LMFDB - Embedded newform 504.2.cj.c.109.5

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			109.5
Root			$-0.716208 - 1.21944i$ of defining polynomial
Character	$\chi$	$=$	504.109
Dual form			504.2.cj.c.37.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.08560 + 0.906347i) q^{2} +(0.357071 + 1.96787i) q^{4} +(1.28690 - 0.742990i) q^{5} +(0.129755 - 2.64257i) q^{7} +(-1.39593 + 2.45995i) q^{8} +O(q^{10})$	\(q+(1.08560 + 0.906347i) q^{2} +(0.357071 + 1.96787i) q^{4} +(1.28690 - 0.742990i) q^{5} +(0.129755 - 2.64257i) q^{7} +(-1.39593 + 2.45995i) q^{8} +(2.07047 + 0.359782i) q^{10} +(4.37021 + 2.52314i) q^{11} +2.58633i q^{13} +(2.53595 - 2.75118i) q^{14} +(-3.74500 + 1.40534i) q^{16} +(0.629755 - 1.09077i) q^{17} +(2.68324 - 1.54917i) q^{19} +(1.92162 + 2.26714i) q^{20} +(2.45748 + 6.70006i) q^{22} +(-0.697966 - 1.20891i) q^{23} +(-1.39593 + 2.41782i) q^{25} +(-2.34411 + 2.80773i) q^{26} +(5.24655 - 0.688244i) q^{28} +0.638384i q^{29} +(1.82772 - 3.16571i) q^{31} +(-5.33931 - 1.86863i) q^{32} +(1.67228 - 0.613365i) q^{34} +(-1.79642 - 3.49712i) q^{35} +(-5.21370 + 3.01013i) q^{37} +(4.31702 + 0.750162i) q^{38} +(0.0313016 + 4.20287i) q^{40} -6.36226 q^{41} +1.02401i q^{43} +(-3.40473 + 9.50094i) q^{44} +(0.337979 - 1.94500i) q^{46} +(-5.48316 - 9.49712i) q^{47} +(-6.96633 - 0.685774i) q^{49} +(-3.70682 + 1.35960i) q^{50} +(-5.08956 + 0.923505i) q^{52} +(-4.99481 - 2.88375i) q^{53} +7.49868 q^{55} +(6.31947 + 4.00804i) q^{56} +(-0.578597 + 0.693032i) q^{58} +(3.01720 + 1.74198i) q^{59} +(11.1614 - 6.44406i) q^{61} +(4.85341 - 1.78015i) q^{62} +(-4.10275 - 6.86786i) q^{64} +(1.92162 + 3.32834i) q^{65} +(0.443410 + 0.256003i) q^{67} +(2.37135 + 0.849793i) q^{68} +(1.21940 - 5.42466i) q^{70} +7.41363 q^{71} +(-4.94731 + 8.56899i) q^{73} +(-8.38823 - 1.45761i) q^{74} +(4.00667 + 4.72709i) q^{76} +(7.23463 - 11.2212i) q^{77} +(-4.35341 - 7.54032i) q^{79} +(-3.77528 + 4.59102i) q^{80} +(-6.90689 - 5.76641i) q^{82} -2.97196i q^{83} -1.87161i q^{85} +(-0.928109 + 1.11167i) q^{86} +(-12.3073 + 7.22839i) q^{88} +(-1.29186 - 2.23757i) q^{89} +(6.83456 + 0.335590i) q^{91} +(2.12976 - 1.80517i) q^{92} +(2.65514 - 15.2798i) q^{94} +(2.30203 - 3.98724i) q^{95} -1.57040 q^{97} +(-6.94112 - 7.05839i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 4 q^{7} - 4 q^{8}+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 $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$	$1$

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	−0.183832	−	0.982958i	$-0.558850\pi$
$5$	1.28690	−	0.742990i	0.575518	−	0.332275i	0.759350	+	0.650682i	$0.225517\pi$
$6$		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	0.983353	−	0.181705i	$-0.0581616\pi$
$11$	4.37021	+	2.52314i	1.31767	+	0.760756i	0.334315	+	0.942461i	$0.391495\pi$
$12$		0			0
$13$			2.58633i			0.717320i	0.933468	+	0.358660i	$0.116766\pi$
$13$			2.58633i			0.717320i	−0.933468	+	0.358660i	$0.883234\pi$
$14$	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	−0.779495	−	0.626408i	$-0.784524\pi$
$17$	0.629755	−	1.09077i	0.152738	−	0.264550i	0.932233	+	0.361858i	$0.117858\pi$
$18$		0			0
$19$	2.68324	−	1.54917i	0.615577	−	0.355404i	−0.159568	−	0.987187i	$-0.551010\pi$
$19$	2.68324	−	1.54917i	0.615577	−	0.355404i	0.775145	+	0.631783i	$0.217677\pi$
$20$	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	0.784037	−	0.620714i	$-0.213157\pi$
$23$	−0.697966	−	1.20891i	−0.145536	−	0.252076i	−0.929573	+	0.368639i	$0.879824\pi$
$24$		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	$0.0188781\pi$
