LMFDB - Embedded newform 756.2.o.a.179.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(179,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 4]))

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

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

chi := DirichletCharacter("756.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.o (of order $6$, degree $2$, not 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.6
Character	$\chi$	$=$	756.179
Dual form			756.2.o.a.359.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32602 - 0.491613i) q^{2} +(1.51663 + 1.30377i) q^{4} +0.834477i q^{5} +(2.47783 - 0.927568i) q^{7} +(-1.37012 - 2.47442i) q^{8} +O(q^{10})$	\(q+(-1.32602 - 0.491613i) q^{2} +(1.51663 + 1.30377i) q^{4} +0.834477i q^{5} +(2.47783 - 0.927568i) q^{7} +(-1.37012 - 2.47442i) q^{8} +(0.410240 - 1.10653i) q^{10} +3.22188 q^{11} +(2.03757 - 3.52917i) q^{13} +(-3.74164 + 0.0118363i) q^{14} +(0.600347 + 3.95469i) q^{16} +(-3.20251 - 1.84897i) q^{17} +(-4.26091 + 2.46004i) q^{19} +(-1.08797 + 1.26559i) q^{20} +(-4.27226 - 1.58392i) q^{22} -1.13464 q^{23} +4.30365 q^{25} +(-4.43684 + 3.67804i) q^{26} +(4.96729 + 1.82374i) q^{28} +(8.69963 - 5.02273i) q^{29} +(-1.82440 + 1.05332i) q^{31} +(1.14811 - 5.53912i) q^{32} +(3.33760 + 4.02617i) q^{34} +(0.774034 + 2.06769i) q^{35} +(0.248579 + 0.430551i) q^{37} +(6.85942 - 1.16733i) q^{38} +(2.06485 - 1.14334i) q^{40} +(6.77313 + 3.91047i) q^{41} +(-7.81676 + 4.51301i) q^{43} +(4.88640 + 4.20060i) q^{44} +(1.50455 + 0.557804i) q^{46} +(1.98528 - 3.43861i) q^{47} +(5.27924 - 4.59670i) q^{49} +(-5.70670 - 2.11573i) q^{50} +(7.69149 - 2.69593i) q^{52} +(-1.36342 - 0.787173i) q^{53} +2.68858i q^{55} +(-5.69012 - 4.86030i) q^{56} +(-14.0051 + 2.38337i) q^{58} +(0.0348298 + 0.0603270i) q^{59} +(0.645679 - 1.11835i) q^{61} +(2.93700 - 0.499815i) q^{62} +(-4.24552 + 6.78053i) q^{64} +(2.94501 + 1.70030i) q^{65} +(11.4998 - 6.63942i) q^{67} +(-2.44640 - 6.97957i) q^{68} +(-0.00987715 - 3.12231i) q^{70} -2.68355 q^{71} +(4.11468 - 7.12683i) q^{73} +(-0.117954 - 0.693122i) q^{74} +(-9.66957 - 1.82429i) q^{76} +(7.98325 - 2.98851i) q^{77} +(11.9760 + 6.91436i) q^{79} +(-3.30010 + 0.500976i) q^{80} +(-7.05883 - 8.51510i) q^{82} +(2.75513 + 4.77203i) q^{83} +(1.54293 - 2.67243i) q^{85} +(12.5838 - 2.14149i) q^{86} +(-4.41437 - 7.97228i) q^{88} +(6.82321 - 3.93938i) q^{89} +(1.77519 - 10.6347i) q^{91} +(-1.72083 - 1.47931i) q^{92} +(-4.32298 + 3.58365i) q^{94} +(-2.05284 - 3.55563i) q^{95} +(-8.60311 - 14.9010i) q^{97} +(-9.26015 + 3.49995i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 3 q^{2} + q^{4}+O(q^{10}) $ 88 * q + 3 * q^2 + q^4	$ 88 q + 3 q^{2} + q^{4} + 2 q^{10} - 4 q^{13} + 3 q^{14} + q^{16} + 6 q^{20} - 6 q^{22} - 60 q^{25} + 6 q^{26} + 24 q^{29} - 27 q^{32} - 4 q^{34} - 4 q^{37} + 8 q^{40} + 12 q^{41} + 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} + 14 q^{52} + 66 q^{56} - 10 q^{58} + 2 q^{61} - 8 q^{64} - 18 q^{65} + 30 q^{70} - 4 q^{73} - 6 q^{76} + 30 q^{77} - 87 q^{80} - 4 q^{82} - 14 q^{85} - 18 q^{88} - 60 q^{89} - 24 q^{92} + 9 q^{94} - 4 q^{97} + 57 q^{98}+O(q^{100}) $ 88 * q + 3 * q^2 + q^4 + 2 * q^10 - 4 * q^13 + 3 * q^14 + q^16 + 6 * q^20 - 6 * q^22 - 60 * q^25 + 6 * q^26 + 24 * q^29 - 27 * q^32 - 4 * q^34 - 4 * q^37 + 8 * q^40 + 12 * q^41 + 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 + 14 * q^52 + 66 * q^56 - 10 * q^58 + 2 * q^61 - 8 * q^64 - 18 * q^65 + 30 * q^70 - 4 * q^73 - 6 * q^76 + 30 * q^77 - 87 * q^80 - 4 * q^82 - 14 * q^85 - 18 * q^88 - 60 * q^89 - 24 * q^92 + 9 * q^94 - 4 * q^97 + 57 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.32602	−	0.491613i	−0.937634	−	0.347623i
$2$	−1.32602	−	0.491613i	−0.937634	−	0.347623i
$3$		0			0
$3$		0			0
$4$	1.51663	+	1.30377i	0.758316	+	0.651887i
$5$			0.834477i			0.373189i	0.982437	+	0.186595i	$0.0597451\pi$
$5$			0.834477i			0.373189i	−0.982437	+	0.186595i	$0.940255\pi$
$6$		0			0
$7$	2.47783	−	0.927568i	0.936530	−	0.350588i
$7$	2.47783	−	0.927568i	0.936530	−	0.350588i
$8$	−1.37012	−	2.47442i	−0.484412	−	0.874840i
$9$		0			0
$10$	0.410240	−	1.10653i	0.129729	−	0.349915i
$11$	3.22188			0.971432			0.485716	−	0.874117i	$-0.338559\pi$
$11$	3.22188			0.971432			0.485716	+	0.874117i	$0.338559\pi$
$12$		0			0
$13$	2.03757	−	3.52917i	0.565120	−	0.978817i	−0.431919	−	0.901913i	$-0.642163\pi$
$13$	2.03757	−	3.52917i	0.565120	−	0.978817i	0.997039	−	0.0769039i	$-0.0245035\pi$
$14$	−3.74164	+	0.0118363i	−0.999995	+	0.00316339i
$15$		0			0
$16$	0.600347	+	3.95469i	0.150087	+	0.988673i
$17$	−3.20251	−	1.84897i	−0.776724	−	0.448442i	0.0585440	−	0.998285i	$-0.481354\pi$
$17$	−3.20251	−	1.84897i	−0.776724	−	0.448442i	−0.835268	+	0.549843i	$0.814688\pi$
$18$		0			0
$19$	−4.26091	+	2.46004i	−0.977520	+	0.564371i	−0.901520	−	0.432737i	$-0.857548\pi$
$19$	−4.26091	+	2.46004i	−0.977520	+	0.564371i	−0.0759994	+	0.997108i	$0.524215\pi$
$20$	−1.08797	+	1.26559i	−0.243277	+	0.282996i
$21$		0			0
$22$	−4.27226	−	1.58392i	−0.910848	−	0.337692i
$23$	−1.13464			−0.236589			−0.118294	−	0.992979i	$-0.537743\pi$
$23$	−1.13464			−0.236589			−0.118294	+	0.992979i	$0.537743\pi$
$24$		0			0
$25$	4.30365			0.860730
$26$	−4.43684	+	3.67804i	−0.870135	+	0.721323i
$27$		0			0
$28$	4.96729	+	1.82374i	0.938729	+	0.344655i
$29$	8.69963	−	5.02273i	1.61548	−	0.932698i	0.627411	−	0.778688i	$-0.284114\pi$
$29$	8.69963	−	5.02273i	1.61548	−	0.932698i	0.988069	−	0.154010i	$-0.0492189\pi$
$30$		0			0
$31$	−1.82440	+	1.05332i	−0.327671	+	0.189181i	−0.654807	−	0.755796i	$-0.727250\pi$
$31$	−1.82440	+	1.05332i	−0.327671	+	0.189181i	0.327136	+	0.944977i	$0.393917\pi$
$32$	1.14811	−	5.53912i	0.202959	−	0.979187i
$33$		0			0
$34$	3.33760	+	4.02617i	0.572394	+	0.690482i
$35$	0.774034	+	2.06769i	0.130836	+	0.349503i
$36$		0			0
$37$	0.248579	+	0.430551i	0.0408661	+	0.0707822i	0.885735	−	0.464191i	$-0.153655\pi$
$37$	0.248579	+	0.430551i	0.0408661	+	0.0707822i	−0.844869	+	0.534973i	$0.820322\pi$
$38$	6.85942	−	1.16733i	1.11274	−	0.189365i
$39$		0			0
$40$	2.06485	−	1.14334i	0.326481	−	0.180778i
$41$	6.77313	+	3.91047i	1.05778	+	0.610712i	0.924819	−	0.380408i	$-0.124217\pi$
$41$	6.77313	+	3.91047i	1.05778	+	0.610712i	0.132966	+	0.991121i	$0.457550\pi$
$42$		0			0
$43$	−7.81676	+	4.51301i	−1.19204	+	0.688227i	−0.958770	−	0.284184i	$-0.908277\pi$
$43$	−7.81676	+	4.51301i	−1.19204	+	0.688227i	−0.233275	+	0.972411i	$0.574944\pi$
$44$	4.88640	+	4.20060i	0.736653	+	0.633264i
$45$		0			0
$46$	1.50455	+	0.557804i	0.221834	+	0.0822438i
$47$	1.98528	−	3.43861i	0.289583	−	0.501572i	−0.684127	−	0.729363i	$-0.739817\pi$
$47$	1.98528	−	3.43861i	0.289583	−	0.501572i	0.973710	+	0.227790i	$0.0731501\pi$
$48$		0			0
$49$	5.27924	−	4.59670i	0.754177	−	0.656672i
$50$	−5.70670	−	2.11573i	−0.807050	−	0.299210i
$51$		0			0
$52$	7.69149	−	2.69593i	1.06662	−	0.373858i
$53$	−1.36342	−	0.787173i	−0.187281	−	0.108127i	0.403428	−	0.915011i	$-0.367818\pi$
$53$	−1.36342	−	0.787173i	−0.187281	−	0.108127i	−0.590709	+	0.806885i	$0.701152\pi$
$54$		0			0
$55$			2.68858i			0.362528i
$56$	−5.69012	−	4.86030i	−0.760375	−	0.649485i
$57$		0			0
$58$	−14.0051	+	2.38337i	−1.83896	+	0.312951i
$59$	0.0348298	+	0.0603270i	0.00453445	+	0.00785390i	0.868284	−	0.496068i	$-0.165223\pi$
$59$	0.0348298	+	0.0603270i	0.00453445	+	0.00785390i	−0.863749	+	0.503922i	$0.831890\pi$
$60$		0			0
$61$	0.645679	−	1.11835i	0.0826708	−	0.143190i	−0.821726	−	0.569883i	$-0.806988\pi$
$61$	0.645679	−	1.11835i	0.0826708	−	0.143190i	0.904396	+	0.426693i	$0.140322\pi$
$62$	2.93700	−	0.499815i	0.372999	−	0.0634765i
$63$		0			0
$64$	−4.24552	+	6.78053i	−0.530690	+	0.847566i
$65$	2.94501	+	1.70030i	0.365284	+	0.210897i
