LMFDB - Embedded newform 504.2.cj.c.37.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(37,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [12,2,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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			37.5
Root			$-0.716208 + 1.21944i$ of defining polynomial
Character	$\chi$	$=$	504.37
Dual form			504.2.cj.c.109.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.08560 - 0.906347i) q^{2} +(0.357071 - 1.96787i) q^{4} +(1.28690 + 0.742990i) q^{5} +(0.129755 + 2.64257i) q^{7} +(-1.39593 - 2.45995i) q^{8} +(2.07047 - 0.359782i) q^{10} +(4.37021 - 2.52314i) q^{11} -2.58633i q^{13} +(2.53595 + 2.75118i) q^{14} +(-3.74500 - 1.40534i) q^{16} +(0.629755 + 1.09077i) q^{17} +(2.68324 + 1.54917i) q^{19} +(1.92162 - 2.26714i) q^{20} +(2.45748 - 6.70006i) q^{22} +(-0.697966 + 1.20891i) q^{23} +(-1.39593 - 2.41782i) q^{25} +(-2.34411 - 2.80773i) q^{26} +(5.24655 + 0.688244i) q^{28} -0.638384i q^{29} +(1.82772 + 3.16571i) q^{31} +(-5.33931 + 1.86863i) q^{32} +(1.67228 + 0.613365i) q^{34} +(-1.79642 + 3.49712i) q^{35} +(-5.21370 - 3.01013i) q^{37} +(4.31702 - 0.750162i) q^{38} +(0.0313016 - 4.20287i) q^{40} -6.36226 q^{41} -1.02401i q^{43} +(-3.40473 - 9.50094i) q^{44} +(0.337979 + 1.94500i) q^{46} +(-5.48316 + 9.49712i) q^{47} +(-6.96633 + 0.685774i) q^{49} +(-3.70682 - 1.35960i) q^{50} +(-5.08956 - 0.923505i) q^{52} +(-4.99481 + 2.88375i) q^{53} +7.49868 q^{55} +(6.31947 - 4.00804i) q^{56} +(-0.578597 - 0.693032i) q^{58} +(3.01720 - 1.74198i) q^{59} +(11.1614 + 6.44406i) q^{61} +(4.85341 + 1.78015i) q^{62} +(-4.10275 + 6.86786i) q^{64} +(1.92162 - 3.32834i) q^{65} +(0.443410 - 0.256003i) q^{67} +(2.37135 - 0.849793i) q^{68} +(1.21940 + 5.42466i) q^{70} +7.41363 q^{71} +(-4.94731 - 8.56899i) q^{73} +(-8.38823 + 1.45761i) q^{74} +(4.00667 - 4.72709i) q^{76} +(7.23463 + 11.2212i) q^{77} +(-4.35341 + 7.54032i) q^{79} +(-3.77528 - 4.59102i) q^{80} +(-6.90689 + 5.76641i) q^{82} +2.97196i q^{83} +1.87161i q^{85} +(-0.928109 - 1.11167i) q^{86} +(-12.3073 - 7.22839i) q^{88} +(-1.29186 + 2.23757i) q^{89} +(6.83456 - 0.335590i) q^{91} +(2.12976 + 1.80517i) q^{92} +(2.65514 + 15.2798i) q^{94} +(2.30203 + 3.98724i) q^{95} -1.57040 q^{97} +(-6.94112 + 7.05839i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

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 $

$2$	1.08560	−	0.906347i	0.767638	−	0.640884i
$2$	1.08560	−	0.906347i	0.767638	−	0.640884i
$3$		0			0
$3$		0			0
$4$	0.357071	−	1.96787i	0.178536	−	0.983933i
$5$	1.28690	+	0.742990i	0.575518	+	0.332275i	0.759350	−	0.650682i	$-0.225517\pi$
$5$	1.28690	+	0.742990i	0.575518	+	0.332275i	−0.183832	+	0.982958i	$0.558850\pi$
$6$		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
$10$	2.07047	−	0.359782i	0.654739	−	0.113773i
$11$	4.37021	−	2.52314i	1.31767	−	0.760756i	0.334315	−	0.942461i	$-0.391495\pi$
$11$	4.37021	−	2.52314i	1.31767	−	0.760756i	0.983353	+	0.181705i	$0.0581616\pi$
$12$		0			0
$13$		−	2.58633i		−	0.717320i	−0.933468	−	0.358660i	$-0.883234\pi$
$13$		−	2.58633i		−	0.717320i	0.933468	−	0.358660i	$-0.116766\pi$
$14$	2.53595	+	2.75118i	0.677760	+	0.735283i
$15$		0			0
$16$	−3.74500	−	1.40534i	−0.936250	−	0.351334i
$17$	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	0.775145	−	0.631783i	$-0.217677\pi$
$19$	2.68324	+	1.54917i	0.615577	+	0.355404i	−0.159568	+	0.987187i	$0.551010\pi$
$20$	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
$26$	−2.34411	−	2.80773i	−0.459719	−	0.550642i
$27$		0			0
$28$	5.24655	+	0.688244i	0.991505	+	0.130066i
$29$		−	0.638384i		−	0.118545i	−0.998242	−	0.0592725i	$-0.981122\pi$
$29$		−	0.638384i		−	0.118545i	0.998242	−	0.0592725i	$-0.0188781\pi$
$30$		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	$0.726868\pi$
$32$	−5.33931	+	1.86863i	−0.943865	+	0.330330i
$33$		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	0.00592229	−	0.999982i	$-0.498115\pi$
$37$	−5.21370	−	3.01013i	−0.857127	−	0.494862i	−0.863049	+	0.505120i	$0.831448\pi$
$38$	4.31702	−	0.750162i	0.700313	−	0.121692i
$39$		0			0
$40$	0.0313016	−	4.20287i	0.00494921	−	0.664532i
$41$	−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	$-0.975121\pi$
$43$		−	1.02401i		−	0.156160i	0.996947	−	0.0780801i	$-0.0248790\pi$
$44$	−3.40473	−	9.50094i	−0.513283	−	1.43232i
$45$		0			0
$46$	0.337979	+	1.94500i	0.0498323	+	0.286774i
$47$	−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
$52$	−5.08956	−	0.923505i	−0.705795	−	0.128067i
$53$	−4.99481	+	2.88375i	−0.686089	+	0.396114i	−0.802145	−	0.597129i	$-0.796308\pi$
$53$	−4.99481	+	2.88375i	−0.686089	+	0.396114i	0.116056	+	0.993243i	$0.462975\pi$
$54$		0			0
$55$	7.49868			1.01112
$56$	6.31947	−	4.00804i	0.844474	−	0.535596i
$57$		0			0
$58$	−0.578597	−	0.693032i	−0.0759735	−	0.0909996i
$59$	3.01720	−	1.74198i	0.392806	−	0.226787i	−0.290569	−	0.956854i	$-0.593845\pi$
$59$	3.01720	−	1.74198i	0.392806	−	0.226787i	0.683375	+	0.730067i	$0.260511\pi$