$29$			0.638384i			0.118545i	−0.998242	+	0.0592725i	$0.981122\pi$
$30$		0			0
$31$	1.82772	−	3.16571i	0.328268	−	0.568578i	−0.653900	−	0.756581i	$-0.726868\pi$
$31$	1.82772	−	3.16571i	0.328268	−	0.568578i	0.982168	+	0.188003i	$0.0602016\pi$
$32$	−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	−0.863049	−	0.505120i	$-0.831448\pi$
$37$	−5.21370	+	3.01013i	−0.857127	+	0.494862i	0.00592229	+	0.999982i	$0.498115\pi$
$38$	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	$0.0248790\pi$
$43$			1.02401i			0.156160i	−0.996947	+	0.0780801i	$0.975121\pi$
$44$	−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	−0.919745	−	0.392516i	$-0.871605\pi$
$47$	−5.48316	−	9.49712i	−0.799802	−	1.38530i	0.119943	−	0.992781i	$-0.461729\pi$
$48$		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	0.116056	−	0.993243i	$-0.462975\pi$
$53$	−4.99481	−	2.88375i	−0.686089	−	0.396114i	−0.802145	+	0.597129i	$0.796308\pi$
$54$		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	0.683375	−	0.730067i	$-0.260511\pi$
$59$	3.01720	+	1.74198i	0.392806	+	0.226787i	−0.290569	+	0.956854i	$0.593845\pi$
$60$		0			0
$61$	11.1614	−	6.44406i	1.42908	−	0.825077i	0.432028	−	0.901860i	$-0.357798\pi$
$61$	11.1614	−	6.44406i	1.42908	−	0.825077i	0.997048	+	0.0767831i	$0.0244649\pi$
$62$	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	$-0.323376\pi$
$67$	0.443410	+	0.256003i	0.0541711	+	0.0312757i	−0.472670	+	0.881240i	$0.656710\pi$
$68$	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	0.416552	+	0.909112i	$0.363239\pi$
$73$	−4.94731	+	8.56899i	−0.579038	+	1.00292i	−0.995590	+	0.0938118i	$0.970095\pi$
$74$	−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	0.510134	−	0.860095i	$-0.329596\pi$
$79$	−4.35341	−	7.54032i	−0.489797	−	0.848353i	−0.999931	+	0.0117420i	$0.996262\pi$
$80$	−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	$-0.947848\pi$
$83$		−	2.97196i		−	0.326215i	0.986608	−	0.163107i	$-0.0521517\pi$
$84$		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	0.789399	−	0.613881i	$-0.210393\pi$
$89$	−1.29186	−	2.23757i	−0.136937	−	0.237182i	−0.926336	+	0.376699i	$0.877059\pi$
$90$		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	0.508987	−	0.860774i	$-0.330020\pi$
$101$	0.181183	+	0.104606i	0.0180284	+	0.0104087i	−0.490959	+	0.871183i	$0.663353\pi$
$102$		0			0
$103$	−3.43846	−	5.95558i	−0.338801	−	0.586821i	0.645406	−	0.763839i	$-0.276688\pi$
$103$	−3.43846	−	5.95558i	−0.338801	−	0.586821i	−0.984207	+	0.177019i	$0.943355\pi$
$104$	−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	$-0.881726\pi$
$107$	−11.2048	+	6.46908i	−1.08321	+	0.625389i	−0.151447	+	0.988465i	$0.548393\pi$
$108$		0			0
$109$	−16.6430	−	9.60883i	−1.59411	−	0.920359i	−0.992591	−	0.121500i	$-0.961230\pi$
$109$	−16.6430	−	9.60883i	−1.59411	−	0.920359i	−0.601517	−	0.798860i	$-0.705437\pi$
$110$	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	0.175849	−	0.984417i	$-0.443733\pi$
$131$	12.7767	−	7.37662i	1.11630	−	0.644498i	0.940455	+	0.339919i	$0.110400\pi$
$132$		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	−0.993718	−	0.111917i	$-0.964301\pi$
$137$	−4.68113	+	8.10795i	−0.399936	+	0.692709i	0.593782	+	0.804626i	$0.297634\pi$
$138$		0			0
$139$			1.69519i			0.143784i	0.997412	+	0.0718921i	$0.0229037\pi$
$139$			1.69519i			0.143784i	−0.997412	+	0.0718921i	$0.977096\pi$
$140$	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	−0.625047	−	0.780587i	$-0.714920\pi$
$149$	−3.19276	+	1.84334i	−0.261561	+	0.151012i	0.363485	+	0.931600i	$0.381587\pi$
$150$		0			0