$66$		0			0
$67$	11.4998	−	6.63942i	1.40493	−	0.811134i	0.410033	−	0.912071i	$-0.365517\pi$
$67$	11.4998	−	6.63942i	1.40493	−	0.811134i	0.994893	+	0.100936i	$0.0321838\pi$
$68$	−2.44640	−	6.97957i	−0.296669	−	0.846397i
$69$		0			0
$70$	−0.00987715	−	3.12231i	−0.00118055	−	0.373188i
$71$	−2.68355			−0.318479			−0.159240	−	0.987240i	$-0.550904\pi$
$71$	−2.68355			−0.318479			−0.159240	+	0.987240i	$0.550904\pi$
$72$		0			0
$73$	4.11468	−	7.12683i	0.481587	−	0.834133i	−0.518190	−	0.855265i	$-0.673394\pi$
$73$	4.11468	−	7.12683i	0.481587	−	0.834133i	0.999777	+	0.0211330i	$0.00672734\pi$
$74$	−0.117954	−	0.693122i	−0.0137119	−	0.0805738i
$75$		0			0
$76$	−9.66957	−	1.82429i	−1.10918	−	0.209260i
$77$	7.98325	−	2.98851i	0.909775	−	0.340572i
$78$		0			0
$79$	11.9760	+	6.91436i	1.34741	+	0.777927i	0.987882	−	0.155208i	$-0.0496048\pi$
$79$	11.9760	+	6.91436i	1.34741	+	0.777927i	0.359527	+	0.933135i	$0.382938\pi$
$80$	−3.30010	+	0.500976i	−0.368962	+	0.0560108i
$81$		0			0
$82$	−7.05883	−	8.51510i	−0.779517	−	0.940335i
$83$	2.75513	+	4.77203i	0.302415	+	0.523799i	0.976683	−	0.214689i	$-0.0688737\pi$
$83$	2.75513	+	4.77203i	0.302415	+	0.523799i	−0.674267	+	0.738487i	$0.735540\pi$
$84$		0			0
$85$	1.54293	−	2.67243i	0.167354	−	0.289865i
$86$	12.5838	−	2.14149i	1.35695	−	0.230923i
$87$		0			0
$88$	−4.41437	−	7.97228i	−0.470574	−	0.849848i
$89$	6.82321	−	3.93938i	0.723259	−	0.417574i	−0.0926922	−	0.995695i	$-0.529547\pi$
$89$	6.82321	−	3.93938i	0.723259	−	0.417574i	0.815951	+	0.578121i	$0.196214\pi$
$90$		0			0
$91$	1.77519	−	10.6347i	0.186091	−	1.11482i
$92$	−1.72083	−	1.47931i	−0.179409	−	0.154229i
$93$		0			0
$94$	−4.32298	+	3.58365i	−0.445881	+	0.369626i
$95$	−2.05284	−	3.55563i	−0.210617	−	0.364800i
$96$		0			0
$97$	−8.60311	−	14.9010i	−0.873513	−	1.51297i	−0.858338	−	0.513084i	$-0.828503\pi$
$97$	−8.60311	−	14.9010i	−0.873513	−	1.51297i	−0.0151750	−	0.999885i	$-0.504831\pi$
$98$	−9.26015	+	3.49995i	−0.935416	+	0.353548i
$99$		0			0
$100$	6.52705	+	5.61098i	0.652705	+	0.561098i
$101$			3.27053i			0.325430i	0.986673	+	0.162715i	$0.0520251\pi$
$101$			3.27053i			0.325430i	−0.986673	+	0.162715i	$0.947975\pi$
$102$		0			0
$103$		−	0.333431i		−	0.0328540i	−0.999865	−	0.0164270i	$-0.994771\pi$
$103$		−	0.333431i		−	0.0328540i	0.999865	−	0.0164270i	$-0.00522910\pi$
$104$	−11.5244	−	0.206396i	−1.13006	−	0.0202388i
$105$		0			0
$106$	1.42094	+	1.71408i	0.138013	+	0.166486i
$107$	7.79018	+	13.4930i	0.753105	+	1.30442i	0.946311	+	0.323258i	$0.104778\pi$
$107$	7.79018	+	13.4930i	0.753105	+	1.30442i	−0.193206	+	0.981158i	$0.561889\pi$
$108$		0			0
$109$	−1.50755	+	2.61115i	−0.144397	+	0.250103i	−0.929148	−	0.369709i	$-0.879457\pi$
$109$	−1.50755	+	2.61115i	−0.144397	+	0.250103i	0.784751	+	0.619811i	$0.212791\pi$
$110$	1.32174	−	3.56510i	0.126023	−	0.339919i
$111$		0			0
$112$	5.15580	+	9.24217i	0.487177	+	0.873303i
$113$	−10.7370	−	6.19900i	−1.01005	−	0.583153i	−0.0988443	−	0.995103i	$-0.531515\pi$
$113$	−10.7370	−	6.19900i	−1.01005	−	0.583153i	−0.911207	+	0.411950i	$0.864848\pi$
$114$		0			0
$115$		−	0.946831i		−	0.0882924i
$116$	19.7426	+	3.72471i	1.83306	+	0.345831i
$117$		0			0
$118$	−0.0165273	−	0.0971172i	−0.00152146	−	0.00894037i
$119$	−9.65032	−	1.61088i	−0.884643	−	0.147669i
$120$		0			0
$121$	−0.619513			−0.0563194
$122$	−1.40598	+	1.16552i	−0.127291	+	0.105522i
$123$		0			0
$124$	−4.14022	−	0.781107i	−0.371803	−	0.0701455i
$125$			7.76368i			0.694405i
$126$		0			0
$127$		−	9.17767i		−	0.814386i	−0.913342	−	0.407193i	$-0.866508\pi$
$127$		−	9.17767i		−	0.814386i	0.913342	−	0.407193i	$-0.133492\pi$
$128$	8.96302	−	6.90393i	0.792226	−	0.610227i
$129$		0			0
$130$	−3.06924	−	3.70244i	−0.269190	−	0.324725i
$131$	−19.1523			−1.67334			−0.836671	−	0.547706i	$-0.815501\pi$
$131$	−19.1523			−1.67334			−0.836671	+	0.547706i	$0.815501\pi$
$132$		0			0
$133$	−8.27594	+	10.0478i	−0.717615	+	0.871257i
$134$	−18.5130	+	3.15051i	−1.59928	+	0.272163i
$135$		0			0
$136$	−0.187292	+	10.4577i	−0.0160602	+	0.896740i
$137$		−	0.344451i		−	0.0294284i	−0.999892	−	0.0147142i	$-0.995316\pi$
$137$		−	0.344451i		−	0.0294284i	0.999892	−	0.0147142i	$-0.00468384\pi$
$138$		0			0
$139$	4.39815	+	2.53927i	0.373046	+	0.215378i	0.674788	−	0.738011i	$-0.264235\pi$
$139$	4.39815	+	2.53927i	0.373046	+	0.215378i	−0.301742	+	0.953390i	$0.597568\pi$
$140$	−1.52187	+	4.14509i	−0.128622	+	0.350324i
$141$		0			0
$142$	3.55843	+	1.31927i	0.298617	+	0.110711i
$143$	6.56480	−	11.3706i	0.548976	−	0.950854i
$144$		0			0
$145$	4.19136	+	7.25964i	0.348073	+	0.602880i
$146$	−8.95977	+	7.42746i	−0.741516	+	0.614701i
$147$		0			0
$148$	−0.184339	+	0.977078i	−0.0151525	+	0.0803153i
$149$			12.8411i			1.05198i	0.850490	+	0.525991i	$0.176305\pi$
$149$			12.8411i			1.05198i	−0.850490	+	0.525991i	$0.823695\pi$
$150$		0			0
$151$			8.78443i			0.714867i	0.933939	+	0.357434i	$0.116348\pi$
$151$			8.78443i			0.714867i	−0.933939	+	0.357434i	$0.883652\pi$
$152$	11.9251	+	7.17273i	0.967257	+	0.581785i
$153$		0			0
$154$	−12.0551	+	0.0381352i	−0.971427	+	0.00307302i
$155$	−0.878968	−	1.52242i	−0.0706004	−	0.122283i
$156$		0			0
$157$	9.17918	+	15.8988i	0.732578	+	1.26886i	0.955778	+	0.294090i	$0.0950166\pi$
$157$	9.17918	+	15.8988i	0.732578	+	1.26886i	−0.223199	+	0.974773i	$0.571650\pi$
$158$	−12.4812	−	15.0561i	−0.992951	−	1.19780i
$159$		0			0
$160$	4.62227	+	0.958071i	0.365422	+	0.0757422i
$161$	−2.81144	+	1.05246i	−0.221572	+	0.0829451i
$162$		0			0
$163$	−3.35074	+	1.93455i	−0.262450	+	0.151526i	−0.625452	−	0.780263i	$-0.715085\pi$
$163$	−3.35074	+	1.93455i	−0.262450	+	0.151526i	0.363001	+	0.931789i	$0.381752\pi$
$164$	5.17398	+	14.7614i	0.404020	+	1.15267i
$165$		0			0
$166$	−1.30735	−	7.68225i	−0.101470	−	0.596258i
$167$	−10.6866	+	18.5097i	−0.826951	+	1.43232i	0.0734682	+	0.997298i	$0.476593\pi$
$167$	−10.6866	+	18.5097i	−0.826951	+	1.43232i	−0.900419	+	0.435023i	$0.856740\pi$
$168$		0			0
$169$	−1.80338	−	3.12354i	−0.138721	−	0.240272i
$170$	−3.35974	+	2.78515i	−0.257681	+	0.213612i
$171$		0			0
$172$	−17.7391	−	3.34671i	−1.35259	−	0.255184i
$173$	5.11300	+	2.95199i	0.388734	+	0.224436i	0.681612	−	0.731714i	$-0.261279\pi$
$173$	5.11300	+	2.95199i	0.388734	+	0.224436i	−0.292877	+	0.956150i	$0.594613\pi$
$174$		0			0
$175$	10.6637	−	3.99192i	0.806099	−	0.301761i
$176$	1.93425	+	12.7415i	0.145799	+	0.960429i
$177$		0			0
$178$	−10.9843	+	1.86930i	−0.823310	+	0.140110i
$179$	−8.36730	+	14.4926i	−0.625401	+	1.08323i	0.363062	+	0.931765i	$0.381731\pi$
$179$	−8.36730	+	14.4926i	−0.625401	+	1.08323i	−0.988463	+	0.151461i	$0.951602\pi$
$180$		0			0
$181$	−4.58906			−0.341102			−0.170551	−	0.985349i	$-0.554555\pi$
$181$	−4.58906			−0.341102			−0.170551	+	0.985349i	$0.554555\pi$
$182$	−7.58207	+	13.2290i	−0.562021	+	0.980599i
$183$		0			0
$184$	1.55460	+	2.80758i	0.114606	+	0.206977i
$185$	−0.359285	+	0.207433i	−0.0264152	+	0.0152508i
$186$		0			0
$187$	−10.3181	−	5.95716i	−0.754535	−	0.435631i
$188$	7.49410	−	2.62674i	0.546564	−	0.191575i
$189$		0			0
$190$	0.974107	+	5.72403i	0.0706691	+	0.415265i
$191$	8.45822	−	14.6501i	0.612015	−	1.06004i	−0.378885	−	0.925444i	$-0.623692\pi$
$191$	8.45822	−	14.6501i	0.612015	−	1.06004i	0.990900	−	0.134598i	$-0.0429742\pi$
$192$		0			0
$193$	1.27662	+	2.21118i	0.0918933	+	0.159164i	0.908308	−	0.418302i	$-0.137375\pi$
$193$	1.27662	+	2.21118i	0.0918933	+	0.159164i	−0.816414	+	0.577466i	$0.804041\pi$
$194$	4.08231	+	23.9884i	0.293093	+	1.72227i
$195$		0			0
$196$	13.9997	−	0.0885746i	0.999980	−	0.00632676i
$197$			3.44064i			0.245136i	0.992460	+	0.122568i	$0.0391129\pi$
$197$			3.44064i			0.245136i	−0.992460	+	0.122568i	$0.960887\pi$
$198$		0			0
$199$	−18.2732	−	10.5500i	−1.29535	−	0.747872i	−0.315755	−	0.948841i	$-0.602258\pi$
