LMFDB - Embedded newform 819.2.s.e.802.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(289,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 2]))

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

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

chi := DirichletCharacter("819.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.s (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + \cdots + 1 $ x^16 + 11x^14 - 4x^13 + 87x^12 - 35x^11 + 326x^10 - 205x^9 + 895x^8 - 481x^7 + 1005x^6 - 544x^5 + 811x^4 - 312x^3 + 195x^2 + 13x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			802.4
Root			$-0.0340180 - 0.0589209i$ of defining polynomial
Character	$\chi$	$=$	819.802
Dual form			819.2.s.e.289.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0680360 q^{2} -1.99537 q^{4} +(-1.52954 - 2.64923i) q^{5} +(0.910236 - 2.48424i) q^{7} +0.271829 q^{8} +O(q^{10})$	\(q-0.0680360 q^{2} -1.99537 q^{4} +(-1.52954 - 2.64923i) q^{5} +(0.910236 - 2.48424i) q^{7} +0.271829 q^{8} +(0.104063 + 0.180243i) q^{10} +(-2.17896 - 3.77408i) q^{11} +(-1.79952 + 3.12437i) q^{13} +(-0.0619288 + 0.169018i) q^{14} +3.97225 q^{16} +3.52867 q^{17} +(-3.45112 + 5.97751i) q^{19} +(3.05199 + 5.28621i) q^{20} +(0.148248 + 0.256773i) q^{22} -3.33524 q^{23} +(-2.17896 + 3.77408i) q^{25} +(0.122432 - 0.212570i) q^{26} +(-1.81626 + 4.95699i) q^{28} +(-4.95991 + 8.59082i) q^{29} +(4.62451 - 8.00989i) q^{31} -0.813913 q^{32} -0.240077 q^{34} +(-7.97359 + 1.38831i) q^{35} -0.109046 q^{37} +(0.234800 - 0.406686i) q^{38} +(-0.415772 - 0.720139i) q^{40} +(-1.76899 + 3.06399i) q^{41} +(-0.844102 - 1.46203i) q^{43} +(4.34784 + 7.53068i) q^{44} +0.226916 q^{46} +(-1.28133 - 2.21933i) q^{47} +(-5.34294 - 4.52250i) q^{49} +(0.148248 - 0.256773i) q^{50} +(3.59072 - 6.23429i) q^{52} +(-2.65681 + 4.60173i) q^{53} +(-6.66561 + 11.5452i) q^{55} +(0.247428 - 0.675289i) q^{56} +(0.337453 - 0.584485i) q^{58} -7.55704 q^{59} +(-2.43658 + 4.22029i) q^{61} +(-0.314633 + 0.544960i) q^{62} -7.88912 q^{64} +(11.0296 - 0.0114818i) q^{65} +(-0.340218 - 0.589274i) q^{67} -7.04101 q^{68} +(0.542491 - 0.0944552i) q^{70} +(2.61572 + 4.53055i) q^{71} +(1.75956 - 3.04764i) q^{73} +0.00741905 q^{74} +(6.88626 - 11.9274i) q^{76} +(-11.3591 + 1.97778i) q^{77} +(4.85408 + 8.40751i) q^{79} +(-6.07570 - 10.5234i) q^{80} +(0.120355 - 0.208461i) q^{82} -5.41662 q^{83} +(-5.39723 - 9.34828i) q^{85} +(0.0574293 + 0.0994705i) q^{86} +(-0.592305 - 1.02590i) q^{88} +7.70414 q^{89} +(6.12372 + 7.31438i) q^{91} +6.65503 q^{92} +(0.0871768 + 0.150995i) q^{94} +21.1144 q^{95} +(-3.86359 - 6.69194i) q^{97} +(0.363512 + 0.307692i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{4} + q^{7} - 12 q^{8}+O(q^{10}) $ 16 * q + 12 * q^4 + q^7 - 12 * q^8	$ 16 q + 12 q^{4} + q^{7} - 12 q^{8} - 4 q^{10} + 2 q^{11} + 5 q^{13} + 7 q^{14} + 12 q^{16} - 4 q^{17} - 11 q^{19} + 20 q^{20} + 7 q^{22} + 8 q^{23} + 2 q^{25} - 33 q^{26} - q^{28} - 15 q^{29} + 3 q^{31} + 6 q^{32} - 68 q^{34} - 8 q^{37} - 2 q^{38} - 25 q^{40} - 19 q^{41} + 11 q^{43} + 16 q^{44} - 4 q^{46} - 5 q^{47} + 7 q^{49} + 7 q^{50} - 18 q^{52} - 36 q^{53} - 15 q^{55} + 51 q^{56} + 20 q^{58} - 34 q^{59} - 22 q^{61} + 6 q^{62} - 20 q^{64} + 24 q^{65} + 26 q^{67} + 10 q^{68} + 46 q^{70} - 9 q^{71} - 6 q^{73} + 30 q^{74} - 16 q^{76} + 36 q^{77} + 16 q^{79} + 28 q^{80} - q^{82} - 36 q^{83} - 4 q^{85} - 16 q^{86} + 24 q^{88} + 40 q^{89} - 10 q^{91} + 94 q^{92} - 20 q^{94} + 7 q^{97} - 18 q^{98}+O(q^{100}) $ 16 * q + 12 * q^4 + q^7 - 12 * q^8 - 4 * q^10 + 2 * q^11 + 5 * q^13 + 7 * q^14 + 12 * q^16 - 4 * q^17 - 11 * q^19 + 20 * q^20 + 7 * q^22 + 8 * q^23 + 2 * q^25 - 33 * q^26 - q^28 - 15 * q^29 + 3 * q^31 + 6 * q^32 - 68 * q^34 - 8 * q^37 - 2 * q^38 - 25 * q^40 - 19 * q^41 + 11 * q^43 + 16 * q^44 - 4 * q^46 - 5 * q^47 + 7 * q^49 + 7 * q^50 - 18 * q^52 - 36 * q^53 - 15 * q^55 + 51 * q^56 + 20 * q^58 - 34 * q^59 - 22 * q^61 + 6 * q^62 - 20 * q^64 + 24 * q^65 + 26 * q^67 + 10 * q^68 + 46 * q^70 - 9 * q^71 - 6 * q^73 + 30 * q^74 - 16 * q^76 + 36 * q^77 + 16 * q^79 + 28 * q^80 - q^82 - 36 * q^83 - 4 * q^85 - 16 * q^86 + 24 * q^88 + 40 * q^89 - 10 * q^91 + 94 * q^92 - 20 * q^94 + 7 * q^97 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.0680360			−0.0481087			−0.0240543	−	0.999711i	$-0.507657\pi$
$2$	−0.0680360			−0.0481087			−0.0240543	+	0.999711i	$0.507657\pi$
$3$		0			0
$3$		0			0
$4$	−1.99537			−0.997686
$5$	−1.52954	−	2.64923i	−0.684030	−	1.18477i	−0.973741	−	0.227660i	$-0.926893\pi$
$5$	−1.52954	−	2.64923i	−0.684030	−	1.18477i	0.289711	−	0.957114i	$-0.406441\pi$
$6$		0			0
$7$	0.910236	−	2.48424i	0.344037	−	0.938956i
$7$	0.910236	−	2.48424i	0.344037	−	0.938956i
$8$	0.271829			0.0961060
$9$		0			0
$10$	0.104063	+	0.180243i	0.0329078	+	0.0569979i
$11$	−2.17896	−	3.77408i	−0.656982	−	1.13793i	−0.981393	−	0.192010i	$-0.938499\pi$
$11$	−2.17896	−	3.77408i	−0.656982	−	1.13793i	0.324411	−	0.945916i	$-0.394834\pi$
$12$		0			0
$13$	−1.79952	+	3.12437i	−0.499098	+	0.866545i
$13$	−1.79952	+	3.12437i	−0.499098	+	0.866545i
$14$	−0.0619288	+	0.169018i	−0.0165512	+	0.0451719i
$15$		0			0
$16$	3.97225			0.993062
$17$	3.52867			0.855829			0.427914	−	0.903819i	$-0.359248\pi$
$17$	3.52867			0.855829			0.427914	+	0.903819i	$0.359248\pi$
$18$		0			0
$19$	−3.45112	+	5.97751i	−0.791741	+	1.37134i	0.133147	+	0.991096i	$0.457492\pi$
$19$	−3.45112	+	5.97751i	−0.791741	+	1.37134i	−0.924888	+	0.380239i	$0.875842\pi$
$20$	3.05199	+	5.28621i	0.682446	+	1.18203i
$21$		0			0
$22$	0.148248	+	0.256773i	0.0316066	+	0.0547442i
$23$	−3.33524			−0.695445			−0.347722	−	0.937598i	$-0.613045\pi$
$23$	−3.33524			−0.695445			−0.347722	+	0.937598i	$0.613045\pi$
$24$		0			0
$25$	−2.17896	+	3.77408i	−0.435793	+	0.754815i
$26$	0.122432	−	0.212570i	0.0240110	−	0.0416884i
$27$		0			0
$28$	−1.81626	+	4.95699i	−0.343241	+	0.936783i
$29$	−4.95991	+	8.59082i	−0.921033	+	1.59528i	−0.123213	+	0.992380i	$0.539320\pi$
$29$	−4.95991	+	8.59082i	−0.921033	+	1.59528i	−0.797820	+	0.602896i	$0.794013\pi$
$30$		0			0
$31$	4.62451	−	8.00989i	0.830587	−	1.43862i	−0.0669867	−	0.997754i	$-0.521339\pi$
$31$	4.62451	−	8.00989i	0.830587	−	1.43862i	0.897574	−	0.440865i	$-0.145328\pi$
$32$	−0.813913			−0.143881
$33$		0			0
$34$	−0.240077			−0.0411728
$35$	−7.97359	+	1.38831i	−1.34778	+	0.234668i
$36$		0			0
$37$	−0.109046			−0.0179270			−0.00896352	−	0.999960i	$-0.502853\pi$
$37$	−0.109046			−0.0179270			−0.00896352	+	0.999960i	$0.502853\pi$
$38$	0.234800	−	0.406686i	0.0380896	−	0.0659731i
$39$		0			0
$40$	−0.415772	−	0.720139i	−0.0657394	−	0.113864i
$41$	−1.76899	+	3.06399i	−0.276270	+	0.478514i	−0.970455	−	0.241283i	$-0.922432\pi$
$41$	−1.76899	+	3.06399i	−0.276270	+	0.478514i	0.694185	+	0.719797i	$0.255765\pi$
$42$		0			0
$43$	−0.844102	−	1.46203i	−0.128724	−	0.222957i	0.794458	−	0.607319i	$-0.207755\pi$
$43$	−0.844102	−	1.46203i	−0.128724	−	0.222957i	−0.923183	+	0.384362i	$0.874422\pi$
$44$	4.34784	+	7.53068i	0.655462	+	1.13529i
$45$		0			0
$46$	0.226916			0.0334569
$47$	−1.28133	−	2.21933i	−0.186902	−	0.323723i	0.757314	−	0.653051i	$-0.226511\pi$
$47$	−1.28133	−	2.21933i	−0.186902	−	0.323723i	−0.944216	+	0.329328i	$0.893178\pi$
$48$		0			0
$49$	−5.34294	−	4.52250i	−0.763277	−	0.646071i
$50$	0.148248	−	0.256773i	0.0209654	−	0.0363132i
$51$		0			0
$52$	3.59072	−	6.23429i	0.497943	−	0.864540i
$53$	−2.65681	+	4.60173i	−0.364941	+	0.632097i	−0.988767	−	0.149467i	$-0.952244\pi$
$53$	−2.65681	+	4.60173i	−0.364941	+	0.632097i	0.623825	+	0.781564i	$0.285578\pi$
$54$		0			0
$55$	−6.66561	+	11.5452i	−0.898791	+	1.55675i
