LMFDB - Embedded newform 819.2.s.f.289.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [819,2,Mod(289,819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [20,0,0,32,0,0,3,12,0,-4,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 18 x^{18} - 4 x^{17} + 211 x^{16} - 59 x^{15} + 1458 x^{14} - 526 x^{13} + 7324 x^{12} + \cdots + 1369 $ x^20 + 18x^18 - 4x^17 + 211x^16 - 59x^15 + 1458x^14 - 526x^13 + 7324x^12 - 2645x^11 + 23428x^10 - 8506x^9 + 54235x^8 - 18801x^7 + 74141x^6 - 25533x^5 + 68867x^4 - 16327x^3 + 16588x^2 + 2997x + 1369
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.4
Root			$0.613260 + 1.06220i$ of defining polynomial
Character	$\chi$	$=$	819.289
Dual form			819.2.s.f.802.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.22652 q^{2} -0.495647 q^{4} +(2.10660 - 3.64874i) q^{5} +(0.113533 - 2.64331i) q^{7} +3.06096 q^{8} +(-2.58379 + 4.47526i) q^{10} +(2.76269 - 4.78512i) q^{11} +(3.59845 + 0.226101i) q^{13} +(-0.139251 + 3.24208i) q^{14} -2.76304 q^{16} -0.178289 q^{17} +(2.25950 + 3.91358i) q^{19} +(-1.04413 + 1.80849i) q^{20} +(-3.38850 + 5.86905i) q^{22} -1.08705 q^{23} +(-6.37556 - 11.0428i) q^{25} +(-4.41358 - 0.277317i) q^{26} +(-0.0562723 + 1.31015i) q^{28} +(0.0731926 + 0.126773i) q^{29} +(4.19459 + 7.26525i) q^{31} -2.73300 q^{32} +0.218676 q^{34} +(-9.40561 - 5.98267i) q^{35} +4.31844 q^{37} +(-2.77133 - 4.80008i) q^{38} +(6.44824 - 11.1687i) q^{40} +(-0.782385 - 1.35513i) q^{41} +(-1.66752 + 2.88823i) q^{43} +(-1.36932 + 2.37173i) q^{44} +1.33329 q^{46} +(-0.636455 + 1.10237i) q^{47} +(-6.97422 - 0.600207i) q^{49} +(7.81976 + 13.5442i) q^{50} +(-1.78356 - 0.112066i) q^{52} +(3.93930 + 6.82307i) q^{53} +(-11.6398 - 20.1607i) q^{55} +(0.347521 - 8.09109i) q^{56} +(-0.0897723 - 0.155490i) q^{58} +2.02119 q^{59} +(1.88279 + 3.26108i) q^{61} +(-5.14476 - 8.91098i) q^{62} +8.87816 q^{64} +(8.40550 - 12.6535i) q^{65} +(0.153689 - 0.266197i) q^{67} +0.0883685 q^{68} +(11.5362 + 7.33787i) q^{70} +(1.62940 - 2.82220i) q^{71} +(-3.53172 - 6.11712i) q^{73} -5.29665 q^{74} +(-1.11992 - 1.93975i) q^{76} +(-12.3349 - 7.84593i) q^{77} +(-2.30707 + 3.99596i) q^{79} +(-5.82063 + 10.0816i) q^{80} +(0.959612 + 1.66210i) q^{82} +8.85136 q^{83} +(-0.375585 + 0.650532i) q^{85} +(2.04525 - 3.54248i) q^{86} +(8.45649 - 14.6471i) q^{88} -13.1970 q^{89} +(1.00620 - 9.48618i) q^{91} +0.538791 q^{92} +(0.780625 - 1.35208i) q^{94} +19.0395 q^{95} +(1.17499 - 2.03514i) q^{97} +(8.55403 + 0.736167i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 32 q^{4} + 3 q^{7} + 12 q^{8} - 4 q^{10} + 8 q^{11} - 5 q^{13} + 9 q^{14} + 40 q^{16} + 7 q^{19} - 12 q^{20} - 9 q^{22} - 28 q^{23} - 32 q^{25} - 13 q^{26} - 23 q^{28} + 9 q^{29} - 9 q^{31} + 34 q^{32}+ \cdots + 76 q^{98}+O(q^{100}) $ 20 * q + 32 * q^4 + 3 * q^7 + 12 * q^8 - 4 * q^10 + 8 * q^11 - 5 * q^13 + 9 * q^14 + 40 * q^16 + 7 * q^19 - 12 * q^20 - 9 * q^22 - 28 * q^23 - 32 * q^25 - 13 * q^26 - 23 * q^28 + 9 * q^29 - 9 * q^31 + 34 * q^32 + 12 * q^34 - 10 * q^35 - 36 * q^37 - 22 * q^38 - 9 * q^40 + q^41 - 11 * q^43 - 8 * q^44 + 20 * q^46 - 13 * q^47 - 3 * q^49 - 5 * q^50 - 44 * q^52 + 6 * q^53 - 19 * q^55 + 23 * q^56 - 30 * q^59 - 22 * q^62 + 72 * q^64 + 6 * q^65 - 22 * q^67 + 78 * q^68 + 30 * q^70 + 11 * q^71 - 6 * q^74 + 6 * q^76 - 56 * q^77 - 36 * q^79 - 48 * q^80 - 13 * q^82 - 40 * q^83 - 16 * q^85 - 4 * q^86 - 12 * q^88 + 4 * q^89 + 30 * q^91 - 66 * q^92 - 44 * q^94 - 72 * q^95 + 21 * q^97 + 76 * q^98

Character values

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

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

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 $

$2$	−1.22652			−0.867281			−0.433641	−	0.901086i	$-0.642771\pi$
$2$	−1.22652			−0.867281			−0.433641	+	0.901086i	$0.642771\pi$
$3$		0			0
$3$		0			0
$4$	−0.495647			−0.247823
$5$	2.10660	−	3.64874i	0.942102	−	1.63177i	0.180649	−	0.983548i	$-0.442180\pi$
$5$	2.10660	−	3.64874i	0.942102	−	1.63177i	0.761452	−	0.648221i	$-0.224487\pi$
$6$		0			0
$7$	0.113533	−	2.64331i	0.0429115	−	0.999079i
$7$	0.113533	−	2.64331i	0.0429115	−	0.999079i
$8$	3.06096			1.08221
$9$		0			0
$10$	−2.58379	+	4.47526i	−0.817067	+	1.41520i
$11$	2.76269	−	4.78512i	0.832982	−	1.44277i	−0.0626804	−	0.998034i	$-0.519965\pi$
$11$	2.76269	−	4.78512i	0.832982	−	1.44277i	0.895663	−	0.444734i	$-0.146702\pi$
$12$		0			0
$13$	3.59845	+	0.226101i	0.998032	+	0.0627091i
$13$	3.59845	+	0.226101i	0.998032	+	0.0627091i
$14$	−0.139251	+	3.24208i	−0.0372163	+	0.866482i
$15$		0			0
$16$	−2.76304			−0.690760
$17$	−0.178289			−0.0432415			−0.0216208	−	0.999766i	$-0.506883\pi$
$17$	−0.178289			−0.0432415			−0.0216208	+	0.999766i	$0.506883\pi$
$18$		0			0
$19$	2.25950	+	3.91358i	0.518366	+	0.897836i	0.999772	+	0.0213385i	$0.00679277\pi$
$19$	2.25950	+	3.91358i	0.518366	+	0.897836i	−0.481406	+	0.876497i	$0.659874\pi$
$20$	−1.04413	+	1.80849i	−0.233475	+	0.404390i
$21$		0			0
$22$	−3.38850	+	5.86905i	−0.722430	+	1.25129i
$23$	−1.08705			−0.226665			−0.113332	−	0.993557i	$-0.536153\pi$
$23$	−1.08705			−0.226665			−0.113332	+	0.993557i	$0.536153\pi$
$24$		0			0
$25$	−6.37556	−	11.0428i	−1.27511	−	2.20856i
$26$	−4.41358	−	0.277317i	−0.865574	−	0.0543864i
$27$		0			0
$28$	−0.0562723	+	1.31015i	−0.0106345	+	0.247595i
$29$	0.0731926	+	0.126773i	0.0135915	+	0.0235412i	0.872741	−	0.488183i	$-0.162340\pi$
$29$	0.0731926	+	0.126773i	0.0135915	+	0.0235412i	−0.859150	+	0.511724i	$0.829007\pi$
$30$		0			0
$31$	4.19459	+	7.26525i	0.753371	+	1.30488i	0.946180	+	0.323641i	$0.104907\pi$
$31$	4.19459	+	7.26525i	0.753371	+	1.30488i	−0.192809	+	0.981236i	$0.561760\pi$
$32$	−2.73300			−0.483130
$33$		0			0
$34$	0.218676			0.0375026
$35$	−9.40561	−	5.98267i	−1.58984	−	1.01126i
$36$		0			0
$37$	4.31844			0.709947			0.354973	−	0.934876i	$-0.384490\pi$
$37$	4.31844			0.709947			0.354973	+	0.934876i	$0.384490\pi$
$38$	−2.77133	−	4.80008i	−0.449569	−	0.778676i
$39$		0			0
$40$	6.44824	−	11.1687i	1.01956	−	1.76592i
$41$	−0.782385	−	1.35513i	−0.122188	−	0.211636i	0.798442	−	0.602071i	$-0.205658\pi$
$41$	−0.782385	−	1.35513i	−0.122188	−	0.211636i	−0.920630	+	0.390436i	$0.872324\pi$
$42$		0			0
$43$	−1.66752	+	2.88823i	−0.254295	+	0.440452i	−0.964704	−	0.263338i	$-0.915177\pi$
$43$	−1.66752	+	2.88823i	−0.254295	+	0.440452i	0.710409	+	0.703789i	$0.248510\pi$
$44$	−1.36932	+	2.37173i	−0.206432	+	0.357551i
$45$		0			0
$46$	1.33329			0.196582
$47$	−0.636455	+	1.10237i	−0.0928365	+	0.160798i	−0.908704	−	0.417442i	$-0.862927\pi$
$47$	−0.636455	+	1.10237i	−0.0928365	+	0.160798i	0.815867	+	0.578239i	$0.196260\pi$
$48$		0			0
$49$	−6.97422	−	0.600207i	−0.996317	−	0.0857439i
$50$	7.81976	+	13.5442i	1.10588	+	1.91544i
$51$		0			0
$52$	−1.78356	−	0.112066i	−0.247336	−	0.0155408i
$53$	3.93930	+	6.82307i	0.541105	+	0.937221i	0.998841	+	0.0481326i	$0.0153270\pi$
$53$	3.93930	+	6.82307i	0.541105	+	0.937221i	−0.457736	+	0.889088i	$0.651340\pi$
$54$		0			0
$55$	−11.6398	−	20.1607i	−1.56951	−	2.71847i
$56$	0.347521	−	8.09109i	0.0464394	−	1.08122i
$57$		0			0
$58$	−0.0897723	−	0.155490i	−0.0117877	−	0.0204169i
$59$	2.02119			0.263136			0.131568	−	0.991307i	$-0.457999\pi$
$59$	2.02119			0.263136			0.131568	+	0.991307i	$0.457999\pi$
$60$		0			0
$61$	1.88279	+	3.26108i	0.241066	+	0.417539i	0.961018	−	0.276485i	$-0.0891696\pi$
$61$	1.88279	+	3.26108i	0.241066	+	0.417539i	−0.719952	+	0.694024i	$0.755836\pi$