$151$	7.13861	−	12.3644i	0.580932	−	1.00620i	−0.414438	−	0.910078i	$-0.636022\pi$
$151$	7.13861	−	12.3644i	0.580932	−	1.00620i	0.995369	−	0.0961252i	$-0.0306449\pi$
$152$	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	0.874197	−	0.485571i	$-0.161388\pi$
$157$	11.1614	+	6.44406i	0.890780	+	0.514292i	0.0165822	+	0.999863i	$0.494721\pi$
$158$	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	−0.605571	−	0.795791i	$-0.707055\pi$
$163$	−2.79831	+	1.61560i	−0.219180	+	0.126544i	0.386390	+	0.922335i	$0.373722\pi$
$164$	−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	−0.699572	−	0.714562i	$-0.746626\pi$
$173$	−5.66273	+	3.26938i	−0.430529	+	0.248566i	0.269043	+	0.963128i	$0.413293\pi$
$174$		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	0.495904	−	0.868377i	$-0.334837\pi$
$179$	−0.109447	−	0.0631891i	−0.00818044	−	0.00472298i	−0.504085	+	0.863654i	$0.668170\pi$
$180$		0			0
$181$			2.71920i			0.202117i	0.994880	+	0.101058i	$0.0322229\pi$
$181$			2.71920i			0.202117i	−0.994880	+	0.101058i	$0.967777\pi$
$182$	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	0.818354	−	0.574715i	$-0.194887\pi$
$191$	−1.22365	−	2.11943i	−0.0885404	−	0.153357i	−0.906894	+	0.421358i	$0.861554\pi$
$192$		0			0
$193$	−1.97431	+	3.41961i	−0.142114	+	0.246149i	−0.928293	−	0.371851i	$-0.878723\pi$
$193$	−1.97431	+	3.41961i	−0.142114	+	0.246149i	0.786178	+	0.618000i	$0.212057\pi$
$194$	−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	$0.245183\pi$
$197$			19.5468i			1.39265i	−0.717727	+	0.696325i	$0.754817\pi$
$198$		0			0
$199$	−10.3981	+	18.0101i	−0.737103	+	1.27670i	0.216692	+	0.976240i	$0.430473\pi$
$199$	−10.3981	+	18.0101i	−0.737103	+	1.27670i	−0.953795	+	0.300460i	$0.902860\pi$
$200$	−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	$0.201860\pi$
$211$			17.2132i			1.18500i	−0.805569	+	0.592502i	$0.798140\pi$
$212$	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	0.0704394	−	0.997516i	$-0.477560\pi$
$227$	−11.4237	−	6.59546i	−0.758215	−	0.437756i	−0.828655	+	0.559760i	$0.810893\pi$
$228$		0			0
$229$	−14.8693	+	8.58482i	−0.982594	+	0.567301i	−0.903052	−	0.429531i	$-0.858679\pi$
$229$	−14.8693	+	8.58482i	−0.982594	+	0.567301i	−0.0795417	+	0.996832i	$0.525346\pi$
$230$	−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	0.909380	+	0.415966i	$0.136556\pi$
$233$	12.4393	+	21.5455i	0.814927	+	1.41149i	−0.0944534	+	0.995529i	$0.530110\pi$
$234$		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	−0.245995	−	0.969271i	$-0.579115\pi$
$241$	11.1218	−	19.2635i	0.716416	−	1.24087i	0.962411	−	0.271598i	$-0.0875521\pi$
$242$	−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	$0.333289\pi$
$251$			27.4386i			1.73191i	−0.500121	+	0.865955i	$0.666711\pi$
$252$		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	−0.945647	−	0.325195i	$-0.894570\pi$
$257$	−12.0948	−	20.9487i	−0.754451	−	1.30675i	0.191196	−	0.981552i	$-0.438763\pi$
$258$		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	−0.983552	−	0.180626i	$-0.942188\pi$
$263$	−5.43846	+	9.41968i	−0.335350	+	0.580842i	0.648202	+	0.761468i	$0.275521\pi$
$264$		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	−0.292992	−	0.956115i	$-0.594651\pi$
$269$	−20.7887	−	12.0024i	−1.26751	−	0.731796i	−0.974516	+	0.224319i	$0.927984\pi$
$270$		0			0
$271$	−3.11160	−	5.38945i	−0.189016	−	0.327386i	0.755906	−	0.654680i	$-0.227197\pi$
$271$	−3.11160	−	5.38945i	−0.189016	−	0.327386i	−0.944922	+	0.327294i	$0.893863\pi$
$272$	−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	$-0.0151838\pi$