$60$		0			0
$61$	11.1614	+	6.44406i	1.42908	+	0.825077i	0.997048	−	0.0767831i	$-0.0244649\pi$
$61$	11.1614	+	6.44406i	1.42908	+	0.825077i	0.432028	+	0.901860i	$0.357798\pi$
$62$	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	−0.472670	−	0.881240i	$-0.656710\pi$
$67$	0.443410	−	0.256003i	0.0541711	−	0.0312757i	0.526841	+	0.849964i	$0.323376\pi$
$68$	2.37135	−	0.849793i	0.287569	−	0.103052i
$69$		0			0
$70$	1.21940	+	5.42466i	0.145746	+	0.648371i
$71$	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	$-0.363239\pi$
$74$	−8.38823	+	1.45761i	−0.975112	+	0.169444i
$75$		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	$0.329596\pi$
$80$	−3.77528	−	4.59102i	−0.422089	−	0.513292i
$81$		0			0
$82$	−6.90689	+	5.76641i	−0.762739	+	0.636794i
$83$			2.97196i			0.326215i	0.986608	+	0.163107i	$0.0521517\pi$
$83$			2.97196i			0.326215i	−0.986608	+	0.163107i	$0.947848\pi$
$84$		0			0
$85$			1.87161i			0.203004i
$86$	−0.928109	−	1.11167i	−0.100081	−	0.119875i
$87$		0			0
$88$	−12.3073	−	7.22839i	−1.31197	−	0.770549i
$89$	−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
$94$	2.65514	+	15.2798i	0.273857	+	1.57599i
$95$	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	$0.525404\pi$
$98$	−6.94112	+	7.05839i	−0.701159	+	0.713005i
$99$		0			0
$100$	−5.25640	+	1.88367i	−0.525640	+	0.188367i
$101$	0.181183	−	0.104606i	0.0180284	−	0.0104087i	−0.490959	−	0.871183i	$-0.663353\pi$
$101$	0.181183	−	0.104606i	0.0180284	−	0.0104087i	0.508987	+	0.860774i	$0.330020\pi$
$102$		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	−0.151447	−	0.988465i	$-0.548393\pi$
$107$	−11.2048	−	6.46908i	−1.08321	−	0.625389i	−0.931759	+	0.363076i	$0.881726\pi$
$108$		0			0
$109$	−16.6430	+	9.60883i	−1.59411	+	0.920359i	−0.601517	+	0.798860i	$0.705437\pi$
$109$	−16.6430	+	9.60883i	−1.59411	+	0.920359i	−0.992591	+	0.121500i	$0.961230\pi$
$110$	8.14060	−	6.79640i	0.776175	−	0.648012i
$111$		0			0
$112$	3.22777	−	10.0788i	0.304995	−	0.952354i
$113$	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
$116$	−1.25625	−	0.227949i	−0.116640	−	0.0211645i
$117$		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
$122$	17.9574	−	3.12044i	1.62579	−	0.282511i
$123$		0			0
$124$	6.88231	−	2.46633i	0.618050	−	0.221483i
$125$		−	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	$0.603619\pi$
$128$	1.77070	+	11.1743i	0.156509	+	0.987676i
$129$		0			0
$130$	−0.930515	−	5.35491i	−0.0816115	−	0.469657i
$131$	12.7767	+	7.37662i	1.11630	+	0.644498i	0.940455	−	0.339919i	$-0.110400\pi$
$131$	12.7767	+	7.37662i	1.11630	+	0.644498i	0.175849	+	0.984417i	$0.443733\pi$
$132$		0			0
$133$	−3.74562	+	7.29165i	−0.324786	+	0.632267i
$134$	0.249340	−	0.679801i	0.0215397	−	0.0587258i
$135$		0			0
$136$	1.80414	−	3.07181i	0.154704	−	0.263405i
$137$	−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	$-0.977096\pi$
$139$		−	1.69519i		−	0.143784i	0.997412	−	0.0718921i	$-0.0229037\pi$
$140$	6.24041	+	4.78383i	0.527411	+	0.404308i
$141$		0			0
$142$	8.04827	−	6.71932i	0.675396	−	0.563873i
$143$	−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	0.363485	−	0.931600i	$-0.381587\pi$
$149$	−3.19276	−	1.84334i	−0.261561	−	0.151012i	−0.625047	+	0.780587i	$0.714920\pi$
$150$		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	$0.636022\pi$
$152$	0.0652653	−	8.76318i	0.00529371	−	0.710788i
$153$		0			0
$154$	18.0242	+	5.62468i	1.45243	+	0.453250i
$155$			5.43191i			0.436302i
$156$		0			0
$157$	11.1614	−	6.44406i	0.890780	−	0.514292i	0.0165822	−	0.999863i	$-0.494721\pi$
$157$	11.1614	−	6.44406i	0.890780	−	0.514292i	0.874197	+	0.485571i	$0.161388\pi$
$158$	2.10807	+	12.1315i	0.167709	+	0.965130i
$159$		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	0.386390	−	0.922335i	$-0.373722\pi$
$163$	−2.79831	−	1.61560i	−0.219180	−	0.126544i	−0.605571	+	0.795791i	$0.707055\pi$
$164$	−2.27178	+	12.5201i	−0.177396	+	0.977654i
$165$		0			0
$166$	2.69363	+	3.22637i	0.209066	+	0.250415i
$167$	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
$170$	1.69633	+	2.03182i	0.130102	+	0.155834i
$171$		0			0
$172$	−2.01512	−	0.365645i	−0.153651	−	0.0278802i
$173$	−5.66273	−	3.26938i	−0.430529	−	0.248566i	0.269043	−	0.963128i	$-0.413293\pi$
$173$	−5.66273	−	3.26938i	−0.430529	−	0.248566i	−0.699572	+	0.714562i	$0.746626\pi$
$174$		0			0
$175$	6.20814	−	4.00257i	0.469291	−	0.302566i
$176$	−19.9123	+	3.30755i	−1.50095	+	0.249316i
$177$		0			0
$178$	0.625565	+	3.59999i	0.0468881	+	0.269831i
$179$	−0.109447	+	0.0631891i	−0.00818044	+	0.00472298i	−0.504085	−	0.863654i	$-0.668170\pi$
$179$	−0.109447	+	0.0631891i	−0.00818044	+	0.00472298i	0.495904	+	0.868377i	$0.334837\pi$
$180$		0			0
$181$		−	2.71920i		−	0.202117i	−0.994880	−	0.101058i	$-0.967777\pi$
$181$		−	2.71920i		−	0.202117i	0.994880	−	0.101058i	$-0.0322229\pi$
$182$	7.11546	−	6.55880i	0.527433	−	0.486170i
$183$		0			0
$184$	3.94818	+	0.0294048i	0.291064	+	0.00216775i