$62$	−5.14476	−	8.91098i	−0.653385	−	1.13170i
$63$		0			0
$64$	8.87816			1.10977
$65$	8.40550	−	12.6535i	1.04257	−	1.56948i
$66$		0			0
$67$	0.153689	−	0.266197i	0.0187761	−	0.0325212i	−0.856485	−	0.516172i	$-0.827356\pi$
$67$	0.153689	−	0.266197i	0.0187761	−	0.0325212i	0.875261	+	0.483651i	$0.160690\pi$
$68$	0.0883685			0.0107163
$69$		0			0
$70$	11.5362	+	7.33787i	1.37884	+	0.877043i
$71$	1.62940	−	2.82220i	0.193374	−	0.334933i	−0.752992	−	0.658029i	$-0.771390\pi$
$71$	1.62940	−	2.82220i	0.193374	−	0.334933i	0.946366	+	0.323096i	$0.104724\pi$
$72$		0			0
$73$	−3.53172	−	6.11712i	−0.413356	−	0.715954i	0.581898	−	0.813262i	$-0.302310\pi$
$73$	−3.53172	−	6.11712i	−0.413356	−	0.715954i	−0.995254	+	0.0973075i	$0.968977\pi$
$74$	−5.29665			−0.615723
$75$		0			0
$76$	−1.11992	−	1.93975i	−0.128463	−	0.222505i
$77$	−12.3349	−	7.84593i	−1.40569	−	0.894126i
$78$		0			0
$79$	−2.30707	+	3.99596i	−0.259566	+	0.449581i	−0.966126	−	0.258072i	$-0.916913\pi$
$79$	−2.30707	+	3.99596i	−0.259566	+	0.449581i	0.706560	+	0.707653i	$0.250246\pi$
$80$	−5.82063	+	10.0816i	−0.650767	+	1.12716i
$81$		0			0
$82$	0.959612	+	1.66210i	0.105971	+	0.183548i
$83$	8.85136			0.971563			0.485782	−	0.874080i	$-0.338535\pi$
$83$	8.85136			0.971563			0.485782	+	0.874080i	$0.338535\pi$
$84$		0			0
$85$	−0.375585	+	0.650532i	−0.0407379	+	0.0705601i
$86$	2.04525	−	3.54248i	0.220545	−	0.381995i
$87$		0			0
$88$	8.45649	−	14.6471i	0.901465	−	1.56138i
$89$	−13.1970			−1.39888			−0.699442	−	0.714690i	$-0.746568\pi$
$89$	−13.1970			−1.39888			−0.699442	+	0.714690i	$0.746568\pi$
$90$		0			0
$91$	1.00620	−	9.48618i	0.105478	−	0.994422i
$92$	0.538791			0.0561729
$93$		0			0
$94$	0.780625	−	1.35208i	0.0805154	−	0.139457i
$95$	19.0395			1.95341
$96$		0			0
$97$	1.17499	−	2.03514i	0.119302	−	0.206637i	−0.800189	−	0.599748i	$-0.795268\pi$
$97$	1.17499	−	2.03514i	0.119302	−	0.206637i	0.919491	+	0.393110i	$0.128601\pi$
$98$	8.55403	+	0.736167i	0.864087	+	0.0743641i
$99$		0			0
$100$	3.16002	+	5.47332i	0.316002	+	0.547332i
$101$	5.06985	−	8.78124i	0.504469	−	0.873766i	−0.495517	−	0.868598i	$-0.665022\pi$
$101$	5.06985	−	8.78124i	0.504469	−	0.873766i	0.999987	−	0.00516840i	$-0.00164516\pi$
$102$		0			0
$103$	−5.01549	+	8.68709i	−0.494191	+	0.855964i	−0.999978	−	0.00669444i	$-0.997869\pi$
$103$	−5.01549	+	8.68709i	−0.494191	+	0.855964i	0.505786	+	0.862659i	$0.331202\pi$
$104$	11.0147	+	0.692086i	1.08008	+	0.0678647i
$105$		0			0
$106$	−4.83163	−	8.36864i	−0.469290	−	0.812834i
$107$	−13.8521			−1.33913			−0.669567	−	0.742751i	$-0.733520\pi$
$107$	−13.8521			−1.33913			−0.669567	+	0.742751i	$0.733520\pi$
$108$		0			0
$109$	0.471229	+	0.816192i	0.0451355	+	0.0781770i	0.887711	−	0.460402i	$-0.152295\pi$
$109$	0.471229	+	0.816192i	0.0451355	+	0.0781770i	−0.842575	+	0.538579i	$0.818961\pi$
$110$	14.2764	+	24.7275i	1.36121	+	2.35768i
$111$		0			0
$112$	−0.313697	+	7.30359i	−0.0296415	+	0.690124i
$113$	−2.86292	+	4.95873i	−0.269321	+	0.466478i	−0.968687	−	0.248286i	$-0.920133\pi$
$113$	−2.86292	+	4.95873i	−0.269321	+	0.466478i	0.699366	+	0.714764i	$0.253466\pi$
$114$		0			0
$115$	−2.28998	+	3.96636i	−0.213541	+	0.369865i
$116$	−0.0362777	−	0.0628348i	−0.00336830	−	0.00583406i
$117$		0			0
$118$	−2.47903			−0.228213
$119$	−0.0202417	+	0.471275i	−0.00185556	+	0.0432017i
$120$		0			0
$121$	−9.76491	−	16.9133i	−0.887719	−	1.53757i
$122$	−2.30928	−	3.99979i	−0.209072	−	0.362124i
$123$		0			0
$124$	−2.07904	−	3.60100i	−0.186703	−	0.323379i
$125$	−32.6571			−2.92094
$126$		0			0
$127$	6.56642	+	11.3734i	0.582676	+	1.00922i	0.995161	+	0.0982595i	$0.0313275\pi$
$127$	6.56642	+	11.3734i	0.582676	+	1.00922i	−0.412485	+	0.910964i	$0.635339\pi$
$128$	−5.42325			−0.479353
$129$		0			0
$130$	−10.3095	+	15.5198i	−0.904205	+	1.36118i
$131$	−5.95196	+	10.3091i	−0.520025	+	0.900710i	0.479704	+	0.877431i	$0.340744\pi$
$131$	−5.95196	+	10.3091i	−0.520025	+	0.900710i	−0.999729	+	0.0232796i	$0.992589\pi$
$132$		0			0
$133$	10.6013	−	5.52826i	0.919253	−	0.479361i
$134$	−0.188503	+	0.326496i	−0.0162842	+	0.0282050i
$135$		0			0
$136$	−0.545737			−0.0467966
$137$	−13.5285			−1.15581			−0.577907	−	0.816102i	$-0.696130\pi$
$137$	−13.5285			−1.15581			−0.577907	+	0.816102i	$0.696130\pi$
$138$		0			0
$139$	−10.9150	+	18.9053i	−0.925796	+	1.60353i	−0.135521	+	0.990774i	$0.543271\pi$
$139$	−10.9150	+	18.9053i	−0.925796	+	1.60353i	−0.790275	+	0.612752i	$0.790062\pi$
$140$	4.66186	+	2.96529i	0.393999	+	0.250613i
$141$		0			0
$142$	−1.99849	+	3.46149i	−0.167710	+	0.290481i
$143$	11.0233	−	16.5944i	0.921818	−	1.38769i
$144$		0			0
$145$	0.616751			0.0512184
$146$	4.33173	+	7.50277i	0.358496	+	0.620934i
$147$		0			0
$148$	−2.14042			−0.175941
$149$	3.83204	+	6.63729i	0.313933	+	0.543748i	0.979210	−	0.202848i	$-0.0650199\pi$
$149$	3.83204	+	6.63729i	0.313933	+	0.543748i	−0.665277	+	0.746597i	$0.731687\pi$
$150$		0			0
$151$	−1.87363	−	3.24522i	−0.152474	−	0.264092i	0.779663	−	0.626200i	$-0.215391\pi$
$151$	−1.87363	−	3.24522i	−0.152474	−	0.264092i	−0.932136	+	0.362108i	$0.882057\pi$
$152$	6.91626	+	11.9793i	0.560983	+	0.971650i
$153$		0			0
$154$	15.1290	+	9.62319i	1.21913	+	0.775459i
$155$	35.3454			2.83901
$156$		0			0
$157$	1.63089	+	2.82478i	0.130159	+	0.225442i	0.923738	−	0.383026i	$-0.125118\pi$
$157$	1.63089	+	2.82478i	0.130159	+	0.225442i	−0.793579	+	0.608467i	$0.791785\pi$
$158$	2.82967	−	4.90113i	0.225116	−	0.389913i
$159$		0			0
$160$	−5.75734	+	9.97201i	−0.455158	+	0.788357i
$161$	−0.123416	+	2.87341i	−0.00972653	+	0.226456i
$162$		0			0
$163$	5.22544	+	9.05073i	0.409288	+	0.708908i	0.994810	−	0.101749i	$-0.0324438\pi$
$163$	5.22544	+	9.05073i	0.409288	+	0.708908i	−0.585522	+	0.810656i	$0.699110\pi$
$164$	0.387787	+	0.671666i	0.0302810	+	0.0524483i
$165$		0			0
$166$	−10.8564			−0.842618
$167$	−5.58474	−	9.67305i	−0.432160	−	0.748523i	0.564899	−	0.825160i	$-0.308915\pi$
$167$	−5.58474	−	9.67305i	−0.432160	−	0.748523i	−0.997059	+	0.0766369i	$0.975582\pi$
$168$		0			0
$169$	12.8978	+	1.62723i	0.992135	+	0.125171i
$170$	0.460663	−	0.797891i	0.0353312	−	0.0611955i
$171$		0			0
$172$	0.826502	−	1.43154i	0.0630202	−	0.109154i
$173$	−6.38332	−	11.0562i	−0.485315	−	0.840590i	0.514543	−	0.857465i	$-0.327962\pi$
$173$	−6.38332	−	11.0562i	−0.485315	−	0.840590i	−0.999858	+	0.0168746i	$0.994628\pi$
$174$		0			0
$175$	−29.9134	+	15.5989i	−2.26124	+	1.17916i
$176$	−7.63343	+	13.2215i	−0.575391	+	0.996607i
$177$		0			0
$178$	16.1864			1.21323
$179$	−6.27632	+	10.8709i	−0.469114	+	0.812529i	−0.999377	−	0.0353041i	$-0.988760\pi$
$179$	−6.27632	+	10.8709i	−0.469114	+	0.812529i	0.530263	+	0.847833i	$0.322093\pi$
$180$		0			0
$181$	13.6821			1.01698			0.508491	−	0.861067i	$-0.330204\pi$
$181$	13.6821			1.01698			0.508491	+	0.861067i	$0.330204\pi$
$182$	−1.23412	+	11.6350i	−0.0914794	+	0.862443i
$183$		0			0
$184$	−3.32741			−0.245300
$185$	9.09723	−	15.7569i	0.668842	−	1.15847i
$186$		0			0
$187$	−0.492558	+	0.853136i	−0.0360194	+	0.0623875i
$188$	0.315457	−	0.546387i	0.0230070	−	0.0398494i
$189$		0			0
$190$	−23.3524			−1.69416
$191$	12.2068	+	21.1428i	0.883252	+	1.52984i	0.847705	+	0.530469i	$0.177984\pi$
$191$	12.2068	+	21.1428i	0.883252	+	1.52984i	0.0355470	+	0.999368i	$0.488683\pi$
$192$		0			0
$193$	6.25469	−	10.8334i	0.450223	−	0.779808i	−0.548177	−	0.836362i	$-0.684678\pi$
