LMFDB - Embedded newform 855.2.da.b.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(199,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 8]))

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

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

chi := DirichletCharacter("855.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.da (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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			289.1
Character	$\chi$	$=$	855.289
Dual form			855.2.da.b.784.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.810919 + 2.22798i) q^{2} +(-2.77422 - 2.32785i) q^{4} +(0.323811 + 2.21250i) q^{5} +(1.41749 + 0.818386i) q^{7} +(3.32944 - 1.92225i) q^{8} +O(q^{10})$	\(q+(-0.810919 + 2.22798i) q^{2} +(-2.77422 - 2.32785i) q^{4} +(0.323811 + 2.21250i) q^{5} +(1.41749 + 0.818386i) q^{7} +(3.32944 - 1.92225i) q^{8} +(-5.19199 - 1.07271i) q^{10} +(1.36374 + 2.36206i) q^{11} +(6.10515 + 1.07650i) q^{13} +(-2.97282 + 2.49449i) q^{14} +(0.325107 + 1.84377i) q^{16} +(-1.06864 + 2.93608i) q^{17} +(3.46824 + 2.64032i) q^{19} +(4.25204 - 6.89175i) q^{20} +(-6.36852 + 1.12294i) q^{22} +(4.69173 - 5.59139i) q^{23} +(-4.79029 + 1.43286i) q^{25} +(-7.34921 + 12.7292i) q^{26} +(-2.02734 - 5.57008i) q^{28} +(-2.09149 + 0.761241i) q^{29} +(-2.21333 + 3.83360i) q^{31} +(3.20067 + 0.564364i) q^{32} +(-5.67494 - 4.76184i) q^{34} +(-1.35168 + 3.40119i) q^{35} +2.04016i q^{37} +(-8.69505 + 5.58609i) q^{38} +(5.33109 + 6.74393i) q^{40} +(-0.681538 - 3.86519i) q^{41} +(0.303946 + 0.362229i) q^{43} +(1.71522 - 9.72747i) q^{44} +(8.65289 + 14.9872i) q^{46} +(-0.787194 - 2.16280i) q^{47} +(-2.16049 - 3.74208i) q^{49} +(0.692149 - 11.8346i) q^{50} +(-14.4311 - 17.1983i) q^{52} +(-4.09062 + 4.87501i) q^{53} +(-4.78447 + 3.78213i) q^{55} +6.29258 q^{56} -5.27711i q^{58} +(-11.5263 - 4.19524i) q^{59} +(-3.66993 - 3.07944i) q^{61} +(-6.74636 - 8.03999i) q^{62} +(-5.72509 + 9.91615i) q^{64} +(-0.404845 + 13.8562i) q^{65} +(-0.229482 - 0.630496i) q^{67} +(9.79940 - 5.65769i) q^{68} +(-6.48168 - 5.76960i) q^{70} +(-2.01848 + 1.69370i) q^{71} +(6.41403 - 1.13097i) q^{73} +(-4.54543 - 1.65440i) q^{74} +(-3.47540 - 15.3984i) q^{76} +4.46426i q^{77} +(-0.715459 - 4.05757i) q^{79} +(-3.97407 + 1.31633i) q^{80} +(9.16425 + 1.61590i) q^{82} +(5.56331 + 3.21198i) q^{83} +(-6.84210 - 1.41364i) q^{85} +(-1.05351 + 0.383448i) q^{86} +(9.08097 + 5.24290i) q^{88} +(3.00487 - 17.0415i) q^{89} +(7.77297 + 6.52229i) q^{91} +(-26.0318 + 4.59011i) q^{92} +5.45702 q^{94} +(-4.71865 + 8.52844i) q^{95} +(0.0444434 - 0.122107i) q^{97} +(10.0893 - 1.77901i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 18 q^{4} + 6 q^{5}+O(q^{10}) $ 48 * q - 18 * q^4 + 6 * q^5	$ 48 q - 18 q^{4} + 6 q^{5} - 15 q^{10} + 12 q^{11} - 6 q^{14} - 42 q^{16} + 12 q^{19} - 42 q^{20} + 12 q^{25} - 12 q^{26} - 42 q^{31} - 36 q^{34} - 6 q^{35} + 66 q^{40} - 6 q^{41} + 6 q^{44} - 6 q^{46} + 12 q^{49} + 18 q^{50} - 36 q^{56} + 36 q^{59} + 48 q^{61} + 18 q^{65} - 123 q^{70} + 24 q^{71} - 84 q^{74} + 66 q^{76} + 48 q^{79} + 39 q^{80} - 84 q^{85} + 42 q^{86} + 12 q^{89} - 30 q^{91} - 72 q^{94} + 63 q^{95}+O(q^{100}) $ 48 * q - 18 * q^4 + 6 * q^5 - 15 * q^10 + 12 * q^11 - 6 * q^14 - 42 * q^16 + 12 * q^19 - 42 * q^20 + 12 * q^25 - 12 * q^26 - 42 * q^31 - 36 * q^34 - 6 * q^35 + 66 * q^40 - 6 * q^41 + 6 * q^44 - 6 * q^46 + 12 * q^49 + 18 * q^50 - 36 * q^56 + 36 * q^59 + 48 * q^61 + 18 * q^65 - 123 * q^70 + 24 * q^71 - 84 * q^74 + 66 * q^76 + 48 * q^79 + 39 * q^80 - 84 * q^85 + 42 * q^86 + 12 * q^89 - 30 * q^91 - 72 * q^94 + 63 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−0.810919	+	2.22798i	−0.573406	+	1.57542i	0.225678	+	0.974202i	$0.427540\pi$
$2$	−0.810919	+	2.22798i	−0.573406	+	1.57542i	−0.799084	+	0.601219i	$0.794682\pi$
$3$		0			0
$3$		0			0
$4$	−2.77422	−	2.32785i	−1.38711	−	1.16392i
$5$	0.323811	+	2.21250i	0.144813	+	0.989459i
$5$	0.323811	+	2.21250i	0.144813	+	0.989459i
$6$		0			0
$7$	1.41749	+	0.818386i	0.535759	+	0.309321i	0.743359	−	0.668893i	$-0.233232\pi$
$7$	1.41749	+	0.818386i	0.535759	+	0.309321i	−0.207599	+	0.978214i	$0.566565\pi$
$8$	3.32944	−	1.92225i	1.17713	−	0.679619i
$9$		0			0
$10$	−5.19199	−	1.07271i	−1.64185	−	0.339221i
$11$	1.36374	+	2.36206i	0.411183	+	0.712189i	0.995019	−	0.0996818i	$-0.0317825\pi$
$11$	1.36374	+	2.36206i	0.411183	+	0.712189i	−0.583837	+	0.811871i	$0.698449\pi$
$12$		0			0
$13$	6.10515	+	1.07650i	1.69326	+	0.298568i	0.935333	−	0.353768i	$-0.115100\pi$
$13$	6.10515	+	1.07650i	1.69326	+	0.298568i	0.757930	+	0.652336i	$0.226211\pi$
$14$	−2.97282	+	2.49449i	−0.794518	+	0.666680i
$15$		0			0
$16$	0.325107	+	1.84377i	0.0812767	+	0.460943i
$17$	−1.06864	+	2.93608i	−0.259184	+	0.712103i	0.740034	+	0.672570i	$0.234809\pi$
$17$	−1.06864	+	2.93608i	−0.259184	+	0.712103i	−0.999218	+	0.0395336i	$0.987413\pi$
$18$		0			0
$19$	3.46824	+	2.64032i	0.795669	+	0.605732i
$19$	3.46824	+	2.64032i	0.795669	+	0.605732i
$20$	4.25204	−	6.89175i	0.950785	−	1.54104i
$21$		0			0
$22$	−6.36852	+	1.12294i	−1.35777	+	0.239412i
$23$	4.69173	−	5.59139i	0.978293	−	1.16588i	−0.00784655	−	0.999969i	$-0.502498\pi$
$23$	4.69173	−	5.59139i	0.978293	−	1.16588i	0.986140	−	0.165915i	$-0.0530579\pi$
$24$		0			0
$25$	−4.79029	+	1.43286i	−0.958059	+	0.286572i
$26$	−7.34921	+	12.7292i	−1.44130	+	2.49640i
$27$		0			0
$28$	−2.02734	−	5.57008i	−0.383132	−	1.05265i
$29$	−2.09149	+	0.761241i	−0.388381	+	0.141359i	−0.528828	−	0.848729i	$-0.677368\pi$
$29$	−2.09149	+	0.761241i	−0.388381	+	0.141359i	0.140447	+	0.990088i	$0.455146\pi$
$30$		0			0
$31$	−2.21333	+	3.83360i	−0.397526	+	0.688535i	−0.993420	−	0.114528i	$-0.963464\pi$
$31$	−2.21333	+	3.83360i	−0.397526	+	0.688535i	0.595894	+	0.803063i	$0.296798\pi$
$32$	3.20067	+	0.564364i	0.565804	+	0.0997665i
$33$		0			0
$34$	−5.67494	−	4.76184i	−0.973244	−	0.816649i
$35$	−1.35168	+	3.40119i	−0.228476	+	0.574906i
$36$		0			0
$37$			2.04016i			0.335400i	0.985838	+	0.167700i	$0.0536339\pi$
$37$			2.04016i			0.335400i	−0.985838	+	0.167700i	$0.946366\pi$
$38$	−8.69505	+	5.58609i	−1.41052	+	0.906183i
$39$		0			0
$40$	5.33109	+	6.74393i	0.842919	+	1.06631i
$41$	−0.681538	−	3.86519i	−0.106438	−	0.603642i	−0.990636	−	0.136529i	$-0.956405\pi$
$41$	−0.681538	−	3.86519i	−0.106438	−	0.603642i	0.884198	−	0.467113i	$-0.154706\pi$
$42$		0			0
$43$	0.303946	+	0.362229i	0.0463513	+	0.0552394i	0.788722	−	0.614750i	$-0.210743\pi$
$43$	0.303946	+	0.362229i	0.0463513	+	0.0552394i	−0.742371	+	0.669989i	$0.766299\pi$
$44$	1.71522	−	9.72747i	0.258579	−	1.46647i
$45$		0			0
$46$	8.65289	+	14.9872i	1.27580	+	2.20975i
$47$	−0.787194	−	2.16280i	−0.114824	−	0.315477i	0.868947	−	0.494905i	$-0.164797\pi$
$47$	−0.787194	−	2.16280i	−0.114824	−	0.315477i	−0.983771	+	0.179429i	$0.942575\pi$
$48$		0			0
$49$	−2.16049	−	3.74208i	−0.308641	−	0.534582i
$50$	0.692149	−	11.8346i	0.0978847	−	1.67367i
$51$		0			0
$52$	−14.4311	−	17.1983i	−2.00123	−	2.38498i
$53$	−4.09062	+	4.87501i	−0.561890	+	0.669634i	−0.969945	−	0.243323i	$-0.921762\pi$
$53$	−4.09062	+	4.87501i	−0.561890	+	0.669634i	0.408056	+	0.912957i	$0.366207\pi$
$54$		0			0
$55$	−4.78447	+	3.78213i	−0.645138	+	0.509983i
$56$	6.29258			0.840881
$57$		0			0
$58$		−	5.27711i		−	0.692919i
$59$	−11.5263	−	4.19524i	−1.50060	−	0.546174i	−0.544385	−	0.838835i	$-0.683237\pi$
$59$	−11.5263	−	4.19524i	−1.50060	−	0.546174i	−0.956216	+	0.292661i	$0.905459\pi$
$60$		0			0
$61$	−3.66993	−	3.07944i	−0.469887	−	0.394282i	0.376867	−	0.926268i	$-0.377002\pi$
$61$	−3.66993	−	3.07944i	−0.469887	−	0.394282i	−0.846753	+	0.531986i	$0.821446\pi$
$62$	−6.74636	−	8.03999i	−0.856788	−	1.02108i
$63$		0			0
$64$	−5.72509	+	9.91615i	−0.715637	+	1.23952i
$65$	−0.404845	+	13.8562i	−0.0502149	+	1.71865i
$66$		0			0
$67$	−0.229482	−	0.630496i	−0.0280357	−	0.0770274i	0.924885	−	0.380246i	$-0.124161\pi$
