LMFDB - Embedded newform 666.2.bj.c.613.2

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			613.2
Root			$0.342020 - 0.939693i$ of defining polynomial
Character	$\chi$	$=$	666.613
Dual form			666.2.bj.c.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.342020 - 0.939693i) q^{2} +(-0.766044 - 0.642788i) q^{4} +(-2.57176 - 0.453471i) q^{5} +(-0.361075 + 2.04776i) q^{7} +(-0.866025 + 0.500000i) q^{8} +O(q^{10})$	\(q+(0.342020 - 0.939693i) q^{2} +(-0.766044 - 0.642788i) q^{4} +(-2.57176 - 0.453471i) q^{5} +(-0.361075 + 2.04776i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.30572 + 2.26157i) q^{10} +(2.99810 + 5.19285i) q^{11} +(2.64632 - 3.15377i) q^{13} +(1.80077 + 1.03967i) q^{14} +(0.173648 + 0.984808i) q^{16} +(0.618710 + 0.737350i) q^{17} +(0.534946 + 1.46975i) q^{19} +(1.67860 + 2.00048i) q^{20} +(5.90509 - 1.04123i) q^{22} +(5.51705 + 3.18527i) q^{23} +(1.70986 + 0.622339i) q^{25} +(-2.05847 - 3.56538i) q^{26} +(1.59287 - 1.33658i) q^{28} +(3.51193 - 2.02761i) q^{29} +3.39997i q^{31} +(0.984808 + 0.173648i) q^{32} +(0.904494 - 0.329209i) q^{34} +(1.85720 - 5.10261i) q^{35} +(6.07068 + 0.383130i) q^{37} +1.56408 q^{38} +(2.45395 - 0.893164i) q^{40} +(-7.94502 - 6.66666i) q^{41} +3.76932i q^{43} +(1.04123 - 5.90509i) q^{44} +(4.88011 - 4.09490i) q^{46} +(-3.08750 + 5.34771i) q^{47} +(2.51491 + 0.915354i) q^{49} +(1.16962 - 1.39389i) q^{50} +(-4.05440 + 0.714901i) q^{52} +(1.39401 + 7.90585i) q^{53} +(-5.35558 - 14.7143i) q^{55} +(-0.711179 - 1.95395i) q^{56} +(-0.704183 - 3.99362i) q^{58} +(-5.02269 + 0.885636i) q^{59} +(-6.25519 + 7.45465i) q^{61} +(3.19493 + 1.16286i) q^{62} +(0.500000 - 0.866025i) q^{64} +(-8.23586 + 6.91071i) q^{65} +(-1.83263 + 10.3934i) q^{67} -0.962542i q^{68} +(-4.15968 - 3.49039i) q^{70} +(10.1503 - 3.69442i) q^{71} +3.55293 q^{73} +(2.43632 - 5.57354i) q^{74} +(0.534946 - 1.46975i) q^{76} +(-11.7162 + 4.26436i) q^{77} +(2.51098 + 0.442753i) q^{79} -2.61144i q^{80} +(-8.98197 + 5.18574i) q^{82} +(-5.29798 + 4.44553i) q^{83} +(-1.25681 - 2.17686i) q^{85} +(3.54200 + 1.28918i) q^{86} +(-5.19285 - 2.99810i) q^{88} +(16.0165 - 2.82414i) q^{89} +(5.50263 + 6.55778i) q^{91} +(-2.17885 - 5.98635i) q^{92} +(3.96922 + 4.73033i) q^{94} +(-0.709264 - 4.02243i) q^{95} +(-14.1175 - 8.15074i) q^{97} +(1.72030 - 2.05018i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$1$	$e\left(\frac{11}{18}\right)$

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 $

$2$	0.342020	−	0.939693i	0.241845	−	0.664463i
$2$	0.342020	−	0.939693i	0.241845	−	0.664463i
$3$		0			0
$3$		0			0
$4$	−0.766044	−	0.642788i	−0.383022	−	0.321394i
$5$	−2.57176	−	0.453471i	−1.15013	−	0.202798i	−0.434096	−	0.900867i	$-0.642932\pi$
$5$	−2.57176	−	0.453471i	−1.15013	−	0.202798i	−0.716031	+	0.698068i	$0.754043\pi$
$6$		0			0
$7$	−0.361075	+	2.04776i	−0.136473	+	0.773979i	0.837349	+	0.546669i	$0.184104\pi$
$7$	−0.361075	+	2.04776i	−0.136473	+	0.773979i	−0.973822	+	0.227311i	$0.927007\pi$
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$		0			0
$10$	−1.30572	+	2.26157i	−0.412904	+	0.715171i
$11$	2.99810	+	5.19285i	0.903960	+	1.56570i	0.822308	+	0.569043i	$0.192686\pi$
$11$	2.99810	+	5.19285i	0.903960	+	1.56570i	0.0816522	+	0.996661i	$0.473980\pi$
$12$		0			0
$13$	2.64632	−	3.15377i	0.733958	−	0.874697i	−0.261949	−	0.965082i	$-0.584365\pi$
$13$	2.64632	−	3.15377i	0.733958	−	0.874697i	0.995907	+	0.0903843i	$0.0288095\pi$
$14$	1.80077	+	1.03967i	0.481275	+	0.277864i
$15$		0			0
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	0.618710	+	0.737350i	0.150059	+	0.178834i	0.835838	−	0.548977i	$-0.184982\pi$
$17$	0.618710	+	0.737350i	0.150059	+	0.178834i	−0.685778	+	0.727810i	$0.740538\pi$
$18$		0			0
$19$	0.534946	+	1.46975i	0.122725	+	0.337184i	0.985808	−	0.167878i	$-0.0536916\pi$
$19$	0.534946	+	1.46975i	0.122725	+	0.337184i	−0.863083	+	0.505063i	$0.831469\pi$
$20$	1.67860	+	2.00048i	0.375346	+	0.447320i
$21$		0			0
$22$	5.90509	−	1.04123i	1.25897	−	0.221990i
$23$	5.51705	+	3.18527i	1.15038	+	0.664174i	0.948981	−	0.315334i	$-0.102117\pi$
$23$	5.51705	+	3.18527i	1.15038	+	0.664174i	0.201403	+	0.979508i	$0.435450\pi$
$24$		0			0
$25$	1.70986	+	0.622339i	0.341973	+	0.124468i
$26$	−2.05847	−	3.56538i	−0.403700	−	0.699229i
$27$		0			0
$28$	1.59287	−	1.33658i	0.301025	−	0.252590i
$29$	3.51193	−	2.02761i	0.652149	−	0.376519i	−0.137130	−	0.990553i	$-0.543788\pi$
$29$	3.51193	−	2.02761i	0.652149	−	0.376519i	0.789279	+	0.614035i	$0.210454\pi$
$30$		0			0
$31$			3.39997i			0.610653i	0.952248	+	0.305326i	$0.0987655\pi$
$31$			3.39997i			0.610653i	−0.952248	+	0.305326i	$0.901234\pi$
$32$	0.984808	+	0.173648i	0.174091	+	0.0306970i
$33$		0			0
$34$	0.904494	−	0.329209i	0.155119	−	0.0564588i
$35$	1.85720	−	5.10261i	0.313924	−	0.862498i
$36$		0			0
$37$	6.07068	+	0.383130i	0.998014	+	0.0629862i
$37$	6.07068	+	0.383130i	0.998014	+	0.0629862i
$38$	1.56408			0.253727
$39$		0			0
$40$	2.45395	−	0.893164i	0.388003	−	0.141222i
$41$	−7.94502	−	6.66666i	−1.24080	−	1.04116i	−0.997461	−	0.0712179i	$-0.977311\pi$
$41$	−7.94502	−	6.66666i	−1.24080	−	1.04116i	−0.243343	−	0.969940i	$-0.578244\pi$
$42$		0			0
$43$			3.76932i			0.574816i	0.957808	+	0.287408i	$0.0927936\pi$
$43$			3.76932i			0.574816i	−0.957808	+	0.287408i	$0.907206\pi$
$44$	1.04123	−	5.90509i	0.156971	−	0.890227i
$45$		0			0
$46$	4.88011	−	4.09490i	0.719534	−	0.603760i
$47$	−3.08750	+	5.34771i	−0.450359	+	0.780044i	−0.998408	−	0.0564019i	$-0.982037\pi$
$47$	−3.08750	+	5.34771i	−0.450359	+	0.780044i	0.548050	+	0.836446i	$0.315371\pi$
$48$		0			0
$49$	2.51491	+	0.915354i	0.359273	+	0.130765i
$50$	1.16962	−	1.39389i	0.165409	−	0.197126i
$51$		0			0
$52$	−4.05440	+	0.714901i	−0.562245	+	0.0991389i
$53$	1.39401	+	7.90585i	0.191483	+	1.08595i	0.917339	+	0.398106i	$0.130332\pi$
$53$	1.39401	+	7.90585i	0.191483	+	1.08595i	−0.725857	+	0.687846i	$0.758556\pi$
$54$		0			0
$55$	−5.35558	−	14.7143i	−0.722146	−	1.98408i
$56$	−0.711179	−	1.95395i	−0.0950352	−	0.261107i
$57$		0			0
$58$	−0.704183	−	3.99362i	−0.0924638	−	0.524388i
$59$	−5.02269	+	0.885636i	−0.653899	+	0.115300i	−0.490749	−	0.871301i	$-0.663277\pi$
$59$	−5.02269	+	0.885636i	−0.653899	+	0.115300i	−0.163150	+	0.986601i	$0.552166\pi$
$60$		0			0
$61$	−6.25519	+	7.45465i	−0.800895	+	0.954470i	−0.999673	−	0.0255750i	$-0.991858\pi$
$61$	−6.25519	+	7.45465i	−0.800895	+	0.954470i	0.198778	+	0.980045i	$0.436303\pi$
$62$	3.19493	+	1.16286i	0.405756	+	0.147683i
$63$		0			0
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	−8.23586	+	6.91071i	−1.02153	+	0.857168i
$66$		0			0
$67$	−1.83263	+	10.3934i	−0.223892	+	1.26975i	0.640901	+	0.767624i	$0.278561\pi$
$67$	−1.83263	+	10.3934i	−0.223892	+	1.26975i	−0.864792	+	0.502130i	$0.832550\pi$
$68$		−	0.962542i		−	0.116725i
$69$		0			0
$70$	−4.15968	−	3.49039i	−0.497177	−	0.417181i
$71$	10.1503	−	3.69442i	1.20462	−	0.438447i	0.339787	−	0.940502i	$-0.389645\pi$
$71$	10.1503	−	3.69442i	1.20462	−	0.438447i	0.864835	+	0.502056i	$0.167423\pi$
$72$		0			0
$73$	3.55293			0.415839			0.207920	−	0.978146i	$-0.433331\pi$
$73$	3.55293			0.415839			0.207920	+	0.978146i	$0.433331\pi$
$74$	2.43632	−	5.57354i	0.283217	−	0.647911i
$75$		0			0
$76$	0.534946	−	1.46975i	0.0613625	−	0.168592i
$77$	−11.7162	+	4.26436i	−1.33519	+	0.485969i
$78$		0			0
$79$	2.51098	+	0.442753i	0.282507	+	0.0498136i	0.313106	−	0.949718i	$-0.398630\pi$
$79$	2.51098	+	0.442753i	0.282507	+	0.0498136i	−0.0305991	+	0.999532i	$0.509742\pi$
$80$		−	2.61144i		−	0.291967i
$81$		0			0
