LMFDB - Embedded newform 539.2.q.b.324.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(214,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 12]))

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

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

chi := DirichletCharacter("539.214");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.q (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
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} - x^{15} - 5 x^{14} + 16 x^{13} + 4 x^{12} - 29 x^{11} + 10 x^{10} - 156 x^{9} + 251 x^{8} + \cdots + 625 $ x^16 - x^15 - 5x^14 + 16x^13 + 4x^12 - 29x^11 + 10x^10 - 156x^9 + 251x^8 + 240x^7 + 390x^6 - 1375x^5 - 300x^4 + 500x^3 + 375x^2 + 625x + 625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			324.1
Root			$0.0812692 + 0.773225i$ of defining polynomial
Character	$\chi$	$=$	539.324
Dual form			539.2.q.b.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73864 - 0.369560i) q^{2} +(0.0646021 - 0.614648i) q^{3} +(1.05921 + 0.471591i) q^{4} +(1.85850 + 2.06407i) q^{5} +(-0.339469 + 1.04478i) q^{6} +(1.20872 + 0.878189i) q^{8} +(2.56082 + 0.544320i) q^{9} +O(q^{10})$	\(q+(-1.73864 - 0.369560i) q^{2} +(0.0646021 - 0.614648i) q^{3} +(1.05921 + 0.471591i) q^{4} +(1.85850 + 2.06407i) q^{5} +(-0.339469 + 1.04478i) q^{6} +(1.20872 + 0.878189i) q^{8} +(2.56082 + 0.544320i) q^{9} +(-2.46847 - 4.27551i) q^{10} +(-3.26882 + 0.561095i) q^{11} +(0.358290 - 0.620576i) q^{12} +(1.32676 + 4.08334i) q^{13} +(1.38874 - 1.00898i) q^{15} +(-3.32864 - 3.69683i) q^{16} +(-2.69534 + 0.572912i) q^{17} +(-4.25120 - 1.89275i) q^{18} +(-1.77145 + 0.788701i) q^{19} +(0.995144 + 3.06274i) q^{20} +(5.89066 + 0.232480i) q^{22} +(-2.18505 + 3.78461i) q^{23} +(0.617863 - 0.686207i) q^{24} +(-0.283734 + 2.69955i) q^{25} +(-0.797718 - 7.58978i) q^{26} +(1.07295 - 3.30220i) q^{27} +(-6.98027 + 5.07146i) q^{29} +(-2.78740 + 1.24103i) q^{30} +(0.134219 - 0.149066i) q^{31} +(2.92705 + 5.06980i) q^{32} +(0.133704 + 2.04542i) q^{33} +4.89796 q^{34} +(2.45576 + 1.78421i) q^{36} +(-0.108237 - 1.02981i) q^{37} +(3.37139 - 0.716612i) q^{38} +(2.59553 - 0.551697i) q^{39} +(0.433766 + 4.12701i) q^{40} +(7.77155 + 5.64636i) q^{41} -4.70820 q^{43} +(-3.72697 - 0.947227i) q^{44} +(3.63577 + 6.29735i) q^{45} +(5.19765 - 5.77258i) q^{46} +(11.9177 - 5.30610i) q^{47} +(-2.48729 + 1.80712i) q^{48} +(1.49096 - 4.58869i) q^{50} +(0.178015 + 1.69370i) q^{51} +(-0.520350 + 4.95080i) q^{52} +(-2.60969 + 2.89835i) q^{53} +(-3.08583 + 5.34482i) q^{54} +(-7.23324 - 5.70428i) q^{55} +(0.370334 + 1.13977i) q^{57} +(14.0104 - 6.23783i) q^{58} +(7.81733 + 3.48050i) q^{59} +(1.94680 - 0.413804i) q^{60} +(0.661508 + 0.734679i) q^{61} +(-0.288448 + 0.209570i) q^{62} +(-0.141042 - 0.434084i) q^{64} +(-5.96253 + 10.3274i) q^{65} +(0.523443 - 3.60567i) q^{66} +(2.70872 + 4.69165i) q^{67} +(-3.12511 - 0.664263i) q^{68} +(2.18505 + 1.58753i) q^{69} +(-0.623302 + 1.91833i) q^{71} +(2.61731 + 2.90682i) q^{72} +(9.10903 + 4.05560i) q^{73} +(-0.192390 + 1.83047i) q^{74} +(1.64094 + 0.348793i) q^{75} -2.24828 q^{76} -4.71658 q^{78} +(-6.15595 - 1.30849i) q^{79} +(1.44425 - 13.7411i) q^{80} +(5.21470 + 2.32174i) q^{81} +(-11.4253 - 12.6891i) q^{82} +(0.531960 - 1.63720i) q^{83} +(-6.19182 - 4.49862i) q^{85} +(8.18588 + 1.73996i) q^{86} +(2.66623 + 4.61804i) q^{87} +(-4.44384 - 2.19243i) q^{88} +(-7.65177 + 13.2532i) q^{89} +(-3.99406 - 12.2925i) q^{90} +(-4.09921 + 2.97825i) q^{92} +(-0.0829522 - 0.0921277i) q^{93} +(-22.6815 + 4.82111i) q^{94} +(-4.92018 - 2.19061i) q^{95} +(3.30524 - 1.47159i) q^{96} +(-3.58961 - 11.0477i) q^{97} +(-8.67628 - 0.342417i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} - 4 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) $ 16 * q + q^2 - 4 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 + 6 * q^8 + 2 * q^9	$ 16 q + q^{2} - 4 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} + 6 q^{8} + 2 q^{9} - 28 q^{10} - 5 q^{11} - 14 q^{12} - 10 q^{13} + 12 q^{15} + 3 q^{16} - 11 q^{17} - 4 q^{18} - 9 q^{19} - 42 q^{20} - 2 q^{22} + 16 q^{23} + 21 q^{24} - 5 q^{25} + 21 q^{26} + 44 q^{27} - 18 q^{29} - 14 q^{30} - 11 q^{31} + 20 q^{32} + 10 q^{33} + 48 q^{34} - 4 q^{36} - 6 q^{37} + 35 q^{38} + 5 q^{39} - 16 q^{40} + 44 q^{41} + 32 q^{43} - 29 q^{44} + 18 q^{45} - 29 q^{46} + 7 q^{47} - 8 q^{48} - 68 q^{50} - 3 q^{51} + 21 q^{52} - 2 q^{53} + 4 q^{54} - 52 q^{55} - 6 q^{57} + 39 q^{58} + 25 q^{59} + 38 q^{60} + 7 q^{61} + 10 q^{62} + 2 q^{64} - 24 q^{65} + 18 q^{66} + 30 q^{67} + 8 q^{68} - 16 q^{69} - 28 q^{71} - 3 q^{72} + 3 q^{73} + 9 q^{74} + 5 q^{75} + 104 q^{76} - 36 q^{78} + 9 q^{79} - 33 q^{80} + 28 q^{81} + 31 q^{82} - 46 q^{83} - 20 q^{85} + 17 q^{86} + 12 q^{87} + 7 q^{88} - 34 q^{89} - 4 q^{90} - 68 q^{92} - 8 q^{93} - 30 q^{94} - 24 q^{95} + 10 q^{96} - 60 q^{97}+O(q^{100}) $ 16 * q + q^2 - 4 