$56$	0.247428	−	0.675289i	0.0330640	−	0.0902393i
$57$		0			0
$58$	0.337453	−	0.584485i	0.0443097	−	0.0767466i
$59$	−7.55704			−0.983843			−0.491921	−	0.870640i	$-0.663705\pi$
$59$	−7.55704			−0.983843			−0.491921	+	0.870640i	$0.663705\pi$
$60$		0			0
$61$	−2.43658	+	4.22029i	−0.311973	+	0.540352i	−0.978789	−	0.204869i	$-0.934323\pi$
$61$	−2.43658	+	4.22029i	−0.311973	+	0.540352i	0.666817	+	0.745222i	$0.267656\pi$
$62$	−0.314633	+	0.544960i	−0.0399584	+	0.0692101i
$63$		0			0
$64$	−7.88912			−0.986140
$65$	11.0296	−	0.0114818i	1.36806	−	0.00142415i
$66$		0			0
$67$	−0.340218	−	0.589274i	−0.0415642	−	0.0719913i	0.844495	−	0.535564i	$-0.179901\pi$
$67$	−0.340218	−	0.589274i	−0.0415642	−	0.0719913i	−0.886059	+	0.463572i	$0.846567\pi$
$68$	−7.04101			−0.853848
$69$		0			0
$70$	0.542491	−	0.0944552i	0.0648400	−	0.0112896i
$71$	2.61572	+	4.53055i	0.310428	+	0.537678i	0.978455	−	0.206460i	$-0.0661942\pi$
$71$	2.61572	+	4.53055i	0.310428	+	0.537678i	−0.668027	+	0.744137i	$0.732861\pi$
$72$		0			0
$73$	1.75956	−	3.04764i	0.205941	−	0.356699i	−0.744491	−	0.667632i	$-0.767308\pi$
$73$	1.75956	−	3.04764i	0.205941	−	0.356699i	0.950432	+	0.310933i	$0.100641\pi$
$74$	0.00741905			0.000862447
$75$		0			0
$76$	6.88626	−	11.9274i	0.789908	−	1.36816i
$77$	−11.3591	+	1.97778i	−1.29449	+	0.225389i
$78$		0			0
$79$	4.85408	+	8.40751i	0.546126	+	0.945919i	0.998535	+	0.0541080i	$0.0172315\pi$
$79$	4.85408	+	8.40751i	0.546126	+	0.945919i	−0.452409	+	0.891811i	$0.649435\pi$
$80$	−6.07570	−	10.5234i	−0.679284	−	1.17655i
$81$		0			0
$82$	0.120355	−	0.208461i	0.0132910	−	0.0230207i
$83$	−5.41662			−0.594551			−0.297275	−	0.954792i	$-0.596078\pi$
$83$	−5.41662			−0.594551			−0.297275	+	0.954792i	$0.596078\pi$
$84$		0			0
$85$	−5.39723	−	9.34828i	−0.585412	−	1.01396i
$86$	0.0574293	+	0.0994705i	0.00619276	+	0.0107262i
$87$		0			0
$88$	−0.592305	−	1.02590i	−0.0631400	−	0.109362i
$89$	7.70414			0.816638			0.408319	−	0.912839i	$-0.366115\pi$
$89$	7.70414			0.816638			0.408319	+	0.912839i	$0.366115\pi$
$90$		0			0
$91$	6.12372	+	7.31438i	0.641940	+	0.766755i
$92$	6.65503			0.693835
$93$		0			0
$94$	0.0871768	+	0.150995i	0.00899160	+	0.0155739i
$95$	21.1144			2.16630
$96$		0			0
$97$	−3.86359	−	6.69194i	−0.392288	−	0.679463i	0.600463	−	0.799653i	$-0.294983\pi$
$97$	−3.86359	−	6.69194i	−0.392288	−	0.679463i	−0.992751	+	0.120189i	$0.961650\pi$
$98$	0.363512	+	0.307692i	0.0367203	+	0.0310816i
$99$		0			0
$100$	4.34784	−	7.53068i	0.434784	−	0.753068i
$101$	−1.94016	−	3.36045i	−0.193053	−	0.334377i	0.753208	−	0.657783i	$-0.228505\pi$
$101$	−1.94016	−	3.36045i	−0.193053	−	0.334377i	−0.946260	+	0.323406i	$0.895172\pi$
$102$		0			0
$103$	−4.29088	−	7.43202i	−0.422793	−	0.732299i	0.573419	−	0.819263i	$-0.305617\pi$
$103$	−4.29088	−	7.43202i	−0.422793	−	0.732299i	−0.996211	+	0.0869638i	$0.972284\pi$
$104$	−0.489163	+	0.849295i	−0.0479663	+	0.0832802i
$105$		0			0
$106$	0.180759	−	0.313083i	0.0175568	−	0.0304093i
$107$	11.2032			1.08305			0.541525	−	0.840684i	$-0.317847\pi$
$107$	11.2032			1.08305			0.541525	+	0.840684i	$0.317847\pi$
$108$		0			0
$109$	6.98282	−	12.0946i	0.668833	−	1.15845i	−0.309398	−	0.950933i	$-0.600128\pi$
$109$	6.98282	−	12.0946i	0.668833	−	1.15845i	0.978231	−	0.207520i	$-0.0665391\pi$
$110$	0.453501	−	0.785487i	0.0432396	−	0.0748932i
$111$		0			0
$112$	3.61568	−	9.86804i	0.341650	−	0.932442i
$113$	3.38888	+	5.86972i	0.318799	+	0.552176i	0.980238	−	0.197823i	$-0.0633871\pi$
$113$	3.38888	+	5.86972i	0.318799	+	0.552176i	−0.661439	+	0.749999i	$0.730054\pi$
$114$		0			0
$115$	5.10137	+	8.83582i	0.475705	+	0.823945i
$116$	9.89687	−	17.1419i	0.918901	−	1.59158i
$117$		0			0
$118$	0.514150			0.0473314
$119$	3.21193	−	8.76609i	0.294437	−	0.803586i
$120$		0			0
$121$	−3.99577	+	6.92087i	−0.363252	+	0.629170i
$122$	0.165775	−	0.287131i	0.0150086	−	0.0259956i
$123$		0			0
$124$	−9.22762	+	15.9827i	−0.828664	+	1.43529i
$125$	−1.96415			−0.175679
$126$		0			0
$127$	−6.68899	+	11.5857i	−0.593552	+	1.02806i	0.400198	+	0.916429i	$0.368941\pi$
$127$	−6.68899	+	11.5857i	−0.593552	+	1.02806i	−0.993750	+	0.111633i	$0.964392\pi$
$128$	2.16457			0.191323
$129$		0			0
$130$	−0.750412		0.000781178i	−0.0658155		6.85139e-5i
$131$	−9.06148	−	15.6949i	−0.791705	−	1.37127i	−0.924910	−	0.380185i	$-0.875860\pi$
$131$	−9.06148	−	15.6949i	−0.791705	−	1.37127i	0.133205	−	0.991089i	$-0.457473\pi$
$132$		0			0
$133$	11.7083	+	14.0144i	1.01524	+	1.21520i
$134$	0.0231470	+	0.0400918i	0.00199960	+	0.00346341i
$135$		0			0
$136$	0.959195			0.0822503
$137$	−21.3405			−1.82324			−0.911622	−	0.411030i	$-0.865169\pi$
$137$	−21.3405			−1.82324			−0.911622	+	0.411030i	$0.865169\pi$
$138$		0			0
$139$	−0.0705287	−	0.122159i	−0.00598217	−	0.0103614i	0.863019	−	0.505172i	$-0.168571\pi$
$139$	−0.0705287	−	0.122159i	−0.00598217	−	0.0103614i	−0.869001	+	0.494810i	$0.835238\pi$
$140$	15.9103	−	2.77020i	1.34466	−	0.234125i
$141$		0			0
$142$	−0.177963	−	0.308240i	−0.0149343	−	0.0258670i
$143$	15.7127	−	0.0163569i	1.31396	−	0.00136784i
$144$		0			0
$145$	30.3455			2.52006
$146$	−0.119713	+	0.207349i	−0.00990753	+	0.0171603i
$147$		0			0
$148$	0.217587			0.0178856
$149$	−7.17797	+	12.4326i	−0.588043	+	1.01852i	0.406446	+	0.913675i	$0.366768\pi$
$149$	−7.17797	+	12.4326i	−0.588043	+	1.01852i	−0.994489	+	0.104845i	$0.966565\pi$
$150$		0			0
$151$	−7.83172	+	13.5649i	−0.637336	+	1.10390i	0.348679	+	0.937242i	$0.386631\pi$
$151$	−7.83172	+	13.5649i	−0.637336	+	1.10390i	−0.986015	+	0.166657i	$0.946703\pi$
$152$	−0.938114	+	1.62486i	−0.0760911	+	0.131794i
$153$		0			0
$154$	0.772827	−	0.134560i	0.0622762	−	0.0108432i
$155$	−28.2934			−2.27258
$156$		0			0
$157$	−6.75022	+	11.6917i	−0.538726	+	0.933101i	0.460247	+	0.887791i	$0.347761\pi$
$157$	−6.75022	+	11.6917i	−0.538726	+	0.933101i	−0.998973	+	0.0453098i	$0.985572\pi$
$158$	−0.330252	−	0.572013i	−0.0262734	−	0.0455069i
$159$		0			0
$160$	1.24491	+	2.15625i	0.0984188	+	0.170466i
$161$	−3.03585	+	8.28554i	−0.239259	+	0.652992i
$162$		0			0
$163$	1.32862	−	2.30124i	0.104066	−	0.180247i	−0.809291	−	0.587409i	$-0.800148\pi$
$163$	1.32862	−	2.30124i	0.104066	−	0.180247i	0.913356	+	0.407162i	$0.133481\pi$
$164$	3.52980	−	6.11379i	0.275631	−	0.477407i
$165$		0			0
$166$	0.368525			0.0286031
$167$	10.9142	−	18.9040i	0.844567	−	1.46283i	−0.0414294	−	0.999141i	$-0.513191\pi$
$167$	10.9142	−	18.9040i	0.844567	−	1.46283i	0.885997	−	0.463692i	$-0.153475\pi$
$168$		0			0
$169$	−6.52343	−	11.2448i	−0.501802	−	0.864983i
$170$	0.367206	+	0.636019i	0.0281634	+	0.0487805i
$171$		0			0
$172$	1.68430	+	2.91729i	0.128426	+	0.222441i
$173$	8.84120	−	15.3134i	0.672184	−	1.16426i	−0.305099	−	0.952321i	$-0.598690\pi$
$173$	8.84120	−	15.3134i	0.672184	−	1.16426i	0.977283	−	0.211936i	$-0.0679770\pi$
$174$		0			0
$175$	7.39236	+	8.84838i	0.558810	+	0.668875i
$176$	−8.65539	−	14.9916i	−0.652424	−	1.13003i
$177$		0			0
$178$	−0.524159			−0.0392874
$179$	4.86499	+	8.42641i	0.363626	+	0.629819i	0.988555	−	0.150863i	$-0.0482051\pi$
$179$	4.86499	+	8.42641i	0.363626	+	0.629819i	−0.624928	+	0.780682i	$0.714872\pi$
$180$		0			0
$181$	4.01332			0.298308			0.149154	−	0.988814i	$-0.452345\pi$
$181$	4.01332			0.298308			0.149154	+	0.988814i	$0.452345\pi$
$182$	−0.416633	−	0.497641i	−0.0308829	−	0.0368876i
$183$		0			0
$184$	−0.906613			−0.0668364
$185$	0.166790	+	0.288888i	0.0122626	+	0.0212395i
$186$		0			0
$187$	−7.68885	−	13.3175i	−0.562265	−	0.973871i
$188$	2.55674	+	4.42840i	0.186469	+	0.322974i
$189$		0			0
$190$	−1.43654			−0.104218
$191$	−7.39519	+	12.8088i	−0.535097	+	0.926816i	0.464061	+	0.885803i	$0.346392\pi$