$185$	−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	$0.878723\pi$
$194$	−1.70483	+	1.42332i	−0.122399	+	0.102189i
$195$		0			0
$196$	−1.13796	+	13.9537i	−0.0812831	+	0.996691i
$197$		−	19.5468i		−	1.39265i	−0.717727	−	0.696325i	$-0.754817\pi$
$197$		−	19.5468i		−	1.39265i	0.717727	−	0.696325i	$-0.245183\pi$
$198$		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	$-0.430473\pi$
$200$	−3.99911	+	6.80905i	−0.282780	+	0.481472i
$201$		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
$206$	1.66502	+	9.58183i	0.116007	+	0.667598i
$207$		0			0
$208$	−3.63467	+	9.68582i	−0.252019	+	0.671590i
$209$	15.6351			1.08150
$210$		0			0
$211$		−	17.2132i		−	1.18500i	−0.805569	−	0.592502i	$-0.798140\pi$
$211$		−	17.2132i		−	1.18500i	0.805569	−	0.592502i	$-0.201860\pi$
$212$	3.89134	+	10.8588i	0.267258	+	0.745787i
$213$		0			0
$214$	−18.0272	+	3.13255i	−1.23231	+	0.214137i
$215$	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
$220$	2.67756	−	14.7564i	0.180521	−	0.994877i
$221$	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	$0.300509\pi$
$224$	−5.63078	−	13.8670i	−0.376222	−	0.926529i
$225$		0			0
$226$	1.14138	−	0.952910i	0.0759232	−	0.0633866i
$227$	−11.4237	+	6.59546i	−0.758215	+	0.437756i	−0.828655	−	0.559760i	$-0.810893\pi$
$227$	−11.4237	+	6.59546i	−0.758215	+	0.437756i	0.0704394	+	0.997516i	$0.477560\pi$
$228$		0			0
$229$	−14.8693	−	8.58482i	−0.982594	−	0.567301i	−0.0795417	−	0.996832i	$-0.525346\pi$
$229$	−14.8693	−	8.58482i	−0.982594	−	0.567301i	−0.903052	+	0.429531i	$0.858679\pi$
$230$	−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
$236$	−2.35063	−	6.55947i	−0.153013	−	0.426985i
$237$		0			0
$238$	−1.40387	+	4.49870i	−0.0909995	+	0.291607i
$239$	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	$0.579115\pi$
$242$	−3.50223	−	20.1546i	−0.225132	−	1.29559i
$243$		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
$248$	5.23612	−	8.91522i	0.332494	−	0.566117i
$249$		0			0
$250$	−10.4942	−	12.5697i	−0.663710	−	0.794979i
$251$		−	27.4386i		−	1.73191i	−0.500121	−	0.865955i	$-0.666711\pi$
$251$		−	27.4386i		−	1.73191i	0.500121	−	0.865955i	$-0.333289\pi$
$252$		0			0
$253$			7.04427i			0.442870i
$254$	−7.82518	+	6.53307i	−0.490995	+	0.409921i
$255$		0			0
$256$	12.0501	+	10.5260i	0.753128	+	0.657874i
$257$	−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
$262$	20.5562	−	3.57201i	1.26996	−	0.220680i
$263$	−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
$266$	2.54251	+	11.3107i	0.155891	+	0.693502i
$267$		0			0
$268$	−0.345451	−	0.963983i	−0.0211018	−	0.0588846i
$269$	−20.7887	+	12.0024i	−1.26751	+	0.731796i	−0.974516	−	0.224319i	$-0.927984\pi$
$269$	−20.7887	+	12.0024i	−1.26751	+	0.731796i	−0.292992	+	0.956115i	$0.594651\pi$
$270$		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	0.458136	−	0.888882i	$-0.348517\pi$
$277$	24.2493	−	14.0003i	1.45700	−	0.841199i	0.998863	+	0.0476832i	$0.0151838\pi$
$278$	−1.53643	−	1.84031i	−0.0921490	−	0.110374i
$279$		0			0
$280$	11.1104	−	0.462628i	0.663975	−	0.0276473i
$281$	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	−0.997404	−	0.0720102i	$-0.977059\pi$
$283$	−24.1193	+	13.9253i	−1.43374	+	0.827772i	−0.436339	+	0.899782i	$0.643725\pi$
$284$	2.64720	−	14.5890i	0.157082	−	0.865700i
$285$		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
$290$	−0.229679	−	1.32175i	−0.0134872	−	0.0776160i
$291$		0			0
$292$	−18.6292	+	6.67590i	−1.09019	+	0.390678i
$293$			20.1851i			1.17923i	0.807685	+	0.589614i	$0.200720\pi$
$293$			20.1851i			1.17923i	−0.807685	+	0.589614i	$0.799280\pi$
$294$		0			0
$295$	5.17710			0.301423
$296$	−0.126814	+	17.0274i	−0.00737094	+	0.989697i
$297$		0			0
$298$	−5.13678	+	0.892611i	−0.297566	+	0.0517075i
$299$	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
$304$	−7.87163	−	9.57249i	−0.451469	−	0.549020i
$305$	9.57574	+	16.5857i	0.548305	+	0.949693i
$306$		0			0
$307$		−	17.8844i		−	1.02071i	−0.859962	−	0.510357i	$-0.829513\pi$
$307$		−	17.8844i		−	1.02071i	0.859962	−	0.510357i	$-0.170487\pi$
$308$	24.6651	−	10.2300i	1.40542	−	0.582910i
$309$		0			0
$310$	4.92320	+	5.89691i	0.279619	+	0.334922i
$311$	−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	0.748840	−	0.662751i	$-0.230611\pi$
$317$	9.78002	+	5.64650i	0.549301	+	0.317139i	−0.199539	+	0.979890i	$0.563944\pi$
$318$		0			0
$319$	−1.61073	−	2.78987i	−0.0901838	−	0.156203i
$320$	−10.3826	+	5.78992i	−0.580403	+	0.323666i
$321$		0			0
$322$	−5.09594	+	1.14551i	−0.283985	+	0.0638366i
$323$			3.90239i			0.217135i
$324$		0			0
$325$	−6.25330	+	3.61034i	−0.346871	+	0.200266i
$326$	−4.50215	+	0.782332i	−0.249351	+	0.0433294i
$327$		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	0.945078	−	0.326845i	$-0.105986\pi$
$331$	20.6415	+	11.9174i	1.13456	+	0.655039i	0.189483	+	0.981884i	$0.439319\pi$
$332$	5.84842	+	1.06120i	0.320974	+	0.0582410i
$333$		0			0
$334$	15.2514	−	12.7330i	0.834517	−	0.696720i