$199$	−18.2732	−	10.5500i	−1.29535	−	0.747872i	−0.979598	+	0.200969i	$0.935591\pi$
$200$	−5.89653	−	10.6490i	−0.416948	−	0.753001i
$201$		0			0
$202$	1.60784	−	4.33678i	0.113127	−	0.305135i
$203$	16.8972	−	20.5150i	1.18595	−	1.43987i
$204$		0			0
$205$	−3.26319	+	5.65202i	−0.227911	+	0.394754i
$206$	−0.163919	+	0.442135i	−0.0114208	+	0.0308050i
$207$		0			0
$208$	15.1800	+	5.93923i	1.05255	+	0.411811i
$209$	−13.7281	+	7.92594i	−0.949594	+	0.548249i
$210$		0			0
$211$	−1.93567	−	1.11756i	−0.133257	−	0.0769359i	0.431890	−	0.901926i	$-0.357847\pi$
$211$	−1.93567	−	1.11756i	−0.133257	−	0.0769359i	−0.565146	+	0.824991i	$0.691180\pi$
$212$	−1.04152	−	2.97145i	−0.0715317	−	0.204080i
$213$		0			0
$214$	−3.69656	−	21.7217i	−0.252692	−	1.48486i
$215$	−3.76600	−	6.52291i	−0.256839	−	0.444859i
$216$		0			0
$217$	−3.54351	+	4.30218i	−0.240549	+	0.292051i
$218$	3.28270	−	2.72129i	0.222333	−	0.184309i
$219$		0			0
$220$	−3.50530	+	4.07759i	−0.236327	+	0.274911i
$221$	−13.0507	+	7.53482i	−0.877885	+	0.506847i
$222$		0			0
$223$	−21.4374	+	12.3769i	−1.43556	+	0.828819i	−0.997537	−	0.0701459i	$-0.977654\pi$
$223$	−21.4374	+	12.3769i	−1.43556	+	0.828819i	−0.438020	+	0.898965i	$0.644320\pi$
$224$	−2.29309	−	14.7899i	−0.153214	−	0.988193i
$225$		0			0
$226$	11.1899	+	13.4984i	0.744341	+	0.897902i
$227$	8.23384			0.546499			0.273250	−	0.961943i	$-0.411902\pi$
$227$	8.23384			0.546499			0.273250	+	0.961943i	$0.411902\pi$
$228$		0			0
$229$	−21.5344			−1.42303			−0.711516	−	0.702670i	$-0.751991\pi$
$229$	−21.5344			−1.42303			−0.711516	+	0.702670i	$0.751991\pi$
$230$	−0.465475	+	1.25551i	−0.0306925	+	0.0827860i
$231$		0			0
$232$	−24.3479	−	14.6448i	−1.59852	−	0.961477i
$233$	−6.51116	+	3.75922i	−0.426560	+	0.246275i	−0.697880	−	0.716215i	$-0.745873\pi$
$233$	−6.51116	+	3.75922i	−0.426560	+	0.246275i	0.271320	+	0.962489i	$0.412540\pi$
$234$		0			0
$235$	2.86944	+	1.65667i	0.187181	+	0.108069i
$236$	−0.0258287	+	0.136904i	−0.00168131	+	0.00891169i
$237$		0			0
$238$	12.0045	+	6.88028i	0.778139	+	0.445982i
$239$	7.03603	−	12.1868i	0.455123	−	0.788296i	−0.543572	−	0.839362i	$-0.682929\pi$
$239$	7.03603	−	12.1868i	0.455123	−	0.788296i	0.998695	+	0.0510665i	$0.0162620\pi$
$240$		0			0
$241$	−12.0573			−0.776681			−0.388340	−	0.921516i	$-0.626952\pi$
$241$	−12.0573			−0.776681			−0.388340	+	0.921516i	$0.626952\pi$
$242$	0.821484	+	0.304561i	0.0528070	+	0.0195779i
$243$		0			0
$244$	2.43733	−	0.854305i	0.156034	−	0.0546913i
$245$	3.83584	+	4.40540i	0.245063	+	0.281451i
$246$		0			0
$247$			20.0500i			1.27575i
$248$	5.10600	+	3.07115i	0.324231	+	0.195018i
$249$		0			0
$250$	3.81673	−	10.2948i	0.241391	−	0.651098i
$251$	−21.1441			−1.33461			−0.667303	−	0.744786i	$-0.732551\pi$
$251$	−21.1441			−1.33461			−0.667303	+	0.744786i	$0.732551\pi$
$252$		0			0
$253$	−3.65567			−0.229830
$254$	−4.51187	+	12.1697i	−0.283100	+	0.763597i
$255$		0			0
$256$	−15.2792	+	4.74838i	−0.954948	+	0.296774i
$257$		−	30.6715i		−	1.91324i	−0.291343	−	0.956619i	$-0.594102\pi$
$257$		−	30.6715i		−	1.91324i	0.291343	−	0.956619i	$-0.405898\pi$
$258$		0			0
$259$	1.01530	+	0.836257i	0.0630877	+	0.0519625i
$260$	2.24969	+	6.41837i	0.139520	+	0.398050i
$261$		0			0
$262$	25.3962	+	9.41551i	1.56898	+	0.581692i
$263$	−1.92432			−0.118659			−0.0593293	−	0.998238i	$-0.518896\pi$
$263$	−1.92432			−0.118659			−0.0593293	+	0.998238i	$0.518896\pi$
$264$		0			0
$265$	0.656878	−	1.13775i	0.0403517	−	0.0698912i
$266$	15.9137	−	9.25501i	0.975730	−	0.567461i
$267$		0			0
$268$	26.0973	+	4.92360i	1.59415	+	0.300757i
$269$	4.77284	+	2.75560i	0.291005	+	0.168012i	0.638395	−	0.769709i	$-0.279599\pi$
$269$	4.77284	+	2.75560i	0.291005	+	0.168012i	−0.347390	+	0.937721i	$0.612932\pi$
$270$		0			0
$271$	−14.7828	+	8.53488i	−0.897993	+	0.518457i	−0.876549	−	0.481313i	$-0.840160\pi$
$271$	−14.7828	+	8.53488i	−0.897993	+	0.518457i	−0.0214448	+	0.999770i	$0.506827\pi$
$272$	5.38950	−	13.7750i	0.326786	−	0.835231i
$273$		0			0
$274$	−0.169337	+	0.456747i	−0.0102300	+	0.0275931i
$275$	13.8658			0.836141
$276$		0			0
$277$	20.2095			1.21427			0.607135	−	0.794599i	$-0.292319\pi$
$277$	20.2095			1.21427			0.607135	+	0.794599i	$0.292319\pi$
$278$	−4.58367	−	5.52930i	−0.274910	−	0.331625i
$279$		0			0
$280$	4.05581	−	4.74828i	0.242381	−	0.283764i
$281$	−13.9780	+	8.07021i	−0.833858	+	0.481428i	−0.855172	−	0.518345i	$-0.826548\pi$
$281$	−13.9780	+	8.07021i	−0.833858	+	0.481428i	0.0213139	+	0.999773i	$0.493215\pi$
$282$		0			0
$283$	−0.526337	+	0.303881i	−0.0312875	+	0.0180638i	−0.515562	−	0.856852i	$-0.672417\pi$
$283$	−0.526337	+	0.303881i	−0.0312875	+	0.0180638i	0.484275	+	0.874916i	$0.339084\pi$
$284$	−4.06996	−	3.49875i	−0.241508	−	0.207612i
$285$		0			0
$286$	−14.2949	+	11.8502i	−0.845277	+	0.700717i
$287$	20.4098	+	3.40692i	1.20476	+	0.201104i
$288$		0			0
$289$	−1.66260	−	2.87971i	−0.0977999	−	0.169394i
$290$	−1.98886	−	11.6869i	−0.116790	−	0.686280i
$291$		0			0
$292$	15.5322	−	5.44417i	0.908955	−	0.318596i
$293$	0.958441	+	0.553356i	0.0559927	+	0.0323274i	0.527735	−	0.849409i	$-0.323041\pi$
$293$	0.958441	+	0.553356i	0.0559927	+	0.0323274i	−0.471742	+	0.881736i	$0.656375\pi$
$294$		0			0
$295$	−0.0503415	+	0.0290647i	−0.00293099	+	0.00169221i
$296$	0.724781	−	1.20500i	0.0421270	−	0.0700390i
$297$		0			0
$298$	6.31285	−	17.0275i	0.365693	−	0.986375i
$299$	−2.31191	+	4.00434i	−0.133701	+	0.231577i
$300$		0			0
$301$	−15.1824	+	18.4330i	−0.875102	+	1.06246i
$302$	4.31855	−	11.6483i	0.248504	−	0.670284i
$303$		0			0
$304$	−12.2867	−	15.3737i	−0.704691	−	0.881743i
$305$	0.933237	+	0.538805i	0.0534370	+	0.0308519i
$306$		0			0
$307$		−	16.8834i		−	0.963589i	−0.876284	−	0.481795i	$-0.839985\pi$
$307$		−	16.8834i		−	0.963589i	0.876284	−	0.481795i	$-0.160015\pi$
$308$	16.0040	+	5.87588i	0.911912	+	0.334809i
$309$		0			0
$310$	0.417084	+	2.45086i	0.0236888	+	0.139199i
$311$	4.82774	+	8.36189i	0.273756	+	0.474159i	0.969820	−	0.243820i	$-0.0784006\pi$
$311$	4.82774	+	8.36189i	0.273756	+	0.474159i	−0.696065	+	0.717979i	$0.745067\pi$
$312$		0			0
$313$	7.05833	−	12.2254i	0.398960	−	0.691020i	−0.594637	−	0.803994i	$-0.702704\pi$
$313$	7.05833	−	12.2254i	0.398960	−	0.691020i	0.993598	+	0.112974i	$0.0360377\pi$
$314$	−4.35566	−	25.5947i	−0.245804	−	1.44439i
$315$		0			0
$316$	9.14847	+	26.1006i	0.514641	+	1.46827i
$317$	−14.4429	−	8.33864i	−0.811197	−	0.468345i	0.0361747	−	0.999345i	$-0.488483\pi$
$317$	−14.4429	−	8.33864i	−0.811197	−	0.468345i	−0.847371	+	0.531001i	$0.821816\pi$
$318$		0			0
$319$	28.0291	−	16.1826i	1.56933	−	0.906053i
$320$	−5.65820	−	3.54279i	−0.316303	−	0.198048i
$321$		0			0
$322$	4.24541	−	0.0134300i	0.236588	−	0.000748424i
$323$	18.1942			1.01235
$324$		0			0
$325$	8.76898	−	15.1883i	0.486416	−	0.842496i
$326$	5.39419	−	0.917975i	0.298756	−	0.0508419i
$327$		0			0
$328$	0.396112	−	22.1174i	0.0218716	−	1.22123i
$329$	1.72964	−	10.3617i	0.0953580	−	0.571262i
$330$		0			0
$331$	4.65095	+	2.68522i	0.255639	+	0.147593i	0.622344	−	0.782744i	$-0.286181\pi$
$331$	4.65095	+	2.68522i	0.255639	+	0.147593i	−0.366705	+	0.930337i	$0.619514\pi$
$332$	−2.04313	+	10.8295i	−0.112131	+	0.594346i
$333$		0			0
$334$	23.2701	−	19.2904i	1.27329	−	1.05553i
$335$	5.54044	+	9.59633i	0.302707	+	0.524304i
$336$		0			0
$337$	−2.08402	+	3.60963i	−0.113524	+	0.196629i	−0.917189	−	0.398453i	$-0.869547\pi$
$337$	−2.08402	+	3.60963i	−0.113524	+	0.196629i	0.803665	+	0.595082i	$0.202881\pi$
$338$	0.855730	+	5.02842i	0.0465456	+	0.273510i
$339$		0			0
$340$	5.82429	−	2.04146i	0.315866	−	0.110714i
$341$	−5.87798	+	3.39365i	−0.318310	+	0.183777i
$342$		0			0
$343$	8.81728	−	16.2867i	0.476088	−	0.879398i
$344$	21.8770	+	13.1586i	1.17953	+	0.709462i
