LMFDB - Embedded newform 666.2.bj.c.559.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(289,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("666.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.bj (of order $18$, degree $6$, 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:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			559.1
Root			$-0.984808 - 0.173648i$ of defining polynomial
Character	$\chi$	$=$	666.559
Dual form			666.2.bj.c.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 - 0.173648i) q^{2} +(0.939693 + 0.342020i) q^{4} +(0.247315 + 0.294739i) q^{5} +(-2.50048 + 2.09815i) q^{7} +(-0.866025 - 0.500000i) q^{8} +O(q^{10})$	\(q+(-0.984808 - 0.173648i) q^{2} +(0.939693 + 0.342020i) q^{4} +(0.247315 + 0.294739i) q^{5} +(-2.50048 + 2.09815i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-0.192377 - 0.333207i) q^{10} +(1.29236 - 2.23843i) q^{11} +(-0.466831 + 1.28261i) q^{13} +(2.82683 - 1.63207i) q^{14} +(0.766044 + 0.642788i) q^{16} +(1.13965 + 3.13118i) q^{17} +(-5.89485 + 1.03942i) q^{19} +(0.131594 + 0.361551i) q^{20} +(-1.66142 + 1.98001i) q^{22} +(-6.53507 + 3.77303i) q^{23} +(0.842535 - 4.77825i) q^{25} +(0.682461 - 1.18206i) q^{26} +(-3.06729 + 1.11640i) q^{28} +(-2.78251 - 1.60649i) q^{29} +2.53737i q^{31} +(-0.642788 - 0.766044i) q^{32} +(-0.578618 - 3.28150i) q^{34} +(-1.23681 - 0.218083i) q^{35} +(0.543196 + 6.05846i) q^{37} +5.98578 q^{38} +(-0.0668119 - 0.378909i) q^{40} +(-7.77046 - 2.82822i) q^{41} -4.33920i q^{43} +(1.98001 - 1.66142i) q^{44} +(7.09097 - 2.58090i) q^{46} +(2.61455 + 4.52853i) q^{47} +(0.634616 - 3.59909i) q^{49} +(-1.65947 + 4.55935i) q^{50} +(-0.877355 + 1.04559i) q^{52} +(6.64254 + 5.57375i) q^{53} +(0.979373 - 0.172690i) q^{55} +(3.21455 - 0.566812i) q^{56} +(2.46128 + 2.06526i) q^{58} +(-8.33530 + 9.93362i) q^{59} +(-2.39847 + 6.58973i) q^{61} +(0.440610 - 2.49882i) q^{62} +(0.500000 + 0.866025i) q^{64} +(-0.493489 + 0.179615i) q^{65} +(-8.60881 + 7.22365i) q^{67} +3.33213i q^{68} +(1.18015 + 0.429540i) q^{70} +(-2.60464 - 14.7717i) q^{71} -15.0792 q^{73} +(0.517097 - 6.06074i) q^{74} +(-5.89485 - 1.03942i) q^{76} +(1.46505 + 8.30870i) q^{77} +(0.940587 + 1.12095i) q^{79} +0.384754i q^{80} +(7.16130 + 4.13458i) q^{82} +(-0.0104473 + 0.00380252i) q^{83} +(-0.641025 + 1.11029i) q^{85} +(-0.753494 + 4.27328i) q^{86} +(-2.23843 + 1.29236i) q^{88} +(0.612745 - 0.730241i) q^{89} +(-1.52380 - 4.18661i) q^{91} +(-7.43141 + 1.31036i) q^{92} +(-1.78845 - 4.91374i) q^{94} +(-1.76424 - 1.48038i) q^{95} +(12.8332 - 7.40927i) q^{97} +(-1.24995 + 3.43421i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{7}+O(q^{10}) $ 12 * q - 12 * q^7	$ 12 q - 12 q^{7} + 6 q^{10} + 6 q^{11} + 6 q^{13} + 18 q^{14} - 18 q^{19} - 18 q^{25} - 12 q^{26} - 6 q^{28} - 18 q^{29} + 12 q^{34} - 18 q^{35} + 30 q^{37} + 24 q^{38} + 12 q^{40} - 24 q^{41} - 6 q^{44} + 30 q^{46} - 6 q^{47} + 12 q^{49} + 36 q^{50} - 12 q^{52} + 12 q^{53} - 18 q^{55} + 6 q^{58} - 36 q^{61} + 6 q^{64} - 36 q^{65} - 30 q^{67} - 12 q^{70} - 12 q^{71} + 48 q^{74} - 18 q^{76} - 12 q^{77} + 6 q^{79} + 48 q^{83} + 18 q^{85} + 36 q^{86} - 36 q^{88} + 18 q^{89} - 6 q^{91} - 18 q^{92} + 36 q^{97} - 36 q^{98}+O(q^{100}) $ 12 * q - 12 * q^7 + 6 * q^10 + 6 * q^11 + 6 * q^13 + 18 * q^14 - 18 * q^19 - 18 * q^25 - 12 * q^26 - 6 * q^28 - 18 * q^29 + 12 * q^34 - 18 * q^35 + 30 * q^37 + 24 * q^38 + 12 * q^40 - 24 * q^41 - 6 * q^44 + 30 * q^46 - 6 * q^47 + 12 * q^49 + 36 * q^50 - 12 * q^52 + 12 * q^53 - 18 * q^55 + 6 * q^58 - 36 * q^61 + 6 * q^64 - 36 * q^65 - 30 * q^67 - 12 * q^70 - 12 * q^71 + 48 * q^74 - 18 * q^76 - 12 * q^77 + 6 * q^79 + 48 * q^83 + 18 * q^85 + 36 * q^86 - 36 * q^88 + 18 * q^89 - 6 * q^91 - 18 * q^92 + 36 * q^97 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$1$	$e\left(\frac{1}{18}\right)$

Coefficient data

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

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

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

$2$	−0.984808	−	0.173648i	−0.696364	−	0.122788i
$2$	−0.984808	−	0.173648i	−0.696364	−	0.122788i
$3$		0			0
$3$		0			0
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$	0.247315	+	0.294739i	0.110603	+	0.131811i	0.818506	−	0.574499i	$-0.194803\pi$
$5$	0.247315	+	0.294739i	0.110603	+	0.131811i	−0.707903	+	0.706310i	$0.750359\pi$
$6$		0			0
$7$	−2.50048	+	2.09815i	−0.945091	+	0.793026i	−0.978464	−	0.206417i	$-0.933820\pi$
$7$	−2.50048	+	2.09815i	−0.945091	+	0.793026i	0.0333729	+	0.999443i	$0.489375\pi$
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$		0			0
$10$	−0.192377	−	0.333207i	−0.0608350	−	0.105369i
$11$	1.29236	−	2.23843i	0.389661	−	0.674912i	−0.602743	−	0.797935i	$-0.705926\pi$
$11$	1.29236	−	2.23843i	0.389661	−	0.674912i	0.992404	+	0.123023i	$0.0392590\pi$
$12$		0			0
$13$	−0.466831	+	1.28261i	−0.129476	+	0.355731i	−0.987444	−	0.157972i	$-0.949504\pi$
$13$	−0.466831	+	1.28261i	−0.129476	+	0.355731i	0.857968	+	0.513703i	$0.171727\pi$
$14$	2.82683	−	1.63207i	0.755502	−	0.436189i
$15$		0			0
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	1.13965	+	3.13118i	0.276407	+	0.759422i	0.997763	+	0.0668568i	$0.0212971\pi$
$17$	1.13965	+	3.13118i	0.276407	+	0.759422i	−0.721356	+	0.692565i	$0.756481\pi$
$18$		0			0
$19$	−5.89485	+	1.03942i	−1.35237	+	0.238459i	−0.802431	−	0.596745i	$-0.796460\pi$
$19$	−5.89485	+	1.03942i	−1.35237	+	0.238459i	−0.549939	+	0.835205i	$0.685349\pi$
$20$	0.131594	+	0.361551i	0.0294253	+	0.0808452i
$21$		0			0
$22$	−1.66142	+	1.98001i	−0.354217	+	0.422139i
$23$	−6.53507	+	3.77303i	−1.36266	+	0.786730i	−0.989977	−	0.141230i	$-0.954894\pi$
$23$	−6.53507	+	3.77303i	−1.36266	+	0.786730i	−0.372680	+	0.927960i	$0.621561\pi$
$24$		0			0
$25$	0.842535	−	4.77825i	0.168507	−	0.955650i
$26$	0.682461	−	1.18206i	0.133842	−	0.231821i
$27$		0			0
$28$	−3.06729	+	1.11640i	−0.579663	+	0.210980i
$29$	−2.78251	−	1.60649i	−0.516700	−	0.298317i	0.218883	−	0.975751i	$-0.429759\pi$
$29$	−2.78251	−	1.60649i	−0.516700	−	0.298317i	−0.735583	+	0.677434i	$0.763092\pi$
$30$		0			0
$31$			2.53737i			0.455726i	0.973693	+	0.227863i	$0.0731738\pi$
$31$			2.53737i			0.455726i	−0.973693	+	0.227863i	$0.926826\pi$
$32$	−0.642788	−	0.766044i	−0.113630	−	0.135419i
$33$		0			0
$34$	−0.578618	−	3.28150i	−0.0992321	−	0.562773i
$35$	−1.23681	−	0.218083i	−0.209059	−	0.0368628i
$36$		0			0
$37$	0.543196	+	6.05846i	0.0893009	+	0.996005i
$37$	0.543196	+	6.05846i	0.0893009	+	0.996005i
$38$	5.98578			0.971022
$39$		0			0
$40$	−0.0668119	−	0.378909i	−0.0105639	−	0.0599108i
$41$	−7.77046	−	2.82822i	−1.21354	−	0.441693i	−0.345611	−	0.938378i	$-0.612328\pi$
$41$	−7.77046	−	2.82822i	−1.21354	−	0.441693i	−0.867931	+	0.496685i	$0.834551\pi$
$42$		0			0
$43$		−	4.33920i		−	0.661722i	−0.943680	−	0.330861i	$-0.892661\pi$
$43$		−	4.33920i		−	0.661722i	0.943680	−	0.330861i	$-0.107339\pi$
$44$	1.98001	−	1.66142i	0.298497	−	0.250469i
$45$		0			0
$46$	7.09097	−	2.58090i	1.04551	−	0.380533i
$47$	2.61455	+	4.52853i	0.381371	+	0.660554i	0.991258	−	0.131934i	$-0.0421188\pi$
$47$	2.61455	+	4.52853i	0.381371	+	0.660554i	−0.609888	+	0.792488i	$0.708785\pi$
$48$		0			0
$49$	0.634616	−	3.59909i	0.0906594	−	0.514155i
$50$	−1.65947	+	4.55935i	−0.234684	+	0.644790i
$51$		0			0
$52$	−0.877355	+	1.04559i	−0.121667	+	0.144997i
$53$	6.64254	+	5.57375i	0.912423	+	0.765614i	0.972578	−	0.232575i	$-0.0747151\pi$
$53$	6.64254	+	5.57375i	0.912423	+	0.765614i	−0.0601551	+	0.998189i	$0.519160\pi$
$54$		0			0
$55$	0.979373	−	0.172690i	0.132059	−	0.0232855i
$56$	3.21455	−	0.566812i	0.429562	−	0.0757434i
$57$		0			0
$58$	2.46128	+	2.06526i	0.323182	+	0.271182i
$59$	−8.33530	+	9.93362i	−1.08516	+	1.29325i	−0.131849	+	0.991270i	$0.542091\pi$
$59$	−8.33530	+	9.93362i	−1.08516	+	1.29325i	−0.953315	+	0.301978i	$0.902353\pi$
$60$		0			0
$61$	−2.39847	+	6.58973i	−0.307092	+	0.843728i	0.686128	+	0.727481i	$0.259309\pi$