$191$	−7.39519	+	12.8088i	−0.535097	+	0.926816i	−0.999159	+	0.0410127i	$0.986942\pi$
$192$		0			0
$193$	−11.1716	−	19.3497i	−0.804146	−	1.39282i	−0.916866	−	0.399195i	$-0.869290\pi$
$193$	−11.1716	−	19.3497i	−0.804146	−	1.39282i	0.112720	−	0.993627i	$-0.464044\pi$
$194$	0.262863	+	0.455292i	0.0188725	+	0.0326881i
$195$		0			0
$196$	10.6611	+	9.02406i	0.761511	+	0.644576i
$197$	3.16282	−	5.47816i	0.225342	−	0.390303i	−0.731080	−	0.682291i	$-0.760984\pi$
$197$	3.16282	−	5.47816i	0.225342	−	0.390303i	0.956422	+	0.291988i	$0.0943169\pi$
$198$		0			0
$199$	−6.03617			−0.427893			−0.213946	−	0.976845i	$-0.568632\pi$
$199$	−6.03617			−0.427893			−0.213946	+	0.976845i	$0.568632\pi$
$200$	−0.592305	+	1.02590i	−0.0418823	+	0.0725423i
$201$		0			0
$202$	0.132000	+	0.228631i	0.00928751	+	0.0160864i
$203$	16.8270	+	20.1413i	1.18102	+	1.41364i
$204$		0			0
$205$	10.8230			0.755908
$206$	0.291934	+	0.505645i	0.0203400	+	0.0352299i
$207$		0			0
$208$	−7.14816	+	12.4108i	−0.495635	+	0.860533i
$209$	30.0795			2.08064
$210$		0			0
$211$	0.646092	−	1.11906i	0.0444788	−	0.0770395i	−0.842929	−	0.538025i	$-0.819171\pi$
$211$	0.646092	−	1.11906i	0.0444788	−	0.0770395i	0.887408	+	0.460985i	$0.152504\pi$
$212$	5.30133	−	9.18217i	0.364097	−	0.630634i
$213$		0			0
$214$	−0.762218			−0.0521041
$215$	−2.58217	+	4.47245i	−0.176103	+	0.305019i
$216$		0			0
$217$	−15.6891	−	18.7793i	−1.06505	−	1.27482i
$218$	−0.475083	+	0.822868i	−0.0321767	+	0.0557316i
$219$		0			0
$220$	13.3004	−	23.0369i	0.896710	−	1.55315i
$221$	−6.34993	+	11.0249i	−0.427143	+	0.741615i
$222$		0			0
$223$	5.79892	−	10.0440i	0.388324	−	0.672597i	−0.603900	−	0.797060i	$-0.706387\pi$
$223$	5.79892	−	10.0440i	0.388324	−	0.672597i	0.992224	+	0.124463i	$0.0397207\pi$
$224$	−0.740853	+	2.02196i	−0.0495004	+	0.135098i
$225$		0			0
$226$	−0.230566	−	0.399352i	−0.0153370	−	0.0265645i
$227$	0.798498			0.0529982			0.0264991	−	0.999649i	$-0.491564\pi$
$227$	0.798498			0.0529982			0.0264991	+	0.999649i	$0.491564\pi$
$228$		0			0
$229$	−11.6073	−	20.1044i	−0.767030	−	1.32854i	−0.939166	−	0.343463i	$-0.888400\pi$
$229$	−11.6073	−	20.1044i	−0.767030	−	1.32854i	0.172136	−	0.985073i	$-0.444933\pi$
$230$	−0.347076	−	0.601154i	−0.0228855	−	0.0396389i
$231$		0			0
$232$	−1.34825	+	2.33523i	−0.0885168	+	0.153316i
$233$	−6.09388	−	10.5549i	−0.399223	−	0.691475i	0.594407	−	0.804164i	$-0.297387\pi$
$233$	−6.09388	−	10.5549i	−0.399223	−	0.691475i	−0.993630	+	0.112689i	$0.964054\pi$
$234$		0			0
$235$	−3.91969	+	6.78911i	−0.255693	+	0.442873i
$236$	15.0791			0.981565
$237$		0			0
$238$	−0.218526	+	0.596409i	−0.0141650	+	0.0386595i
$239$	0.484332			0.0313289			0.0156644	−	0.999877i	$-0.495014\pi$
$239$	0.484332			0.0313289			0.0156644	+	0.999877i	$0.495014\pi$
$240$		0			0
$241$	−2.32012			−0.149452			−0.0747261	−	0.997204i	$-0.523808\pi$
$241$	−2.32012			−0.149452			−0.0747261	+	0.997204i	$0.523808\pi$
$242$	0.271856	−	0.470868i	0.0174756	−	0.0302686i
$243$		0			0
$244$	4.86189	−	8.42104i	0.311251	−	0.539102i
$245$	−3.80894	+	21.0720i	−0.243344	+	1.34624i
$246$		0			0
$247$	−12.4656	−	21.5393i	−0.793168	−	1.37051i
$248$	1.25708	−	2.17732i	0.0798244	−	0.138260i
$249$		0			0
$250$	0.133633			0.00845166
$251$	−13.7950	−	23.8936i	−0.870732	−	1.50815i	−0.861241	−	0.508197i	$-0.830312\pi$
$251$	−13.7950	−	23.8936i	−0.870732	−	1.50815i	−0.00949135	−	0.999955i	$-0.503021\pi$
$252$		0			0
$253$	7.26736	+	12.5874i	0.456895	+	0.791365i
$254$	0.455092	−	0.788242i	0.0285550	−	0.0494587i
$255$		0			0
$256$	15.6310			0.976936
$257$	−9.13005			−0.569517			−0.284758	−	0.958599i	$-0.591913\pi$
$257$	−9.13005			−0.569517			−0.284758	+	0.958599i	$0.591913\pi$
$258$		0			0
$259$	−0.0992576	+	0.270897i	−0.00616757	+	0.0168327i
$260$	−22.0082	+	0.0229105i	−1.36489	+	0.00142085i
$261$		0			0
$262$	0.616507	+	1.06782i	0.0380879	+	0.0659702i
$263$	−2.79485	−	4.84082i	−0.172338	−	0.298498i	0.766899	−	0.641768i	$-0.221799\pi$
$263$	−2.79485	−	4.84082i	−0.172338	−	0.298498i	−0.939237	+	0.343270i	$0.888465\pi$
$264$		0			0
$265$	16.2548			0.998522
$266$	−0.796583	−	0.953481i	−0.0488417	−	0.0584617i
$267$		0			0
$268$	0.678860	+	1.17582i	0.0414680	+	0.0718247i
$269$	−21.2921			−1.29820			−0.649102	−	0.760701i	$-0.724855\pi$
$269$	−21.2921			−1.29820			−0.649102	+	0.760701i	$0.724855\pi$
$270$		0			0
$271$	11.3270			0.688064			0.344032	−	0.938958i	$-0.388207\pi$
$271$	11.3270			0.688064			0.344032	+	0.938958i	$0.388207\pi$
$272$	14.0168			0.849891
$273$		0			0
$274$	1.45192			0.0877139
$275$	18.9915			1.14523
$276$		0			0
$277$	−11.3623			−0.682696			−0.341348	−	0.939937i	$-0.610883\pi$
$277$	−11.3623			−0.682696			−0.341348	+	0.939937i	$0.610883\pi$
$278$	0.00479849	+	0.00831123i	0.000287794	+	0.000498474i
$279$		0			0
$280$	−2.16745	+	0.377384i	−0.129530	+	0.0225530i
$281$	−7.98667			−0.476445			−0.238222	−	0.971211i	$-0.576565\pi$
$281$	−7.98667			−0.476445			−0.238222	+	0.971211i	$0.576565\pi$
$282$		0			0
$283$	−2.06937	−	3.58425i	−0.123011	−	0.213062i	0.797943	−	0.602733i	$-0.205922\pi$
$283$	−2.06937	−	3.58425i	−0.123011	−	0.213062i	−0.920954	+	0.389672i	$0.872588\pi$
$284$	−5.21932	−	9.04013i	−0.309710	−	0.536433i
$285$		0			0
$286$	−1.06903	+	0.00111286i	−0.0632131	+	6.58048e-5i
$287$	6.00149	+	7.18356i	0.354257	+	0.424032i
$288$		0			0
$289$	−4.54846			−0.267557
$290$	−2.06458			−0.121237
$291$		0			0
$292$	−3.51097	+	6.08118i	−0.205464	+	0.355874i
$293$	14.1626	+	24.5303i	0.827385	+	1.43307i	0.900083	+	0.435719i	$0.143506\pi$
$293$	14.1626	+	24.5303i	0.827385	+	1.43307i	−0.0726976	+	0.997354i	$0.523161\pi$
$294$		0			0
$295$	11.5588	+	20.0204i	0.672977	+	1.16563i
$296$	−0.0296418			−0.00172290
$297$		0			0
$298$	0.488360	−	0.845865i	0.0282900	−	0.0489996i
$299$	6.00184	−	10.4205i	0.347095	−	0.602634i
$300$		0			0
$301$	−4.40037	+	0.766166i	−0.253633	+	0.0441611i
$302$	0.532839	−	0.922904i	0.0306614	−	0.0531071i
$303$		0			0
$304$	−13.7087	+	23.7442i	−0.786248	+	1.36182i
$305$	14.9074			0.853594
$306$		0			0
$307$	18.0617			1.03083			0.515417	−	0.856939i	$-0.327637\pi$
$307$	18.0617			1.03083			0.515417	+	0.856939i	$0.327637\pi$
$308$	22.6656	−	3.94640i	1.29149	−	0.224867i
$309$		0			0
$310$	1.92497			0.109331
$311$	6.03959	−	10.4609i	0.342474	−	0.593182i	−0.642418	−	0.766355i	$-0.722069\pi$
$311$	6.03959	−	10.4609i	0.342474	−	0.593182i	0.984891	+	0.173173i	$0.0554019\pi$
$312$		0			0
$313$	−10.3790	−	17.9769i	−0.586654	−	1.01611i	−0.994667	−	0.103138i	$-0.967112\pi$
$313$	−10.3790	−	17.9769i	−0.586654	−	1.01611i	0.408013	−	0.912976i	$-0.366222\pi$
$314$	0.459257	−	0.795457i	0.0259174	−	0.0448902i
$315$		0			0
$316$	−9.68569	−	16.7761i	−0.544862	−	0.943729i
$317$	8.73476	+	15.1290i	0.490593	+	0.849732i	0.999941	−	0.0108284i	$-0.00344685\pi$
$317$	8.73476	+	15.1290i	0.490593	+	0.849732i	−0.509348	+	0.860560i	$0.670114\pi$
$318$		0			0
$319$	43.2299			2.42041
$320$	12.0667	+	20.9001i	0.674549	+	1.16835i
$321$		0			0
$322$	0.206547	−	0.563715i	0.0115104	−	0.0314146i
$323$	−12.1779	+	21.0927i	−0.677595	+	1.17363i
$324$		0			0
$325$	−7.87053	−	13.5994i	−0.436578	−	0.754361i
$326$	−0.0903939	+	0.156567i	−0.00500646	+	0.00867144i
$327$		0			0
$328$	−0.480863	+	0.832880i	−0.0265512	+	0.0459881i
$329$	−6.67969	+	1.16303i	−0.368263	+	0.0641198i
$330$		0			0
$331$	−3.56309	+	6.17145i	−0.195845	+	0.339213i	−0.947177	−	0.320711i	$-0.896078\pi$
$331$	−3.56309	+	6.17145i	−0.195845	+	0.339213i	0.751332	+	0.659924i	$0.229412\pi$
$332$	10.8082			0.593175
$333$		0			0
$334$	−0.742559	+	1.28615i	−0.0406310	+	0.0703750i