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 + 6 * q^8 + 2 * q^9 - 28 * q^10 - 5 * q^11 - 14 * q^12 - 10 * q^13 + 12 * q^15 + 3 * q^16 - 11 * q^17 - 4 * q^18 - 9 * q^19 - 42 * q^20 - 2 * q^22 + 16 * q^23 + 21 * q^24 - 5 * q^25 + 21 * q^26 + 44 * q^27 - 18 * q^29 - 14 * q^30 - 11 * q^31 + 20 * q^32 + 10 * q^33 + 48 * q^34 - 4 * q^36 - 6 * q^37 + 35 * q^38 + 5 * q^39 - 16 * q^40 + 44 * q^41 + 32 * q^43 - 29 * q^44 + 18 * q^45 - 29 * q^46 + 7 * q^47 - 8 * q^48 - 68 * q^50 - 3 * q^51 + 21 * q^52 - 2 * q^53 + 4 * q^54 - 52 * q^55 - 6 * q^57 + 39 * q^58 + 25 * q^59 + 38 * q^60 + 7 * q^61 + 10 * q^62 + 2 * q^64 - 24 * q^65 + 18 * q^66 + 30 * q^67 + 8 * q^68 - 16 * q^69 - 28 * q^71 - 3 * q^72 + 3 * q^73 + 9 * q^74 + 5 * q^75 + 104 * q^76 - 36 * q^78 + 9 * q^79 - 33 * q^80 + 28 * q^81 + 31 * q^82 - 46 * q^83 - 20 * q^85 + 17 * q^86 + 12 * q^87 + 7 * q^88 - 34 * q^89 - 4 * q^90 - 68 * q^92 - 8 * q^93 - 30 * q^94 - 24 * q^95 + 10 * q^96 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−1.73864	−	0.369560i	−1.22941	−	0.261318i	−0.452976	−	0.891523i	$-0.649638\pi$
$2$	−1.73864	−	0.369560i	−1.22941	−	0.261318i	−0.776429	+	0.630204i	$0.782971\pi$
$3$	0.0646021	−	0.614648i	0.0372981	−	0.354867i	−0.959917	−	0.280285i	$-0.909571\pi$
$3$	0.0646021	−	0.614648i	0.0372981	−	0.354867i	0.997215	−	0.0745823i	$-0.0237623\pi$
$4$	1.05921	+	0.471591i	0.529605	+	0.235795i
$5$	1.85850	+	2.06407i	0.831146	+	0.923082i	0.998020	−	0.0628968i	$-0.0200339\pi$
$5$	1.85850	+	2.06407i	0.831146	+	0.923082i	−0.166874	+	0.985978i	$0.553367\pi$
$6$	−0.339469	+	1.04478i	−0.138588	+	0.426529i
$7$		0			0
$7$		0			0
$8$	1.20872	+	0.878189i	0.427348	+	0.310487i
$9$	2.56082	+	0.544320i	0.853608	+	0.181440i
$10$	−2.46847	−	4.27551i	−0.780598	−	1.35204i
$11$	−3.26882	+	0.561095i	−0.985586	+	0.169177i
$11$	−3.26882	+	0.561095i	−0.985586	+	0.169177i
$12$	0.358290	−	0.620576i	0.103429	−	0.179145i
$13$	1.32676	+	4.08334i	0.367976	+	1.13251i	0.948096	+	0.317983i	$0.103006\pi$
$13$	1.32676	+	4.08334i	0.367976	+	1.13251i	−0.580120	+	0.814531i	$0.696994\pi$
$14$		0			0
$15$	1.38874	−	1.00898i	0.358572	−	0.260518i
$16$	−3.32864	−	3.69683i	−0.832160	−	0.924208i
$17$	−2.69534	+	0.572912i	−0.653716	+	0.138952i	−0.522818	−	0.852444i	$-0.675119\pi$
$17$	−2.69534	+	0.572912i	−0.653716	+	0.138952i	−0.130898	+	0.991396i	$0.541786\pi$
$18$	−4.25120	−	1.89275i	−1.00202	−	0.446127i
$19$	−1.77145	+	0.788701i	−0.406399	+	0.180940i	−0.599747	−	0.800190i	$-0.704732\pi$
$19$	−1.77145	+	0.788701i	−0.406399	+	0.180940i	0.193348	+	0.981130i	$0.438065\pi$
$20$	0.995144	+	3.06274i	0.222521	+	0.684849i
$21$		0			0
$22$	5.89066	+	0.232480i	1.25589	+	0.0495649i
$23$	−2.18505	+	3.78461i	−0.455614	+	0.789146i	−0.998723	−	0.0505157i	$-0.983914\pi$
$23$	−2.18505	+	3.78461i	−0.455614	+	0.789146i	0.543109	+	0.839662i	$0.317247\pi$
$24$	0.617863	−	0.686207i	0.126121	−	0.140071i
$25$	−0.283734	+	2.69955i	−0.0567468	+	0.539910i
$26$	−0.797718	−	7.58978i	−0.156445	−	1.48848i
$27$	1.07295	−	3.30220i	0.206489	−	0.635508i
$28$		0			0
$29$	−6.98027	+	5.07146i	−1.29620	+	0.941747i	−0.999911	−	0.0133499i	$-0.995750\pi$
$29$	−6.98027	+	5.07146i	−1.29620	+	0.941747i	−0.296293	+	0.955097i	$0.595750\pi$
$30$	−2.78740	+	1.24103i	−0.508908	+	0.226580i
$31$	0.134219	−	0.149066i	0.0241065	−	0.0267730i	−0.730971	−	0.682409i	$-0.760933\pi$
$31$	0.134219	−	0.149066i	0.0241065	−	0.0267730i	0.755078	+	0.655636i	$0.227599\pi$
$32$	2.92705	+	5.06980i	0.517434	+	0.896223i
$33$	0.133704	+	2.04542i	0.0232748	+	0.356062i
$34$	4.89796			0.839993
$35$		0			0
$36$	2.45576	+	1.78421i	0.409293	+	0.297368i
$37$	−0.108237	−	1.02981i	−0.0177941	−	0.169299i	0.982016	−	0.188799i	$-0.0604594\pi$
$37$	−0.108237	−	1.02981i	−0.0177941	−	0.169299i	−0.999810	+	0.0194995i	$0.993793\pi$
$38$	3.37139	−	0.716612i	0.546912	−	0.116250i
$39$	2.59553	−	0.551697i	0.415617	−	0.0883422i
$40$	0.433766	+	4.12701i	0.0685844	+	0.652537i
$41$	7.77155	+	5.64636i	1.21371	+	0.881813i	0.995563	−	0.0941021i	$-0.0299980\pi$
$41$	7.77155	+	5.64636i	1.21371	+	0.881813i	0.218149	+	0.975915i	$0.429998\pi$
$42$		0			0
$43$	−4.70820			−0.717994			−0.358997	−	0.933339i	$-0.616881\pi$
$43$	−4.70820			−0.717994			−0.358997	+	0.933339i	$0.616881\pi$
$44$	−3.72697	−	0.947227i	−0.561862	−	0.142800i
$45$	3.63577	+	6.29735i	0.541989	+	0.938753i
$46$	5.19765	−	5.77258i	0.766352	−	0.851121i
$47$	11.9177	−	5.30610i	1.73837	−	0.773974i	0.743984	−	0.668198i	$-0.232934\pi$
$47$	11.9177	−	5.30610i	1.73837	−	0.773974i	0.994390	−	0.105776i	$-0.0337327\pi$
$48$	−2.48729	+	1.80712i	−0.359009	+	0.260835i
$49$		0			0
$50$	1.49096	−	4.58869i	0.210853	−	0.648939i
$51$	0.178015	+	1.69370i	0.0249271	+	0.237165i
$52$	−0.520350	+	4.95080i	−0.0721596	+	0.686553i
$53$	−2.60969	+	2.89835i	−0.358468	+	0.398119i	−0.895223	−	0.445619i	$-0.852984\pi$
$53$	−2.60969	+	2.89835i	−0.358468	+	0.398119i	0.536754	+	0.843739i	$0.319650\pi$