$277$	24.2493	+	14.0003i	1.45700	+	0.841199i	0.458136	+	0.888882i	$0.348517\pi$
$278$	−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	−0.436339	−	0.899782i	$-0.643725\pi$
$283$	−24.1193	−	13.9253i	−1.43374	−	0.827772i	−0.997404	+	0.0720102i	$0.977059\pi$
$284$	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	$-0.799280\pi$
$293$		−	20.1851i		−	1.17923i	0.807685	−	0.589614i	$-0.200720\pi$
$294$		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	$0.170487\pi$
$307$			17.8844i			1.02071i	−0.859962	+	0.510357i	$0.829513\pi$
$308$	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	−0.885603	−	0.464443i	$-0.846254\pi$
$311$	−0.715667	+	1.23957i	−0.0405818	+	0.0702897i	0.845021	+	0.534733i	$0.179588\pi$
$312$		0			0
$313$	−2.42829	−	4.20591i	−0.137255	−	0.237732i	0.789202	−	0.614134i	$-0.210495\pi$
$313$	−2.42829	−	4.20591i	−0.137255	−	0.237732i	−0.926457	+	0.376402i	$0.877161\pi$
$314$	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	$-0.563944\pi$
$317$	9.78002	−	5.64650i	0.549301	−	0.317139i	0.748840	+	0.662751i	$0.230611\pi$
$318$		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	0.189483	−	0.981884i	$-0.439319\pi$
$331$	20.6415	−	11.9174i	1.13456	−	0.655039i	0.945078	+	0.326845i	$0.105986\pi$
$332$	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	0.572940	−	0.819597i	$-0.305803\pi$
$347$	2.78706	+	1.60911i	0.149617	+	0.0863817i	−0.423322	+	0.905979i	$0.639136\pi$
$348$		0			0
$349$			22.8716i			1.22429i	0.790747	+	0.612143i	$0.209692\pi$
$349$			22.8716i			1.22429i	−0.790747	+	0.612143i	$0.790308\pi$
$350$	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	−0.368725	−	0.929538i	$-0.620206\pi$
$353$	11.6608	−	20.1971i	0.620641	−	1.07498i	0.989367	−	0.145444i	$-0.0464609\pi$
$354$		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	0.790696	−	0.612210i	$-0.209719\pi$
$359$	−2.55488	−	4.42518i	−0.134841	−	0.233552i	−0.925537	+	0.378658i	$0.876386\pi$
$360$		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	0.219922	+	0.975517i	$0.429420\pi$
$367$	−14.0779	+	24.3837i	−0.734862	+	1.27282i	−0.954784	+	0.297301i	$0.903914\pi$
$368$	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	−0.333679	−	0.942687i	$-0.608290\pi$
$373$	6.10052	−	3.52214i	0.315873	−	0.182369i	0.649551	+	0.760318i	$0.274957\pi$
$374$	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	$-0.889927\pi$
$379$		−	13.1974i		−	0.677905i	0.940803	−	0.338953i	$-0.110073\pi$
$380$	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	0.796136	−	0.605118i	$-0.206874\pi$
$383$	−2.46546	−	4.27031i	−0.125979	−	0.218202i	−0.922115	+	0.386915i	$0.873541\pi$
$384$		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	0.910495	−	0.413520i	$-0.135701\pi$
$389$	19.8735	+	11.4739i	1.00762	+	0.581752i	0.0971291	+	0.995272i	$0.469034\pi$
$390$		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	0.319827	−	0.947476i	$-0.396375\pi$
$397$	25.9079	−	14.9579i	1.30028	−	0.750716i	0.980452	+	0.196760i	$0.0630420\pi$
$398$	−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	0.601344	−	0.798990i	$-0.294632\pi$
$401$	−7.83525	−	13.5711i	−0.391274	−	0.677706i	−0.992618	+	0.121284i	$0.961299\pi$
$402$		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	−0.339358	−	0.940657i	$-0.610210\pi$
$409$	13.0434	−	22.5918i	0.644954	−	1.11709i	0.984312	−	0.176436i	$-0.0564568\pi$
$410$	−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	$-0.998035\pi$
$419$		−	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	$0.852261\pi$
$422$	−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	−0.319377	−	0.947628i	$-0.603473\pi$