$67$	−0.229482	−	0.630496i	−0.0280357	−	0.0770274i	−0.952921	+	0.303219i	$0.901939\pi$
$68$	9.79940	−	5.65769i	1.18835	−	0.686095i
$69$		0			0
$70$	−6.48168	−	5.76960i	−0.774709	−	0.689600i
$71$	−2.01848	+	1.69370i	−0.239549	+	0.201006i	−0.754657	−	0.656120i	$-0.772197\pi$
$71$	−2.01848	+	1.69370i	−0.239549	+	0.201006i	0.515107	+	0.857126i	$0.327752\pi$
$72$		0			0
$73$	6.41403	−	1.13097i	0.750706	−	0.132370i	0.214812	−	0.976655i	$-0.431086\pi$
$73$	6.41403	−	1.13097i	0.750706	−	0.132370i	0.535893	+	0.844286i	$0.319975\pi$
$74$	−4.54543	−	1.65440i	−0.528395	−	0.192320i
$75$		0			0
$76$	−3.47540	−	15.3984i	−0.398656	−	1.76632i
$77$			4.46426i			0.508750i
$78$		0			0
$79$	−0.715459	−	4.05757i	−0.0804954	−	0.456512i	−0.998238	−	0.0593365i	$-0.981101\pi$
$79$	−0.715459	−	4.05757i	−0.0804954	−	0.456512i	0.917743	−	0.397176i	$-0.130010\pi$
$80$	−3.97407	+	1.31633i	−0.444314	+	0.147170i
$81$		0			0
$82$	9.16425	+	1.61590i	1.01202	+	0.178447i
$83$	5.56331	+	3.21198i	0.610653	+	0.352560i	0.773221	−	0.634137i	$-0.218644\pi$
$83$	5.56331	+	3.21198i	0.610653	+	0.352560i	−0.162568	+	0.986697i	$0.551978\pi$
$84$		0			0
$85$	−6.84210	−	1.41364i	−0.742130	−	0.153331i
$86$	−1.05351	+	0.383448i	−0.113603	+	0.0413483i
$87$		0			0
$88$	9.08097	+	5.24290i	0.968034	+	0.558895i
$89$	3.00487	−	17.0415i	0.318516	−	1.80639i	−0.233276	−	0.972411i	$-0.574944\pi$
$89$	3.00487	−	17.0415i	0.318516	−	1.80639i	0.551791	−	0.833982i	$-0.313944\pi$
$90$		0			0
$91$	7.77297	+	6.52229i	0.814828	+	0.683722i
$92$	−26.0318	+	4.59011i	−2.71400	+	0.478552i
$93$		0			0
$94$	5.45702			0.562849
$95$	−4.71865	+	8.52844i	−0.484124	+	0.875000i
$96$		0			0
$97$	0.0444434	−	0.122107i	0.00451254	−	0.0123981i	−0.937416	−	0.348212i	$-0.886789\pi$
$97$	0.0444434	−	0.122107i	0.00451254	−	0.0123981i	0.941928	+	0.335814i	$0.109011\pi$
$98$	10.0893	−	1.77901i	1.01917	−	0.179707i
$99$		0			0
$100$	16.6248	+	7.17600i	1.66248	+	0.717600i
$101$	−0.648657	+	3.67872i	−0.0645438	+	0.366046i	0.935379	+	0.353646i	$0.115058\pi$
$101$	−0.648657	+	3.67872i	−0.0645438	+	0.366046i	−0.999923	+	0.0123999i	$0.996053\pi$
$102$		0			0
$103$	−5.71537	+	3.29977i	−0.563152	+	0.325136i	−0.754410	−	0.656404i	$-0.772077\pi$
$103$	−5.71537	+	3.29977i	−0.563152	+	0.325136i	0.191258	+	0.981540i	$0.438743\pi$
$104$	22.3960	−	8.15148i	2.19611	−	0.799319i
$105$		0			0
$106$	−7.54427	−	13.0671i	−0.732764	−	1.26918i
$107$	10.2150	+	5.89764i	0.987522	+	0.570146i	0.904533	−	0.426404i	$-0.140220\pi$
$107$	10.2150	+	5.89764i	0.987522	+	0.570146i	0.0829897	+	0.996550i	$0.473553\pi$
$108$		0			0
$109$	−5.54468	+	4.65254i	−0.531084	+	0.445632i	−0.868475	−	0.495732i	$-0.834900\pi$
$109$	−5.54468	+	4.65254i	−0.531084	+	0.445632i	0.337392	+	0.941364i	$0.390455\pi$
$110$	−4.54670	−	13.7267i	−0.433511	−	1.30879i
$111$		0			0
$112$	−1.04808	+	2.87958i	−0.0990345	+	0.272095i
$113$		−	13.2879i		−	1.25002i	−0.780616	−	0.625010i	$-0.785095\pi$
$113$		−	13.2879i		−	1.25002i	0.780616	−	0.625010i	$-0.214905\pi$
$114$		0			0
$115$	13.8902	+	8.56989i	1.29526	+	0.799146i
$116$	7.57432	+	2.75683i	0.703258	+	0.255965i
$117$		0			0
$118$	18.6939	−	22.2785i	1.72091	−	2.05090i
$119$	−3.91763	+	3.28728i	−0.359129	+	0.301345i
$120$		0			0
$121$	1.78043	−	3.08380i	0.161858	−	0.280345i
$122$	9.83695	−	5.67937i	0.890596	−	0.514186i
$123$		0			0
$124$	15.0643	−	5.48296i	1.35282	−	0.492384i
$125$	−4.72135	−	10.1345i	−0.422291	−	0.906460i
$126$		0			0
$127$	8.56161	+	1.50964i	0.759720	+	0.133959i	0.540071	−	0.841620i	$-0.318397\pi$
$127$	8.56161	+	1.50964i	0.759720	+	0.133959i	0.219650	+	0.975579i	$0.429509\pi$
$128$	−13.2722	−	15.8172i	−1.17311	−	1.39806i
$129$		0			0
$130$	−30.5431	−	12.1382i	−2.67881	−	1.06459i
$131$	9.90994	+	3.60692i	0.865835	+	0.315138i	0.736479	−	0.676460i	$-0.236487\pi$
$131$	9.90994	+	3.60692i	0.865835	+	0.315138i	0.129356	+	0.991598i	$0.458709\pi$
$132$		0			0
$133$	2.75538	+	6.58098i	0.238922	+	0.570643i
$134$	1.59083			0.137426
$135$		0			0
$136$	2.08589	+	11.8297i	0.178864	+	1.01439i
$137$	−0.255327	+	0.304287i	−0.0218141	+	0.0259970i	−0.776841	−	0.629697i	$-0.783179\pi$
$137$	−0.255327	+	0.304287i	−0.0218141	+	0.0259970i	0.755027	+	0.655694i	$0.227624\pi$
$138$		0			0
$139$	1.30330	−	7.39141i	0.110545	−	0.626931i	−0.878315	−	0.478082i	$-0.841332\pi$
$139$	1.30330	−	7.39141i	0.110545	−	0.626931i	0.988860	−	0.148849i	$-0.0475568\pi$
$140$	11.6673	−	6.28915i	0.986068	−	0.531530i
$141$		0			0
$142$	−2.13672	−	5.87059i	−0.179310	−	0.492649i
$143$	5.78306	+	15.8888i	0.483604	+	1.32869i
$144$		0			0
$145$	−2.36149	−	4.38093i	−0.196111	−	0.363816i
$146$	−2.68149	+	15.2075i	−0.221922	+	1.25858i
$147$		0			0
$148$	4.74918	−	5.65985i	0.390380	−	0.465237i
$149$	−0.640034	−	3.62981i	−0.0524336	−	0.297366i	0.947302	−	0.320341i	$-0.103797\pi$
$149$	−0.640034	−	3.62981i	−0.0524336	−	0.297366i	−0.999736	+	0.0229749i	$0.992686\pi$
$150$		0			0
$151$	−4.49051			−0.365433			−0.182716	−	0.983166i	$-0.558489\pi$
$151$	−4.49051			−0.365433			−0.182716	+	0.983166i	$0.558489\pi$
$152$	16.6227	+	2.12396i	1.34828	+	0.172276i
$153$		0			0
$154$	−9.94629	−	3.62015i	−0.801495	−	0.291720i
$155$	−9.19853	−	3.65563i	−0.738844	−	0.293627i
$156$		0			0
$157$	13.0262	+	15.5240i	1.03960	+	1.23895i	0.970439	+	0.241345i	$0.0775886\pi$
$157$	13.0262	+	15.5240i	1.03960	+	1.23895i	0.0691635	+	0.997605i	$0.477967\pi$
$158$	9.62037	+	1.69633i	0.765355	+	0.134953i
$159$		0			0
$160$	−0.212243	+	7.26422i	−0.0167793	+	0.574287i
$161$	11.2264	−	4.08607i	0.884762	−	0.322027i
$162$		0			0
$163$	−13.5611	+	7.82949i	−1.06219	+	0.613253i	−0.926036	−	0.377436i	$-0.876806\pi$
$163$	−13.5611	+	7.82949i	−1.06219	+	0.613253i	−0.136149	+	0.990688i	$0.543473\pi$
$164$	−7.10685	+	12.3094i	−0.554952	+	0.961205i
$165$		0			0
$166$	−11.6676	+	9.79030i	−0.905583	+	0.759875i
$167$	3.88610	−	4.63128i	0.300716	−	0.358379i	−0.594434	−	0.804144i	$-0.702624\pi$
$167$	3.88610	−	4.63128i	0.300716	−	0.358379i	0.895150	+	0.445765i	$0.147068\pi$
$168$		0			0
$169$	23.8980	+	8.69815i	1.83831	+	0.669088i
$170$	8.69795	−	14.0977i	0.667103	−	1.08125i
$171$		0			0
$172$		−	1.71244i		−	0.130573i
$173$	0.561050	−	1.54147i	0.0426558	−	0.117196i	−0.916536	−	0.399952i	$-0.869027\pi$
$173$	0.561050	−	1.54147i	0.0426558	−	0.117196i	0.959192	+	0.282757i	$0.0912489\pi$
$174$		0			0
$175$	−7.96281	−	1.88925i	−0.601932	−	0.142814i
$176$	−3.91175	+	3.28235i	−0.294859	+	0.247416i
$177$		0			0
$178$	35.5314	+	20.5141i	2.66319	+	1.53759i
$179$	7.09424	+	12.2876i	0.530248	+	0.918417i	0.999377	+	0.0352872i	$0.0112346\pi$
$179$	7.09424	+	12.2876i	0.530248	+	0.918417i	−0.469129	+	0.883130i	$0.655432\pi$
$180$		0			0
$181$	−21.5620	+	7.84794i	−1.60269	+	0.583333i	−0.979976	−	0.199113i	$-0.936194\pi$
$181$	−21.5620	+	7.84794i	−1.60269	+	0.583333i	−0.622718	+	0.782446i	$0.713972\pi$
$182$	−20.8348	+	12.0290i	−1.54438	+	0.891647i
$183$		0			0
$184$	4.87277	−	27.6349i	0.359226	−	2.03727i
$185$	−4.51384	+	0.660625i	−0.331864	+	0.0485701i
$186$		0			0
$187$	−8.39256	+	1.47983i	−0.613724	+	0.108216i
$188$	−2.85082	+	7.83255i	−0.207917	+	0.571248i
$189$		0			0
$190$	−15.1748	−	17.4289i	−1.10089	−	1.26443i
$191$	−10.2099			−0.738762			−0.369381	−	0.929278i	$-0.620430\pi$
$191$	−10.2099			−0.738762			−0.369381	+	0.929278i	$0.620430\pi$
$192$		0			0
$193$	−11.6515	+	2.05447i	−0.838693	+	0.147884i	−0.576465	−	0.817122i	$-0.695568\pi$
$193$	−11.6515	+	2.05447i	−0.838693	+	0.147884i	−0.262228	+	0.965006i	$0.584457\pi$
$194$	0.236012	+	0.198038i	0.0169447	+	0.0142183i
$195$		0			0
$196$	−2.71731	+	15.4106i	−0.194094	+	1.10076i
$197$	2.36143	+	1.36337i	0.168245	+	0.0971363i	0.581758	−	0.813362i	$-0.302365\pi$
$197$	2.36143	+	1.36337i	0.168245	+	0.0971363i	−0.413513	+	0.910498i	$0.635698\pi$
$198$		0			0
$199$	4.20830	−	1.53170i	0.298319	−	0.108579i	−0.188525	−	0.982068i	$-0.560371\pi$
$199$	4.20830	−	1.53170i	0.298319	−	0.108579i	0.486843	+	0.873489i	$0.338148\pi$