$54$	−3.08583	+	5.34482i	−0.419929	+	0.727338i
$55$	−7.23324	−	5.70428i	−0.975330	−	0.769165i
$56$		0			0
$57$	0.370334	+	1.13977i	0.0490520	+	0.150966i
$58$	14.0104	−	6.23783i	1.83966	−	0.819068i
$59$	7.81733	+	3.48050i	1.01773	+	0.453122i	0.846659	−	0.532137i	$-0.178611\pi$
$59$	7.81733	+	3.48050i	1.01773	+	0.453122i	0.171071	+	0.985259i	$0.445277\pi$
$60$	1.94680	−	0.413804i	0.251330	−	0.0534219i
$61$	0.661508	+	0.734679i	0.0846975	+	0.0940661i	0.784004	−	0.620756i	$-0.213174\pi$
$61$	0.661508	+	0.734679i	0.0846975	+	0.0940661i	−0.699306	+	0.714822i	$0.746508\pi$
$62$	−0.288448	+	0.209570i	−0.0366330	+	0.0266154i
$63$		0			0
$64$	−0.141042	−	0.434084i	−0.0176303	−	0.0542605i
$65$	−5.96253	+	10.3274i	−0.739561	+	1.28096i
$66$	0.523443	−	3.60567i	0.0644313	−	0.443827i
$67$	2.70872	+	4.69165i	0.330923	+	0.573176i	0.982693	−	0.185241i	$-0.0593066\pi$
$67$	2.70872	+	4.69165i	0.330923	+	0.573176i	−0.651770	+	0.758417i	$0.725973\pi$
$68$	−3.12511	−	0.664263i	−0.378976	−	0.0805538i
$69$	2.18505	+	1.58753i	0.263049	+	0.191116i
$70$		0			0
$71$	−0.623302	+	1.91833i	−0.0739724	+	0.227664i	−0.981206	−	0.192964i	$-0.938190\pi$
$71$	−0.623302	+	1.91833i	−0.0739724	+	0.227664i	0.907234	+	0.420627i	$0.138190\pi$
$72$	2.61731	+	2.90682i	0.308453	+	0.342572i
$73$	9.10903	+	4.05560i	1.06613	+	0.474672i	0.863378	−	0.504557i	$-0.168344\pi$
$73$	9.10903	+	4.05560i	1.06613	+	0.474672i	0.202754	+	0.979230i	$0.435011\pi$
$74$	−0.192390	+	1.83047i	−0.0223649	+	0.212787i
$75$	1.64094	+	0.348793i	0.189480	+	0.0402752i
$76$	−2.24828			−0.257896
$77$		0			0
$78$	−4.71658			−0.534047
$79$	−6.15595	−	1.30849i	−0.692598	−	0.147216i	−0.151854	−	0.988403i	$-0.548524\pi$
$79$	−6.15595	−	1.30849i	−0.692598	−	0.147216i	−0.540745	+	0.841187i	$0.681858\pi$
$80$	1.44425	−	13.7411i	0.161472	−	1.53630i
$81$	5.21470	+	2.32174i	0.579412	+	0.257971i
$82$	−11.4253	−	12.6891i	−1.26171	−	1.40127i
$83$	0.531960	−	1.63720i	0.0583902	−	0.179707i	−0.917607	−	0.397488i	$-0.869882\pi$
$83$	0.531960	−	1.63720i	0.0583902	−	0.179707i	0.975998	+	0.217781i	$0.0698820\pi$
$84$		0			0
$85$	−6.19182	−	4.49862i	−0.671598	−	0.487944i
$86$	8.18588	+	1.73996i	0.882706	+	0.187625i
$87$	2.66623	+	4.61804i	0.285849	+	0.495106i
$88$	−4.44384	−	2.19243i	−0.473715	−	0.233714i
$89$	−7.65177	+	13.2532i	−0.811086	+	1.40484i	0.101019	+	0.994884i	$0.467790\pi$
$89$	−7.65177	+	13.2532i	−0.811086	+	1.40484i	−0.912105	+	0.409957i	$0.865544\pi$
$90$	−3.99406	−	12.2925i	−0.421011	−	1.29574i
$91$		0			0
$92$	−4.09921	+	2.97825i	−0.427373	+	0.310504i
$93$	−0.0829522	−	0.0921277i	−0.00860174	−	0.00955320i
$94$	−22.6815	+	4.82111i	−2.33942	+	0.497259i
$95$	−4.92018	−	2.19061i	−0.504800	−	0.224751i
$96$	3.30524	−	1.47159i	0.337339	−	0.150193i
$97$	−3.58961	−	11.0477i	−0.364470	−	1.12172i	−0.950313	−	0.311297i	$-0.899236\pi$
$97$	−3.58961	−	11.0477i	−0.364470	−	1.12172i	0.585843	−	0.810425i	$-0.300764\pi$
$98$		0			0
$99$	−8.67628	−	0.342417i	−0.871999	−	0.0344142i
$100$	−1.57362	+	2.72558i	−0.157362	+	0.272558i
$101$	−2.28293	+	2.53545i	−0.227160	+	0.252287i	−0.845941	−	0.533277i	$-0.820960\pi$
$101$	−2.28293	+	2.53545i	−0.227160	+	0.252287i	0.618780	+	0.785564i	$0.287627\pi$
$102$	0.316419	−	3.01052i	0.0313301	−	0.298086i
$103$	−1.90060	−	18.0830i	−0.187271	−	1.78177i	−0.535676	−	0.844424i	$-0.679943\pi$
$103$	−1.90060	−	18.0830i	−0.187271	−	1.78177i	0.348404	−	0.937344i	$-0.386724\pi$
$104$	−1.98226	+	6.10077i	−0.194377	+	0.598230i
$105$		0			0
$106$	5.60843	−	4.07476i	0.544739	−	0.395776i
$107$	2.96670	−	1.32086i	0.286802	−	0.127692i	−0.258293	−	0.966067i	$-0.583160\pi$
$107$	2.96670	−	1.32086i	0.286802	−	0.127692i	0.545095	+	0.838374i	$0.316493\pi$
$108$	2.69377	−	2.99173i	0.259208	−	0.287879i
$109$	−6.34558	−	10.9909i	−0.607796	−	1.05273i	−0.991603	−	0.129320i	$-0.958720\pi$
$109$	−6.34558	−	10.9909i	−0.607796	−	1.05273i	0.383807	−	0.923413i	$-0.374613\pi$
$110$	10.4679	+	12.5908i	0.998079	+	1.20049i
$111$	−0.639962			−0.0607425
$112$		0			0
$113$	14.9248	+	10.8435i	1.40401	+	1.02007i	0.994160	+	0.107915i	$0.0344173\pi$
$113$	14.9248	+	10.8435i	1.40401	+	1.02007i	0.409845	+	0.912155i	$0.365583\pi$
$114$	−0.222665	−	2.11852i	−0.0208545	−	0.198417i
$115$	−11.8726	+	2.52360i	−1.10713	+	0.235327i
$116$	−9.78523	+	2.07992i	−0.908536	+	0.193115i
$117$	1.17495	+	11.1789i	0.108624	+	1.03349i
$118$	−12.3053	−	8.94031i	−1.13279	−	0.823022i
$119$		0			0
$120$	2.56468			0.234122
$121$	10.3703	−	3.66824i	0.942759	−	0.333476i
$122$	−0.878618	−	1.52181i	−0.0795464	−	0.137778i
$123$	3.97258	−	4.41200i	0.358196	−	0.397817i
$124$	0.212465	−	0.0945954i	0.0190799	−	0.00849492i
$125$	5.13577	−	3.73136i	0.459358	−	0.333743i
$126$		0			0
$127$	6.02870	−	18.5544i	0.534961	−	1.64644i	−0.208772	−	0.977964i	$-0.566947\pi$
$127$	6.02870	−	18.5544i	0.534961	−	1.64644i	0.743733	−	0.668476i	$-0.233053\pi$
$128$	−1.13904	−	10.8372i	−0.100678	−	0.957884i
$129$	−0.304160	+	2.89389i	−0.0267798	+	0.254793i