$61$	−2.39847	+	6.58973i	−0.307092	+	0.843728i	−0.993220	+	0.116248i	$0.962913\pi$
$62$	0.440610	−	2.49882i	0.0559576	−	0.317351i
$63$		0			0
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−0.493489	+	0.179615i	−0.0612098	+	0.0222785i
$66$		0			0
$67$	−8.60881	+	7.22365i	−1.05173	+	0.882509i	−0.993275	−	0.115781i	$-0.963063\pi$
$67$	−8.60881	+	7.22365i	−1.05173	+	0.882509i	−0.0584586	+	0.998290i	$0.518619\pi$
$68$			3.33213i			0.404080i
$69$		0			0
$70$	1.18015	+	0.429540i	0.141055	+	0.0513399i
$71$	−2.60464	−	14.7717i	−0.309114	−	1.75307i	−0.603477	−	0.797380i	$-0.706219\pi$
$71$	−2.60464	−	14.7717i	−0.309114	−	1.75307i	0.294363	−	0.955694i	$-0.404893\pi$
$72$		0			0
$73$	−15.0792			−1.76489			−0.882445	−	0.470416i	$-0.844104\pi$
$73$	−15.0792			−1.76489			−0.882445	+	0.470416i	$0.844104\pi$
$74$	0.517097	−	6.06074i	0.0601113	−	0.704547i
$75$		0			0
$76$	−5.89485	−	1.03942i	−0.676185	−	0.119230i
$77$	1.46505	+	8.30870i	0.166958	+	0.946864i
$78$		0			0
$79$	0.940587	+	1.12095i	0.105824	+	0.126117i	0.816357	−	0.577548i	$-0.195990\pi$
$79$	0.940587	+	1.12095i	0.105824	+	0.126117i	−0.710532	+	0.703664i	$0.751546\pi$
$80$			0.384754i			0.0430169i
$81$		0			0
$82$	7.16130	+	4.13458i	0.790833	+	0.456588i
$83$	−0.0104473	+	0.00380252i	−0.00114674	+	0.000417381i	−0.342593	−	0.939484i	$-0.611305\pi$
$83$	−0.0104473	+	0.00380252i	−0.00114674	+	0.000417381i	0.341447	+	0.939901i	$0.389083\pi$
$84$		0			0
$85$	−0.641025	+	1.11029i	−0.0695290	+	0.120428i
$86$	−0.753494	+	4.27328i	−0.0812514	+	0.460799i
$87$		0			0
$88$	−2.23843	+	1.29236i	−0.238617	+	0.137766i
$89$	0.612745	−	0.730241i	0.0649509	−	0.0774054i	−0.732591	−	0.680669i	$-0.761689\pi$
$89$	0.612745	−	0.730241i	0.0649509	−	0.0774054i	0.797542	+	0.603264i	$0.206133\pi$
$90$		0			0
$91$	−1.52380	−	4.18661i	−0.159738	−	0.438876i
$92$	−7.43141	+	1.31036i	−0.774778	+	0.136614i
$93$		0			0
$94$	−1.78845	−	4.91374i	−0.184465	−	0.506814i
$95$	−1.76424	−	1.48038i	−0.181008	−	0.151883i
$96$		0			0
$97$	12.8332	−	7.40927i	1.30302	−	0.752297i	0.322097	−	0.946707i	$-0.395612\pi$
$97$	12.8332	−	7.40927i	1.30302	−	0.752297i	0.980920	+	0.194410i	$0.0622791\pi$
$98$	−1.24995	+	3.43421i	−0.126264	+	0.346907i
$99$		0			0
$100$	2.42598	−	4.20192i	0.242598	−	0.420192i
$101$	0.636260	+	1.10204i	0.0633103	+	0.109657i	0.895943	−	0.444169i	$-0.146501\pi$
$101$	0.636260	+	1.10204i	0.0633103	+	0.109657i	−0.832633	+	0.553825i	$0.813168\pi$
$102$		0			0
$103$	9.39301	+	5.42306i	0.925521	+	0.534350i	0.885392	−	0.464845i	$-0.153890\pi$
$103$	9.39301	+	5.42306i	0.925521	+	0.534350i	0.0401287	+	0.999195i	$0.487223\pi$
$104$	1.04559	−	0.877355i	0.102529	−	0.0860318i
$105$		0			0
$106$	−5.57375	−	6.64254i	−0.541371	−	0.645181i
$107$	−4.47254	−	1.62787i	−0.432377	−	0.157372i	0.116657	−	0.993172i	$-0.462782\pi$
$107$	−4.47254	−	1.62787i	−0.432377	−	0.157372i	−0.549034	+	0.835800i	$0.685004\pi$
$108$		0			0
$109$	9.49102	+	1.67352i	0.909075	+	0.160294i	0.608583	−	0.793490i	$-0.291738\pi$
$109$	9.49102	+	1.67352i	0.909075	+	0.160294i	0.300492	+	0.953784i	$0.402849\pi$
$110$	−0.994481			−0.0948201
$111$		0			0
$112$	−3.26414			−0.308432
$113$	12.7581	+	2.24960i	1.20018	+	0.211624i	0.737777	−	0.675044i	$-0.235876\pi$
$113$	12.7581	+	2.24960i	1.20018	+	0.211624i	0.462405	+	0.886669i	$0.346987\pi$
$114$		0			0
$115$	−2.72828	−	0.993013i	−0.254414	−	0.0925990i
$116$	−2.06526	−	2.46128i	−0.191754	−	0.228524i
$117$		0			0
$118$	9.93362	−	8.33530i	0.914464	−	0.767327i
$119$	−9.41935	−	5.43826i	−0.863470	−	0.498525i
$120$		0			0
$121$	2.15962	+	3.74057i	0.196329	+	0.340052i
$122$	3.50632	−	6.07313i	0.317447	−	0.549835i
$123$		0			0
$124$	−0.867833	+	2.38435i	−0.0779337	+	0.214121i
$125$	3.28274	−	1.89529i	0.293618	−	0.169520i
$126$		0			0
$127$	8.61094	+	7.22543i	0.764097	+	0.641154i	0.939190	−	0.343398i	$-0.111578\pi$
$127$	8.61094	+	7.22543i	0.764097	+	0.641154i	−0.175093	+	0.984552i	$0.556023\pi$
$128$	−0.342020	−	0.939693i	−0.0302306	−	0.0830579i
$129$		0			0
$130$	0.517182	−	0.0911931i	0.0453598	−	0.00799816i
$131$	−2.86257	−	7.86484i	−0.250104	−	0.687154i	−0.999681	−	0.0252378i	$-0.991966\pi$
$131$	−2.86257	−	7.86484i	−0.250104	−	0.687154i	0.749578	−	0.661916i	$-0.230257\pi$
$132$		0			0
$133$	12.5591	−	14.9673i	1.08901	−	1.29783i
$134$	9.73239	−	5.61900i	0.840751	−	0.485408i
$135$		0			0
$136$	0.578618	−	3.28150i	0.0496161	−	0.281387i
$137$	−1.99206	+	3.45036i	−0.170194	+	0.294784i	−0.938487	−	0.345313i	$-0.887773\pi$
$137$	−1.99206	+	3.45036i	−0.170194	+	0.294784i	0.768294	+	0.640097i	$0.221106\pi$
$138$		0			0
$139$	−4.80315	+	1.74820i	−0.407398	+	0.148281i	−0.537586	−	0.843209i	$-0.680664\pi$
$139$	−4.80315	+	1.74820i	−0.407398	+	0.148281i	0.130189	+	0.991489i	$0.458442\pi$
$140$	−1.08763	−	0.627946i	−0.0919219	−	0.0530711i
$141$		0			0
$142$			14.9995i			1.25873i
$143$	2.26771	+	2.70256i	0.189636	+	0.225999i
$144$		0			0
$145$	−0.214665	−	1.21742i	−0.0178269	−	0.101102i
$146$	14.8501	+	2.61848i	1.22901	+	0.216707i
$147$		0			0
$148$	−1.56168	+	5.87887i	−0.128369	+	0.483240i
$149$	15.8700			1.30012			0.650060	−	0.759883i	$-0.274744\pi$
$149$	15.8700			1.30012			0.650060	+	0.759883i	$0.274744\pi$
$150$		0			0
$151$	−3.77998	−	21.4373i	−0.307611	−	1.74455i	−0.610955	−	0.791665i	$-0.709214\pi$
$151$	−3.77998	−	21.4373i	−0.307611	−	1.74455i	0.303344	−	0.952881i	$-0.401897\pi$
$152$	5.62480	+	2.04726i	0.456231	+	0.166055i
$153$		0			0
$154$		−	8.43688i		−	0.679863i
$155$	−0.747863	+	0.627531i	−0.0600698	+	0.0504045i
$156$		0			0
$157$	9.16333	−	3.33518i	0.731314	−	0.266176i	0.0505928	−	0.998719i	$-0.483889\pi$
$157$	9.16333	−	3.33518i	0.731314	−	0.266176i	0.680721	+	0.732543i	$0.261667\pi$
$158$	−0.731647	−	1.26725i	−0.0582067	−	0.100817i
$159$		0			0
$160$	0.0668119	−	0.378909i	0.00528195	−	0.0299554i
$161$	8.42442	−	23.1459i	0.663937	−	1.82415i
$162$		0			0
$163$	8.46213	−	10.0848i	0.662805	−	0.789901i	−0.324980	−	0.945721i	$-0.605358\pi$
$163$	8.46213	−	10.0848i	0.662805	−	0.789901i	0.987785	+	0.155820i	$0.0498021\pi$
$164$	−6.33454	−	5.31531i	−0.494644	−	0.415056i
$165$		0			0
$166$	0.0109489	−	0.00193059i	0.000849801	−	0.000149843i
$167$	−5.51717	+	0.972826i	−0.426932	+	0.0752796i	−0.382986	−	0.923754i	$-0.625104\pi$
$167$	−5.51717	+	0.972826i	−0.426932	+	0.0752796i	−0.0439461	+	0.999034i	$0.513993\pi$
$168$		0			0
$169$	8.53143	+	7.15872i	0.656264	+	0.550671i
$170$	0.824086	−	0.982108i	0.0632045	−	0.0753242i
$171$		0			0
$172$	1.48409	−	4.07751i	0.113161	−	0.310908i
$173$	1.88155	−	10.6708i	0.143051	−	0.811285i	−0.825860	−	0.563876i	$-0.809310\pi$
$173$	1.88155	−	10.6708i	0.143051	−	0.811285i	0.968911	−	0.247409i	$-0.0795791\pi$
$174$		0			0
$175$	7.91874	+	13.7157i	0.598601	+	1.03681i
$176$	2.42884	−	0.884025i	0.183081	−	0.0666359i
$177$		0			0
$178$	−0.730241	+	0.612745i	−0.0547339	+	0.0459272i
$179$			6.07192i			0.453837i	0.973914	+	0.226918i	$0.0728651\pi$
$179$			6.07192i			0.453837i	−0.973914	+	0.226918i	$0.927135\pi$
$180$		0			0
$181$	−20.2540	−	7.37185i	−1.50547	−	0.547945i	−0.547997	−	0.836480i	$-0.684610\pi$
$181$	−20.2540	−	7.37185i	−1.50547	−	0.547945i	−0.957469	+	0.288535i	$0.906832\pi$
$182$	0.773654	+	4.38761i	0.0573471	+	0.325231i
$183$		0			0
$184$	7.54605			0.556302
$185$	−1.65132	+	1.65845i	−0.121408	+	0.121932i
$186$		0			0
$187$	8.48176	+	1.49556i	0.620248	+	0.109366i
$188$	0.908022	+	5.14965i	0.0662243	+	0.375577i
$189$		0			0
$190$	1.48038	+	1.76424i	0.107398	+	0.127992i
$191$			6.62693i			0.479508i	0.970834	+	0.239754i	$0.0770668\pi$
$191$			6.62693i			0.479508i	−0.970834	+	0.239754i	$0.922933\pi$
$192$		0			0
$193$	−19.7925	−	11.4272i	−1.42469	−	0.822548i	−0.428000	−	0.903779i	$-0.640782\pi$
$193$	−19.7925	−	11.4272i	−1.42469	−	0.822548i	−0.996695	+	0.0812309i	$0.974115\pi$
$194$	−13.9249	+	5.06824i	−0.999747	+	0.363878i
$195$		0			0
$196$	1.82730	−	3.16498i	0.130522	−	0.226070i