$193$	6.25469	−	10.8334i	0.450223	−	0.779808i	0.998400	+	0.0565540i	$0.0180113\pi$
$194$	−1.44115	+	2.49614i	−0.103468	+	0.179213i
$195$		0			0
$196$	3.45675	+	0.297491i	0.246911	+	0.0212493i
$197$	9.75853	+	16.9023i	0.695266	+	1.20424i	0.970091	+	0.242742i	$0.0780469\pi$
$197$	9.75853	+	16.9023i	0.695266	+	1.20424i	−0.274825	+	0.961494i	$0.588620\pi$
$198$		0			0
$199$	−4.78770			−0.339391			−0.169695	−	0.985497i	$-0.554278\pi$
$199$	−4.78770			−0.339391			−0.169695	+	0.985497i	$0.554278\pi$
$200$	−19.5153	−	33.8016i	−1.37994	−	2.39013i
$201$		0			0
$202$	−6.21828	+	10.7704i	−0.437517	+	0.757801i
$203$	0.343411	−	0.179078i	0.0241028	−	0.0125688i
$204$		0			0
$205$	−6.59270			−0.460454
$206$	6.15161	−	10.6549i	0.428603	−	0.742362i
$207$		0			0
$208$	−9.94268	−	0.624726i	−0.689401	−	0.0433170i
$209$	24.9692			1.72716
$210$		0			0
$211$	−2.28135	−	3.95141i	−0.157054	−	0.272026i	0.776751	−	0.629808i	$-0.216866\pi$
$211$	−2.28135	−	3.95141i	−0.157054	−	0.272026i	−0.933805	+	0.357782i	$0.883533\pi$
$212$	−1.95250	−	3.38183i	−0.134098	−	0.232265i
$213$		0			0
$214$	16.9899			1.16141
$215$	7.02562	+	12.1687i	0.479143	+	0.829900i
$216$		0			0
$217$	19.6806	−	10.2628i	1.33600	−	0.696683i
$218$	−0.577972	−	1.00108i	−0.0391452	−	0.0678015i
$219$		0			0
$220$	5.76922	+	9.99258i	0.388961	+	0.673700i
$221$	−0.641566	−	0.0403114i	−0.0431564	−	0.00271164i
$222$		0			0
$223$	−3.76290	−	6.51754i	−0.251983	−	0.436447i	0.712089	−	0.702089i	$-0.247749\pi$
$223$	−3.76290	−	6.51754i	−0.251983	−	0.436447i	−0.964072	+	0.265643i	$0.914416\pi$
$224$	−0.310286	+	7.22417i	−0.0207318	+	0.482685i
$225$		0			0
$226$	3.51143	−	6.08198i	0.233577	−	0.404567i
$227$	3.68109			0.244322			0.122161	−	0.992510i	$-0.461018\pi$
$227$	3.68109			0.244322			0.122161	+	0.992510i	$0.461018\pi$
$228$		0			0
$229$	−2.35083	+	4.07176i	−0.155347	+	0.269069i	−0.933185	−	0.359395i	$-0.882983\pi$
$229$	−2.35083	+	4.07176i	−0.155347	+	0.269069i	0.777838	+	0.628465i	$0.216316\pi$
$230$	2.80871	−	4.86482i	0.185201	−	0.320777i
$231$		0			0
$232$	0.224040	+	0.388048i	0.0147089	+	0.0254766i
$233$	−1.20491	+	2.08697i	−0.0789365	+	0.136722i	−0.902791	−	0.430079i	$-0.858486\pi$
$233$	−1.20491	+	2.08697i	−0.0789365	+	0.136722i	0.823855	+	0.566801i	$0.191819\pi$
$234$		0			0
$235$	2.68152	+	4.64452i	0.174923	+	0.302975i
$236$	−1.00180			−0.0652114
$237$		0			0
$238$	0.0248269	−	0.578028i	0.00160929	−	0.0374680i
$239$	−7.96050			−0.514922			−0.257461	−	0.966289i	$-0.582886\pi$
$239$	−7.96050			−0.514922			−0.257461	+	0.966289i	$0.582886\pi$
$240$		0			0
$241$	29.8755			1.92445			0.962225	−	0.272254i	$-0.0877691\pi$
$241$	29.8755			1.92445			0.962225	+	0.272254i	$0.0877691\pi$
$242$	11.9769	+	20.7445i	0.769902	+	1.33351i
$243$		0			0
$244$	−0.933197	−	1.61634i	−0.0597418	−	0.103476i
$245$	−16.8819	+	24.1828i	−1.07855	+	1.54498i
$246$		0			0
$247$	7.24586	+	14.5937i	0.461043	+	0.928575i
$248$	12.8395	+	22.2387i	0.815309	+	1.41216i
$249$		0			0
$250$	40.0546			2.53327
$251$	−11.1062	+	19.2366i	−0.701019	+	1.21420i	0.267090	+	0.963672i	$0.413938\pi$
$251$	−11.1062	+	19.2366i	−0.701019	+	1.21420i	−0.968109	+	0.250529i	$0.919396\pi$
$252$		0			0
$253$	−3.00317	+	5.20165i	−0.188808	+	0.327025i
$254$	−8.05385	−	13.9497i	−0.505344	−	0.875281i
$255$		0			0
$256$	−11.1046			−0.694037
$257$	3.23354			0.201703			0.100851	−	0.994902i	$-0.467843\pi$
$257$	3.23354			0.201703			0.100851	+	0.994902i	$0.467843\pi$
$258$		0			0
$259$	0.490285	−	11.4150i	0.0304649	−	0.709293i
$260$	−4.16616	+	6.27168i	−0.258374	+	0.388953i
$261$		0			0
$262$	7.30020	−	12.6443i	0.451008	−	0.781169i
$263$	3.74123	−	6.48000i	0.230694	−	0.399574i	−0.727318	−	0.686300i	$-0.759234\pi$
$263$	3.74123	−	6.48000i	0.230694	−	0.399574i	0.958013	+	0.286726i	$0.0925670\pi$
$264$		0			0
$265$	33.1942			2.03910
$266$	−13.0028	+	6.78053i	−0.797251	+	0.415741i
$267$		0			0
$268$	−0.0761754	+	0.131940i	−0.00465316	+	0.00805950i
$269$	3.03178			0.184851			0.0924253	−	0.995720i	$-0.470538\pi$
$269$	3.03178			0.184851			0.0924253	+	0.995720i	$0.470538\pi$
$270$		0			0
$271$	−21.6160			−1.31308			−0.656540	−	0.754291i	$-0.727981\pi$
$271$	−21.6160			−1.31308			−0.656540	+	0.754291i	$0.727981\pi$
$272$	0.492621			0.0298695
$273$		0			0
$274$	16.5929			1.00242
$275$	−70.4548			−4.24858
$276$		0			0
$277$	−9.50681			−0.571209			−0.285604	−	0.958348i	$-0.592194\pi$
$277$	−9.50681			−0.571209			−0.285604	+	0.958348i	$0.592194\pi$
$278$	13.3874	−	23.1877i	0.802926	−	1.39071i
$279$		0			0
$280$	−28.7902	−	18.3127i	−1.72054	−	1.09439i
$281$	−31.6740			−1.88951			−0.944757	−	0.327771i	$-0.893703\pi$
$281$	−31.6740			−1.88951			−0.944757	+	0.327771i	$0.893703\pi$
$282$		0			0
$283$	7.25720	−	12.5698i	0.431396	−	0.747199i	−0.565598	−	0.824681i	$-0.691355\pi$
$283$	7.25720	−	12.5698i	0.431396	−	0.747199i	0.996994	+	0.0774816i	$0.0246879\pi$
$284$	−0.807605	+	1.39881i	−0.0479225	+	0.0830043i
$285$		0			0
$286$	−13.5203	+	20.3534i	−0.799475	+	1.20352i
$287$	−3.67086	+	1.91424i	−0.216684	+	0.112994i
$288$		0			0
$289$	−16.9682			−0.998130
$290$	−0.756458			−0.0444208
$291$		0			0
$292$	1.75048	+	3.03193i	0.102439	+	0.177430i
$293$	10.3725	−	17.9658i	0.605970	−	1.04957i	−0.385927	−	0.922529i	$-0.626118\pi$
$293$	10.3725	−	17.9658i	0.605970	−	1.04957i	0.991897	−	0.127042i	$-0.0405483\pi$
$294$		0			0
$295$	4.25785	−	7.37481i	0.247901	−	0.429378i
$296$	13.2186			0.768314
$297$		0			0
$298$	−4.70008	−	8.14078i	−0.272268	−	0.471583i
$299$	−3.91169	−	0.245782i	−0.226219	−	0.0142140i
$300$		0			0
$301$	7.44519	+	4.73570i	0.429134	+	0.272961i
$302$	2.29804	+	3.98033i	0.132237	+	0.229042i
$303$		0			0
$304$	−6.24310	−	10.8134i	−0.358067	−	0.620189i
$305$	15.8651			0.908436
$306$		0			0
$307$	13.9276			0.794892			0.397446	−	0.917625i	$-0.369897\pi$
$307$	13.9276			0.794892			0.397446	+	0.917625i	$0.369897\pi$
$308$	6.11376	+	3.88881i	0.348364	+	0.221585i
$309$		0			0
$310$	−43.3518			−2.46222
$311$	2.28996	+	3.96633i	0.129852	+	0.224910i	0.923619	−	0.383312i	$-0.125216\pi$
$311$	2.28996	+	3.96633i	0.129852	+	0.224910i	−0.793767	+	0.608222i	$0.791883\pi$
$312$		0			0
$313$	6.75197	−	11.6948i	0.381644	−	0.661026i	−0.609654	−	0.792668i	$-0.708691\pi$
$313$	6.75197	−	11.6948i	0.381644	−	0.661026i	0.991297	+	0.131642i	$0.0420248\pi$
$314$	−2.00032	−	3.46465i	−0.112884	−	0.195521i
$315$		0			0
$316$	1.14349	−	1.98059i	0.0643264	−	0.111417i
$317$	−2.86564	+	4.96343i	−0.160950	+	0.278774i	−0.935210	−	0.354094i	$-0.884789\pi$
$317$	−2.86564	+	4.96343i	−0.160950	+	0.278774i	0.774259	+	0.632868i	$0.218123\pi$
$318$		0			0
$319$	0.808834			0.0452860
$320$	18.7028	−	32.3941i	1.04552	−	1.81089i
$321$		0			0
$322$	0.151372	−	3.52429i	0.00843564	−	0.196401i
$323$	−0.402845	−	0.697749i	−0.0224149	−	0.0388238i
$324$		0			0
$325$	−20.4454	−	41.1785i	−1.13411	−	2.28417i
$326$	−6.40911	−	11.1009i	−0.354968	−	0.614822i
$327$		0			0
$328$	−2.39485	−	4.14801i	−0.132234	−	0.229035i
$329$	2.84166	+	1.80751i	0.156666	+	0.0996511i
$330$		0			0
$331$	12.2592	+	21.2335i	0.673824	+	1.16710i	0.976811	+	0.214103i	$0.0686828\pi$
$331$	12.2592	+	21.2335i	0.673824	+	1.16710i	−0.302987	+	0.952995i	$0.597984\pi$
$332$	−4.38715			−0.240776
$333$		0			0
$334$	6.84980	+	11.8642i	0.374804	+	0.649180i
$335$	−0.647524	−	1.12154i	−0.0353780	−	0.0612765i
$336$		0			0
$337$	23.7122			1.29168			0.645842	−	0.763471i	$-0.276506\pi$