$200$	−13.1947	+	13.9788i	−0.933003	+	0.988449i
$201$		0			0
$202$	−7.67010	−	4.42834i	−0.539666	−	0.311577i
$203$	−3.58765	−	0.632600i	−0.251804	−	0.0443998i
$204$		0			0
$205$	8.33104	−	2.75949i	0.581865	−	0.192731i
$206$	−2.71712	−	15.4096i	−0.189311	−	1.07364i
$207$		0			0
$208$			11.6065i			0.804764i
$209$	−1.50684	+	11.7929i	−0.104230	+	0.815733i
$210$		0			0
$211$	6.89756	+	2.51051i	0.474847	+	0.172830i	0.568347	−	0.822789i	$-0.307583\pi$
$211$	6.89756	+	2.51051i	0.474847	+	0.172830i	−0.0934995	+	0.995619i	$0.529805\pi$
$212$	22.6966	−	4.00202i	1.55881	−	0.274860i
$213$		0			0
$214$	−21.4234	+	17.9763i	−1.46447	+	1.22884i
$215$	−0.703009	+	0.789774i	−0.0479448	+	0.0538621i
$216$		0			0
$217$	−6.27473	+	3.62272i	−0.425956	+	0.245926i
$218$	−5.86948	−	16.1263i	−0.397532	−	1.09221i
$219$		0			0
$220$	22.0774	+	0.645049i	1.48846	+	0.0434892i
$221$	−9.68493	+	16.7748i	−0.651479	+	1.12839i
$222$		0			0
$223$	−10.6581	−	12.7019i	−0.713721	−	0.850580i	0.280284	−	0.959917i	$-0.409571\pi$
$223$	−10.6581	−	12.7019i	−0.713721	−	0.850580i	−0.994005	+	0.109338i	$0.965127\pi$
$224$	4.07504	+	3.41936i	0.272275	+	0.228466i
$225$		0			0
$226$	29.6052	+	10.7754i	1.96931	+	0.716770i
$227$			11.7828i			0.782052i	0.920380	+	0.391026i	$0.127880\pi$
$227$			11.7828i			0.782052i	−0.920380	+	0.391026i	$0.872120\pi$
$228$		0			0
$229$	7.82331			0.516979			0.258490	−	0.966014i	$-0.416775\pi$
$229$	7.82331			0.516979			0.258490	+	0.966014i	$0.416775\pi$
$230$	−30.3574	+	23.9975i	−2.00170	+	1.58235i
$231$		0			0
$232$	−5.50020	+	6.55488i	−0.361106	+	0.430349i
$233$	4.31937	+	5.14763i	0.282971	+	0.337232i	0.888742	−	0.458407i	$-0.151580\pi$
$233$	4.31937	+	5.14763i	0.282971	+	0.337232i	−0.605771	+	0.795639i	$0.707135\pi$
$234$		0			0
$235$	4.53028	−	2.44200i	0.295523	−	0.159299i
$236$	22.2107	+	38.4701i	1.44580	+	2.50419i
$237$		0			0
$238$	−4.14713	−	11.3941i	−0.268818	−	0.738572i
$239$	7.98728	+	13.8344i	0.516654	+	0.894871i	0.999813	+	0.0193382i	$0.00615593\pi$
$239$	7.98728	+	13.8344i	0.516654	+	0.894871i	−0.483159	+	0.875533i	$0.660511\pi$
$240$		0			0
$241$	1.81557	−	10.2966i	0.116951	−	0.663261i	−0.868815	−	0.495137i	$-0.835118\pi$
$241$	1.81557	−	10.2966i	0.116951	−	0.663261i	0.985766	−	0.168124i	$-0.0537710\pi$
$242$	5.42686	+	6.46748i	0.348852	+	0.415746i
$243$		0			0
$244$	3.01274	+	17.0861i	0.192871	+	1.09383i
$245$	7.57974	−	5.99180i	0.484252	−	0.382802i
$246$		0			0
$247$	18.3318	+	19.8531i	1.16642	+	1.26322i
$248$			17.0183i			1.08066i
$249$		0			0
$250$	26.4082	−	2.30080i	1.67020	−	0.145515i
$251$	9.08999	+	7.62741i	0.573755	+	0.481438i	0.882890	−	0.469581i	$-0.155595\pi$
$251$	9.08999	+	7.62741i	0.573755	+	0.481438i	−0.309135	+	0.951018i	$0.600039\pi$
$252$		0			0
$253$	19.6055	+	3.45698i	1.23259	+	0.217339i
$254$	−10.3062	+	17.8509i	−0.646670	+	1.12007i
$255$		0			0
$256$	24.4839	−	8.91141i	1.53024	−	0.556963i
$257$	−1.30525	−	3.58614i	−0.0814191	−	0.223697i	0.892303	−	0.451437i	$-0.149089\pi$
$257$	−1.30525	−	3.58614i	−0.0814191	−	0.223697i	−0.973722	+	0.227740i	$0.926866\pi$
$258$		0			0
$259$	−1.66963	+	2.89189i	−0.103746	+	0.179693i
$260$	33.3783	−	37.4978i	2.07003	−	2.32551i
$261$		0			0
$262$	−16.0723	+	19.1542i	−0.992951	+	1.18335i
$263$	2.08737	−	0.368060i	0.128713	−	0.0226956i	−0.108921	−	0.994050i	$-0.534739\pi$
$263$	2.08737	−	0.368060i	0.128713	−	0.0226956i	0.237633	+	0.971355i	$0.423628\pi$
$264$		0			0
$265$	−12.1105	−	7.47190i	−0.743944	−	0.458995i
$266$	−16.8967	+	0.802292i	−1.03600	+	0.0491917i
$267$		0			0
$268$	−0.831067	+	2.28334i	−0.0507655	+	0.139477i
$269$	−0.682137	−	3.86859i	−0.0415906	−	0.235872i	0.956925	−	0.290335i	$-0.0937666\pi$
$269$	−0.682137	−	3.86859i	−0.0415906	−	0.235872i	−0.998516	+	0.0544625i	$0.982655\pi$
$270$		0			0
$271$	14.5057	−	12.1717i	0.881159	−	0.739380i	−0.0852584	−	0.996359i	$-0.527172\pi$
$271$	14.5057	−	12.1717i	0.881159	−	0.739380i	0.966417	+	0.256979i	$0.0827271\pi$
$272$	−5.76088	−	1.01580i	−0.349305	−	0.0615918i
$273$		0			0
$274$	−0.470897	−	0.815617i	−0.0284479	−	0.0492732i
$275$	−9.91722	−	9.36093i	−0.598031	−	0.564486i
$276$		0			0
$277$	13.0141	−	7.51370i	0.781942	−	0.451454i	−0.0551762	−	0.998477i	$-0.517572\pi$
$277$	13.0141	−	7.51370i	0.781942	−	0.451454i	0.837118	+	0.547022i	$0.184239\pi$
$278$	15.4110	+	8.89757i	0.924293	+	0.533641i
$279$		0			0
$280$	2.03761	+	13.9223i	0.121770	+	0.832017i
$281$	−21.0532	−	17.6657i	−1.25593	−	1.05385i	−0.996103	−	0.0881948i	$-0.971890\pi$
$281$	−21.0532	−	17.6657i	−1.25593	−	1.05385i	−0.259826	−	0.965655i	$-0.583665\pi$
$282$		0			0
$283$	−6.95521	+	19.1093i	−0.413444	+	1.13593i	0.541902	+	0.840442i	$0.317704\pi$
$283$	−6.95521	+	19.1093i	−0.413444	+	1.13593i	−0.955347	+	0.295488i	$0.904518\pi$
$284$	9.54240			0.566237
$285$		0			0
$286$	−40.0896			−2.37055
$287$	2.19715	−	6.03662i	0.129694	−	0.356330i
$288$		0			0
$289$	5.54421	+	4.65214i	0.326130	+	0.273656i
$290$	11.6756	−	1.70879i	0.685615	−	0.100343i
$291$		0			0
$292$	−20.4267	−	11.7934i	−1.19538	−	0.690154i
$293$	3.97210	−	2.29329i	0.232053	−	0.133976i	−0.379466	−	0.925206i	$-0.623892\pi$
$293$	3.97210	−	2.29329i	0.232053	−	0.133976i	0.611519	+	0.791230i	$0.290559\pi$
$294$		0			0
$295$	5.54961	−	26.8605i	0.323111	−	1.56388i
$296$	3.92169	+	6.79257i	0.227944	+	0.394810i
$297$		0			0
$298$	8.60617	+	1.51750i	0.498542	+	0.0879064i
$299$	34.6628	−	29.0856i	2.00460	−	1.68206i
$300$		0			0
$301$	0.134396	+	0.762200i	0.00774648	+	0.0439325i
$302$	3.64144	−	10.0048i	0.209541	−	0.575710i
$303$		0			0
$304$	−3.74061	+	7.25303i	−0.214538	+	0.415990i
$305$	5.62489	−	9.11687i	0.322080	−	0.522031i
$306$		0			0
$307$	23.9533	−	4.22361i	1.36709	−	0.241054i	0.558536	−	0.829480i	$-0.311363\pi$
$307$	23.9533	−	4.22361i	1.36709	−	0.241054i	0.808551	+	0.588426i	$0.200252\pi$
$308$	10.3921	−	12.3849i	0.592146	−	0.705692i
$309$		0			0
$310$	15.6039	−	17.5297i	0.886243	−	0.995622i
$311$	11.0103	−	19.0703i	0.624334	−	1.08138i	−0.364335	−	0.931268i	$-0.618704\pi$
$311$	11.0103	−	19.0703i	0.624334	−	1.08138i	0.988669	−	0.150111i	$-0.0479630\pi$
$312$		0			0
$313$	−10.0833	−	27.7037i	−0.569943	−	1.56591i	−0.804593	−	0.593827i	$-0.797616\pi$
$313$	−10.0833	−	27.7037i	−0.569943	−	1.56591i	0.234649	−	0.972080i	$-0.424606\pi$
$314$	−45.1504	+	16.4334i	−2.54798	+	0.927390i
$315$		0			0
$316$	−7.46057	+	12.9221i	−0.419690	+	0.726924i
$317$	−7.92095	−	1.39668i	−0.444885	−	0.0784452i	−0.0532818	−	0.998580i	$-0.516968\pi$
$317$	−7.92095	−	1.39668i	−0.444885	−	0.0784452i	−0.391603	+	0.920134i	$0.628079\pi$
$318$		0			0
$319$	−4.65035	−	3.90211i	−0.260370	−	0.218476i
$320$	−23.7933	−	9.45580i	−1.33009	−	0.528595i
$321$		0			0
$322$			28.3256i			1.57853i
$323$	−11.4585	+	7.36145i	−0.637568	+	0.409602i
$324$		0			0
$325$	−30.7879	+	3.59107i	−1.70781	+	0.199197i
$326$	−6.44702	−	36.5629i	−0.357068	−	2.02503i
$327$		0			0
$328$	−9.69901	−	11.5588i	−0.535538	−	0.638230i
$329$	0.654167	−	3.70997i	0.0360654	−	0.204537i
$330$		0			0
$331$	−9.10916	−	15.7775i	−0.500685	−	0.867212i	−1.00000		0.000790925i	$-0.999748\pi$
$331$	−9.10916	−	15.7775i	−0.500685	−	0.867212i	0.499315	−	0.866421i	$-0.333585\pi$
$332$	−7.95686	−	21.8613i	−0.436689	−	1.19979i
$333$		0			0
$334$	7.16709	+	12.4138i	0.392166	+	0.679251i
$335$	1.32066	−	0.711890i	0.0721555	−	0.0388947i
$336$		0			0
$337$	−6.17287	−	7.35654i	−0.336258	−	0.400736i	0.571247	−	0.820778i	$-0.306460\pi$
$337$	−6.17287	−	7.35654i	−0.336258	−	0.400736i	−0.907505	+	0.420042i	$0.862015\pi$
$338$	−38.7586	+	46.1907i	−2.10819	+	2.51244i
$339$		0			0
$340$	15.6908	+	19.8491i	0.850952	+	1.07647i
$341$	−12.0736			−0.653823
$342$		0			0
$343$		−	18.5299i		−	1.00052i
$344$	1.70826	+	0.621757i	0.0921035	+	0.0335229i
$345$		0			0
$346$	2.97940	+	2.50002i	0.160174	+	0.134402i
$347$	0.813944	+	0.970021i	0.0436948	+	0.0520734i	0.787449	−	0.616379i	$-0.211401\pi$
$347$	0.813944	+	0.970021i	0.0436948	+	0.0520734i	−0.743754	+	0.668453i	$0.766957\pi$