$82$	−8.98197	+	5.18574i	−0.991893	+	0.572670i
$83$	−5.29798	+	4.44553i	−0.581529	+	0.487960i	−0.885449	−	0.464737i	$-0.846149\pi$
$83$	−5.29798	+	4.44553i	−0.581529	+	0.487960i	0.303920	+	0.952698i	$0.401704\pi$
$84$		0			0
$85$	−1.25681	−	2.17686i	−0.136320	−	0.236113i
$86$	3.54200	+	1.28918i	0.381944	+	0.139016i
$87$		0			0
$88$	−5.19285	−	2.99810i	−0.553560	−	0.319598i
$89$	16.0165	−	2.82414i	1.69774	−	0.299358i	0.760838	−	0.648942i	$-0.224788\pi$
$89$	16.0165	−	2.82414i	1.69774	−	0.299358i	0.936905	+	0.349584i	$0.113677\pi$
$90$		0			0
$91$	5.50263	+	6.55778i	0.576832	+	0.687442i
$92$	−2.17885	−	5.98635i	−0.227161	−	0.624120i
$93$		0			0
$94$	3.96922	+	4.73033i	0.409394	+	0.487896i
$95$	−0.709264	−	4.02243i	−0.0727689	−	0.412693i
$96$		0			0
$97$	−14.1175	−	8.15074i	−1.43342	−	0.827583i	−0.436036	−	0.899929i	$-0.643618\pi$
$97$	−14.1175	−	8.15074i	−1.43342	−	0.827583i	−0.997380	+	0.0723469i	$0.976951\pi$
$98$	1.72030	−	2.05018i	0.173777	−	0.207099i
$99$		0			0
$100$	−0.909799	−	1.57582i	−0.0909799	−	0.157582i
$101$	2.05124	−	3.55285i	0.204106	−	0.353521i	−0.745742	−	0.666235i	$-0.767905\pi$
$101$	2.05124	−	3.55285i	0.204106	−	0.353521i	0.949847	+	0.312714i	$0.101238\pi$
$102$		0			0
$103$	9.35250	−	5.39967i	0.921530	−	0.532045i	0.0374069	−	0.999300i	$-0.488090\pi$
$103$	9.35250	−	5.39967i	0.921530	−	0.532045i	0.884123	+	0.467255i	$0.154757\pi$
$104$	−0.714901	+	4.05440i	−0.0701018	+	0.397567i
$105$		0			0
$106$	7.90585	+	1.39401i	0.767884	+	0.135399i
$107$	−15.5549	−	13.0521i	−1.50375	−	1.26180i	−0.874930	−	0.484249i	$-0.839093\pi$
$107$	−15.5549	−	13.0521i	−1.50375	−	1.26180i	−0.628823	−	0.777549i	$-0.716463\pi$
$108$		0			0
$109$	2.13072	−	5.85411i	0.204086	−	0.560722i	−0.794851	−	0.606804i	$-0.792451\pi$
$109$	2.13072	−	5.85411i	0.204086	−	0.560722i	0.998938	+	0.0460817i	$0.0146734\pi$
$110$	−15.6587			−1.49300
$111$		0			0
$112$	−2.07935			−0.196480
$113$	−2.09726	+	5.76217i	−0.197294	+	0.542059i	−0.998405	−	0.0564555i	$-0.982020\pi$
$113$	−2.09726	+	5.76217i	−0.197294	+	0.542059i	0.801112	+	0.598515i	$0.204242\pi$
$114$		0			0
$115$	−12.7441	−	10.6936i	−1.18839	−	0.997181i
$116$	−3.99362	−	0.704183i	−0.370798	−	0.0653818i
$117$		0			0
$118$	−0.885636	+	5.02269i	−0.0815294	+	0.462376i
$119$	−1.73331	+	1.00073i	−0.158893	+	0.0917367i
$120$		0			0
$121$	−12.4772	+	21.6111i	−1.13429	+	1.96464i
$122$	4.86567	+	8.42760i	0.440517	+	0.762999i
$123$		0			0
$124$	2.18546	−	2.60453i	0.196260	−	0.233893i
$125$	7.19270	+	4.15271i	0.643335	+	0.371429i
$126$		0			0
$127$	−1.10807	−	6.28420i	−0.0983257	−	0.557633i	−0.993677	−	0.112273i	$-0.964187\pi$
$127$	−1.10807	−	6.28420i	−0.0983257	−	0.557633i	0.895352	−	0.445360i	$-0.146924\pi$
$128$	−0.642788	−	0.766044i	−0.0568149	−	0.0677094i
$129$		0			0
$130$	3.67711	+	10.1028i	0.322504	+	0.886072i
$131$	−6.71929	−	8.00774i	−0.587067	−	0.699640i	0.387972	−	0.921671i	$-0.373176\pi$
$131$	−6.71929	−	8.00774i	−0.587067	−	0.699640i	−0.975039	+	0.222032i	$0.928731\pi$
$132$		0			0
$133$	−3.20285	+	0.564749i	−0.277722	+	0.0489699i
$134$	9.13979	+	5.27686i	0.789557	+	0.455851i
$135$		0			0
$136$	−0.904494	−	0.329209i	−0.0775597	−	0.0282294i
$137$	3.12091	+	5.40557i	0.266637	+	0.461829i	0.967991	−	0.250984i	$-0.0807542\pi$
$137$	3.12091	+	5.40557i	0.266637	+	0.461829i	−0.701354	+	0.712813i	$0.747421\pi$
$138$		0			0
$139$	5.27989	−	4.43035i	0.447834	−	0.375778i	−0.390797	−	0.920477i	$-0.627801\pi$
$139$	5.27989	−	4.43035i	0.447834	−	0.375778i	0.838632	+	0.544699i	$0.183356\pi$
$140$	−4.70259	+	2.71504i	−0.397441	+	0.229463i
$141$		0			0
$142$		−	10.8018i		−	0.906463i
$143$	24.3110	+	4.28668i	2.03299	+	0.358470i
$144$		0			0
$145$	−9.95132	+	3.62198i	−0.826412	+	0.300789i
$146$	1.21517	−	3.33866i	0.100569	−	0.276310i
$147$		0			0
$148$	−4.40414	−	4.19566i	−0.362018	−	0.344881i
$149$	−3.49508			−0.286328			−0.143164	−	0.989699i	$-0.545728\pi$
$149$	−3.49508			−0.286328			−0.143164	+	0.989699i	$0.545728\pi$
$150$		0			0
$151$	8.84115	−	3.21791i	0.719482	−	0.261870i	0.0437763	−	0.999041i	$-0.486061\pi$
$151$	8.84115	−	3.21791i	0.719482	−	0.261870i	0.675706	+	0.737171i	$0.263839\pi$
$152$	−1.19815	−	1.00537i	−0.0971830	−	0.0815462i
$153$		0			0
$154$			12.4682i			1.00471i
$155$	1.54179	−	8.74391i	0.123839	−	0.702328i
$156$		0			0
$157$	1.94170	−	1.62928i	0.154964	−	0.130030i	−0.562009	−	0.827131i	$-0.689971\pi$
$157$	1.94170	−	1.62928i	0.154964	−	0.130030i	0.716973	+	0.697101i	$0.245527\pi$
$158$	1.27486	−	2.20812i	0.101422	−	0.175668i
$159$		0			0
$160$	−2.45395	−	0.893164i	−0.194002	−	0.0706108i
$161$	−8.51472	+	10.1475i	−0.671054	+	0.799731i
$162$		0			0
$163$	−9.23549	+	1.62847i	−0.723379	+	0.127551i	−0.523202	−	0.852208i	$-0.675263\pi$
$163$	−9.23549	+	1.62847i	−0.723379	+	0.127551i	−0.200177	+	0.979760i	$0.564152\pi$
$164$	1.80099	+	10.2139i	0.140634	+	0.797573i
$165$		0			0
$166$	2.36542	+	6.49893i	0.183592	+	0.504415i
$167$	3.56469	+	9.79392i	0.275844	+	0.757876i	0.997822	+	0.0659599i	$0.0210110\pi$
$167$	3.56469	+	9.79392i	0.275844	+	0.757876i	−0.721978	+	0.691916i	$0.756767\pi$
$168$		0			0
$169$	−0.685785	−	3.88928i	−0.0527527	−	0.299175i
$170$	−2.47543	+	0.436485i	−0.189857	+	0.0334769i
$171$		0			0
$172$	2.42287	−	2.88747i	0.184742	−	0.220167i
$173$	2.75312	+	1.00205i	0.209316	+	0.0761846i	0.444550	−	0.895754i	$-0.353364\pi$
$173$	2.75312	+	1.00205i	0.209316	+	0.0761846i	−0.235234	+	0.971939i	$0.575586\pi$
$174$		0			0
$175$	−1.89179	+	3.27667i	−0.143006	+	0.247693i
$176$	−4.59335	+	3.85428i	−0.346237	+	0.290527i
$177$		0			0
$178$	2.82414	−	16.0165i	0.211678	−	1.20049i
$179$		−	8.76703i		−	0.655279i	−0.944803	−	0.327639i	$-0.893747\pi$
$179$		−	8.76703i		−	0.655279i	0.944803	−	0.327639i	$-0.106253\pi$
$180$		0			0
$181$	−20.4965	−	17.1986i	−1.52349	−	1.27836i	−0.829750	−	0.558135i	$-0.811517\pi$
$181$	−20.4965	−	17.1986i	−1.52349	−	1.27836i	−0.693740	−	0.720225i	$-0.744038\pi$
$182$	8.04430	−	2.92789i	0.596283	−	0.217029i
$183$		0			0
$184$	−6.37054			−0.469642
$185$	−15.4386	−	3.73820i	−1.13507	−	0.274838i
$186$		0			0
$187$	−1.97400	+	5.42352i	−0.144353	+	0.396607i
$188$	5.80261	−	2.11198i	0.423199	−	0.154032i
$189$		0			0
$190$	−4.02243	−	0.709264i	−0.291818	−	0.0514554i
$191$			1.81758i			0.131515i	0.997836	+	0.0657577i	$0.0209464\pi$
$191$			1.81758i			0.131515i	−0.997836	+	0.0657577i	$0.979054\pi$
$192$		0			0
$193$	0.922363	−	0.532526i	0.0663931	−	0.0383321i	−0.466436	−	0.884555i	$-0.654462\pi$
$193$	0.922363	−	0.532526i	0.0663931	−	0.0383321i	0.532829	+	0.846223i	$0.321129\pi$
$194$	−12.4877	+	10.4784i	−0.896562	+	0.752305i
$195$		0			0
$196$	−1.33816	−	2.31776i	−0.0955827	−	0.165554i
$197$	−14.8064	−	5.38909i	−1.05491	−	0.383957i	−0.244398	−	0.969675i	$-0.578590\pi$
$197$	−14.8064	−	5.38909i	−1.05491	−	0.383957i	−0.810515	+	0.585718i	$0.800813\pi$
$198$		0			0
$199$	17.8722	+	10.3185i	1.26693	+	0.731461i	0.974406	−	0.224797i	$-0.0721719\pi$
$199$	17.8722	+	10.3185i	1.26693	+	0.731461i	0.292523	+	0.956259i	$0.405505\pi$
$200$	−1.79195	+	0.315970i	−0.126710	+	0.0223424i
$201$		0			0
$202$	−2.63702	−	3.14268i	−0.185540	−	0.221118i
$203$	2.88399	+	7.92370i	0.202417	+	0.556135i
$204$		0			0
$205$	17.4096	+	20.7479i	1.21594	+	1.44910i
$206$	−1.87529	−	10.6353i	−0.130657	−	0.740995i
$207$		0			0
$208$	3.56538	+	2.05847i	0.247215	+	0.142730i
$209$	−6.02839	+	7.18435i	−0.416992	+	0.496952i
$210$		0			0
$211$	−3.10070	−	5.37057i	−0.213461	−	0.369725i	0.739335	−	0.673338i	$-0.235140\pi$
