pi$
$827$			22.0460i			0.766615i	−0.923621	+	0.383307i	$0.874785\pi$
$828$		0			0
$829$	4.74751	−	2.74098i	0.164888	−	0.0951980i	−0.415285	−	0.909691i	$-0.636318\pi$
$829$	4.74751	−	2.74098i	0.164888	−	0.0951980i	0.580173	+	0.814493i	$0.302985\pi$
$830$	4.79432	+	4.00267i	0.166413	+	0.138935i
$831$		0			0
$832$	17.7626	−	10.6111i	0.615806	−	0.367873i
$833$	−5.13510	−	7.16678i	−0.177921	−	0.248314i
$834$		0			0
$835$	−18.0793	−	10.4381i	−0.625659	−	0.361224i
$836$	−29.4371	−	10.5490i	−1.01810	−	0.364845i
$837$		0			0
$838$	−0.352174	−	0.0611968i	−0.0121657	−	0.00211401i
$839$	−28.7512			−0.992601			−0.496301	−	0.868151i	$-0.665309\pi$
$839$	−28.7512			−0.992601			−0.496301	+	0.868151i	$0.665309\pi$
$840$		0			0
$841$	28.5925			0.985947
$842$	25.5956	+	4.44771i	0.882084	+	0.153278i
$843$		0			0
$844$	11.6137	−	32.4083i	0.399762	−	1.11554i
$845$	−8.12145	−	4.68892i	−0.279387	−	0.161304i
$846$		0			0
$847$	34.0421	+	17.4869i	1.16970	+	0.600858i
$848$	22.7582	+	3.78027i	0.781519	+	0.129815i
$849$		0			0
$850$	−3.81740	−	3.18706i	−0.130936	−	0.109315i
$851$	−7.27797	+	4.20194i	−0.249486	+	0.144041i
$852$		0			0
$853$		−	21.7605i		−	0.745064i	−0.928019	−	0.372532i	$-0.878490\pi$
$853$		−	21.7605i		−	0.745064i	0.928019	−	0.372532i	$-0.121510\pi$
$854$	−38.4889	−	29.0526i	−1.31706	−	0.994161i
$855$		0			0
$856$	−31.5547	+	18.5328i	−1.07852	+	0.633439i
$857$	5.89593	+	10.2121i	0.201401	+	0.348837i	0.948980	−	0.315336i	$-0.102117\pi$
$857$	5.89593	+	10.2121i	0.201401	+	0.348837i	−0.747579	+	0.664173i	$0.768784\pi$
$858$		0			0
$859$	4.15132	+	2.39676i	0.141641	+	0.0817766i	0.569146	−	0.822237i	$-0.307274\pi$
$859$	4.15132	+	2.39676i	0.141641	+	0.0817766i	−0.427505	+	0.904013i	$0.640607\pi$
$860$	−2.32158	+	1.96776i	−0.0791651	+	0.0671000i
$861$		0			0
$862$	36.4389	−	13.3652i	1.24111	−	0.455220i
$863$	−0.0628642	+	0.108884i	−0.00213992	+	0.00370646i	−0.867093	−	0.498146i	$-0.834014\pi$
$863$	−0.0628642	+	0.108884i	−0.00213992	+	0.00370646i	0.864953	+	0.501852i	$0.167348\pi$
$864$		0			0
$865$	−4.85823	−	8.41471i	−0.165185	−	0.286109i
$866$	−1.75829	+	10.1186i	−0.0597492	+	0.343844i
$867$		0			0
$868$	18.8397	−	4.38260i	0.639463	−	0.148755i
$869$		−	43.9371i		−	1.49046i
$870$		0			0
$871$	−0.662108	−	1.14681i	−0.0224347	−	0.0388580i
$872$	0.404812	+	54.3543i	0.0137087	+	1.84067i
$873$		0			0
$874$	−2.10625	−	5.74249i	−0.0712451	−	0.194242i