$345$		0			0
$346$	−5.32868	−	6.42801i	−0.286472	−	0.345572i
$347$	6.26374	+	10.8491i	0.336255	+	0.582411i	0.983725	−	0.179680i	$-0.0575061\pi$
$347$	6.26374	+	10.8491i	0.336255	+	0.582411i	−0.647470	+	0.762091i	$0.724173\pi$
$348$		0			0
$349$	14.8357	+	25.6962i	0.794138	+	1.37549i	0.923385	+	0.383875i	$0.125411\pi$
$349$	14.8357	+	25.6962i	0.794138	+	1.37549i	−0.129247	+	0.991612i	$0.541256\pi$
$350$	−16.1027	+	0.0509394i	−0.860725	+	0.00272283i
$351$		0			0
$352$	3.69907	−	17.8464i	0.197161	−	0.951214i
$353$			4.36164i			0.232147i	0.993241	+	0.116073i	$0.0370308\pi$
$353$			4.36164i			0.232147i	−0.993241	+	0.116073i	$0.962969\pi$
$354$		0			0
$355$		−	2.23936i		−	0.118853i
$356$	15.4844	+	2.92133i	0.820670	+	0.154830i
$357$		0			0
$358$	18.2199	−	15.1039i	0.962952	−	0.798266i
$359$	−13.4744	−	23.3383i	−0.711151	−	1.23175i	−0.964426	−	0.264355i	$-0.914841\pi$
$359$	−13.4744	−	23.3383i	−0.711151	−	1.23175i	0.253275	−	0.967394i	$-0.418492\pi$
$360$		0			0
$361$	2.60357	−	4.50952i	0.137030	−	0.237343i
$362$	6.08516	+	2.25604i	0.319829	+	0.118575i
$363$		0			0
$364$	16.5575	−	13.8144i	0.867849	−	0.724072i
$365$	5.94718	+	3.43360i	0.311289	+	0.179723i
$366$		0			0
$367$			17.6486i			0.921251i	0.887595	+	0.460626i	$0.152375\pi$
$367$			17.6486i			0.921251i	−0.887595	+	0.460626i	$0.847625\pi$
$368$	−0.681178	−	4.48715i	−0.0355089	−	0.233909i
$369$		0			0
$370$	0.578394	−	0.0984303i	0.0300693	−	0.00511715i
$371$	−4.10848	−	0.685810i	−0.213302	−	0.0356055i
$372$		0			0
$373$	−16.6333			−0.861238			−0.430619	−	0.902534i	$-0.641705\pi$
$373$	−16.6333			−0.861238			−0.430619	+	0.902534i	$0.641705\pi$
$374$	10.7533	+	12.9718i	0.556042	+	0.670756i
$375$		0			0
$376$	−11.2286	−	0.201099i	−0.579073	−	0.0103709i
$377$		−	40.9367i		−	2.10835i
$378$		0			0
$379$		−	12.2312i		−	0.628274i	−0.949378	−	0.314137i	$-0.898285\pi$
$379$		−	12.2312i		−	0.628274i	0.949378	−	0.314137i	$-0.101715\pi$
$380$	1.52233	−	8.06903i	0.0780938	−	0.413933i
$381$		0			0
$382$	−18.4179	+	15.2680i	−0.942341	+	0.781180i
$383$	−10.9795			−0.561028			−0.280514	−	0.959850i	$-0.590505\pi$
$383$	−10.9795			−0.561028			−0.280514	+	0.959850i	$0.590505\pi$
$384$		0			0
$385$	2.49384	+	6.66184i	0.127098	+	0.339519i
$386$	−0.605777	−	3.55966i	−0.0308333	−	0.181182i
$387$		0			0
$388$	6.37981	−	33.8159i	0.323886	−	1.71674i
$389$		−	32.7637i		−	1.66119i	−0.556879	−	0.830594i	$-0.688001\pi$
$389$		−	32.7637i		−	1.66119i	0.556879	−	0.830594i	$-0.311999\pi$
$390$		0			0
$391$	3.63370	+	2.09792i	0.183764	+	0.106096i
$392$	−18.6074	−	6.76500i	−0.939815	−	0.341684i
$393$		0			0
$394$	1.69147	−	4.56235i	0.0852149	−	0.229848i
$395$	−5.76988	+	9.99372i	−0.290314	+	0.502839i
$396$		0			0
$397$	5.06480	+	8.77250i	0.254195	+	0.440279i	0.964677	−	0.263437i	$-0.0848561\pi$
$397$	5.06480	+	8.77250i	0.254195	+	0.440279i	−0.710481	+	0.703716i	$0.751523\pi$
$398$	19.0440	+	22.9729i	0.954589	+	1.15153i
$399$		0			0
$400$	2.58368	+	17.0196i	0.129184	+	0.850980i
$401$		−	7.23456i		−	0.361277i	−0.983550	−	0.180638i	$-0.942184\pi$
$401$		−	7.23456i		−	0.361277i	0.983550	−	0.180638i	$-0.0578164\pi$
$402$		0			0
$403$			8.58481i			0.427640i
$404$	−4.26404	+	4.96020i	−0.212144	+	0.246779i
$405$		0			0
$406$	−32.4914	+	18.8962i	−1.61252	+	0.937804i
$407$	0.800890	+	1.38718i	0.0396986	+	0.0687601i
$408$		0			0
$409$	−6.77937	−	11.7422i	−0.335218	−	0.580615i	0.648309	−	0.761378i	$-0.275477\pi$
$409$	−6.77937	−	11.7422i	−0.335218	−	0.580615i	−0.983527	+	0.180763i	$0.942143\pi$
$410$	7.10565	−	5.89043i	0.350923	−	0.290908i
$411$		0			0
$412$	0.434719	−	0.505693i	0.0214171	−	0.0249137i
$413$	0.142259	+	0.117173i	0.00700013	+	0.00576569i
$414$		0			0
$415$	−3.98215	+	2.29910i	−0.195476	+	0.112858i
$416$	−17.2092	−	15.3382i	−0.843748	−	0.752018i
$417$		0			0
$418$	22.1002	−	3.76098i	1.08096	−	0.183956i
$419$	−7.76845	+	13.4554i	−0.379514	+	0.657337i	−0.990992	−	0.133925i	$-0.957242\pi$
$419$	−7.76845	+	13.4554i	−0.379514	+	0.657337i	0.611478	+	0.791262i	$0.290575\pi$
$420$		0			0
$421$	16.4578	+	28.5058i	0.802106	+	1.38929i	0.918228	+	0.396053i	$0.129620\pi$
$421$	16.4578	+	28.5058i	0.802106	+	1.38929i	−0.116122	+	0.993235i	$0.537046\pi$
$422$	2.01732	+	2.43350i	0.0982015	+	0.118461i
$423$		0			0
$424$	−0.0797369	+	4.45221i	−0.00387237	+	0.216218i
$425$	−13.7825	−	7.95733i	−0.668549	−	0.385987i
$426$		0			0
$427$	0.562536	−	3.36999i	0.0272230	−	0.163085i
$428$	−5.77696	+	30.6205i	−0.279240	+	1.48010i
$429$		0			0
$430$	1.78703	+	10.5009i	0.0861781	+	0.506398i
$431$	−4.19876	+	7.27246i	−0.202247	+	0.350302i	−0.949252	−	0.314516i	$-0.898158\pi$
$431$	−4.19876	+	7.27246i	−0.202247	+	0.350302i	0.747005	+	0.664818i	$0.231491\pi$
$432$		0			0
$433$	−25.5642			−1.22853			−0.614267	−	0.789098i	$-0.710548\pi$
$433$	−25.5642			−1.22853			−0.614267	+	0.789098i	$0.710548\pi$
$434$	6.81376	−	3.96272i	0.327071	−	0.190217i
$435$		0			0
$436$	−5.69074	+	1.99465i	−0.272537	+	0.0955264i
$437$	4.83460	−	2.79126i	0.231270	−	0.133524i
$438$		0			0
$439$	5.00342	+	2.88872i	0.238800	+	0.137871i	0.614625	−	0.788819i	$-0.289307\pi$
$439$	5.00342	+	2.88872i	0.238800	+	0.137871i	−0.375825	+	0.926691i	$0.622641\pi$
$440$	6.65268	−	3.68369i	0.317154	−	0.175613i
$441$		0			0
$442$	21.0096	−	3.57539i	0.999326	−	0.170064i
$443$	−5.88705	+	10.1967i	−0.279702	+	0.484458i	−0.971311	−	0.237814i	$-0.923569\pi$
$443$	−5.88705	+	10.1967i	−0.279702	+	0.484458i	0.691609	+	0.722272i	$0.256902\pi$
$444$		0			0
$445$	3.28732	+	5.69381i	0.155834	+	0.269913i
$446$	34.5110	−	5.87304i	1.63414	−	0.278096i
$447$		0			0
$448$	−4.23025	+	20.7390i	−0.199860	+	0.979824i
$449$			17.9255i			0.845956i	0.906140	+	0.422978i	$0.139015\pi$
$449$			17.9255i			0.845956i	−0.906140	+	0.422978i	$0.860985\pi$
$450$		0			0
$451$	21.8222	+	12.5990i	1.02757	+	0.593266i
$452$	−8.20197	−	23.4002i	−0.385788	−	1.10065i
$453$		0			0
$454$	−10.9182	−	4.04787i	−0.512416	−	0.189976i
$455$	8.87438	+	1.48136i	0.416037	+	0.0694471i
$456$		0			0
$457$	12.4931	−	21.6387i	0.584404	−	1.01222i	−0.410546	−	0.911840i	$-0.634662\pi$
$457$	12.4931	−	21.6387i	0.584404	−	1.01222i	0.994949	−	0.100377i	$-0.0320049\pi$
$458$	28.5549	+	10.5866i	1.33428	+	0.494679i
$459$		0			0
$460$	1.23445	−	1.43599i	0.0575567	−	0.0669536i
$461$	−11.9270	+	6.88605i	−0.555495	+	0.320715i	−0.751335	−	0.659920i	$-0.770590\pi$
$461$	−11.9270	+	6.88605i	−0.555495	+	0.320715i	0.195840	+	0.980636i	$0.437257\pi$
$462$		0			0
$463$	−21.7956	−	12.5837i	−1.01293	−	0.584814i	−0.100880	−	0.994899i	$-0.532166\pi$
$463$	−21.7956	−	12.5837i	−1.01293	−	0.584814i	−0.912047	+	0.410085i	$0.865499\pi$
$464$	25.0862	+	31.3890i	1.16460	+	1.45720i
$465$		0			0
$466$	10.4820	−	1.78381i	0.485568	−	0.0826333i
$467$	−21.1486	−	36.6305i	−0.978641	−	1.69506i	−0.667356	−	0.744738i	$-0.732574\pi$
$467$	−21.1486	−	36.6305i	−0.978641	−	1.69506i	−0.311284	−	0.950317i	$-0.600759\pi$
$468$		0			0
$469$	22.3360	−	27.1182i	1.03138	−	1.25220i
$470$	−2.99048	−	3.60742i	−0.137940	−	0.166398i
$471$		0			0
$472$	0.101553	−	0.168839i	0.00467436	−	0.00777144i
$473$	−25.1846	+	14.5404i	−1.15799	+	0.668566i
$474$		0			0
$475$	−18.3375	+	10.5871i	−0.841380	+	0.485771i
$476$	−12.5358	−	15.0250i	−0.574576	−	0.688668i
$477$		0			0
$478$	−15.3211	+	12.7008i	−0.700769	+	0.580922i
$479$	−29.1409			−1.33148			−0.665741	−	0.746183i	$-0.731885\pi$
$479$	−29.1409			−1.33148			−0.665741	+	0.746183i	$0.731885\pi$
$480$		0			0
$481$	2.02599			0.0923770
$482$	15.9882	+	5.92755i	0.728243	+	0.269992i
$483$		0			0
$484$	−0.939573	−	0.807705i	−0.0427079	−	0.0367139i
$485$	12.4346	−	7.17910i	0.564624	−	0.325986i
$486$		0			0
$487$	30.0519	+	17.3505i	1.36178	+	0.786224i	0.989861	−	0.142040i	$-0.0453663\pi$