$337$	23.7122			1.29168			0.645842	+	0.763471i	$0.276506\pi$
$338$	−15.8194	−	1.99583i	−0.860460	−	0.108559i
$339$		0			0
$340$	0.186157	−	0.322434i	0.0100958	−	0.0174864i
$341$	46.3534			2.51018
$342$		0			0
$343$	−2.37834	+	18.3669i	−0.128418	+	0.991720i
$344$	−5.10422	+	8.84078i	−0.275201	+	0.476663i
$345$		0			0
$346$	7.82928	+	13.5607i	0.420905	+	0.729028i
$347$	2.18748			0.117430			0.0587150	−	0.998275i	$-0.481300\pi$
$347$	2.18748			0.117430			0.0587150	+	0.998275i	$0.481300\pi$
$348$		0			0
$349$	−14.2613	−	24.7014i	−0.763392	−	1.32223i	−0.941092	−	0.338149i	$-0.890199\pi$
$349$	−14.2613	−	24.7014i	−0.763392	−	1.32223i	0.177700	−	0.984085i	$-0.443134\pi$
$350$	36.6894	−	19.1324i	1.96113	−	1.02267i
$351$		0			0
$352$	−7.55042	+	13.0777i	−0.402439	+	0.697045i
$353$	5.14324	−	8.90835i	0.273747	−	0.474143i	−0.696071	−	0.717973i	$-0.745070\pi$
$353$	5.14324	−	8.90835i	0.273747	−	0.474143i	0.969818	+	0.243829i	$0.0784036\pi$
$354$		0			0
$355$	−6.86499	−	11.8905i	−0.364356	−	0.631083i
$356$	6.54107			0.346676
$357$		0			0
$358$	7.69804	−	13.3334i	0.406854	−	0.704691i
$359$	−0.247010	+	0.427834i	−0.0130367	+	0.0225802i	−0.872470	−	0.488667i	$-0.837483\pi$
$359$	−0.247010	+	0.427834i	−0.0130367	+	0.0225802i	0.859433	+	0.511248i	$0.170816\pi$
$360$		0			0
$361$	−0.710719	+	1.23100i	−0.0374063	+	0.0647896i
$362$	−16.7814			−0.882009
$363$		0			0
$364$	−0.498719	+	4.70179i	−0.0261400	+	0.246441i
$365$	−29.7597			−1.55770
$366$		0			0
$367$	10.4744	−	18.1422i	0.546759	−	0.947014i	−0.451735	−	0.892152i	$-0.649195\pi$
$367$	10.4744	−	18.1422i	0.546759	−	0.947014i	0.998494	−	0.0548622i	$-0.0174719\pi$
$368$	3.00356			0.156571
$369$		0			0
$370$	−11.1579	+	19.3261i	−0.580074	+	1.00472i
$371$	18.4828	−	9.63817i	0.959577	−	0.500389i
$372$		0			0
$373$	−14.2085	−	24.6099i	−0.735689	−	1.27425i	−0.954420	−	0.298466i	$-0.903525\pi$
$373$	−14.2085	−	24.6099i	−0.735689	−	1.27425i	0.218731	−	0.975785i	$-0.429808\pi$
$374$	0.604133	−	1.04639i	0.0312390	−	0.0541075i
$375$		0			0
$376$	−1.94817	+	3.37432i	−0.100469	+	0.174017i
$377$	0.234717	+	0.472737i	0.0120885	+	0.0243472i
$378$		0			0
$379$	17.5547	+	30.4056i	0.901724	+	1.56183i	0.825255	+	0.564760i	$0.191031\pi$
$379$	17.5547	+	30.4056i	0.901724	+	1.56183i	0.0764691	+	0.997072i	$0.475635\pi$
$380$	−9.43687			−0.484101
$381$		0			0
$382$	−14.9719	−	25.9320i	−0.766028	−	1.32680i
$383$	−18.1226	−	31.3892i	−0.926020	−	1.60391i	−0.789913	−	0.613219i	$-0.789874\pi$
$383$	−18.1226	−	31.3892i	−0.926020	−	1.60391i	−0.136107	−	0.990694i	$-0.543459\pi$
$384$		0			0
$385$	−54.6126	+	28.4787i	−2.78331	+	1.45141i
$386$	−7.67151	+	13.2874i	−0.390470	+	0.676313i
$387$		0			0
$388$	−0.582380	+	1.00871i	−0.0295658	+	0.0512095i
$389$	−18.5269	−	32.0895i	−0.939349	−	1.62700i	−0.766688	−	0.642020i	$-0.778097\pi$
$389$	−18.5269	−	32.0895i	−0.939349	−	1.62700i	−0.172661	−	0.984981i	$-0.555237\pi$
$390$		0			0
$391$	0.193809			0.00980134
$392$	−21.3478	−	1.83721i	−1.07823	−	0.0927932i
$393$		0			0
$394$	−11.9690	−	20.7310i	−0.602991	−	1.04441i
$395$	9.72017	+	16.8358i	0.489075	+	0.847102i
$396$		0			0
$397$	15.4921	+	26.8331i	0.777527	+	1.34672i	0.933363	+	0.358933i	$0.116860\pi$
$397$	15.4921	+	26.8331i	0.777527	+	1.34672i	−0.155836	+	0.987783i	$0.549807\pi$
$398$	5.87221			0.294347
$399$		0			0
$400$	17.6159	+	30.5117i	0.880797	+	1.52558i
$401$	30.2120			1.50872			0.754359	−	0.656463i	$-0.227948\pi$
$401$	30.2120			1.50872			0.754359	+	0.656463i	$0.227948\pi$
$402$		0			0
$403$	13.4514	+	27.0921i	0.670061	+	1.34955i
$404$	−2.51286	+	4.35239i	−0.125019	+	0.216540i
$405$		0			0
$406$	−0.421201	+	0.219643i	−0.0209039	+	0.0109007i
$407$	11.9305	−	20.6642i	0.591373	−	1.02429i
$408$		0			0
$409$	−13.8598			−0.685321			−0.342661	−	0.939459i	$-0.611328\pi$
$409$	−13.8598			−0.685321			−0.342661	+	0.939459i	$0.611328\pi$
$410$	8.08609			0.399343
$411$		0			0
$412$	2.48591	−	4.30573i	0.122472	−	0.212128i
$413$	0.229472	−	5.34264i	0.0112916	−	0.262894i
$414$		0			0
$415$	18.6463	−	32.2964i	0.915311	−	1.58537i
$416$	−9.83457	−	0.617933i	−0.482179	−	0.0302967i
$417$		0			0
$418$	−30.6253			−1.49793
$419$	10.3550	+	17.9355i	0.505877	+	0.876204i	0.999977	+	0.00679920i	$0.00216427\pi$
$419$	10.3550	+	17.9355i	0.505877	+	0.876204i	−0.494100	+	0.869405i	$0.664502\pi$
$420$		0			0
$421$	−37.6001			−1.83252			−0.916259	−	0.400586i	$-0.868806\pi$
$421$	−37.6001			−1.83252			−0.916259	+	0.400586i	$0.868806\pi$
$422$	2.79812	+	4.84648i	0.136210	+	0.235923i
$423$		0			0
$424$	12.0581	+	20.8852i	0.585591	+	1.01427i
$425$	1.13669	+	1.96881i	0.0551378	+	0.0955014i
$426$		0			0
$427$	8.83383	−	4.60656i	0.427499	−	0.222927i
$428$	6.86575			0.331869
$429$		0			0
$430$	−8.61707	−	14.9252i	−0.415552	−	0.719757i
$431$	−12.4088	+	21.4927i	−0.597712	+	1.03527i	0.395446	+	0.918489i	$0.370590\pi$
$431$	−12.4088	+	21.4927i	−0.597712	+	1.03527i	−0.993158	+	0.116778i	$0.962743\pi$
$432$		0			0
$433$	12.3713	−	21.4277i	0.594526	−	1.02975i	−0.399087	−	0.916913i	$-0.630673\pi$
$433$	12.3713	−	21.4277i	0.594526	−	1.02975i	0.993614	−	0.112837i	$-0.0359937\pi$
$434$	−24.1386	+	12.5875i	−1.15869	+	0.604220i
$435$		0			0
$436$	−0.233563	−	0.404543i	−0.0111856	−	0.0193741i
$437$	−2.45619	−	4.25424i	−0.117495	−	0.203508i
$438$		0			0
$439$	−28.0121			−1.33694			−0.668472	−	0.743737i	$-0.733051\pi$
$439$	−28.0121			−1.33694			−0.668472	+	0.743737i	$0.733051\pi$
$440$	−35.6289	−	61.7112i	−1.69854	−	2.94196i
$441$		0			0
$442$	0.786894	+	0.0494427i	0.0374287	+	0.00235175i
$443$	14.5799	−	25.2531i	0.692711	−	1.19981i	−0.278235	−	0.960513i	$-0.589749\pi$
$443$	14.5799	−	25.2531i	0.692711	−	1.19981i	0.970946	−	0.239298i	$-0.0769173\pi$
$444$		0			0
$445$	−27.8009	+	48.1526i	−1.31789	+	2.28265i
$446$	4.61528	+	7.99390i	0.218540	+	0.378522i
$447$		0			0
$448$	1.00797	−	23.4678i	0.0476219	−	1.10875i
$449$	12.6725	−	21.9494i	0.598052	−	1.03586i	−0.395056	−	0.918657i	$-0.629275\pi$
$449$	12.6725	−	21.9494i	0.598052	−	1.03586i	0.993108	−	0.117200i	$-0.0373918\pi$
$450$		0			0
$451$	−8.64595			−0.407122
$452$	1.41900	−	2.45778i	0.0667440	−	0.115604i
$453$		0			0
$454$	−4.51493			−0.211896
$455$	−32.4930	−	23.6550i	−1.52329	−	1.10896i
$456$		0			0
$457$	12.7325			0.595599			0.297799	−	0.954628i	$-0.403747\pi$
$457$	12.7325			0.595599			0.297799	+	0.954628i	$0.403747\pi$
$458$	2.88334	−	4.99410i	0.134730	−	0.233359i
$459$		0			0
$460$	1.13502	−	1.96591i	0.0529206	−	0.0916611i
$461$	0.654119	−	1.13297i	0.0304653	−	0.0527675i	−0.850391	−	0.526152i	$-0.823634\pi$
$461$	0.654119	−	1.13297i	0.0304653	−	0.0527675i	0.880856	+	0.473384i	$0.156968\pi$
$462$		0			0
$463$	17.5365			0.814992			0.407496	−	0.913207i	$-0.366402\pi$
$463$	17.5365			0.814992			0.407496	+	0.913207i	$0.366402\pi$
$464$	−0.202234	−	0.350280i	−0.00938849	−	0.0162613i
$465$		0			0
$466$	1.47785	−	2.55971i	0.0684601	−	0.118576i
$467$	21.5106	−	37.2575i	0.995392	−	1.72407i	0.414657	−	0.909978i	$-0.363902\pi$
$467$	21.5106	−	37.2575i	0.995392	−	1.72407i	0.580735	−	0.814092i	$-0.302765\pi$
$468$		0			0
$469$	−0.686194	−	0.436471i	−0.0316855	−	0.0201543i
$470$	−3.28894	−	5.69661i	−0.151707	−	0.262765i
$471$		0			0
$472$	6.18679			0.284770
$473$	9.21370	+	15.9586i	0.423646	+	0.733777i
$474$		0			0
$475$	28.8112	−	49.9025i	1.32195	−	2.28968i
$476$	0.0100327	−	0.233586i	0.000459850	−	0.0107064i
$477$		0			0