$875$	−30.5971	+	1.50238i	−1.03437	+	0.0507897i
$876$		0			0
$877$	25.9534	+	14.9842i	0.876385	+	0.505981i	0.869465	−	0.493995i	$-0.164464\pi$
$877$	25.9534	+	14.9842i	0.876385	+	0.505981i	0.00692013	+	0.999976i	$0.497797\pi$
$878$	32.5729	+	27.1944i	1.09928	+	0.917765i
$879$		0			0
$880$	23.1676	+	19.0511i	0.780980	+	0.642213i
$881$	30.2728			1.01992			0.509959	−	0.860199i	$-0.329661\pi$
$881$	30.2728			1.01992			0.509959	+	0.860199i	$0.329661\pi$
$882$		0			0
$883$		−	43.3423i		−	1.45858i	−0.684203	−	0.729291i	$-0.739850\pi$
$883$		−	43.3423i		−	1.45858i	0.684203	−	0.729291i	$-0.260150\pi$
$884$	6.41035	−	1.16316i	0.215603	−	0.0391214i
$885$		0			0
$886$	−31.7985	+	38.0876i	−1.06829	+	1.27958i
$887$	7.56821	−	13.1085i	0.254116	−	0.440141i	−0.710539	−	0.703658i	$-0.751549\pi$
$887$	7.56821	−	13.1085i	0.254116	−	0.440141i	0.964655	+	0.263516i	$0.0848823\pi$
$888$		0			0
$889$	−0.935294	−	19.0480i	−0.0313687	−	0.638849i
$890$	−1.86972	−	5.09761i	−0.0626732	−	0.170872i
$891$		0			0
$892$	−32.9791	−	11.8183i	−1.10422	−	0.395706i
$893$	29.4253	−	16.9887i	0.984680	−	0.568505i
$894$		0			0
$895$	−0.187796			−0.00627731
$896$	−12.0826	−	27.3863i	−0.403653	−	0.914912i
$897$		0			0
$898$	5.08705	−	29.2749i	0.169757	−	0.976916i
$899$	−2.02094	+	1.16679i	−0.0674020	+	0.0389146i
$900$		0			0
$901$	6.29101	+	3.63212i	0.209584	+	0.121003i
$902$	−15.6351	−	42.6275i	−0.520592	−	1.41934i
$903$		0			0
$904$	−1.46765	+	2.58633i	−0.0488132	+	0.0860201i
$905$	2.02034	−	3.49933i	0.0671584	−	0.116322i
$906$		0			0
$907$	27.4761	−	15.8633i	0.912328	−	0.526733i	0.0311488	−	0.999515i	$-0.490083\pi$
$907$	27.4761	−	15.8633i	0.912328	−	0.526733i	0.881180	+	0.472782i	$0.156750\pi$
$908$	−25.9580	+	4.71009i	−0.861445	+	0.156310i
$909$		0			0
$910$	8.66350	−	11.4774i	0.287192	−	0.380472i
$911$	−29.4757			−0.976574			−0.488287	−	0.872683i	$-0.662378\pi$
$911$	−29.4757			−0.976574			−0.488287	+	0.872683i	$0.662378\pi$
$912$		0			0
$913$	7.49868	+	12.9881i	0.248170	+	0.429843i
$914$	14.5206	+	12.1229i	0.480299	+	0.400991i
$915$		0			0
$916$	−22.2032	−	26.1955i	−0.733614	−	0.865524i
$917$	17.8354	−	34.7204i	0.588976	−	1.14657i
$918$		0			0
$919$	−8.85875	+	15.3438i	−0.292223	+	0.506146i	−0.974335	−	0.225102i	$-0.927728\pi$
$919$	−8.85875	+	15.3438i	−0.292223	+	0.506146i	0.682112	+	0.731248i	$0.261062\pi$
$920$	0.0436949	+	5.86692i	0.00144058	+	0.193427i
$921$		0			0