$487$	30.0519	+	17.3505i	1.36178	+	0.786224i	0.371920	+	0.928265i	$0.378700\pi$
$488$	−3.65193	−	0.0654043i	−0.165315	−	0.00296071i
$489$		0			0
$490$	−2.92063	−	7.72738i	−0.131941	−	0.349087i
$491$	9.32230	−	16.1467i	0.420710	−	0.728690i	−0.575300	−	0.817943i	$-0.695114\pi$
$491$	9.32230	−	16.1467i	0.420710	−	0.728690i	0.996009	+	0.0892526i	$0.0284478\pi$
$492$		0			0
$493$	−37.1476			−1.67304
$494$	9.85684	−	26.5866i	0.443480	−	1.19619i
$495$		0			0
$496$	−5.26081	−	6.58257i	−0.236217	−	0.295566i
$497$	−6.64937	+	2.48918i	−0.298265	+	0.111655i
$498$		0			0
$499$		−	18.1290i		−	0.811567i	−0.913969	−	0.405783i	$-0.866999\pi$
$499$		−	18.1290i		−	0.811567i	0.913969	−	0.405783i	$-0.133001\pi$
$500$	−10.1221	+	11.7746i	−0.452673	+	0.526578i
$501$		0			0
$502$	28.0375	+	10.3947i	1.25137	+	0.463940i
$503$	23.0610			1.02824			0.514119	−	0.857719i	$-0.328119\pi$
$503$	23.0610			1.02824			0.514119	+	0.857719i	$0.328119\pi$
$504$		0			0
$505$	−2.72918			−0.121447
$506$	4.84747	+	1.79718i	0.215496	+	0.0798942i
$507$		0			0
$508$	11.9656	−	13.9191i	0.530888	−	0.617562i
$509$			20.3870i			0.903637i	0.892110	+	0.451818i	$0.149224\pi$
$509$			20.3870i			0.903637i	−0.892110	+	0.451818i	$0.850776\pi$
$510$		0			0
$511$	3.58484	−	21.4757i	0.158584	−	0.950028i
$512$	22.5948	+	1.21502i	0.998557	+	0.0536970i
$513$		0			0
$514$	−15.0785	+	40.6709i	−0.665086	+	1.79392i
$515$	0.278241			0.0122607
$516$		0			0
$517$	6.39633	−	11.0788i	0.281310	−	0.487243i
$518$	−0.935188	−	1.60802i	−0.0410898	−	0.0706525i
$519$		0			0
$520$	0.172233	−	9.61683i	0.00755291	−	0.421726i
$521$	3.66713	+	2.11722i	0.160660	+	0.0927571i	0.578174	−	0.815913i	$-0.303765\pi$
$521$	3.66713	+	2.11722i	0.160660	+	0.0927571i	−0.417514	+	0.908670i	$0.637099\pi$
$522$		0			0
$523$	−30.0719	+	17.3620i	−1.31495	+	0.759188i	−0.982912	−	0.184077i	$-0.941070\pi$
$523$	−30.0719	+	17.3620i	−1.31495	+	0.759188i	−0.332040	+	0.943265i	$0.607737\pi$
$524$	−29.0469	−	24.9702i	−1.26892	−	1.09083i
$525$		0			0
$526$	2.55168	+	0.946021i	0.111258	+	0.0412485i
$527$	7.79021			0.339347
$528$		0			0
$529$	−21.7126			−0.944026
$530$	−1.43036	+	1.18574i	−0.0621309	+	0.0515052i
$531$		0			0
$532$	−25.6517	+	4.44890i	−1.11214	+	0.192884i
$533$	27.6014	−	15.9357i	1.19555	−	0.690251i
$534$		0			0
$535$	−11.2596	+	6.50072i	−0.486794	+	0.281051i
$536$	−32.1849	−	19.3585i	−1.39018	−	0.836162i
$537$		0			0
$538$	−4.97417	−	6.00037i	−0.214452	−	0.258694i
$539$	17.0090	−	14.8100i	0.732632	−	0.637912i
$540$		0			0
$541$	7.40181	+	12.8203i	0.318229	+	0.551188i	0.980119	−	0.198413i	$-0.0635787\pi$
$541$	7.40181	+	12.8203i	0.318229	+	0.551188i	−0.661890	+	0.749601i	$0.730245\pi$
$542$	23.7981	−	4.04993i	1.02222	−	0.173959i
$543$		0			0
$544$	−13.9185	+	15.6163i	−0.596752	+	0.669543i
$545$	−2.17894	−	1.25801i	−0.0933356	−	0.0538874i
$546$		0			0
$547$	40.1566	−	23.1844i	1.71697	−	0.991294i	0.792654	−	0.609672i	$-0.208699\pi$
$547$	40.1566	−	23.1844i	1.71697	−	0.991294i	0.924318	−	0.381622i	$-0.124634\pi$
$548$	0.449086	−	0.522405i	0.0191840	−	0.0223160i
$549$		0			0
$550$	−18.3863	−	6.81663i	−0.783994	−	0.290662i
$551$	−24.7122	+	42.8028i	−1.05278	+	1.82346i
$552$		0			0
$553$	36.0880	+	6.02401i	1.53462	+	0.256167i
$554$	−26.7981	−	9.93526i	−1.13854	−	0.422109i
$555$		0			0
$556$	3.35974	+	9.58533i	0.142485	+	0.406509i
$557$	19.7641	+	11.4108i	0.837433	+	0.483492i	0.856391	−	0.516328i	$-0.172701\pi$
$557$	19.7641	+	11.4108i	0.837433	+	0.483492i	−0.0189577	+	0.999820i	$0.506035\pi$
$558$		0			0
$559$			36.7823i			1.55572i
$560$	−7.71238	+	4.30240i	−0.325908	+	0.181809i
$561$		0			0
$562$	22.5025	−	3.82944i	0.949209	−	0.161535i
$563$	−12.9021	−	22.3470i	−0.543757	−	0.941815i	−0.998684	−	0.0512859i	$-0.983668\pi$
$563$	−12.9021	−	22.3470i	−0.543757	−	0.941815i	0.454927	−	0.890529i	$-0.349665\pi$
$564$		0			0
$565$	5.17293	−	8.95977i	0.217627	−	0.376940i
$566$	0.847323	−	0.144196i	0.0356156	−	0.00606102i
$567$		0			0
$568$	3.67680	+	6.64024i	0.154275	+	0.278618i
$569$	5.18560	+	2.99391i	0.217392	+	0.125511i	0.604742	−	0.796422i	$-0.293276\pi$
$569$	5.18560	+	2.99391i	0.217392	+	0.125511i	−0.387350	+	0.921933i	$0.626610\pi$
$570$		0			0
$571$	−17.3123	+	9.99524i	−0.724496	+	0.418288i	−0.816405	−	0.577479i	$-0.804036\pi$
$571$	−17.3123	+	9.99524i	−0.724496	+	0.418288i	0.0919092	+	0.995767i	$0.470703\pi$
$572$	24.7810	−	8.68595i	1.03615	−	0.363178i
$573$		0			0
$574$	−25.3889	−	14.5514i	−1.05971	−	0.607363i
$575$	−4.88309			−0.203639
$576$		0			0
$577$	1.21653	−	2.10710i	0.0506449	−	0.0877196i	−0.839592	−	0.543218i	$-0.817206\pi$
$577$	1.21653	−	2.10710i	0.0506449	−	0.0877196i	0.890237	+	0.455499i	$0.150539\pi$
$578$	0.788929	+	4.63589i	0.0328151	+	0.192828i
$579$		0			0
$580$	−3.10818	+	16.4748i	−0.129060	+	0.684078i
$581$	11.2531	+	9.26869i	0.466858	+	0.384530i
$582$		0			0
$583$	−4.39278	−	2.53617i	−0.181930	−	0.105038i
$584$	−23.2724	−	0.416797i	−0.963019	−	0.0172472i
$585$		0			0
$586$	−0.998870	−	1.20494i	−0.0412629	−	0.0497757i
$587$	−15.7756	−	27.3241i	−0.651128	−	1.12779i	−0.982850	−	0.184409i	$-0.940963\pi$
$587$	−15.7756	−	27.3241i	−0.651128	−	1.12779i	0.331721	−	0.943377i	$-0.392371\pi$
$588$		0			0
$589$	5.18239	−	8.97617i	0.213537	−	0.369856i
$590$	0.0810421	−	0.0137916i	0.00333645	−	0.000567792i
$591$		0			0
$592$	−1.55346	+	1.24153i	−0.0638469	+	0.0510267i
$593$	−29.4235	+	16.9877i	−1.20828	+	0.697600i	−0.962383	−	0.271696i	$-0.912415\pi$
$593$	−29.4235	+	16.9877i	−1.20828	+	0.697600i	−0.245896	+	0.969296i	$0.579082\pi$
$594$		0			0
$595$	1.34424	−	8.05297i	0.0551087	−	0.330140i
$596$	−16.7419	+	19.4752i	−0.685773	+	0.797735i
$597$		0			0
$598$	5.03421	−	4.17325i	0.205864	−	0.170657i
$599$	22.2494	+	38.5370i	0.909084	+	1.57458i	0.815339	+	0.578984i	$0.196551\pi$
$599$	22.2494	+	38.5370i	0.909084	+	1.57458i	0.0937457	+	0.995596i	$0.470116\pi$
$600$		0			0
$601$	9.53221	+	16.5103i	0.388827	+	0.673468i	0.992292	−	0.123922i	$-0.0395471\pi$
$601$	9.53221	+	16.5103i	0.388827	+	0.673468i	−0.603465	+	0.797389i	$0.706214\pi$
$602$	29.1941	−	16.9786i	1.18986	−	0.691995i
$603$		0			0
$604$	−11.4529	+	13.3228i	−0.466013	+	0.542095i
$605$		−	0.516969i		−	0.0210178i
$606$		0			0
$607$			27.3950i			1.11193i	0.831206	+	0.555964i	$0.187651\pi$
$607$			27.3950i			1.11193i	−0.831206	+	0.555964i	$0.812349\pi$
$608$	8.73445	+	26.4261i	0.354229	+	1.07172i
$609$		0			0
$610$	−0.972603	−	1.17325i	−0.0393795	−	0.0475037i
$611$	−8.09029	−	14.0128i	−0.327298	−	0.566897i
$612$		0			0
$613$	−22.2408	+	38.5222i	−0.898298	+	1.55590i	−0.0686300	+	0.997642i	$0.521863\pi$
$613$	−22.2408	+	38.5222i	−0.898298	+	1.55590i	−0.829668	+	0.558256i	$0.811471\pi$
$614$	−8.30013	+	22.3877i	−0.334966	+	0.903494i
$615$		0			0
$616$	−18.3329	−	15.6593i	−0.738652	−	0.630931i
$617$	−12.5297	−	7.23402i	−0.504426	−	0.291231i	0.226113	−	0.974101i	$-0.427398\pi$
$617$	−12.5297	−	7.23402i	−0.504426	−	0.291231i	−0.730539	+	0.682870i	$0.760731\pi$
$618$		0			0
$619$		−	14.8587i		−	0.597222i	−0.954375	−	0.298611i	$-0.903477\pi$
$619$		−	14.8587i		−	0.597222i	0.954375	−	0.298611i	$-0.0965233\pi$
$620$	0.651816	−	3.45492i	0.0261776	−	0.138753i
$621$		0			0
$622$	−2.29084	−	13.4614i	−0.0918542	−	0.539752i
$623$	13.2527	−	16.0901i	0.530957	−	0.644636i
$624$		0			0
$625$	15.0396			0.601585
$626$	−15.3696	+	12.7411i	−0.614294	+	0.509236i
$627$		0			0
$628$	−6.80701	+	36.0802i	−0.271629	+	1.43976i
$629$		−	1.83846i		−	0.0733043i
$630$		0			0
$631$		−	29.4851i		−	1.17378i	−0.809666	−	0.586891i	$-0.800352\pi$
$631$		−	29.4851i		−	1.17378i	0.809666	−	0.586891i	$-0.199648\pi$
$632$	0.700392	−	39.1073i	0.0278601	−	1.55560i
$633$		0			0
$634$	15.0522	+	18.1575i	0.597798	+	0.721127i