$478$	9.76372			0.446582
$479$	4.72689	−	8.18722i	0.215977	−	0.374083i	−0.737597	−	0.675241i	$-0.764040\pi$
$479$	4.72689	−	8.18722i	0.215977	−	0.374083i	0.953574	+	0.301157i	$0.0973730\pi$
$480$		0			0
$481$	15.5397	+	0.976402i	0.708549	+	0.0445201i
$482$	−36.6429			−1.66904
$483$		0			0
$484$	4.83994	+	8.38303i	0.219997	+	0.381047i
$485$	−4.95048	−	8.57448i	−0.224790	−	0.389347i
$486$		0			0
$487$	7.86312			0.356312			0.178156	−	0.984002i	$-0.442987\pi$
$487$	7.86312			0.356312			0.178156	+	0.984002i	$0.442987\pi$
$488$	5.76314	+	9.98205i	0.260885	+	0.451866i
$489$		0			0
$490$	20.7060	−	29.6607i	0.935403	−	1.33993i
$491$	14.7190	+	25.4941i	0.664261	+	1.15053i	0.979485	+	0.201516i	$0.0645869\pi$
$491$	14.7190	+	25.4941i	0.664261	+	1.15053i	−0.315224	+	0.949017i	$0.602080\pi$
$492$		0			0
$493$	−0.0130495	−	0.0226023i	−0.000587718	−	0.00101796i
$494$	−8.88720	−	17.8995i	−0.399854	−	0.805336i
$495$		0			0
$496$	−11.5898	−	20.0742i	−0.520399	−	0.901357i
$497$	−7.27497	−	4.62742i	−0.326327	−	0.207568i
$498$		0			0
$499$	−4.14699	+	7.18281i	−0.185645	+	0.321547i	−0.943794	−	0.330535i	$-0.892771\pi$
$499$	−4.14699	+	7.18281i	−0.185645	+	0.321547i	0.758149	+	0.652082i	$0.226104\pi$
$500$	16.1864			0.723876
$501$		0			0
$502$	13.6220	−	23.5940i	0.607981	−	1.05305i
$503$	−1.86348	+	3.22764i	−0.0830885	+	0.143913i	−0.904575	−	0.426314i	$-0.859812\pi$
$503$	−1.86348	+	3.22764i	−0.0830885	+	0.143913i	0.821487	+	0.570228i	$0.193145\pi$
$504$		0			0
$505$	−21.3603	−	36.9972i	−0.950523	−	1.64635i
$506$	3.68346	−	6.37993i	0.163750	−	0.283623i
$507$		0			0
$508$	−3.25462	−	5.63717i	−0.144401	−	0.250109i
$509$	1.27399			0.0564685			0.0282342	−	0.999601i	$-0.491012\pi$
$509$	1.27399			0.0564685			0.0282342	+	0.999601i	$0.491012\pi$
$510$		0			0
$511$	−16.5704	+	8.64095i	−0.733033	+	0.382253i
$512$	24.4665			1.08128
$513$		0			0
$514$	−3.96601			−0.174933
$515$	21.1313	+	36.6005i	0.931157	+	1.61281i
$516$		0			0
$517$	3.51666	+	6.09103i	0.154662	+	0.267883i
$518$	−0.601345	+	14.0007i	−0.0264216	+	0.615156i
$519$		0			0
$520$	25.7289	−	38.7320i	1.12829	−	1.69851i
$521$	−3.53913	−	6.12995i	−0.155052	−	0.268558i	0.778026	−	0.628232i	$-0.216221\pi$
$521$	−3.53913	−	6.12995i	−0.155052	−	0.268558i	−0.933078	+	0.359674i	$0.882888\pi$
$522$		0			0
$523$	12.2461			0.535486			0.267743	−	0.963490i	$-0.413722\pi$
$523$	12.2461			0.535486			0.267743	+	0.963490i	$0.413722\pi$
$524$	2.95007	−	5.10967i	0.128874	−	0.223217i
$525$		0			0
$526$	−4.58870	+	7.94786i	−0.200077	+	0.346543i
$527$	−0.747851	−	1.29532i	−0.0325769	−	0.0564249i
$528$		0			0
$529$	−21.8183			−0.948623
$530$	−40.7134			−1.76848
$531$		0			0
$532$	−5.25452	+	2.74006i	−0.227812	+	0.118797i
$533$	−2.50898	−	5.05328i	−0.108676	−	0.218882i
$534$		0			0
$535$	−29.1809	+	50.5428i	−1.26160	+	2.18516i
$536$	0.470436	−	0.814820i	0.0203198	−	0.0351949i
$537$		0			0
$538$	−3.71854			−0.160317
$539$	−22.1397	+	31.7143i	−0.953623	+	1.36603i
$540$		0			0
$541$	12.5429	−	21.7249i	0.539261	−	0.934027i	−0.459683	−	0.888083i	$-0.652037\pi$
$541$	12.5429	−	21.7249i	0.539261	−	0.934027i	0.998944	−	0.0459441i	$-0.0146296\pi$
$542$	26.5125			1.13881
$543$		0			0
$544$	0.487264			0.0208913
$545$	3.97077			0.170089
$546$		0			0
$547$	−1.32955			−0.0568473			−0.0284236	−	0.999596i	$-0.509049\pi$
$547$	−1.32955			−0.0568473			−0.0284236	+	0.999596i	$0.509049\pi$
$548$	6.70534			0.286438
$549$		0			0
$550$	86.4143			3.68472
$551$	−0.330758	+	0.572890i	−0.0140908	+	0.0244059i
$552$		0			0
$553$	10.3007	+	6.55199i	0.438029	+	0.278619i
$554$	11.6603			0.495399
$555$		0			0
$556$	5.40997	−	9.37035i	0.229434	−	0.397391i
$557$	−3.96066	+	6.86007i	−0.167819	+	0.290670i	−0.937653	−	0.347574i	$-0.887006\pi$
$557$	−3.96066	+	6.86007i	−0.167819	+	0.290670i	0.769834	+	0.638244i	$0.220339\pi$
$558$		0			0
$559$	−6.65354	+	10.0162i	−0.281415	+	0.423638i
$560$	25.9881	+	16.5304i	1.09820	+	0.698535i
$561$		0			0
$562$	38.8489			1.63874
$563$	−5.75094			−0.242373			−0.121187	−	0.992630i	$-0.538670\pi$
$563$	−5.75094			−0.242373			−0.121187	+	0.992630i	$0.538670\pi$
$564$		0			0
$565$	12.0621	+	20.8921i	0.507456	+	0.878939i
$566$	−8.90111	+	15.4172i	−0.374141	+	0.648032i
$567$		0			0
$568$	4.98752	−	8.63864i	0.209272	−	0.362469i
$569$	6.44298			0.270104			0.135052	−	0.990839i	$-0.456880\pi$
$569$	6.44298			0.270104			0.135052	+	0.990839i	$0.456880\pi$
$570$		0			0
$571$	−16.3076	−	28.2456i	−0.682451	−	1.18204i	−0.974231	−	0.225555i	$-0.927581\pi$
$571$	−16.3076	−	28.2456i	−0.682451	−	1.18204i	0.291779	−	0.956486i	$-0.405753\pi$
$572$	−5.46368	+	8.22495i	−0.228448	+	0.343903i
$573$		0			0
$574$	4.50239	−	2.34785i	0.187926	−	0.0979975i
$575$	6.93053	+	12.0040i	0.289023	+	0.500603i
$576$		0			0
$577$	−10.1701	−	17.6152i	−0.423388	−	0.733330i	0.572880	−	0.819639i	$-0.305826\pi$
$577$	−10.1701	−	17.6152i	−0.423388	−	0.733330i	−0.996268	+	0.0863089i	$0.972493\pi$
$578$	20.8119			0.865660
$579$		0			0
$580$	−0.305691			−0.0126931
$581$	1.00492	−	23.3969i	0.0416912	−	0.970668i
$582$		0			0
$583$	43.5323			1.80292
$584$	−10.8105	−	18.7243i	−0.447340	−	0.774816i
$585$		0			0
$586$	−12.7221	+	22.0354i	−0.525547	+	0.910274i
$587$	14.8490	+	25.7192i	0.612883	+	1.06154i	0.990752	+	0.135685i	$0.0433235\pi$
$587$	14.8490	+	25.7192i	0.612883	+	1.06154i	−0.377869	+	0.925859i	$0.623343\pi$
$588$		0			0
$589$	−18.9554	+	32.8317i	−0.781044	+	1.35281i
$590$	−5.22234	+	9.04535i	−0.215000	+	0.372391i
$591$		0			0
$592$	−11.9320			−0.490403
$593$	−8.00200	+	13.8599i	−0.328603	+	0.569157i	−0.982235	−	0.187656i	$-0.939911\pi$
$593$	−8.00200	+	13.8599i	−0.328603	+	0.569157i	0.653632	+	0.756813i	$0.273244\pi$
$594$		0			0
$595$	1.67692	+	1.06665i	0.0687470	+	0.0437282i
$596$	−1.89934	−	3.28975i	−0.0777999	−	0.134753i
$597$		0			0
$598$	4.79777	+	0.301457i	0.196195	+	0.0123275i
$599$	8.13858	+	14.0964i	0.332533	+	0.575965i	0.983008	−	0.183563i	$-0.0587633\pi$
$599$	8.13858	+	14.0964i	0.332533	+	0.575965i	−0.650475	+	0.759528i	$0.725430\pi$
$600$		0			0
$601$	21.2956	+	36.8850i	0.868664	+	1.50457i	0.863362	+	0.504585i	$0.168354\pi$
$601$	21.2956	+	36.8850i	0.868664	+	1.50457i	0.00530223	+	0.999986i	$0.498312\pi$
$602$	−9.13168	−	5.80843i	−0.372180	−	0.236734i
$603$		0			0
$604$	0.928657	+	1.60848i	0.0377865	+	0.0654481i
$605$	−82.2832			−3.34529
$606$		0			0
$607$	9.31348	+	16.1314i	0.378022	+	0.654754i	0.990774	−	0.135521i	$-0.0432709\pi$
$607$	9.31348	+	16.1314i	0.378022	+	0.654754i	−0.612752	+	0.790275i	$0.709938\pi$
$608$	−6.17522	−	10.6958i	−0.250438	−	0.433772i
$609$		0			0
$610$	−19.4589			−0.787869
$611$	−2.53950	+	3.82293i	−0.102737	+	0.154659i
$612$		0			0
$613$	−10.1790	+	17.6305i	−0.411126	+	0.712091i	−0.995013	−	0.0997438i	$-0.968198\pi$
$613$	−10.1790	+	17.6305i	−0.411126	+	0.712091i	0.583887	+	0.811835i	$0.301531\pi$
$614$	−17.0825			−0.689395
$615$		0			0
$616$	−37.7567	−	24.0161i	−1.52126	−	0.967636i
$617$	−15.7193	+	27.2266i	−0.632835	+	1.09610i	0.354134	+	0.935195i	$0.384776\pi$
$617$	−15.7193	+	27.2266i	−0.632835	+	1.09610i	−0.986969	+	0.160908i	$0.948558\pi$
$618$		0			0
$619$	4.84802	+	8.39703i	0.194859	+	0.337505i	0.946854	−	0.321663i	$-0.104242\pi$
$619$	4.84802	+	8.39703i	0.194859	+	0.337505i	−0.751996	+	0.659168i	$0.770909\pi$
$620$	−17.5188			−0.703573
$621$		0			0
$622$	−2.80869	−	4.86479i	−0.112618	−	0.195060i