$211$	−3.10070	−	5.37057i	−0.213461	−	0.369725i	−0.952795	+	0.303613i	$0.901807\pi$
$212$	4.01391	−	6.95229i	0.275676	−	0.477485i
$213$		0			0
$214$	−17.5851	+	10.1528i	−1.20209	+	0.694029i
$215$	1.70928	−	9.69380i	0.116572	−	0.661112i
$216$		0			0
$217$	−6.96231	−	1.22764i	−0.472633	−	0.0833379i
$218$	−4.77232	−	4.00445i	−0.323222	−	0.271216i
$219$		0			0
$220$	−5.35558	+	14.7143i	−0.361073	+	0.992040i
$221$	3.96274			0.266563
$222$		0			0
$223$	0.839150			0.0561936			0.0280968	−	0.999605i	$-0.491055\pi$
$223$	0.839150			0.0561936			0.0280968	+	0.999605i	$0.491055\pi$
$224$	−0.711179	+	1.95395i	−0.0475176	+	0.130554i
$225$		0			0
$226$	4.69737	+	3.94156i	0.312464	+	0.262188i
$227$	−6.42458	−	1.13283i	−0.426415	−	0.0751884i	−0.0436775	−	0.999046i	$-0.513907\pi$
$227$	−6.42458	−	1.13283i	−0.426415	−	0.0751884i	−0.382737	+	0.923857i	$0.625019\pi$
$228$		0			0
$229$	1.14680	−	6.50380i	0.0757824	−	0.429784i	−0.923185	−	0.384355i	$-0.874424\pi$
$229$	1.14680	−	6.50380i	0.0757824	−	0.429784i	0.998968	−	0.0454281i	$-0.0144652\pi$
$230$	−14.4074	+	8.31813i	−0.949997	+	0.548481i
$231$		0			0
$232$	−2.02761	+	3.51193i	−0.133119	+	0.230570i
$233$	−11.3047	−	19.5803i	−0.740594	−	1.28275i	−0.952225	−	0.305396i	$-0.901211\pi$
$233$	−11.3047	−	19.5803i	−0.740594	−	1.28275i	0.211632	−	0.977349i	$-0.432122\pi$
$234$		0			0
$235$	10.3654	−	12.3530i	0.676161	−	0.805818i
$236$	4.41688	+	2.55009i	0.287515	+	0.165997i
$237$		0			0
$238$	0.347550	+	1.97105i	0.0225283	+	0.127764i
$239$	11.0221	+	13.1357i	0.712962	+	0.849675i	0.993927	−	0.110043i	$-0.0350988\pi$
$239$	11.0221	+	13.1357i	0.712962	+	0.849675i	−0.280965	+	0.959718i	$0.590654\pi$
$240$		0			0
$241$	1.94526	+	5.34455i	0.125305	+	0.344273i	0.986444	−	0.164096i	$-0.0524708\pi$
$241$	1.94526	+	5.34455i	0.125305	+	0.344273i	−0.861139	+	0.508369i	$0.830249\pi$
$242$	16.0403	+	19.1161i	1.03111	+	1.22883i
$243$		0			0
$244$	9.58351	−	1.68983i	0.613521	−	0.108180i
$245$	−6.05267	−	3.49451i	−0.386691	−	0.223256i
$246$		0			0
$247$	6.05089	+	2.20235i	0.385009	+	0.140132i
$248$	−1.69998	−	2.94446i	−0.107949	−	0.186973i
$249$		0			0
$250$	6.36232	−	5.33862i	0.402388	−	0.337644i
$251$	21.9528	−	12.6745i	1.38565	−	0.800006i	0.392829	−	0.919611i	$-0.371496\pi$
$251$	21.9528	−	12.6745i	1.38565	−	0.800006i	0.992821	+	0.119606i	$0.0381630\pi$
$252$		0			0
$253$			38.1990i			2.40155i
$254$	−6.28420	−	1.10807i	−0.394306	−	0.0695268i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−1.76857	+	4.85911i	−0.110320	+	0.303103i	−0.982551	−	0.185991i	$-0.940450\pi$
$257$	−1.76857	+	4.85911i	−0.110320	+	0.303103i	0.872231	+	0.489094i	$0.162673\pi$
$258$		0			0
$259$	−2.97653	+	12.2929i	−0.184953	+	0.763847i
$260$	10.7512			0.666758
$261$		0			0
$262$	−9.82295	+	3.57526i	−0.606864	+	0.220880i
$263$	−7.40923	−	6.21708i	−0.456873	−	0.383362i	0.385106	−	0.922872i	$-0.374165\pi$
$263$	−7.40923	−	6.21708i	−0.456873	−	0.383362i	−0.841979	+	0.539511i	$0.818609\pi$
$264$		0			0
$265$		−	20.9641i		−	1.28782i
$266$	−0.564749	+	3.20285i	−0.0346270	+	0.196379i
$267$		0			0
$268$	8.08462	−	6.78380i	0.493847	−	0.414386i
$269$	−11.9383	+	20.6777i	−0.727889	+	1.26074i	0.229885	+	0.973218i	$0.426165\pi$
$269$	−11.9383	+	20.6777i	−0.727889	+	1.26074i	−0.957774	+	0.287523i	$0.907168\pi$
$270$		0			0
$271$	−17.2047	−	6.26199i	−1.04511	−	0.380389i	−0.238295	−	0.971193i	$-0.576589\pi$
$271$	−17.2047	−	6.26199i	−1.04511	−	0.380389i	−0.806815	+	0.590804i	$0.798811\pi$
$272$	−0.618710	+	0.737350i	−0.0375148	+	0.0447084i
$273$		0			0
$274$	6.14698	−	1.08388i	0.371353	−	0.0654795i
$275$	1.89462	+	10.7449i	0.114250	+	0.647942i
$276$		0			0
$277$	−6.06459	−	16.6623i	−0.364386	−	1.00114i	−0.977461	−	0.211117i	$-0.932290\pi$
$277$	−6.06459	−	16.6623i	−0.364386	−	1.00114i	0.613075	−	0.790025i	$-0.289932\pi$
$278$	−2.35734	−	6.47674i	−0.141384	−	0.388449i
$279$		0			0
$280$	0.942924	+	5.34759i	0.0563505	+	0.319579i
$281$	15.0167	−	2.64786i	0.895824	−	0.157958i	0.293264	−	0.956032i	$-0.405259\pi$
$281$	15.0167	−	2.64786i	0.895824	−	0.157958i	0.602560	+	0.798074i	$0.294147\pi$
$282$		0			0
$283$	15.7182	−	18.7322i	0.934350	−	1.11351i	−0.0589858	−	0.998259i	$-0.518787\pi$
$283$	15.7182	−	18.7322i	0.934350	−	1.11351i	0.993336	−	0.115256i	$-0.0367689\pi$
$284$	−10.1503	−	3.69442i	−0.602311	−	0.219223i
$285$		0			0
$286$	12.3430	−	21.3787i	0.729857	−	1.26415i
$287$	16.5205	−	13.8623i	0.975172	−	0.818266i
$288$		0			0
$289$	2.79114	−	15.8293i	0.164184	−	0.931136i
$290$			10.5900i			0.621864i
$291$		0			0
$292$	−2.72170	−	2.28378i	−0.159276	−	0.133648i
$293$	11.8143	−	4.30005i	0.690199	−	0.251212i	0.0269784	−	0.999636i	$-0.491411\pi$
$293$	11.8143	−	4.30005i	0.690199	−	0.251212i	0.663220	+	0.748424i	$0.269189\pi$
$294$		0			0
$295$	13.3188			0.775450
$296$	−5.44893	+	2.70354i	−0.316713	+	0.157140i
$297$		0			0
$298$	−1.19539	+	3.28430i	−0.0692469	+	0.190254i
$299$	24.6455	−	8.97022i	1.42529	−	0.518761i
$300$		0			0
$301$	−7.71866	−	1.36101i	−0.444896	−	0.0784472i
$302$		−	9.40855i		−	0.541401i
$303$		0			0
$304$	−1.35453	+	0.782038i	−0.0776876	+	0.0448530i
$305$	19.4673	−	16.3350i	1.11470	−	0.935341i
$306$		0			0
$307$	−4.70103	−	8.14242i	−0.268302	−	0.464713i	0.700122	−	0.714024i	$-0.253129\pi$
$307$	−4.70103	−	8.14242i	−0.268302	−	0.464713i	−0.968423	+	0.249311i	$0.919796\pi$
$308$	11.7162	+	4.26436i	0.667595	+	0.242985i
$309$		0			0
$310$	−7.68927	−	4.43940i	−0.436721	−	0.252141i
$311$	15.8568	−	2.79599i	0.899158	−	0.158546i	0.295082	−	0.955472i	$-0.404653\pi$
$311$	15.8568	−	2.79599i	0.899158	−	0.158546i	0.604077	+	0.796926i	$0.293542\pi$
$312$		0			0
$313$	0.370220	+	0.441211i	0.0209261	+	0.0249387i	0.776406	−	0.630233i	$-0.217041\pi$
$313$	0.370220	+	0.441211i	0.0209261	+	0.0249387i	−0.755480	+	0.655172i	$0.772596\pi$
$314$	−0.866920	−	2.38184i	−0.0489231	−	0.134415i
$315$		0			0
$316$	−1.63893	−	1.95319i	−0.0921967	−	0.109876i
$317$	−2.04083	−	11.5741i	−0.114624	−	0.650067i	−0.986935	−	0.161116i	$-0.948491\pi$
$317$	−2.04083	−	11.5741i	−0.114624	−	0.650067i	0.872311	−	0.488951i	$-0.162620\pi$
$318$		0			0
$319$	21.0582	+	12.1580i	1.17903	+	0.680715i
$320$	−1.67860	+	2.00048i	−0.0938365	+	0.111830i
$321$		0			0
$322$	6.62328	+	11.4719i	0.369101	+	0.639302i
$323$	−0.752745	+	1.30379i	−0.0418838	+	0.0725449i
$324$		0			0
$325$	6.48757	−	3.74560i	0.359865	−	0.207768i
$326$	−1.62847	+	9.23549i	−0.0901924	+	0.511506i
$327$		0			0
$328$	10.2139	+	1.80099i	0.563970	+	0.0994430i
$329$	−9.83600	−	8.25338i	−0.542276	−	0.455024i
$330$		0			0
$331$	4.83530	−	13.2849i	0.265772	−	0.730202i	−0.732980	−	0.680250i	$-0.761871\pi$
$331$	4.83530	−	13.2849i	0.265772	−	0.730202i	0.998752	−	0.0499518i	$-0.0159068\pi$
$332$	6.91602			0.379566
$333$		0			0
$334$	10.4225			0.570292
$335$	9.42620	−	25.8983i	0.515008	−	1.41497i
$336$		0			0
$337$	8.21240	+	6.89102i	0.447358	+	0.375378i	0.838454	−	0.544972i	$-0.183460\pi$
$337$	8.21240	+	6.89102i	0.447358	+	0.375378i	−0.391096	+	0.920350i	$0.627904\pi$
$338$	−3.88928	−	0.685785i	−0.211549	−	0.0373018i
$339$		0			0
$340$	−0.436485	+	2.47543i	−0.0236717	+	0.134249i
$341$	−17.6555	+	10.1934i	−0.956101	+	0.552005i
$342$		0			0
$343$	−10.0602	+	17.4248i	−0.543200	+	0.940850i
$344$	−1.88466	−	3.26433i	−0.101614	−	0.176001i
$345$		0			0
$346$	1.88324	−	2.24436i	0.101244	−	0.120658i
$347$	6.10989	+	3.52754i	0.327996	+	0.189368i	0.654951	−	0.755671i	$-0.272689\pi$
$347$	6.10989	+	3.52754i	0.327996	+	0.189368i	−0.326955	+	0.945040i	$0.606023\pi$
$348$		0			0