$635$	7.65855			0.303920
$636$		0			0
$637$	−5.46574	−	27.9974i	−0.216561	−	1.10930i
$638$	−45.1227	+	7.67891i	−1.78642	+	0.304011i
$639$		0			0
$640$	5.76117	+	7.47943i	0.227730	+	0.295651i
$641$			7.37204i			0.291178i	0.989345	+	0.145589i	$0.0465077\pi$
$641$			7.37204i			0.291178i	−0.989345	+	0.145589i	$0.953492\pi$
$642$		0			0
$643$	14.1342	+	8.16036i	0.557397	+	0.321813i	0.752100	−	0.659049i	$-0.229041\pi$
$643$	14.1342	+	8.16036i	0.557397	+	0.321813i	−0.194703	+	0.980862i	$0.562374\pi$
$644$	−5.63608	−	2.06929i	−0.222093	−	0.0815416i
$645$		0			0
$646$	−24.1257	−	8.94450i	−0.949215	−	0.351917i
$647$	1.41719	−	2.45464i	0.0557153	−	0.0965017i	−0.836823	−	0.547474i	$-0.815589\pi$
$647$	1.41719	−	2.45464i	0.0557153	−	0.0965017i	0.892538	+	0.450972i	$0.148923\pi$
$648$		0			0
$649$	0.112217	+	0.194366i	0.00440491	+	0.00762953i
$650$	−19.0946	+	15.8290i	−0.748951	+	0.620864i
$651$		0			0
$652$	−7.60406	−	1.43461i	−0.297798	−	0.0561835i
$653$			22.9343i			0.897488i	0.893660	+	0.448744i	$0.148128\pi$
$653$			22.9343i			0.897488i	−0.893660	+	0.448744i	$0.851872\pi$
$654$		0			0
$655$		−	15.9821i		−	0.624473i
$656$	−11.3985	+	29.1333i	−0.445035	+	1.13746i
$657$		0			0
$658$	−7.38750	+	12.8895i	−0.287995	+	0.502486i
$659$	13.8038	+	23.9089i	0.537720	+	0.931359i	0.999026	+	0.0441177i	$0.0140477\pi$
$659$	13.8038	+	23.9089i	0.537720	+	0.931359i	−0.461306	+	0.887241i	$0.652619\pi$
$660$		0			0
$661$	15.5736	+	26.9742i	0.605742	+	1.04918i	0.991934	+	0.126757i	$0.0404570\pi$
$661$	15.5736	+	26.9742i	0.605742	+	1.04918i	−0.386192	+	0.922419i	$0.626210\pi$
$662$	−4.84713	−	5.84712i	−0.188389	−	0.227255i
$663$		0			0
$664$	8.03314	−	13.3556i	0.311746	−	0.518299i
$665$	−8.38468	−	6.90608i	−0.325144	−	0.267806i
$666$		0			0
$667$	−9.87095	+	5.69899i	−0.382205	+	0.220666i
$668$	−40.3400	+	14.1395i	−1.56080	+	0.547074i
$669$		0			0
$670$	−2.62903	−	15.4486i	−0.101568	−	0.596833i
$671$	2.08030	−	3.60318i	0.0803090	−	0.139099i
$672$		0			0
$673$	−8.88948	−	15.3970i	−0.342664	−	0.593512i	0.642262	−	0.766485i	$-0.277996\pi$
$673$	−8.88948	−	15.3970i	−0.342664	−	0.593512i	−0.984927	+	0.172973i	$0.944663\pi$
$674$	4.53799	−	3.76190i	0.174797	−	0.144903i
$675$		0			0
$676$	1.33733	−	7.08845i	0.0514358	−	0.272633i
$677$	34.9366	+	20.1706i	1.34272	+	0.775221i	0.987206	−	0.159449i	$-0.0509719\pi$
$677$	34.9366	+	20.1706i	1.34272	+	0.775221i	0.355516	+	0.934670i	$0.384305\pi$
$678$		0			0
$679$	−35.1387	−	28.9422i	−1.34850	−	1.11070i
$680$	−8.72670	−	0.156291i	−0.334654	−	0.00599349i
$681$		0			0
$682$	9.46265	−	1.61034i	0.362344	−	0.0616631i
$683$	−12.8385	+	22.2369i	−0.491250	+	0.850870i	−0.999949	−	0.0100743i	$-0.996793\pi$
$683$	−12.8385	+	22.2369i	−0.491250	+	0.850870i	0.508699	+	0.860944i	$0.330127\pi$
$684$		0			0
$685$	0.287436			0.0109824
$686$	−19.6986	+	17.2617i	−0.752096	+	0.659054i
$687$		0			0
$688$	−22.5403	−	28.2035i	−0.859342	−	1.07525i
$689$	−5.55614	+	3.20784i	−0.211672	+	0.122209i
$690$		0			0
$691$	8.12990	+	4.69380i	0.309276	+	0.178561i	0.646602	−	0.762827i	$-0.276189\pi$
$691$	8.12990	+	4.69380i	0.309276	+	0.178561i	−0.337326	+	0.941388i	$0.609523\pi$
$692$	3.90581	+	11.1433i	0.148477	+	0.423604i
$693$		0			0
$694$	−2.97224	−	17.4654i	−0.112825	−	0.662979i
$695$	−2.11896	+	3.67015i	−0.0803769	+	0.139217i
$696$		0			0
$697$	−14.4607	−	25.0467i	−0.547738	−	0.948710i
$698$	−7.03978	−	41.3670i	−0.266460	−	1.56577i
$699$		0			0
$700$	21.3775	+	7.84876i	0.807992	+	0.296655i
$701$			22.1516i			0.836655i	0.908296	+	0.418327i	$0.137383\pi$
$701$			22.1516i			0.836655i	−0.908296	+	0.418327i	$0.862617\pi$
$702$		0			0
$703$	−2.11834	−	1.22303i	−0.0798948	−	0.0461273i
$704$	−13.6785	+	21.8460i	−0.515529	+	0.823353i
$705$		0			0
$706$	2.14424	−	5.78360i	0.0806996	−	0.217669i
$707$	3.03364	+	8.10381i	0.114092	+	0.304775i
$708$		0			0
$709$	−6.92727	+	11.9984i	−0.260159	+	0.450609i	−0.966284	−	0.257479i	$-0.917108\pi$
$709$	−6.92727	+	11.9984i	−0.260159	+	0.450609i	0.706125	+	0.708087i	$0.250442\pi$
$710$	−1.10090	+	2.96943i	−0.0413161	+	0.111441i
$711$		0			0
$712$	−19.0963	−	11.4860i	−0.715665	−	0.430458i
$713$	2.07003	−	1.19513i	0.0775233	−	0.0447581i
$714$		0			0
$715$	9.48847	+	5.47817i	0.354849	+	0.204872i
$716$	−31.5852	+	11.0709i	−1.18039	+	0.413737i
$717$		0			0
$718$	6.39380	+	37.5711i	0.238615	+	1.40214i
$719$	8.60856	+	14.9105i	0.321045	+	0.556066i	0.980704	−	0.195499i	$-0.0626326\pi$
$719$	8.60856	+	14.9105i	0.321045	+	0.556066i	−0.659659	+	0.751565i	$0.729299\pi$
$720$		0			0
$721$	−0.309280	−	0.826184i	−0.0115182	−	0.0307687i
$722$	−5.66931	+	4.69974i	−0.210990	+	0.174906i
$723$		0			0
$724$	−6.95991	−	5.98309i	−0.258663	−	0.222360i
$725$	37.4401	−	21.6161i	1.39049	−	0.802801i
$726$		0			0
$727$	25.3409	−	14.6306i	0.939841	−	0.542617i	0.0499304	−	0.998753i	$-0.484100\pi$
$727$	25.3409	−	14.6306i	0.939841	−	0.542617i	0.889910	+	0.456135i	$0.150767\pi$
$728$	−28.7469	+	10.1782i	−1.06543	+	0.377230i
$729$		0			0
$730$	−6.19804	−	7.47672i	−0.229400	−	0.276726i
$731$	33.3777			1.23452
$732$		0			0
$733$	−25.1580			−0.929233			−0.464616	−	0.885512i	$-0.653808\pi$
$733$	−25.1580			−0.929233			−0.464616	+	0.885512i	$0.653808\pi$
$734$	8.67631	−	23.4024i	0.320248	−	0.863797i
$735$		0			0
$736$	−1.30269	+	6.28491i	−0.0480178	+	0.231665i
$737$	37.0510	−	21.3914i	1.36479	−	0.787962i
$738$		0			0
$739$	7.22239	+	4.16985i	0.265680	+	0.153390i	0.626923	−	0.779081i	$-0.284314\pi$
$739$	7.22239	+	4.16985i	0.265680	+	0.153390i	−0.361243	+	0.932472i	$0.617647\pi$
$740$	−0.815349	−	0.153826i	−0.0299728	−	0.00565477i
$741$		0			0
$742$	5.11076	+	2.92918i	0.187622	+	0.107534i
$743$	4.45643	−	7.71876i	0.163490	−	0.283174i	−0.772628	−	0.634859i	$-0.781058\pi$
$743$	4.45643	−	7.71876i	0.163490	−	0.283174i	0.936118	+	0.351686i	$0.114391\pi$
$744$		0			0
$745$	−10.7156			−0.392589
$746$	22.0560	+	8.17714i	0.807527	+	0.299386i
$747$		0			0
$748$	−7.88198	−	22.4873i	−0.288194	−	0.822217i
$749$	31.8184	+	26.2073i	1.16262	+	0.957595i
$750$		0			0
$751$		−	2.64406i		−	0.0964829i	−0.998836	−	0.0482415i	$-0.984638\pi$
$751$		−	2.64406i		−	0.0964829i	0.998836	−	0.0482415i	$-0.0153617\pi$
$752$	14.7905	+	5.78681i	0.539353	+	0.211023i
$753$		0			0
$754$	−20.1250	+	54.2826i	−0.732910	+	1.97686i
$755$	−7.33041			−0.266781
$756$		0			0
$757$	−7.03030			−0.255521			−0.127760	−	0.991805i	$-0.540779\pi$
$757$	−7.03030			−0.255521			−0.127760	+	0.991805i	$0.540779\pi$
$758$	−6.01302	+	16.2187i	−0.218403	+	0.589091i
$759$		0			0
$760$	−5.98548	+	9.95126i	−0.217116	+	0.360970i
$761$		−	6.63045i		−	0.240354i	−0.992753	−	0.120177i	$-0.961654\pi$
$761$		−	6.63045i		−	0.240354i	0.992753	−	0.120177i	$-0.0383461\pi$
$762$		0			0
$763$	−1.31342	+	7.86832i	−0.0475491	+	0.284852i
$764$	31.9284	−	11.1912i	1.15513	−	0.404882i
$765$		0			0
$766$	14.5590	+	5.39769i	0.526039	+	0.195026i
$767$	0.283872			0.0102500
$768$		0			0
$769$	7.78773	−	13.4887i	0.280833	−	0.486417i	−0.690757	−	0.723087i	$-0.742723\pi$
$769$	7.78773	−	13.4887i	0.280833	−	0.486417i	0.971590	+	0.236670i	$0.0760561\pi$
$770$	−0.0318230	−	10.0597i	−0.00114682	−	0.362526i
$771$		0			0
$772$	−0.946705	+	5.01797i	−0.0340727	+	0.180601i
$773$	−14.6607	−	8.46438i	−0.527310	−	0.304443i	0.212610	−	0.977137i	$-0.431804\pi$
$773$	−14.6607	−	8.46438i	−0.527310	−	0.304443i	−0.739920	+	0.672694i	$0.765137\pi$
$774$		0			0
$775$	−7.85156	+	4.53310i	−0.282036	+	0.162834i
$776$	−25.0841	+	41.7040i	−0.900465	+	1.49708i
$777$		0			0
$778$	−16.1071	+	43.4452i	−0.577467	+	1.55759i
$779$	−38.4796			−1.37867
$780$		0			0
$781$	−8.64607			−0.309381
$782$	−3.78698	−	4.56825i	−0.135422	−	0.163360i
$783$		0			0
$784$	21.3479	+	18.1181i	0.762425	+	0.647076i