$348$		0			0
$349$	13.3074	−	23.0491i	0.712330	−	1.23379i	−0.251650	−	0.967818i	$-0.580973\pi$
$349$	13.3074	−	23.0491i	0.712330	−	1.23379i	0.963980	−	0.265974i	$-0.0856934\pi$
$350$	10.6664	−	16.2090i	0.570143	−	0.866406i
$351$		0			0
$352$	3.03181	+	8.32983i	0.161596	+	0.443982i
$353$	23.2738	−	13.4371i	1.23874	−	0.715187i	0.269903	−	0.962888i	$-0.413008\pi$
$353$	23.2738	−	13.4371i	1.23874	−	0.715187i	0.968837	+	0.247701i	$0.0796751\pi$
$354$		0			0
$355$	−4.40092	−	3.91744i	−0.233577	−	0.207916i
$356$	−48.0062	+	40.2820i	−2.54432	+	2.13494i
$357$		0			0
$358$	−33.1294	+	5.84160i	−1.75094	+	0.308738i
$359$	19.7868	+	7.20180i	1.04431	+	0.380097i	0.806511	−	0.591219i	$-0.201353\pi$
$359$	19.7868	+	7.20180i	1.04431	+	0.380097i	0.237795	+	0.971315i	$0.423575\pi$
$360$		0			0
$361$	5.05739	+	18.3146i	0.266178	+	0.963924i
$362$		−	54.4039i		−	2.85940i
$363$		0			0
$364$	−6.38103	−	36.1886i	−0.334457	−	1.89680i
$365$	4.57920	+	13.8248i	0.239686	+	0.723624i
$366$		0			0
$367$	10.8503	+	1.91320i	0.566381	+	0.0998682i	0.449504	−	0.893278i	$-0.351601\pi$
$367$	10.8503	+	1.91320i	0.566381	+	0.0998682i	0.116877	+	0.993146i	$0.462712\pi$
$368$	11.8346	+	6.83268i	0.616919	+	0.356178i
$369$		0			0
$370$	2.18850	−	10.5925i	0.113775	−	0.550676i
$371$	−9.78803	+	3.56255i	−0.508169	+	0.184959i
$372$		0			0
$373$	−4.18558	−	2.41654i	−0.216721	−	0.125124i	0.387710	−	0.921781i	$-0.373266\pi$
$373$	−4.18558	−	2.41654i	−0.216721	−	0.125124i	−0.604431	+	0.796657i	$0.706599\pi$
$374$	3.50864	−	19.8985i	0.181427	−	1.02893i
$375$		0			0
$376$	−6.77836	−	5.68772i	−0.349567	−	0.293322i
$377$	−13.5884	+	2.39599i	−0.699836	+	0.123400i
$378$		0			0
$379$	−2.03721			−0.104644			−0.0523221	−	0.998630i	$-0.516662\pi$
$379$	−2.03721			−0.104644			−0.0523221	+	0.998630i	$0.516662\pi$
$380$	32.9435	−	12.6755i	1.68997	−	0.650238i
$381$		0			0
$382$	8.27940	−	22.7475i	0.423611	−	1.16386i
$383$	−34.0551	+	6.00483i	−1.74013	+	0.306833i	−0.951413	−	0.307918i	$-0.900368\pi$
$383$	−34.0551	+	6.00483i	−1.74013	+	0.306833i	−0.788721	+	0.614751i	$0.789257\pi$
$384$		0			0
$385$	−9.87716	+	1.44558i	−0.503387	+	0.0736734i
$386$	4.87109	−	27.6253i	0.247932	−	1.40609i
$387$		0			0
$388$	−0.407543	+	0.235295i	−0.0206899	+	0.0119453i
$389$	4.25700	−	1.54942i	0.215839	−	0.0785588i	−0.231838	−	0.972754i	$-0.574474\pi$
$389$	4.25700	−	1.54942i	0.215839	−	0.0785588i	0.447676	+	0.894196i	$0.352252\pi$
$390$		0			0
$391$	11.4029	+	19.7505i	0.576672	+	0.998825i
$392$	−14.3864	−	8.30601i	−0.726624	−	0.419517i
$393$		0			0
$394$	−4.95250	+	4.15564i	−0.249503	+	0.209358i
$395$	8.74569	−	2.89684i	0.440043	−	0.145756i
$396$		0			0
$397$	8.59660	−	23.6190i	0.431451	−	1.18540i	−0.513471	−	0.858107i	$-0.671641\pi$
$397$	8.59660	−	23.6190i	0.431451	−	1.18540i	0.944922	−	0.327295i	$-0.106137\pi$
$398$			10.6181i			0.532237i
$399$		0			0
$400$	−4.19923	−	8.36637i	−0.209961	−	0.418319i
$401$	27.1680	+	9.88834i	1.35671	+	0.493800i	0.915034	−	0.403377i	$-0.132164\pi$
$401$	27.1680	+	9.88834i	1.35671	+	0.493800i	0.441671	+	0.897177i	$0.354386\pi$
$402$		0			0
$403$	−17.6396	+	21.0220i	−0.878690	+	1.04718i
$404$	10.3630	−	8.69560i	0.515579	−	0.432622i
$405$		0			0
$406$	4.31872	−	7.48024i	0.214334	−	0.371238i
$407$	−4.81898	+	2.78224i	−0.238868	+	0.137910i
$408$		0			0
$409$	−21.5769	+	7.85333i	−1.06691	+	0.388322i	−0.815019	−	0.579434i	$-0.803274\pi$
$409$	−21.5769	+	7.85333i	−1.06691	+	0.388322i	−0.251888	+	0.967756i	$0.581051\pi$
$410$	−0.607701	+	20.7991i	−0.0300122	+	1.02720i
$411$		0			0
$412$	23.5371	+	4.15022i	1.15959	+	0.204467i
$413$	−12.9051	−	15.3797i	−0.635018	−	0.756785i
$414$		0			0
$415$	−5.30504	+	13.3489i	−0.260414	+	0.655271i
$416$	18.9330	+	6.89106i	0.928268	+	0.337862i
$417$		0			0
$418$	−25.0525	−	12.9203i	−1.22536	−	0.631953i
$419$	8.98058			0.438730			0.219365	−	0.975643i	$-0.429601\pi$
$419$	8.98058			0.438730			0.219365	+	0.975643i	$0.429601\pi$
$420$		0			0
$421$	−5.91109	−	33.5235i	−0.288089	−	1.63383i	−0.694038	−	0.719938i	$-0.744170\pi$
$421$	−5.91109	−	33.5235i	−0.288089	−	1.63383i	0.405949	−	0.913896i	$-0.366941\pi$
$422$	−11.1867	+	13.3318i	−0.544561	+	0.648983i
$423$		0			0
$424$	−4.24846	+	24.0942i	−0.206324	+	1.17012i
$425$	0.912128	−	15.5959i	0.0442447	−	0.756512i
$426$		0			0
$427$	−2.68191	−	7.36848i	−0.129787	−	0.356586i
$428$	−14.6099	−	40.1404i	−0.706196	−	1.94026i
$429$		0			0
$430$	−1.18952	−	2.20673i	−0.0573636	−	0.106418i
$431$	−6.59394	+	37.3961i	−0.317619	+	1.80131i	0.239525	+	0.970890i	$0.423008\pi$
$431$	−6.59394	+	37.3961i	−0.317619	+	1.80131i	−0.557144	+	0.830416i	$0.688103\pi$
$432$		0			0
$433$	−23.7703	+	28.3283i	−1.14233	+	1.36137i	−0.219749	+	0.975556i	$0.570524\pi$
$433$	−23.7703	+	28.3283i	−1.14233	+	1.36137i	−0.922576	+	0.385814i	$0.873921\pi$
$434$	−2.98305	−	16.9177i	−0.143191	−	0.812076i
$435$		0			0
$436$	26.2126			1.25535
$437$	31.0351	−	7.00459i	1.48461	−	0.335075i
$438$		0			0
$439$	20.8452	+	7.58705i	0.994889	+	0.362110i	0.787611	−	0.616172i	$-0.211318\pi$
$439$	20.8452	+	7.58705i	0.994889	+	0.362110i	0.207277	+	0.978282i	$0.433540\pi$
$440$	−8.65939	+	21.7893i	−0.412820	+	1.03877i
$441$		0			0
$442$	−29.5202	−	35.1808i	−1.40413	−	1.67338i
$443$	−9.69917	−	1.71023i	−0.460822	−	0.0812553i	−0.0615822	−	0.998102i	$-0.519615\pi$
$443$	−9.69917	−	1.71023i	−0.460822	−	0.0812553i	−0.399239	+	0.916847i	$0.630726\pi$
$444$		0			0
$445$	38.6772	+	1.13006i	1.83348	+	0.0535698i
$446$	36.9424	−	13.4459i	1.74927	−	0.636683i
$447$		0			0
$448$	−16.2305	+	9.37067i	−0.766818	+	0.442723i
$449$	18.6520	−	32.3061i	0.880240	−	1.52462i	0.0291671	−	0.999575i	$-0.490715\pi$
$449$	18.6520	−	32.3061i	0.880240	−	1.52462i	0.851073	−	0.525047i	$-0.175952\pi$
$450$		0			0
$451$	8.20040	−	6.88095i	0.386142	−	0.324011i
$452$	−30.9322	+	36.8636i	−1.45493	+	1.73392i
$453$		0			0
$454$	−26.2519	−	9.55490i	−1.23206	−	0.448434i
$455$	−11.9136	+	19.3097i	−0.558518	+	0.905251i
$456$		0			0
$457$			14.0343i			0.656498i	0.944591	+	0.328249i	$0.106458\pi$
$457$			14.0343i			0.656498i	−0.944591	+	0.328249i	$0.893542\pi$
$458$	−6.34407	+	17.4302i	−0.296439	+	0.814460i
$459$		0			0
$460$	−18.5850	−	56.1090i	−0.866530	−	2.61610i
$461$	7.76457	−	6.51525i	0.361632	−	0.303445i	−0.443809	−	0.896122i	$-0.646373\pi$
$461$	7.76457	−	6.51525i	0.361632	−	0.303445i	0.805441	+	0.592676i	$0.201929\pi$
$462$		0			0
$463$	−0.625383	−	0.361065i	−0.0290640	−	0.0167801i	0.485398	−	0.874294i	$-0.338675\pi$
$463$	−0.625383	−	0.361065i	−0.0290640	−	0.0167801i	−0.514462	+	0.857513i	$0.672008\pi$
$464$	−2.08351	−	3.60875i	−0.0967247	−	0.167532i
$465$		0			0
$466$	−14.9715	+	5.44917i	−0.693540	+	0.252428i
$467$	30.3258	−	17.5086i	1.40331	−	0.810201i	0.408579	−	0.912723i	$-0.366024\pi$
$467$	30.3258	−	17.5086i	1.40331	−	0.810201i	0.994731	+	0.102522i	$0.0326911\pi$
$468$		0			0
$469$	0.190702	−	1.08152i	0.00880580	−	0.0499402i
$470$	1.76704	+	12.0737i	0.0815077	+	0.556916i
$471$		0			0
$472$	−46.4406	+	8.18872i	−2.13760	+	0.376917i
$473$	−0.441105	+	1.21193i	−0.0202820	+	0.0557244i
$474$		0			0
$475$	−20.3971	−	7.67841i	−0.935883	−	0.352310i
$476$	18.5207			0.848895
$477$		0			0
$478$	−37.2997	+	6.57695i	−1.70605	+	0.300823i
$479$	−20.6527	−	17.3296i	−0.943645	−	0.791812i	0.0345713	−	0.999402i	$-0.488993\pi$
$479$	−20.6527	−	17.3296i	−0.943645	−	0.791812i	−0.978216	+	0.207590i	$0.933438\pi$
$480$		0			0
$481$	−2.19623	+	12.4555i	−0.100140	+	0.567920i
$482$	21.4683	+	12.3947i	0.977855	+	0.564565i
$483$		0			0
$484$	−12.1179	+	4.41057i	−0.550816	+	0.200480i
$485$	0.284553	+	0.0587912i	0.0129209	+	0.00266957i
$486$		0			0
$487$	−2.65660	−	1.53379i	−0.120382	−	0.0695026i	0.438600	−	0.898682i	$-0.355475\pi$
$487$	−2.65660	−	1.53379i	−0.120382	−	0.0695026i	−0.558982	+	0.829180i	$0.688808\pi$
$488$	−18.1383	−	3.19827i	−0.821081	−	0.144779i
$489$		0			0
$490$	7.20306	+	21.7464i	0.325401	+	0.982402i