$349$	4.45331	+	25.2560i	0.238380	+	1.35192i	0.835376	+	0.549679i	$0.185250\pi$
$349$	4.45331	+	25.2560i	0.238380	+	1.35192i	−0.596996	+	0.802244i	$0.703639\pi$
$350$	2.43204	+	2.89839i	0.129998	+	0.154925i
$351$		0			0
$352$	2.05082	+	5.63458i	0.109309	+	0.300324i
$353$	−4.22017	−	5.02940i	−0.224617	−	0.267688i	0.641953	−	0.766744i	$-0.278125\pi$
$353$	−4.22017	−	5.02940i	−0.224617	−	0.267688i	−0.866570	+	0.499056i	$0.833680\pi$
$354$		0			0
$355$	−27.7795	+	4.89828i	−1.47438	+	0.259974i
$356$	−14.0847	−	8.13178i	−0.746485	−	0.430983i
$357$		0			0
$358$	−8.23831	−	2.99850i	−0.435408	−	0.158476i
$359$	9.92813	+	17.1960i	0.523987	+	0.907572i	0.999610	+	0.0279226i	$0.00888919\pi$
$359$	9.92813	+	17.1960i	0.523987	+	0.907572i	−0.475623	+	0.879649i	$0.657777\pi$
$360$		0			0
$361$	12.6808	−	10.6405i	0.667413	−	0.560026i
$362$	−23.1716	+	13.3781i	−1.21787	+	0.703138i
$363$		0			0
$364$		−	8.56057i		−	0.448696i
$365$	−9.13730	−	1.61115i	−0.478268	−	0.0843315i
$366$		0			0
$367$	20.2967	−	7.38739i	1.05948	−	0.385619i	0.247246	−	0.968953i	$-0.420474\pi$
$367$	20.2967	−	7.38739i	1.05948	−	0.385619i	0.812233	+	0.583334i	$0.198252\pi$
$368$	−2.17885	+	5.98635i	−0.113581	+	0.312060i
$369$		0			0
$370$	−8.79308	+	13.2290i	−0.457130	+	0.687744i
$371$	−16.6926			−0.866637
$372$		0			0
$373$	29.3944	−	10.6987i	1.52198	−	0.553956i	0.560340	−	0.828263i	$-0.310670\pi$
$373$	29.3944	−	10.6987i	1.52198	−	0.553956i	0.961642	+	0.274306i	$0.0884482\pi$
$374$	4.42129	+	3.70990i	0.228619	+	0.191835i
$375$		0			0
$376$		−	6.17501i		−	0.318452i
$377$	2.89909	−	16.4415i	0.149311	−	0.846782i
$378$		0			0
$379$	−15.3668	+	12.8943i	−0.789339	+	0.662334i	−0.945582	−	0.325384i	$-0.894506\pi$
$379$	−15.3668	+	12.8943i	−0.789339	+	0.662334i	0.156243	+	0.987719i	$0.450062\pi$
$380$	−2.04224	+	3.53727i	−0.104765	+	0.181458i
$381$		0			0
$382$	1.70796	+	0.621648i	0.0873871	+	0.0318063i
$383$	−10.6054	+	12.6391i	−0.541913	+	0.645826i	−0.965615	−	0.259975i	$-0.916286\pi$
$383$	−10.6054	+	12.6391i	−0.541913	+	0.645826i	0.423703	+	0.905801i	$0.360730\pi$
$384$		0			0
$385$	32.0652	−	5.65395i	1.63419	−	0.288152i
$386$	−0.184945	−	1.04887i	−0.00941343	−	0.0533862i
$387$		0			0
$388$	5.57544	+	15.3184i	0.283050	+	0.777673i
$389$	−0.282656	−	0.776592i	−0.0143312	−	0.0393748i	0.932321	−	0.361632i	$-0.117780\pi$
$389$	−0.282656	−	0.776592i	−0.0143312	−	0.0393748i	−0.946652	+	0.322258i	$0.895558\pi$
$390$		0			0
$391$	1.06479	+	6.03875i	0.0538490	+	0.305393i
$392$	−2.63566	+	0.464737i	−0.133121	+	0.0234728i
$393$		0			0
$394$	−10.1282	+	12.0703i	−0.510251	+	0.608093i
$395$	−6.25687	−	2.27731i	−0.314817	−	0.114584i
$396$		0			0
$397$	−4.52451	+	7.83669i	−0.227079	+	0.393312i	−0.956941	−	0.290282i	$-0.906251\pi$
$397$	−4.52451	+	7.83669i	−0.227079	+	0.393312i	0.729862	+	0.683594i	$0.239584\pi$
$398$	15.8089	−	13.2653i	0.792429	−	0.664927i
$399$		0			0
$400$	−0.315970	+	1.79195i	−0.0157985	+	0.0895977i
$401$			13.1254i			0.655452i	0.944773	+	0.327726i	$0.106282\pi$
$401$			13.1254i			0.655452i	−0.944773	+	0.327726i	$0.893718\pi$
$402$		0			0
$403$	10.7227	+	8.99742i	0.534136	+	0.448194i
$404$	−3.85506	+	1.40313i	−0.191797	+	0.0698083i
$405$		0			0
$406$	8.43223			0.418484
$407$	16.2110	+	32.6728i	0.803547	+	1.61953i
$408$		0			0
$409$	2.70223	−	7.42432i	0.133617	−	0.367109i	−0.854783	−	0.518986i	$-0.826310\pi$
$409$	2.70223	−	7.42432i	0.133617	−	0.367109i	0.988399	+	0.151877i	$0.0485318\pi$
$410$	25.4511	−	9.26344i	1.25694	−	0.457489i
$411$		0			0
$412$	−10.6353	−	1.87529i	−0.523962	−	0.0923887i
$413$		−	10.6050i		−	0.521840i
$414$		0			0
$415$	15.6411	−	9.03037i	0.767789	−	0.443283i
$416$	3.15377	−	2.64632i	0.154626	−	0.129747i
$417$		0			0
$418$	4.68925	+	8.12202i	0.229359	+	0.397261i
$419$	−30.0521	−	10.9381i	−1.46814	−	0.534361i	−0.520548	−	0.853832i	$-0.674272\pi$
$419$	−30.0521	−	10.9381i	−1.46814	−	0.534361i	−0.947596	+	0.319472i	$0.896494\pi$
$420$		0			0
$421$	−4.86073	−	2.80634i	−0.236897	−	0.136773i	0.376853	−	0.926273i	$-0.377006\pi$
$421$	−4.86073	−	2.80634i	−0.236897	−	0.136773i	−0.613750	+	0.789501i	$0.710340\pi$
$422$	−6.10718	+	1.07686i	−0.297293	+	0.0524208i
$423$		0			0
$424$	−5.16018	−	6.14966i	−0.250600	−	0.298654i
$425$	0.599028	+	1.64581i	0.0290571	+	0.0798337i
$426$		0			0
$427$	−13.0067	−	15.5008i	−0.629439	−	0.750136i
$428$	3.52602	+	19.9970i	0.170437	+	0.966594i
$429$		0			0
$430$	−8.52459	−	4.92167i	−0.411092	−	0.237344i
$431$	12.8250	−	15.2842i	0.617757	−	0.736214i	−0.362926	−	0.931818i	$-0.618222\pi$
$431$	12.8250	−	15.2842i	0.617757	−	0.736214i	0.980683	+	0.195604i	$0.0626666\pi$
$432$		0			0
$433$	7.91046	+	13.7013i	0.380152	+	0.658443i	0.991084	−	0.133240i	$-0.0425382\pi$
$433$	7.91046	+	13.7013i	0.380152	+	0.658443i	−0.610931	+	0.791684i	$0.709205\pi$
$434$	−3.53486	+	6.12255i	−0.169679	+	0.293892i
$435$		0			0
$436$	−5.39518	+	3.11491i	−0.258382	+	0.149177i
$437$	−1.73023	+	9.81263i	−0.0827682	+	0.469402i
$438$		0			0
$439$	3.01674	+	0.531932i	0.143981	+	0.0253878i	0.245174	−	0.969479i	$-0.421155\pi$
$439$	3.01674	+	0.531932i	0.143981	+	0.0253878i	−0.101193	+	0.994867i	$0.532266\pi$
$440$	11.9952	+	10.0652i	0.571850	+	0.479839i
$441$		0			0
$442$	1.35534	−	3.72375i	0.0644668	−	0.177121i
$443$	2.75923			0.131095			0.0655475	−	0.997849i	$-0.479121\pi$
$443$	2.75923			0.131095			0.0655475	+	0.997849i	$0.479121\pi$
$444$		0			0
$445$	−42.4712			−2.01333
$446$	0.287006	−	0.788543i	0.0135901	−	0.0373386i
$447$		0			0
$448$	1.59287	+	1.33658i	0.0752561	+	0.0631474i
$449$	22.3120	+	3.93421i	1.05297	+	0.185667i	0.673235	−	0.739428i	$-0.264904\pi$
$449$	22.3120	+	3.93421i	1.05297	+	0.185667i	0.379735	+	0.925095i	$0.376015\pi$
$450$		0			0
$451$	10.7991	−	61.2446i	0.508509	−	2.88390i
$452$	5.31045	−	3.06599i	0.249782	−	0.144212i
$453$		0			0
$454$	−3.26185	+	5.64968i	−0.153086	+	0.265153i
$455$	−11.1777	−	19.3603i	−0.524018	−	0.907626i
$456$		0			0
$457$	−18.9638	+	22.6002i	−0.887089	+	1.05719i	0.110902	+	0.993831i	$0.464626\pi$
$457$	−18.9638	+	22.6002i	−0.887089	+	1.05719i	−0.997991	+	0.0633601i	$0.979818\pi$
$458$	−5.71935	−	3.30207i	−0.267248	−	0.154296i
$459$		0			0
$460$	2.88885	+	16.3835i	0.134694	+	0.763885i
$461$	−2.61917	−	3.12141i	−0.121987	−	0.145378i	0.701594	−	0.712576i	$-0.252472\pi$
$461$	−2.61917	−	3.12141i	−0.121987	−	0.145378i	−0.823581	+	0.567198i	$0.808027\pi$
$462$		0			0
$463$	−1.00637	−	2.76497i	−0.0467699	−	0.128499i	0.914109	−	0.405469i	$-0.132892\pi$
$463$	−1.00637	−	2.76497i	−0.0467699	−	0.128499i	−0.960879	+	0.276970i	$0.910670\pi$
$464$	2.60665	+	3.10649i	0.121011	+	0.144215i
$465$		0			0
$466$	−22.2659	+	3.92607i	−1.03145	+	0.181872i
$467$	−4.59204	−	2.65121i	−0.212494	−	0.122684i	0.389976	−	0.920825i	$-0.372483\pi$
$467$	−4.59204	−	2.65121i	−0.212494	−	0.122684i	−0.602470	+	0.798142i	$0.705817\pi$
$468$		0			0
$469$	−20.6214	−	7.50558i	−0.952208	−	0.346575i
$470$	−8.06282	−	13.9652i	−0.371910	−	0.644167i
$471$		0			0
$472$	3.90696	−	3.27833i	0.179833	−	0.150897i
$473$	−19.5735	+	11.3008i	−0.899992	+	0.519611i
$474$		0			0
$475$			2.84599i			0.130583i
$476$	1.97105	+	0.347550i	0.0903430	+	0.0159299i
$477$		0			0
$478$	16.1133	−	5.86475i	0.737004	−	0.268248i
$479$	6.11079	−	16.7893i	0.279209	−	0.767121i	−0.718244	−	0.695792i	$-0.755054\pi$
$479$	6.11079	−	16.7893i	0.279209	−	0.767121i	0.997453	−	0.0713293i	$-0.0227241\pi$
$480$		0			0
$481$	17.2733	−	18.1316i	0.787595	−	0.826731i
$482$	5.68755			0.259061
$483$		0			0
$484$	23.4494	−	8.53487i	1.06588	−	0.387949i
$485$	32.6107	+	27.3637i	1.48078	+	1.24252i