$785$	−13.2672	+	7.65982i	−0.473526	+	0.273391i
$786$		0			0
$787$	−36.5083	+	21.0781i	−1.30138	+	0.751352i	−0.980641	−	0.195816i	$-0.937264\pi$
$787$	−36.5083	+	21.0781i	−1.30138	+	0.751352i	−0.320738	+	0.947168i	$0.603931\pi$
$788$	−4.48582	+	5.21819i	−0.159801	+	0.185890i
$789$		0			0
$790$	12.5640	−	10.4153i	0.447007	−	0.370559i
$791$	−32.3544	−	5.40076i	−1.15039	−	0.192029i
$792$		0			0
$793$	−2.63123	−	4.55743i	−0.0934378	−	0.161839i
$794$	−2.40333	−	14.1224i	−0.0852909	−	0.501185i
$795$		0			0
$796$	−13.9589	−	39.8246i	−0.494759	−	1.41155i
$797$	20.8601	+	12.0436i	0.738902	+	0.426605i	0.821670	−	0.569964i	$-0.193043\pi$
$797$	20.8601	+	12.0436i	0.738902	+	0.426605i	−0.0827680	+	0.996569i	$0.526376\pi$
$798$		0			0
$799$	−12.7158	+	7.34146i	−0.449852	+	0.259722i
$800$	4.94106	−	23.8384i	0.174693	−	0.842815i
$801$		0			0
$802$	−3.55661	+	9.59314i	−0.125588	+	0.338746i
$803$	13.2570	−	22.9618i	0.467829	−	0.810303i
$804$		0			0
$805$	−0.878250	−	2.34608i	−0.0309542	−	0.0826885i
$806$	4.22041	−	11.3836i	0.148658	−	0.400970i
$807$		0			0
$808$	8.09267	−	4.48104i	0.284699	−	0.157642i
$809$	32.6788	+	18.8671i	1.14892	+	0.663332i	0.948625	−	0.316403i	$-0.102475\pi$
$809$	32.6788	+	18.8671i	1.14892	+	0.663332i	0.200300	+	0.979735i	$0.435808\pi$
$810$		0			0
$811$			24.1642i			0.848521i	0.905540	+	0.424260i	$0.139466\pi$
$811$			24.1642i			0.848521i	−0.905540	+	0.424260i	$0.860534\pi$
$812$	52.3738	−	9.08346i	1.83796	−	0.318767i
$813$		0			0
$814$	−0.380035	−	2.23315i	−0.0133202	−	0.0782720i
$815$	−1.61434	−	2.79612i	−0.0565478	−	0.0979437i
$816$		0			0
$817$	22.2043	−	38.4590i	0.776832	−	1.34551i
$818$	3.21692	+	18.9032i	0.112477	+	0.660934i
$819$		0			0
$820$	−12.3180	+	4.31757i	−0.430164	+	0.150776i
$821$	−12.4765	−	7.20332i	−0.435433	−	0.251397i	0.266225	−	0.963911i	$-0.414223\pi$
$821$	−12.4765	−	7.20332i	−0.435433	−	0.251397i	−0.701659	+	0.712513i	$0.747557\pi$
$822$		0			0
$823$	29.4566	−	17.0067i	1.02679	−	0.592818i	0.110727	−	0.993851i	$-0.464682\pi$
$823$	29.4566	−	17.0067i	1.02679	−	0.592818i	0.916064	+	0.401033i	$0.131349\pi$
$824$	−0.825049	+	0.456842i	−0.0287419	+	0.0159149i
$825$		0			0
$826$	−0.131035	−	0.225309i	−0.00455927	−	0.00783952i
$827$	21.2801			0.739982			0.369991	−	0.929035i	$-0.379361\pi$
$827$	21.2801			0.739982			0.369991	+	0.929035i	$0.379361\pi$
$828$		0			0
$829$	8.62653	−	14.9416i	0.299612	−	0.518943i	−0.676435	−	0.736502i	$-0.736476\pi$
$829$	8.62653	−	14.9416i	0.299612	−	0.518943i	0.976047	+	0.217559i	$0.0698095\pi$
$830$	6.41066	−	1.09096i	0.222517	−	0.0378677i
$831$		0			0
$832$	15.2791	+	28.7990i	0.529709	+	0.998424i
$833$	−25.4060	+	4.95984i	−0.880266	+	0.171848i
$834$		0			0
$835$	−15.4459	−	8.91769i	−0.534527	−	0.308609i
$836$	−31.1541	−	5.87764i	−1.07749	−	0.203282i
$837$		0			0
$838$	16.9159	−	14.0229i	0.584351	−	0.484414i
$839$	−12.4500	−	21.5640i	−0.429820	−	0.744470i	0.567037	−	0.823692i	$-0.308090\pi$
$839$	−12.4500	−	21.5640i	−0.429820	−	0.744470i	−0.996857	+	0.0792220i	$0.974756\pi$
$840$		0			0
$841$	35.9557	−	62.2771i	1.23985	−	2.14749i
$842$	−7.80950	−	45.8900i	−0.269133	−	1.58147i
$843$		0			0
$844$	−1.47865	−	4.21860i	−0.0508973	−	0.145210i
$845$	2.60652	−	1.50488i	0.0896671	−	0.0517693i
$846$		0			0
$847$	−1.53504	+	0.574640i	−0.0527448	+	0.0197449i
$848$	2.29450	−	5.86450i	0.0787934	−	0.201388i
$849$		0			0
$850$	14.3639	+	17.3272i	0.492677	+	0.594318i
$851$	−0.282047	−	0.488520i	−0.00966846	−	0.0167463i
$852$		0			0
$853$	2.07188	+	3.58860i	0.0709397	+	0.122871i	0.899313	−	0.437305i	$-0.144067\pi$
$853$	2.07188	+	3.58860i	0.0709397	+	0.122871i	−0.828374	+	0.560176i	$0.810734\pi$
$854$	−2.40266	+	4.19210i	−0.0822174	+	0.143451i
$855$		0			0
$856$	22.7138	−	37.7632i	0.776342	−	1.29072i
$857$		−	32.0393i		−	1.09444i	−0.836988	−	0.547221i	$-0.815686\pi$
$857$		−	32.0393i		−	1.09444i	0.836988	−	0.547221i	$-0.184314\pi$
$858$		0			0
$859$			5.83407i			0.199056i	0.995035	+	0.0995280i	$0.0317333\pi$
$859$			5.83407i			0.199056i	−0.995035	+	0.0995280i	$0.968267\pi$
$860$	2.79275	−	14.8029i	0.0952321	−	0.504774i
$861$		0			0
$862$	9.14286	−	7.57923i	0.311407	−	0.258150i
$863$	19.0028	+	32.9139i	0.646864	+	1.12040i	0.983868	+	0.178898i	$0.0572534\pi$
$863$	19.0028	+	32.9139i	0.646864	+	1.12040i	−0.337003	+	0.941504i	$0.609413\pi$
$864$		0			0
$865$	−2.46337	+	4.26668i	−0.0837571	+	0.145072i
$866$	33.8985	+	12.5677i	1.15192	+	0.427067i
$867$		0			0
$868$	−10.9833	+	1.90489i	−0.372797	+	0.0646562i
$869$	38.5853	+	22.2772i	1.30892	+	0.755703i
$870$		0			0
$871$		−	54.1131i		−	1.83355i
$872$	8.52660	+	0.152707i	0.288747	+	0.00517132i
$873$		0			0
$874$	−7.78297	+	1.32450i	−0.263263	+	0.0448017i
$875$	7.20134	+	19.2370i	0.243450	+	0.650331i
$876$		0			0
$877$	5.89561			0.199080			0.0995402	−	0.995034i	$-0.468263\pi$
$877$	5.89561			0.199080			0.0995402	+	0.995034i	$0.468263\pi$
$878$	−5.21447	−	6.29024i	−0.175980	−	0.212285i
$879$		0			0
$880$	−10.6325	+	1.61408i	−0.358422	+	0.0544107i
$881$		−	35.1050i		−	1.18272i	−0.806408	−	0.591359i	$-0.798592\pi$
$881$		−	35.1050i		−	1.18272i	0.806408	−	0.591359i	$-0.201408\pi$
$882$		0			0
$883$			8.65372i			0.291221i	0.989342	+	0.145610i	$0.0465146\pi$
$883$			8.65372i			0.291221i	−0.989342	+	0.145610i	$0.953485\pi$
$884$	−29.6168	−	5.58760i	−0.996121	−	0.187931i
$885$		0			0
$886$	12.8191	−	10.6268i	0.430667	−	0.357014i
$887$	20.1266			0.675785			0.337893	−	0.941185i	$-0.390286\pi$
$887$	20.1266			0.675785			0.337893	+	0.941185i	$0.390286\pi$
$888$		0			0
$889$	−8.51291	−	22.7407i	−0.285514	−	0.762697i
$890$	−1.55989	−	9.16617i	−0.0522875	−	0.307251i
$891$		0			0
$892$	−48.6494	−	9.17835i	−1.62890	−	0.307314i
$893$			19.5355i			0.653729i
$894$		0			0
$895$	−12.0937	−	6.98232i	−0.404249	−	0.233393i
$896$	15.8049	−	25.4205i	0.528006	−	0.849241i
$897$		0			0
$898$	8.81241	−	23.7695i	0.294074	−	0.793198i
$899$	−10.5810	+	18.3269i	−0.352898	+	0.611237i
$900$		0			0
$901$	2.91092	+	5.04187i	0.0969769	+	0.167969i
$902$	−22.7427	−	27.4346i	−0.757248	−	0.913472i
$903$		0			0
$904$	−0.627930	+	35.0612i	−0.0208846	+	1.16612i
$905$		−	3.82946i		−	0.127296i
$906$		0			0
$907$			26.7122i			0.886963i	0.896284	+	0.443481i	$0.146257\pi$
$907$			26.7122i			0.886963i	−0.896284	+	0.443481i	$0.853743\pi$
$908$	12.4877	+	10.7351i	0.414419	+	0.356256i
$909$		0			0
$910$	−11.0393	−	6.32707i	−0.365949	−	0.209740i
$911$	−16.6755	−	28.8829i	−0.552485	−	0.956932i	−0.998094	−	0.0617044i	$-0.980346\pi$
$911$	−16.6755	−	28.8829i	−0.552485	−	0.956932i	0.445610	−	0.895227i	$-0.352987\pi$
$912$		0			0
$913$	8.87670	+	15.3749i	0.293776	+	0.508835i
$914$	−27.2040	+	22.5515i	−0.899827	+	0.745937i
$915$		0			0
$916$	−32.6597	−	28.0760i	−1.07911	−	0.927656i
$917$	−47.4560	+	17.7650i	−1.56713	+	0.586653i
$918$		0			0
$919$	1.30767	−	0.754984i	0.0431361	−	0.0249046i	−0.478277	−	0.878209i	$-0.658738\pi$
$919$	1.30767	−	0.754984i	0.0431361	−	0.0249046i	0.521413	+	0.853304i	$0.325405\pi$
$920$	−2.34286	+	1.29728i	−0.0772417	+	0.0427699i
$921$		0			0
$922$	19.2006	−	3.26754i	0.632339	−	0.107611i
$923$	−5.46792	+	9.47072i	−0.179979	+	0.311733i
$924$		0			0
$925$	1.06980	+	1.85294i	0.0351747	+	0.0609243i
$926$	22.7150	+	27.4012i	0.746461	+	0.900459i
$927$		0			0
$928$	−17.8334	−	53.9549i	−0.585410	−	1.77116i
$929$	20.1730	+	11.6469i	0.661856	+	0.382123i	0.792984	−	0.609243i	$-0.208526\pi$
$929$	20.1730	+	11.6469i	0.661856	+	0.382123i	−0.131128	+	0.991365i	$0.541860\pi$
$930$		0			0
$931$	−11.1863	+	32.5733i	−0.366616	+	1.06755i
$932$	−14.7762	−	2.78772i	−0.484011	−	0.0913149i
$933$		0			0
$934$	10.0353	+	58.9695i	0.328366	+	1.92954i
$935$	4.97111	−	8.61022i	0.162573	−	0.281584i
$936$		0			0
$937$	7.37883			0.241056			0.120528	−	0.992710i	$-0.461541\pi$