$197$	2.56236	−	14.5319i	0.182561	−	1.03535i	−0.746488	−	0.665398i	$-0.768262\pi$
$197$	2.56236	−	14.5319i	0.182561	−	1.03535i	0.929049	−	0.369956i	$-0.120627\pi$
$198$		0			0
$199$	−1.27720	+	0.737389i	−0.0905380	+	0.0522721i	−0.544585	−	0.838705i	$-0.683313\pi$
$199$	−1.27720	+	0.737389i	−0.0905380	+	0.0522721i	0.454047	+	0.890978i	$0.349980\pi$
$200$	−3.11878	+	3.71682i	−0.220531	+	0.262819i
$201$		0			0
$202$	−0.435228	−	1.19578i	−0.0306225	−	0.0841347i
$203$	10.3283	−	1.82115i	0.724901	−	0.127820i
$204$		0			0
$205$	−1.08817	−	2.98972i	−0.0760010	−	0.208811i
$206$	−8.30861	−	6.97175i	−0.578888	−	0.485745i
$207$		0			0
$208$	−1.18206	+	0.682461i	−0.0819609	+	0.0473202i
$209$	−5.29158	+	14.5385i	−0.366026	+	1.00565i
$210$		0			0
$211$	1.20976	−	2.09537i	0.0832835	−	0.144251i	−0.821375	−	0.570389i	$-0.806793\pi$
$211$	1.20976	−	2.09537i	0.0832835	−	0.144251i	0.904658	+	0.426137i	$0.140126\pi$
$212$	4.33561	+	7.50950i	0.297771	+	0.515755i
$213$		0			0
$214$	4.12192	+	2.37979i	0.281769	+	0.162679i
$215$	1.27893	−	1.07315i	0.0872224	−	0.0731883i
$216$		0			0
$217$	−5.32379	−	6.34464i	−0.361402	−	0.430702i
$218$	−9.05623	−	3.29620i	−0.613365	−	0.223247i
$219$		0			0
$220$	0.979373	+	0.172690i	0.0660293	+	0.0116427i
$221$	−4.54809			−0.305938
$222$		0			0
$223$	−6.94726			−0.465223			−0.232611	−	0.972570i	$-0.574727\pi$
$223$	−6.94726			−0.465223			−0.232611	+	0.972570i	$0.574727\pi$
$224$	3.21455	+	0.566812i	0.214781	+	0.0378717i
$225$		0			0
$226$	−12.1736	−	4.43084i	−0.809779	−	0.294735i
$227$	14.0443	+	16.7373i	0.932150	+	1.11089i	0.993619	+	0.112785i	$0.0359770\pi$
$227$	14.0443	+	16.7373i	0.932150	+	1.11089i	−0.0614692	+	0.998109i	$0.519579\pi$
$228$		0			0
$229$	−3.25576	+	2.73191i	−0.215147	+	0.180530i	−0.743992	−	0.668189i	$-0.767070\pi$
$229$	−3.25576	+	2.73191i	−0.215147	+	0.180530i	0.528845	+	0.848719i	$0.322625\pi$
$230$	2.51440	+	1.45169i	0.165794	+	0.0957215i
$231$		0			0
$232$	1.60649	+	2.78251i	0.105471	+	0.182681i
$233$	8.67215	−	15.0206i	0.568131	−	0.984032i	−0.428619	−	0.903485i	$-0.641000\pi$
$233$	8.67215	−	15.0206i	0.568131	−	0.984032i	0.996751	−	0.0805473i	$-0.0256668\pi$
$234$		0			0
$235$	−0.688116	+	1.89058i	−0.0448877	+	0.123328i
$236$	−11.2301	+	6.48371i	−0.731019	+	0.422054i
$237$		0			0
$238$	8.33190	+	6.99130i	0.540077	+	0.453178i
$239$	6.27893	+	17.2512i	0.406150	+	1.11589i	0.959197	+	0.282738i	$0.0912428\pi$
$239$	6.27893	+	17.2512i	0.406150	+	1.11589i	−0.553047	+	0.833150i	$0.686535\pi$
$240$		0			0
$241$	23.1096	−	4.07485i	1.48862	−	0.262484i	0.630604	−	0.776105i	$-0.282807\pi$
$241$	23.1096	−	4.07485i	1.48862	−	0.262484i	0.858017	+	0.513621i	$0.171696\pi$
$242$	−1.47727	−	4.05876i	−0.0949624	−	0.260907i
$243$		0			0
$244$	−4.50764	+	5.37200i	−0.288572	+	0.343907i
$245$	1.21774	−	0.703063i	0.0777986	−	0.0449171i
$246$		0			0
$247$	1.41873	−	8.04601i	0.0902715	−	0.511955i
$248$	1.26869	−	2.19743i	0.0805617	−	0.139537i
$249$		0			0
$250$	−3.56199	+	1.29646i	−0.225280	+	0.0819951i
$251$	−5.28405	−	3.05074i	−0.333526	−	0.192561i	0.323879	−	0.946098i	$-0.395013\pi$
$251$	−5.28405	−	3.05074i	−0.333526	−	0.192561i	−0.657405	+	0.753537i	$0.728346\pi$
$252$		0			0
$253$			19.5044i			1.22623i
$254$	−7.22543	−	8.61094i	−0.453364	−	0.540298i
$255$		0			0
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−4.28106	−	0.754866i	−0.267045	−	0.0470873i	0.0385222	−	0.999258i	$-0.487735\pi$
$257$	−4.28106	−	0.754866i	−0.267045	−	0.0470873i	−0.305567	+	0.952170i	$0.598846\pi$
$258$		0			0
$259$	−14.0698	−	14.0093i	−0.874255	−	0.870497i
$260$	−0.525160			−0.0325690
$261$		0			0
$262$	1.45336	+	8.24243i	0.0897891	+	0.509219i
$263$	−3.81031	−	1.38684i	−0.234954	−	0.0855163i	0.221860	−	0.975079i	$-0.428787\pi$
$263$	−3.81031	−	1.38684i	−0.234954	−	0.0855163i	−0.456814	+	0.889562i	$0.651009\pi$
$264$		0			0
$265$			3.33629i			0.204947i
$266$	−14.9673	+	12.5591i	−0.917704	+	0.770045i
$267$		0			0
$268$	−10.5603	+	3.84362i	−0.645071	+	0.234787i
$269$	4.39669	+	7.61528i	0.268071	+	0.464312i	0.968364	−	0.249544i	$-0.0802806\pi$
$269$	4.39669	+	7.61528i	0.268071	+	0.464312i	−0.700293	+	0.713856i	$0.746947\pi$
$270$		0			0
$271$	−2.24218	+	12.7160i	−0.136203	+	0.772444i	0.837812	+	0.545959i	$0.183835\pi$
$271$	−2.24218	+	12.7160i	−0.136203	+	0.772444i	−0.974015	+	0.226485i	$0.927276\pi$
$272$	−1.13965	+	3.13118i	−0.0691017	+	0.189855i
$273$		0			0
$274$	2.56095	−	3.05202i	0.154713	−	0.184379i
$275$	−9.60693	−	8.06117i	−0.579319	−	0.486107i
$276$		0			0
$277$	7.65829	−	1.35036i	0.460142	−	0.0811355i	0.0612280	−	0.998124i	$-0.480498\pi$
$277$	7.65829	−	1.35036i	0.460142	−	0.0811355i	0.398914	+	0.916988i	$0.369387\pi$
$278$	5.03375	−	0.887586i	0.301904	−	0.0532338i
$279$		0			0
$280$	0.962069	+	0.807272i	0.0574946	+	0.0482437i
$281$	−0.149454	+	0.178113i	−0.00891569	+	0.0106253i	−0.770484	−	0.637459i	$-0.779985\pi$
$281$	−0.149454	+	0.178113i	−0.00891569	+	0.0106253i	0.761568	+	0.648085i	$0.224430\pi$
$282$		0			0
$283$	−4.38915	+	12.0591i	−0.260908	+	0.716838i	0.738199	+	0.674583i	$0.235676\pi$
$283$	−4.38915	+	12.0591i	−0.260908	+	0.716838i	−0.999107	+	0.0422550i	$0.986546\pi$
$284$	2.60464	−	14.7717i	0.154557	−	0.876537i
$285$		0			0
$286$	−1.76397	−	3.05528i	−0.104306	−	0.180663i
$287$	25.3639	−	9.23169i	1.49718	−	0.544930i
$288$		0			0
$289$	4.51731	−	3.79047i	0.265724	−	0.222969i
$290$			1.23620i			0.0725925i
$291$		0			0
$292$	−14.1698	−	5.15740i	−0.829227	−	0.301814i
$293$	4.27944	+	24.2699i	0.250007	+	1.41786i	0.808570	+	0.588400i	$0.200242\pi$
$293$	4.27944	+	24.2699i	0.250007	+	1.41786i	−0.558563	+	0.829462i	$0.688647\pi$
$294$		0			0
$295$	−4.98927			−0.290487
$296$	2.55881	−	5.51838i	0.148728	−	0.320749i
$297$		0			0
$298$	−15.6289	−	2.75579i	−0.905357	−	0.159639i
$299$	−1.78854	−	10.1433i	−0.103434	−	0.586602i
$300$		0			0
$301$	9.10429	+	10.8501i	0.524762	+	0.625387i
$302$			21.7680i			1.25261i
$303$		0			0
$304$	−5.18384	−	2.99289i	−0.297314	−	0.171654i
$305$	−2.53543	+	0.922820i	−0.145178	+	0.0528405i
$306$		0			0
$307$	−3.45566	+	5.98538i	−0.197225	+	0.341604i	−0.947628	−	0.319377i	$-0.896526\pi$
$307$	−3.45566	+	5.98538i	−0.197225	+	0.341604i	0.750403	+	0.660981i	$0.229860\pi$
$308$	−1.46505	+	8.30870i	−0.0834789	+	0.473432i
$309$		0			0
$310$	0.845471	−	0.488133i	0.0480195	−	0.0277241i
$311$	−1.06612	+	1.27056i	−0.0604542	+	0.0720466i	−0.795424	−	0.606053i	$-0.792752\pi$
$311$	−1.06612	+	1.27056i	−0.0604542	+	0.0720466i	0.734970	+	0.678100i	$0.237196\pi$
$312$		0			0
$313$	8.87573	+	24.3859i	0.501686	+	1.37837i	0.889628	+	0.456687i	$0.150964\pi$
$313$	8.87573	+	24.3859i	0.501686	+	1.37837i	−0.387942	+	0.921684i	$0.626814\pi$
$314$	−9.60327	+	1.69332i	−0.541944	+	0.0955593i
$315$		0			0
$316$	0.500476	+	1.37505i	0.0281540	+	0.0773524i
$317$	8.69447	+	7.29553i	0.488330	+	0.409758i	0.853427	−	0.521212i	$-0.174520\pi$
$317$	8.69447	+	7.29553i	0.488330	+	0.409758i	−0.365097	+	0.930969i	$0.618964\pi$
$318$		0			0
$319$	−7.19201	+	4.15231i	−0.402675	+	0.232485i
$320$	−0.131594	+	0.361551i	−0.00735632	+	0.0202113i
$321$		0			0
$322$	−12.3157	+	21.3314i	−0.686326	+	1.18875i
$323$	−9.97269	−	17.2732i	−0.554896	−	0.961107i
$324$		0			0
$325$	5.73530	+	3.31128i	0.318137	+	0.183677i
$326$	−10.0848	+	8.46213i	−0.558544	+	0.468674i
$327$		0			0
$328$	5.31531	+	6.33454i	0.293489	+	0.349766i
$329$	−16.0391	−	5.83777i	−0.884266	−	0.321847i
$330$		0			0
$331$	−12.6426	−	2.22924i	−0.694903	−	0.122530i	−0.184970	−	0.982744i	$-0.559219\pi$
$331$	−12.6426	−	2.22924i	−0.694903	−	0.122530i	−0.509933	+	0.860214i	$0.670330\pi$
$332$	−0.0111178			−0.000610170
$333$		0			0
$334$	5.60228			0.306543
$335$	−4.25818	−	0.750832i	−0.232649	−	0.0410224i
$336$		0			0
$337$	−5.36736	−	1.95356i	−0.292379	−	0.106417i	0.191666	−	0.981460i	$-0.438611\pi$
$337$	−5.36736	−	1.95356i	−0.292379	−	0.106417i	−0.484045	+	0.875043i	$0.660833\pi$