$130$	14.1833	−	15.7522i	1.24396	−	1.38156i
$131$	−3.44898	+	5.97381i	−0.301339	+	0.521934i	−0.976439	−	0.215792i	$-0.930767\pi$
$131$	−3.44898	+	5.97381i	−0.301339	+	0.521934i	0.675101	+	0.737726i	$0.264100\pi$
$132$	−0.822982	+	2.22959i	−0.0716314	+	0.194061i
$133$		0			0
$134$	−2.97566	−	9.15813i	−0.257058	−	0.791142i
$135$	8.81005	−	3.92249i	0.758249	−	0.337594i
$136$	−3.76105	−	1.67453i	−0.322507	−	0.143589i
$137$	2.55365	−	0.542794i	0.218173	−	0.0463741i	−0.0975283	−	0.995233i	$-0.531094\pi$
$137$	2.55365	−	0.542794i	0.218173	−	0.0463741i	0.315701	+	0.948859i	$0.397760\pi$
$138$	−3.21233	−	3.56765i	−0.273451	−	0.303699i
$139$	−0.810097	+	0.588570i	−0.0687116	+	0.0499219i	−0.621611	−	0.783326i	$-0.713521\pi$
$139$	−0.810097	+	0.588570i	−0.0687116	+	0.0499219i	0.552899	+	0.833248i	$0.313521\pi$
$140$		0			0
$141$	−2.49148	−	7.66797i	−0.209820	−	0.645760i
$142$	1.79264	−	3.10494i	0.150435	−	0.260561i
$143$	−6.62807	−	12.6033i	−0.554267	−	1.05394i
$144$	−6.51180	−	11.2788i	−0.542650	−	0.939898i
$145$	−23.4407	−	4.98248i	−1.94664	−	0.413772i
$146$	−14.3386	−	10.4176i	−1.18667	−	0.862165i
$147$		0			0
$148$	0.371002	−	1.14183i	0.0304962	−	0.0938576i
$149$	−9.96654	−	11.0690i	−0.816491	−	0.906805i	0.180559	−	0.983564i	$-0.442209\pi$
$149$	−9.96654	−	11.0690i	−0.816491	−	0.906805i	−0.997050	+	0.0767594i	$0.975543\pi$
$150$	−2.72411	−	1.21285i	−0.222423	−	0.0990291i
$151$	−1.65203	+	15.7180i	−0.134440	+	1.27911i	0.694384	+	0.719605i	$0.255677\pi$
$151$	−1.65203	+	15.7180i	−0.134440	+	1.27911i	−0.828824	+	0.559509i	$0.810990\pi$
$152$	−2.83382	−	0.602348i	−0.229853	−	0.0488569i
$153$	−7.21414			−0.583229
$154$		0			0
$155$	0.557129			0.0447497
$156$	3.00939	+	0.639665i	0.240944	+	0.0512142i
$157$	0.479914	−	4.56608i	0.0383013	−	0.364412i	−0.958538	−	0.284965i	$-0.908018\pi$
$157$	0.479914	−	4.56608i	0.0383013	−	0.364412i	0.996839	−	0.0794471i	$-0.0253155\pi$
$158$	10.2194	+	4.54998i	0.813014	+	0.361977i
$159$	1.61288	+	1.79128i	0.127909	+	0.142058i
$160$	−5.02452	+	15.4639i	−0.397223	+	1.22253i
$161$		0			0
$162$	−8.20848	−	5.96381i	−0.644919	−	0.468561i
$163$	−7.86200	−	1.67112i	−0.615799	−	0.130892i	−0.110557	−	0.993870i	$-0.535264\pi$
$163$	−7.86200	−	1.67112i	−0.615799	−	0.130892i	−0.505242	+	0.862978i	$0.668597\pi$
$164$	5.56893	+	9.64568i	0.434861	+	0.753201i
$165$	−3.97341	+	4.07739i	−0.309330	+	0.317424i
$166$	−1.52993	+	2.64992i	−0.118746	+	0.205674i
$167$	4.14296	+	12.7507i	0.320592	+	0.986681i	0.973391	+	0.229150i	$0.0735946\pi$
$167$	4.14296	+	12.7507i	0.320592	+	0.986681i	−0.652799	+	0.757531i	$0.726405\pi$
$168$		0			0
$169$	−4.39615	+	3.19399i	−0.338165	+	0.245691i
$170$	9.10285	+	10.1097i	0.698157	+	0.775382i
$171$	−4.96568	+	1.05549i	−0.379735	+	0.0807152i
$172$	−4.98698	−	2.22035i	−0.380254	−	0.169300i
$173$	18.8027	−	8.37148i	1.42954	−	0.636472i	0.461471	−	0.887156i	$-0.347322\pi$
$173$	18.8027	−	8.37148i	1.42954	−	0.636472i	0.968069	+	0.250683i	$0.0806553\pi$
$174$	−2.92897	−	9.01445i	−0.222045	−	0.683383i
$175$		0			0
$176$	12.9550	+	10.2166i	0.976520	+	0.770104i
$177$	2.64430	−	4.58006i	0.198758	−	0.344258i
$178$	18.2015	−	20.2149i	1.36426	−	1.51517i
$179$	0.388344	−	3.69484i	0.0290262	−	0.276166i	−0.970376	−	0.241599i	$-0.922328\pi$
$179$	0.388344	−	3.69484i	0.0290262	−	0.276166i	0.999402	−	0.0345668i	$-0.0110051\pi$
$180$	0.881279	+	8.38481i	0.0656867	+	0.624967i
$181$	−1.47458	+	4.53828i	−0.109604	+	0.337327i	−0.990783	−	0.135455i	$-0.956750\pi$
$181$	−1.47458	+	4.53828i	−0.109604	+	0.337327i	0.881179	+	0.472783i	$0.156750\pi$
$182$		0			0
$183$	0.494304	−	0.359133i	0.0365400	−	0.0265479i
$184$	−5.96472	+	2.65566i	−0.439725	+	0.195778i
$185$	1.92444	−	2.13731i	0.141488	−	0.157138i
$186$	0.110177	+	0.190833i	0.00807860	+	0.0139925i
$187$	8.48912	−	3.38509i	0.620786	−	0.247542i
$188$	15.1257			1.10315
$189$		0			0
$190$	7.74487	+	5.62698i	0.561872	+	0.408224i
$191$	0.0866707	+	0.824616i	0.00627127	+	0.0596671i	0.997210	−	0.0746479i	$-0.0237833\pi$
$191$	0.0866707	+	0.824616i	0.00627127	+	0.0596671i	−0.990939	+	0.134315i	$0.957117\pi$
$192$	−0.275921	+	0.0586487i	−0.0199129	+	0.00423261i
$193$	6.59078	−	1.40091i	0.474415	−	0.100840i	0.0355021	−	0.999370i	$-0.488697\pi$
$193$	6.59078	−	1.40091i	0.474415	−	0.100840i	0.438913	+	0.898530i	$0.355364\pi$
$194$	2.15827	+	20.5345i	0.154955	+	1.47429i
$195$	5.96253	+	4.33203i	0.426986	+	0.310223i
$196$		0			0
$197$	−10.9216			−0.778129			−0.389065	−	0.921210i	$-0.627202\pi$
$197$	−10.9216			−0.778129			−0.389065	+	0.921210i	$0.627202\pi$
$198$	14.9584	+	3.80174i	1.06305	+	0.270178i
$199$	10.4873	+	18.1645i	0.743424	+	1.28765i	0.950927	+	0.309414i	$0.100133\pi$
$199$	10.4873	+	18.1645i	0.743424	+	1.28765i	−0.207503	+	0.978234i	$0.566534\pi$
$200$	−2.71367	+	3.01384i	−0.191885	+	0.213110i
$201$	3.05870	−	1.36182i	0.215744	−	0.0960555i
$202$	4.90620	−	3.56457i	0.345199	−	0.250802i