$491$	−0.216866	−	1.22991i	−0.00978703	−	0.0555050i	0.979523	−	0.201332i	$-0.0645269\pi$
$491$	−0.216866	−	1.22991i	−0.00978703	−	0.0555050i	−0.989310	+	0.145827i	$0.953416\pi$
$492$		0			0
$493$		−	6.95428i		−	0.313205i
$494$	−59.0980	+	24.7436i	−2.65895	+	1.11327i
$495$		0			0
$496$	−7.78785	−	2.83455i	−0.349685	−	0.127275i
$497$	−4.24727	+	0.748908i	−0.190516	+	0.0335931i
$498$		0			0
$499$	−14.9931	+	12.5807i	−0.671181	+	0.563188i	−0.913415	−	0.407030i	$-0.866564\pi$
$499$	−14.9931	+	12.5807i	−0.671181	+	0.563188i	0.242233	+	0.970218i	$0.422120\pi$
$500$	−10.4936	+	39.1061i	−0.469288	+	1.74888i
$501$		0			0
$502$	−24.3650	+	14.0671i	−1.08746	+	0.627846i
$503$	1.75066	+	4.80990i	0.0780581	+	0.214463i	0.972583	−	0.232555i	$-0.0747084\pi$
$503$	1.75066	+	4.80990i	0.0780581	+	0.214463i	−0.894525	+	0.447017i	$0.852486\pi$
$504$		0			0
$505$	−8.34919	−	0.243943i	−0.371534	−	0.0108553i
$506$	−23.6006	+	40.8774i	−1.04917	+	1.81722i
$507$		0			0
$508$	−20.2376	−	24.1182i	−0.897898	−	1.07007i
$509$	−12.1303	−	10.1785i	−0.537664	−	0.451154i	0.333074	−	0.942901i	$-0.391914\pi$
$509$	−12.1303	−	10.1785i	−0.537664	−	0.451154i	−0.870738	+	0.491747i	$0.836359\pi$
$510$		0			0
$511$	10.0174	+	3.64603i	0.443143	+	0.161291i
$512$			20.4803i			0.905108i
$513$		0			0
$514$	9.04830			0.399103
$515$	−9.15143	−	11.5767i	−0.403260	−	0.510132i
$516$		0			0
$517$	4.03514	−	4.80890i	0.177465	−	0.211495i
$518$	−5.08914	−	6.06501i	−0.223604	−	0.266481i
$519$		0			0
$520$	25.2872	+	46.9116i	1.10892	+	2.05721i
$521$	−14.9866	−	25.9576i	−0.656575	−	1.13722i	−0.981496	−	0.191481i	$-0.938671\pi$
$521$	−14.9866	−	25.9576i	−0.656575	−	1.13722i	0.324921	−	0.945741i	$-0.394662\pi$
$522$		0			0
$523$	10.3894	+	28.5446i	0.454296	+	1.24817i	0.929673	+	0.368386i	$0.120090\pi$
$523$	10.3894	+	28.5446i	0.454296	+	1.24817i	−0.475377	+	0.879782i	$0.657688\pi$
$524$	−19.0960	−	33.0752i	−0.834213	−	1.44490i
$525$		0			0
$526$	−0.872659	+	4.94909i	−0.0380497	+	0.215791i
$527$	−8.89048	−	10.5953i	−0.387275	−	0.461537i
$528$		0			0
$529$	−5.25736	−	29.8160i	−0.228581	−	1.29635i
$530$	26.4679	−	20.9229i	1.14969	−	0.908834i
$531$		0			0
$532$	7.67550	−	24.6712i	0.332775	−	1.06963i
$533$		−	24.3313i		−	1.05390i
$534$		0			0
$535$	−9.74078	+	24.5104i	−0.421131	+	1.05968i
$536$	−1.97602	−	1.65808i	−0.0853510	−	0.0716180i
$537$		0			0
$538$	9.17230	+	1.61732i	0.395446	+	0.0697278i
$539$	5.89268	−	10.2064i	0.253816	−	0.439622i
$540$		0			0
$541$	22.4204	−	8.16035i	0.963927	−	0.350841i	0.188356	−	0.982101i	$-0.439684\pi$
$541$	22.4204	−	8.16035i	0.963927	−	0.350841i	0.775571	+	0.631260i	$0.217462\pi$
$542$	15.3554	+	42.1887i	0.659573	+	1.81216i
$543$		0			0
$544$	−5.07740	+	8.79431i	−0.217692	+	0.377053i
$545$	−12.0892	−	10.7610i	−0.517843	−	0.460953i
$546$		0			0
$547$	8.83204	−	10.5256i	0.377631	−	0.450043i	−0.543434	−	0.839452i	$-0.682876\pi$
$547$	8.83204	−	10.5256i	0.377631	−	0.450043i	0.921065	+	0.389409i	$0.127321\pi$
$548$	1.41667	−	0.249797i	0.0605171	−	0.0106708i
$549$		0			0
$550$	28.8980	−	14.5044i	1.23222	−	0.618471i
$551$	−9.26373	−	2.88205i	−0.394648	−	0.122779i
$552$		0			0
$553$	2.30650	−	6.33707i	0.0980826	−	0.269480i
$554$	6.18699	+	35.0882i	0.262860	+	1.49075i
$555$		0			0
$556$	−20.8217	+	17.4715i	−0.883038	+	0.740957i
$557$	26.6208	+	4.69396i	1.12796	+	0.198889i	0.706332	−	0.707881i	$-0.250349\pi$
$557$	26.6208	+	4.69396i	1.12796	+	0.198889i	0.421626	+	0.906770i	$0.361460\pi$
$558$		0			0
$559$	1.46570	+	2.53866i	0.0619923	+	0.107374i
$560$	−6.71045	−	1.38644i	−0.283568	−	0.0585878i
$561$		0			0
$562$	56.4314	−	32.5807i	2.38042	−	1.37433i
$563$	−33.0543	−	19.0839i	−1.39307	−	0.804290i	−0.399417	−	0.916769i	$-0.630787\pi$
$563$	−33.0543	−	19.0839i	−1.39307	−	0.804290i	−0.993654	+	0.112479i	$0.964121\pi$
$564$		0			0
$565$	29.3995	−	4.30277i	1.23684	−	0.181019i
$566$	−36.9350	−	30.9922i	−1.55250	−	1.30270i
$567$		0			0
$568$	−3.46467	+	9.51911i	−0.145374	+	0.399413i
$569$	2.28061			0.0956082			0.0478041	−	0.998857i	$-0.484778\pi$
$569$	2.28061			0.0956082			0.0478041	+	0.998857i	$0.484778\pi$
$570$		0			0
$571$	−14.4656			−0.605367			−0.302683	−	0.953091i	$-0.597883\pi$
$571$	−14.4656			−0.605367			−0.302683	+	0.953091i	$0.597883\pi$
$572$	20.9433	−	57.5412i	0.875683	−	2.40592i
$573$		0			0
$574$	11.6678	+	9.79042i	0.487003	+	0.408644i
$575$	−14.4631	+	33.5070i	−0.603152	+	1.39734i
$576$		0			0
$577$	−7.08262	−	4.08915i	−0.294853	−	0.170234i	0.345275	−	0.938501i	$-0.387786\pi$
$577$	−7.08262	−	4.08915i	−0.294853	−	0.170234i	−0.640128	+	0.768268i	$0.721119\pi$
$578$	−14.8608	+	8.57989i	−0.618128	+	0.356876i
$579$		0			0
$580$	−3.64683	+	17.6509i	−0.151426	+	0.732912i
$581$	5.25728	+	9.10587i	0.218109	+	0.377775i
$582$		0			0
$583$	−17.0936	−	3.01407i	−0.707945	−	0.124830i
$584$	19.1811	−	16.0949i	0.793721	−	0.666011i
$585$		0			0
$586$	1.88836	+	10.7094i	0.0780076	+	0.442403i
$587$	−11.7776	+	32.3587i	−0.486114	+	1.33559i	0.418058	+	0.908420i	$0.362711\pi$
$587$	−11.7776	+	32.3587i	−0.486114	+	1.33559i	−0.904172	+	0.427168i	$0.859511\pi$
$588$		0			0
$589$	−17.7983	+	7.45194i	−0.733366	+	0.307052i
$590$	55.3443	+	34.1461i	2.27849	+	1.40577i
$591$		0			0
$592$	−3.76158	+	0.663268i	−0.154600	+	0.0272602i
$593$	1.70415	−	2.03093i	0.0699812	−	0.0834003i	−0.729918	−	0.683535i	$-0.760442\pi$
$593$	1.70415	−	2.03093i	0.0699812	−	0.0834003i	0.799899	+	0.600134i	$0.204886\pi$
$594$		0			0
$595$	−8.54168	−	7.60330i	−0.350175	−	0.311705i
$596$	−6.67406	+	11.5598i	−0.273380	+	0.473508i
$597$		0			0
$598$	36.6934	+	100.814i	1.50050	+	4.12260i
$599$	2.30660	−	0.839535i	0.0942453	−	0.0343025i	−0.294467	−	0.955662i	$-0.595142\pi$
$599$	2.30660	−	0.839535i	0.0942453	−	0.0343025i	0.388712	+	0.921359i	$0.372920\pi$
$600$		0			0
$601$	−7.48153	+	12.9584i	−0.305178	+	0.528584i	−0.977301	−	0.211856i	$-0.932049\pi$
$601$	−7.48153	+	12.9584i	−0.305178	+	0.528584i	0.672123	+	0.740440i	$0.265383\pi$
$602$	−1.80715	−	0.318649i	−0.0736540	−	0.0129872i
$603$		0			0
$604$	12.4577	+	10.4532i	0.506896	+	0.425336i
$605$	7.39942	+	2.94064i	0.300829	+	0.119554i
$606$		0			0
$607$			43.0431i			1.74706i	0.486767	+	0.873532i	$0.338176\pi$
$607$			43.0431i			1.74706i	−0.486767	+	0.873532i	$0.661824\pi$
$608$	9.61059	+	10.4082i	0.389761	+	0.422106i
$609$		0			0
$610$	15.7509	+	19.9252i	0.637735	+	0.806747i
$611$	−2.47768	−	14.0516i	−0.100236	−	0.568468i
$612$		0			0
$613$	−25.1922	−	30.0229i	−1.01750	−	1.21261i	−0.976957	−	0.213437i	$-0.931534\pi$
$613$	−25.1922	−	30.0229i	−1.01750	−	1.21261i	−0.0405478	−	0.999178i	$-0.512910\pi$
$614$	−10.0141	+	56.7925i	−0.404134	+	2.29196i
$615$		0			0
$616$	8.58143	+	14.8635i	0.345756	+	0.598866i
$617$	−9.54332	−	26.2201i	−0.384200	−	1.05558i	−0.969570	−	0.244814i	$-0.921273\pi$
$617$	−9.54332	−	26.2201i	−0.384200	−	1.05558i	0.585370	−	0.810766i	$-0.300949\pi$
$618$		0			0
$619$	−12.4298	−	21.5291i	−0.499597	−	0.865327i	0.500403	−	0.865792i	$-0.333185\pi$
$619$	−12.4298	−	21.5291i	−0.499597	−	0.865327i	−1.00000		0.000465813i	$0.999852\pi$
$620$	17.0090	+	31.5543i	0.683099	+	1.26725i
$621$		0			0
$622$	33.5599	+	39.9951i	1.34563	+	1.60366i
$623$	18.2059	−	21.6969i	0.729403	−	0.869268i
$624$		0			0
$625$	20.8938	−	13.7277i	0.835753	−	0.549106i
$626$	69.9001			2.79377
$627$		0			0
$628$		−	73.3901i		−	2.92858i
$629$	−5.99005	−	2.18020i	−0.238839	−	0.0869303i
$630$		0			0
$631$	33.9105	+	28.4543i	1.34995	+	1.13275i	0.978947	+	0.204116i	$0.0654320\pi$
$631$	33.9105	+	28.4543i	1.34995	+	1.13275i	0.371007	+	0.928630i	$0.379012\pi$
$632$	−10.1817	−	12.1341i	−0.405008	−	0.482670i
$633$		0			0
$634$	9.53501	−	16.5151i	0.378684	−	0.655900i
$635$	−0.567739	+	19.4314i	−0.0225300	+	0.771111i
$636$		0			0
$637$	−9.16175	−	25.1717i	−0.363002	−	0.997339i
$638$	12.4649	−	7.19661i	0.493490	−	0.284916i
$639$		0			0
$640$	30.6979	−	34.4866i	1.21344	−	1.36320i