$922$	3.74306	+	0.650426i	0.123271	+	0.0214206i
$923$			19.1741i			0.631124i
$924$		0			0
$925$		−	16.8077i		−	0.552635i
$926$	−5.09368	+	29.3130i	−0.167389	+	0.963285i
$927$		0			0
$928$	2.35542	+	2.73735i	0.0773205	+	0.0898579i
$929$	26.6338	−	46.1311i	0.873826	−	1.51351i	0.0158180	−	0.999875i	$-0.494965\pi$
$929$	26.6338	−	46.1311i	0.873826	−	1.51351i	0.858008	−	0.513636i	$-0.171702\pi$
$930$		0			0
$931$	19.7547	+	8.95192i	0.647434	+	0.293387i
$932$	−37.9570	+	32.1722i	−1.24332	+	1.05384i
$933$		0			0
$934$	−22.3805	+	26.8069i	−0.732313	+	0.877150i
$935$	4.72233	+	8.17932i	0.154437	+	0.267492i
$936$		0			0
$937$	−38.2055			−1.24812			−0.624060	−	0.781377i	$-0.714518\pi$
$937$	−38.2055			−1.24812			−0.624060	+	0.781377i	$0.714518\pi$
$938$	−1.76407	+	0.747106i	−0.0575988	+	0.0243939i
$939$		0			0
$940$	−32.0679	+	5.81874i	−1.04594	+	0.189786i
$941$	8.31195	−	4.79890i	0.270962	−	0.156440i	−0.358363	−	0.933582i	$-0.616665\pi$
$941$	8.31195	−	4.79890i	0.270962	−	0.156440i	0.629325	+	0.777143i	$0.283332\pi$
$942$		0			0
$943$	4.44064	−	7.69141i	0.144607	−	0.250467i
$944$	−13.7475	−	2.28354i	−0.447443	−	0.0743229i
$945$		0			0
$946$	−6.86094	+	2.51648i	−0.223068	+	0.0818179i
$947$	14.3314	+	8.27425i	0.465709	+	0.268877i	0.714442	−	0.699695i	$-0.246681\pi$
$947$	14.3314	+	8.27425i	0.465709	+	0.268877i	−0.248733	+	0.968572i	$0.580014\pi$
$948$		0			0
$949$	22.1622	−	12.7954i	0.719417	−	0.415356i
$950$	12.0525	+	2.09435i	0.391036	+	0.0679496i
$951$		0			0
$952$	−0.532342	−	9.41027i	−0.0172533	−	0.304989i
$953$	−6.08942			−0.197256			−0.0986278	−	0.995124i	$-0.531445\pi$
$953$	−6.08942			−0.197256			−0.0986278	+	0.995124i	$0.531445\pi$
$954$		0			0
$955$	3.14943	−	1.81832i	0.101913	−	0.0588396i
$956$	−25.0863	−	8.98986i	−0.811348	−	0.290753i
$957$		0			0
$958$	−54.3201	+	19.9238i	−1.75500	+	0.643708i
$959$	20.8184	−	13.4223i	0.672262	−	0.433427i
$960$		0			0
$961$	8.81887	−	15.2747i	0.284480	−	0.492733i
$962$	16.9033	+	14.1122i	0.544984	+	0.454995i
$963$		0			0
$964$	−7.94253	−	43.7723i	−0.255812	−	1.40981i
$965$			5.86758i			0.188884i
$966$		0			0
$967$	21.5430			0.692778			0.346389	−	0.938091i	$-0.387408\pi$
$967$	21.5430			0.692778			0.346389	+	0.938091i	$0.387408\pi$
$968$	20.7199	+	35.2786i	0.665963	+	1.13390i
$969$		0			0
$970$	2.11503	−	2.53334i	0.0679095	−	0.0813406i
$971$	−2.27385	−	1.31281i	−0.0729715	−	0.0421301i	0.463070	−	0.886322i	$-0.346748\pi$