$203$		0			0
$204$	−0.610177	+	1.87793i	−0.0427210	+	0.131482i
$205$	2.78892	+	26.5348i	0.194787	+	1.85327i
$206$	−3.37828	+	32.1422i	−0.235376	+	2.23945i
$207$	−7.65556	+	8.50236i	−0.532098	+	0.590955i
$208$	10.6791	−	18.4968i	0.740463	−	1.28252i
$209$	5.34802	−	3.57207i	0.369930	−	0.247086i
$210$		0			0
$211$	−1.86140	−	5.72879i	−0.128144	−	0.394386i	0.866317	−	0.499495i	$-0.166481\pi$
$211$	−1.86140	−	5.72879i	−0.128144	−	0.394386i	−0.994461	+	0.105109i	$0.966481\pi$
$212$	−4.13105	+	1.83926i	−0.283721	+	0.126321i
$213$	1.13883	+	0.507040i	0.0780313	+	0.0347418i
$214$	−5.64617	+	1.20013i	−0.385964	+	0.0820392i
$215$	−8.75020	−	9.71808i	−0.596758	−	0.662767i
$216$	4.19685	−	3.04919i	0.285560	−	0.207471i
$217$		0			0
$218$	6.97091	+	21.4542i	0.472129	+	1.45306i
$219$	3.08123	−	5.33685i	0.208210	−	0.360631i
$220$	−4.97143	−	9.45317i	−0.335174	−	0.637332i
$221$	−5.91546	−	10.2459i	−0.397917	−	0.689212i
$222$	1.11266	+	0.236504i	0.0746772	+	0.0158731i
$223$	−3.74176	−	2.71855i	−0.250567	−	0.182048i	0.455411	−	0.890281i	$-0.349492\pi$
$223$	−3.74176	−	2.71855i	−0.250567	−	0.182048i	−0.705978	+	0.708234i	$0.749492\pi$
$224$		0			0
$225$	−2.19601	+	6.75863i	−0.146401	+	0.450575i
$226$	−21.9415	−	24.3685i	−1.45953	−	1.62097i
$227$	−15.8046	−	7.03668i	−1.04899	−	0.467041i	−0.191475	−	0.981498i	$-0.561327\pi$
$227$	−15.8046	−	7.03668i	−1.04899	−	0.467041i	−0.857516	+	0.514457i	$0.827994\pi$
$228$	−0.145244	+	1.38190i	−0.00961902	+	0.0915189i
$229$	−4.32940	−	0.920242i	−0.286095	−	0.0608113i	0.0626290	−	0.998037i	$-0.480052\pi$
$229$	−4.32940	−	0.920242i	−0.286095	−	0.0608113i	−0.348724	+	0.937226i	$0.613385\pi$
$230$	21.5749			1.42260
$231$		0			0
$232$	−12.8909			−0.846330
$233$	10.3029	+	2.18994i	0.674963	+	0.143468i	0.532627	−	0.846350i	$-0.321205\pi$
$233$	10.3029	+	2.18994i	0.674963	+	0.143468i	0.142337	+	0.989818i	$0.454538\pi$
$234$	2.08845	−	19.8703i	0.136526	−	1.29896i
$235$	33.1012	+	14.7376i	2.15928	+	0.961375i
$236$	6.63882	+	7.37316i	0.432151	+	0.479952i
$237$	−1.20195	+	3.69921i	−0.0780748	+	0.240290i
$238$		0			0
$239$	7.89314	+	5.73470i	0.510565	+	0.370947i	0.813038	−	0.582211i	$-0.197812\pi$
$239$	7.89314	+	5.73470i	0.510565	+	0.370947i	−0.302473	+	0.953158i	$0.597812\pi$
$240$	−8.35265	−	1.77541i	−0.539161	−	0.114602i
$241$	6.27504	+	10.8687i	0.404211	+	0.700114i	0.994229	−	0.107276i	$-0.0342128\pi$
$241$	6.27504	+	10.8687i	0.404211	+	0.700114i	−0.590018	+	0.807390i	$0.700879\pi$
$242$	−19.3859	+	2.54529i	−1.24618	+	0.163617i
$243$	6.97214	−	12.0761i	0.447263	−	0.774682i
$244$	0.354208	+	1.09014i	0.0226759	+	0.0697892i
$245$		0			0
$246$	−8.53740	+	6.20278i	−0.544325	+	0.395475i
$247$	−5.57082	−	6.18702i	−0.354463	−	0.393671i
$248$	0.293142	−	0.0623093i	0.0186145	−	0.00395664i
$249$	−0.971939	−	0.432735i	−0.0615942	−	0.0274235i
$250$	−10.3082	+	4.58952i	−0.651950	+	0.290267i
$251$	3.39646	+	10.4532i	0.214383	+	0.659803i	0.999197	+	0.0400713i	$0.0127585\pi$
$251$	3.39646	+	10.4532i	0.214383	+	0.659803i	−0.784814	+	0.619732i	$0.787241\pi$
$252$		0			0
$253$	5.01899	−	13.5972i	0.315541	−	0.854850i
$254$	−17.3387	+	30.0316i	−1.08793	+	1.88435i
$255$	−3.16508	+	3.51517i	−0.198205	+	0.220129i
$256$	−2.12004	+	20.1708i	−0.132503	+	1.26068i
$257$	0.557429	+	5.30358i	0.0347715	+	0.330828i	0.998055	+	0.0623418i	$0.0198569\pi$
$257$	0.557429	+	5.30358i	0.0347715	+	0.330828i	−0.963283	+	0.268487i	$0.913476\pi$
$258$	1.59829	−	4.91903i	0.0995052	−	0.306246i
$259$		0			0
$260$	−11.1859	+	8.12702i	−0.693719	+	0.504017i
$261$	−20.6357	+	9.18762i	−1.27732	+	0.568700i
$262$	8.20422	−	9.11171i	0.506858	−	0.562923i
$263$	4.09017	+	7.08438i	0.252211	+	0.436842i	0.964134	−	0.265415i	$-0.0855091\pi$
$263$	4.09017	+	7.08438i	0.252211	+	0.436842i	−0.711923	+	0.702257i	$0.752176\pi$
$264$	−1.63466	+	2.58977i	−0.100606	+	0.159389i
$265$	−10.8325			−0.665436
$266$		0			0
$267$	7.65177	+	5.55933i	0.468280	+	0.340226i
$268$	0.656570	+	6.24685i	0.0401064	+	0.381587i
$269$	12.5632	−	2.67040i	0.765994	−	0.162817i	0.191686	−	0.981456i	$-0.438604\pi$
$269$	12.5632	−	2.67040i	0.765994	−	0.162817i	0.574308	+	0.818639i	$0.305271\pi$
$270$	−16.7671	+	3.56396i	−1.02041	+	0.216896i
$271$	−2.30456	−	21.9264i	−0.139992	−	1.33194i	−0.808617	−	0.588336i	$-0.799783\pi$
$271$	−2.30456	−	21.9264i	−0.139992	−	1.33194i	0.668624	−	0.743600i	$-0.266883\pi$
$272$	11.0898	+	8.05720i	0.672417	+	0.488539i
$273$		0			0
$274$	−4.64047			−0.280341
$275$	−0.587229	−	8.98354i	−0.0354113	−	0.541728i
$276$	1.56576	+	2.71198i	0.0942477	+	0.163242i
$277$	16.1106	−	17.8927i	0.967994	−	1.07507i	−0.0291524	−	0.999575i	$-0.509281\pi$
$277$	16.1106	−	17.8927i	0.967994	−	1.07507i	0.997146	−	0.0754914i	$-0.0240525\pi$
$278$	1.62598	−	0.723934i	0.0975199	−	0.0434186i
$279$	0.424852	−	0.308673i	0.0254352	−	0.0184798i
$280$		0			0
$281$	4.77179	−	14.6861i	0.284661	−	0.876097i	−0.701839	−	0.712336i	$-0.747637\pi$