$641$	−15.5815	+	13.0744i	−0.615432	+	0.516409i	−0.896364	−	0.443319i	$-0.853801\pi$
$641$	−15.5815	+	13.0744i	−0.615432	+	0.516409i	0.280932	+	0.959728i	$0.409356\pi$
$642$		0			0
$643$	29.9093	−	5.27382i	1.17951	−	0.207979i	0.450686	−	0.892682i	$-0.351179\pi$
$643$	29.9093	−	5.27382i	1.17951	−	0.207979i	0.728822	+	0.684703i	$0.240068\pi$
$644$	−40.6562	−	14.7977i	−1.60208	−	0.583109i
$645$		0			0
$646$	−7.10926	−	31.4989i	−0.279710	−	1.23931i
$647$			48.5913i			1.91032i	0.296087	+	0.955161i	$0.404318\pi$
$647$			48.5913i			1.91032i	−0.296087	+	0.955161i	$0.595682\pi$
$648$		0			0
$649$	−5.80948	−	32.9472i	−0.228042	−	1.29329i
$650$	16.9657	−	71.5070i	0.665448	−	2.80474i
$651$		0			0
$652$	55.8473	+	9.84739i	2.18715	+	0.385653i
$653$	17.2820	+	9.97774i	0.676295	+	0.390459i	0.798458	−	0.602051i	$-0.205650\pi$
$653$	17.2820	+	9.97774i	0.676295	+	0.390459i	−0.122163	+	0.992510i	$0.538983\pi$
$654$		0			0
$655$	−4.77136	+	23.0937i	−0.186432	+	0.902344i
$656$	6.90496	−	2.51320i	0.269594	−	0.0981240i
$657$		0			0
$658$	7.73526	+	4.46595i	0.301552	+	0.174101i
$659$	−2.95696	+	16.7698i	−0.115187	+	0.653257i	0.871471	+	0.490448i	$0.163167\pi$
$659$	−2.95696	+	16.7698i	−0.115187	+	0.653257i	−0.986658	+	0.162810i	$0.947944\pi$
$660$		0			0
$661$	−21.0919	−	17.6982i	−0.820379	−	0.688380i	0.132682	−	0.991159i	$-0.457641\pi$
$661$	−21.0919	−	17.6982i	−0.820379	−	0.688380i	−0.953061	+	0.302779i	$0.902086\pi$
$662$	42.5388	−	7.50074i	1.65332	−	0.291525i
$663$		0			0
$664$	24.6969			0.958427
$665$	−13.6682	+	8.22727i	−0.530029	+	0.319040i
$666$		0			0
$667$	−5.55633	+	15.2659i	−0.215142	+	0.591098i
$668$	−21.5618	+	3.80193i	−0.834253	+	0.147101i
$669$		0			0
$670$	0.515127	+	3.51970i	0.0199011	+	0.135978i
$671$	2.26901	−	12.8682i	0.0875940	−	0.496770i
$672$		0			0
$673$	32.2647	−	18.6280i	1.24371	−	0.718057i	0.273864	−	0.961768i	$-0.411698\pi$
$673$	32.2647	−	18.6280i	1.24371	−	0.718057i	0.969848	+	0.243711i	$0.0783649\pi$
$674$	21.3959	−	7.78748i	0.824140	−	0.299962i
$675$		0			0
$676$	−46.0503	−	79.7615i	−1.77117	−	3.06775i
$677$	19.7350	+	11.3940i	0.758478	+	0.437907i	0.828749	−	0.559621i	$-0.189053\pi$
$677$	19.7350	+	11.3940i	0.758478	+	0.437907i	−0.0702711	+	0.997528i	$0.522386\pi$
$678$		0			0
$679$	0.162929	−	0.136713i	0.00625263	−	0.00524658i
$680$	−25.4977	+	8.44562i	−0.977793	+	0.323875i
$681$		0			0
$682$	9.79072	−	26.8998i	0.374906	−	1.03005i
$683$		−	4.61408i		−	0.176553i	−0.996096	−	0.0882764i	$-0.971864\pi$
$683$		−	4.61408i		−	0.176553i	0.996096	−	0.0882764i	$-0.0281359\pi$
$684$		0			0
$685$	−0.755912	−	0.466379i	−0.0288819	−	0.0178194i
$686$	41.2842	+	15.0262i	1.57624	+	0.573704i
$687$		0			0
$688$	−0.569052	+	0.678170i	−0.0216949	+	0.0258550i
$689$	−30.2218	+	25.3591i	−1.15136	+	0.966104i
$690$		0			0
$691$	−17.8800	+	30.9690i	−0.680186	+	1.17812i	0.294738	+	0.955578i	$0.404768\pi$
$691$	−17.8800	+	30.9690i	−0.680186	+	1.17812i	−0.974924	+	0.222538i	$0.928566\pi$
$692$	−5.14479	+	2.97035i	−0.195576	+	0.112916i
$693$		0			0
$694$	−2.82123	+	1.02684i	−0.107092	+	0.0389785i
$695$	16.7755	+	0.490140i	0.636331	+	0.0185921i
$696$		0			0
$697$	12.0768	+	2.12947i	0.457442	+	0.0806594i
$698$	40.5618	+	48.3397i	1.53529	+	1.82968i
$699$		0			0
$700$	17.6927	+	23.7774i	0.668722	+	0.898702i
$701$	30.8939	+	11.2444i	1.16685	+	0.424697i	0.851538	−	0.524293i	$-0.175670\pi$
$701$	30.8939	+	11.2444i	1.16685	+	0.424697i	0.315307	+	0.948990i	$0.397892\pi$
$702$		0			0
$703$	−5.38667	+	7.07575i	−0.203162	+	0.266867i
$704$	−31.2301			−1.17703
$705$		0			0
$706$	11.0645	+	62.7500i	0.416419	+	2.36163i
$707$	−3.93007	+	4.68368i	−0.147806	+	0.176148i
$708$		0			0
$709$	−7.71396	+	43.7480i	−0.289704	+	1.64299i	0.398279	+	0.917264i	$0.369608\pi$
$709$	−7.71396	+	43.7480i	−0.289704	+	1.64299i	−0.687983	+	0.725727i	$0.741504\pi$
$710$	12.2968	−	6.62845i	0.461490	−	0.248761i
$711$		0			0
$712$	−22.7535	−	62.5147i	−0.852723	−	2.34284i
$713$	11.0508	+	30.3618i	0.413855	+	1.13706i
$714$		0			0
$715$	−33.2814	+	17.9400i	−1.24465	+	0.670917i
$716$	8.92264	−	50.6028i	0.333455	−	1.89112i
$717$		0			0
$718$	−32.0910	+	38.2445i	−1.19762	+	1.42727i
$719$	−3.48789	−	19.7808i	−0.130076	−	0.737699i	−0.978163	−	0.207841i	$-0.933356\pi$
$719$	−3.48789	−	19.7808i	−0.130076	−	0.737699i	0.848086	−	0.529858i	$-0.177755\pi$
$720$		0			0
$721$	−10.8019			−0.402285
$722$	−44.9056	−	3.58385i	−1.67121	−	0.133377i
$723$		0			0
$724$	78.0868	+	28.4213i	2.90207	+	1.05627i
$725$	8.92811	−	6.64339i	0.331582	−	0.246729i
$726$		0			0
$727$	−0.469102	−	0.559054i	−0.0173980	−	0.0207342i	0.757275	−	0.653096i	$-0.226530\pi$
$727$	−0.469102	−	0.559054i	−0.0173980	−	0.0207342i	−0.774673	+	0.632362i	$0.782086\pi$
$728$	38.4171	+	6.77397i	1.42383	+	0.251060i
$729$		0			0
$730$	−34.5148	−	1.00844i	−1.27745	−	0.0373240i
$731$	−1.38834	+	0.505315i	−0.0513497	+	0.0186898i
$732$		0			0
$733$	25.5432	−	14.7474i	0.943461	−	0.544707i	0.0524171	−	0.998625i	$-0.483307\pi$
$733$	25.5432	−	14.7474i	0.943461	−	0.544707i	0.891043	+	0.453918i	$0.149974\pi$
$734$	−13.0613	+	22.6228i	−0.482101	+	0.835023i
$735$		0			0
$736$	18.1723	−	15.2483i	0.669838	−	0.562061i
$737$	1.17632	−	1.40188i	0.0433303	−	0.0516390i
$738$		0			0
$739$	−38.0572	−	13.8517i	−1.39996	−	0.509542i	−0.471790	−	0.881711i	$-0.656392\pi$
$739$	−38.0572	−	13.8517i	−1.39996	−	0.509542i	−0.928165	+	0.372169i	$0.878614\pi$
$740$	14.0602	+	8.67482i	0.516864	+	0.318893i
$741$		0			0
$742$		−	24.6965i		−	0.906637i
$743$	−6.64673	+	18.2617i	−0.243845	+	0.669958i	0.756036	+	0.654530i	$0.227133\pi$
$743$	−6.64673	+	18.2617i	−0.243845	+	0.669958i	−0.999881	+	0.0154284i	$0.995089\pi$
$744$		0			0
$745$	7.82370	−	2.59145i	0.286638	−	0.0949432i
$746$	8.77818	−	7.36576i	0.321392	−	0.269680i
$747$		0			0
$748$	26.7277	+	15.4312i	0.977260	+	0.564221i
$749$	9.65309	+	16.7196i	0.352716	+	0.610923i
$750$		0			0
$751$	−5.32221	+	1.93713i	−0.194210	+	0.0706868i	−0.437294	−	0.899318i	$-0.644063\pi$
$751$	−5.32221	+	1.93713i	−0.194210	+	0.0706868i	0.243084	+	0.970005i	$0.421841\pi$
$752$	3.73178	−	2.15455i	0.136084	−	0.0785682i
$753$		0			0
$754$	5.68082	−	32.2176i	0.206883	−	1.17329i
$755$	−1.45408	−	9.93524i	−0.0529193	−	0.361581i
$756$		0			0
$757$	12.3875	−	2.18425i	0.450231	−	0.0793879i	0.0560650	−	0.998427i	$-0.482145\pi$
$757$	12.3875	−	2.18425i	0.450231	−	0.0793879i	0.394166	+	0.919039i	$0.371033\pi$
$758$	1.65201	−	4.53886i	0.0600037	−	0.164859i
$759$		0			0
$760$	0.683342	+	37.4654i	0.0247874	+	1.35901i
$761$	−50.0335			−1.81371			−0.906857	−	0.421439i	$-0.861525\pi$
$761$	−50.0335			−1.81371			−0.906857	+	0.421439i	$0.861525\pi$
$762$		0			0
$763$	−11.6671	+	2.05722i	−0.422377	+	0.0744764i
$764$	28.3245	+	23.7671i	1.02475	+	0.859864i
$765$		0			0
$766$	14.2373	−	80.7436i	0.514413	−	2.91738i
$767$	−65.8538	−	38.0207i	−2.37784	−	1.37285i
$768$		0			0
$769$	−29.8303	+	10.8573i	−1.07571	+	0.391525i	−0.818308	−	0.574780i	$-0.805088\pi$
$769$	−29.8303	+	10.8573i	−1.07571	+	0.391525i	−0.257399	+	0.966305i	$0.582865\pi$
$770$	4.78886	−	23.1784i	0.172579	−	0.835291i
$771$		0			0
$772$	37.1064	+	21.4234i	1.33549	+	0.771044i
$773$	−11.2636	−	1.98608i	−0.405124	−	0.0714342i	−0.0326266	−	0.999468i	$-0.510387\pi$
$773$	−11.2636	−	1.98608i	−0.405124	−	0.0714342i	−0.372497	+	0.928033i	$0.621498\pi$
$774$		0			0
$775$	5.10948	−	21.5355i	0.183538	−	0.773576i
$776$	−0.0867493	−	0.491980i	−0.00311412	−	0.0176610i
$777$		0			0
$778$			10.7410i			0.385083i
$779$	7.84162	−	15.2049i	0.280955	−	0.544772i
$780$		0			0
$781$	−6.75332	−	2.45801i	−0.241653	−	0.0879544i
$782$	−53.2506	+	9.38951i	−1.90424	+	0.335768i
$783$		0			0
$784$	6.19714	−	5.20002i	0.221327	−	0.185715i
$785$	−30.1288	+	33.8473i	−1.07534	+	1.20806i
$786$		0			0
$787$	−5.75062	+	3.32012i	−0.204987	+	0.118350i	−0.598980	−	0.800764i	$-0.704427\pi$
$787$	−5.75062	+	3.32012i	−0.204987	+	0.118350i	0.393992	+	0.919114i	$0.371094\pi$