$971$	−2.27385	−	1.31281i	−0.0729715	−	0.0421301i	−0.536042	+	0.844191i	$0.680081\pi$
$972$		0			0
$973$	−4.47966	+	0.219960i	−0.143611	+	0.00705160i
$974$	−23.2804	+	8.53887i	−0.745951	+	0.273603i
$975$		0			0
$976$	−18.1122	−	48.2660i	−0.579756	−	1.54496i
$977$	−17.2338	−	29.8499i	−0.551359	−	0.954982i	−0.998177	−	0.0603567i	$-0.980776\pi$
$977$	−17.2338	−	29.8499i	−0.551359	−	0.954982i	0.446818	−	0.894625i	$-0.352557\pi$
$978$		0			0
$979$		−	13.0382i		−	0.416704i
$980$	−14.9414	−	14.4758i	−0.477285	−	0.462414i
$981$		0			0
$982$	21.9463	+	3.81358i	0.700335	+	0.121696i
$983$	26.2210	+	45.4161i	0.836320	+	1.44855i	0.892951	+	0.450154i	$0.148631\pi$
$983$	26.2210	+	45.4161i	0.836320	+	1.44855i	−0.0566303	+	0.998395i	$0.518036\pi$
$984$		0			0
$985$	14.5230	−	25.1547i	0.462743	−	0.801494i
$986$	0.391563	+	1.06756i	0.0124699	+	0.0339979i
$987$		0			0
$988$	−12.2258	+	10.3626i	−0.388956	+	0.329677i
$989$	−1.23794	−	0.714725i	−0.0393642	−	0.0227269i
$990$		0			0
$991$	8.08057	+	13.9960i	0.256688	+	0.444596i	0.965353	−	0.260949i	$-0.0840355\pi$
$991$	8.08057	+	13.9960i	0.256688	+	0.444596i	−0.708665	+	0.705545i	$0.750702\pi$
$992$	19.5175	+	6.83067i	0.619682	+	0.216874i
$993$		0			0
$994$	27.5297	+	3.40300i	0.873191	+	0.107937i
$995$			30.9028i			0.979684i
$996$		0			0
$997$	34.0954	−	19.6850i	1.07981	−	0.623430i	0.148967	−	0.988842i	$-0.452405\pi$
$997$	34.0954	−	19.6850i	1.07981	−	0.623430i	0.930846	+	0.365412i	$0.119072\pi$
$998$	9.23219	−	11.0581i	0.292240	−	0.350039i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cj.c.37.3		12
3.2	odd	2		56.2.p.a.37.4	yes	12
4.3	odd	2		2016.2.cr.c.1297.2		12
7.4	even	3	inner	504.2.cj.c.109.5		12
8.3	odd	2		2016.2.cr.c.1297.5		12
8.5	even	2	inner	504.2.cj.c.37.5		12
12.11	even	2		224.2.t.a.177.6		12
21.2	odd	6		392.2.b.e.197.5		6
21.5	even	6		392.2.b.f.197.5		6
21.11	odd	6		56.2.p.a.53.2	yes	12
21.17	even	6		392.2.p.g.165.2		12
21.20	even	2		392.2.p.g.373.4		12
24.5	odd	2		56.2.p.a.37.2	✓	12
24.11	even	2		224.2.t.a.177.1		12
28.11	odd	6		2016.2.cr.c.1873.5		12
56.11	odd	6		2016.2.cr.c.1873.2		12
56.53	even	6	inner	504.2.cj.c.109.3		12
84.11	even	6		224.2.t.a.81.1		12
84.23	even	6		1568.2.b.f.785.6		6
84.47	odd	6		1568.2.b.e.785.1		6
84.59	odd	6		1568.2.t.g.753.6		12
84.83	odd	2		1568.2.t.g.177.1		12
168.5	even	6		392.2.b.f.197.6		6
168.11	even	6		224.2.t.a.81.6		12