$623$	−1.49830	+	34.8839i	−0.0600281	+	1.39759i
$624$		0			0
$625$	−36.9177	+	63.9434i	−1.47671	+	2.55773i
$626$	−8.28143	+	14.3439i	−0.330993	+	0.573296i
$627$		0			0
$628$	−0.808343	−	1.40009i	−0.0322564	−	0.0558697i
$629$	−0.769931			−0.0306992
$630$		0			0
$631$	−9.65738	+	16.7271i	−0.384454	+	0.665895i	−0.991693	−	0.128625i	$-0.958944\pi$
$631$	−9.65738	+	16.7271i	−0.384454	+	0.665895i	0.607239	+	0.794519i	$0.292277\pi$
$632$	−7.06186	+	12.2315i	−0.280906	+	0.486543i
$633$		0			0
$634$	3.51477	−	6.08776i	0.139589	−	0.241776i
$635$	55.3314			2.19576
$636$		0			0
$637$	−24.9607	−	3.73670i	−0.988979	−	0.148053i
$638$	−0.992052			−0.0392757
$639$		0			0
$640$	−11.4246	+	19.7881i	−0.451599	+	0.782192i
$641$	−18.4537			−0.728878			−0.364439	−	0.931227i	$-0.618739\pi$
$641$	−18.4537			−0.728878			−0.364439	+	0.931227i	$0.618739\pi$
$642$		0			0
$643$	10.8340	−	18.7650i	0.427250	−	0.740019i	−0.569378	−	0.822076i	$-0.692816\pi$
$643$	10.8340	−	18.7650i	0.427250	−	0.740019i	0.996628	+	0.0820574i	$0.0261491\pi$
$644$	0.0611706	−	1.42419i	0.00241046	−	0.0561211i
$645$		0			0
$646$	0.494098	+	0.855804i	0.0194400	+	0.0336711i
$647$	−10.8685	+	18.8249i	−0.427287	+	0.740082i	−0.996631	−	0.0820171i	$-0.973864\pi$
$647$	−10.8685	+	18.8249i	−0.427287	+	0.740082i	0.569344	+	0.822099i	$0.307197\pi$
$648$		0			0
$649$	5.58392	−	9.67163i	0.219188	−	0.379645i
$650$	25.0767	+	50.5063i	0.983588	+	1.98102i
$651$		0			0
$652$	−2.58997	−	4.48596i	−0.101431	−	0.175684i
$653$	22.5832			0.883750			0.441875	−	0.897077i	$-0.354314\pi$
$653$	22.5832			0.883750			0.441875	+	0.897077i	$0.354314\pi$
$654$		0			0
$655$	25.0768	+	43.4344i	0.979834	+	1.69712i
$656$	2.16176	+	3.74428i	0.0844027	+	0.146190i
$657$		0			0
$658$	−3.48535	−	2.21694i	−0.135873	−	0.0864255i
$659$	−1.42864	+	2.47447i	−0.0556517	+	0.0963916i	−0.892509	−	0.451029i	$-0.851057\pi$
$659$	−1.42864	+	2.47447i	−0.0556517	+	0.0963916i	0.836857	+	0.547421i	$0.184390\pi$
$660$		0			0
$661$	−4.81655	+	8.34251i	−0.187342	+	0.324486i	−0.944363	−	0.328904i	$-0.893321\pi$
$661$	−4.81655	+	8.34251i	−0.187342	+	0.324486i	0.757021	+	0.653390i	$0.226654\pi$
$662$	−15.0361	−	26.0433i	−0.584395	−	1.01220i
$663$		0			0
$664$	27.0937			1.05144
$665$	2.16162	−	50.3274i	0.0838239	−	1.95161i
$666$		0			0
$667$	−0.0795638	−	0.137809i	−0.00308072	−	0.00533597i
$668$	2.76806	+	4.79441i	0.107099	+	0.185501i
$669$		0			0
$670$	0.794201	+	1.37560i	0.0306827	+	0.0531440i
$671$	20.8062			0.803216
$672$		0			0
$673$	15.4999	+	26.8466i	0.597476	+	1.03486i	0.993192	+	0.116486i	$0.0371631\pi$
$673$	15.4999	+	26.8466i	0.597476	+	1.03486i	−0.395716	+	0.918373i	$0.629504\pi$
$674$	−29.0835			−1.12025
$675$		0			0
$676$	−6.39273	−	0.806530i	−0.245874	−	0.0310204i
$677$	5.44610	−	9.43293i	0.209311	−	0.362537i	−0.742187	−	0.670193i	$-0.766211\pi$
$677$	5.44610	−	9.43293i	0.209311	−	0.362537i	0.951498	+	0.307656i	$0.0995446\pi$
$678$		0			0
$679$	−5.24612	−	3.33692i	−0.201328	−	0.128059i
$680$	−1.14965	+	1.99125i	−0.0440871	+	0.0763611i
$681$		0			0
$682$	−56.8535			−2.17703
$683$	26.5283			1.01508			0.507538	−	0.861629i	$-0.330556\pi$
$683$	26.5283			1.01508			0.507538	+	0.861629i	$0.330556\pi$
$684$		0			0
$685$	−28.4991	+	49.3619i	−1.08890	+	1.88602i
$686$	2.91709	−	22.5274i	0.111375	−	0.860100i
$687$		0			0
$688$	4.60743	−	7.98031i	0.175657	−	0.304246i
$689$	12.6327	+	25.4432i	0.481267	+	0.969308i
$690$		0			0
$691$	−4.75519			−0.180896			−0.0904480	−	0.995901i	$-0.528830\pi$
$691$	−4.75519			−0.180896			−0.0904480	+	0.995901i	$0.528830\pi$
$692$	3.16387	+	5.47999i	0.120272	+	0.208318i
$693$		0			0
$694$	−2.68299			−0.101845
$695$	45.9871	+	79.6519i	1.74439	+	3.02137i
$696$		0			0
$697$	0.139491	+	0.241605i	0.00528360	+	0.00915146i
$698$	17.4918	+	30.2967i	0.662076	+	1.14675i
$699$		0			0
$700$	14.8265	−	7.73153i	0.560388	−	0.292225i
$701$	−19.5899			−0.739898			−0.369949	−	0.929052i	$-0.620625\pi$
$701$	−19.5899			−0.739898			−0.369949	+	0.929052i	$0.620625\pi$
$702$		0			0
$703$	9.75753	+	16.9005i	0.368012	+	0.637416i
$704$	24.5276	−	42.4831i	0.924419	−	1.60114i
$705$		0			0
$706$	−6.30829	+	10.9263i	−0.237416	+	0.411216i
$707$	−22.6360	−	14.3982i	−0.851314	−	0.541499i
$708$		0			0
$709$	8.09898	+	14.0278i	0.304164	+	0.526827i	0.977075	−	0.212896i	$-0.0682897\pi$
$709$	8.09898	+	14.0278i	0.304164	+	0.526827i	−0.672911	+	0.739723i	$0.734956\pi$
$710$	8.42005	+	14.5840i	0.315999	+	0.547326i
$711$		0			0
$712$	−40.3956			−1.51389
$713$	−4.55972	−	7.89767i	−0.170763	−	0.295770i
$714$		0			0
$715$	−37.3269	−	75.1791i	−1.39595	−	2.81154i
$716$	3.11084	−	5.38813i	0.116257	−	0.201364i
$717$		0			0
$718$	0.302963	−	0.524747i	0.0113065	−	0.0195834i
$719$	−13.8464	−	23.9827i	−0.516384	−	0.894403i	−0.999819	−	0.0190228i	$-0.993944\pi$
$719$	−13.8464	−	23.9827i	−0.516384	−	0.894403i	0.483435	−	0.875380i	$-0.339389\pi$
$720$		0			0
$721$	22.3933	+	14.2438i	0.833969	+	0.530467i
$722$	0.871712	−	1.50985i	0.0324418	−	0.0561908i
$723$		0			0
$724$	−6.78148			−0.252032
$725$	0.933288	−	1.61650i	0.0346614	−	0.0600354i
$726$		0			0
$727$	29.2681			1.08549			0.542746	−	0.839897i	$-0.317384\pi$
$727$	29.2681			1.08549			0.542746	+	0.839897i	$0.317384\pi$
$728$	3.07994	−	29.0368i	0.114150	−	1.07618i
$729$		0			0
$730$	36.5009			1.35096
$731$	0.297301	−	0.514941i	0.0109961	−	0.0190458i
$732$		0			0
$733$	11.0284	−	19.1017i	0.407343	−	0.705538i	−0.587248	−	0.809407i	$-0.699789\pi$
$733$	11.0284	−	19.1017i	0.407343	−	0.705538i	0.994591	+	0.103869i	$0.0331222\pi$
$734$	−12.8471	+	22.2518i	−0.474194	+	0.821328i
$735$		0			0
$736$	2.97090			0.109509
$737$	−0.849190	−	1.47084i	−0.0312803	−	0.0541791i
$738$		0			0
$739$	4.86234	−	8.42182i	0.178864	−	0.309802i	−0.762628	−	0.646838i	$-0.776091\pi$
$739$	4.86234	−	8.42182i	0.178864	−	0.309802i	0.941492	+	0.337036i	$0.109424\pi$
$740$	−4.50901	+	7.80984i	−0.165755	+	0.287095i
$741$		0			0
$742$	−22.6695	+	11.8214i	−0.832223	+	0.433978i
$743$	−18.6574	−	32.3156i	−0.684475	−	1.18554i	−0.973602	−	0.228254i	$-0.926698\pi$
$743$	−18.6574	−	32.3156i	−0.684475	−	1.18554i	0.289127	−	0.957291i	$-0.406635\pi$
$744$		0			0
$745$	32.2904			1.18303
$746$	17.4270	+	30.1845i	0.638049	+	1.10513i
$747$		0			0
$748$	0.244135	−	0.422854i	0.00892645	−	0.0154611i
$749$	−1.57267	+	36.6155i	−0.0574642	+	1.33790i
$750$		0			0
$751$	1.82332			0.0665340			0.0332670	−	0.999447i	$-0.489409\pi$
$751$	1.82332			0.0665340			0.0332670	+	0.999447i	$0.489409\pi$
$752$	1.75855	−	3.04590i	0.0641278	−	0.111073i
$753$		0			0
$754$	−0.287885	−	0.579822i	−0.0104842	−	0.0211159i
$755$	−15.7880			−0.574583
$756$		0			0
$757$	−4.43646	−	7.68417i	−0.161246	−	0.279286i	0.774070	−	0.633100i	$-0.218218\pi$
$757$	−4.43646	−	7.68417i	−0.161246	−	0.279286i	−0.935316	+	0.353814i	$0.884885\pi$
$758$	−21.5312	−	37.2931i	−0.782048	−	1.35455i
$759$		0			0
$760$	58.2793			2.11401
$761$	12.0487	+	20.8689i	0.436764	+	0.756497i	0.997438	−	0.0715397i	$-0.0227913\pi$
$761$	12.0487	+	20.8689i	0.436764	+	0.756497i	−0.560674	+	0.828037i	$0.689458\pi$
$762$		0			0
$763$	2.21095	−	1.15294i	0.0800419	−	0.0417393i
$764$	−6.05025	−	10.4793i	−0.218890	−	0.379129i
$765$		0			0
$766$	22.2277	+	38.4995i	0.803119	+	1.39104i
$767$	7.27316	+	0.456993i	0.262619	+	0.0165011i
$768$		0			0
$769$	−20.3128	−	35.1829i	−0.732499	−	1.26873i	−0.955812	−	0.293979i	$-0.905020\pi$