$335$	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	$0.351975\pi$
$338$	6.85112	−	5.71985i	0.372652	−	0.311119i
$339$		0			0
$340$	3.68307	+	0.668297i	0.199743	+	0.0362435i
$341$	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
$346$	−9.11067	+	1.58315i	−0.489793	+	0.0851105i
$347$	2.78706	−	1.60911i	0.149617	−	0.0863817i	−0.423322	−	0.905979i	$-0.639136\pi$
$347$	2.78706	−	1.60911i	0.149617	−	0.0863817i	0.572940	+	0.819597i	$0.305803\pi$
$348$		0			0
$349$		−	22.8716i		−	1.22429i	−0.790747	−	0.612143i	$-0.790308\pi$
$349$		−	22.8716i		−	1.22429i	0.790747	−	0.612143i	$-0.209692\pi$
$350$	3.11186	−	9.97193i	0.166336	−	0.533022i
$351$		0			0
$352$	−18.6191	+	21.6381i	−0.992401	+	1.15332i
$353$	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
$362$	−2.46454	−	2.95198i	−0.129533	−	0.155152i
$363$		0			0
$364$	1.78003	−	13.5693i	0.0932988	−	0.711226i
$365$		−	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	$-0.429420\pi$
$368$	4.31281	−	3.54650i	0.224821	−	0.184874i
$369$		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	0.649551	−	0.760318i	$-0.274957\pi$
$373$	6.10052	+	3.52214i	0.315873	+	0.182369i	−0.333679	+	0.942687i	$0.608290\pi$
$374$	8.85582	−	1.53886i	0.457924	−	0.0795727i
$375$		0			0
$376$	31.0166	+	0.231001i	1.59956	+	0.0119130i
$377$	−1.65107			−0.0850346
$378$		0			0
$379$			13.1974i			0.677905i	0.940803	+	0.338953i	$0.110073\pi$
$379$			13.1974i			0.677905i	−0.940803	+	0.338953i	$0.889927\pi$
$380$	8.66835	−	3.10637i	0.444677	−	0.159353i
$381$		0			0
$382$	0.592535	+	3.40991i	0.0303167	+	0.174466i
$383$	−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
$388$	−0.560743	+	3.09033i	−0.0284674	+	0.156888i
$389$	19.8735	−	11.4739i	1.00762	−	0.581752i	0.0971291	−	0.995272i	$-0.469034\pi$
$389$	19.8735	−	11.4739i	1.00762	−	0.581752i	0.910495	+	0.413520i	$0.135701\pi$
$390$		0			0
$391$	−1.75819			−0.0889155
$392$	11.4115	+	16.1796i	0.576367	+	0.817191i
$393$		0			0
$394$	−17.7161	−	21.2200i	−0.892526	−	1.06905i
$395$	−11.2048	+	6.46908i	−0.563773	+	0.325495i
$396$		0			0
$397$	25.9079	+	14.9579i	1.30028	+	0.750716i	0.980452	−	0.196760i	$-0.0630420\pi$
$397$	25.9079	+	14.9579i	1.30028	+	0.750716i	0.319827	+	0.947476i	$0.396375\pi$
$398$	−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
$404$	−0.141155	−	0.393896i	−0.00702275	−	0.0195970i
$405$		0			0
$406$	1.75631	−	1.61891i	0.0871641	−	0.0803450i
$407$	−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	$0.610210\pi$
$410$	−13.1728	+	2.28902i	−0.650560	+	0.113047i
$411$		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
$416$	4.83290	+	13.8092i	0.236952	+	0.677053i
$417$		0			0
$418$	16.9735	−	14.1708i	0.830202	−	0.693118i
$419$			0.252757i			0.0123480i	0.999981	+	0.00617398i	$0.00196525\pi$
$419$			0.252757i			0.0123480i	−0.999981	+	0.00617398i	$0.998035\pi$
$420$		0			0
$421$		−	18.3701i		−	0.895302i	−0.894208	−	0.447651i	$-0.852261\pi$
$421$		−	18.3701i		−	0.895302i	0.894208	−	0.447651i	$-0.147739\pi$
$422$	−15.6011	−	18.6867i	−0.759450	−	0.909654i
$423$		0			0
$424$	14.0663	+	8.26147i	0.683120	+	0.401212i
$425$	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
$430$	−0.368420	−	2.12018i	−0.0177668	−	0.102244i
$431$	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	$0.555830\pi$
$434$	−4.07442	+	13.0564i	−0.195578	+	0.626729i
$435$		0			0
$436$	12.9662	+	36.1822i	0.620967	+	1.73281i
$437$	−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	0.998086	−	0.0618342i	$-0.0196950\pi$
$443$	30.3838	+	17.5421i	1.44358	+	0.833451i	0.445493	+	0.895285i	$0.353028\pi$
$444$		0			0
$445$	−3.32499	+	1.91968i	−0.157620	+	0.0910017i
$446$	19.0159	−	15.8759i	0.900427	−	0.751746i
$447$		0			0
$448$	−18.6811	−	9.95065i	−0.882600	−	0.470124i
$449$	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
$452$	0.375415	−	2.06896i	0.0176581	−	0.0973159i
$453$		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	$0.267948\pi$
$458$	−23.9230	+	4.15707i	−1.11785	+	0.194247i
$459$		0			0
$460$	1.39955	+	3.90546i	0.0652543	+	0.182093i
$461$		−	2.68641i		−	0.125118i	−0.998041	−	0.0625592i	$-0.980074\pi$
$461$		−	2.68641i		−	0.125118i	0.998041	−	0.0625592i	$-0.0199262\pi$
$462$		0			0
$463$	−21.0380			−0.977721			−0.488860	−	0.872362i	$-0.662587\pi$
$463$	−21.0380			−0.977721			−0.488860	+	0.872362i	$0.662587\pi$
$464$	−0.897145	+	2.39075i	−0.0416489	+	0.110988i
$465$		0			0
$466$	−6.02355	−	34.6643i	−0.279036	−	1.60579i
$467$	21.3849	+	12.3466i	0.989574	+	0.571331i	0.905147	−	0.425099i	$-0.139761\pi$
$467$	21.3849	+	12.3466i	0.989574	+	0.571331i	0.0844270	+	0.996430i	$0.473094\pi$
$468$		0			0
$469$	0.734040	+	1.13852i	0.0338948	+	0.0525721i
$470$	−7.93582	+	21.6362i	−0.366052	+	0.998004i
$471$		0			0
$472$	−8.49701	−	4.99049i	−0.391106	−	0.229706i
$473$	−2.58373	−	4.47515i	−0.118800	−	0.205767i
$474$		0			0
$475$		−	8.65014i		−	0.396896i
$476$	2.55333	+	6.15620i	0.117032	+	0.282169i