$431$	13.7223	−	23.7678i	0.660982	−	1.14485i	0.980358	−	0.197226i	$-0.0631932\pi$
$432$		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	−0.962567	−	0.271045i	$-0.912631\pi$
$439$	−15.0022	−	25.9845i	−0.716015	−	1.24017i	0.246551	−	0.969130i	$-0.420703\pi$
$440$	−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	$-0.353028\pi$
$443$	30.3838	−	17.5421i	1.44358	−	0.833451i	0.998086	+	0.0618342i	$0.0196950\pi$
$444$		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	0.666135	−	0.745832i	$-0.267948\pi$
$457$	−6.68780	−	11.5836i	−0.312842	−	0.541858i	−0.978976	+	0.203974i	$0.934614\pi$
$458$	−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	$0.0199262\pi$
$461$			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	$0.662587\pi$
$464$	−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	0.0844270	−	0.996430i	$-0.473094\pi$
$467$	21.3849	−	12.3466i	0.989574	−	0.571331i	0.905147	+	0.425099i	$0.139761\pi$
$468$		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	−0.159437	+	0.987208i	$0.550968\pi$
$479$	−20.4562	+	35.4311i	−0.934666	+	1.61889i	−0.775229	+	0.631680i	$0.782366\pi$
$480$		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	−0.993388	−	0.114802i	$-0.963377\pi$
$487$	−8.76704	+	15.1850i	−0.397273	+	0.688096i	0.596116	+	0.802898i	$0.296710\pi$
$488$	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	$0.115660\pi$
$491$			15.7509i			0.710830i	−0.934709	+	0.355415i	$0.884340\pi$
$492$		0			0
$493$	0.696329	+	0.402026i	0.0313611	+	0.0181063i
$494$	−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	−0.684282	−	0.729217i	$-0.739884\pi$
$499$	−8.82147	+	5.09308i	−0.394903	+	0.227997i	0.289379	+	0.957215i	$0.406551\pi$
$500$	−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	−0.00303361	−	0.999995i	$-0.500966\pi$
$509$	19.4357	−	11.2212i	0.861471	−	0.497371i	0.864505	+	0.502625i	$0.167632\pi$
$510$		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	−0.956311	−	0.292350i	$-0.905563\pi$
$521$	−5.13510	+	8.89426i	−0.224973	+	0.389664i	0.731338	+	0.682015i	$0.238896\pi$
$522$		0			0
$523$	−15.4655	+	8.92903i	−0.676261	+	0.390439i	−0.798445	−	0.602068i	$-0.794344\pi$
$523$	−15.4655	+	8.92903i	−0.676261	+	0.390439i	0.122184	+	0.992507i	$0.461010\pi$
$524$	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	−0.862963	−	0.505268i	$-0.831394\pi$
$541$	−19.9303	+	11.5067i	−0.856869	+	0.494714i	0.00609356	+	0.999981i	$0.498060\pi$
$542$	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	$-0.937668\pi$
$547$		−	9.10136i		−	0.389146i	0.980888	−	0.194573i	$-0.0623321\pi$
$548$	−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	0.147295	−	0.989093i	$-0.452943\pi$
$557$	−15.0016	−	8.66116i	−0.635637	−	0.366985i	−0.782932	+	0.622107i	$0.786277\pi$
$558$		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	0.638599	−	0.769540i	$-0.279514\pi$
$563$	6.91560	+	3.99272i	0.291458	+	0.168273i	−0.347141	+	0.937813i	$0.612848\pi$
$564$		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	0.963779	−	0.266702i	$-0.0859339\pi$
$569$	5.98535	+	10.3669i	0.250919	+	0.434604i	−0.712860	+	0.701306i	$0.752601\pi$
$570$		0			0
$571$	36.9016	+	21.3051i	1.54428	+	0.891592i	0.998561	+	0.0536265i	$0.0170780\pi$
$571$	36.9016	+	21.3051i	1.54428	+	0.891592i	0.545722	+	0.837966i	$0.316255\pi$
$572$	−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	−0.365922	−	0.930645i	$-0.619246\pi$
$577$	14.9650	−	25.9202i	0.623001	−	1.07907i	0.988924	−	0.148425i	$-0.0474203\pi$
$578$	−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	$-0.868692\pi$