$338$	−7.15872	−	8.53143i	−0.389383	−	0.464048i
$339$		0			0
$340$	−0.982108	+	0.824086i	−0.0532623	+	0.0446924i
$341$	5.67973	+	3.27919i	0.307575	+	0.177578i
$342$		0			0
$343$	−5.45991	−	9.45685i	−0.294808	−	0.510622i
$344$	−2.16960	+	3.75786i	−0.116977	+	0.202610i
$345$		0			0
$346$	−3.70592	+	10.1819i	−0.199232	+	0.547385i
$347$	−28.0087	+	16.1708i	−1.50358	+	0.868095i	−0.503593	+	0.863941i	$0.667989\pi$
$347$	−28.0087	+	16.1708i	−1.50358	+	0.868095i	−0.999991	+	0.00415382i	$0.998678\pi$
$348$		0			0
$349$	−19.0990	−	16.0260i	−1.02235	−	0.857852i	−0.0324270	−	0.999474i	$-0.510324\pi$
$349$	−19.0990	−	16.0260i	−1.02235	−	0.857852i	−0.989921	+	0.141622i	$0.954768\pi$
$350$	−5.41674	−	14.8824i	−0.289537	−	0.795496i
$351$		0			0
$352$	−2.54545	+	0.448831i	−0.135673	+	0.0239228i
$353$	−2.95544	−	8.12001i	−0.157302	−	0.432185i	0.835858	−	0.548946i	$-0.184971\pi$
$353$	−2.95544	−	8.12001i	−0.157302	−	0.432185i	−0.993160	+	0.116762i	$0.962749\pi$
$354$		0			0
$355$	3.70962	−	4.42095i	0.196886	−	0.234640i
$356$	0.825549	−	0.476631i	0.0437540	−	0.0252614i
$357$		0			0
$358$	1.05438	−	5.97968i	0.0557256	−	0.316036i
$359$	1.92924	−	3.34154i	0.101821	−	0.176360i	−0.810614	−	0.585581i	$-0.800866\pi$
$359$	1.92924	−	3.34154i	0.101821	−	0.176360i	0.912435	+	0.409221i	$0.134200\pi$
$360$		0			0
$361$	15.8146	−	5.75606i	0.832350	−	0.302951i
$362$	18.6662	+	10.7769i	0.981072	+	0.566422i
$363$		0			0
$364$		−	4.45530i		−	0.233521i
$365$	−3.72932	−	4.44444i	−0.195202	−	0.232632i
$366$		0			0
$367$	1.81571	+	10.2974i	0.0947794	+	0.537521i	0.994815	+	0.101704i	$0.0324294\pi$
$367$	1.81571	+	10.2974i	0.0947794	+	0.537521i	−0.900035	+	0.435817i	$0.856460\pi$
$368$	−7.43141	−	1.31036i	−0.387389	−	0.0683071i
$369$		0			0
$370$	1.91422	−	1.34651i	0.0995157	−	0.0700015i
$371$	−28.3041			−1.46947
$372$		0			0
$373$	1.71315	+	9.71578i	0.0887038	+	0.503064i	0.996496	+	0.0836434i	$0.0266557\pi$
$373$	1.71315	+	9.71578i	0.0887038	+	0.503064i	−0.907792	+	0.419421i	$0.862233\pi$
$374$	−8.09320	−	2.94568i	−0.418489	−	0.152318i
$375$		0			0
$376$		−	5.22909i		−	0.269670i
$377$	3.35945	−	2.81892i	0.173021	−	0.145182i
$378$		0			0
$379$	−2.33157	+	0.848623i	−0.119765	+	0.0435908i	−0.401207	−	0.915987i	$-0.631409\pi$
$379$	−2.33157	+	0.848623i	−0.119765	+	0.0435908i	0.281443	+	0.959578i	$0.409187\pi$
$380$	−1.15153	−	1.99451i	−0.0590722	−	0.102316i
$381$		0			0
$382$	1.15075	−	6.52625i	0.0588777	−	0.333912i
$383$	−8.74336	+	24.0222i	−0.446765	+	1.22748i	0.488199	+	0.872733i	$0.337654\pi$
$383$	−8.74336	+	24.0222i	−0.446765	+	1.22748i	−0.934963	+	0.354744i	$0.884568\pi$
$384$		0			0
$385$	−2.08657	+	2.48668i	−0.106341	+	0.126733i
$386$	17.5075	+	14.6905i	0.891108	+	0.747728i
$387$		0			0
$388$	14.5934	−	2.57321i	0.740868	−	0.130635i
$389$	6.27824	−	1.10702i	0.318319	−	0.0561283i	−0.0122057	−	0.999926i	$-0.503885\pi$
$389$	6.27824	−	1.10702i	0.318319	−	0.0561283i	0.330525	+	0.943797i	$0.392774\pi$
$390$		0			0
$391$	−19.2617	−	16.1625i	−0.974107	−	0.817373i
$392$	−2.34914	+	2.79959i	−0.118649	+	0.141401i
$393$		0			0
$394$	−5.04687	+	13.8662i	−0.254258	+	0.698567i
$395$	−0.0977655	+	0.554456i	−0.00491911	+	0.0278977i
$396$		0			0
$397$	18.7489	+	32.4740i	0.940979	+	1.62982i	0.763609	+	0.645679i	$0.223426\pi$
$397$	18.7489	+	32.4740i	0.940979	+	1.62982i	0.177370	+	0.984144i	$0.443241\pi$
$398$	1.38584	−	0.504404i	0.0694658	−	0.0252835i
$399$		0			0
$400$	3.71682	−	3.11878i	0.185841	−	0.155939i
$401$			35.1464i			1.75513i	0.479462	+	0.877563i	$0.340832\pi$
$401$			35.1464i			1.75513i	−0.479462	+	0.877563i	$0.659168\pi$
$402$		0			0
$403$	−3.25445	−	1.18452i	−0.162116	−	0.0590054i
$404$	0.220971	+	1.25319i	0.0109937	+	0.0623484i
$405$		0			0
$406$	−10.4876			−0.520490
$407$	14.2634	+	6.61379i	0.707013	+	0.327834i
$408$		0			0
$409$	0.443894	+	0.0782704i	0.0219491	+	0.00387022i	0.184612	−	0.982811i	$-0.440897\pi$
$409$	0.443894	+	0.0782704i	0.0219491	+	0.00387022i	−0.162663	+	0.986682i	$0.552008\pi$
$410$	0.552478	+	3.13326i	0.0272849	+	0.154741i
$411$		0			0
$412$	6.97175	+	8.30861i	0.343473	+	0.409336i
$413$		−	42.3275i		−	2.08280i
$414$		0			0
$415$	−0.00370454	−	0.00213882i	−0.000181849	−	0.000104990i
$416$	1.28261	−	0.466831i	0.0628850	−	0.0228883i
$417$		0			0
$418$	7.73578	−	13.3988i	0.378369	−	0.655355i
$419$	2.65878	−	15.0787i	0.129890	−	0.736642i	−0.848393	−	0.529367i	$-0.822429\pi$
$419$	2.65878	−	15.0787i	0.129890	−	0.736642i	0.978283	−	0.207275i	$-0.0664594\pi$
$420$		0			0
$421$	−19.3959	+	11.1982i	−0.945299	+	0.545769i	−0.891617	−	0.452789i	$-0.850429\pi$
$421$	−19.3959	+	11.1982i	−0.945299	+	0.545769i	−0.0536815	+	0.998558i	$0.517096\pi$
$422$	−1.55524	+	1.85346i	−0.0757079	+	0.0902252i
$423$		0			0
$424$	−2.96573	−	8.14828i	−0.144029	−	0.395716i
$425$	15.9217	−	2.80743i	0.772318	−	0.136180i
$426$		0			0
$427$	−7.82893	−	21.5098i	−0.378868	−	1.04093i
$428$	−3.64605	−	3.05940i	−0.176239	−	0.147882i
$429$		0			0
$430$	−1.44585	+	0.834763i	−0.0697252	+	0.0402559i
$431$	0.0349134	−	0.0959236i	0.00168172	−	0.00462048i	−0.938849	−	0.344329i	$-0.888106\pi$
$431$	0.0349134	−	0.0959236i	0.00168172	−	0.00462048i	0.940531	+	0.339709i	$0.110329\pi$
$432$		0			0
$433$	−3.96357	+	6.86510i	−0.190477	+	0.329916i	−0.945408	−	0.325888i	$-0.894337\pi$
$433$	−3.96357	+	6.86510i	−0.190477	+	0.329916i	0.754931	+	0.655804i	$0.227670\pi$
$434$	4.14117	+	7.17272i	0.198783	+	0.344301i
$435$		0			0
$436$	8.34627	+	4.81872i	0.399714	+	0.230775i
$437$	34.6015	−	29.0341i	1.65521	−	1.38889i
$438$		0			0
$439$	4.86630	+	5.79944i	0.232256	+	0.276792i	0.869567	−	0.493815i	$-0.164398\pi$
$439$	4.86630	+	5.79944i	0.232256	+	0.276792i	−0.637311	+	0.770607i	$0.719953\pi$
$440$	−0.934507	−	0.340133i	−0.0445509	−	0.0162152i
$441$		0			0
$442$	4.47900	+	0.789768i	0.213044	+	0.0375654i
$443$	−15.9856			−0.759499			−0.379749	−	0.925089i	$-0.623990\pi$
$443$	−15.9856			−0.759499			−0.379749	+	0.925089i	$0.623990\pi$
$444$		0			0
$445$	0.366772			0.0173867
$446$	6.84171	+	1.20638i	0.323964	+	0.0571237i
$447$		0			0
$448$	−3.06729	−	1.11640i	−0.144916	−	0.0527450i
$449$	18.4321	+	21.9666i	0.869866	+	1.03667i	0.998985	+	0.0450373i	$0.0143407\pi$
$449$	18.4321	+	21.9666i	0.869866	+	1.03667i	−0.129119	+	0.991629i	$0.541215\pi$
$450$		0			0
$451$	−16.3730	+	13.7386i	−0.770974	+	0.646924i
$452$	11.2193	+	6.47746i	0.527711	+	0.304674i
$453$		0			0
$454$	−10.9245	−	18.9218i	−0.512712	−	0.888043i
$455$	0.857098	−	1.48454i	0.0401814	−	0.0695962i
$456$		0			0
$457$	0.0359519	−	0.0987770i	0.00168176	−	0.00462059i	−0.938849	−	0.344329i	$-0.888106\pi$
$457$	0.0359519	−	0.0987770i	0.00168176	−	0.00462059i	0.940531	+	0.339709i	$0.110329\pi$
$458$	3.68069	−	2.12505i	0.171987	−	0.0992970i
$459$		0			0
$460$	−2.22412	−	1.86625i	−0.103700	−	0.0870146i
$461$	−8.19825	−	22.5245i	−0.381831	−	1.04907i	−0.970585	−	0.240759i	$-0.922604\pi$
$461$	−8.19825	−	22.5245i	−0.381831	−	1.04907i	0.588754	−	0.808312i	$-0.299619\pi$
$462$		0			0
$463$	−20.4361	+	3.60344i	−0.949747	+	0.167466i	−0.627000	−	0.779019i	$-0.715717\pi$
$463$	−20.4361	+	3.60344i	−0.949747	+	0.167466i	−0.322747	+	0.946485i	$0.604606\pi$
$464$	−1.09890	−	3.01921i	−0.0510152	−	0.140163i
$465$		0			0
$466$	−11.1487	+	13.2865i	−0.516454	+	0.615485i
$467$	−15.1492	+	8.74642i	−0.701023	+	0.404736i	−0.807728	−	0.589555i	$-0.799303\pi$
$467$	−15.1492	+	8.74642i	−0.701023	+	0.404736i	0.106705	+	0.994291i	$0.465970\pi$
$468$		0			0
$469$	6.36983	−	36.1251i	0.294132	−	1.66810i
$470$	1.00596	−	1.74237i	0.0464014	−	0.0803696i
$471$		0			0
$472$	12.1854	−	4.43512i	0.560878	−	0.204143i
$473$	−9.71300	−	5.60780i	−0.446604	−	0.257847i
$474$		0			0
$475$			29.0428i			1.33258i
$476$	−6.99130	−	8.33190i	−0.320446	−	0.381892i
$477$		0			0
$478$	−3.18790	−	18.0795i	−0.145811	−	0.826935i
$479$	6.77593	+	1.19478i	0.309600	+	0.0545909i	0.326290	−	0.945270i	$-0.394202\pi$