$281$	4.77179	−	14.6861i	0.284661	−	0.876097i	0.986500	−	0.163761i	$-0.0523626\pi$
$282$	1.49801	+	14.2526i	0.0892052	+	0.848731i
$283$	−0.350935	+	3.33893i	−0.0208609	+	0.198479i	−0.999989	−	0.00476742i	$-0.998482\pi$
$283$	−0.350935	+	3.33893i	−0.0208609	+	0.198479i	0.979128	+	0.203246i	$0.0651491\pi$
$284$	−1.56487	+	1.73797i	−0.0928582	+	0.103129i
$285$	−1.66431	+	2.88266i	−0.0985850	+	0.170754i
$286$	6.86618	+	24.3620i	0.406006	+	1.44056i
$287$		0			0
$288$	4.73607	+	14.5761i	0.279075	+	0.858906i
$289$	−8.59364	+	3.82613i	−0.505508	+	0.225067i
$290$	38.9137	+	17.3255i	2.28509	+	1.01739i
$291$	−7.02233	+	1.49264i	−0.411657	+	0.0875003i
$292$	7.73580	+	8.59148i	0.452703	+	0.502778i
$293$	5.53129	−	4.01872i	0.323142	−	0.234776i	−0.414373	−	0.910107i	$-0.635999\pi$
$293$	5.53129	−	4.01872i	0.323142	−	0.234776i	0.737515	+	0.675331i	$0.235999\pi$
$294$		0			0
$295$	7.34450	+	22.6040i	0.427613	+	1.31606i
$296$	0.773537	−	1.33981i	0.0449609	−	0.0778746i
$297$	−1.65443	+	11.3963i	−0.0959996	+	0.661281i
$298$	13.2376	+	22.9282i	0.766834	+	1.32819i
$299$	−18.3529	−	3.90102i	−1.06137	−	0.225602i
$300$	1.57362	+	1.14330i	0.0908528	+	0.0660084i
$301$		0			0
$302$	8.68103	−	26.7175i	0.499537	−	1.53742i
$303$	1.41093	+	1.56700i	0.0810558	+	0.0900216i
$304$	8.81222	+	3.92345i	0.505416	+	0.225025i
$305$	−0.287019	+	2.73080i	−0.0164347	+	0.156365i
$306$	12.5428	+	2.66606i	0.717025	+	0.152408i
$307$	11.7970			0.673293			0.336646	−	0.941631i	$-0.390707\pi$
$307$	11.7970			0.673293			0.336646	+	0.941631i	$0.390707\pi$
$308$		0			0
$309$	−11.2375			−0.639276
$310$	−0.968649	−	0.205893i	−0.0550155	−	0.0116939i
$311$	2.64602	−	25.1752i	0.150042	−	1.42756i	−0.617507	−	0.786565i	$-0.711857\pi$
$311$	2.64602	−	25.1752i	0.150042	−	1.42756i	0.767549	−	0.640990i	$-0.221476\pi$
$312$	3.62177	+	1.61252i	0.205042	+	0.0912907i
$313$	13.1513	+	14.6060i	0.743357	+	0.825581i	0.989633	−	0.143618i	$-0.0458738\pi$
$313$	13.1513	+	14.6060i	0.743357	+	0.825581i	−0.246277	+	0.969200i	$0.579207\pi$
$314$	−2.52184	+	7.76141i	−0.142315	+	0.438002i
$315$		0			0
$316$	−5.90337	−	4.28905i	−0.332091	−	0.241278i
$317$	−3.53166	−	0.750678i	−0.198358	−	0.0421623i	0.107661	−	0.994188i	$-0.465664\pi$
$317$	−3.53166	−	0.750678i	−0.198358	−	0.0421623i	−0.306019	+	0.952025i	$0.598997\pi$
$318$	−2.14223	−	3.71045i	−0.120130	−	0.208072i
$319$	19.9717	−	20.4943i	1.11820	−	1.14746i
$320$	0.633854	−	1.09787i	0.0354335	−	0.0613726i
$321$	−0.620210	−	1.90881i	−0.0346167	−	0.106539i
$322$		0			0
$323$	4.32281	−	3.14071i	0.240528	−	0.174754i
$324$	4.42856	+	4.91841i	0.246031	+	0.273245i
$325$	−11.3996	+	2.42306i	−0.632337	+	0.134407i
$326$	13.0516	+	5.81096i	0.722863	+	0.321839i
$327$	−7.16545	+	3.19027i	−0.396250	+	0.176422i
$328$	4.43508	+	13.6498i	0.244886	+	0.753683i
$329$		0			0
$330$	8.41518	−	5.62071i	0.463240	−	0.309410i
$331$	13.2667	−	22.9787i	0.729205	−	1.26302i	−0.228014	−	0.973658i	$-0.573223\pi$
$331$	13.2667	−	22.9787i	0.729205	−	1.26302i	0.957219	−	0.289363i	$-0.0934435\pi$
$332$	1.33555	−	1.48328i	0.0732978	−	0.0814054i
$333$	0.283369	−	2.69607i	0.0155285	−	0.147744i
$334$	−2.49097	−	23.7000i	−0.136300	−	1.29681i
$335$	−4.64974	+	14.3104i	−0.254042	+	0.781862i
$336$		0			0
$337$	0.554969	−	0.403208i	0.0302311	−	0.0219642i	−0.572567	−	0.819858i	$-0.694052\pi$
$337$	0.554969	−	0.403208i	0.0302311	−	0.0219642i	0.602798	+	0.797894i	$0.294052\pi$
$338$	8.82370	−	3.92856i	0.479946	−	0.213686i
$339$	7.62911	−	8.47298i	0.414356	−	0.460189i
$340$	−4.43693	−	7.68500i	−0.240627	−	0.416777i
$341$	−0.355099	+	0.562579i	−0.0192297	+	0.0304653i
$342$	9.02361			0.487941
$343$		0			0
$344$	−5.69091	−	4.13469i	−0.306834	−	0.222928i
$345$	0.784132	+	7.46052i	0.0422163	+	0.401661i
$346$	−35.7849	+	7.60631i	−1.92381	+	0.408918i
$347$	−21.0355	+	4.47124i	−1.12925	+	0.240029i	−0.734399	−	0.678718i	$-0.762536\pi$
$347$	−21.0355	+	4.47124i	−1.12925	+	0.240029i	−0.394847	+	0.918747i	$0.629202\pi$
$348$	0.646270	+	6.14884i	0.0346437	+	0.329613i
$349$	15.7296	+	11.4282i	0.841987	+	0.611739i	0.922925	−	0.384980i	$-0.125792\pi$
$349$	15.7296	+	11.4282i	0.841987	+	0.611739i	−0.0809381	+	0.996719i	$0.525792\pi$
$350$		0			0
$351$	14.9075			0.795705
$352$	−12.4126	−	14.9299i	−0.661596	−	0.795767i
$353$	−10.4654	−	18.1265i	−0.557015	−	0.964778i	−0.997744	−	0.0671378i	$-0.978613\pi$
$353$	−10.4654	−	18.1265i	−0.557015	−	0.964778i	0.440729	−	0.897640i	$-0.354720\pi$
$354$	−6.29009	+	6.98586i	−0.334315	+	0.371294i
$355$	−5.11797	+	2.27867i	−0.271634	+	0.120939i
$356$	−14.3549	+	10.4295i	−0.760810	+	0.552761i
$357$		0			0
$358$	−2.04066	+	6.28050i	−0.107852	+	0.331935i
$359$	−1.02138	−	9.71774i	−0.0539062	−	0.512883i	−0.987844	−	0.155448i	$-0.950318\pi$
$359$	−1.02138	−	9.71774i	−0.0539062	−	0.512883i	0.933938	−	0.357435i	$-0.116349\pi$
$360$	−1.13561	+	10.8046i	−0.0598521	+	0.569455i
$361$	−10.1975	+	11.3255i	−0.536710	+	0.596077i