$937$	7.37883			0.241056			0.120528	+	0.992710i	$0.461541\pi$
$938$	−42.9496	+	24.9784i	−1.40235	+	0.815575i
$939$		0			0
$940$	2.19196	+	6.25366i	0.0714938	+	0.203972i
$941$	−7.19423	+	4.15359i	−0.234525	+	0.135403i	−0.612658	−	0.790348i	$-0.709900\pi$
$941$	−7.19423	+	4.15359i	−0.234525	+	0.135403i	0.378133	+	0.925751i	$0.376566\pi$
$942$		0			0
$943$	−7.68506	−	4.43697i	−0.250260	−	0.144488i
$944$	−0.217664	+	0.173958i	−0.00708438	+	0.00566186i
$945$		0			0
$946$	40.5434	−	6.89963i	1.31818	−	0.224326i
$947$	−2.55824	+	4.43100i	−0.0831316	+	0.143988i	−0.904594	−	0.426275i	$-0.859826\pi$
$947$	−2.55824	+	4.43100i	−0.0831316	+	0.143988i	0.821462	+	0.570263i	$0.193159\pi$
$948$		0			0
$949$	−16.7679	−	29.0428i	−0.544308	−	0.942770i
$950$	29.5205	−	5.02376i	0.957772	−	0.162992i
$951$		0			0
$952$	9.23614	+	26.0861i	0.299345	+	0.845454i
$953$		−	40.3390i		−	1.30671i	−0.757053	−	0.653354i	$-0.773361\pi$
$953$		−	40.3390i		−	1.30671i	0.757053	−	0.653354i	$-0.226639\pi$
$954$		0			0
$955$	12.2251	+	7.05819i	0.395596	+	0.228398i
$956$	26.5598	−	9.30944i	0.859007	−	0.301089i
$957$		0			0
$958$	38.6413	+	14.3261i	1.24844	+	0.462854i
$959$	−0.319501	−	0.853488i	−0.0103172	−	0.0275606i
$960$		0			0
$961$	−13.2811	+	23.0035i	−0.428421	+	0.742047i
$962$	−2.68649	−	0.996002i	−0.0866158	−	0.0321124i
$963$		0			0
$964$	−18.2865	−	15.7200i	−0.588970	−	0.506308i
$965$	−1.84518	+	1.06531i	−0.0593983	+	0.0342936i
$966$		0			0
$967$	5.32448	+	3.07409i	0.171224	+	0.0988560i	0.583163	−	0.812355i	$-0.301815\pi$
$967$	5.32448	+	3.07409i	0.171224	+	0.0988560i	−0.411939	+	0.911211i	$0.635148\pi$
$968$	0.848810	+	1.53294i	0.0272818	+	0.0492704i
$969$		0			0
$970$	−20.0178	+	3.40659i	−0.642731	+	0.109379i
$971$	−3.82677	−	6.62817i	−0.122807	−	0.212708i	0.798067	−	0.602569i	$-0.205856\pi$
$971$	−3.82677	−	6.62817i	−0.122807	−	0.212708i	−0.920874	+	0.389861i	$0.872523\pi$
$972$		0			0
$973$	13.2532	+	2.21229i	0.424878	+	0.0709228i
$974$	−31.3195	−	37.7809i	−1.00354	−	1.21058i
$975$		0			0
$976$	4.81036	+	1.88206i	0.153976	+	0.0602434i
$977$	−8.95120	+	5.16798i	−0.286374	+	0.165338i	−0.636306	−	0.771437i	$-0.719538\pi$
$977$	−8.95120	+	5.16798i	−0.286374	+	0.165338i	0.349931	+	0.936775i	$0.386205\pi$
$978$		0			0
$979$	21.9835	−	12.6922i	0.702597	−	0.405644i
$980$	0.0739135	+	11.6824i	0.00236108	+	0.373182i
$981$		0			0
$982$	−20.2994	+	16.8278i	−0.647781	+	0.536997i
$983$	1.30705			0.0416884			0.0208442	−	0.999783i	$-0.493365\pi$
$983$	1.30705			0.0416884			0.0208442	+	0.999783i	$0.493365\pi$
$984$		0			0
$985$	−2.87114			−0.0914821
$986$	49.2583	+	18.2623i	1.56870	+	0.581589i
$987$		0			0
$988$	−26.1406	+	30.4085i	−0.831645	+	0.967422i
$989$	8.86921	−	5.12064i	0.282024	−	0.162827i
$990$		0			0
$991$	32.8273	+	18.9529i	1.04280	+	0.602058i	0.920624	−	0.390451i	$-0.127681\pi$
$991$	32.8273	+	18.9529i	1.04280	+	0.602058i	0.122171	+	0.992509i	$0.461014\pi$
$992$	3.73983	+	11.3149i	0.118740	+	0.359247i
$993$		0			0
$994$	10.0409	−	0.0317634i	0.318478	−	0.00100748i
$995$	8.80376	−	15.2486i	0.279098	−	0.483412i
$996$		0			0
$997$	44.0850			1.39619			0.698094	−	0.716007i	$-0.254032\pi$
$997$	44.0850			1.39619			0.698094	+	0.716007i	$0.254032\pi$
$998$	−8.91247	+	24.0394i	−0.282119	+	0.760953i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.o.a.179.6		88
3.2	odd	2		252.2.o.a.95.39	yes	88
4.3	odd	2	inner	756.2.o.a.179.10		88
7.2	even	3		756.2.bb.a.611.25		88
9.2	odd	6		756.2.bb.a.683.20		88
9.7	even	3		252.2.bb.a.11.25	yes	88
12.11	even	2		252.2.o.a.95.35	✓	88
21.2	odd	6		252.2.bb.a.23.20	yes	88
28.23	odd	6		756.2.bb.a.611.20		88
36.7	odd	6		252.2.bb.a.11.20	yes	88
36.11	even	6		756.2.bb.a.683.25		88
63.2	odd	6	inner	756.2.o.a.359.10		88
63.16	even	3		252.2.o.a.191.35	yes	88
84.23	even	6		252.2.bb.a.23.25	yes	88
252.79	odd	6		252.2.o.a.191.39	yes	88
252.191	even	6	inner	756.2.o.a.359.6		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.o.a.95.35	✓	88	12.11	even	2
252.2.o.a.95.39	yes	88	3.2	odd	2
252.2.o.a.191.35	yes	88	63.16	even	3
252.2.o.a.191.39	yes	88	252.79	odd	6
252.2.bb.a.11.20	yes	88	36.7	odd	6
252.2.bb.a.11.25	yes	88	9.7	even	3
252.2.bb.a.23.20	yes	88	21.2	odd	6
252.2.bb.a.23.25	yes	88	84.23	even	6
756.2.o.a.179.6		88	1.1	even	1	trivial
756.2.o.a.179.10		88	4.3	odd	2	inner
756.2.o.a.359.6		88	252.191	even	6	inner
756.2.o.a.359.10		88	63.2	odd	6	inner
756.2.bb.a.611.20		88	28.23	odd	6
756.2.bb.a.611.25		88	7.2	even	3
756.2.bb.a.683.20		88	9.2	odd	6
756.2.bb.a.683.25		88	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.32602 - 0.491613i) q^{2} +(1.51663 + 1.30377i) q^{4} +0.834477i q^{5} +(2.47783 - 0.927568i) q^{7} +(-1.37012 - 2.47442i) q^{8} +O(q^{10})\)	\(q+(-1.32602 - 0.491613i) q^{2} +(1.51663 + 1.30377i) q^{4} +0.834477i q^{5} +(2.47783 - 0.927568i) q^{7} +(-1.37012 - 2.47442i) q^{8} +(0.410240 - 1.10653i) q^{10} +3.22188 q^{11} +(2.03757 - 3.52917i) q^{13} +(-3.74164 + 0.0118363i) q^{14} +(0.600347 + 3.95469i) q^{16} +(-3.20251 - 1.84897i) q^{17} +(-4.26091 + 2.46004i) q^{19} +(-1.08797 + 1.26559i) q^{20} +(-4.27226 - 1.58392i) q^{22} -1.13464 q^{23} +4.30365 q^{25} +(-4.43684 + 3.67804i) q^{26} +(4.96729 + 1.82374i) q^{28} +(8.69963 - 5.02273i) q^{29} +(-1.82440 + 1.05332i) q^{31} +(1.14811 - 5.53912i) q^{32} +(3.33760 + 4.02617i) q^{34} +(0.774034 + 2.06769i) q^{35} +(0.248579 + 0.430551i) q^{37} +(6.85942 - 1.16733i) q^{38} +(2.06485 - 1.14334i) q^{40} +(6.77313 + 3.91047i) q^{41} +(-7.81676 + 4.51301i) q^{43} +(4.88640 + 4.20060i) q^{44} +(1.50455 + 0.557804i) q^{46} +(1.98528 - 3.43861i) q^{47} +(5.27924 - 4.59670i) q^{49} +(-5.70670 - 2.11573i) q^{50} +(7.69149 - 2.69593i) q^{52} +(-1.36342 - 0.787173i) q^{53} +2.68858i q^{55} +(-5.69012 - 4.86030i) q^{56} +(-14.0051 + 2.38337i) q^{58} +(0.0348298 + 0.0603270i) q^{59} +(0.645679 - 1.11835i) q^{61} +(2.93700 - 0.499815i) q^{62} +(-4.24552 + 6.78053i) q^{64} +(2.94501 + 1.70030i) q^{65} +(11.4998 - 6.63942i) q^{67} +(-2.44640 - 6.97957i) q^{68} +(-0.00987715 - 3.12231i) q^{70} -2.68355 q^{71} +(4.11468 - 7.12683i) q^{73} +(-0.117954 - 0.693122i) q^{74} +(-9.66957 - 1.82429i) q^{76} +(7.98325 - 2.98851i) q^{77} +(11.9760 + 6.91436i) q^{79} +(-3.30010 + 0.500976i) q^{80} +(-7.05883 - 8.51510i) q^{82} +(2.75513 + 4.77203i) q^{83} +(1.54293 - 2.67243i) q^{85} +(12.5838 - 2.14149i) q^{86} +(-4.41437 - 7.97228i) q^{88} +(6.82321 - 3.93938i) q^{89} +(1.77519 - 10.6347i) q^{91} +(-1.72083 - 1.47931i) q^{92} +(-4.32298 + 3.58365i) q^{94} +(-2.05284 - 3.55563i) q^{95} +(-8.60311 - 14.9010i) q^{97} +(-9.26015 + 3.49995i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 3 q^{2} + q^{4}+O(q^{10}) \) 88 * q + 3 * q^2 + q^4	\( 88 q + 3 q^{2} + q^{4} + 2 q^{10} - 4 q^{13} + 3 q^{14} + q^{16} + 6 q^{20} - 6 q^{22} - 60 q^{25} + 6 q^{26} + 24 q^{29} - 27 q^{32} - 4 q^{34} - 4 q^{37} + 8 q^{40} + 12 q^{41} + 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} + 14 q^{52} + 66 q^{56} - 10 q^{58} + 2 q^{61} - 8 q^{64} - 18 q^{65} + 30 q^{70} - 4 q^{73} - 6 q^{76} + 30 q^{77} - 87 q^{80} - 4 q^{82} - 14 q^{85} - 18 q^{88} - 60 q^{89} - 24 q^{92} + 9 q^{94} - 4 q^{97} + 57 q^{98}+O(q^{100}) \) 88 * q + 3 * q^2 + q^4 + 2 * q^10 - 4 * q^13 + 3 * q^14 + q^16 + 6 * q^20 - 6 * q^22 - 60 * q^25 + 6 * q^26 + 24 * q^29 - 27 * q^32 - 4 * q^34 - 4 * q^37 + 8 * q^40 + 12 * q^41 + 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 + 14 * q^52 + 66 * q^56 - 10 * q^58 + 2 * q^61 - 8 * q^64 - 18 * q^65 + 30 * q^70 - 4 * q^73 - 6 * q^76 + 30 * q^77 - 87 * q^80 - 4 * q^82 - 14 * q^85 - 18 * q^88 - 60 * q^89 - 24 * q^92 + 9 * q^94 - 4 * q^97 + 57 * q^98

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