$587$		−	19.4269i		−	0.801833i	0.916115	−	0.400916i	$-0.131308\pi$
$588$		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	0.617237	−	0.786777i	$-0.288252\pi$
$593$	−9.07706	−	15.7219i	−0.372750	−	0.645622i	−0.989988	+	0.141155i	$0.954919\pi$
$594$		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	−0.728859	−	0.684664i	$-0.759949\pi$
$599$	5.59258	−	9.68663i	0.228507	−	0.395785i	0.957366	+	0.288879i	$0.0932824\pi$
$600$		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	0.998071	+	0.0620841i	$0.0197747\pi$
$607$	13.6196	+	23.5898i	0.552802	+	0.957481i	−0.445269	+	0.895397i	$0.646892\pi$
$608$	−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	$-0.357138\pi$
$613$	−3.20401	−	1.84984i	−0.129409	−	0.0747141i	−0.563307	+	0.826248i	$0.690471\pi$
$614$	−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	0.940541	−	0.339681i	$-0.110319\pi$
$619$	27.7816	+	16.0397i	1.11664	+	0.644692i	0.176098	+	0.984373i	$0.443652\pi$
$620$	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	−0.0750839	−	0.997177i	$-0.523922\pi$
$641$	20.9136	−	36.2235i	0.826039	−	1.43074i	0.901123	−	0.433564i	$-0.142744\pi$
$642$		0			0
$643$		−	42.9368i		−	1.69326i	−0.532180	−	0.846631i	$-0.678627\pi$
$643$		−	42.9368i		−	1.69326i	0.532180	−	0.846631i	$-0.321373\pi$
$644$	−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	−0.941617	−	0.336687i	$-0.890694\pi$
$647$	−4.55891	+	7.89626i	−0.179229	+	0.310434i	0.762388	+	0.647121i	$0.224027\pi$
$648$		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	$-0.806876\pi$
$653$	−18.8716	+	10.8955i	−0.738502	+	0.426374i	0.0830227	+	0.996548i	$0.473543\pi$
$654$		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	$0.000946600\pi$
$659$			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	$-0.147032\pi$
$661$	24.6004	+	14.2031i	0.956845	+	0.552435i	0.0616446	+	0.998098i	$0.480365\pi$
$662$	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	−0.574969	−	0.818175i	$-0.694986\pi$
$677$	−4.00416	+	2.31180i	−0.153892	+	0.0888498i	0.421076	+	0.907025i	$0.361652\pi$
$678$		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	0.786396	−	0.617723i	$-0.211945\pi$
$683$	16.8469	+	9.72659i	0.644631	+	0.372178i	−0.141765	+	0.989900i	$0.545278\pi$
$684$		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	−0.758081	−	0.652160i	$-0.773863\pi$
$691$	−15.0449	+	8.68618i	−0.572335	+	0.330438i	0.185746	+	0.982598i	$0.440530\pi$
$692$	−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	$0.157316\pi$
$701$			25.1180i			0.948695i	−0.880338	+	0.474348i	$0.842684\pi$
$702$		0			0
$703$	−9.32640	+	16.1538i	−0.351752	+	0.609252i
$704$	−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	−0.135972	−	0.990713i	$-0.543416\pi$
$709$	17.4147	−	10.0544i	0.654024	−	0.377601i	0.789996	+	0.613112i	$0.210082\pi$
$710$	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	−0.962606	−	0.270906i	$-0.912677\pi$
$719$	−19.1966	−	33.2496i	−0.715914	−	1.24000i	0.246692	−	0.969094i	$-0.420656\pi$
$720$		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	−0.987727	−	0.156192i	$-0.950078\pi$
$733$	−36.4503	+	21.0446i	−1.34632	+	0.777300i	−0.358597	+	0.933492i	$0.616745\pi$
$734$	−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	$-0.258374\pi$
$739$	10.9859	+	6.34270i	0.404122	+	0.233320i	−0.284139	+	0.958783i	$0.591708\pi$
$740$	−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	−0.982071	−	0.188513i	$-0.939633\pi$
$751$	−17.9305	−	31.0565i	−0.654292	−	1.13327i	0.327779	−	0.944755i	$-0.393700\pi$
$752$	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	$0.188597\pi$