$486$		0			0
$487$		−	31.2962i		−	1.41817i	−0.705124	−	0.709084i	$-0.749109\pi$
$487$		−	31.2962i		−	1.41817i	0.705124	−	0.709084i	$-0.250891\pi$
$488$	1.68983	−	9.58351i	0.0764951	−	0.433825i
$489$		0			0
$490$	−5.35390	+	4.49246i	−0.241865	+	0.202949i
$491$	−6.72900	+	11.6550i	−0.303676	+	0.525982i	−0.976966	−	0.213397i	$-0.931547\pi$
$491$	−6.72900	+	11.6550i	−0.303676	+	0.525982i	0.673290	+	0.739379i	$0.264881\pi$
$492$		0			0
$493$	3.66793	+	1.33502i	0.165195	+	0.0601261i
$494$	4.13905	−	4.93273i	0.186225	−	0.221934i
$495$		0			0
$496$	−3.34832	+	0.590399i	−0.150344	+	0.0265097i
$497$	3.90024	+	22.1194i	0.174950	+	0.992189i
$498$		0			0
$499$	12.5759	+	34.5520i	0.562974	+	1.54676i	0.815253	+	0.579104i	$0.196598\pi$
$499$	12.5759	+	34.5520i	0.562974	+	1.54676i	−0.252279	+	0.967654i	$0.581180\pi$
$500$	−2.84062	−	7.80454i	−0.127036	−	0.349030i
$501$		0			0
$502$	−4.40180	−	24.9638i	−0.196462	−	1.11419i
$503$	−6.15105	+	1.08460i	−0.274262	+	0.0483597i	−0.309087	−	0.951034i	$-0.600024\pi$
$503$	−6.15105	+	1.08460i	−0.274262	+	0.0483597i	0.0348257	+	0.999393i	$0.488912\pi$
$504$		0			0
$505$	−6.88641	+	8.20690i	−0.306441	+	0.365202i
$506$	35.8953	+	13.0648i	1.59574	+	0.580802i
$507$		0			0
$508$	−3.19057	+	5.52624i	−0.141559	+	0.245187i
$509$	6.29668	−	5.28355i	0.279096	−	0.234189i	−0.492484	−	0.870321i	$-0.663911\pi$
$509$	6.29668	−	5.28355i	0.279096	−	0.234189i	0.771580	+	0.636132i	$0.219467\pi$
$510$		0			0
$511$	−1.28287	+	7.27554i	−0.0567510	+	0.321851i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	3.96118	+	3.32383i	0.174720	+	0.146608i
$515$	−26.5010	+	9.64558i	−1.16777	+	0.425035i
$516$		0			0
$517$	−37.0265			−1.62842
$518$	10.5336	+	7.00146i	0.462818	+	0.307626i
$519$		0			0
$520$	3.67711	−	10.1028i	0.161252	−	0.443036i
$521$	20.8518	−	7.58945i	0.913536	−	0.332500i	0.157872	−	0.987460i	$-0.449537\pi$
$521$	20.8518	−	7.58945i	0.913536	−	0.332500i	0.755664	+	0.654960i	$0.227314\pi$
$522$		0			0
$523$	−13.7427	−	2.42321i	−0.600927	−	0.105960i	−0.135095	−	0.990833i	$-0.543134\pi$
$523$	−13.7427	−	2.42321i	−0.600927	−	0.105960i	−0.465832	+	0.884873i	$0.654245\pi$
$524$			10.4534i			0.456657i
$525$		0			0
$526$	−8.37625	+	4.83603i	−0.365222	+	0.210861i
$527$	−2.50697	+	2.10360i	−0.109205	+	0.0916340i
$528$		0			0
$529$	8.79187	+	15.2280i	0.382255	+	0.662086i
$530$	−19.6998	−	7.17015i	−0.855706	−	0.311451i
$531$		0			0
$532$	2.81654	+	1.62613i	0.122112	+	0.0705016i
$533$	−42.0502	+	7.41459i	−1.82140	+	0.321161i
$534$		0			0
$535$	34.0848	+	40.6207i	1.47362	+	1.75619i
$536$	−3.60958	−	9.91725i	−0.155910	−	0.428360i
$537$		0			0
$538$	15.3475	+	18.2905i	0.661679	+	0.788559i
$539$	2.78665	+	15.8039i	0.120030	+	0.680722i
$540$		0			0
$541$	20.9379	+	12.0885i	0.900192	+	0.519726i	0.877262	−	0.480011i	$-0.159367\pi$
$541$	20.9379	+	12.0885i	0.900192	+	0.519726i	0.0229292	+	0.999737i	$0.492701\pi$
$542$	−11.7687	+	14.0254i	−0.505509	+	0.602442i
$543$		0			0
$544$	0.481271	+	0.833586i	0.0206343	+	0.0357397i
$545$	−8.13439	+	14.0892i	−0.348439	+	0.603514i
$546$		0			0
$547$	−32.2382	+	18.6127i	−1.37840	+	0.795822i	−0.991967	−	0.126494i	$-0.959628\pi$
$547$	−32.2382	+	18.6127i	−1.37840	+	0.795822i	−0.386437	+	0.922316i	$0.626294\pi$
$548$	1.08388	−	6.14698i	0.0463010	−	0.262586i
$549$		0			0
$550$	10.7449	+	1.89462i	0.458164	+	0.0807867i
$551$	4.85878	+	4.07700i	0.206991	+	0.173686i
$552$		0			0
$553$	−1.81330	+	4.98201i	−0.0771095	+	0.211857i
$554$	−17.7317			−0.753347
$555$		0			0
$556$	−6.89241			−0.292303
$557$	−0.974054	+	2.67619i	−0.0412720	+	0.113394i	−0.958617	−	0.284700i	$-0.908106\pi$
$557$	−0.974054	+	2.67619i	−0.0412720	+	0.113394i	0.917345	+	0.398094i	$0.130328\pi$
$558$		0			0
$559$	11.8876	+	9.97485i	0.502790	+	0.421891i
$560$	5.34759	+	0.942924i	0.225977	+	0.0398458i
$561$		0			0
$562$	2.64786	−	15.0167i	0.111693	−	0.633443i
$563$	21.5088	−	12.4181i	0.906489	−	0.523362i	0.0271895	−	0.999630i	$-0.491344\pi$
$563$	21.5088	−	12.4181i	0.906489	−	0.523362i	0.879300	+	0.476268i	$0.158011\pi$
$564$		0			0
$565$	8.00663	−	13.8679i	0.336841	−	0.583427i
$566$	−12.2266	−	21.1771i	−0.513922	−	0.890139i
$567$		0			0
$568$	−6.94323	+	8.27462i	−0.291332	+	0.347195i
$569$	8.80519	+	5.08368i	0.369133	+	0.213119i	0.673080	−	0.739570i	$-0.264971\pi$
$569$	8.80519	+	5.08368i	0.369133	+	0.213119i	−0.303947	+	0.952689i	$0.598304\pi$
$570$		0			0
$571$	3.25922	+	18.4839i	0.136394	+	0.773528i	0.973879	+	0.227068i	$0.0729140\pi$
$571$	3.25922	+	18.4839i	0.136394	+	0.773528i	−0.837485	+	0.546460i	$0.815975\pi$
$572$	−15.8679	−	18.9106i	−0.663469	−	0.790691i
$573$		0			0
$574$	−7.37598	−	20.2653i	−0.307868	−	0.845859i
$575$	7.45108	+	8.87985i	0.310731	+	0.370315i
$576$		0			0
$577$	−18.5265	+	3.26672i	−0.771267	+	0.135995i	−0.545415	−	0.838166i	$-0.683628\pi$
$577$	−18.5265	+	3.26672i	−0.771267	+	0.135995i	−0.225852	+	0.974162i	$0.572517\pi$
$578$	−13.9201	−	8.03676i	−0.578999	−	0.334285i
$579$		0			0
$580$	9.95132	+	3.62198i	0.413206	+	0.150395i
$581$	−7.19040	−	12.4541i	−0.298308	−	0.516685i
$582$		0			0
$583$	−36.8745	+	30.9414i	−1.52719	+	1.28146i
$584$	−3.07693	+	1.77647i	−0.127324	+	0.0735107i
$585$		0			0
$586$		−	12.5725i		−	0.519366i
$587$	−30.2531	−	5.33444i	−1.24868	−	0.220176i	−0.490048	−	0.871696i	$-0.663021\pi$
$587$	−30.2531	−	5.33444i	−1.24868	−	0.220176i	−0.758632	+	0.651520i	$0.774132\pi$
$588$		0			0
$589$	−4.99711	+	1.81880i	−0.205902	+	0.0749423i
$590$	4.55529	−	12.5156i	0.187538	−	0.515258i
$591$		0			0
$592$	0.676854	+	6.04499i	0.0278185	+	0.248447i
$593$	−6.18887			−0.254147			−0.127073	−	0.991893i	$-0.540558\pi$
$593$	−6.18887			−0.254147			−0.127073	+	0.991893i	$0.540558\pi$
$594$		0			0
$595$	4.91147	−	1.78763i	0.201351	−	0.0732857i
$596$	2.67738	+	2.24659i	0.109670	+	0.0920240i
$597$		0			0
$598$		−	26.2272i		−	1.07251i
$599$	0.183355	−	1.03986i	0.00749169	−	0.0424875i	−0.980833	−	0.194852i	$-0.937578\pi$
$599$	0.183355	−	1.03986i	0.00749169	−	0.0424875i	0.988324	+	0.152364i	$0.0486886\pi$
$600$		0			0
$601$	−11.9378	+	10.0170i	−0.486954	+	0.408603i	−0.852933	−	0.522020i	$-0.825179\pi$
$601$	−11.9378	+	10.0170i	−0.486954	+	0.408603i	0.365979	+	0.930623i	$0.380734\pi$
$602$	−3.91887	+	6.78767i	−0.159721	+	0.276645i
$603$		0			0
$604$	−8.84115	−	3.21791i	−0.359741	−	0.130935i
$605$	41.8883	−	49.9205i	1.70300	−	2.02956i
$606$		0			0
$607$	−31.7497	+	5.59834i	−1.28868	+	0.227229i	−0.775663	−	0.631147i	$-0.782584\pi$
$607$	−31.7497	+	5.59834i	−1.28868	+	0.227229i	−0.513020	+	0.858377i	$0.671473\pi$
$608$	0.271599	+	1.54031i	0.0110148	+	0.0624680i
$609$		0			0
$610$	−8.69169	−	23.8802i	−0.351916	−	0.966882i
$611$	8.69490	+	23.8890i	0.351758	+	0.966447i
$612$		0			0
$613$	−0.968237	−	5.49114i	−0.0391067	−	0.221785i	0.958991	−	0.283436i	$-0.0914745\pi$
$613$	−0.968237	−	5.49114i	−0.0391067	−	0.221785i	−0.998098	+	0.0616512i	$0.980363\pi$
$614$	−9.25922	+	1.63265i	−0.373672	+	0.0658884i
$615$		0			0
$616$	8.01438	−	9.55117i	0.322909	−	0.384827i
$617$	3.80891	+	1.38633i	0.153341	+	0.0558116i	0.417550	−	0.908654i	$-0.362889\pi$
$617$	3.80891	+	1.38633i	0.153341	+	0.0558116i	−0.264209	+	0.964465i	$0.585111\pi$
$618$		0			0
$619$	3.68705	−	6.38616i	0.148195	−	0.256681i	−0.782365	−	0.622820i	$-0.785987\pi$
$619$	3.68705	−	6.38616i	0.148195	−	0.256681i	0.930560	+	0.366138i	$0.119320\pi$
$620$	−6.80156	+	5.70718i	−0.273157	+	0.229206i
$621$		0			0
$622$	2.79599	−	15.8568i	0.112109	−	0.635801i
$623$			33.8176i			1.35487i
$624$		0			0