$362$	4.24092	−	7.34550i	0.222898	−	0.386071i
$363$	−1.58473	−	6.61109i	−0.0831767	−	0.346992i
$364$		0			0
$365$	8.55808	+	26.3390i	0.447950	+	1.37865i
$366$	−0.992139	+	0.441729i	−0.0518600	+	0.0230895i
$367$	−9.04381	−	4.02656i	−0.472083	−	0.210185i	0.156884	−	0.987617i	$-0.449855\pi$
$367$	−9.04381	−	4.02656i	−0.472083	−	0.210185i	−0.628967	+	0.777432i	$0.716522\pi$
$368$	21.2643	−	4.51987i	1.10848	−	0.235614i
$369$	16.8281	+	18.6895i	0.876038	+	0.972939i
$370$	−4.13577	+	3.00482i	−0.215009	+	0.156213i
$371$		0			0
$372$	−0.0444172	−	0.136702i	−0.00230293	−	0.00708768i
$373$	2.13737	−	3.70204i	0.110669	−	0.191684i	−0.805371	−	0.592771i	$-0.798034\pi$
$373$	2.13737	−	3.70204i	0.110669	−	0.191684i	0.916040	+	0.401086i	$0.131367\pi$
$374$	−16.0105	+	2.74822i	−0.827885	+	0.142107i
$375$	−1.96169	−	3.39775i	−0.101301	−	0.175459i
$376$	19.0649	+	4.05238i	0.983199	+	0.208985i
$377$	−29.9696	−	21.7742i	−1.54351	−	1.12143i
$378$		0			0
$379$	1.33679	−	4.11421i	0.0686662	−	0.211333i	−0.910835	−	0.412770i	$-0.864561\pi$
$379$	1.33679	−	4.11421i	0.0686662	−	0.211333i	0.979501	+	0.201437i	$0.0645612\pi$
$380$	−4.17844	−	4.64062i	−0.214349	−	0.238059i
$381$	−11.0150	−	4.90419i	−0.564315	−	0.251249i
$382$	0.154056	−	1.46574i	0.00788218	−	0.0749939i
$383$	−1.29321	−	0.274880i	−0.0660799	−	0.0140457i	0.174753	−	0.984612i	$-0.444087\pi$
$383$	−1.29321	−	0.274880i	−0.0660799	−	0.0140457i	−0.240833	+	0.970567i	$0.577421\pi$
$384$	−6.73467			−0.343677
$385$		0			0
$386$	−11.9767			−0.609600
$387$	−12.0569	−	2.56277i	−0.612886	−	0.130273i
$388$	1.40783	−	13.3946i	0.0714719	−	0.680010i
$389$	−35.1799	−	15.6631i	−1.78369	−	0.794150i	−0.979971	−	0.199141i	$-0.936185\pi$
$389$	−35.1799	−	15.6631i	−1.78369	−	0.794150i	−0.803719	−	0.595009i	$-0.797149\pi$
$390$	−8.76576	−	9.73536i	−0.443872	−	0.492969i
$391$	3.72119	−	11.4527i	0.188189	−	0.579186i
$392$		0			0
$393$	3.44898	+	2.50583i	0.173978	+	0.126402i
$394$	18.9887	+	4.03617i	0.956637	+	0.203339i
$395$	−8.74002	−	15.1382i	−0.439758	−	0.761683i
$396$	−9.02853	−	4.45435i	−0.453701	−	0.223839i
$397$	−0.205054	+	0.355165i	−0.0102914	+	0.0178252i	−0.871125	−	0.491061i	$-0.836609\pi$
$397$	−0.205054	+	0.355165i	−0.0102914	+	0.0178252i	0.860834	+	0.508886i	$0.169943\pi$
$398$	−11.5208	−	35.4573i	−0.577484	−	1.77731i
$399$		0			0
$400$	10.9242	−	7.93691i	0.546211	−	0.396846i
$401$	−1.04842	−	1.16439i	−0.0523556	−	0.0581468i	0.716398	−	0.697692i	$-0.245789\pi$
$401$	−1.04842	−	1.16439i	−0.0523556	−	0.0581468i	−0.768754	+	0.639545i	$0.779123\pi$
$402$	−5.82126	+	1.23735i	−0.290338	+	0.0617133i
$403$	0.786763	+	0.350289i	0.0391914	+	0.0174492i
$404$	−3.61380	+	1.60897i	−0.179793	+	0.0800492i
$405$	4.89929	+	15.0785i	0.243448	+	0.749255i
$406$		0			0
$407$	0.931628	+	3.30552i	0.0461791	+	0.163849i
$408$	−1.27222	+	2.20354i	−0.0629841	+	0.109092i
$409$	4.53572	−	5.03742i	0.224277	−	0.249085i	−0.620496	−	0.784209i	$-0.713069\pi$
$409$	4.53572	−	5.03742i	0.224277	−	0.249085i	0.844773	+	0.535125i	$0.179735\pi$
$410$	4.95726	−	47.1652i	0.244822	−	2.32932i
$411$	−0.168657	−	1.60466i	−0.00831922	−	0.0791521i
$412$	6.51463	−	20.0500i	0.320953	−	0.987792i
$413$		0			0
$414$	16.4524	−	11.9534i	0.808592	−	0.587476i
$415$	4.36796	−	1.94474i	0.214415	−	0.0954635i
$416$	−16.8182	+	18.6785i	−0.824581	+	0.915790i
$417$	0.309430	+	0.535948i	0.0151528	+	0.0262455i
$418$	−10.6184	+	4.23415i	−0.519362	+	0.207099i
$419$	−28.7218			−1.40315			−0.701577	−	0.712594i	$-0.747520\pi$
$419$	−28.7218			−1.40315			−0.701577	+	0.712594i	$0.747520\pi$
$420$		0			0
$421$	−9.89070	−	7.18601i	−0.482043	−	0.350225i	0.320073	−	0.947393i	$-0.396293\pi$
$421$	−9.89070	−	7.18601i	−0.482043	−	0.350225i	−0.802116	+	0.597168i	$0.796293\pi$
$422$	1.11917	+	10.6482i	0.0544805	+	0.518347i
$423$	33.4073	−	7.10094i	1.62432	−	0.345260i
$424$	−5.69969	+	1.21151i	−0.276802	+	0.0588360i
$425$	−0.781845	−	7.43876i	−0.0379251	−	0.360833i
$426$	−1.79264	−	1.30243i	−0.0868535	−	0.0631028i
$427$		0			0
$428$	3.76527			0.182001
$429$	−8.17476	+	3.25973i	−0.394681	+	0.157381i
$430$	11.6220	+	20.1300i	0.560465	+	0.970754i
$431$	2.46996	−	2.74316i	0.118974	−	0.132134i	−0.680715	−	0.732548i	$-0.738331\pi$
$431$	2.46996	−	2.74316i	0.118974	−	0.132134i	0.799689	+	0.600414i	$0.204998\pi$
$432$	−15.7791	+	7.02532i	−0.759174	+	0.338006i
$433$	23.5221	−	17.0898i	1.13040	−	0.821283i	0.144646	−	0.989483i	$-0.453796\pi$
$433$	23.5221	−	17.0898i	1.13040	−	0.821283i	0.985753	+	0.168201i	$0.0537957\pi$
$434$		0			0
$435$	−4.57679	+	14.0859i	−0.219440	+	0.675368i
$436$	−1.53811	−	14.6342i	−0.0736622	−	0.700849i
$437$	0.885777	−	8.42761i	0.0423725	−	0.403147i
$438$	−7.32945	+	8.14018i	−0.350215	+	0.388953i
$439$	−7.10086	+	12.2990i	−0.338905	+	0.587001i	−0.984227	−	0.176910i	$-0.943390\pi$
$439$	−7.10086	+	12.2990i	−0.338905	+	0.587001i	0.645322	+	0.763911i	$0.276723\pi$
$440$	−3.73355	−	13.2470i	−0.177990	−	0.631528i