$479$	6.77593	+	1.19478i	0.309600	+	0.0545909i	−0.0166894	+	0.999861i	$0.505313\pi$
$480$		0			0
$481$	−8.02421	−	2.13157i	−0.365872	−	0.0971912i
$482$	−23.4661			−1.06885
$483$		0			0
$484$	0.750028	+	4.25362i	0.0340922	+	0.193346i
$485$	5.35766	+	1.95003i	0.243279	+	0.0885462i
$486$		0			0
$487$		−	1.70810i		−	0.0774014i	−0.999251	−	0.0387007i	$-0.987678\pi$
$487$		−	1.70810i		−	0.0774014i	0.999251	−	0.0387007i	$-0.0123219\pi$
$488$	5.37200	−	4.50764i	0.243179	−	0.204051i
$489$		0			0
$490$	−1.32133	+	0.480924i	−0.0596915	+	0.0217259i
$491$	5.31153	+	9.19983i	0.239706	+	0.415183i	0.960630	−	0.277831i	$-0.0896157\pi$
$491$	5.31153	+	9.19983i	0.239706	+	0.415183i	−0.720924	+	0.693014i	$0.756282\pi$
$492$		0			0
$493$	1.85908	−	10.5434i	0.0837288	−	0.474850i
$494$	−2.79435	+	7.67741i	−0.125724	+	0.345423i
$495$		0			0
$496$	−1.63099	+	1.94374i	−0.0732337	+	0.0872765i
$497$	37.5060	+	31.4713i	1.68237	+	1.41168i
$498$		0			0
$499$	34.9319	−	6.15943i	1.56376	−	0.275734i	0.676306	−	0.736621i	$-0.263580\pi$
$499$	34.9319	−	6.15943i	1.56376	−	0.275734i	0.887459	+	0.460887i	$0.152469\pi$
$500$	3.73300	−	0.658229i	0.166945	−	0.0294369i
$501$		0			0
$502$	4.67401	+	3.92196i	0.208611	+	0.175046i
$503$	19.3402	−	23.0487i	0.862336	−	1.02769i	−0.136975	−	0.990574i	$-0.543738\pi$
$503$	19.3402	−	23.0487i	0.862336	−	1.02769i	0.999311	−	0.0371171i	$-0.0118174\pi$
$504$		0			0
$505$	−0.167456	+	0.460081i	−0.00745168	+	0.0204733i
$506$	3.38690	−	19.2081i	0.150566	−	0.853903i
$507$		0			0
$508$	5.62039	+	9.73480i	0.249364	+	0.431912i
$509$	−22.6380	+	8.23957i	−1.00341	+	0.365213i	−0.790900	−	0.611946i	$-0.790387\pi$
$509$	−22.6380	+	8.23957i	−1.00341	+	0.365213i	−0.212513	+	0.977158i	$0.568165\pi$
$510$		0			0
$511$	37.7052	−	31.6385i	1.66798	−	1.39960i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	4.08494	+	1.48680i	0.180179	+	0.0655798i
$515$	0.724650	+	4.10969i	0.0319319	+	0.181095i
$516$		0			0
$517$	13.5157			0.594421
$518$	11.4234	+	16.2397i	0.501913	+	0.713531i
$519$		0			0
$520$	0.517182	+	0.0911931i	0.0226799	+	0.00399908i
$521$	0.130158	+	0.738160i	0.00570231	+	0.0323394i	0.987526	−	0.157455i	$-0.0503289\pi$
$521$	0.130158	+	0.738160i	0.00570231	+	0.0323394i	−0.981824	+	0.189794i	$0.939218\pi$
$522$		0			0
$523$	1.31038	+	1.56165i	0.0572989	+	0.0682862i	0.793933	−	0.608006i	$-0.208030\pi$
$523$	1.31038	+	1.56165i	0.0572989	+	0.0682862i	−0.736634	+	0.676292i	$0.763586\pi$
$524$		−	8.36959i		−	0.365627i
$525$		0			0
$526$	3.51160	+	2.02743i	0.153113	+	0.0884000i
$527$	−7.94496	+	2.89173i	−0.346088	+	0.125966i
$528$		0			0
$529$	16.9714	−	29.3954i	0.737889	−	1.27806i
$530$	0.579341	−	3.28561i	0.0251650	−	0.142718i
$531$		0			0
$532$	16.9208	−	9.76922i	0.733609	−	0.423549i
$533$	7.25498	−	8.64615i	0.314248	−	0.374506i
$534$		0			0
$535$	−0.626331	−	1.72083i	−0.0270787	−	0.0743980i
$536$	11.0673	−	1.95146i	0.478033	−	0.0842902i
$537$		0			0
$538$	−3.00751	−	8.26307i	−0.129663	−	0.356246i
$539$	−7.23615	−	6.07185i	−0.311683	−	0.261533i
$540$		0			0
$541$	−27.1442	+	15.6717i	−1.16702	+	0.673778i	−0.952976	−	0.303046i	$-0.901996\pi$
$541$	−27.1442	+	15.6717i	−1.16702	+	0.673778i	−0.214042	+	0.976824i	$0.568663\pi$
$542$	4.41623	−	12.1335i	0.189694	−	0.521179i
$543$		0			0
$544$	1.66606	−	2.88571i	0.0714319	−	0.123724i
$545$	1.85402	+	3.21126i	0.0794176	+	0.137555i
$546$		0			0
$547$	15.7325	+	9.08317i	0.672674	+	0.388368i	0.797089	−	0.603862i	$-0.206372\pi$
$547$	15.7325	+	9.08317i	0.672674	+	0.388368i	−0.124415	+	0.992230i	$0.539706\pi$
$548$	−3.05202	+	2.56095i	−0.130376	+	0.109398i
$549$		0			0
$550$	8.06117	+	9.60693i	0.343729	+	0.409641i
$551$	18.0723	+	6.57778i	0.769906	+	0.280223i
$552$		0			0
$553$	−4.70383	−	0.829413i	−0.200027	−	0.0352702i
$554$	−7.77643			−0.330389
$555$		0			0
$556$	−5.11140			−0.216772
$557$	−32.4061	−	5.71408i	−1.37309	−	0.242113i	−0.562051	−	0.827102i	$-0.689988\pi$
$557$	−32.4061	−	5.71408i	−1.37309	−	0.242113i	−0.811041	+	0.584989i	$0.801099\pi$
$558$		0			0
$559$	5.56549	+	2.02567i	0.235395	+	0.0856768i
$560$	−0.807272	−	0.962069i	−0.0341135	−	0.0406548i
$561$		0			0
$562$	0.178113	−	0.149454i	0.00751323	−	0.00630435i
$563$	−29.7054	−	17.1504i	−1.25193	−	0.722804i	−0.280440	−	0.959872i	$-0.590480\pi$
$563$	−29.7054	−	17.1504i	−1.25193	−	0.722804i	−0.971493	+	0.237068i	$0.923814\pi$
$564$		0			0
$565$	2.49223	+	4.31667i	0.104849	+	0.181604i
$566$	6.41650	−	11.1137i	0.269706	−	0.467144i
$567$		0			0
$568$	−5.13014	+	14.0950i	−0.215256	+	0.591411i
$569$	−18.3769	+	10.6099i	−0.770398	+	0.444789i	−0.833017	−	0.553248i	$-0.813388\pi$
$569$	−18.3769	+	10.6099i	−0.770398	+	0.444789i	0.0626186	+	0.998038i	$0.480055\pi$
$570$		0			0
$571$	12.5989	+	10.5717i	0.527247	+	0.442413i	0.867150	−	0.498048i	$-0.165950\pi$
$571$	12.5989	+	10.5717i	0.527247	+	0.442413i	−0.339902	+	0.940461i	$0.610394\pi$
$572$	1.20663	+	3.31518i	0.0504516	+	0.138614i
$573$		0			0
$574$	−26.5816	+	4.68705i	−1.10949	+	0.195634i
$575$	12.5224	+	34.4051i	0.522222	+	1.43479i
$576$		0			0
$577$	−23.3471	+	27.8240i	−0.971952	+	1.15833i	0.0154162	+	0.999881i	$0.495093\pi$
$577$	−23.3471	+	27.8240i	−0.971952	+	1.15833i	−0.987368	+	0.158446i	$0.949352\pi$
$578$	−5.10689	+	2.94846i	−0.212419	+	0.122640i
$579$		0			0
$580$	0.214665	−	1.21742i	0.00891347	−	0.0505508i
$581$	0.0181451	−	0.0314282i	0.000752784	−	0.00130386i
$582$		0			0
$583$	21.0610	−	7.66558i	0.872258	−	0.317476i
$584$	13.0590	+	7.53961i	0.540385	+	0.311991i
$585$		0			0
$586$		−	24.6443i		−	1.01805i
$587$	−24.1202	−	28.7453i	−0.995547	−	1.18645i	−0.982449	−	0.186532i	$-0.940275\pi$
$587$	−24.1202	−	28.7453i	−0.995547	−	1.18645i	−0.0130981	−	0.999914i	$-0.504169\pi$
$588$		0			0
$589$	−2.63740	−	14.9574i	−0.108672	−	0.616310i
$590$	4.91348	+	0.866378i	0.202285	+	0.0356682i
$591$		0			0
$592$	−3.47819	+	4.99021i	−0.142953	+	0.205096i
$593$	10.0159			0.411302			0.205651	−	0.978625i	$-0.434069\pi$
$593$	10.0159			0.411302			0.205651	+	0.978625i	$0.434069\pi$
$594$		0			0
$595$	−0.726682	−	4.12122i	−0.0297910	−	0.168953i
$596$	14.9129	+	5.42786i	0.610857	+	0.222334i
$597$		0			0
$598$			10.2998i			0.421189i
$599$	25.7808	−	21.6326i	1.05337	−	0.883886i	0.0599300	−	0.998203i	$-0.480912\pi$
$599$	25.7808	−	21.6326i	1.05337	−	0.883886i	0.993444	+	0.114317i	$0.0364678\pi$
$600$		0			0
$601$	40.2252	−	14.6408i	1.64082	−	0.597209i	0.653637	−	0.756808i	$-0.273242\pi$
$601$	40.2252	−	14.6408i	1.64082	−	0.597209i	0.987182	+	0.159599i	$0.0510202\pi$
$602$	−7.08188	−	12.2662i	−0.288636	−	0.499932i
$603$		0			0
$604$	3.77998	−	21.4373i	0.153805	−	0.872273i
$605$	−0.568385	+	1.56163i	−0.0231081	+	0.0634891i
$606$		0			0
$607$	3.45545	−	4.11804i	0.140252	−	0.167146i	−0.691346	−	0.722524i	$-0.742982\pi$
$607$	3.45545	−	4.11804i	0.140252	−	0.167146i	0.831598	+	0.555378i	$0.187426\pi$
$608$	4.58538	+	3.84759i	0.185962	+	0.156040i
$609$		0			0
$610$	2.65715	−	0.468528i	0.107585	−	0.0189701i
$611$	−7.02887	+	1.23938i	−0.284358	+	0.0501400i
$612$		0			0
$613$	−25.6002	−	21.4811i	−1.03398	−	0.867614i	−0.0426623	−	0.999090i	$-0.513584\pi$
$613$	−25.6002	−	21.4811i	−1.03398	−	0.867614i	−0.991319	+	0.131476i	$0.958028\pi$
$614$	4.44251	−	5.29438i	0.179285	−	0.213664i
$615$		0			0
$616$	2.88558	−	7.92807i	0.116263	−	0.319431i
$617$	0.878588	−	4.98272i	0.0353706	−	0.200597i	−0.962002	−	0.273044i	$-0.911970\pi$
$617$	0.878588	−	4.98272i	0.0353706	−	0.200597i	0.997372	+	0.0724469i	$0.0230808\pi$
$618$		0			0
$619$	−17.8909	−	30.9879i	−0.719096	−	1.24551i	−0.961358	−	0.275300i	$-0.911223\pi$
$619$	−17.8909	−	30.9879i	−0.719096	−	1.24551i	0.242263	−	0.970211i	$-0.422110\pi$
$620$	−0.917390	+	0.333902i	−0.0368433	+	0.0134098i
$621$		0			0
$622$	1.27056	−	1.06612i	0.0509446	−	0.0427476i
$623$			3.11158i			0.124663i
$624$		0			0
$625$	−21.4263	−	7.79853i	−0.857051	−	0.311941i
$626$	−4.50633	−	25.5566i	−0.180109	−	1.02145i
$627$		0			0