168.53	odd	6		56.2.p.a.53.4	yes	12
168.59	odd	6		1568.2.t.g.753.1		12
168.83	odd	2		1568.2.t.g.177.6		12
168.101	even	6		392.2.p.g.165.4		12
168.107	even	6		1568.2.b.f.785.1		6
168.125	even	2		392.2.p.g.373.2		12
168.131	odd	6		1568.2.b.e.785.6		6
168.149	odd	6		392.2.b.e.197.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.p.a.37.2	✓	12	24.5	odd	2
56.2.p.a.37.4	yes	12	3.2	odd	2
56.2.p.a.53.2	yes	12	21.11	odd	6
56.2.p.a.53.4	yes	12	168.53	odd	6
224.2.t.a.81.1		12	84.11	even	6
224.2.t.a.81.6		12	168.11	even	6
224.2.t.a.177.1		12	24.11	even	2
224.2.t.a.177.6		12	12.11	even	2
392.2.b.e.197.5		6	21.2	odd	6
392.2.b.e.197.6		6	168.149	odd	6
392.2.b.f.197.5		6	21.5	even	6
392.2.b.f.197.6		6	168.5	even	6
392.2.p.g.165.2		12	21.17	even	6
392.2.p.g.165.4		12	168.101	even	6
392.2.p.g.373.2		12	168.125	even	2
392.2.p.g.373.4		12	21.20	even	2
504.2.cj.c.37.3		12	1.1	even	1	trivial
504.2.cj.c.37.5		12	8.5	even	2	inner
504.2.cj.c.109.3		12	56.53	even	6	inner
504.2.cj.c.109.5		12	7.4	even	3	inner
1568.2.b.e.785.1		6	84.47	odd	6
1568.2.b.e.785.6		6	168.131	odd	6
1568.2.b.f.785.1		6	168.107	even	6
1568.2.b.f.785.6		6	84.23	even	6
1568.2.t.g.177.1		12	84.83	odd	2
1568.2.t.g.177.6		12	168.83	odd	2
1568.2.t.g.753.1		12	168.59	odd	6
1568.2.t.g.753.6		12	84.59	odd	6
2016.2.cr.c.1297.2		12	4.3	odd	2
2016.2.cr.c.1297.5		12	8.3	odd	2
2016.2.cr.c.1873.2		12	56.11	odd	6
2016.2.cr.c.1873.5		12	28.11	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.242117 - 1.39333i) q^{2} +(-1.88276 - 0.674701i) q^{4} +(-1.28690 - 0.742990i) q^{5} +(0.129755 + 2.64257i) q^{7} +(-1.39593 + 2.45995i) q^{8} +O(q^{10})\)	\(q+(0.242117 - 1.39333i) q^{2} +(-1.88276 - 0.674701i) q^{4} +(-1.28690 - 0.742990i) q^{5} +(0.129755 + 2.64257i) q^{7} +(-1.39593 + 2.45995i) q^{8} +(-1.34681 + 1.61319i) q^{10} +(-4.37021 + 2.52314i) q^{11} +2.58633i q^{13} +(3.71339 + 0.459019i) q^{14} +(3.08956 + 2.54060i) q^{16} +(0.629755 + 1.09077i) q^{17} +(-2.68324 - 1.54917i) q^{19} +(1.92162 + 2.26714i) q^{20} +(2.45748 + 6.70006i) q^{22} +(-0.697966 + 1.20891i) q^{23} +(-1.39593 - 2.41782i) q^{25} +(3.60362 + 0.626196i) q^{26} +(1.53864 - 5.06286i) q^{28} +0.638384i q^{29} +(1.82772 + 3.16571i) q^{31} +(4.28794 - 3.68966i) q^{32} +(1.67228 - 0.613365i) q^{34} +(1.79642 - 3.49712i) q^{35} +(5.21370 + 3.01013i) q^{37} +(-2.80817 + 3.36357i) q^{38} +(3.62414 - 2.12854i) q^{40} -6.36226 