$477$		0			0
$478$	14.4648	−	12.0764i	0.661605	−	0.552360i
$479$	−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	$0.963377\pi$
$488$	0.271483	−	36.4521i	0.0122895	−	1.65011i
$489$		0			0
$490$	−14.1768	+	3.92623i	−0.640443	+	0.177369i
$491$		−	15.7509i		−	0.710830i	−0.934709	−	0.355415i	$-0.884340\pi$
$491$		−	15.7509i		−	0.710830i	0.934709	−	0.355415i	$-0.115660\pi$
$492$		0			0
$493$	0.696329	−	0.402026i	0.0313611	−	0.0181063i
$494$	−1.94017	−	11.1652i	−0.0872922	−	0.502348i
$495$		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	0.289379	−	0.957215i	$-0.406551\pi$
$499$	−8.82147	−	5.09308i	−0.394903	−	0.227997i	−0.684282	+	0.729217i	$0.739884\pi$
$500$	−22.7851	−	4.13437i	−1.01898	−	0.184895i
$501$		0			0
$502$	−24.8689	−	29.7875i	−1.10995	−	1.32948i
$503$	−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
$506$	6.38455	+	7.64729i	0.283828	+	0.339963i
$507$		0			0
$508$	−2.57382	+	14.1847i	−0.114195	+	0.629342i
$509$	19.4357	+	11.2212i	0.861471	+	0.497371i	0.864505	−	0.502625i	$-0.167632\pi$
$509$	19.4357	+	11.2212i	0.861471	+	0.497371i	−0.00303361	+	0.999995i	$0.500966\pi$
$510$		0			0
$511$	22.0022	−	14.1855i	0.973319	−	0.627528i
$512$	22.6218	+	0.505513i	0.999750	+	0.0223407i
$513$		0			0
$514$	5.85670	+	33.7041i	0.258328	+	1.48662i
$515$	−8.84987	+	5.10948i	−0.389972	+	0.225150i
$516$		0			0
$517$			55.3392i			2.43382i
$518$	−4.94025	−	21.9773i	−0.217062	−	0.965629i
$519$		0			0
$520$	−10.8700	−	0.0809563i	−0.476682	−	0.00355017i
$521$	−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	0.122184	−	0.992507i	$-0.461010\pi$
$523$	−15.4655	−	8.92903i	−0.676261	−	0.390439i	−0.798445	+	0.602068i	$0.794344\pi$
$524$	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
$530$	−9.30405	+	7.76775i	−0.404142	+	0.337409i
$531$		0			0
$532$	13.0116	+	9.97452i	0.564122	+	0.432450i
$533$			16.4549i			0.712742i
$534$		0			0
$535$	−9.61292	−	16.6501i	−0.415603	−	0.719845i
$536$	−1.24873	−	0.733406i	−0.0539367	−	0.0316783i
$537$		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	0.00609356	−	0.999981i	$-0.498060\pi$
$541$	−19.9303	−	11.5067i	−0.856869	−	0.494714i	−0.862963	+	0.505268i	$0.831394\pi$
$542$	1.50674	+	8.67099i	0.0647202	+	0.372451i
$543$		0			0
$544$	−5.40070	−	4.64717i	−0.231553	−	0.199246i
$545$	−28.5571			−1.22325
$546$		0			0
$547$			9.10136i			0.389146i	0.980888	+	0.194573i	$0.0623321\pi$
$547$			9.10136i			0.389146i	−0.980888	+	0.194573i	$0.937668\pi$
$548$	−17.6269	+	6.31672i	−0.752983	+	0.269837i
$549$		0			0
$550$	−19.6300	+	3.41108i	−0.837028	+	0.145449i
$551$	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
$556$	−3.33591	−	0.605304i	−0.141474	−	0.0256706i
$557$	−15.0016	+	8.66116i	−0.635637	+	0.366985i	−0.782932	−	0.622107i	$-0.786277\pi$
$557$	−15.0016	+	8.66116i	−0.635637	+	0.366985i	0.147295	+	0.989093i	$0.452943\pi$
$558$		0			0
$559$	−2.64843			−0.112017
$560$	11.6422	−	10.5721i	0.491974	−	0.446754i
$561$		0			0
$562$	18.1417	−	15.1461i	0.765263	−	0.638901i
$563$	6.91560	−	3.99272i	0.291458	−	0.168273i	−0.347141	−	0.937813i	$-0.612848\pi$
$563$	6.91560	−	3.99272i	0.291458	−	0.168273i	0.638599	+	0.769540i	$0.279514\pi$
$564$		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	$-0.316255\pi$
$571$	36.9016	−	21.3051i	1.54428	−	0.891592i	0.998561	−	0.0536265i	$-0.0170780\pi$
$572$	−24.5726	+	8.80577i	−1.02743	+	0.368188i
$573$		0			0
$574$	−16.1343	−	17.5037i	−0.673434	−	0.730591i
$575$	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	$0.619246\pi$
$578$	−3.73191	−	21.4763i	−0.155227	−	0.893298i
$579$		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
$584$	−14.1732	+	24.1319i	−0.586492	+	0.998584i
$585$		0			0
$586$	18.2947	+	21.9131i	0.755749	+	0.905221i
$587$			19.4269i			0.801833i	0.916115	+	0.400916i	$0.131308\pi$
$587$			19.4269i			0.801833i	−0.916115	+	0.400916i	$0.868692\pi$
$588$		0			0
$589$			11.3258i			0.466671i
$590$	5.62028	−	4.69225i	0.231383	−	0.193177i
$591$		0			0
$592$	15.2951	+	18.5999i	0.628623	+	0.764453i
$593$	−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
$598$	5.03041	−	0.874127i	0.205709	−	0.0357457i
$599$	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	$0.527423\pi$
$602$	2.81724	−	2.59684i	0.114822	−	0.105839i
$603$		0			0
$604$	26.8805	−	9.63284i	1.09375	−	0.391955i
$605$	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	−0.563307	−	0.826248i	$-0.690471\pi$
$613$	−3.20401	+	1.84984i	−0.129409	+	0.0747141i	0.433898	+	0.900962i	$0.357138\pi$
$614$	−16.2094	−	19.4153i	−0.654160	−	0.783539i
$615$		0			0
$616$	17.5046	−	33.4609i	0.705279	−	1.34818i
$617$	−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	0.176098	−	0.984373i	$-0.443652\pi$
$619$	27.7816	−	16.0397i	1.11664	−	0.644692i	0.940541	+	0.339681i	$0.110319\pi$
$620$	10.6893	+	1.93958i	0.429292	+	0.0778954i
$621$		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
$626$	1.17586	+	6.76682i	0.0469968	+	0.270457i