$628$	9.75142			0.389124
$629$	−18.3510	+	8.60539i	−0.731704	+	0.343119i
$630$		0			0
$631$	6.52046	+	1.14973i	0.259576	+	0.0457702i	0.301921	−	0.953333i	$-0.402372\pi$
$631$	6.52046	+	1.14973i	0.259576	+	0.0457702i	−0.0423458	+	0.999103i	$0.513483\pi$
$632$	−0.254098	−	1.44106i	−0.0101075	−	0.0573224i
$633$		0			0
$634$	−7.29553	−	8.69447i	−0.289742	−	0.345301i
$635$			4.32494i			0.171630i
$636$		0			0
$637$	4.31996	+	2.49413i	0.171163	+	0.0988210i
$638$	7.80379	−	2.84035i	0.308955	−	0.112450i
$639$		0			0
$640$	0.192377	−	0.333207i	0.00760438	−	0.0131712i
$641$	6.18098	−	35.0541i	0.244134	−	1.38455i	−0.578361	−	0.815781i	$-0.696307\pi$
$641$	6.18098	−	35.0541i	0.244134	−	1.38455i	0.822495	−	0.568772i	$-0.192582\pi$
$642$		0			0
$643$	4.34087	−	2.50620i	0.171187	−	0.0988350i	−0.411958	−	0.911203i	$-0.635155\pi$
$643$	4.34087	−	2.50620i	0.171187	−	0.0988350i	0.583146	+	0.812368i	$0.301822\pi$
$644$	15.8327	−	18.8687i	0.623897	−	0.743532i
$645$		0			0
$646$	6.82172	+	18.7425i	0.268397	+	0.737415i
$647$	34.7348	−	6.12469i	1.36557	−	0.240786i	0.557647	−	0.830078i	$-0.311704\pi$
$647$	34.7348	−	6.12469i	1.36557	−	0.240786i	0.807920	+	0.589292i	$0.200593\pi$
$648$		0			0
$649$	11.4635	+	31.4958i	0.449983	+	1.23632i
$650$	−5.07317	−	4.25690i	−0.198986	−	0.166969i
$651$		0			0
$652$	11.4010	−	6.58237i	0.446498	−	0.257785i
$653$	−0.925218	+	2.54201i	−0.0362066	+	0.0994767i	−0.956479	−	0.291802i	$-0.905745\pi$
$653$	−0.925218	+	2.54201i	−0.0362066	+	0.0994767i	0.920272	+	0.391279i	$0.127967\pi$
$654$		0			0
$655$	1.61012	−	2.78881i	0.0629125	−	0.108968i
$656$	−4.13458	−	7.16130i	−0.161428	−	0.279602i
$657$		0			0
$658$	14.7817	+	8.53424i	0.576252	+	0.332699i
$659$	−21.3419	+	17.9080i	−0.831363	+	0.697597i	−0.955604	−	0.294655i	$-0.904795\pi$
$659$	−21.3419	+	17.9080i	−0.831363	+	0.697597i	0.124240	+	0.992252i	$0.460351\pi$
$660$		0			0
$661$	−6.82156	−	8.12962i	−0.265328	−	0.316205i	0.616888	−	0.787051i	$-0.288393\pi$
$661$	−6.82156	−	8.12962i	−0.265328	−	0.316205i	−0.882216	+	0.470846i	$0.843949\pi$
$662$	12.0635	+	4.39075i	0.468860	+	0.170651i
$663$		0			0
$664$	0.0109489	+	0.00193059i	0.000424900	+	7.49214e-5i
$665$	7.51750			0.291516
$666$		0			0
$667$	24.2452			0.938779
$668$	−5.51717	−	0.972826i	−0.213466	−	0.0376398i
$669$		0			0
$670$	4.06311	+	1.47885i	0.156972	+	0.0571330i
$671$	11.6510	+	13.8851i	0.449781	+	0.536028i
$672$		0			0
$673$	−0.503594	+	0.422565i	−0.0194121	+	0.0162887i	−0.652442	−	0.757839i	$-0.726255\pi$
$673$	−0.503594	+	0.422565i	−0.0194121	+	0.0162887i	0.633030	+	0.774127i	$0.281811\pi$
$674$	4.94659	+	2.85591i	0.190535	+	0.110006i
$675$		0			0
$676$	5.56849	+	9.64491i	0.214173	+	0.370958i
$677$	−16.0036	+	27.7190i	−0.615067	+	1.06533i	0.375306	+	0.926901i	$0.377538\pi$
$677$	−16.0036	+	27.7190i	−0.615067	+	1.06533i	−0.990373	+	0.138426i	$0.955796\pi$
$678$		0			0
$679$	−16.5434	+	45.4527i	−0.634879	+	1.74432i
$680$	1.11029	−	0.641025i	0.0425776	−	0.0245822i
$681$		0			0
$682$	−5.02402	−	4.21565i	−0.192380	−	0.161426i
$683$	1.36647	+	3.75435i	0.0522866	+	0.143656i	0.963087	−	0.269191i	$-0.0867564\pi$
$683$	1.36647	+	3.75435i	0.0522866	+	0.143656i	−0.910800	+	0.412848i	$0.864534\pi$
$684$		0			0
$685$	−1.50962	+	0.266187i	−0.0576797	+	0.0101705i
$686$	3.73480	+	10.2613i	0.142595	+	0.391778i
$687$		0			0
$688$	2.78918	−	3.32402i	0.106337	−	0.126727i
$689$	−10.2499	+	5.91777i	−0.390489	+	0.225449i
$690$		0			0
$691$	−0.763380	+	4.32934i	−0.0290404	+	0.164696i	−0.995879	−	0.0906920i	$-0.971092\pi$
$691$	−0.763380	+	4.32934i	−0.0290404	+	0.164696i	0.966839	+	0.255388i	$0.0822032\pi$
$692$	5.41770	−	9.38373i	0.205950	−	0.356716i
$693$		0			0
$694$	30.3912	−	11.0615i	1.15363	−	0.419888i
$695$	−1.70316	−	0.983317i	−0.0646044	−	0.0372993i
$696$		0			0
$697$		−	27.5539i		−	1.04368i
$698$	16.0260	+	19.0990i	0.606593	+	0.722909i
$699$		0			0
$700$	2.75015	+	15.5969i	0.103946	+	0.589507i
$701$	−14.1350	−	2.49237i	−0.533870	−	0.0941356i	−0.0997873	−	0.995009i	$-0.531816\pi$
$701$	−14.1350	−	2.49237i	−0.533870	−	0.0941356i	−0.434082	+	0.900873i	$0.642927\pi$
$702$		0			0
$703$	−9.49934	−	35.1491i	−0.358274	−	1.32567i
$704$	2.58472			0.0974152
$705$		0			0
$706$	1.50052	+	8.50986i	0.0564727	+	0.320273i
$707$	−3.90319	−	1.42064i	−0.146794	−	0.0534288i
$708$		0			0
$709$		−	6.87475i		−	0.258187i	−0.991632	−	0.129093i	$-0.958793\pi$
$709$		−	6.87475i		−	0.258187i	0.991632	−	0.129093i	$-0.0412067\pi$
$710$	−4.42095	+	3.70962i	−0.165915	+	0.139219i
$711$		0			0
$712$	−0.895774	+	0.326035i	−0.0335705	+	0.0122187i
$713$	−9.57357	−	16.5819i	−0.358533	−	0.620998i
$714$		0			0
$715$	−0.235708	+	1.33677i	−0.00881499	+	0.0499923i
$716$	−2.07672	+	5.70574i	−0.0776107	+	0.213234i
$717$		0			0
$718$	−2.48018	+	2.95577i	−0.0925596	+	0.110308i
$719$	13.0967	+	10.9894i	0.488424	+	0.409836i	0.853461	−	0.521157i	$-0.174499\pi$
$719$	13.0967	+	10.9894i	0.488424	+	0.409836i	−0.365037	+	0.930993i	$0.618944\pi$
$720$		0			0
$721$	−34.8654	+	6.14771i	−1.29845	+	0.228953i
$722$	−16.5739	+	2.92243i	−0.616817	+	0.108762i
$723$		0			0
$724$	−16.5112	−	13.8545i	−0.613634	−	0.514900i
$725$	−10.0206	+	11.9420i	−0.372154	+	0.443516i
$726$		0			0
$727$	−14.5792	+	40.0561i	−0.540713	+	1.48560i	0.305206	+	0.952286i	$0.401275\pi$
$727$	−14.5792	+	40.0561i	−0.540713	+	1.48560i	−0.845919	+	0.533311i	$0.820948\pi$
$728$	−0.773654	+	4.38761i	−0.0286735	+	0.162616i
$729$		0			0
$730$	2.90090	+	5.02451i	0.107367	+	0.185965i
$731$	13.5868	−	4.94519i	0.502526	−	0.182904i
$732$		0			0
$733$	32.6482	−	27.3951i	1.20589	−	1.01186i	0.206447	−	0.978458i	$-0.433810\pi$
$733$	32.6482	−	27.3951i	1.20589	−	1.01186i	0.999442	−	0.0334033i	$-0.0106346\pi$
$734$		−	10.4563i		−	0.385948i
$735$		0			0
$736$	7.09097	+	2.58090i	0.261377	+	0.0951333i
$737$	5.04397	+	28.6058i	0.185797	+	1.05371i
$738$		0			0
$739$	1.69175			0.0622321			0.0311161	−	0.999516i	$-0.490094\pi$
$739$	1.69175			0.0622321			0.0311161	+	0.999516i	$0.490094\pi$
$740$	−2.11896	+	0.993649i	−0.0778945	+	0.0365272i
$741$		0			0
$742$	27.8741	+	4.91495i	1.02329	+	0.180434i
$743$	2.22382	+	12.6119i	0.0815839	+	0.462685i	0.998042	+	0.0625538i	$0.0199245\pi$
$743$	2.22382	+	12.6119i	0.0815839	+	0.462685i	−0.916458	+	0.400132i	$0.868964\pi$
$744$		0			0
$745$	3.92489	+	4.67751i	0.143797	+	0.171371i
$746$		−	9.86566i		−	0.361208i
$747$		0			0
$748$	7.45873	+	4.30630i	0.272718	+	0.157454i
$749$	14.5990	−	5.31360i	0.533436	−	0.194155i
$750$		0			0
$751$	24.2360	−	41.9780i	0.884384	−	1.53180i	0.0379668	−	0.999279i	$-0.487912\pi$
$751$	24.2360	−	41.9780i	0.884384	−	1.53180i	0.846418	−	0.532520i	$-0.178755\pi$
$752$	−0.908022	+	5.14965i	−0.0331122	+	0.187788i
$753$		0			0
$754$	−3.79792	+	2.19273i	−0.138312	+	0.0798544i
$755$	5.38357	−	6.41589i	0.195928	−	0.233498i
$756$		0			0
$757$	10.9913	+	30.1984i	0.399486	+	1.09758i	0.962535	+	0.271156i	$0.0874060\pi$
$757$	10.9913	+	30.1984i	0.399486	+	1.09758i	−0.563049	+	0.826424i	$0.690372\pi$
$758$	2.44351	−	0.430857i	0.0887524	−	0.0156494i
$759$		0			0
$760$	0.787692	+	2.16417i	0.0285726	+	0.0785025i
$761$	−7.94619	−	6.66765i	−0.288049	−	0.241702i	0.487300	−	0.873235i	$-0.337982\pi$
$761$	−7.94619	−	6.66765i	−0.288049	−	0.241702i	−0.775349	+	0.631533i	$0.782426\pi$
$762$		0			0
$763$	−27.2434	+	15.7290i	−0.986277	+	0.569427i
$764$	−2.26654	+	6.22728i	−0.0820007	+	0.225295i
$765$		0			0
$766$	12.7819	−	22.1390i	0.461830	−	0.799913i
$767$	−8.84976	−	15.3282i	−0.319546	−	0.553471i
$768$		0			0
$769$	29.3819	+	16.9637i	1.05954	+	0.611725i	0.925305	−	0.379225i	$-0.123809\pi$
$769$	29.3819	+	16.9637i	1.05954	+	0.611725i	0.134234	+	0.990950i	$0.457143\pi$
$770$	2.48668	−	2.08657i	0.0896136	−	0.0751947i
$771$		0			0
$772$	−14.6905	−	17.5075i	−0.528724	−	0.630108i
$773$	−27.2363	−	9.91322i	−0.979623	−	0.356554i	−0.197930	−	0.980216i	$-0.563422\pi$
$773$	−27.2363	−	9.91322i	−0.979623	−	0.356554i	−0.781694	+	0.623662i	$0.785644\pi$