$335$	−1.04075	+	1.80263i	−0.0568623	+	0.0984883i
$336$		0			0
$337$	−22.8396			−1.24415			−0.622077	−	0.782956i	$-0.713711\pi$
$337$	−22.8396			−1.24415			−0.622077	+	0.782956i	$0.713711\pi$
$338$	0.443828	+	0.765049i	0.0241410	+	0.0416132i
$339$		0			0
$340$	10.7695	+	18.6533i	0.584057	+	1.01162i
$341$	−40.3066			−2.18272
$342$		0			0
$343$	−16.0983	+	9.15663i	−0.869228	+	0.494412i
$344$	−0.229451	−	0.397422i	−0.0123712	−	0.0214275i
$345$		0			0
$346$	−0.601520	+	1.04186i	−0.0323379	+	0.0560109i
$347$	17.2581			0.926462			0.463231	−	0.886238i	$-0.346690\pi$
$347$	17.2581			0.926462			0.463231	+	0.886238i	$0.346690\pi$
$348$		0			0
$349$	−15.3687	+	26.6193i	−0.822665	+	1.42490i	0.0810257	+	0.996712i	$0.474180\pi$
$349$	−15.3687	+	26.6193i	−0.822665	+	1.42490i	−0.903691	+	0.428186i	$0.859153\pi$
$350$	−0.502946	−	0.602008i	−0.0268836	−	0.0321787i
$351$		0			0
$352$	1.77349	+	3.07177i	0.0945272	+	0.163726i
$353$	−0.480320	−	0.831939i	−0.0255649	−	0.0442797i	0.852960	−	0.521976i	$-0.174805\pi$
$353$	−0.480320	−	0.831939i	−0.0255649	−	0.0442797i	−0.878525	+	0.477697i	$0.841472\pi$
$354$		0			0
$355$	8.00167	−	13.8593i	0.424684	−	0.735575i
$356$	−15.3726			−0.814748
$357$		0			0
$358$	−0.330994	−	0.573299i	−0.0174936	−	0.0302998i
$359$	−16.4526	−	28.4967i	−0.868334	−	1.50400i	−0.863698	−	0.504009i	$-0.831858\pi$
$359$	−16.4526	−	28.4967i	−0.868334	−	1.50400i	−0.00463555	−	0.999989i	$-0.501476\pi$
$360$		0			0
$361$	−14.3204	−	24.8037i	−0.753707	−	1.30546i
$362$	−0.273050			−0.0143512
$363$		0			0
$364$	−12.2191	−	14.5949i	−0.640454	−	0.764980i
$365$	−10.7652			−0.563478
$366$		0			0
$367$	−11.0277	−	19.1006i	−0.575643	−	0.997042i	−0.995972	−	0.0896703i	$-0.971419\pi$
$367$	−11.0277	−	19.1006i	−0.575643	−	0.997042i	0.420329	−	0.907372i	$-0.361915\pi$
$368$	−13.2484			−0.690620
$369$		0			0
$370$	−0.0113477	−	0.0196548i	−0.000589939	−	0.00102180i
$371$	9.01351	+	10.7888i	0.467958	+	0.560128i
$372$		0			0
$373$	−12.9560	+	22.4404i	−0.670835	+	1.16192i	0.306833	+	0.951763i	$0.400731\pi$
$373$	−12.9560	+	22.4404i	−0.670835	+	1.16192i	−0.977668	+	0.210157i	$0.932603\pi$
$374$	0.523118	+	0.906068i	0.0270498	+	0.0468516i
$375$		0			0
$376$	−0.348303	−	0.603279i	−0.0179624	−	0.0311118i
$377$	−17.9155	−	30.9560i	−0.922693	−	1.59432i
$378$		0			0
$379$	−1.77121	+	3.06783i	−0.0909811	+	0.157584i	−0.907924	−	0.419134i	$-0.862334\pi$
$379$	−1.77121	+	3.06783i	−0.0909811	+	0.157584i	0.816943	+	0.576718i	$0.195667\pi$
$380$	−42.1312			−2.16128
$381$		0			0
$382$	0.503139	−	0.871462i	0.0257428	−	0.0445879i
$383$	−14.6975	+	25.4569i	−0.751008	+	1.30078i	0.196326	+	0.980539i	$0.437099\pi$
$383$	−14.6975	+	25.4569i	−0.751008	+	1.30078i	−0.947334	+	0.320246i	$0.896234\pi$
$384$		0			0
$385$	22.6138	+	27.0678i	1.15250	+	1.37950i
$386$	0.760067	+	1.31648i	0.0386864	+	0.0670068i
$387$		0			0
$388$	7.70930	+	13.3529i	0.391380	+	0.677891i
$389$	−1.32057	+	2.28730i	−0.0669556	+	0.115971i	−0.897560	−	0.440893i	$-0.854662\pi$
$389$	−1.32057	+	2.28730i	−0.0669556	+	0.115971i	0.830604	+	0.556863i	$0.187995\pi$
$390$		0			0
$391$	−11.7690			−0.595182
$392$	−1.45237	−	1.22935i	−0.0733555	−	0.0620913i
$393$		0			0
$394$	−0.215185	+	0.372712i	−0.0108409	+	0.0187770i
$395$	14.8490	−	25.7192i	0.747133	−	1.29407i
$396$		0			0
$397$	−0.287989	+	0.498811i	−0.0144537	+	0.0250346i	−0.873162	−	0.487430i	$-0.837934\pi$
$397$	−0.287989	+	0.498811i	−0.0144537	+	0.0250346i	0.858708	+	0.512465i	$0.171268\pi$
$398$	0.410677			0.0205854
$399$		0			0
$400$	−8.65539	+	14.9916i	−0.432769	+	0.749578i
$401$	9.51197			0.475005			0.237503	−	0.971387i	$-0.423671\pi$
$401$	9.51197			0.475005			0.237503	+	0.971387i	$0.423671\pi$
$402$		0			0
$403$	16.7040	+	28.8627i	0.832084	+	1.43775i
$404$	3.87133	+	6.70534i	0.192606	+	0.333603i
$405$		0			0
$406$	−1.14484	−	1.37033i	−0.0568176	−	0.0680085i
$407$	0.237607	+	0.411548i	0.0117778	+	0.0203997i
$408$		0			0
$409$	−0.186321			−0.00921299			−0.00460649	−	0.999989i	$-0.501466\pi$
$409$	−0.186321			−0.00921299			−0.00460649	+	0.999989i	$0.501466\pi$
$410$	−0.736350			−0.0363657
$411$		0			0
$412$	8.56190	+	14.8296i	0.421814	+	0.730604i
$413$	−6.87869	+	18.7735i	−0.338478	+	0.923785i
$414$		0			0
$415$	8.28491	+	14.3499i	0.406690	+	0.704408i
$416$	1.46466	−	2.54297i	0.0718107	−	0.124679i
$417$		0			0
$418$	−2.04648			−0.100097
$419$	0.448814	−	0.777369i	0.0219260	−	0.0379769i	−0.854854	−	0.518868i	$-0.826354\pi$
$419$	0.448814	−	0.777369i	0.0219260	−	0.0379769i	0.876780	+	0.480891i	$0.159687\pi$
$420$		0			0
$421$	−4.34862			−0.211939			−0.105969	−	0.994369i	$-0.533795\pi$
$421$	−4.34862			−0.211939			−0.105969	+	0.994369i	$0.533795\pi$
$422$	−0.0439575	+	0.0761366i	−0.00213982	+	0.00370627i
$423$		0			0
$424$	−0.722198	+	1.25088i	−0.0350731	+	0.0607483i
$425$	−7.68885	+	13.3175i	−0.372964	+	0.645993i
$426$		0			0
$427$	8.26636	+	9.89453i	0.400037	+	0.478830i
$428$	−22.3545			−1.08054
$429$		0			0
$430$	0.175680	−	0.304287i	0.00847206	−	0.0146740i
$431$	−5.36333	−	9.28956i	−0.258342	−	0.447462i	0.707456	−	0.706758i	$-0.249843\pi$
$431$	−5.36333	−	9.28956i	−0.258342	−	0.447462i	−0.965798	+	0.259296i	$0.916510\pi$
$432$		0			0
$433$	3.46111	+	5.99482i	0.166330	+	0.288093i	0.937127	−	0.348989i	$-0.113475\pi$
$433$	3.46111	+	5.99482i	0.166330	+	0.288093i	−0.770797	+	0.637081i	$0.780142\pi$
$434$	1.06742	+	1.27767i	0.0512380	+	0.0613300i
$435$		0			0
$436$	−13.9333	+	24.1332i	−0.667285	+	1.15577i
$437$	11.5103	−	19.9364i	0.550612	−	0.953688i
$438$		0			0
$439$	25.2180			1.20359			0.601794	−	0.798652i	$-0.294453\pi$
$439$	25.2180			1.20359			0.601794	+	0.798652i	$0.294453\pi$
$440$	−1.81191	+	3.13831i	−0.0863792	+	0.149613i
$441$		0			0
$442$	0.432024	−	0.750089i	0.0205493	−	0.0356781i
$443$	8.71266	+	15.0908i	0.413951	+	0.716984i	0.995318	−	0.0966574i	$-0.0308151\pi$
$443$	8.71266	+	15.0908i	0.413951	+	0.716984i	−0.581367	+	0.813642i	$0.697482\pi$
$444$		0			0
$445$	−11.7838	−	20.4101i	−0.558604	−	0.967531i
$446$	−0.394535	+	0.683354i	−0.0186818	+	0.0323578i
$447$		0			0
$448$	−7.18096	+	19.5985i	−0.339269	+	0.925942i
$449$	5.91239	+	10.2406i	0.279023	+	0.483282i	0.971142	−	0.238501i	$-0.0766561\pi$
$449$	5.91239	+	10.2406i	0.279023	+	0.483282i	−0.692119	+	0.721783i	$0.743323\pi$
$450$		0			0
$451$	15.4183			0.726019
$452$	−6.76208	−	11.7123i	−0.318061	−	0.550898i
$453$		0			0
$454$	−0.0543266			−0.00254967
$455$	10.0111	−	27.4108i	0.469325	−	1.28504i
$456$		0			0
$457$	−8.33251			−0.389779			−0.194889	−	0.980825i	$-0.562435\pi$
$457$	−8.33251			−0.389779			−0.194889	+	0.980825i	$0.562435\pi$
$458$	0.789712	+	1.36782i	0.0369008	+	0.0639141i
$459$		0			0
$460$	−10.1791	−	17.6307i	−0.474604	−	0.822038i
$461$	−2.20305	−	3.81579i	−0.102606	−	0.177719i	0.810152	−	0.586221i	$-0.199385\pi$
$461$	−2.20305	−	3.81579i	−0.102606	−	0.177719i	−0.912758	+	0.408502i	$0.866051\pi$
$462$		0			0
$463$	20.2243			0.939904			0.469952	−	0.882692i	$-0.344271\pi$
$463$	20.2243			0.939904			0.469952	+	0.882692i	$0.344271\pi$
$464$	−19.7020	+	34.1249i	−0.914643	+	1.58421i
$465$		0			0
$466$	0.414603	+	0.718113i	0.0192061	+	0.0332660i
$467$	3.27010	+	5.66398i	0.151322	+	0.262098i	0.931714	−	0.363193i	$-0.118314\pi$
$467$	3.27010	+	5.66398i	0.151322	+	0.262098i	−0.780392	+	0.625291i	$0.784980\pi$
$468$		0			0
$469$	−1.77358	+	0.308805i	−0.0818963	+	0.0142593i
$470$	0.266680	−	0.461903i	0.0123010	−	0.0213060i
$471$		0			0
$472$	−2.05422			−0.0945532
$473$	−3.67854	+	6.37141i	−0.169139	+	0.292958i
$474$		0			0
$475$	−15.0397	−	26.0496i	−0.690070	−	1.19524i
$476$	−6.40898	+	17.4916i	−0.293755	+	0.801726i