q^{41} +1.02401i q^{43} +(9.93042 - 1.80188i) q^{44} +(1.51543 + 1.26520i) q^{46} +(-5.48316 + 9.49712i) q^{47} +(-6.96633 + 0.685774i) q^{49} +(-3.70682 + 1.35960i) q^{50} +(1.74500 - 4.86944i) q^{52} +(4.99481 - 2.88375i) q^{53} +7.49868 q^{55} +(-6.68172 - 3.36965i) q^{56} +(0.889482 + 0.154564i) q^{58} +(-3.01720 + 1.74198i) q^{59} +(-11.1614 - 6.44406i) q^{61} +(4.85341 - 1.78015i) q^{62} +(-4.10275 - 6.86786i) q^{64} +(1.92162 - 3.32834i) q^{65} +(-0.443410 + 0.256003i) q^{67} +(-0.449735 - 2.47855i) q^{68} +(-4.43771 - 3.34973i) q^{70} +7.41363 q^{71} +(-4.94731 - 8.56899i) q^{73} +(5.45644 - 6.53562i) q^{74} +(4.00667 + 4.72709i) q^{76} +(-7.23463 - 11.2212i) q^{77} +(-4.35341 + 7.54032i) q^{79} +(-2.08830 - 5.56500i) q^{80} +(-1.54041 + 8.86475i) q^{82} -2.97196i q^{83} -1.87161i q^{85} +(1.42679 + 0.247931i) q^{86} +(-0.106298 - 14.2727i) q^{88} +(-1.29186 + 2.23757i) q^{89} +(-6.83456 + 0.335590i) q^{91} +(2.12976 - 1.80517i) q^{92} +(11.9051 + 9.93929i) q^{94} +(2.30203 + 3.98724i) q^{95} -1.57040 q^{97} +(-0.731157 + 9.87246i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 4 q^{7} - 4 q^{8}+O(q^{10}) \) 12 * q + 2 * q^2 - 4 * q^7 - 4 * q^8	\( 12 q + 2 q^{2} - 4 q^{7} - 4 q^{8} - 8 q^{10} + 16 q^{14} + 8 q^{16} + 2 q^{17} - 8 q^{20} + 12 q^{22} - 2 q^{23} - 4 q^{25} + 2 q^{26} + 26 q^{28} + 10 q^{31} + 12 q^{32} + 32 q^{34} - 18 q^{38} + 10 q^{40} + 8 q^{41} + 30 q^{44} - 4 q^{46} - 30 q^{47} - 12 q^{49} + 16 q^{50} - 32 q^{52} + 4 q^{55} + 40 q^{56} - 22 q^{58} + 28 q^{62} + 24 q^{64} - 8 q^{65} - 4 q^{68} - 48 q^{70} - 32 q^{71} - 10 q^{73} - 18 q^{74} + 52 q^{76} - 22 q^{79} - 36 q^{80} - 26 q^{82} - 40 q^{86} - 14 q^{88} + 10 q^{89} + 20 q^{92} + 42 q^{94} + 34 q^{95} + 40 q^{97} - 52 q^{98}+O(q^{100}) \) 12 * q + 2 * q^2 - 4 * q^7 - 4 * q^8 - 8 * q^10 + 16 * q^14 + 8 * q^16 + 2 * q^17 - 8 * q^20 + 12 * q^22 - 2 * q^23 - 4 * q^25 + 2 * q^26 + 26 * q^28 + 10 * q^31 + 12 * q^32 + 32 * q^34 - 18 * q^38 + 10 * q^40 + 8 * q^41 + 30 * q^44 - 4 * q^46 - 30 * q^47 - 12 * q^49 + 16 * q^50 - 32 * q^52 + 4 * q^55 + 40 * q^56 - 22 * q^58 + 28 * q^62 + 24 * q^64 - 8 * q^65 - 4 * q^68 - 48 * q^70 - 32 * q^71 - 10 * q^73 - 18 * q^74 + 52 * q^76 - 22 * q^79 - 36 * q^80 - 26 * q^82 - 40 * q^86 - 14 * q^88 + 10 * q^89 + 20 * q^92 + 42 * q^94 + 34 * q^95 + 40 * q^97 - 52 * q^98

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