$627$		0			0
$628$	−8.69562	−	24.2652i	−0.346993	−	0.968287i
$629$		−	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	$0.424833\pi$
$632$	24.6259	+	0.183406i	0.979566	+	0.00729548i
$633$		0			0
$634$	15.7349	−	2.73423i	0.624913	−	0.108590i
$635$	−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
$640$	−6.02367	+	15.6958i	−0.238107	+	0.620429i
$641$	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	$0.321373\pi$
$643$			42.9368i			1.69326i	−0.532180	+	0.846631i	$0.678627\pi$
$644$	−4.49394	+	5.86225i	−0.177086	+	0.231005i
$645$		0			0
$646$	3.53692	+	4.23645i	0.139158	+	0.166681i
$647$	−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	0.0830227	−	0.996548i	$-0.473543\pi$
$653$	−18.8716	−	10.8955i	−0.738502	−	0.426374i	−0.821524	+	0.570174i	$0.806876\pi$
$654$		0			0
$655$	10.9615	+	18.9859i	0.428301	+	0.741840i
$656$	23.8267	+	8.94112i	0.930275	+	0.349092i
$657$		0			0
$658$	−40.0333	+	8.99901i	−1.56066	+	0.350818i
$659$		−	0.152682i		−	0.00594765i	−0.999996	−	0.00297383i	$-0.999053\pi$
$659$		−	0.152682i		−	0.00594765i	0.999996	−	0.00297383i	$-0.000946600\pi$
$660$		0			0
$661$	24.6004	−	14.2031i	0.956845	−	0.552435i	0.0616446	−	0.998098i	$-0.480365\pi$
$661$	24.6004	−	14.2031i	0.956845	−	0.552435i	0.895201	+	0.445663i	$0.147032\pi$
$662$	33.2098	−	5.77081i	1.29074	−	0.224289i
$663$		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
$668$	5.01640	−	27.6460i	0.194090	−	1.06966i
$669$		0			0
$670$	0.825960	−	0.689576i	0.0319096	−	0.0266406i
$671$	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	$0.331119\pi$
$674$	17.8745	−	14.9230i	0.688499	−	0.574813i
$675$		0			0
$676$	2.25344	−	12.4190i	0.0866706	−	0.477653i
$677$	−4.00416	−	2.31180i	−0.153892	−	0.0888498i	0.421076	−	0.907025i	$-0.361652\pi$
$677$	−4.00416	−	2.31180i	−0.153892	−	0.0888498i	−0.574969	+	0.818175i	$0.694986\pi$
$678$		0			0
$679$	−0.203767	−	4.14988i	−0.00781986	−	0.159258i
$680$	4.60407	−	2.61264i	0.176558	−	0.100190i
$681$		0			0
$682$	25.7020	−	4.46620i	0.984181	−	0.171020i
$683$	16.8469	−	9.72659i	0.644631	−	0.372178i	−0.141765	−	0.989900i	$-0.545278\pi$
$683$	16.8469	−	9.72659i	0.644631	−	0.372178i	0.786396	+	0.617723i	$0.211945\pi$
$684$		0			0
$685$		−	13.9121i		−	0.531555i
$686$	−19.5529	−	17.4265i	−0.746534	−	0.665348i
$687$		0			0
$688$	−1.43908	+	3.83492i	−0.0548645	+	0.146205i
$689$	7.45834	+	12.9182i	0.284140	+	0.492145i
$690$		0			0
$691$	−15.0449	−	8.68618i	−0.572335	−	0.330438i	0.185746	−	0.982598i	$-0.440530\pi$
$691$	−15.0449	−	8.68618i	−0.572335	−	0.330438i	−0.758081	+	0.652160i	$0.773863\pi$
$692$	−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
$698$	−20.7296	−	24.8294i	−0.784625	−	0.939808i
$699$		0			0
$700$	−5.65978	−	13.6460i	−0.213919	−	0.515770i
$701$		−	25.1180i		−	0.948695i	−0.880338	−	0.474348i	$-0.842684\pi$
$701$		−	25.1180i		−	0.948695i	0.880338	−	0.474348i	$-0.157316\pi$
$702$		0			0
$703$	−9.32640	−	16.1538i	−0.351752	−	0.609252i
$704$	−0.601296	+	40.3658i	−0.0226622	+	1.52134i
$705$		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	0.789996	−	0.613112i	$-0.210082\pi$
$709$	17.4147	+	10.0544i	0.654024	+	0.377601i	−0.135972	+	0.990713i	$0.543416\pi$
$710$	15.3497	−	2.66729i	0.576063	−	0.100102i
$711$		0			0
$712$	7.30768	+	0.0544252i	0.273867	+	0.00203967i
$713$	−5.10275			−0.191099
$714$		0			0
$715$		−	19.3941i		−	0.725297i
$716$	0.0852675	+	0.237940i	0.00318660	+	0.00889223i
$717$		0			0
$718$	1.23716	+	7.11960i	0.0461704	+	0.265701i
$719$	−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
$724$	−5.35103	−	0.970949i	−0.198869	−	0.0360850i
$725$	−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	$0.411087\pi$
$728$	−10.3661	−	16.3442i	−0.384194	−	0.605758i
$729$		0			0
$730$	−13.3262	−	15.9618i	−0.493225	−	0.590774i
$731$	1.11696	−	0.644877i	0.0413122	−	0.0238516i
$732$		0			0
$733$	−36.4503	−	21.0446i	−1.34632	−	0.777300i	−0.358597	−	0.933492i	$-0.616745\pi$
$733$	−36.4503	−	21.0446i	−1.34632	−	0.777300i	−0.987727	+	0.156192i	$0.950078\pi$
$734$	−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	−0.284139	−	0.958783i	$-0.591708\pi$
$739$	10.9859	−	6.34270i	0.404122	−	0.233320i	0.688261	+	0.725463i	$0.258374\pi$
$740$	−16.8431	+	6.03586i	−0.619166	+	0.221883i
$741$		0			0
$742$	−20.6003	−	6.42856i	−0.756260	−	0.236000i
$743$	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
$746$	9.81502	−	1.70554i	0.359354	−	0.0624443i
$747$		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	$0.939633\pi$
$752$	33.8811	−	27.8610i	1.23552	−	1.01599i
$753$		0			0
$754$	−1.79241	+	1.49644i	−0.0652758	+	0.0544973i
$755$			21.2157i			0.772117i
$756$		0			0
$757$		−	30.7289i		−	1.11686i	−0.829551	−	0.558431i	$-0.811403\pi$
$757$		−	30.7289i		−	1.11686i	0.829551	−	0.558431i	$-0.188597\pi$
$758$	11.9614	+	14.3272i	0.434458	+	0.520386i
$759$		0			0
$760$	6.59494	−	11.2288i	0.239224	−	0.407312i
$761$	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