$477$		0			0
$478$	−0.0329520			−0.00150719
$479$	−3.90667	−	6.76656i	−0.178500	−	0.309172i	0.762867	−	0.646556i	$-0.223791\pi$
$479$	−3.90667	−	6.76656i	−0.178500	−	0.309172i	−0.941367	+	0.337384i	$0.890458\pi$
$480$		0			0
$481$	0.196231	−	0.340700i	0.00894736	−	0.0155346i
$482$	0.157852			0.00718995
$483$		0			0
$484$	7.97304	−	13.8097i	0.362411	−	0.627714i
$485$	−11.8190	+	20.4711i	−0.536674	+	0.929546i
$486$		0			0
$487$	−21.0741			−0.954959			−0.477479	−	0.878643i	$-0.658449\pi$
$487$	−21.0741			−0.954959			−0.477479	+	0.878643i	$0.658449\pi$
$488$	−0.662334	+	1.14720i	−0.0299824	+	0.0519311i
$489$		0			0
$490$	0.259145	−	1.43366i	0.0117070	−	0.0647660i
$491$	4.36913	−	7.56755i	0.197176	−	0.341519i	−0.750436	−	0.660943i	$-0.770156\pi$
$491$	4.36913	−	7.56755i	0.197176	−	0.341519i	0.947612	+	0.319425i	$0.103490\pi$
$492$		0			0
$493$	−17.5019	+	30.3142i	−0.788247	+	1.36528i
$494$	0.848110	+	1.46544i	0.0381583	+	0.0659335i
$495$		0			0
$496$	18.3697	−	31.8173i	0.824824	−	1.42864i
$497$	13.6359	−	2.37420i	0.611655	−	0.106498i
$498$		0			0
$499$	−10.6426	−	18.4336i	−0.476430	−	0.825200i	0.523206	−	0.852206i	$-0.324736\pi$
$499$	−10.6426	−	18.4336i	−0.476430	−	0.825200i	−0.999635	+	0.0270062i	$0.991403\pi$
$500$	3.91920			0.175272
$501$		0			0
$502$	0.938555	+	1.62563i	0.0418898	+	0.0725552i
$503$	2.29846	+	3.98105i	0.102483	+	0.177506i	0.912707	−	0.408614i	$-0.133988\pi$
$503$	2.29846	+	3.98105i	0.102483	+	0.177506i	−0.810224	+	0.586120i	$0.800655\pi$
$504$		0			0
$505$	−5.93508	+	10.2799i	−0.264107	+	0.457448i
$506$	−0.494442	−	0.856398i	−0.0219806	−	0.0380715i
$507$		0			0
$508$	13.3470	−	23.1177i	0.592178	−	1.02568i
$509$	13.7063			0.607522			0.303761	−	0.952748i	$-0.401758\pi$
$509$	13.7063			0.607522			0.303761	+	0.952748i	$0.401758\pi$
$510$		0			0
$511$	−5.96947	−	7.14524i	−0.264074	−	0.316087i
$512$	−5.39261			−0.238322
$513$		0			0
$514$	0.621172			0.0273987
$515$	−13.1261	+	22.7351i	−0.578406	+	1.00183i
$516$		0			0
$517$	−5.58396	+	9.67170i	−0.245582	+	0.425361i
$518$	0.00675308	−	0.0184307i	0.000296713	−	0.000809800i
$519$		0			0
$520$	2.99817	−	0.00312110i	0.131479	−	0.000136869i
$521$	2.13457	−	3.69718i	0.0935172	−	0.161977i	−0.815472	−	0.578797i	$-0.803522\pi$
$521$	2.13457	−	3.69718i	0.0935172	−	0.161977i	0.908989	+	0.416821i	$0.136856\pi$
$522$		0			0
$523$	−28.1706			−1.23181			−0.615907	−	0.787819i	$-0.711210\pi$
$523$	−28.1706			−1.23181			−0.615907	+	0.787819i	$0.711210\pi$
$524$	18.0810	+	31.3172i	0.789873	+	1.36810i
$525$		0			0
$526$	0.190150	+	0.329350i	0.00829094	+	0.0143603i
$527$	16.3184	−	28.2643i	0.710840	−	1.23121i
$528$		0			0
$529$	−11.8762			−0.516357
$530$	−1.10591			−0.0480376
$531$		0			0
$532$	−23.3623	−	27.9639i	−1.01289	−	1.21239i
$533$	−6.38969	−	11.0407i	−0.276768	−	0.478226i
$534$		0			0
$535$	−17.1356	−	29.6798i	−0.740839	−	1.28317i
$536$	−0.0924810	−	0.160182i	−0.00399457	−	0.00691880i
$537$		0			0
$538$	1.44863			0.0624549
$539$	−5.42618	+	30.0190i	−0.233722	+	1.29301i
$540$		0			0
$541$	9.24717	+	16.0166i	0.397567	+	0.688606i	0.993425	−	0.114484i	$-0.0365214\pi$
$541$	9.24717	+	16.0166i	0.397567	+	0.688606i	−0.595858	+	0.803089i	$0.703188\pi$
$542$	−0.770641			−0.0331019
$543$		0			0
$544$	−2.87203			−0.123137
$545$	−42.7219			−1.83001
$546$		0			0
$547$	24.6951			1.05589			0.527943	−	0.849280i	$-0.322963\pi$
$547$	24.6951			1.05589			0.527943	+	0.849280i	$0.322963\pi$
$548$	42.5823			1.81902
$549$		0			0
$550$	−1.29211			−0.0550956
$551$	−34.2345	−	59.2959i	−1.45844	−	2.52609i
$552$		0			0
$553$	25.3047	−	4.40590i	1.07606	−	0.187358i
$554$	0.773046			0.0328436
$555$		0			0
$556$	0.140731	+	0.243753i	0.00596832	+	0.0103374i
$557$	−1.48587	−	2.57361i	−0.0629584	−	0.109047i	0.832828	−	0.553532i	$-0.186720\pi$
$557$	−1.48587	−	2.57361i	−0.0629584	−	0.109047i	−0.895787	+	0.444485i	$0.853387\pi$
$558$		0			0
$559$	6.08691	−	0.00633646i	0.257449	−	0.000268004i
$560$	−31.6731	+	5.51472i	−1.33843	+	0.233040i
$561$		0			0
$562$	0.543380			0.0229211
$563$	3.20058			0.134889			0.0674443	−	0.997723i	$-0.478516\pi$
$563$	3.20058			0.134889			0.0674443	+	0.997723i	$0.478516\pi$
$564$		0			0
$565$	10.3668	−	17.9559i	0.436136	−	0.755410i
$566$	0.140791	+	0.243858i	0.00591791	+	0.0102501i
$567$		0			0
$568$	0.711027	+	1.23154i	0.0298340	+	0.0516741i
$569$	12.5838			0.527539			0.263770	−	0.964586i	$-0.415034\pi$
$569$	12.5838			0.527539			0.263770	+	0.964586i	$0.415034\pi$
$570$		0			0
$571$	11.8472	−	20.5200i	0.495792	−	0.858736i	−0.504197	−	0.863589i	$-0.668211\pi$
$571$	11.8472	−	20.5200i	0.495792	−	0.858736i	0.999988	+	0.00485262i	$0.00154464\pi$
$572$	−31.3527	+	0.0326381i	−1.31092	+	0.00136467i
$573$		0			0
$574$	−0.408317	−	0.488740i	−0.0170428	−	0.0203996i
$575$	7.26736	−	12.5874i	0.303070	−	0.524932i
$576$		0			0
$577$	−1.67873	+	2.90764i	−0.0698863	+	0.121047i	−0.898851	−	0.438254i	$-0.855597\pi$
$577$	−1.67873	+	2.90764i	−0.0698863	+	0.121047i	0.828965	+	0.559301i	$0.188930\pi$
$578$	0.309459			0.0128718
$579$		0			0
$580$	−60.5505			−2.51422
$581$	−4.93040	+	13.4562i	−0.204547	+	0.558257i
$582$		0			0
$583$	23.1564			0.959040
$584$	0.478298	−	0.828437i	0.0197921	−	0.0342810i
$585$		0			0
$586$	−0.963563	−	1.66894i	−0.0398044	−	0.0689433i
$587$	4.99547	−	8.65242i	0.206185	−	0.357123i	−0.744324	−	0.667818i	$-0.767228\pi$
$587$	4.99547	−	8.65242i	0.206185	−	0.357123i	0.950510	+	0.310695i	$0.100562\pi$
$588$		0			0
$589$	31.9195	+	55.2862i	1.31522	+	2.27803i
$590$	−0.786412	−	1.36210i	−0.0323761	−	0.0560770i
$591$		0			0
$592$	−0.433158			−0.0178027
$593$	16.4331	+	28.4629i	0.674825	+	1.16883i	0.976520	+	0.215426i	$0.0691141\pi$
$593$	16.4331	+	28.4629i	0.674825	+	1.16883i	−0.301695	+	0.953404i	$0.597553\pi$
$594$		0			0
$595$	−28.1362	+	4.89890i	−1.15347	+	0.200835i
$596$	14.3227	−	24.8077i	0.586682	−	1.01616i
$597$		0			0
$598$	−0.408341	+	0.708970i	−0.0166983	+	0.0289920i
$599$	−10.6138	+	18.3836i	−0.433667	+	0.751133i	−0.997186	−	0.0749700i	$-0.976114\pi$
$599$	−10.6138	+	18.3836i	−0.433667	+	0.751133i	0.563519	+	0.826103i	$0.309447\pi$
$600$		0			0
$601$	0.776508	−	1.34495i	0.0316744	−	0.0548617i	−0.849754	−	0.527180i	$-0.823249\pi$
$601$	0.776508	−	1.34495i	0.0316744	−	0.0548617i	0.881428	+	0.472318i	$0.156583\pi$
$602$	0.299383	−	0.0521268i	0.0122020	−	0.00212453i
$603$		0			0
$604$	15.6272	−	27.0671i	0.635861	−	1.10134i
$605$	24.4467			0.993899
$606$		0			0
$607$	−3.30552	+	5.72533i	−0.134167	+	0.232384i	−0.925279	−	0.379287i	$-0.876169\pi$
$607$	−3.30552	+	5.72533i	−0.134167	+	0.232384i	0.791112	+	0.611671i	$0.209502\pi$
$608$	2.80891	−	4.86518i	0.113916	−	0.197309i
$609$		0			0
$610$	−1.01424			−0.0410653
$611$	9.23982	−	0.00961865i	0.373803	−	0.000389129i
$612$		0			0
$613$	6.02920	+	10.4429i	0.243517	+	0.421784i	0.961714	−	0.274056i	$-0.0883655\pi$
$613$	6.02920	+	10.4429i	0.243517	+	0.421784i	−0.718197	+	0.695840i	$0.755032\pi$
$614$	−1.22884			−0.0495921
$615$		0			0
$616$	−3.08773	+	0.537617i	−0.124408	+	0.0216612i
$617$	16.5723	+	28.7040i	0.667175	+	1.15558i	0.978691	+	0.205340i	$0.0658301\pi$
$617$	16.5723	+	28.7040i	0.667175	+	1.15558i	−0.311515	+	0.950241i	$0.600837\pi$
$618$		0			0
$619$	23.8269	−	41.2695i	0.957686	−	1.65876i	0.229587	−	0.973288i	$-0.426263\pi$
$619$	23.8269	−	41.2695i	0.957686	−	1.65876i	0.728099	−	0.685472i	$-0.240404\pi$
$620$	56.4559			2.26732
$621$		0			0
$622$	−0.410909	+	0.711716i	−0.0164760	+	0.0285372i
$623$	7.01259	−	19.1390i	0.280953	−	0.766787i
$624$		0			0
$625$	13.8991	+	24.0739i	0.555962	+	0.962955i