$769$	−20.3128	−	35.1829i	−0.732499	−	1.26873i	0.223312	−	0.974747i	$-0.428313\pi$
$770$	66.9835	−	34.9297i	2.41392	−	1.25878i
$771$		0			0
$772$	−3.10012	+	5.36956i	−0.111576	+	0.193255i
$773$	0.0294562			0.00105947			0.000529733	−	1.00000i	$-0.499831\pi$
$773$	0.0294562			0.00105947			0.000529733		1.00000i	$0.499831\pi$
$774$		0			0
$775$	53.4858	−	92.6400i	1.92126	−	3.32773i
$776$	3.59660	−	6.22949i	0.129110	−	0.223626i
$777$		0			0
$778$	22.7236	+	39.3584i	0.814680	+	1.41107i
$779$	3.53561	−	6.12385i	0.126676	−	0.219410i
$780$		0			0
$781$	−9.00304	−	15.5937i	−0.322154	−	0.557987i
$782$	−0.237711			−0.00850051
$783$		0			0
$784$	19.2701	+	1.65840i	0.688216	+	0.0592285i
$785$	13.7425			0.490492
$786$		0			0
$787$	−45.1774			−1.61040			−0.805199	−	0.593004i	$-0.797942\pi$
$787$	−45.1774			−1.61040			−0.805199	+	0.593004i	$0.797942\pi$
$788$	−4.83678	−	8.37755i	−0.172303	−	0.298438i
$789$		0			0
$790$	−11.9220	−	20.6495i	−0.424165	−	0.734676i
$791$	12.7824	+	8.13058i	0.454491	+	0.289090i
$792$		0			0
$793$	6.03779	+	12.1606i	0.214408	+	0.431834i
$794$	−19.0014	−	32.9114i	−0.674335	−	1.16798i
$795$		0			0
$796$	2.37301			0.0841090
$797$	6.89239	−	11.9380i	0.244141	−	0.422864i	−0.717749	−	0.696302i	$-0.754827\pi$
$797$	6.89239	−	11.9380i	0.244141	−	0.422864i	0.961890	+	0.273438i	$0.0881607\pi$
$798$		0			0
$799$	0.113473	−	0.196541i	0.00401439	−	0.00695313i
$800$	17.4244	+	30.1799i	0.616045	+	1.06702i
$801$		0			0
$802$	−37.0557			−1.30848
$803$	−39.0282			−1.37727
$804$		0			0
$805$	10.2243	+	6.50344i	0.360361	+	0.229216i
$806$	−16.4984	−	33.2290i	−0.581131	−	1.17044i
$807$		0			0
$808$	15.5186	−	26.8791i	0.545944	−	0.945602i
$809$	−9.19880	+	15.9328i	−0.323413	+	0.560167i	−0.981190	−	0.193045i	$-0.938164\pi$
$809$	−9.19880	+	15.9328i	−0.323413	+	0.560167i	0.657777	+	0.753213i	$0.271497\pi$
$810$		0			0
$811$	−28.7233			−1.00861			−0.504306	−	0.863525i	$-0.668252\pi$
$811$	−28.7233			−1.00861			−0.504306	+	0.863525i	$0.668252\pi$
$812$	−0.170211	+	0.0887594i	−0.00597322	+	0.00311485i
$813$		0			0
$814$	−14.6330	+	25.3451i	−0.512887	+	0.888346i
$815$	44.0317			1.54236
$816$		0			0
$817$	−15.0711			−0.527271
$818$	16.9993			0.594366
$819$		0			0
$820$	3.26765			0.114111
$821$	−12.1643			−0.424537			−0.212268	−	0.977211i	$-0.568085\pi$
$821$	−12.1643			−0.424537			−0.212268	+	0.977211i	$0.568085\pi$
$822$		0			0
$823$	13.2985			0.463555			0.231777	−	0.972769i	$-0.425546\pi$
$823$	13.2985			0.463555			0.231777	+	0.972769i	$0.425546\pi$
$824$	−15.3522	+	26.5909i	−0.534821	+	0.926336i
$825$		0			0
$826$	−0.281452	+	6.55286i	−0.00979297	+	0.228003i
$827$	−39.3333			−1.36775			−0.683876	−	0.729598i	$-0.739707\pi$
$827$	−39.3333			−1.36775			−0.683876	+	0.729598i	$0.739707\pi$
$828$		0			0
$829$	−2.68959	+	4.65851i	−0.0934134	+	0.161797i	−0.908945	−	0.416915i	$-0.863111\pi$
$829$	−2.68959	+	4.65851i	−0.0934134	+	0.161797i	0.815532	+	0.578712i	$0.196444\pi$
$830$	−22.8701	+	39.6122i	−0.793832	+	1.37496i
$831$		0			0
$832$	31.9477	+	2.00736i	1.10759	+	0.0695927i
$833$	1.24343	+	0.107011i	0.0430823	+	0.00370770i
$834$		0			0
$835$	−47.0593			−1.62856
$836$	−12.3759			−0.428030
$837$		0			0
$838$	−12.7007	−	21.9982i	−0.438737	−	0.759915i
$839$	14.7620	−	25.5686i	0.509642	−	0.882726i	−0.490295	−	0.871556i	$-0.663111\pi$
$839$	14.7620	−	25.5686i	0.509642	−	0.882726i	0.999938	−	0.0111700i	$-0.00355560\pi$
$840$		0			0
$841$	14.4893	−	25.0962i	0.499631	−	0.865385i
$842$	46.1173			1.58931
$843$		0			0
$844$	1.13074	+	1.95850i	0.0389217	+	0.0674144i
$845$	33.1078	−	43.6327i	1.13894	−	1.50101i
$846$		0			0
$847$	−45.8159	+	23.8915i	−1.57425	+	0.820922i
$848$	−10.8845	−	18.8524i	−0.373774	−	0.647395i
$849$		0			0
$850$	−1.39418	−	2.41479i	−0.0478200	−	0.0828266i
$851$	−4.69434			−0.160920
$852$		0			0
$853$	−12.4764			−0.427184			−0.213592	−	0.976923i	$-0.568516\pi$
$853$	−12.4764			−0.427184			−0.213592	+	0.976923i	$0.568516\pi$
$854$	−10.8349	+	5.65004i	−0.370762	+	0.193340i
$855$		0			0
$856$	−42.4008			−1.44923
$857$	22.7205	+	39.3531i	0.776118	+	1.34428i	0.934164	+	0.356844i	$0.116147\pi$
$857$	22.7205	+	39.3531i	0.776118	+	1.34428i	−0.158046	+	0.987432i	$0.550519\pi$
$858$		0			0
$859$	26.2027	−	45.3845i	0.894026	−	1.54850i	0.0590202	−	0.998257i	$-0.481202\pi$
$859$	26.2027	−	45.3845i	0.894026	−	1.54850i	0.835006	−	0.550241i	$-0.185464\pi$
$860$	−3.48222	−	6.03139i	−0.118743	−	0.205669i
$861$		0			0
$862$	15.2197	−	26.3613i	0.518384	−	0.897868i
$863$	12.9896	−	22.4986i	0.442170	−	0.765862i	−0.555680	−	0.831396i	$-0.687542\pi$
$863$	12.9896	−	22.4986i	0.442170	−	0.765862i	0.997850	+	0.0655347i	$0.0208753\pi$
$864$		0			0
$865$	−53.7885			−1.82886
$866$	−15.1736	+	26.2815i	−0.515621	+	0.893083i
$867$		0			0
$868$	−9.75460	+	5.08671i	−0.331093	+	0.172654i
$869$	12.7474	+	22.0792i	0.432427	+	0.748986i
$870$		0			0
$871$	0.613230	−	0.923149i	0.0207785	−	0.0312797i
$872$	1.44241	+	2.49833i	0.0488463	+	0.0846043i
$873$		0			0
$874$	3.01256	+	5.21792i	0.101902	+	0.176499i
$875$	−3.70766	+	86.3229i	−0.125342	+	2.91825i
$876$		0			0
$877$	3.49065	+	6.04599i	0.117871	+	0.204158i	0.918924	−	0.394435i	$-0.129060\pi$
$877$	3.49065	+	6.04599i	0.117871	+	0.204158i	−0.801053	+	0.598594i	$0.795726\pi$
$878$	34.3574			1.15951
$879$		0			0
$880$	32.1612	+	55.7048i	1.08415	+	1.87781i
$881$	10.2063	+	17.6779i	0.343859	+	0.595582i	0.985146	−	0.171720i	$-0.0549323\pi$
$881$	10.2063	+	17.6779i	0.343859	+	0.595582i	−0.641286	+	0.767302i	$0.721599\pi$
$882$		0			0
$883$	2.69268			0.0906160			0.0453080	−	0.998973i	$-0.485573\pi$
$883$	2.69268			0.0906160			0.0453080	+	0.998973i	$0.485573\pi$
$884$	0.317990	+	0.0199802i	0.0106952	+	0.000672007i
$885$		0			0
$886$	−17.8825	+	30.9735i	−0.600775	+	1.04057i
$887$	25.5964			0.859444			0.429722	−	0.902961i	$-0.358612\pi$
$887$	25.5964			0.859444			0.429722	+	0.902961i	$0.358612\pi$
$888$		0			0
$889$	30.8089	−	16.0659i	1.03330	−	0.538832i
$890$	34.0984	−	59.0602i	1.14298	−	1.97970i
$891$		0			0
$892$	1.86507	+	3.23039i	0.0624471	+	0.108162i
$893$	−5.75229			−0.192493
$894$		0			0
$895$	26.4434	+	45.8014i	0.883906	+	1.53097i
$896$	−0.615719	+	14.3354i	−0.0205697	+	0.478911i
$897$		0			0
$898$	−15.5431	+	26.9214i	−0.518679	+	0.898379i
$899$	−0.614026	+	1.06352i	−0.0204789	+	0.0354705i
$900$		0			0
$901$	−0.702335	−	1.21648i	−0.0233982	−	0.0405268i
$902$	10.6044			0.353089
$903$		0			0
$904$	−8.76330	+	15.1785i	−0.291463	+	0.504829i
$905$	28.8227	−	49.9224i	0.958100	−	1.65948i
$906$		0			0
$907$	28.4910	−	49.3478i	0.946027	−	1.63857i	0.192345	−	0.981327i	$-0.438391\pi$
$907$	28.4910	−	49.3478i	0.946027	−	1.63857i	0.753682	−	0.657239i	$-0.228276\pi$
$908$	−1.82452			−0.0605488
$909$		0			0
$910$	39.8533	+	29.0133i	1.32112	+	0.961783i
$911$	−43.0338			−1.42577			−0.712887	−	0.701279i	$-0.752613\pi$
$911$	−43.0338			−1.42577			−0.712887	+	0.701279i	$0.752613\pi$
$912$		0			0
$913$	24.4536	−	42.3548i	0.809295	−	1.40174i
$914$	−15.6166			−0.516552
$915$		0			0
$916$	1.16518	−	2.01815i	0.0384987	−	0.0666817i
$917$	26.5744	+	16.9033i	0.877565	+	0.558197i
$918$		0			0
$919$	3.05206	+	5.28632i	0.100678	+	0.174380i	0.911964	−	0.410270i	$-0.134565\pi$
$919$	3.05206	+	5.28632i	0.100678	+	0.174380i	−0.811286	+	0.584649i	$0.801232\pi$
$920$	−7.00954	+	12.1409i	−0.231098	+	0.400273i
$921$		0			0
$922$	−0.802290	+	1.38961i	−0.0264220	+	0.0457643i