$625$	−23.5843	−	19.7895i	−0.943370	−	0.791581i
$626$	0.541225	−	0.196990i	0.0216317	−	0.00787330i
$627$		0			0
$628$	−2.53470			−0.101146
$629$	3.47349	+	4.71327i	0.138497	+	0.187930i
$630$		0			0
$631$	2.86348	−	7.86734i	0.113993	−	0.313194i	−0.869556	−	0.493834i	$-0.835595\pi$
$631$	2.86348	−	7.86734i	0.113993	−	0.313194i	0.983549	+	0.180641i	$0.0578171\pi$
$632$	−2.39595	+	0.872054i	−0.0953057	+	0.0346884i
$633$		0			0
$634$	−11.5741	−	2.04083i	−0.459667	−	0.0810517i
$635$			16.6640i			0.661289i
$636$		0			0
$637$	9.54209	−	5.50913i	0.378071	−	0.218280i
$638$	18.6271	−	15.6300i	0.737453	−	0.618797i
$639$		0			0
$640$	1.30572	+	2.26157i	0.0516130	+	0.0893964i
$641$	−11.1583	−	4.06129i	−0.440726	−	0.160411i	0.112120	−	0.993695i	$-0.464236\pi$
$641$	−11.1583	−	4.06129i	−0.440726	−	0.160411i	−0.552846	+	0.833283i	$0.686458\pi$
$642$		0			0
$643$	−33.5232	−	19.3547i	−1.32203	−	0.763273i	−0.337976	−	0.941155i	$-0.609742\pi$
$643$	−33.5232	−	19.3547i	−1.32203	−	0.763273i	−0.984052	+	0.177882i	$0.943076\pi$
$644$	13.0453	−	2.30024i	0.514057	−	0.0906422i
$645$		0			0
$646$	0.967710	+	1.15327i	0.0380740	+	0.0453749i
$647$	−6.03672	−	16.5857i	−0.237328	−	0.652053i	−0.999986	−	0.00525130i	$-0.998328\pi$
$647$	−6.03672	−	16.5857i	−0.237328	−	0.652053i	0.762658	−	0.646801i	$-0.223894\pi$
$648$		0			0
$649$	−19.6575	−	23.4269i	−0.771624	−	0.919586i
$650$	−1.30083	−	7.37739i	−0.0510228	−	0.289365i
$651$		0			0
$652$	8.12155	+	4.68898i	0.318065	+	0.183635i
$653$	−9.49773	+	11.3189i	−0.371675	+	0.442945i	−0.919168	−	0.393865i	$-0.871138\pi$
$653$	−9.49773	+	11.3189i	−0.371675	+	0.442945i	0.547493	+	0.836810i	$0.315582\pi$
$654$		0			0
$655$	13.6491	+	23.6410i	0.533316	+	0.923731i
$656$	5.18574	−	8.98197i	0.202469	−	0.350687i
$657$		0			0
$658$	−11.1198	+	6.41999i	−0.433493	+	0.250277i
$659$	−1.14933	+	6.51815i	−0.0447714	+	0.253911i	−0.998976	−	0.0452437i	$-0.985594\pi$
$659$	−1.14933	+	6.51815i	−0.0447714	+	0.253911i	0.954205	+	0.299155i	$0.0967047\pi$
$660$		0			0
$661$	6.22992	+	1.09850i	0.242316	+	0.0427268i	0.293487	−	0.955963i	$-0.405184\pi$
$661$	6.22992	+	1.09850i	0.242316	+	0.0427268i	−0.0511712	+	0.998690i	$0.516295\pi$
$662$	−10.8299	−	9.08738i	−0.420917	−	0.353191i
$663$		0			0
$664$	2.36542	−	6.49893i	0.0917960	−	0.252207i
$665$	8.49307			0.329347
$666$		0			0
$667$	25.8340			1.00030
$668$	3.56469	−	9.79392i	0.137922	−	0.378938i
$669$		0			0
$670$	−21.1125	−	17.7155i	−0.815645	−	0.684408i
$671$	−57.4645	−	10.1325i	−2.21839	−	0.391163i
$672$		0			0
$673$	4.26450	−	24.1852i	0.164384	−	0.932269i	−0.785313	−	0.619099i	$-0.787498\pi$
$673$	4.26450	−	24.1852i	0.164384	−	0.932269i	0.949697	−	0.313170i	$-0.101391\pi$
$674$	9.28425	−	5.36027i	0.357616	−	0.206470i
$675$		0			0
$676$	−1.97464	+	3.42017i	−0.0759476	+	0.131545i
$677$	−11.2322	−	19.4547i	−0.431687	−	0.747704i	0.565332	−	0.824864i	$-0.308748\pi$
$677$	−11.2322	−	19.4547i	−0.431687	−	0.747704i	−0.997019	+	0.0771600i	$0.975415\pi$
$678$		0			0
$679$	21.7882	−	25.9662i	0.836155	−	0.996491i
$680$	2.17686	+	1.25681i	0.0834786	+	0.0481964i
$681$		0			0
$682$	3.54014	+	20.0771i	0.135559	+	0.768794i
$683$	−21.2410	−	25.3140i	−0.812764	−	0.968614i	0.187142	−	0.982333i	$-0.440077\pi$
$683$	−21.2410	−	25.3140i	−0.812764	−	0.968614i	−0.999906	+	0.0137189i	$0.995633\pi$
$684$		0			0
$685$	−5.57496	−	15.3171i	−0.213008	−	0.585235i
$686$	12.9332	+	15.4131i	0.493790	+	0.588476i
$687$		0			0
$688$	−3.71206	+	0.654536i	−0.141521	+	0.0249540i
$689$	28.6222	+	16.5251i	1.09042	+	0.629554i
$690$		0			0
$691$	−32.8077	−	11.9410i	−1.24806	−	0.454258i	−0.368317	−	0.929700i	$-0.620066\pi$
$691$	−32.8077	−	11.9410i	−1.24806	−	0.454258i	−0.879747	+	0.475442i	$0.842288\pi$
$692$	−1.46490	−	2.53729i	−0.0556872	−	0.0964531i
$693$		0			0
$694$	5.40451	−	4.53492i	0.205152	−	0.172143i
$695$	−15.5877	+	8.99954i	−0.591274	+	0.341372i
$696$		0			0
$697$		−	9.98299i		−	0.378133i
$698$	25.2560	+	4.45331i	0.955954	+	0.168560i
$699$		0			0
$700$	3.55540	−	1.29406i	0.134381	−	0.0489108i
$701$	−9.15308	+	25.1479i	−0.345707	+	0.949823i	0.637999	+	0.770037i	$0.279763\pi$
$701$	−9.15308	+	25.1479i	−0.345707	+	0.949823i	−0.983706	+	0.179785i	$0.942460\pi$
$702$		0			0
$703$	2.68438	+	9.12735i	0.101243	+	0.344245i
$704$	5.99619			0.225990
$705$		0			0
$706$	−6.16948	+	2.24551i	−0.232191	+	0.0845107i
$707$	6.53472	+	5.48328i	0.245763	+	0.206220i
$708$		0			0
$709$			6.67084i			0.250529i	0.992123	+	0.125264i	$0.0399779\pi$
$709$			6.67084i			0.250529i	−0.992123	+	0.125264i	$0.960022\pi$
$710$	−4.89828	+	27.7795i	−0.183829	+	1.04255i
$711$		0			0
$712$	−12.4586	+	10.4540i	−0.466906	+	0.391781i
$713$	−10.8298	+	18.7578i	−0.405580	+	0.702485i
$714$		0			0
$715$	−60.5782	−	22.0487i	−2.26550	−	0.824573i
$716$	−5.63534	+	6.71594i	−0.210603	+	0.250986i
$717$		0			0
$718$	19.5546	−	3.44800i	0.729771	−	0.128678i
$719$	−8.26991	−	46.9010i	−0.308416	−	1.74911i	−0.606975	−	0.794721i	$-0.707617\pi$
$719$	−8.26991	−	46.9010i	−0.308416	−	1.74911i	0.298559	−	0.954391i	$-0.403494\pi$
$720$		0			0
$721$	7.68026	+	21.1013i	0.286028	+	0.785855i
$722$	−5.66169	−	15.5554i	−0.210706	−	0.578910i
$723$		0			0
$724$	4.64617	+	26.3498i	0.172674	+	0.979281i
$725$	7.26679	−	1.28133i	0.269882	−	0.0475874i
$726$		0			0
$727$	−32.2308	+	38.4112i	−1.19537	+	1.42459i	−0.315802	+	0.948825i	$0.602274\pi$
$727$	−32.2308	+	38.4112i	−1.19537	+	1.42459i	−0.879572	+	0.475766i	$0.842171\pi$
$728$	−8.04430	−	2.92789i	−0.298142	−	0.108515i
$729$		0			0
$730$	−4.63913	+	8.03520i	−0.171702	+	0.297396i
$731$	−2.77931	+	2.33212i	−0.102796	+	0.0862565i
$732$		0			0
$733$	4.88298	−	27.6927i	0.180357	−	1.02285i	−0.751420	−	0.659824i	$-0.770631\pi$
$733$	4.88298	−	27.6927i	0.180357	−	1.02285i	0.931777	−	0.363031i	$-0.118258\pi$
$734$		−	21.5993i		−	0.797244i
$735$		0			0
$736$	4.88011	+	4.09490i	0.179883	+	0.150940i
$737$	−59.4657	+	21.6438i	−2.19045	+	0.797258i
$738$		0			0
$739$	32.3511			1.19006			0.595028	−	0.803705i	$-0.297141\pi$
$739$	32.3511			1.19006			0.595028	+	0.803705i	$0.297141\pi$
$740$	9.42380	+	12.7874i	0.346426	+	0.470073i
$741$		0			0
$742$	−5.70921	+	15.6859i	−0.209592	+	0.575848i
$743$	7.05630	−	2.56828i	0.258871	−	0.0942212i	−0.209325	−	0.977846i	$-0.567127\pi$
$743$	7.05630	−	2.56828i	0.258871	−	0.0942212i	0.468195	+	0.883625i	$0.344904\pi$
$744$		0			0
$745$	8.98851	+	1.58492i	0.329313	+	0.0580668i
$746$		−	31.2808i		−	1.14527i
$747$		0			0
$748$	4.99834	−	2.88579i	0.182757	−	0.105515i
$749$	32.3441	−	27.1399i	1.18183	−	0.991672i
$750$		0			0
$751$	−7.37086	−	12.7667i	−0.268966	−	0.465863i	0.699629	−	0.714506i	$-0.253349\pi$
$751$	−7.37086	−	12.7667i	−0.268966	−	0.465863i	−0.968595	+	0.248643i	$0.920015\pi$
$752$	−5.80261	−	2.11198i	−0.211599	−	0.0770159i
$753$		0			0
$754$	−14.4584	−	8.34759i	−0.526546	−	0.304001i
$755$	−24.1966	+	4.26651i	−0.880603	+	0.155274i
$756$		0			0
$757$	−14.2111	−	16.9361i	−0.516511	−	0.615553i	0.443241	−	0.896402i	$-0.353828\pi$
$757$	−14.2111	−	16.9361i	−0.516511	−	0.615553i	−0.959752	+	0.280849i	$0.909384\pi$
$758$	6.86090	+	18.8502i	0.249199	+	0.684669i
$759$		0			0
$760$	2.62546	+	3.12890i	0.0952353	+	0.113497i
$761$	−5.52983	−	31.3612i	−0.200456	−	1.13684i	−0.904431	−	0.426619i	$-0.859704\pi$
$761$	−5.52983	−	31.3612i	−0.200456	−	1.13684i	0.703975	−	0.710225i	$-0.251407\pi$
$762$		0			0
$763$	11.2185	+	6.47698i	0.406135	+	0.234482i
$764$	1.16832	−	1.39235i	0.0422682	−	0.0503733i
$765$		0			0
$766$	8.24957	+	14.2887i	0.298069	+	0.516271i