$626$	0.706143	+	1.22308i	0.0282231	+	0.0488839i
$627$		0			0
$628$	13.4692	−	23.3293i	0.537479	−	0.930941i
$629$	−0.384788			−0.0153425
$630$		0			0
$631$	1.28825	+	2.23132i	0.0512846	+	0.0888276i	0.890528	−	0.454928i	$-0.150335\pi$
$631$	1.28825	+	2.23132i	0.0512846	+	0.0888276i	−0.839243	+	0.543756i	$0.817002\pi$
$632$	1.31948	+	2.28540i	0.0524860	+	0.0909085i
$633$		0			0
$634$	−0.594278	−	1.02932i	−0.0236018	−	0.0408795i
$635$	40.9242			1.62403
$636$		0			0
$637$	23.7447	−	8.55500i	0.940800	−	0.338961i
$638$	−2.94119			−0.116443
$639$		0			0
$640$	−3.31079	−	5.73446i	−0.130870	−	0.226674i
$641$	−40.7526			−1.60963			−0.804815	−	0.593526i	$-0.797735\pi$
$641$	−40.7526			−1.60963			−0.804815	+	0.593526i	$0.797735\pi$
$642$		0			0
$643$	−4.68006	−	8.10610i	−0.184564	−	0.319674i	0.758866	−	0.651247i	$-0.225754\pi$
$643$	−4.68006	−	8.10610i	−0.184564	−	0.319674i	−0.943429	+	0.331574i	$0.892420\pi$
$644$	6.05765	−	16.5327i	0.238705	−	0.651481i
$645$		0			0
$646$	0.828533	−	1.43506i	0.0325982	−	0.0564617i
$647$	12.5098	+	21.6677i	0.491812	+	0.851844i	0.999956	−	0.00942863i	$-0.00300127\pi$
$647$	12.5098	+	21.6677i	0.491812	+	0.851844i	−0.508143	+	0.861273i	$0.669668\pi$
$648$		0			0
$649$	16.4665	+	28.5208i	0.646367	+	1.11954i
$650$	0.535479	+	0.925251i	0.0210032	+	0.0362913i
$651$		0			0
$652$	−2.65109	+	4.59182i	−0.103825	+	0.179830i
$653$	18.5614			0.726364			0.363182	−	0.931718i	$-0.381690\pi$
$653$	18.5614			0.726364			0.363182	+	0.931718i	$0.381690\pi$
$654$		0			0
$655$	−27.7197	+	48.0120i	−1.08310	+	1.87598i
$656$	−7.02688	+	12.1709i	−0.274353	+	0.475194i
$657$		0			0
$658$	0.454459	−	0.0791277i	0.0177167	−	0.00308472i
$659$	−18.4907	−	32.0268i	−0.720295	−	1.24759i	−0.960882	−	0.276960i	$-0.910673\pi$
$659$	−18.4907	−	32.0268i	−0.720295	−	1.24759i	0.240587	−	0.970628i	$-0.422660\pi$
$660$		0			0
$661$	−7.96164	−	13.7900i	−0.309672	−	0.536368i	0.668619	−	0.743606i	$-0.266886\pi$
$661$	−7.96164	−	13.7900i	−0.309672	−	0.536368i	−0.978291	+	0.207238i	$0.933553\pi$
$662$	0.242418	−	0.419880i	0.00942184	−	0.0163191i
$663$		0			0
$664$	−1.47239			−0.0571399
$665$	19.2191	−	52.4534i	0.745286	−	2.03406i
$666$		0			0
$667$	16.5425	−	28.6524i	0.640528	−	1.10943i
$668$	−21.7779	+	37.7204i	−0.842612	+	1.45945i
$669$		0			0
$670$	0.0708085	−	0.122644i	0.00273557	−	0.00473814i
$671$	21.2369			0.819842
$672$		0			0
$673$	10.9624	−	18.9874i	0.422569	−	0.731910i	−0.573621	−	0.819121i	$-0.694462\pi$
$673$	10.9624	−	18.9874i	0.422569	−	0.731910i	0.996190	+	0.0872103i	$0.0277952\pi$
$674$	1.55392			0.0598546
$675$		0			0
$676$	13.0167	+	22.4375i	0.500641	+	0.862981i
$677$	16.0122	+	27.7339i	0.615398	+	1.06590i	0.990315	+	0.138842i	$0.0443380\pi$
$677$	16.0122	+	27.7339i	0.615398	+	1.06590i	−0.374917	+	0.927059i	$0.622329\pi$
$678$		0			0
$679$	−20.1412	+	3.50686i	−0.772948	+	0.134581i
$680$	−1.46712	−	2.54113i	−0.0562617	−	0.0974480i
$681$		0			0
$682$	2.74230			0.105008
$683$	3.02269			0.115660			0.0578300	−	0.998326i	$-0.481582\pi$
$683$	3.02269			0.115660			0.0578300	+	0.998326i	$0.481582\pi$
$684$		0			0
$685$	32.6411	+	56.5361i	1.24715	+	2.16013i
$686$	1.09527	−	0.622980i	0.0418174	−	0.0237855i
$687$		0			0
$688$	−3.35298	−	5.80754i	−0.127831	−	0.221410i
$689$	−9.59654	−	16.5818i	−0.365599	−	0.631717i
$690$		0			0
$691$	−11.8991			−0.452662			−0.226331	−	0.974050i	$-0.572673\pi$
$691$	−11.8991			−0.452662			−0.226331	+	0.974050i	$0.572673\pi$
$692$	−17.6415	+	30.5559i	−0.670628	+	1.16156i
$693$		0			0
$694$	−1.17417			−0.0445709
$695$	−0.215752	+	0.373694i	−0.00818396	+	0.0141750i
$696$		0			0
$697$	−6.24220	+	10.8118i	−0.236440	+	0.409526i
$698$	1.04562	−	1.81107i	0.0395773	−	0.0685500i
$699$		0			0
$700$	−14.7505	−	17.6558i	−0.557516	−	0.667327i
$701$	−2.07215			−0.0782642			−0.0391321	−	0.999234i	$-0.512459\pi$
$701$	−2.07215			−0.0782642			−0.0391321	+	0.999234i	$0.512459\pi$
$702$		0			0
$703$	0.376331	−	0.651824i	0.0141936	−	0.0245840i
$704$	17.1901	+	29.7741i	0.647877	+	1.12216i
$705$		0			0
$706$	0.0326791	+	0.0566018i	0.00122989	+	0.00213024i
$707$	−10.1142	+	1.76102i	−0.380383	+	0.0662300i
$708$		0			0
$709$	−3.61999	+	6.27001i	−0.135952	+	0.235475i	−0.925961	−	0.377620i	$-0.876743\pi$
$709$	−3.61999	+	6.27001i	−0.135952	+	0.235475i	0.790009	+	0.613095i	$0.210076\pi$
$710$	−0.544401	+	0.942930i	−0.0204310	+	0.0353875i
$711$		0			0
$712$	2.09421			0.0784838
$713$	−15.4238	+	26.7149i	−0.577627	+	1.00048i
$714$		0			0
$715$	−24.0765	−	41.6017i	−0.900411	−	1.55581i
$716$	−9.70746	−	16.8138i	−0.362785	−	0.628362i
$717$		0			0
$718$	1.11937	+	1.93880i	0.0417744	+	0.0723554i
$719$	25.4653	−	44.1071i	0.949694	−	1.64492i	0.203626	−	0.979049i	$-0.434727\pi$
$719$	25.4653	−	44.1071i	0.949694	−	1.64492i	0.746068	−	0.665870i	$-0.231939\pi$
$720$		0			0
$721$	−22.3687	+	3.89470i	−0.833053	+	0.145046i
$722$	0.974305	+	1.68755i	0.0362599	+	0.0628039i
$723$		0			0
$724$	−8.00806			−0.297617
$725$	−21.6150	−	37.4382i	−0.802759	−	1.39042i
$726$		0			0
$727$	−21.6848			−0.804244			−0.402122	−	0.915586i	$-0.631727\pi$
$727$	−21.6848			−0.804244			−0.402122	+	0.915586i	$0.631727\pi$
$728$	1.66460	+	1.98826i	0.0616943	+	0.0736898i
$729$		0			0
$730$	0.732422			0.0271082
$731$	−2.97856	−	5.15902i	−0.110166	−	0.190813i
$732$		0			0
$733$	10.8930	+	18.8673i	0.402343	+	0.696879i	0.994008	−	0.109305i	$-0.0348625\pi$
$733$	10.8930	+	18.8673i	0.402343	+	0.696879i	−0.591665	+	0.806184i	$0.701529\pi$
$734$	0.750282	+	1.29953i	0.0276934	+	0.0479664i
$735$		0			0
$736$	2.71459			0.100061
$737$	−1.48264	+	2.56801i	−0.0546139	+	0.0945940i
$738$		0			0
$739$	−17.9533	−	31.0960i	−0.660421	−	1.14388i	−0.980505	−	0.196494i	$-0.937044\pi$
$739$	−17.9533	−	31.0960i	−0.660421	−	1.14388i	0.320084	−	0.947389i	$-0.396289\pi$
$740$	−0.332808	−	0.576440i	−0.0122342	−	0.0211903i
$741$		0			0
$742$	−0.613242	−	0.734029i	−0.0225128	−	0.0269470i
$743$	−25.6310	+	44.3942i	−0.940310	+	1.62867i	−0.175431	+	0.984492i	$0.556132\pi$
$743$	−25.6310	+	44.3942i	−0.940310	+	1.62867i	−0.764879	+	0.644174i	$0.777201\pi$
$744$		0			0
$745$	43.9159			1.60895
$746$	0.881472	−	1.52675i	0.0322730	−	0.0558984i
$747$		0			0
$748$	15.3421	+	26.5733i	0.560963	+	0.971617i
$749$	10.1975	−	27.8314i	0.372609	−	1.01694i
$750$		0			0
$751$	48.7540			1.77906			0.889530	−	0.456877i	$-0.151032\pi$
$751$	48.7540			1.77906			0.889530	+	0.456877i	$0.151032\pi$
$752$	−5.08977	−	8.81575i	−0.185605	−	0.321477i
$753$		0			0
$754$	1.21890	+	2.10612i	0.0443896	+	0.0767005i
$755$	47.9156			1.74383
$756$		0			0
$757$	7.41023	−	12.8349i	0.269329	−	0.466492i	−0.699360	−	0.714770i	$-0.746531\pi$
$757$	7.41023	−	12.8349i	0.269329	−	0.466492i	0.968689	+	0.248278i	$0.0798647\pi$
$758$	0.120506	−	0.208723i	0.00437698	−	0.00758115i
$759$		0			0
$760$	5.73952			0.208194
$761$	5.65515	−	9.79500i	0.204999	−	0.355068i	−0.745134	−	0.666915i	$-0.767614\pi$
$761$	5.65515	−	9.79500i	0.204999	−	0.355068i	0.950132	+	0.311847i	$0.100948\pi$
$762$		0			0
$763$	−23.6899	−	28.3560i	−0.857633	−	1.02656i
$764$	14.7562	−	25.5584i	0.533859	−	0.924671i
$765$		0			0
$766$	0.999960	−	1.73198i	0.0361300	−	0.0625790i
$767$	13.5991	−	23.6110i	0.491034	−	0.852544i
$768$		0			0
$769$	8.92963	−	15.4666i	0.322011	−	0.557739i	−0.658892	−	0.752238i	$-0.728975\pi$
$769$	8.92963	−	15.4666i	0.322011	−	0.557739i	0.980903	+	0.194498i	$0.0623079\pi$
$770$	−1.53855	−	1.84159i	−0.0554454	−	0.0663662i
$771$		0			0
$772$	22.2914	+	38.6098i	0.802285	+	1.38960i
$773$	−2.86552			−0.103066			−0.0515329	−	0.998671i	$-0.516411\pi$
$773$	−2.86552			−0.103066			−0.0515329	+	0.998671i	$0.516411\pi$