$757$			30.7289i			1.11686i	−0.829551	+	0.558431i	$0.811403\pi$
$758$	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	0.907236	+	0.420621i	$0.138188\pi$
$761$	22.5624	+	39.0792i	0.817887	+	1.41662i	−0.0893497	+	0.996000i	$0.528479\pi$
$762$		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	0.930588	−	0.366069i	$-0.119297\pi$
$773$	29.9953	+	17.3178i	1.07886	+	0.622878i	0.148268	+	0.988947i	$0.452630\pi$
$774$		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	0.924835	−	0.380368i	$-0.124203\pi$
$787$	29.6763	+	17.1336i	1.05784	+	0.610747i	0.133009	+	0.991115i	$0.457536\pi$
$788$	−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	$-0.881220\pi$
$797$		−	20.5838i		−	0.729114i	0.931181	−	0.364557i	$-0.118780\pi$
$798$		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	0.0778526	+	0.996965i	$0.475194\pi$
$809$	−23.4504	+	40.6172i	−0.824471	+	1.42802i	−0.902323	+	0.431060i	$0.858140\pi$
$810$		0			0
$811$			22.2462i			0.781168i	0.920567	+	0.390584i	$0.127727\pi$
$811$			22.2462i			0.781168i	−0.920567	+	0.390584i	$0.872273\pi$
$812$	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	−0.905688	−	0.423945i	$-0.860645\pi$
$821$	−28.4062	+	16.4003i	−0.991384	+	0.572376i	−0.0856966	+	0.996321i	$0.527312\pi$
$822$		0			0
$823$	6.88576	−	11.9265i	0.240023	−	0.415731i	−0.720698	−	0.693249i	$-0.756178\pi$
$823$	6.88576	−	11.9265i	0.240023	−	0.415731i	0.960720	+	0.277518i	$0.0895118\pi$
$824$	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	$0.125215\pi$
$827$			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	$-0.363682\pi$
$829$	−4.74751	−	2.74098i	−0.164888	−	0.0951980i	−0.580173	+	0.814493i	$0.697015\pi$
$830$	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	$-0.878490\pi$
$853$		−	21.7605i		−	0.745064i	0.928019	−	0.372532i	$-0.121510\pi$
$854$	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	−0.747579	−	0.664173i	$-0.768784\pi$
$857$	5.89593	−	10.2121i	0.201401	−	0.348837i	0.948980	+	0.315336i	$0.102117\pi$
$858$		0			0
$859$	−4.15132	+	2.39676i	−0.141641	+	0.0817766i	−0.569146	−	0.822237i	$-0.692726\pi$
$859$	−4.15132	+	2.39676i	−0.141641	+	0.0817766i	0.427505	+	0.904013i	$0.359393\pi$
$860$	−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	0.864953	−	0.501852i	$-0.167348\pi$
$863$	−0.0628642	−	0.108884i	−0.00213992	−	0.00370646i	−0.867093	+	0.498146i	$0.834014\pi$
$864$		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	−0.869465	−	0.493995i	$-0.835536\pi$
$877$	−25.9534	+	14.9842i	−0.876385	+	0.505981i	−0.00692013	+	0.999976i	$0.502203\pi$
$878$	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	$-0.739850\pi$
$883$		−	43.3423i		−	1.45858i	0.684203	−	0.729291i	$-0.260150\pi$
$884$	−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	0.964655	−	0.263516i	$-0.0848823\pi$
$887$	7.56821	+	13.1085i	0.254116	+	0.440141i	−0.710539	+	0.703658i	$0.751549\pi$
$888$		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	−0.0311488	−	0.999515i	$-0.509917\pi$
$907$	−27.4761	−	15.8633i	−0.912328	−	0.526733i	−0.881180	+	0.472782i	$0.843250\pi$
$908$	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	0.682112	−	0.731248i	$-0.261062\pi$
$919$	−8.85875	−	15.3438i	−0.292223	−	0.506146i	−0.974335	+	0.225102i	$0.927728\pi$
$920$	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	0.858008	+	0.513636i	$0.171702\pi$
$929$	26.6338	+	46.1311i	0.873826	+	1.51351i	0.0158180	+	0.999875i	$0.494965\pi$
$930$		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	0.358363	−	0.933582i	$-0.383335\pi$