$766$	1.19386	+	6.87042i	0.0431360	+	0.248239i
$767$	−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	$0.668565\pi$
$770$	19.0162	+	20.6302i	0.685298	+	0.743461i
$771$		0			0
$772$	−7.43431	+	2.66414i	−0.267567	+	0.0958845i
$773$	29.9953	−	17.3178i	1.07886	−	0.622878i	0.148268	−	0.988947i	$-0.452630\pi$
$773$	29.9953	−	17.3178i	1.07886	−	0.622878i	0.930588	+	0.366069i	$0.119297\pi$
$774$		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
$782$	−1.90870	+	1.59353i	−0.0682549	+	0.0569845i
$783$		0			0
$784$	27.0526	+	7.22181i	0.966166	+	0.257922i
$785$	19.1515			0.683546
$786$		0			0
$787$	29.6763	−	17.1336i	1.05784	−	0.610747i	0.133009	−	0.991115i	$-0.457536\pi$
$787$	29.6763	−	17.1336i	1.05784	−	0.610747i	0.924835	+	0.380368i	$0.124203\pi$
$788$	−38.4654	−	6.97959i	−1.37027	−	0.248637i
$789$		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
$794$	41.6827	−	7.24314i	1.47926	−	0.257049i
$795$		0			0
$796$	−39.1543	+	14.0312i	−1.38779	+	0.497324i
$797$			20.5838i			0.729114i	0.931181	+	0.364557i	$0.118780\pi$
$797$			20.5838i			0.729114i	−0.931181	+	0.364557i	$0.881220\pi$
$798$		0			0
$799$	−13.8122			−0.488641
$800$	11.9713	+	10.3010i	0.423250	+	0.364197i
$801$		0			0
$802$	3.79410	+	21.8342i	0.133974	+	0.770994i
$803$	−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
$808$	−0.510245	−	0.299679i	−0.0179504	−	0.0105427i
$809$	−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	$-0.872273\pi$
$811$		−	22.2462i		−	0.781168i	0.920567	−	0.390584i	$-0.127727\pi$
$812$	0.439364	−	3.34932i	0.0154186	−	0.117538i
$813$		0			0
$814$	−32.9806	+	27.5348i	−1.15597	+	0.965093i
$815$	−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	−0.0856966	−	0.996321i	$-0.527312\pi$
$821$	−28.4062	−	16.4003i	−0.991384	−	0.572376i	−0.905688	+	0.423945i	$0.860645\pi$
$822$		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	$0.756178\pi$
$824$	19.4503	+	0.144859i	0.677583	+	0.00504642i
$825$		0			0
$826$	12.4440	+	3.88329i	0.432981	+	0.135117i
$827$		−	22.0460i		−	0.766615i	−0.923621	−	0.383307i	$-0.874785\pi$
$827$		−	22.0460i		−	0.766615i	0.923621	−	0.383307i	$-0.125215\pi$
$828$		0			0
$829$	−4.74751	+	2.74098i	−0.164888	+	0.0951980i	−0.580173	−	0.814493i	$-0.697015\pi$
$829$	−4.74751	+	2.74098i	−0.164888	+	0.0951980i	0.415285	+	0.909691i	$0.363682\pi$
$830$	1.06926	+	6.15334i	0.0371144	+	0.213586i
$831$		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
$836$	5.58284	−	30.7678i	0.193087	−	1.06413i
$837$		0			0
$838$	0.229085	+	0.274393i	0.00791361	+	0.00947877i
$839$	−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
$842$	−16.6497	−	19.9426i	−0.573785	−	0.687268i
$843$		0			0
$844$	−33.8733	−	6.14633i	−1.16597	−	0.211566i
$845$	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
$850$	−0.851377	−	4.89949i	−0.0292020	−	0.168051i
$851$	7.27797	−	4.20194i	0.249486	−	0.144041i
$852$		0			0
$853$			21.7605i			0.745064i	0.928019	+	0.372532i	$0.121510\pi$
$853$			21.7605i			0.745064i	−0.928019	+	0.372532i	$0.878490\pi$
$854$	10.5760	+	47.0489i	0.361905	+	1.60998i
$855$		0			0
$856$	−0.272537	+	36.5936i	−0.00931513	+	1.25074i
$857$	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	0.427505	−	0.904013i	$-0.359393\pi$
$859$	−4.15132	−	2.39676i	−0.141641	−	0.0817766i	−0.569146	+	0.822237i	$0.692726\pi$
$860$	−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
$866$	−7.88382	+	6.58203i	−0.267903	+	0.223666i
$867$		0			0
$868$	7.41046	+	17.8670i	0.251527	+	0.606444i
$869$			43.9371i			1.49046i
$870$		0			0
$871$	−0.662108	−	1.14681i	−0.0224347	−	0.0388580i
$872$	46.8698	+	27.5277i	1.58721	+	0.932206i
$873$		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	−0.00692013	−	0.999976i	$-0.502203\pi$
$877$	−25.9534	−	14.9842i	−0.876385	−	0.505981i	−0.869465	+	0.493995i	$0.835536\pi$
$878$	7.26458	+	41.8061i	0.245168	+	1.41089i
$879$		0			0
$880$	−28.0826	−	10.5382i	−0.946663	−	0.355242i
$881$	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	$0.260150\pi$
$883$			43.3423i			1.45858i	−0.684203	+	0.729291i	$0.739850\pi$
$884$	−2.19785	−	6.13311i	−0.0739216	−	0.206279i
$885$		0			0
$886$	48.8841	−	8.49450i	1.64229	−	0.285378i
$887$	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
$892$	6.25460	−	34.4699i	0.209419	−	1.15414i
$893$	−29.4253	+	16.9887i	−0.984680	+	0.568505i
$894$		0			0
$895$	−0.187796			−0.00627731
$896$	−29.2990	+	6.12912i	−0.978812	+	0.204759i
$897$		0			0
$898$	22.8093	−	19.0430i	0.761156	−	0.635472i
$899$	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	−0.881180	−	0.472782i	$-0.843250\pi$
$907$	−27.4761	+	15.8633i	−0.912328	+	0.526733i	−0.0311488	+	0.999515i	$0.509917\pi$
$908$	8.89992	+	24.8353i	0.295354	+	0.824188i
$909$		0			0
$910$	14.0300	−	3.15378i	0.465089	−	0.104547i
$911$	−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
$914$	3.23846	+	18.6367i	0.107119	+	0.616446i