$923$	6.50141	−	9.78715i	0.213997	−	0.322148i
$924$		0			0
$925$	−27.5324	−	47.6876i	−0.905261	−	1.56796i
$926$	−21.5089			−0.706827
$927$		0			0
$928$	−0.200035	−	0.346471i	−0.00656648	−	0.0113735i
$929$	0.948999	+	1.64371i	0.0311357	+	0.0539285i	0.881173	−	0.472793i	$-0.156754\pi$
$929$	0.948999	+	1.64371i	0.0311357	+	0.0539285i	−0.850038	+	0.526722i	$0.823421\pi$
$930$		0			0
$931$	−13.4093	−	28.6503i	−0.439473	−	0.938976i
$932$	0.597211	−	1.03440i	0.0195623	−	0.0338829i
$933$		0			0
$934$	−26.3832	+	45.6971i	−0.863285	+	1.49525i
$935$	2.07525	+	3.59444i	0.0678679	+	0.117551i
$936$		0			0
$937$	6.34000			0.207119			0.103559	−	0.994623i	$-0.466977\pi$
$937$	6.34000			0.207119			0.103559	+	0.994623i	$0.466977\pi$
$938$	0.841631	+	0.535340i	0.0274802	+	0.0174795i
$939$		0			0
$940$	−1.32908	−	2.30204i	−0.0433500	−	0.0750843i
$941$	−8.66104	−	15.0014i	−0.282342	−	0.489030i	0.689619	−	0.724172i	$-0.257778\pi$
$941$	−8.66104	−	15.0014i	−0.282342	−	0.489030i	−0.971961	+	0.235142i	$0.924445\pi$
$942$		0			0
$943$	0.850490	+	1.47309i	0.0276958	+	0.0479705i
$944$	−5.58463			−0.181764
$945$		0			0
$946$	−11.3008	−	19.5735i	−0.367420	−	0.636391i
$947$	−22.0647			−0.717007			−0.358503	−	0.933528i	$-0.616713\pi$
$947$	−22.0647			−0.717007			−0.358503	+	0.933528i	$0.616713\pi$
$948$		0			0
$949$	−11.3256	−	22.8107i	−0.367646	−	0.740466i
$950$	−35.3375	+	61.2064i	−1.14650	+	1.98580i
$951$		0			0
$952$	−0.0619592	+	1.44255i	−0.00200811	+	0.0467535i
$953$	−9.89509	+	17.1388i	−0.320533	+	0.555180i	−0.980598	−	0.196028i	$-0.937196\pi$
$953$	−9.89509	+	17.1388i	−0.320533	+	0.555180i	0.660065	+	0.751209i	$0.270529\pi$
$954$		0			0
$955$	102.859			3.32845
$956$	3.94559			0.127610
$957$		0			0
$958$	−5.79763	+	10.0418i	−0.187313	+	0.324436i
$959$	−1.53593	+	35.7600i	−0.0495977	+	1.15475i
$960$		0			0
$961$	−19.6892	+	34.1027i	−0.635136	+	1.10009i
$962$	−19.0598	−	1.19758i	−0.614511	−	0.0386115i
$963$		0			0
$964$	−14.8077			−0.476924
$965$	−26.3523	−	45.6436i	−0.848311	−	1.46932i
$966$		0			0
$967$	−40.1430			−1.29091			−0.645457	−	0.763797i	$-0.723333\pi$
$967$	−40.1430			−1.29091			−0.645457	+	0.763797i	$0.723333\pi$
$968$	−29.8900	−	51.7710i	−0.960702	−	1.66398i
$969$		0			0
$970$	6.07186	+	10.5168i	0.194956	+	0.337673i
$971$	−15.4318	−	26.7286i	−0.495229	−	0.857762i	0.504756	−	0.863262i	$-0.331583\pi$
$971$	−15.4318	−	26.7286i	−0.495229	−	0.857762i	−0.999985	+	0.00550014i	$0.998249\pi$
$972$		0			0
$973$	48.7334	+	30.9981i	1.56232	+	0.993753i
$974$	−9.64428			−0.309023
$975$		0			0
$976$	−5.20222	−	9.01051i	−0.166519	−	0.288419i
$977$	10.6615	−	18.4662i	0.341090	−	0.590786i	−0.643545	−	0.765408i	$-0.722537\pi$
$977$	10.6615	−	18.4662i	0.341090	−	0.590786i	0.984635	+	0.174622i	$0.0558705\pi$
$978$		0			0
$979$	−36.4593	+	63.1494i	−1.16524	+	2.01826i
$980$	8.36747	−	11.9861i	0.267289	−	0.382882i
$981$		0			0
$982$	−18.0532	−	31.2691i	−0.576101	−	0.997836i
$983$	−18.7115	−	32.4092i	−0.596803	−	1.03369i	−0.993290	−	0.115652i	$-0.963104\pi$
$983$	−18.7115	−	32.4092i	−0.596803	−	1.03369i	0.396487	−	0.918040i	$-0.370229\pi$
$984$		0			0
$985$	82.2294			2.62005
$986$	0.0160054	+	0.0277222i	0.000509717	+	0.000882855i
$987$		0			0
$988$	−3.59139	−	7.23332i	−0.114257	−	0.230123i
$989$	1.81268	−	3.13965i	0.0576397	−	0.0998349i
$990$		0			0
$991$	−1.65951	+	2.87436i	−0.0527161	+	0.0913070i	−0.891179	−	0.453651i	$-0.850121\pi$
$991$	−1.65951	+	2.87436i	−0.0527161	+	0.0913070i	0.838463	+	0.544958i	$0.183455\pi$
$992$	−11.4638	−	19.8559i	−0.363976	−	0.630426i
$993$		0			0
$994$	8.92290	+	5.67563i	0.283017	+	0.180020i
$995$	−10.0858	+	17.4691i	−0.319741	+	0.553807i
$996$		0			0
$997$	24.1254			0.764058			0.382029	−	0.924150i	$-0.375226\pi$
$997$	24.1254			0.764058			0.382029	+	0.924150i	$0.375226\pi$
$998$	5.08638	−	8.80986i	0.161006	−	0.278871i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.s.f.289.4		20
3.2	odd	2		273.2.l.c.16.7	yes	20
7.4	even	3		819.2.n.f.172.7		20
13.9	even	3		819.2.n.f.100.7		20
21.11	odd	6		273.2.j.c.172.4	yes	20
39.35	odd	6		273.2.j.c.100.4	✓	20
91.74	even	3	inner	819.2.s.f.802.4		20
273.74	odd	6		273.2.l.c.256.7	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.c.100.4	✓	20	39.35	odd	6
273.2.j.c.172.4	yes	20	21.11	odd	6
273.2.l.c.16.7	yes	20	3.2	odd	2
273.2.l.c.256.7	yes	20	273.74	odd	6
819.2.n.f.100.7		20	13.9	even	3
819.2.n.f.172.7		20	7.4	even	3
819.2.s.f.289.4		20	1.1	even	1	trivial
819.2.s.f.802.4		20	91.74	even	3	inner

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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q-1.22652 q^{2} -0.495647 q^{4} +(2.10660 - 3.64874i) q^{5} +(0.113533 - 2.64331i) q^{7} +3.06096 q^{8} +(-2.58379 + 4.47526i) q^{10} +(2.76269 - 4.78512i) q^{11} +(3.59845 + 0.226101i) q^{13} +(-0.139251 + 3.24208i) q^{14} -2.76304 q^{16} -0.178289 q^{17} +(2.25950 + 3.91358i) q^{19} +(-1.04413 + 1.80849i) q^{20} +(-3.38850 + 5.86905i) q^{22} -1.08705 q^{23} +(-6.37556 - 11.0428i) q^{25} +(-4.41358 - 0.277317i) q^{26} +(-0.0562723 + 1.31015i) q^{28} +(0.0731926 + 0.126773i) q^{29} +(4.19459 + 7.26525i) q^{31} -2.73300 q^{32} +0.218676 q^{34} +(-9.40561 - 5.98267i) q^{35} +4.31844 q^{37} +(-2.77133 - 4.80008i) q^{38} +(6.44824 - 11.1687i) q^{40} +(-0.782385 - 1.35513i) q^{41} +(-1.66752 + 2.88823i) q^{43} +(-1.36932 + 2.37173i) q^{44} +1.33329 q^{46} +(-0.636455 + 1.10237i) q^{47} +(-6.97422 - 0.600207i) q^{49} +(7.81976 + 13.5442i) q^{50} +(-1.78356 - 0.112066i) q^{52} +(3.93930 + 6.82307i) q^{53} +(-11.6398 - 20.1607i) q^{55} +(0.347521 - 8.09109i) q^{56} +(-0.0897723 - 0.155490i) q^{58} +2.02119 q^{59} +(1.88279 + 3.26108i) q^{61} +(-5.14476 - 8.91098i) q^{62} +8.87816 q^{64} +(8.40550 - 12.6535i) q^{65} +(0.153689 - 0.266197i) q^{67} +0.0883685 q^{68} +(11.5362 + 7.33787i) q^{70} +(1.62940 - 2.82220i) q^{71} +(-3.53172 - 6.11712i) q^{73} -5.29665 q^{74} +(-1.11992 - 1.93975i) q^{76} +(-12.3349 - 7.84593i) q^{77} +(-2.30707 + 3.99596i) q^{79} +(-5.82063 + 10.0816i) q^{80} +(0.959612 + 1.66210i) q^{82} +8.85136 q^{83} +(-0.375585 + 0.650532i) q^{85} +(2.04525 - 3.54248i) q^{86} +(8.45649 - 14.6471i) q^{88} -13.1970 q^{89} +(1.00620 - 9.48618i) q^{91} +0.538791 q^{92} +(0.780625 - 1.35208i) q^{94} +19.0395 q^{95} +(1.17499 - 2.03514i) q^{97} +(8.55403 + 0.736167i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 32 q^{4} + 3 q^{7} + 12 q^{8} - 4 q^{10} + 8 q^{11} - 5 q^{13} + 9 q^{14} + 40 q^{16} + 7 q^{19} - 12 q^{20} - 9 q^{22} - 28 q^{23} - 32 q^{25} - 13 q^{26} - 23 q^{28} + 9 q^{29} - 9 q^{31} + 34 q^{32}+ \cdots + 76 q^{98}+O(q^{100}) \) 20 * q + 32 * q^4 + 3 * q^7 + 12 * q^8 - 4 * q^10 + 8 * q^11 - 5 * q^13 + 9 * q^14 + 40 * q^16 + 7 * q^19 - 12 * q^20 - 9 * q^22 - 28 * q^23 - 32 * q^25 - 13 * q^26 - 23 * q^28 + 9 * q^29 - 9 * q^31 + 34 * q^32 + 12 * q^34 - 10 * q^35 - 36 * q^37 - 22 * q^38 - 9 * q^40 + q^41 - 11 * q^43 - 8 * q^44 + 20 * q^46 - 13 * q^47 - 3 * q^49 - 5 * q^50 - 44 * q^52 + 6 * q^53 - 19 * q^55 + 23 * q^56 - 30 * q^59 - 22 * q^62 + 72 * q^64 + 6 * q^65 - 22 * q^67 + 78 * q^68 + 30 * q^70 + 11 * q^71 - 6 * q^74 + 6 * q^76 - 56 * q^77 - 36 * q^79 - 48 * q^80 - 13 * q^82 - 40 * q^83 - 16 * q^85 - 4 * q^86 - 12 * q^88 + 4 * q^89 + 30 * q^91 - 66 * q^92 - 44 * q^94 - 72 * q^95 + 21 * q^97 + 76 * q^98

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