$941$	−8.31195	−	4.79890i	−0.270962	−	0.156440i	−0.629325	+	0.777143i	$0.716668\pi$
$942$		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	$-0.753319\pi$
$947$	−14.3314	+	8.27425i	−0.465709	+	0.268877i	0.248733	+	0.968572i	$0.419986\pi$
$948$		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	−0.463070	−	0.886322i	$-0.653252\pi$
$971$	2.27385	−	1.31281i	0.0729715	−	0.0421301i	0.536042	+	0.844191i	$0.319919\pi$
$972$		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	0.446818	+	0.894625i	$0.352557\pi$
$977$	−17.2338	+	29.8499i	−0.551359	+	0.954982i	−0.998177	+	0.0603567i	$0.980776\pi$
$978$		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	−0.0566303	−	0.998395i	$-0.518036\pi$
$983$	26.2210	−	45.4161i	0.836320	−	1.44855i	0.892951	−	0.450154i	$-0.148631\pi$
$984$		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	−0.708665	−	0.705545i	$-0.750702\pi$
$991$	8.08057	−	13.9960i	0.256688	−	0.444596i	0.965353	+	0.260949i	$0.0840355\pi$
$992$	−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	−0.148967	−	0.988842i	$-0.547595\pi$
$997$	−34.0954	−	19.6850i	−1.07981	−	0.623430i	−0.930846	+	0.365412i	$0.880928\pi$
$998$	−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.109.5		12
3.2	odd	2		56.2.p.a.53.2	yes	12
4.3	odd	2		2016.2.cr.c.1873.5		12
7.2	even	3	inner	504.2.cj.c.37.3		12
8.3	odd	2		2016.2.cr.c.1873.2		12
8.5	even	2	inner	504.2.cj.c.109.3		12
12.11	even	2		224.2.t.a.81.1		12
21.2	odd	6		56.2.p.a.37.4	yes	12
21.5	even	6		392.2.p.g.373.4		12
21.11	odd	6		392.2.b.e.197.5		6
21.17	even	6		392.2.b.f.197.5		6
21.20	even	2		392.2.p.g.165.2		12
24.5	odd	2		56.2.p.a.53.4	yes	12
24.11	even	2		224.2.t.a.81.6		12
28.23	odd	6		2016.2.cr.c.1297.2		12
56.37	even	6	inner	504.2.cj.c.37.5		12
56.51	odd	6		2016.2.cr.c.1297.5		12
84.11	even	6		1568.2.b.f.785.6		6
84.23	even	6		224.2.t.a.177.6		12
84.47	odd	6		1568.2.t.g.177.1		12
84.59	odd	6		1568.2.b.e.785.1		6
84.83	odd	2		1568.2.t.g.753.6		12
168.5	even	6		392.2.p.g.373.2		12
168.11	even	6		1568.2.b.f.785.1		6
168.53	odd	6		392.2.b.e.197.6		6
168.59	odd	6		1568.2.b.e.785.6		6
168.83	odd	2		1568.2.t.g.753.1		12
168.101	even	6		392.2.b.f.197.6		6
168.107	even	6		224.2.t.a.177.1		12
168.125	even	2		392.2.p.g.165.4		12
168.131	odd	6		1568.2.t.g.177.6		12
168.149	odd	6		56.2.p.a.37.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.p.a.37.2	✓	12	168.149	odd	6
56.2.p.a.37.4	yes	12	21.2	odd	6
56.2.p.a.53.2	yes	12	3.2	odd	2
56.2.p.a.53.4	yes	12	24.5	odd	2
224.2.t.a.81.1		12	12.11	even	2
224.2.t.a.81.6		12	24.11	even	2
224.2.t.a.177.1		12	168.107	even	6
224.2.t.a.177.6		12	84.23	even	6
392.2.b.e.197.5		6	21.11	odd	6
392.2.b.e.197.6		6	168.53	odd	6
392.2.b.f.197.5		6	21.17	even	6
392.2.b.f.197.6		6	168.101	even	6
392.2.p.g.165.2		12	21.20	even	2
392.2.p.g.165.4		12	168.125	even	2
392.2.p.g.373.2		12	168.5	even	6
392.2.p.g.373.4		12	21.5	even	6
504.2.cj.c.37.3		12	7.2	even	3	inner
504.2.cj.c.37.5		12	56.37	even	6	inner
504.2.cj.c.109.3		12	8.5	even	2	inner
504.2.cj.c.109.5		12	1.1	even	1	trivial
1568.2.b.e.785.1		6	84.59	odd	6
1568.2.b.e.785.6		6	168.59	odd	6
1568.2.b.f.785.1		6	168.11	even	6
1568.2.b.f.785.6		6	84.11	even	6
1568.2.t.g.177.1		12	84.47	odd	6
1568.2.t.g.177.6		12	168.131	odd	6
1568.2.t.g.753.1		12	168.83	odd	2
1568.2.t.g.753.6		12	84.83	odd	2
2016.2.cr.c.1297.2		12	28.23	odd	6
2016.2.cr.c.1297.5		12	56.51	odd	6
2016.2.cr.c.1873.2		12	8.3	odd	2
2016.2.cr.c.1873.5		12	4.3	odd	2

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)

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