$788$	−3.37741	−	9.27935i	−0.120315	−	0.330563i
$789$		0			0
$790$	−0.637947	+	21.8343i	−0.0226971	+	0.776831i
$791$	10.8746	−	18.8354i	0.386657	−	0.669710i
$792$		0			0
$793$	−19.0905	−	22.7511i	−0.677922	−	0.807916i
$794$	45.6515	+	38.3061i	1.62011	+	1.35943i
$795$		0			0
$796$	−15.2403	−	5.54703i	−0.540179	−	0.196609i
$797$		−	0.186468i		−	0.00660502i	−0.999995	−	0.00330251i	$-0.998949\pi$
$797$		−	0.186468i		−	0.00660502i	0.999995	−	0.00330251i	$-0.00105122\pi$
$798$		0			0
$799$	7.19137			0.254412
$800$	−16.1408	+	1.88265i	−0.570663	+	0.0665616i
$801$		0			0
$802$	−44.0621	+	52.5112i	−1.55589	+	1.85423i
$803$	11.4185	+	13.6080i	0.402950	+	0.480217i
$804$		0			0
$805$	12.6756	+	23.5152i	0.446758	+	0.828803i
$806$	−32.5324	−	56.3478i	−1.14591	−	1.98477i
$807$		0			0
$808$	4.91176	+	13.4949i	0.172795	+	0.474750i
$809$	−0.609985	−	1.05652i	−0.0214459	−	0.0371454i	0.855103	−	0.518458i	$-0.173494\pi$
$809$	−0.609985	−	1.05652i	−0.0214459	−	0.0371454i	−0.876549	+	0.481312i	$0.840160\pi$
$810$		0			0
$811$	−3.31560	+	18.8037i	−0.116427	+	0.660288i	0.869608	+	0.493744i	$0.164372\pi$
$811$	−3.31560	+	18.8037i	−0.116427	+	0.660288i	−0.986034	+	0.166544i	$0.946739\pi$
$812$	8.48035	+	10.1065i	0.297602	+	0.354668i
$813$		0			0
$814$	−2.29098	−	12.9928i	−0.0802987	−	0.455396i
$815$	−21.7139	−	27.4686i	−0.760606	−	0.962182i
$816$		0			0
$817$	0.0977570	+	2.05881i	0.00342008	+	0.0720287i
$818$		−	54.4413i		−	1.90349i
$819$		0			0
$820$	−29.5359	−	11.7380i	−1.03144	−	0.409908i
$821$	7.64305	+	6.41328i	0.266744	+	0.223825i	0.766343	−	0.642432i	$-0.222075\pi$
$821$	7.64305	+	6.41328i	0.266744	+	0.223825i	−0.499598	+	0.866257i	$0.666519\pi$
$822$		0			0
$823$	−27.7792	−	4.89822i	−0.968322	−	0.170741i	−0.332948	−	0.942945i	$-0.608043\pi$
$823$	−27.7792	−	4.89822i	−0.968322	−	0.170741i	−0.635375	+	0.772204i	$0.719154\pi$
$824$	−12.6860	+	21.9727i	−0.441937	+	0.765457i
$825$		0			0
$826$	44.7307	−	16.2806i	1.55638	−	0.566476i
$827$	−3.02789	−	8.31907i	−0.105290	−	0.289283i	0.875849	−	0.482585i	$-0.160302\pi$
$827$	−3.02789	−	8.31907i	−0.105290	−	0.289283i	−0.981139	+	0.193303i	$0.938080\pi$
$828$		0			0
$829$	22.8446	−	39.5680i	0.793425	−	1.37425i	−0.130409	−	0.991460i	$-0.541629\pi$
$829$	22.8446	−	39.5680i	0.793425	−	1.37425i	0.923834	−	0.382793i	$-0.125038\pi$
$830$	−25.4391	−	22.6444i	−0.883005	−	0.785998i
$831$		0			0
$832$	−45.6273	+	54.3765i	−1.58184	+	1.88517i
$833$	13.2958	−	2.34441i	0.460673	−	0.0812290i
$834$		0			0
$835$	11.5051	+	7.09834i	0.398149	+	0.245648i
$836$	31.6325	−	29.2085i	1.09403	−	1.01020i
$837$		0			0
$838$	−7.28252	+	20.0086i	−0.251570	+	0.691184i
$839$	0.0317008	+	0.179784i	0.00109443	+	0.00620684i	0.985350	−	0.170544i	$-0.0545525\pi$
$839$	0.0317008	+	0.179784i	0.00109443	+	0.00620684i	−0.984256	+	0.176751i	$0.943441\pi$
$840$		0			0
$841$	−18.4204	+	15.4566i	−0.635187	+	0.532985i
$842$	79.4831	+	14.0150i	2.73917	+	0.482989i
$843$		0			0
$844$	−13.2913	−	23.0212i	−0.457505	−	0.792422i
$845$	−11.5062	+	55.6908i	−0.395826	+	1.91582i
$846$		0			0
$847$	5.04748	−	2.91416i	0.173433	−	0.100132i
$848$	−10.3183	−	5.95727i	−0.354332	−	0.204573i
$849$		0			0
$850$	34.0077	+	14.6792i	1.16645	+	0.503493i
$851$	11.4073	+	9.57186i	0.391037	+	0.328119i
$852$		0			0
$853$	16.8337	−	46.2501i	0.576374	−	1.58357i	−0.217872	−	0.975977i	$-0.569911\pi$
$853$	16.8337	−	46.2501i	0.576374	−	1.58357i	0.794246	−	0.607597i	$-0.207866\pi$
$854$	18.5917			0.636193
$855$		0			0
$856$	45.3470			1.54993
$857$	−10.7975	+	29.6660i	−0.368837	+	1.01337i	0.606968	+	0.794727i	$0.292386\pi$
$857$	−10.7975	+	29.6660i	−0.368837	+	1.01337i	−0.975805	+	0.218645i	$0.929836\pi$
$858$		0			0
$859$	8.18869	+	6.87112i	0.279394	+	0.234440i	0.771706	−	0.635979i	$-0.219404\pi$
$859$	8.18869	+	6.87112i	0.279394	+	0.234440i	−0.492312	+	0.870419i	$0.663848\pi$
$860$	3.78878	−	0.554508i	0.129196	−	0.0189086i
$861$		0			0
$862$	−77.9706	−	45.0164i	−2.65569	−	1.53326i
$863$	22.1552	−	12.7913i	0.754170	−	0.435420i	−0.0730285	−	0.997330i	$-0.523266\pi$
$863$	22.1552	−	12.7913i	0.754170	−	0.435420i	0.827199	+	0.561909i	$0.189933\pi$
$864$		0			0
$865$	3.59218	+	0.742176i	0.122138	+	0.0252347i
$866$	−43.8392	−	75.9316i	−1.48971	−	2.58026i
$867$		0			0
$868$	25.8406	+	4.55640i	0.877088	+	0.154654i
$869$	8.60854	−	7.22342i	0.292025	−	0.245038i
$870$		0			0
$871$	−0.722290	−	4.09631i	−0.0244739	−	0.138798i
$872$	−9.51731	+	26.1486i	−0.322297	+	0.885503i
$873$		0			0
$874$	−9.56087	+	74.8258i	−0.323401	+	2.53102i
$875$	1.60151	−	18.2295i	0.0541409	−	0.616268i
$876$		0			0
$877$	30.6228	−	5.39963i	1.03406	−	0.182332i	0.369237	−	0.929335i	$-0.379619\pi$
$877$	30.6228	−	5.39963i	1.03406	−	0.182332i	0.664821	+	0.747003i	$0.268508\pi$
$878$	−33.8076	+	40.2903i	−1.14095	+	1.35973i
$879$		0			0
$880$	−8.52885	−	7.59187i	−0.287508	−	0.255922i
$881$	−23.7233	+	41.0899i	−0.799257	+	1.38435i	0.120844	+	0.992672i	$0.461440\pi$
$881$	−23.7233	+	41.0899i	−0.799257	+	1.38435i	−0.920101	+	0.391682i	$0.871893\pi$
$882$		0			0
$883$	4.97065	+	13.6568i	0.167276	+	0.459586i	0.994801	−	0.101843i	$-0.0324739\pi$
$883$	4.97065	+	13.6568i	0.167276	+	0.459586i	−0.827525	+	0.561429i	$0.810252\pi$
$884$	65.9173	−	23.9919i	2.21704	−	0.806936i
$885$		0			0
$886$	11.6756	−	20.2227i	0.392249	−	0.679396i
$887$	36.5629	+	6.44703i	1.22766	+	0.216470i	0.749621	−	0.661867i	$-0.230236\pi$
$887$	36.5629	+	6.44703i	1.22766	+	0.216470i	0.478042	+	0.878337i	$0.341347\pi$
$888$		0			0
$889$	10.9005	+	9.14660i	0.365591	+	0.306767i
$890$	−33.8818	+	85.2558i	−1.13572	+	2.85778i
$891$		0			0
$892$			60.0483i			2.01057i
$893$	2.98031	−	9.57955i	0.0997322	−	0.320567i
$894$		0			0
$895$	−24.8891	+	19.6748i	−0.831949	+	0.657657i
$896$	−5.86861	−	33.2825i	−0.196056	−	1.11189i
$897$		0			0
$898$	56.8523	+	67.7539i	1.89718	+	2.26098i
$899$	1.71087	−	9.70283i	0.0570607	−	0.323607i
$900$		0			0
$901$	−9.94198	−	17.2200i	−0.331215	−	0.573682i
$902$	8.68077	+	23.8502i	0.289038	+	0.794126i
$903$		0			0
$904$	−25.5427	−	44.2412i	−0.849537	−	1.47144i
$905$	−24.3456	−	45.1647i	−0.809275	−	1.50133i
$906$		0			0
$907$	6.98432	+	8.32358i	0.231910	+	0.276380i	0.869432	−	0.494052i	$-0.164485\pi$
$907$	6.98432	+	8.32358i	0.231910	+	0.276380i	−0.637522	+	0.770432i	$0.720040\pi$
$908$	27.4286	−	32.6881i	0.910250	−	1.08479i
$909$		0			0
$910$	−33.3606	−	42.2018i	−1.10589	−	1.39898i
$911$	39.5522			1.31042			0.655211	−	0.755446i	$-0.272580\pi$
$911$	39.5522			1.31042			0.655211	+	0.755446i	$0.272580\pi$
$912$		0			0
$913$			17.5212i			0.579867i
$914$	−31.2682	−	11.3807i	−1.03426	−	0.376440i
$915$		0			0
$916$	−21.7036	−	18.2115i	−0.717108	−	0.601725i
$917$	11.0953	+	13.2229i	0.366400	+	0.436659i
$918$		0			0
$919$	16.0782	−	27.8483i	0.530372	−	0.918631i	−0.469000	−	0.883198i	$-0.655386\pi$
$919$	16.0782	−	27.8483i	0.530372	−	0.918631i	0.999372	−	0.0354331i	$-0.0112811\pi$
$920$	62.7199	+	1.83253i	2.06781	+	0.0604166i
$921$		0			0
$922$	8.21942	+	22.5827i	0.270692	+	0.743720i
$923$	−14.1464	+	8.16742i	−0.465634	+	0.268834i
$924$		0			0
$925$	−2.92326	−	9.77294i	−0.0961162	−	0.321332i
$926$	1.31158	−	1.10055i	0.0431012	−	0.0361662i
$927$		0			0
$928$	−7.12380	+	1.25612i	−0.233850	+	0.0412341i
$929$	10.2742	+	3.73950i	0.337085	+	0.122689i	0.505016	−	0.863110i	$-0.331486\pi$
$929$	10.2742	+	3.73950i	0.337085	+	0.122689i	−0.167931	+	0.985799i	$0.553709\pi$
$930$		0			0
$931$	2.38720	−	18.6828i	0.0782372	−	0.612304i
$932$		−	24.3355i		−	0.797136i
$933$		0			0
$934$	14.4171	+	81.7633i	0.471741	+	2.67538i
$935$	−5.99173	−	18.0893i	−0.195951	−	0.591584i
$936$		0			0
$937$	−44.3460	−	7.81940i	−1.44872	−	0.255449i	−0.606716	−	0.794918i	$-0.707514\pi$
$937$	−44.3460	−	7.81940i	−1.44872	−	0.255449i	−0.842005	+	0.539470i	$0.818625\pi$
$938$	2.25497	+	1.30191i	0.0736275	+	0.0425088i
$939$		0			0
$940$	−18.2526	−	3.77116i	−0.595335	−	0.123002i