$774$		0			0
$775$	20.1533	+	34.9065i	0.723928	+	1.25388i
$776$	−1.05024	−	1.81906i	−0.0377013	−	0.0653005i
$777$		0			0
$778$	0.0898463	−	0.155618i	0.00322115	−	0.00557919i
$779$	−12.2100	−	21.1484i	−0.437469	−	0.757718i
$780$		0			0
$781$	11.3991	−	19.7438i	0.407892	−	0.706489i
$782$	0.800712			0.0286334
$783$		0			0
$784$	−21.2235	−	17.9645i	−0.757982	−	0.641589i
$785$	41.2988			1.47402
$786$		0			0
$787$	3.16514			0.112825			0.0564125	−	0.998408i	$-0.482034\pi$
$787$	3.16514			0.112825			0.0564125	+	0.998408i	$0.482034\pi$
$788$	−6.31100	+	10.9310i	−0.224820	+	0.389400i
$789$		0			0
$790$	−1.01026	+	1.74983i	−0.0359436	+	0.0622561i
$791$	17.6665	−	3.07598i	0.628148	−	0.109369i
$792$		0			0
$793$	−8.80106	−	15.2073i	−0.312535	−	0.540027i
$794$	0.0195936	−	0.0339371i	0.000695350	−	0.00120438i
$795$		0			0
$796$	12.0444			0.426902
$797$	−12.0425	−	20.8583i	−0.426568	−	0.738838i	0.569997	−	0.821647i	$-0.306944\pi$
$797$	−12.0425	−	20.8583i	−0.426568	−	0.738838i	−0.996565	+	0.0828085i	$0.973611\pi$
$798$		0			0
$799$	−4.52141	−	7.83131i	−0.159956	−	0.277052i
$800$	1.77349	−	3.07177i	0.0627023	−	0.108604i
$801$		0			0
$802$	−0.647156			−0.0228519
$803$	−15.3360			−0.541197
$804$		0			0
$805$	26.5938	−	4.63035i	0.937308	−	0.163198i
$806$	−1.13647	−	1.96370i	−0.0400305	−	0.0691684i
$807$		0			0
$808$	−0.527390	−	0.913467i	−0.0185535	−	0.0321357i
$809$	−19.1556	−	33.1784i	−0.673474	−	1.16649i	−0.976912	−	0.213640i	$-0.931468\pi$
$809$	−19.1556	−	33.1784i	−0.673474	−	1.16649i	0.303438	−	0.952851i	$-0.401865\pi$
$810$		0			0
$811$	2.79091			0.0980022			0.0490011	−	0.998799i	$-0.484396\pi$
$811$	2.79091			0.0980022			0.0490011	+	0.998799i	$0.484396\pi$
$812$	−33.5761	−	40.1894i	−1.17829	−	1.41037i
$813$		0			0
$814$	−0.0161658	−	0.0280000i	−0.000566612	−	0.000981401i
$815$	−8.12869			−0.284736
$816$		0			0
$817$	11.6524			0.407666
$818$	0.0126765			0.000443225
$819$		0			0
$820$	−21.5958			−0.754158
$821$	44.3710			1.54856			0.774279	−	0.632844i	$-0.218113\pi$
$821$	44.3710			1.54856			0.774279	+	0.632844i	$0.218113\pi$
$822$		0			0
$823$	−8.21493			−0.286354			−0.143177	−	0.989697i	$-0.545732\pi$
$823$	−8.21493			−0.286354			−0.143177	+	0.989697i	$0.545732\pi$
$824$	−1.16639	−	2.02024i	−0.0406329	−	0.0703783i
$825$		0			0
$826$	0.467998	−	1.27728i	0.0162837	−	0.0444421i
$827$	37.0687			1.28900			0.644502	−	0.764603i	$-0.277065\pi$
$827$	37.0687			1.28900			0.644502	+	0.764603i	$0.277065\pi$
$828$		0			0
$829$	21.2293	+	36.7702i	0.737323	+	1.27708i	0.953696	+	0.300771i	$0.0972439\pi$
$829$	21.2293	+	36.7702i	0.737323	+	1.27708i	−0.216373	+	0.976311i	$0.569423\pi$
$830$	−0.563672	−	0.976309i	−0.0195653	−	0.0338882i
$831$		0			0
$832$	14.1967	−	24.6486i	0.492181	−	0.854535i
$833$	−18.8535	−	15.9584i	−0.653235	−	0.552926i
$834$		0			0
$835$	−66.7747			−2.31084
$836$	−60.0197			−2.07582
$837$		0			0
$838$	−0.0305355	+	0.0528890i	−0.00105483	+	0.00182702i
$839$	−0.873903	−	1.51365i	−0.0301705	−	0.0522568i	0.850546	−	0.525901i	$-0.176272\pi$
$839$	−0.873903	−	1.51365i	−0.0301705	−	0.0522568i	−0.880716	+	0.473644i	$0.842938\pi$
$840$		0			0
$841$	−34.7015	−	60.1048i	−1.19660	−	2.07258i
$842$	0.295863			0.0101961
$843$		0			0
$844$	−1.28919	+	2.23295i	−0.0443759	+	0.0768612i
$845$	−19.8122	+	34.4814i	−0.681561	+	1.18620i
$846$		0			0
$847$	13.5560	+	16.2261i	0.465791	+	0.557535i
$848$	−10.5535	+	18.2792i	−0.362409	+	0.627711i
$849$		0			0
$850$	0.523118	−	0.906068i	0.0179428	−	0.0310779i
$851$	0.363694			0.0124673
$852$		0			0
$853$	−55.5244			−1.90112			−0.950560	−	0.310540i	$-0.899490\pi$
$853$	−55.5244			−1.90112			−0.950560	+	0.310540i	$0.899490\pi$
$854$	−0.562409	−	0.673184i	−0.0192453	−	0.0230359i
$855$		0			0
$856$	3.04534			0.104088
$857$	−14.8303	+	25.6869i	−0.506595	+	0.877448i	0.493376	+	0.869816i	$0.335763\pi$
$857$	−14.8303	+	25.6869i	−0.506595	+	0.877448i	−0.999971	+	0.00763209i	$0.997571\pi$
$858$		0			0
$859$	−10.6791	−	18.4967i	−0.364365	−	0.631098i	0.624309	−	0.781177i	$-0.285381\pi$
$859$	−10.6791	−	18.4967i	−0.364365	−	0.631098i	−0.988674	+	0.150079i	$0.952047\pi$
$860$	5.15239	−	8.92420i	0.175695	−	0.304313i
$861$		0			0
$862$	0.364899	+	0.632024i	0.0124285	+	0.0215268i
$863$	−17.5615	−	30.4174i	−0.597800	−	1.03542i	−0.993145	−	0.116887i	$-0.962708\pi$
$863$	−17.5615	−	30.4174i	−0.597800	−	1.03542i	0.395345	−	0.918533i	$-0.370625\pi$
$864$		0			0
$865$	−54.0918			−1.83917
$866$	−0.235480	−	0.407863i	−0.00800194	−	0.0138598i
$867$		0			0
$868$	31.3056	+	37.4717i	1.06258	+	1.27187i
$869$	21.1537	−	36.6393i	0.717591	−	1.24290i
$870$		0			0
$871$	2.45334	−	0.00255393i	0.0831283	−	8.65365e-5i
$872$	1.89813	−	3.28766i	0.0642789	−	0.111334i
$873$		0			0
$874$	−0.783114	+	1.35639i	−0.0264892	+	0.0458807i
$875$	−1.78784	+	4.87942i	−0.0604399	+	0.164954i
$876$		0			0
$877$	−9.40278	+	16.2861i	−0.317509	+	0.549943i	−0.979968	−	0.199156i	$-0.936180\pi$
$877$	−9.40278	+	16.2861i	−0.317509	+	0.549943i	0.662458	+	0.749099i	$0.269513\pi$
$878$	−1.71573			−0.0579030
$879$		0			0
$880$	−26.4775	+	45.8603i	−0.892555	+	1.54595i
$881$	22.3970	−	38.7927i	0.754573	−	1.30696i	−0.191013	−	0.981587i	$-0.561177\pi$
$881$	22.3970	−	38.7927i	0.754573	−	1.30696i	0.945586	−	0.325371i	$-0.105489\pi$
$882$		0			0
$883$	−2.57264			−0.0865764			−0.0432882	−	0.999063i	$-0.513783\pi$
$883$	−2.57264			−0.0865764			−0.0432882	+	0.999063i	$0.513783\pi$
$884$	12.6705	−	21.9988i	0.426154	−	0.739898i
$885$		0			0
$886$	−0.592774	−	1.02672i	−0.0199146	−	0.0344932i
$887$	36.8102			1.23597			0.617983	−	0.786191i	$-0.287950\pi$
$887$	36.8102			1.23597			0.617983	+	0.786191i	$0.287950\pi$
$888$		0			0
$889$	22.6931	+	27.1628i	0.761101	+	0.911010i
$890$	0.801720	+	1.38862i	0.0268737	+	0.0465466i
$891$		0			0
$892$	−11.5710	+	20.0415i	−0.387425	+	0.671041i
$893$	17.6881			0.591911
$894$		0			0
$895$	14.8824	−	25.7770i	0.497462	−	0.861630i
$896$	1.97027	−	5.37732i	0.0658221	−	0.179644i
$897$		0			0
$898$	−0.402255	−	0.696726i	−0.0134234	−	0.0232501i
$899$	45.8744	+	79.4567i	1.53000	+	2.65003i
$900$		0			0
$901$	−9.37502	+	16.2380i	−0.312327	+	0.540967i
$902$	−1.04900			−0.0349278
$903$		0			0
$904$	0.921196	+	1.59556i	0.0306385	+	0.0530675i
$905$	−6.13852	−	10.6322i	−0.204051	−	0.353427i
$906$		0			0
$907$	−1.92469	−	3.33367i	−0.0639084	−	0.110693i	0.832301	−	0.554324i	$-0.187023\pi$
$907$	−1.92469	−	3.33367i	−0.0639084	−	0.110693i	−0.896209	+	0.443632i	$0.853690\pi$
$908$	−1.59330			−0.0528755
$909$		0			0
$910$	−0.681111	+	1.86492i	−0.0225786	+	0.0618214i
$911$	47.0839			1.55996			0.779980	−	0.625804i	$-0.215229\pi$
$911$	47.0839			1.55996			0.779980	+	0.625804i	$0.215229\pi$
$912$		0			0
$913$	11.8026	+	20.4427i	0.390609	+	0.676555i
$914$	0.566911			0.0187517
$915$		0			0
$916$	23.1608	+	40.1157i	0.765255	+	1.32546i
$917$	−47.2382	+	8.22483i	−1.55994	+	0.271608i
$918$		0			0
$919$	27.8881	−	48.3036i	0.919943	−	1.59339i	0.120443	−	0.992720i	$-0.461568\pi$
$919$	27.8881	−	48.3036i	0.919943	−	1.59339i	0.799499	−	0.600667i	$-0.205098\pi$
$920$	1.38670	+	2.40183i	0.0457181	+	0.0791861i
$921$		0			0
$922$	0.149886	+	0.259611i	0.00493625	+	0.00854983i
$923$	−18.8622	+	0.0196355i	−0.620856	+	0.000646311i
$924$		0			0
$925$	0.237607	−	0.411548i	0.00781248	−	0.0135316i
$926$	−1.37598			−0.0452175
$927$		0			0
$928$	4.03694	−	6.99219i	0.132519	−	0.229530i
$929$	19.4720	−	33.7264i	0.638855	−	1.10653i	−0.346830	−	0.937928i	$-0.612742\pi$
$929$	19.4720	−	33.7264i	0.638855	−	1.10653i	0.985684	−	0.168601i	$-0.0539248\pi$
$930$		0			0
$931$	45.4724	−	16.3298i	1.49030	−	0.535188i