$767$	−10.4986	+	18.1841i	−0.379082	+	0.656589i
$768$		0			0
$769$	19.6375	−	11.3377i	0.708148	−	0.408849i	−0.102227	−	0.994761i	$-0.532597\pi$
$769$	19.6375	−	11.3377i	0.708148	−	0.408849i	0.810375	+	0.585912i	$0.199263\pi$
$770$	5.65395	−	32.0652i	0.203754	−	1.15555i
$771$		0			0
$772$	−1.04887	−	0.184945i	−0.0377497	−	0.00665630i
$773$	−9.05550	−	7.59846i	−0.325704	−	0.273298i	0.465243	−	0.885183i	$-0.345967\pi$
$773$	−9.05550	−	7.59846i	−0.325704	−	0.273298i	−0.790947	+	0.611885i	$0.790411\pi$
$774$		0			0
$775$	−2.11593	+	5.81348i	−0.0760066	+	0.208826i
$776$	16.3015			0.585189
$777$		0			0
$778$	−0.826432			−0.0296290
$779$	5.54818	−	15.2435i	0.198784	−	0.546155i
$780$		0			0
$781$	49.6162	+	41.6329i	1.77541	+	1.48974i
$782$	6.03875	+	1.06479i	0.215945	+	0.0380770i
$783$		0			0
$784$	−0.464737	+	2.63566i	−0.0165978	+	0.0941306i
$785$	−5.73241	+	3.30961i	−0.204598	+	0.118125i
$786$		0			0
$787$	−4.07295	+	7.05455i	−0.145185	+	0.251468i	−0.929442	−	0.368969i	$-0.879711\pi$
$787$	−4.07295	+	7.05455i	−0.145185	+	0.251468i	0.784257	+	0.620436i	$0.213044\pi$
$788$	7.87833	+	13.6457i	0.280654	+	0.486107i
$789$		0			0
$790$	−4.27995	+	5.10064i	−0.152274	+	0.181473i
$791$	−11.0423	−	6.37525i	−0.392618	−	0.226678i
$792$		0			0
$793$	6.95695	+	39.4548i	0.247049	+	1.40108i
$794$	5.81660	+	6.93196i	0.206424	+	0.246006i
$795$		0			0
$796$	−7.05829	−	19.3925i	−0.250175	−	0.687349i
$797$	16.0737	+	19.1558i	0.569358	+	0.678535i	0.971499	−	0.237043i	$-0.0761782\pi$
$797$	16.0737	+	19.1558i	0.569358	+	0.678535i	−0.402141	+	0.915578i	$0.631734\pi$
$798$		0			0
$799$	−5.85340	+	1.03211i	−0.207079	+	0.0365135i
$800$	1.57582	+	0.909799i	0.0557136	+	0.0321663i
$801$		0			0
$802$	12.3339	+	4.48916i	0.435524	+	0.158518i
$803$	10.6520	+	18.4499i	0.375902	+	0.651081i
$804$		0			0
$805$	26.4994	−	22.2357i	0.933982	−	0.783704i
$806$	12.1222	−	6.99875i	0.426986	−	0.246521i
$807$		0			0
$808$			4.10247i			0.144325i
$809$	−6.92526	−	1.22111i	−0.243479	−	0.0429319i	0.0505767	−	0.998720i	$-0.483894\pi$
$809$	−6.92526	−	1.22111i	−0.243479	−	0.0429319i	−0.294056	+	0.955788i	$0.595005\pi$
$810$		0			0
$811$	7.62149	−	2.77399i	0.267627	−	0.0974081i	−0.204721	−	0.978820i	$-0.565629\pi$
$811$	7.62149	−	2.77399i	0.267627	−	0.0974081i	0.472348	+	0.881412i	$0.343407\pi$
$812$	2.88399	−	7.92370i	0.101208	−	0.278067i
$813$		0			0
$814$	36.2469	−	4.05854i	1.27045	−	0.142252i
$815$	24.4899			0.857845
$816$		0			0
$817$	−5.53997	+	2.01638i	−0.193819	+	0.0705443i
$818$	−6.05236	−	5.07854i	−0.211616	−	0.177567i
$819$		0			0
$820$		−	27.0845i		−	0.945831i
$821$	8.00236	−	45.3837i	0.279284	−	1.58390i	−0.445730	−	0.895167i	$-0.647056\pi$
$821$	8.00236	−	45.3837i	0.279284	−	1.58390i	0.725015	−	0.688733i	$-0.241833\pi$
$822$		0			0
$823$	9.04503	−	7.58968i	0.315290	−	0.264560i	−0.471384	−	0.881928i	$-0.656246\pi$
$823$	9.04503	−	7.58968i	0.315290	−	0.264560i	0.786674	+	0.617368i	$0.211801\pi$
$824$	−5.39967	+	9.35250i	−0.188106	+	0.325810i
$825$		0			0
$826$	−9.96548	−	3.62714i	−0.346743	−	0.126204i
$827$	−18.3297	+	21.8445i	−0.637387	+	0.759608i	−0.983955	−	0.178417i	$-0.942902\pi$
$827$	−18.3297	+	21.8445i	−0.637387	+	0.759608i	0.346568	+	0.938025i	$0.387347\pi$
$828$		0			0
$829$	0.266399	−	0.0469734i	0.00925242	−	0.00163145i	−0.169020	−	0.985613i	$-0.554060\pi$
$829$	0.266399	−	0.0469734i	0.00925242	−	0.00163145i	0.178272	+	0.983981i	$0.442949\pi$
$830$	−3.13621	−	17.7864i	−0.108860	−	0.617374i
$831$		0			0
$832$	−1.40808	−	3.86867i	−0.0488164	−	0.134122i
$833$	0.881066	+	2.42071i	0.0305271	+	0.0838726i
$834$		0			0
$835$	−4.72629	−	26.8041i	−0.163560	−	0.927595i
$836$	9.23602	−	1.62856i	0.319435	−	0.0563249i
$837$		0			0
$838$	−20.5569	+	24.4987i	−0.710126	+	0.846295i
$839$	21.9497	+	7.98904i	0.757788	+	0.275812i	0.691879	−	0.722013i	$-0.256783\pi$
$839$	21.9497	+	7.98904i	0.757788	+	0.275812i	0.0659091	+	0.997826i	$0.479005\pi$
$840$		0			0
$841$	−6.27756	+	10.8731i	−0.216468	+	0.374933i
$842$	−4.29957	+	3.60776i	−0.148173	+	0.124332i
$843$		0			0
$844$	−1.07686	+	6.10718i	−0.0370671	+	0.210218i
$845$			10.3133i			0.354788i
$846$		0			0
$847$	−39.7490	−	33.3534i	−1.36579	−	1.14604i
$848$	−7.54368	+	2.74567i	−0.259051	+	0.0942868i
$849$		0			0
$850$	1.75144			0.0600739
$851$	32.2719	+	21.4505i	1.10627	+	0.735314i
$852$		0			0
$853$	−6.83552	+	18.7804i	−0.234044	+	0.643030i	0.765956	+	0.642893i	$0.222266\pi$
$853$	−6.83552	+	18.7804i	−0.234044	+	0.643030i	−1.00000		0.000137243i	$0.999956\pi$
$854$	−19.0145	+	6.92073i	−0.650664	+	0.236822i
$855$		0			0
$856$	19.9970	+	3.52602i	0.683485	+	0.120517i
$857$		−	16.1108i		−	0.550334i	−0.961396	−	0.275167i	$-0.911267\pi$
$857$		−	16.1108i		−	0.550334i	0.961396	−	0.275167i	$-0.0887331\pi$
$858$		0			0
$859$	−2.89285	+	1.67019i	−0.0987029	+	0.0569861i	−0.548539	−	0.836125i	$-0.684816\pi$
$859$	−2.89285	+	1.67019i	−0.0987029	+	0.0569861i	0.449836	+	0.893111i	$0.351482\pi$
$860$	−7.54044	+	6.32718i	−0.257127	+	0.215755i
$861$		0			0
$862$	−9.97606	−	17.2790i	−0.339786	−	0.588526i
$863$	36.4573	+	13.2694i	1.24102	+	0.451695i	0.877359	−	0.479835i	$-0.159303\pi$
$863$	36.4573	+	13.2694i	1.24102	+	0.451695i	0.363664	+	0.931530i	$0.381526\pi$
$864$		0			0
$865$	−6.62596	−	3.82550i	−0.225289	−	0.130071i
$866$	15.5806	−	2.74727i	0.529449	−	0.0933562i
$867$		0			0
$868$	4.54433	+	5.41572i	0.154244	+	0.183821i
$869$	5.22900	+	14.3666i	0.177382	+	0.487352i
$870$		0			0
$871$	27.9286	+	33.2840i	0.946323	+	1.12778i
$872$	1.08180	+	6.13517i	0.0366343	+	0.207763i
$873$		0			0
$874$	8.62909	+	4.98200i	0.291883	+	0.168519i
$875$	−11.1008	+	13.2295i	−0.375277	+	0.447238i
$876$		0			0
$877$	1.42022	+	2.45989i	0.0479573	+	0.0830644i	0.889008	−	0.457892i	$-0.151396\pi$
$877$	1.42022	+	2.45989i	0.0479573	+	0.0830644i	−0.841050	+	0.540957i	$0.818062\pi$
$878$	1.53164	−	2.65288i	0.0516903	−	0.0895302i
$879$		0			0
$880$	13.5608	−	7.82933i	0.457135	−	0.263927i
$881$	8.77517	−	49.7665i	0.295643	−	1.67668i	−0.368934	−	0.929456i	$-0.620277\pi$
$881$	8.77517	−	49.7665i	0.295643	−	1.67668i	0.664577	−	0.747220i	$-0.268612\pi$
$882$		0			0
$883$	28.2429	+	4.97998i	0.950448	+	0.167590i	0.627317	−	0.778764i	$-0.284153\pi$
$883$	28.2429	+	4.97998i	0.950448	+	0.167590i	0.323132	+	0.946354i	$0.395264\pi$
$884$	−3.03563	−	2.54720i	−0.102099	−	0.0856715i
$885$		0			0
$886$	0.943712	−	2.59283i	0.0317046	−	0.0871077i
$887$	14.6784			0.492851			0.246425	−	0.969162i	$-0.420744\pi$
$887$	14.6784			0.492851			0.246425	+	0.969162i	$0.420744\pi$
$888$		0			0
$889$	13.2686			0.445015
$890$	−14.5260	+	39.9099i	−0.486913	+	1.33778i
$891$		0			0
$892$	−0.642826	−	0.539395i	−0.0215234	−	0.0180603i
$893$	−9.51145	−	1.67713i	−0.318289	−	0.0561229i
$894$		0			0
$895$	−3.97560	+	22.5467i	−0.132889	+	0.753654i
$896$	1.80077	−	1.03967i	0.0601594	−	0.0347331i
$897$		0			0
$898$	11.3281	−	19.6209i	0.378024	−	0.654757i
$899$	6.89383	+	11.9405i	0.229922	+	0.398237i
$900$		0			0
$901$	−4.96689	+	5.91931i	−0.165471	+	0.197201i
$902$	−53.8576	−	31.0947i	−1.79326	−	1.03534i
$903$		0			0
$904$	−1.06481	−	6.03882i	−0.0354149	−	0.200848i
$905$	44.9130	+	53.5252i	1.49296	+	1.77924i
$906$		0			0
$907$	15.3162	+	42.0808i	0.508565	+	1.39727i	0.882717	+	0.469904i	$0.155711\pi$
$907$	15.3162	+	42.0808i	0.508565	+	1.39727i	−0.374152	+	0.927367i	$0.622066\pi$
$908$	4.19335	+	4.99744i	0.139161	+	0.165846i
$909$		0			0
$910$	−22.0157	+	3.88197i	−0.729815	+	0.128686i
$911$	−5.76500	−	3.32842i	−0.191003	−	0.110276i	0.401449	−	0.915881i	$-0.368507\pi$