$941$	−40.0794	+	14.5877i	−1.30655	+	0.475545i	−0.899125	−	0.437693i	$-0.855796\pi$
$941$	−40.0794	+	14.5877i	−1.30655	+	0.475545i	−0.407426	+	0.913238i	$0.633573\pi$
$942$		0			0
$943$	−24.8094	−	14.3237i	−0.807905	−	0.466444i
$944$	3.98778	−	22.6158i	0.129791	−	0.736083i
$945$		0			0
$946$	−2.34245	−	1.96555i	−0.0761596	−	0.0639055i
$947$	−24.3377	+	4.29139i	−0.790869	+	0.139452i	−0.554469	−	0.832204i	$-0.687079\pi$
$947$	−24.3377	+	4.29139i	−0.790869	+	0.139452i	−0.236400	+	0.971656i	$0.575968\pi$
$948$		0			0
$949$	40.3761			1.31066
$950$	33.6478	−	39.2178i	1.09168	−	1.27239i
$951$		0			0
$952$	−6.72453	+	18.4755i	−0.217943	+	0.598794i
$953$	−15.2813	+	2.69451i	−0.495010	+	0.0872836i	−0.415580	−	0.909557i	$-0.636421\pi$
$953$	−15.2813	+	2.69451i	−0.495010	+	0.0872836i	−0.0794303	+	0.996840i	$0.525310\pi$
$954$		0			0
$955$	−3.30608	−	22.5894i	−0.106982	−	0.730975i
$956$	10.0458	−	56.9728i	0.324906	−	1.84263i
$957$		0			0
$958$	55.3578	−	31.9608i	1.78853	−	1.03261i
$959$	−0.610947	+	0.222367i	−0.0197285	+	0.00718059i
$960$		0			0
$961$	5.70235	+	9.87675i	0.183947	+	0.318605i
$962$	−25.9695	−	14.9935i	−0.837292	−	0.483411i
$963$		0			0
$964$	−29.0057	+	24.3387i	−0.934210	+	0.783895i
$965$	−8.31840	−	25.1137i	−0.267779	−	0.808437i
$966$		0			0
$967$	−5.48978	+	15.0830i	−0.176539	+	0.485038i	−0.996128	−	0.0879145i	$-0.971980\pi$
$967$	−5.48978	+	15.0830i	−0.176539	+	0.485038i	0.819589	+	0.572952i	$0.194202\pi$
$968$		−	13.6898i		−	0.440006i
$969$		0			0
$970$	−0.361735	+	0.586304i	−0.0116146	+	0.0188251i
$971$	−5.42132	−	1.97320i	−0.173978	−	0.0633230i	0.253562	−	0.967319i	$-0.418398\pi$
$971$	−5.42132	−	1.97320i	−0.173978	−	0.0633230i	−0.427541	+	0.903996i	$0.640620\pi$
$972$		0			0
$973$	7.89644	−	9.41061i	0.253148	−	0.301690i
$974$	5.57154	−	4.67507i	0.178524	−	0.149799i
$975$		0			0
$976$	4.48466	−	7.76766i	0.143551	−	0.248637i
$977$	40.5060	−	23.3862i	1.29590	−	0.748190i	0.316209	−	0.948689i	$-0.397590\pi$
$977$	40.5060	−	23.3862i	1.29590	−	0.748190i	0.979694	+	0.200499i	$0.0642565\pi$
$978$		0			0
$979$	44.3509	−	16.1424i	1.41746	−	0.515914i
$980$	−34.9759	−	1.02191i	−1.11726	−	0.0326438i
$981$		0			0
$982$	2.91607	+	0.514183i	0.0930557	+	0.0164082i
$983$	21.6002	+	25.7421i	0.688939	+	0.821046i	0.991227	−	0.132171i	$-0.0421947\pi$
$983$	21.6002	+	25.7421i	0.688939	+	0.821046i	−0.302288	+	0.953217i	$0.597750\pi$
$984$		0			0
$985$	−2.25180	+	5.66613i	−0.0717484	+	0.180538i
$986$	15.4940	+	5.63936i	0.493430	+	0.179594i
$987$		0			0
$988$	−4.64142	−	97.7507i	−0.147663	−	3.10986i
$989$	3.45139			0.109748
$990$		0			0
$991$	−7.91905	−	44.9112i	−0.251557	−	1.42665i	−0.804758	−	0.593602i	$-0.797705\pi$
$991$	−7.91905	−	44.9112i	−0.251557	−	1.42665i	0.553202	−	0.833047i	$-0.313406\pi$
$992$	−9.24768	+	11.0210i	−0.293614	+	0.349916i
$993$		0			0
$994$	1.77564	−	10.0701i	0.0563198	−	0.319406i
$995$	4.75157	+	8.81488i	0.150635	+	0.279450i
$996$		0			0
$997$	1.64213	+	4.51171i	0.0520067	+	0.142887i	0.962976	−	0.269587i	$-0.0868870\pi$
$997$	1.64213	+	4.51171i	0.0520067	+	0.142887i	−0.910969	+	0.412474i	$0.864665\pi$
$998$	−15.8713	−	43.6062i	−0.502399	−	1.38033i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.da.b.289.1		48
3.2	odd	2		95.2.p.a.4.8	yes	48
5.4	even	2	inner	855.2.da.b.289.8		48
15.2	even	4		475.2.l.f.251.8		48
15.8	even	4		475.2.l.f.251.1		48
15.14	odd	2		95.2.p.a.4.1	✓	48
19.5	even	9	inner	855.2.da.b.784.8		48
57.5	odd	18		95.2.p.a.24.1	yes	48
57.29	even	18		1805.2.b.l.1084.2		24
57.47	odd	18		1805.2.b.k.1084.23		24
95.24	even	18	inner	855.2.da.b.784.1		48
285.29	even	18		1805.2.b.l.1084.23		24
285.47	even	36		9025.2.a.cu.1.2		24
285.62	even	36		475.2.l.f.176.8		48
285.104	odd	18		1805.2.b.k.1084.2		24
285.119	odd	18		95.2.p.a.24.8	yes	48
285.143	odd	36		9025.2.a.ct.1.2		24
285.218	even	36		9025.2.a.cu.1.23		24
285.233	even	36		475.2.l.f.176.1		48
285.257	odd	36		9025.2.a.ct.1.23		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.4.1	✓	48	15.14	odd	2
95.2.p.a.4.8	yes	48	3.2	odd	2
95.2.p.a.24.1	yes	48	57.5	odd	18
95.2.p.a.24.8	yes	48	285.119	odd	18
475.2.l.f.176.1		48	285.233	even	36
475.2.l.f.176.8		48	285.62	even	36
475.2.l.f.251.1		48	15.8	even	4
475.2.l.f.251.8		48	15.2	even	4
855.2.da.b.289.1		48	1.1	even	1	trivial
855.2.da.b.289.8		48	5.4	even	2	inner
855.2.da.b.784.1		48	95.24	even	18	inner
855.2.da.b.784.8		48	19.5	even	9	inner
1805.2.b.k.1084.2		24	285.104	odd	18
1805.2.b.k.1084.23		24	57.47	odd	18
1805.2.b.l.1084.2		24	57.29	even	18
1805.2.b.l.1084.23		24	285.29	even	18
9025.2.a.ct.1.2		24	285.143	odd	36
9025.2.a.ct.1.23		24	285.257	odd	36
9025.2.a.cu.1.2		24	285.47	even	36
9025.2.a.cu.1.23		24	285.218	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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.da (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.810919 + 2.22798i) q^{2} +(-2.77422 - 2.32785i) q^{4} +(0.323811 + 2.21250i) q^{5} +(1.41749 + 0.818386i) q^{7} +(3.32944 - 1.92225i) q^{8} +O(q^{10})\)	\(q+(-0.810919 + 2.22798i) q^{2} +(-2.77422 - 2.32785i) q^{4} +(0.323811 + 2.21250i) q^{5} +(1.41749 + 0.818386i) q^{7} +(3.32944 - 1.92225i) q^{8} +(-5.19199 - 1.07271i) q^{10} +(1.36374 + 2.36206i) q^{11} +(6.10515 + 1.07650i) q^{13} +(-2.97282 + 2.49449i) q^{14} +(0.325107 + 1.84377i) q^{16} +(-1.06864 + 2.93608i) q^{17} +(3.46824 + 2.64032i) q^{19} +(4.25204 - 6.89175i) q^{20} +(-6.36852 + 1.12294i) q^{22} +(4.69173 - 5.59139i) q^{23} +(-4.79029 + 1.43286i) q^{25} +(-7.34921 + 12.7292i) q^{26} +(-2.02734 - 5.57008i) q^{28} +(-2.09149 + 0.761241i) q^{29} +(-2.21333 + 3.83360i) q^{31} +(3.20067 + 0.564364i) q^{32} +(-5.67494 - 4.76184i) q^{34} +(-1.35168 + 3.40119i) q^{35} +2.04016i q^{37} +(-8.69505 + 5.58609i) q^{38} +(5.33109 + 6.74393i) q^{40} +(-0.681538 - 3.86519i) q^{41} +(0.303946 + 0.362229i) q^{43} +(1.71522 - 9.72747i) q^{44} +(8.65289 + 14.9872i) q^{46} +(-0.787194 - 2.16280i) q^{47} +(-2.16049 - 3.74208i) q^{49} +(0.692149 - 11.8346i) q^{50} +(-14.4311 - 17.1983i) q^{52} +(-4.09062 + 4.87501i) q^{53} +(-4.78447 + 3.78213i) q^{55} +6.29258 q^{56} -5.27711i q^{58} +(-11.5263 - 4.19524i) q^{59} +(-3.66993 - 3.07944i) q^{61} +(-6.74636 - 8.03999i) q^{62} +(-5.72509 + 9.91615i) q^{64} +(-0.404845 + 13.8562i) q^{65} +(-0.229482 - 0.630496i) q^{67} +(9.79940 - 5.65769i) q^{68} +(-6.48168 - 5.76960i) q^{70} +(-2.01848 + 1.69370i) q^{71} +(6.41403 - 1.13097i) q^{73} +(-4.54543 - 1.65440i) q^{74} +(-3.47540 - 15.3984i) q^{76} +4.46426i q^{77} +(-0.715459 - 4.05757i) q^{79} +(-3.97407 + 1.31633i) q^{80} +(9.16425 + 1.61590i) q^{82} +(5.56331 + 3.21198i) q^{83} +(-6.84210 - 1.41364i) q^{85} +(-1.05351 + 0.383448i) q^{86} +(9.08097 + 5.24290i) q^{88} +(3.00487 - 17.0415i) q^{89} +(7.77297 + 6.52229i) q^{91} +(-26.0318 + 4.59011i) q^{92} +5.45702 q^{94} +(-4.71865 + 8.52844i) q^{95} +(0.0444434 - 0.122107i) q^{97} +(10.0893 - 1.77901i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 18 q^{4} + 6 q^{5}+O(q^{10}) \) 48 * q - 18 * q^4 + 6 * q^5	\( 48 q - 18 q^{4} + 6 q^{5} - 15 q^{10} + 12 q^{11} - 6 q^{14} - 42 q^{16} + 12 q^{19} - 42 q^{20} + 12 q^{25} - 12 q^{26} - 42 q^{31} - 36 q^{34} - 6 q^{35} + 66 q^{40} - 6 q^{41} + 6 q^{44} - 6 q^{46} + 12 q^{49} + 18 q^{50} - 36 q^{56} + 36 q^{59} + 48 q^{61} + 18 q^{65} - 123 q^{70} + 24 q^{71} - 84 q^{74} + 66 q^{76} + 48 q^{79} + 39 q^{80} - 84 q^{85} + 42 q^{86} + 12 q^{89} - 30 q^{91} - 72 q^{94} + 63 q^{95}+O(q^{100}) \) 48 * q - 18 * q^4 + 6 * q^5 - 15 * q^10 + 12 * q^11 - 6 * q^14 - 42 * q^16 + 12 * q^19 - 42 * q^20 + 12 * q^25 - 12 * q^26 - 42 * q^31 - 36 * q^34 - 6 * q^35 + 66 * q^40 - 6 * q^41 + 6 * q^44 - 6 * q^46 + 12 * q^49 + 18 * q^50 - 36 * q^56 + 36 * q^59 + 48 * q^61 + 18 * q^65 - 123 * q^70 + 24 * q^71 - 84 * q^74 + 66 * q^76 + 48 * q^79 + 39 * q^80 - 84 * q^85 + 42 * q^86 + 12 * q^89 - 30 * q^91 - 72 * q^94 + 63 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more