$932$	12.1596	+	21.0610i	0.398299	+	0.689875i
$933$		0			0
$934$	−0.222484	−	0.385354i	−0.00727991	−	0.0126092i
$935$	−23.5208	+	40.7392i	−0.769211	+	1.33231i
$936$		0			0
$937$	19.5763			0.639531			0.319765	−	0.947497i	$-0.396396\pi$
$937$	19.5763			0.639531			0.319765	+	0.947497i	$0.396396\pi$
$938$	0.120667	−	0.0210098i	0.00393992	−	0.000685996i
$939$		0			0
$940$	7.82124	−	13.5468i	0.255101	−	0.441848i
$941$	−3.84200	+	6.65455i	−0.125246	+	0.216932i	−0.921829	−	0.387597i	$-0.873305\pi$
$941$	−3.84200	+	6.65455i	−0.125246	+	0.216932i	0.796583	+	0.604529i	$0.206639\pi$
$942$		0			0
$943$	5.90001	−	10.2191i	0.192131	−	0.332780i
$944$	−30.0184			−0.977017
$945$		0			0
$946$	0.250273	−	0.433485i	0.00813707	−	0.0140938i
$947$	−34.3969			−1.11775			−0.558874	−	0.829253i	$-0.688766\pi$
$947$	−34.3969			−1.11775			−0.558874	+	0.829253i	$0.688766\pi$
$948$		0			0
$949$	6.35561	+	10.9818i	0.206312	+	0.356485i
$950$	1.02324	+	1.77231i	0.0331984	+	0.0575012i
$951$		0			0
$952$	0.873094	−	2.38288i	0.0282971	−	0.0772294i
$953$	23.8888	+	41.3766i	0.773834	+	1.34032i	0.935447	+	0.353466i	$0.114997\pi$
$953$	23.8888	+	41.3766i	0.773834	+	1.34032i	−0.161613	+	0.986854i	$0.551670\pi$
$954$		0			0
$955$	45.2449			1.46409
$956$	−0.966423			−0.0312563
$957$		0			0
$958$	0.265794	+	0.460369i	0.00858742	+	0.0148739i
$959$	−19.4249	+	53.0151i	−0.627263	+	1.71195i
$960$		0			0
$961$	−27.2722	−	47.2369i	−0.879749	−	1.52377i
$962$	−0.0133508	+	0.0231799i	−0.000430446	+	0.000747349i
$963$		0			0
$964$	4.62951			0.149106
$965$	−34.1746	+	59.1921i	−1.10012	+	1.90546i
$966$		0			0
$967$	52.1099			1.67574			0.837871	−	0.545869i	$-0.183800\pi$
$967$	52.1099			1.67574			0.837871	+	0.545869i	$0.183800\pi$
$968$	−1.08617	+	1.88129i	−0.0349107	+	0.0604671i
$969$		0			0
$970$	0.804118	−	1.39277i	0.0258187	−	0.0447192i
$971$	10.3147	−	17.8656i	0.331014	−	0.573333i	−0.651697	−	0.758479i	$-0.725943\pi$
$971$	10.3147	−	17.8656i	0.331014	−	0.573333i	0.982711	+	0.185146i	$0.0592759\pi$
$972$		0			0
$973$	−0.367671	+	0.0640167i	−0.0117870	+	0.00205228i
$974$	1.43380			0.0459418
$975$		0			0
$976$	−9.67871	+	16.7640i	−0.309808	+	0.536603i
$977$	−12.9795	−	22.4811i	−0.415251	−	0.719235i	0.580204	−	0.814471i	$-0.302973\pi$
$977$	−12.9795	−	22.4811i	−0.415251	−	0.719235i	−0.995455	+	0.0952360i	$0.969639\pi$
$978$		0			0
$979$	−16.7871	−	29.0760i	−0.536516	−	0.929274i
$980$	7.60024	−	42.0465i	0.242781	−	1.34313i
$981$		0			0
$982$	−0.297258	+	0.514866i	−0.00948588	+	0.0164300i
$983$	19.0424	−	32.9825i	0.607359	−	1.05198i	−0.384315	−	0.923202i	$-0.625562\pi$
$983$	19.0424	−	32.9825i	0.607359	−	1.05198i	0.991674	−	0.128775i	$-0.0411045\pi$
$984$		0			0
$985$	−19.3506			−0.616561
$986$	1.19076	−	2.06246i	0.0379215	−	0.0656820i
$987$		0			0
$988$	24.8735	+	42.9788i	0.791332	+	1.36734i
$989$	2.81528	+	4.87621i	0.0895207	+	0.155054i
$990$		0			0
$991$	30.6807	+	53.1406i	0.974605	+	1.68807i	0.681232	+	0.732068i	$0.261445\pi$
$991$	30.6807	+	53.1406i	0.974605	+	1.68807i	0.293373	+	0.955998i	$0.405222\pi$
$992$	−3.76395	+	6.51936i	−0.119506	+	0.206990i
$993$		0			0
$994$	−0.927733	+	0.161531i	−0.0294259	+	0.00512346i
$995$	9.23254	+	15.9912i	0.292691	+	0.506956i
$996$		0			0
$997$	−19.3317			−0.612240			−0.306120	−	0.951993i	$-0.599031\pi$
$997$	−19.3317			−0.612240			−0.306120	+	0.951993i	$0.599031\pi$
$998$	0.724082	+	1.25415i	0.0229204	+	0.0396993i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.s.e.802.4		16
3.2	odd	2		273.2.l.b.256.5	yes	16
7.2	even	3		819.2.n.e.100.5		16
13.3	even	3		819.2.n.e.172.5		16
21.2	odd	6		273.2.j.b.100.4	✓	16
39.29	odd	6		273.2.j.b.172.4	yes	16
91.16	even	3	inner	819.2.s.e.289.4		16
273.107	odd	6		273.2.l.b.16.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.b.100.4	✓	16	21.2	odd	6
273.2.j.b.172.4	yes	16	39.29	odd	6
273.2.l.b.16.5	yes	16	273.107	odd	6
273.2.l.b.256.5	yes	16	3.2	odd	2
819.2.n.e.100.5		16	7.2	even	3
819.2.n.e.172.5		16	13.3	even	3
819.2.s.e.289.4		16	91.16	even	3	inner
819.2.s.e.802.4		16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.0680360 q^{2} -1.99537 q^{4} +(-1.52954 - 2.64923i) q^{5} +(0.910236 - 2.48424i) q^{7} +0.271829 q^{8} +O(q^{10})\)	\(q-0.0680360 q^{2} -1.99537 q^{4} +(-1.52954 - 2.64923i) q^{5} +(0.910236 - 2.48424i) q^{7} +0.271829 q^{8} +(0.104063 + 0.180243i) q^{10} +(-2.17896 - 3.77408i) q^{11} +(-1.79952 + 3.12437i) q^{13} +(-0.0619288 + 0.169018i) q^{14} +3.97225 q^{16} +3.52867 q^{17} +(-3.45112 + 5.97751i) q^{19} +(3.05199 + 5.28621i) q^{20} +(0.148248 + 0.256773i) q^{22} -3.33524 q^{23} +(-2.17896 + 3.77408i) q^{25} +(0.122432 - 0.212570i) q^{26} +(-1.81626 + 4.95699i) q^{28} +(-4.95991 + 8.59082i) q^{29} +(4.62451 - 8.00989i) q^{31} -0.813913 q^{32} -0.240077 q^{34} +(-7.97359 + 1.38831i) q^{35} -0.109046 q^{37} +(0.234800 - 0.406686i) q^{38} +(-0.415772 - 0.720139i) q^{40} +(-1.76899 + 3.06399i) q^{41} +(-0.844102 - 1.46203i) q^{43} +(4.34784 + 7.53068i) q^{44} +0.226916 q^{46} +(-1.28133 - 2.21933i) q^{47} +(-5.34294 - 4.52250i) q^{49} +(0.148248 - 0.256773i) q^{50} +(3.59072 - 6.23429i) q^{52} +(-2.65681 + 4.60173i) q^{53} +(-6.66561 + 11.5452i) q^{55} +(0.247428 - 0.675289i) q^{56} +(0.337453 - 0.584485i) q^{58} -7.55704 q^{59} +(-2.43658 + 4.22029i) q^{61} +(-0.314633 + 0.544960i) q^{62} -7.88912 q^{64} +(11.0296 - 0.0114818i) q^{65} +(-0.340218 - 0.589274i) q^{67} -7.04101 q^{68} +(0.542491 - 0.0944552i) q^{70} +(2.61572 + 4.53055i) q^{71} +(1.75956 - 3.04764i) q^{73} +0.00741905 q^{74} +(6.88626 - 11.9274i) q^{76} +(-11.3591 + 1.97778i) q^{77} +(4.85408 + 8.40751i) q^{79} +(-6.07570 - 10.5234i) q^{80} +(0.120355 - 0.208461i) q^{82} -5.41662 q^{83} +(-5.39723 - 9.34828i) q^{85} +(0.0574293 + 0.0994705i) q^{86} +(-0.592305 - 1.02590i) q^{88} +7.70414 q^{89} +(6.12372 + 7.31438i) q^{91} +6.65503 q^{92} +(0.0871768 + 0.150995i) q^{94} +21.1144 q^{95} +(-3.86359 - 6.69194i) q^{97} +(0.363512 + 0.307692i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} + q^{7} - 12 q^{8}+O(q^{10}) \) 16 * q + 12 * q^4 + q^7 - 12 * q^8	\( 16 q + 12 q^{4} + q^{7} - 12 q^{8} - 4 q^{10} + 2 q^{11} + 5 q^{13} + 7 q^{14} + 12 q^{16} - 4 q^{17} - 11 q^{19} + 20 q^{20} + 7 q^{22} + 8 q^{23} + 2 q^{25} - 33 q^{26} - q^{28} - 15 q^{29} + 3 q^{31} + 6 q^{32} - 68 q^{34} - 8 q^{37} - 2 q^{38} - 25 q^{40} - 19 q^{41} + 11 q^{43} + 16 q^{44} - 4 q^{46} - 5 q^{47} + 7 q^{49} + 7 q^{50} - 18 q^{52} - 36 q^{53} - 15 q^{55} + 51 q^{56} + 20 q^{58} - 34 q^{59} - 22 q^{61} + 6 q^{62} - 20 q^{64} + 24 q^{65} + 26 q^{67} + 10 q^{68} + 46 q^{70} - 9 q^{71} - 6 q^{73} + 30 q^{74} - 16 q^{76} + 36 q^{77} + 16 q^{79} + 28 q^{80} - q^{82} - 36 q^{83} - 4 q^{85} - 16 q^{86} + 24 q^{88} + 40 q^{89} - 10 q^{91} + 94 q^{92} - 20 q^{94} + 7 q^{97} - 18 q^{98}+O(q^{100}) \) 16 * q + 12 * q^4 + q^7 - 12 * q^8 - 4 * q^10 + 2 * q^11 + 5 * q^13 + 7 * q^14 + 12 * q^16 - 4 * q^17 - 11 * q^19 + 20 * q^20 + 7 * q^22 + 8 * q^23 + 2 * q^25 - 33 * q^26 - q^28 - 15 * q^29 + 3 * q^31 + 6 * q^32 - 68 * q^34 - 8 * q^37 - 2 * q^38 - 25 * q^40 - 19 * q^41 + 11 * q^43 + 16 * q^44 - 4 * q^46 - 5 * q^47 + 7 * q^49 + 7 * q^50 - 18 * q^52 - 36 * q^53 - 15 * q^55 + 51 * q^56 + 20 * q^58 - 34 * q^59 - 22 * q^61 + 6 * q^62 - 20 * q^64 + 24 * q^65 + 26 * q^67 + 10 * q^68 + 46 * q^70 - 9 * q^71 - 6 * q^73 + 30 * q^74 - 16 * q^76 + 36 * q^77 + 16 * q^79 + 28 * q^80 - q^82 - 36 * q^83 - 4 * q^85 - 16 * q^86 + 24 * q^88 + 40 * q^89 - 10 * q^91 + 94 * q^92 - 20 * q^94 + 7 * q^97 - 18 * q^98

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