$774$		0			0
$775$	12.1242	+	2.13782i	0.435514	+	0.0767929i
$776$	−14.8185			−0.531954
$777$		0			0
$778$	−6.37509			−0.228558
$779$	48.7454	+	8.59512i	1.74648	+	0.307952i
$780$		0			0
$781$	−36.4315	−	13.2600i	−1.30362	−	0.474479i
$782$	16.1625	+	19.2617i	0.577970	+	0.688798i
$783$		0			0
$784$	2.79959	−	2.34914i	0.0999854	−	0.0838977i
$785$	3.24924	+	1.87595i	0.115970	+	0.0669555i
$786$		0			0
$787$	8.35500	+	14.4713i	0.297823	+	0.515845i	0.975638	−	0.219388i	$-0.0704060\pi$
$787$	8.35500	+	14.4713i	0.297823	+	0.515845i	−0.677814	+	0.735233i	$0.737073\pi$
$788$	7.37803	−	12.7791i	0.262832	−	0.455238i
$789$		0			0
$790$	0.192560	−	0.529055i	0.00685099	−	0.0188229i
$791$	−36.6213	+	21.1433i	−1.30210	+	0.751771i
$792$		0			0
$793$	−7.33236	−	6.15258i	−0.260380	−	0.218484i
$794$	−12.8250	−	35.2364i	−0.455142	−	1.25049i
$795$		0			0
$796$	−1.45237	+	0.256093i	−0.0514780	+	0.00907696i
$797$	−1.78348	−	4.90007i	−0.0631741	−	0.173569i	0.904090	−	0.427343i	$-0.140550\pi$
$797$	−1.78348	−	4.90007i	−0.0631741	−	0.173569i	−0.967264	+	0.253774i	$0.918328\pi$
$798$		0			0
$799$	−11.1999	+	13.3476i	−0.396225	+	0.472203i
$800$	−4.20192	+	2.42598i	−0.148560	+	0.0857714i
$801$		0			0
$802$	6.10310	−	34.6124i	0.215508	−	1.22221i
$803$	−19.4878	+	33.7538i	−0.687708	+	1.19115i
$804$		0			0
$805$	8.90549	−	3.24133i	0.313877	−	0.114242i
$806$	2.99932	+	1.73166i	0.105647	+	0.0609951i
$807$		0			0
$808$		−	1.27252i		−	0.0447671i
$809$	−32.5001	−	38.7321i	−1.14264	−	1.36175i	−0.922369	−	0.386310i	$-0.873749\pi$
$809$	−32.5001	−	38.7321i	−1.14264	−	1.36175i	−0.220274	−	0.975438i	$-0.570695\pi$
$810$		0			0
$811$	6.26321	+	35.5205i	0.219931	+	1.24729i	0.872141	+	0.489254i	$0.162731\pi$
$811$	6.26321	+	35.5205i	0.219931	+	1.24729i	−0.652210	+	0.758038i	$0.726158\pi$
$812$	10.3283	+	1.82115i	0.362451	+	0.0639098i
$813$		0			0
$814$	−12.8983	−	8.99014i	−0.452084	−	0.315104i
$815$	5.06519			0.177426
$816$		0			0
$817$	4.51025	+	25.5789i	0.157794	+	0.894893i
$818$	−0.423558	−	0.154163i	−0.0148094	−	0.00539017i
$819$		0			0
$820$		−	3.18159i		−	0.111106i
$821$	−39.1705	+	32.8679i	−1.36706	+	1.14710i	−0.393328	+	0.919398i	$0.628676\pi$
$821$	−39.1705	+	32.8679i	−1.36706	+	1.14710i	−0.973731	+	0.227701i	$0.926879\pi$
$822$		0			0
$823$	−7.59472	+	2.76425i	−0.264735	+	0.0963558i	−0.470978	−	0.882145i	$-0.656099\pi$
$823$	−7.59472	+	2.76425i	−0.264735	+	0.0963558i	0.206242	+	0.978501i	$0.433877\pi$
$824$	−5.42306	−	9.39301i	−0.188921	−	0.327221i
$825$		0			0
$826$	−7.35009	+	41.6844i	−0.255742	+	1.45039i
$827$	−8.84209	+	24.2934i	−0.307469	+	0.844765i	0.685679	+	0.727904i	$0.259505\pi$
$827$	−8.84209	+	24.2934i	−0.307469	+	0.844765i	−0.993148	+	0.116861i	$0.962717\pi$
$828$		0			0
$829$	5.26941	−	6.27984i	0.183014	−	0.218108i	−0.666735	−	0.745295i	$-0.732309\pi$
$829$	5.26941	−	6.27984i	0.183014	−	0.218108i	0.849749	+	0.527187i	$0.176753\pi$
$830$	0.00327685	+	0.00274961i	0.000113741	+	9.54403e-5i
$831$		0			0
$832$	−1.34419	+	0.237016i	−0.0466013	+	0.00821706i
$833$	11.9926	−	2.11462i	0.415519	−	0.0732673i
$834$		0			0
$835$	−1.65121	−	1.38553i	−0.0571425	−	0.0479483i
$836$	−9.94492	+	11.8519i	−0.343952	+	0.409906i
$837$		0			0
$838$	−5.23677	+	14.3879i	−0.180901	+	0.497022i
$839$	9.17699	−	52.0453i	0.316825	−	1.79680i	−0.244975	−	0.969529i	$-0.578780\pi$
$839$	9.17699	−	52.0453i	0.316825	−	1.79680i	0.561800	−	0.827273i	$-0.310109\pi$
$840$		0			0
$841$	−9.33841	−	16.1746i	−0.322014	−	0.557745i
$842$	21.0458	−	7.66004i	0.725286	−	0.263983i
$843$		0			0
$844$	1.85346	−	1.55524i	0.0637988	−	0.0535336i
$845$			4.28501i			0.147409i
$846$		0			0
$847$	−13.2484	−	4.82201i	−0.455219	−	0.165686i
$848$	1.50574	+	8.53949i	0.0517074	+	0.293247i
$849$		0			0
$850$	−16.1674			−0.554536
$851$	−26.4085	−	37.5430i	−0.905273	−	1.28696i
$852$		0			0
$853$	−32.4894	−	5.72875i	−1.11241	−	0.196149i	−0.412907	−	0.910773i	$-0.635486\pi$
$853$	−32.4894	−	5.72875i	−1.11241	−	0.196149i	−0.699508	+	0.714625i	$0.746598\pi$
$854$	3.97485	+	22.5425i	0.136017	+	0.771388i
$855$		0			0
$856$	3.05940	+	3.64605i	0.104568	+	0.124619i
$857$			38.4078i			1.31199i	0.754767	+	0.655993i	$0.227750\pi$
$857$			38.4078i			1.31199i	−0.754767	+	0.655993i	$0.772250\pi$
$858$		0			0
$859$	−17.9404	−	10.3579i	−0.612119	−	0.353407i	0.161676	−	0.986844i	$-0.448310\pi$
$859$	−17.9404	−	10.3579i	−0.612119	−	0.353407i	−0.773794	+	0.633437i	$0.781644\pi$
$860$	1.56884	−	0.571012i	0.0534971	−	0.0194713i
$861$		0			0
$862$	−0.0510399	+	0.0884037i	−0.00173843	+	0.00301104i
$863$	−6.14125	+	34.8288i	−0.209051	+	1.18559i	0.681886	+	0.731458i	$0.261160\pi$
$863$	−6.14125	+	34.8288i	−0.209051	+	1.18559i	−0.890937	+	0.454127i	$0.849951\pi$
$864$		0			0
$865$	3.61043	−	2.08448i	0.122758	−	0.0708746i
$866$	5.09547	−	6.07254i	0.173151	−	0.206353i
$867$		0			0
$868$	−2.83273	−	7.78285i	−0.0961490	−	0.264167i
$869$	3.72474	−	0.656772i	0.126353	−	0.0222795i
$870$		0			0
$871$	−5.24625	−	14.4139i	−0.177762	−	0.488398i
$872$	−7.38271	−	6.19483i	−0.250010	−	0.209783i
$873$		0			0
$874$	−39.1175	+	22.5845i	−1.32317	+	0.763932i
$875$	−4.23182	+	11.6268i	−0.143062	+	0.393058i
$876$		0			0
$877$	−13.1851	+	22.8373i	−0.445230	+	0.771160i	−0.998068	−	0.0621282i	$-0.980211\pi$
$877$	−13.1851	+	22.8373i	−0.445230	+	0.771160i	0.552839	+	0.833288i	$0.313545\pi$
$878$	−3.78531	−	6.55635i	−0.127748	−	0.221266i
$879$		0			0
$880$	0.861246	+	0.497241i	0.0290326	+	0.0167620i
$881$	−25.8314	+	21.6752i	−0.870283	+	0.730254i	−0.964158	−	0.265330i	$-0.914519\pi$
$881$	−25.8314	+	21.6752i	−0.870283	+	0.730254i	0.0938745	+	0.995584i	$0.470075\pi$
$882$		0			0
$883$	−37.1901	−	44.3215i	−1.25155	−	1.49154i	−0.800857	−	0.598856i	$-0.795622\pi$
$883$	−37.1901	−	44.3215i	−1.25155	−	1.49154i	−0.450690	−	0.892680i	$-0.648822\pi$
$884$	−4.27381	−	1.55554i	−0.143744	−	0.0523185i
$885$		0			0
$886$	15.7427	+	2.77587i	0.528888	+	0.0932572i
$887$	44.4679			1.49309			0.746544	−	0.665336i	$-0.231712\pi$
$887$	44.4679			1.49309			0.746544	+	0.665336i	$0.231712\pi$
$888$		0			0
$889$	−36.6915			−1.23059
$890$	−0.361200	−	0.0636893i	−0.0121074	−	0.00213487i
$891$		0			0
$892$	−6.52829	−	2.37610i	−0.218583	−	0.0795578i
$893$	−20.1194	−	23.9774i	−0.673270	−	0.802372i
$894$		0			0
$895$	−1.78963	+	1.50168i	−0.0598208	+	0.0501956i
$896$	2.82683	+	1.63207i	0.0944377	+	0.0545236i
$897$		0			0
$898$	−14.3377	−	24.8336i	−0.478454	−	0.828706i
$899$	4.07625	−	7.06028i	0.135951	−	0.235473i
$900$		0			0
$901$	−9.88220	+	27.1511i	−0.329224	+	0.904535i
$902$	18.5099	−	10.6867i	0.616313	−	0.355828i
$903$		0			0
$904$	−9.92405	−	8.32726i	−0.330069	−	0.276961i
$905$	−2.83635	−	7.79281i	−0.0942835	−	0.259042i
$906$		0			0
$907$	−12.8961	+	2.27393i	−0.428209	+	0.0755048i	−0.383599	−	0.923500i	$-0.625316\pi$
$907$	−12.8961	+	2.27393i	−0.428209	+	0.0755048i	−0.0446097	+	0.999004i	$0.514204\pi$
$908$	7.47280	+	20.5313i	0.247993	+	0.681356i
$909$		0			0
$910$	−1.10186	+	1.31315i	−0.0365264	+	0.0435305i
$911$	33.2957	−	19.2233i	1.10314	−	0.636896i	0.166093	−	0.986110i	$-0.446885\pi$
$911$	33.2957	−	19.2233i	1.10314	−	0.636896i	0.937043	+	0.349215i	$0.113552\pi$
$912$		0			0
$913$	−0.00499003	+	0.0282998i	−0.000165146	+	0.000936588i
$914$	−0.0525581	+	0.0910334i	−0.00173847	+	0.00301112i
$915$		0			0
$916$	−3.99379	+	1.45362i	−0.131958	+	0.0480289i
$917$	23.6594	+	13.6597i	0.781301	+	0.451085i
$918$		0			0
$919$			14.8613i			0.490229i	0.969494	+	0.245115i	$0.0788256\pi$
$919$			14.8613i			0.490229i	−0.969494	+	0.245115i	$0.921174\pi$
$920$	1.86625	+	2.22412i	0.0615286	+	0.0733269i
$921$		0			0
$922$	4.16236	+	23.6059i	0.137080	+	0.777420i
$923$	20.1622	+	3.55514i	0.663646	+	0.117019i
$924$		0			0
$925$	29.4065	+	2.50894i	0.966880	+	0.0824933i
$926$	20.7514			0.681933
$927$		0			0
$928$	0.557927	+	3.16416i	0.0183148	+	0.103869i