$915$		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	$0.261062\pi$
$920$	5.05905	+	2.97130i	0.166792	+	0.0979609i
$921$		0			0
$922$	−2.43482	−	2.91637i	−0.0801864	−	0.0960456i
$923$		−	19.1741i		−	0.631124i
$924$		0			0
$925$			16.8077i			0.552635i
$926$	−22.8390	+	19.0678i	−0.750535	+	0.626605i
$927$		0			0
$928$	1.19290	+	3.40853i	0.0391590	+	0.111890i
$929$	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
$934$	34.4058	−	5.97863i	1.12579	−	0.195627i
$935$	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	$0.714518\pi$
$938$	1.82877	+	0.570691i	0.0597115	+	0.0186337i
$939$		0			0
$940$	10.9947	+	30.6809i	0.358609	+	1.00070i
$941$	−8.31195	+	4.79890i	−0.270962	+	0.156440i	−0.629325	−	0.777143i	$-0.716668\pi$
$941$	−8.31195	+	4.79890i	−0.270962	+	0.156440i	0.358363	+	0.933582i	$0.383335\pi$
$942$		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	0.248733	−	0.968572i	$-0.419986\pi$
$947$	−14.3314	−	8.27425i	−0.465709	−	0.268877i	−0.714442	+	0.699695i	$0.753319\pi$
$948$		0			0
$949$	−22.1622	+	12.7954i	−0.719417	+	0.415356i
$950$	−7.84002	−	9.39062i	−0.254364	−	0.304672i
$951$		0			0
$952$	8.35155	+	4.36899i	0.270675	+	0.141600i
$953$	−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
$956$	4.75769	−	26.2203i	0.153875	−	0.848025i
$957$		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
$962$	3.76986	+	21.6948i	0.121545	+	0.699467i
$963$		0			0
$964$	41.8792	−	15.0077i	1.34884	−	0.483366i
$965$		−	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	$0.387408\pi$
$968$	−40.9121	−	0.304700i	−1.31496	−	0.00979342i
$969$		0			0
$970$	−3.25145	+	0.564999i	−0.104398	+	0.0181410i
$971$	2.27385	+	1.31281i	0.0729715	+	0.0421301i	0.536042	−	0.844191i	$-0.319919\pi$
$971$	2.27385	+	1.31281i	0.0729715	+	0.0421301i	−0.463070	+	0.886322i	$0.653252\pi$
$972$		0			0
$973$	4.47966	−	0.219960i	0.143611	−	0.00705160i
$974$	−23.2804	−	8.53887i	−0.745951	−	0.273603i
$975$		0			0
$976$	−32.7435	−	39.8186i	−1.04809	−	1.27456i
$977$	−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
$980$	−11.8319	+	17.1114i	−0.377956	+	0.546605i
$981$		0			0
$982$	−14.2758	−	17.0993i	−0.455559	−	0.545660i
$983$	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	$0.750702\pi$
$992$	−15.6743	−	13.4874i	−0.497660	−	0.428224i
$993$		0			0
$994$	18.8006	+	20.3962i	0.596318	+	0.646929i
$995$		−	30.9028i		−	0.979684i
$996$		0			0
$997$	−34.0954	+	19.6850i	−1.07981	+	0.623430i	−0.930846	−	0.365412i	$-0.880928\pi$
$997$	−34.0954	+	19.6850i	−1.07981	+	0.623430i	−0.148967	+	0.988842i	$0.547595\pi$
$998$	−14.1927	+	2.46625i	−0.449263	+	0.0780676i
$999$		0			0

Twists

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

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.08560 - 0.906347i) q^{2} +(0.357071 - 1.96787i) q^{4} +(1.28690 + 0.742990i) q^{5} +(0.129755 + 2.64257i) q^{7} +(-1.39593 - 2.45995i) q^{8} +(2.07047 - 0.359782i) q^{10} +(4.37021 - 2.52314i) q^{11} -2.58633i q^{13} +(2.53595 + 2.75118i) q^{14} +(-3.74500 - 1.40534i) q^{16} +(0.629755 + 1.09077i) q^{17} +(2.68324 + 1.54917i) q^{19} +(1.92162 - 2.26714i) q^{20} +(2.45748 - 6.70006i) q^{22} +(-0.697966 + 1.20891i) q^{23} +(-1.39593 - 2.41782i) q^{25} +(-2.34411 - 2.80773i) q^{26} +(5.24655 + 0.688244i) q^{28} -0.638384i q^{29} +(1.82772 + 3.16571i) q^{31} +(-5.33931 + 1.86863i) q^{32} +(1.67228 + 0.613365i) q^{34} +(-1.79642 + 3.49712i) q^{35} +(-5.21370 - 3.01013i) q^{37} +(4.31702 - 0.750162i) q^{38} +(0.0313016 - 4.20287i) q^{40} -6.36226 q^{41} -1.02401i q^{43} +(-3.40473 - 9.50094i) q^{44} +(0.337979 + 1.94500i) q^{46} +(-5.48316 + 9.49712i) q^{47} +(-6.96633 + 0.685774i) q^{49} +(-3.70682 - 1.35960i) q^{50} +(-5.08956 - 0.923505i) q^{52} +(-4.99481 + 2.88375i) q^{53} +7.49868 q^{55} +(6.31947 - 4.00804i) q^{56} +(-0.578597 - 0.693032i) q^{58} +(3.01720 - 1.74198i) q^{59} +(11.1614 + 6.44406i) q^{61} +(4.85341 + 1.78015i) q^{62} +(-4.10275 + 6.86786i) q^{64} +(1.92162 - 3.32834i) q^{65} +(0.443410 - 0.256003i) q^{67} +(2.37135 - 0.849793i) q^{68} +(1.21940 + 5.42466i) q^{70} +7.41363 q^{71} +(-4.94731 - 8.56899i) q^{73} +(-8.38823 + 1.45761i) q^{74} +(4.00667 - 4.72709i) q^{76} +(7.23463 + 11.2212i) q^{77} +(-4.35341 + 7.54032i) q^{79} +(-3.77528 - 4.59102i) q^{80} +(-6.90689 + 5.76641i) q^{82} +2.97196i q^{83} +1.87161i q^{85} +(-0.928109 - 1.11167i) q^{86} +(-12.3073 - 7.22839i) q^{88} +(-1.29186 + 2.23757i) q^{89} +(6.83456 - 0.335590i) q^{91} +(2.12976 + 1.80517i) q^{92} +(2.65514 + 15.2798i) q^{94} +(2.30203 + 3.98724i) q^{95} -1.57040 q^{97} +(-6.94112 + 7.05839i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 4 q^{7} - 4 q^{8} - 8 q^{10} + 16 q^{14} + 8 q^{16} + 2 q^{17} - 8 q^{20} + 12 q^{22} - 2 q^{23} - 4 q^{25} + 2 q^{26} + 26 q^{28} + 10 q^{31} + 12 q^{32} + 32 q^{34} - 18 q^{38} + 10 q^{40}+ \cdots - 52 q^{98}+O(q^{100}) \) 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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