$911$	−5.76500	−	3.32842i	−0.191003	−	0.110276i	−0.592452	+	0.805606i	$0.701840\pi$
$912$		0			0
$913$	−38.9688	−	14.1835i	−1.28968	−	0.469405i
$914$	14.7512	+	25.5499i	0.487927	+	0.845114i
$915$		0			0
$916$	−5.05906	+	4.24506i	−0.167156	+	0.140261i
$917$	18.8241	−	10.8681i	0.621626	−	0.358896i
$918$		0			0
$919$		−	44.6670i		−	1.47343i	−0.676203	−	0.736715i	$-0.736376\pi$
$919$		−	44.6670i		−	1.47343i	0.676203	−	0.736715i	$-0.263624\pi$
$920$	16.3835	+	2.88885i	0.540148	+	0.0952427i
$921$		0			0
$922$	−3.82897	+	1.39363i	−0.126100	+	0.0458968i
$923$	15.2097	−	41.7884i	0.500634	−	1.37548i
$924$		0			0
$925$	10.1416	+	4.43313i	0.333454	+	0.145760i
$926$	−2.94242			−0.0966941
$927$		0			0
$928$	3.81067	−	1.38697i	0.125091	−	0.0455295i
$929$	−1.25524	−	1.05327i	−0.0411831	−	0.0345567i	0.621964	−	0.783046i	$-0.286335\pi$
$929$	−1.25524	−	1.05327i	−0.0411831	−	0.0345567i	−0.663147	+	0.748489i	$0.730780\pi$
$930$		0			0
$931$			4.18596i			0.137189i
$932$	−3.92607	+	22.2659i	−0.128603	+	0.729342i
$933$		0			0
$934$	−4.06190	+	3.40834i	−0.132909	+	0.111524i
$935$	7.53606	−	13.0528i	0.246456	−	0.426874i
$936$		0			0
$937$	36.9995	+	13.4667i	1.20872	+	0.439938i	0.866260	−	0.499594i	$-0.166517\pi$
$937$	36.9995	+	13.4667i	1.20872	+	0.439938i	0.342461	+	0.939532i	$0.388740\pi$
$938$	−14.1059	+	16.8107i	−0.460573	+	0.548890i
$939$		0			0
$940$	−15.8806	+	2.80019i	−0.517970	+	0.0913320i
$941$	5.32651	+	30.2081i	0.173639	+	0.984757i	0.939703	+	0.341992i	$0.111102\pi$
$941$	5.32651	+	30.2081i	0.173639	+	0.984757i	−0.766064	+	0.642765i	$0.777787\pi$
$942$		0			0
$943$	−22.5979	−	62.0873i	−0.735890	−	2.02184i
$944$	−1.74436	−	4.79260i	−0.0567742	−	0.155986i
$945$		0			0
$946$	3.92472	+	22.2582i	0.127604	+	0.723677i
$947$	21.6531	−	3.81803i	0.703632	−	0.124069i	0.189626	−	0.981856i	$-0.439272\pi$
$947$	21.6531	−	3.81803i	0.703632	−	0.124069i	0.514005	+	0.857787i	$0.328161\pi$
$948$		0			0
$949$	9.40221	−	11.2051i	0.305209	−	0.363734i
$950$	2.67436	+	0.973386i	0.0867676	+	0.0315808i
$951$		0			0
$952$	1.00073	−	1.73331i	0.0324338	−	0.0561770i
$953$	−10.5688	+	8.86830i	−0.342358	+	0.287272i	−0.797713	−	0.603038i	$-0.793957\pi$
$953$	−10.5688	+	8.86830i	−0.342358	+	0.287272i	0.455355	+	0.890310i	$0.349512\pi$
$954$		0			0
$955$	0.824219	−	4.67438i	0.0266711	−	0.151259i
$956$		−	17.1474i		−	0.554586i
$957$		0			0
$958$	−13.6867	−	11.4845i	−0.442198	−	0.371048i
$959$	−12.1962	+	4.43904i	−0.393835	+	0.143344i
$960$		0			0
$961$	19.4402			0.627103
$962$	−11.1303	−	22.4330i	−0.358857	−	0.723268i
$963$		0			0
$964$	1.94526	−	5.34455i	0.0626525	−	0.172136i
$965$	−2.61358	+	0.951267i	−0.0841342	+	0.0306224i
$966$		0			0
$967$	−42.1185	−	7.42663i	−1.35444	−	0.238824i	−0.551147	−	0.834408i	$-0.685810\pi$
$967$	−42.1185	−	7.42663i	−1.35444	−	0.238824i	−0.803293	+	0.595584i	$0.796921\pi$
$968$		−	24.9543i		−	0.802062i
$969$		0			0
$970$	36.8670	−	21.2851i	1.18373	−	0.683425i
$971$	−42.7120	+	35.8396i	−1.37069	+	1.15015i	−0.398178	+	0.917308i	$0.630357\pi$
$971$	−42.7120	+	35.8396i	−1.37069	+	1.15015i	−0.972515	+	0.232840i	$0.925198\pi$
$972$		0			0
$973$	7.16585	+	12.4116i	0.229727	+	0.397898i
$974$	−29.4088	−	10.7039i	−0.942320	−	0.342976i
$975$		0			0
$976$	−8.42760	−	4.86567i	−0.269761	−	0.155746i
$977$	18.0002	−	3.17393i	0.575878	−	0.101543i	0.121879	−	0.992545i	$-0.461108\pi$
$977$	18.0002	−	3.17393i	0.575878	−	0.101543i	0.453999	+	0.891002i	$0.349997\pi$
$978$		0			0
$979$	62.6842	+	74.7042i	2.00340	+	2.38756i
$980$	2.39039	+	6.56754i	0.0763581	+	0.209792i
$981$		0			0
$982$	8.65064	+	10.3094i	0.276053	+	0.328987i
$983$	4.37560	+	24.8153i	0.139560	+	0.791485i	0.971575	+	0.236731i	$0.0760762\pi$
$983$	4.37560	+	24.8153i	0.139560	+	0.791485i	−0.832015	+	0.554753i	$0.812813\pi$
$984$		0			0
$985$	35.6348	+	20.5738i	1.13542	+	0.655534i
$986$	2.50901	−	2.99012i	0.0799032	−	0.0952249i
$987$		0			0
$988$	−3.21961	−	5.57653i	−0.102430	−	0.177413i
$989$	−12.0063	+	20.7955i	−0.381778	+	0.661259i
$990$		0			0
$991$	−25.7428	+	14.8626i	−0.817748	+	0.472127i	−0.849639	−	0.527364i	$-0.823180\pi$
$991$	−25.7428	+	14.8626i	−0.817748	+	0.472127i	0.0318914	+	0.999491i	$0.489847\pi$
$992$	−0.590399	+	3.34832i	−0.0187452	+	0.106309i
$993$		0			0
$994$	22.1194	+	3.90024i	0.701584	+	0.123708i
$995$	−41.2840	−	34.6414i	−1.30879	−	1.09820i
$996$		0			0
$997$	−3.03661	+	8.34301i	−0.0961703	+	0.264226i	−0.978444	−	0.206510i	$-0.933789\pi$
$997$	−3.03661	+	8.34301i	−0.0961703	+	0.264226i	0.882274	+	0.470736i	$0.156012\pi$
$998$	36.7694			1.16392
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.bj.c.613.2		12
3.2	odd	2		74.2.h.a.21.1	✓	12
12.11	even	2		592.2.bq.b.465.2		12
37.30	even	18	inner	666.2.bj.c.289.2		12
111.17	even	36		2738.2.a.r.1.3		6
111.20	even	36		2738.2.a.s.1.4		6
111.104	odd	18		74.2.h.a.67.1	yes	12
444.215	even	18		592.2.bq.b.289.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.h.a.21.1	✓	12	3.2	odd	2
74.2.h.a.67.1	yes	12	111.104	odd	18
592.2.bq.b.289.2		12	444.215	even	18
592.2.bq.b.465.2		12	12.11	even	2
666.2.bj.c.289.2		12	37.30	even	18	inner
666.2.bj.c.613.2		12	1.1	even	1	trivial
2738.2.a.r.1.3		6	111.17	even	36
2738.2.a.s.1.4		6	111.20	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)

\(f(q)\)	\(=\)	\(q+(0.342020 - 0.939693i) q^{2} +(-0.766044 - 0.642788i) q^{4} +(-2.57176 - 0.453471i) q^{5} +(-0.361075 + 2.04776i) q^{7} +(-0.866025 + 0.500000i) q^{8} +O(q^{10})\)	\(q+(0.342020 - 0.939693i) q^{2} +(-0.766044 - 0.642788i) q^{4} +(-2.57176 - 0.453471i) q^{5} +(-0.361075 + 2.04776i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.30572 + 2.26157i) q^{10} +(2.99810 + 5.19285i) q^{11} +(2.64632 - 3.15377i) q^{13} +(1.80077 + 1.03967i) q^{14} +(0.173648 + 0.984808i) q^{16} +(0.618710 + 0.737350i) q^{17} +(0.534946 + 1.46975i) q^{19} +(1.67860 + 2.00048i) q^{20} +(5.90509 - 1.04123i) q^{22} +(5.51705 + 3.18527i) q^{23} +(1.70986 + 0.622339i) q^{25} +(-2.05847 - 3.56538i) q^{26} +(1.59287 - 1.33658i) q^{28} +(3.51193 - 2.02761i) q^{29} +3.39997i q^{31} +(0.984808 + 0.173648i) q^{32} +(0.904494 - 0.329209i) q^{34} +(1.85720 - 5.10261i) q^{35} +(6.07068 + 0.383130i) q^{37} +1.56408 q^{38} +(2.45395 - 0.893164i) q^{40} +(-7.94502 - 6.66666i) q^{41} +3.76932i q^{43} +(1.04123 - 5.90509i) q^{44} +(4.88011 - 4.09490i) q^{46} +(-3.08750 + 5.34771i) q^{47} +(2.51491 + 0.915354i) q^{49} +(1.16962 - 1.39389i) q^{50} +(-4.05440 + 0.714901i) q^{52} +(1.39401 + 7.90585i) q^{53} +(-5.35558 - 14.7143i) q^{55} +(-0.711179 - 1.95395i) q^{56} +(-0.704183 - 3.99362i) q^{58} +(-5.02269 + 0.885636i) q^{59} +(-6.25519 + 7.45465i) q^{61} +(3.19493 + 1.16286i) q^{62} +(0.500000 - 0.866025i) q^{64} +(-8.23586 + 6.91071i) q^{65} +(-1.83263 + 10.3934i) q^{67} -0.962542i q^{68} +(-4.15968 - 3.49039i) q^{70} +(10.1503 - 3.69442i) q^{71} +3.55293 q^{73} +(2.43632 - 5.57354i) q^{74} +(0.534946 - 1.46975i) q^{76} +(-11.7162 + 4.26436i) q^{77} +(2.51098 + 0.442753i) q^{79} -2.61144i q^{80} +(-8.98197 + 5.18574i) q^{82} +(-5.29798 + 4.44553i) q^{83} +(-1.25681 - 2.17686i) q^{85} +(3.54200 + 1.28918i) q^{86} +(-5.19285 - 2.99810i) q^{88} +(16.0165 - 2.82414i) q^{89} +(5.50263 + 6.55778i) q^{91} +(-2.17885 - 5.98635i) q^{92} +(3.96922 + 4.73033i) q^{94} +(-0.709264 - 4.02243i) q^{95} +(-14.1175 - 8.15074i) q^{97} +(1.72030 - 2.05018i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{7}+O(q^{10}) \) 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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