$929$	6.82712	+	2.48487i	0.223990	+	0.0815258i	0.451578	−	0.892232i	$-0.350861\pi$
$929$	6.82712	+	2.48487i	0.223990	+	0.0815258i	−0.227587	+	0.973758i	$0.573084\pi$
$930$		0			0
$931$			21.8757i			0.716947i
$932$	13.2865	−	11.1487i	0.435214	−	0.365188i
$933$		0			0
$934$	16.4379	−	5.98290i	0.537864	−	0.195767i
$935$	1.65687	+	2.86978i	0.0541854	+	0.0938519i
$936$		0			0
$937$	−4.58137	+	25.9822i	−0.149667	+	0.848802i	0.813834	+	0.581097i	$0.197376\pi$
$937$	−4.58137	+	25.9822i	−0.149667	+	0.848802i	−0.963501	+	0.267705i	$0.913735\pi$
$938$	−12.5461	+	34.4702i	−0.409645	+	1.12549i
$939$		0			0
$940$	−1.29324	+	1.54122i	−0.0421807	+	0.0502690i
$941$	−27.6990	−	23.2422i	−0.902961	−	0.757674i	0.0678062	−	0.997699i	$-0.478400\pi$
$941$	−27.6990	−	23.2422i	−0.902961	−	0.757674i	−0.970767	+	0.240025i	$0.922844\pi$
$942$		0			0
$943$	61.4514	−	10.8355i	2.00113	−	0.352854i
$944$	−12.7704	+	2.25177i	−0.415642	+	0.0732889i
$945$		0			0
$946$	8.59165	+	7.20925i	0.279339	+	0.234393i
$947$	30.2846	−	36.0917i	0.984116	−	1.17282i	−0.000836789	−	1.00000i	$-0.500266\pi$
$947$	30.2846	−	36.0917i	0.984116	−	1.17282i	0.984953	−	0.172824i	$-0.0552892\pi$
$948$		0			0
$949$	7.03945	−	19.3407i	0.228510	−	0.627827i
$950$	5.04323	−	28.6016i	0.163624	−	0.927958i
$951$		0			0
$952$	5.43826	+	9.41935i	0.176255	+	0.305283i
$953$	8.78776	−	3.19848i	0.284663	−	0.103609i	−0.195742	−	0.980655i	$-0.562712\pi$
$953$	8.78776	−	3.19848i	0.284663	−	0.103609i	0.480406	+	0.877046i	$0.340489\pi$
$954$		0			0
$955$	−1.95322	+	1.63894i	−0.0632046	+	0.0530349i
$956$			18.3584i			0.593752i
$957$		0			0
$958$	−6.46552	−	2.35326i	−0.208891	−	0.0760303i
$959$	−2.25825	−	12.8072i	−0.0729228	−	0.413565i
$960$		0			0
$961$	24.5617			0.792314
$962$	7.53216	+	3.49258i	0.242847	+	0.112605i
$963$		0			0
$964$	23.1096	+	4.07485i	0.744310	+	0.131242i
$965$	−1.52695	−	8.65974i	−0.0491541	−	0.278767i
$966$		0			0
$967$	32.1046	+	38.2608i	1.03242	+	1.23039i	0.972675	+	0.232171i	$0.0745830\pi$
$967$	32.1046	+	38.2608i	1.03242	+	1.23039i	0.0597409	+	0.998214i	$0.480973\pi$
$968$		−	4.31924i		−	0.138826i
$969$		0			0
$970$	−4.93764	−	2.85075i	−0.158538	−	0.0915320i
$971$	35.3500	−	12.8664i	1.13444	−	0.412901i	0.294536	−	0.955641i	$-0.404835\pi$
$971$	35.3500	−	12.8664i	1.13444	−	0.412901i	0.839901	+	0.542739i	$0.182613\pi$
$972$		0			0
$973$	8.34216	−	14.4491i	0.267437	−	0.463215i
$974$	−0.296609	+	1.68215i	−0.00950395	+	0.0538996i
$975$		0			0
$976$	−6.07313	+	3.50632i	−0.194396	+	0.112235i
$977$	−18.0852	+	21.5531i	−0.578597	+	0.689545i	−0.973372	−	0.229233i	$-0.926378\pi$
$977$	−18.0852	+	21.5531i	−0.578597	+	0.689545i	0.394775	+	0.918778i	$0.370823\pi$
$978$		0			0
$979$	−0.842708	−	2.31532i	−0.0269331	−	0.0739980i
$980$	1.38476	−	0.244171i	0.0442347	−	0.00779977i
$981$		0			0
$982$	−3.63330	−	9.98241i	−0.115943	−	0.318551i
$983$	25.2349	+	21.1746i	0.804867	+	0.675364i	0.949377	−	0.314140i	$-0.101716\pi$
$983$	25.2349	+	21.1746i	0.804867	+	0.675364i	−0.144510	+	0.989503i	$0.546160\pi$
$984$		0			0
$985$	4.91683	−	2.83873i	0.156663	−	0.0904495i
$986$	−3.66168	+	10.0604i	−0.116612	+	0.320388i
$987$		0			0
$988$	4.08506	−	7.07554i	0.129963	−	0.225103i
$989$	16.3719	+	28.3570i	0.520597	+	0.901700i
$990$		0			0
$991$	33.7743	+	19.4996i	1.07288	+	0.619426i	0.928966	−	0.370164i	$-0.120699\pi$
$991$	33.7743	+	19.4996i	1.07288	+	0.619426i	0.143911	+	0.989591i	$0.454032\pi$
$992$	1.94374	−	1.63099i	0.0617138	−	0.0517840i
$993$		0			0
$994$	−31.4713	−	37.5060i	−0.998208	−	1.18962i
$995$	−0.533207	−	0.194072i	−0.0169038	−	0.00615248i
$996$		0			0
$997$	−7.85922	−	1.38579i	−0.248904	−	0.0438885i	0.0478041	−	0.998857i	$-0.484778\pi$
$997$	−7.85922	−	1.38579i	−0.248904	−	0.0438885i	−0.296708	+	0.954968i	$0.595889\pi$
$998$	−35.4707			−1.12281
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.bj.c.559.1		12
3.2	odd	2		74.2.h.a.41.2	✓	12
12.11	even	2		592.2.bq.b.337.2		12
37.28	even	18	inner	666.2.bj.c.361.1		12
111.56	even	36		2738.2.a.s.1.6		6
111.65	odd	18		74.2.h.a.65.2	yes	12
111.92	even	36		2738.2.a.r.1.5		6
444.287	even	18		592.2.bq.b.65.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.h.a.41.2	✓	12	3.2	odd	2
74.2.h.a.65.2	yes	12	111.65	odd	18
592.2.bq.b.65.2		12	444.287	even	18
592.2.bq.b.337.2		12	12.11	even	2
666.2.bj.c.361.1		12	37.28	even	18	inner
666.2.bj.c.559.1		12	1.1	even	1	trivial
2738.2.a.r.1.5		6	111.92	even	36
2738.2.a.s.1.6		6	111.56	even	36

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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.bj (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.984808 - 0.173648i) q^{2} +(0.939693 + 0.342020i) q^{4} +(0.247315 + 0.294739i) q^{5} +(-2.50048 + 2.09815i) q^{7} +(-0.866025 - 0.500000i) q^{8} +O(q^{10})\)	\(q+(-0.984808 - 0.173648i) q^{2} +(0.939693 + 0.342020i) q^{4} +(0.247315 + 0.294739i) q^{5} +(-2.50048 + 2.09815i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-0.192377 - 0.333207i) q^{10} +(1.29236 - 2.23843i) q^{11} +(-0.466831 + 1.28261i) q^{13} +(2.82683 - 1.63207i) q^{14} +(0.766044 + 0.642788i) q^{16} +(1.13965 + 3.13118i) q^{17} +(-5.89485 + 1.03942i) q^{19} +(0.131594 + 0.361551i) q^{20} +(-1.66142 + 1.98001i) q^{22} +(-6.53507 + 3.77303i) q^{23} +(0.842535 - 4.77825i) q^{25} +(0.682461 - 1.18206i) q^{26} +(-3.06729 + 1.11640i) q^{28} +(-2.78251 - 1.60649i) q^{29} +2.53737i q^{31} +(-0.642788 - 0.766044i) q^{32} +(-0.578618 - 3.28150i) q^{34} +(-1.23681 - 0.218083i) q^{35} +(0.543196 + 6.05846i) q^{37} +5.98578 q^{38} +(-0.0668119 - 0.378909i) q^{40} +(-7.77046 - 2.82822i) q^{41} -4.33920i q^{43} +(1.98001 - 1.66142i) q^{44} +(7.09097 - 2.58090i) q^{46} +(2.61455 + 4.52853i) q^{47} +(0.634616 - 3.59909i) q^{49} +(-1.65947 + 4.55935i) q^{50} +(-0.877355 + 1.04559i) q^{52} +(6.64254 + 5.57375i) q^{53} +(0.979373 - 0.172690i) q^{55} +(3.21455 - 0.566812i) q^{56} +(2.46128 + 2.06526i) q^{58} +(-8.33530 + 9.93362i) q^{59} +(-2.39847 + 6.58973i) q^{61} +(0.440610 - 2.49882i) q^{62} +(0.500000 + 0.866025i) q^{64} +(-0.493489 + 0.179615i) q^{65} +(-8.60881 + 7.22365i) q^{67} +3.33213i q^{68} +(1.18015 + 0.429540i) q^{70} +(-2.60464 - 14.7717i) q^{71} -15.0792 q^{73} +(0.517097 - 6.06074i) q^{74} +(-5.89485 - 1.03942i) q^{76} +(1.46505 + 8.30870i) q^{77} +(0.940587 + 1.12095i) q^{79} +0.384754i q^{80} +(7.16130 + 4.13458i) q^{82} +(-0.0104473 + 0.00380252i) q^{83} +(-0.641025 + 1.11029i) q^{85} +(-0.753494 + 4.27328i) q^{86} +(-2.23843 + 1.29236i) q^{88} +(0.612745 - 0.730241i) q^{89} +(-1.52380 - 4.18661i) q^{91} +(-7.43141 + 1.31036i) q^{92} +(-1.78845 - 4.91374i) q^{94} +(-1.76424 - 1.48038i) q^{95} +(12.8332 - 7.40927i) q^{97} +(-1.24995 + 3.43421i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{7}+O(q^{10}) \) 12 * q - 12 * q^7	\( 12 q - 12 q^{7} + 6 q^{10} + 6 q^{11} + 6 q^{13} + 18 q^{14} - 18 q^{19} - 18 q^{25} - 12 q^{26} - 6 q^{28} - 18 q^{29} + 12 q^{34} - 18 q^{35} + 30 q^{37} + 24 q^{38} + 12 q^{40} - 24 q^{41} - 6 q^{44} + 30 q^{46} - 6 q^{47} + 12 q^{49} + 36 q^{50} - 12 q^{52} + 12 q^{53} - 18 q^{55} + 6 q^{58} - 36 q^{61} + 6 q^{64} - 36 q^{65} - 30 q^{67} - 12 q^{70} - 12 q^{71} + 48 q^{74} - 18 q^{76} - 12 q^{77} + 6 q^{79} + 48 q^{83} + 18 q^{85} + 36 q^{86} - 36 q^{88} + 18 q^{89} - 6 q^{91} - 18 q^{92} + 36 q^{97} - 36 q^{98}+O(q^{100}) \) 12 * q - 12 * q^7 + 6 * q^10 + 6 * q^11 + 6 * q^13 + 18 * q^14 - 18 * q^19 - 18 * q^25 - 12 * q^26 - 6 * q^28 - 18 * q^29 + 12 * q^34 - 18 * q^35 + 30 * q^37 + 24 * q^38 + 12 * q^40 - 24 * q^41 - 6 * q^44 + 30 * q^46 - 6 * q^47 + 12 * q^49 + 36 * q^50 - 12 * q^52 + 12 * q^53 - 18 * q^55 + 6 * q^58 - 36 * q^61 + 6 * q^64 - 36 * q^65 - 30 * q^67 - 12 * q^70 - 12 * q^71 + 48 * q^74 - 18 * q^76 - 12 * q^77 + 6 * q^79 + 48 * q^83 + 18 * q^85 + 36 * q^86 - 36 * q^88 + 18 * q^89 - 6 * q^91 - 18 * q^92 + 36 * q^97 - 36 * q^98

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