$441$		0			0
$442$	6.49840	+	20.0000i	0.309097	+	0.951304i
$443$	24.8809	−	11.0777i	1.18213	−	0.526318i	0.280932	−	0.959728i	$-0.409356\pi$
$443$	24.8809	−	11.0777i	1.18213	−	0.526318i	0.901197	+	0.433410i	$0.142690\pi$
$444$	−0.677854	−	0.301800i	−0.0321695	−	0.0143228i
$445$	−41.5765	+	8.83735i	−1.97091	+	0.418931i
$446$	5.50092	+	6.10939i	0.260476	+	0.289288i
$447$	−7.44738	+	5.41084i	−0.352249	+	0.255924i
$448$		0			0
$449$	−12.9527	−	39.8644i	−0.611277	−	1.88132i	−0.445888	−	0.895089i	$-0.647112\pi$
$449$	−12.9527	−	39.8644i	−0.611277	−	1.88132i	−0.165389	−	0.986228i	$-0.552888\pi$
$450$	6.31579	−	10.9393i	0.297729	−	0.515682i
$451$	−28.5719	−	14.0963i	−1.34540	−	0.663771i
$452$	10.6948	+	18.5239i	0.503041	+	0.871292i
$453$	9.55432	+	2.03083i	0.448901	+	0.0954169i
$454$	24.8781	+	18.0750i	1.16759	+	0.848303i
$455$		0			0
$456$	−0.553303	+	1.70289i	−0.0259108	+	0.0797452i
$457$	13.0465	+	14.4896i	0.610289	+	0.677795i	0.966517	−	0.256604i	$-0.0826037\pi$
$457$	13.0465	+	14.4896i	0.610289	+	0.677795i	−0.356227	+	0.934399i	$0.615937\pi$
$458$	7.18719	+	3.19994i	0.335835	+	0.149523i
$459$	−1.00009	+	9.51525i	−0.0466804	+	0.444134i
$460$	−13.7657	−	2.92599i	−0.641830	−	0.136425i
$461$	−12.2251			−0.569380			−0.284690	−	0.958620i	$-0.591891\pi$
$461$	−12.2251			−0.569380			−0.284690	+	0.958620i	$0.591891\pi$
$462$		0			0
$463$	13.8550			0.643894			0.321947	−	0.946758i	$-0.395663\pi$
$463$	13.8550			0.643894			0.321947	+	0.946758i	$0.395663\pi$
$464$	41.9832	+	8.92380i	1.94902	+	0.414277i
$465$	0.0359918	−	0.342439i	0.00166908	−	0.0158802i
$466$	−17.1037	−	7.61505i	−0.792313	−	0.352760i
$467$	10.9876	+	12.2030i	0.508446	+	0.564687i	0.941643	−	0.336613i	$-0.109281\pi$
$467$	10.9876	+	12.2030i	0.508446	+	0.564687i	−0.433197	+	0.901299i	$0.642615\pi$
$468$	−4.02734	+	12.3949i	−0.186164	+	0.572954i
$469$		0			0
$470$	−52.1047	−	37.8563i	−2.40341	−	1.74618i
$471$	−2.77553	−	0.589957i	−0.127890	−	0.0271838i
$472$	6.39245	+	11.0720i	0.294236	+	0.509632i
$473$	15.3903	−	2.64175i	0.707645	−	0.121468i
$474$	3.45684	−	5.98741i	0.158778	−	0.275011i
$475$	−1.62652	−	5.00590i	−0.0746297	−	0.229687i
$476$		0			0
$477$	−8.26058	+	6.00167i	−0.378226	+	0.274797i
$478$	−11.6040	−	12.8876i	−0.530756	−	0.589464i
$479$	−24.2496	+	5.15442i	−1.10799	+	0.235511i	−0.725347	−	0.688383i	$-0.758321\pi$
$479$	−24.2496	+	5.15442i	−1.10799	+	0.235511i	−0.382647	+	0.923895i	$0.624987\pi$
$480$	9.18025	+	4.08731i	0.419019	+	0.186559i
$481$	4.06145	−	1.80827i	0.185186	−	0.0824502i
$482$	−6.89342	−	21.2158i	−0.313987	−	0.966352i
$483$		0			0
$484$	12.7143	+	1.00512i	0.577922	+	0.0456875i
$485$	16.1319	−	27.9413i	0.732513	−	1.26875i
$486$	−16.5849	+	18.4194i	−0.752306	+	0.835520i
$487$	1.49833	−	14.2557i	0.0678958	−	0.645985i	−0.906663	−	0.421855i	$-0.861379\pi$
$487$	1.49833	−	14.2557i	0.0678958	−	0.645985i	0.974559	−	0.224130i	$-0.0719542\pi$
$488$	0.154393	+	1.46895i	0.00698905	+	0.0664964i
$489$	−1.53505	+	4.72441i	−0.0694175	+	0.213645i
$490$		0			0
$491$	17.8140	−	12.9426i	0.803935	−	0.584093i	−0.108131	−	0.994137i	$-0.534486\pi$
$491$	17.8140	−	12.9426i	0.803935	−	0.584093i	0.912066	+	0.410044i	$0.134486\pi$
$492$	6.28846	−	2.79980i	0.283506	−	0.126225i
$493$	15.9087	−	17.6684i	0.716492	−	0.795745i
$494$	7.39919	+	12.8158i	0.332905	+	0.576609i
$495$	−15.4181	−	18.5449i	−0.692992	−	0.833530i
$496$	−0.997839			−0.0448043
$497$		0			0
$498$	1.52993	+	1.11156i	0.0685579	+	0.0498103i
$499$	2.64580	+	25.1731i	0.118442	+	1.12690i	0.878731	+	0.477317i	$0.158390\pi$
$499$	2.64580	+	25.1731i	0.118442	+	1.12690i	−0.760289	+	0.649585i	$0.774943\pi$
$500$	7.19954	−	1.53031i	0.321973	−	0.0684375i
$501$	8.10486	−	1.72274i	0.362098	−	0.0769664i
$502$	−2.04214	−	19.4296i	−0.0911451	−	0.867187i
$503$	−21.0518	−	15.2950i	−0.938653	−	0.681971i	0.00944301	−	0.999955i	$-0.496994\pi$
$503$	−21.0518	−	15.2950i	−0.938653	−	0.681971i	−0.948096	+	0.317984i	$0.896994\pi$
$504$		0			0
$505$	−9.47619			−0.421685
$506$	−13.7512	+	21.7859i	−0.611316	+	0.968501i
$507$	1.67918	+	2.90842i	0.0745750	+	0.129168i
$508$	15.1358	−	16.8100i	0.671541	−	0.745822i
$509$	−34.8307	+	15.5076i	−1.54384	+	0.687363i	−0.989448	−	0.144892i	$-0.953717\pi$
$509$	−34.8307	+	15.5076i	−1.54384	+	0.687363i	−0.554394	+	0.832254i	$0.687050\pi$
$510$	6.80200	−	4.94194i	0.301198	−	0.218833i
$511$		0			0
$512$	4.40566	−	13.5592i	0.194704	−	0.599238i
$513$	0.703770	+	6.69592i	0.0310722	+	0.295632i
$514$	0.990821	−	9.42704i	0.0437033	−	0.415809i
$515$	33.7923	−	37.5302i	1.48907	−	1.65378i
$516$	−1.68690	+	2.92180i	−0.0742617	+	0.128625i
$517$	−35.9795	+	24.0316i	−1.58238	+	1.05691i
$518$		0			0
$519$	−3.93083	−	12.0978i	−0.172544	−	0.531036i
$520$	−16.2765	+	7.24675i	−0.713770	+	0.317791i
$521$	23.7905	+	10.5922i	1.04228	+	0.464054i	0.855204	−	0.518291i	$-0.173432\pi$
$521$	23.7905	+	10.5922i	1.04228	+	0.464054i	0.187078	+	0.982345i	$0.440098\pi$
$522$	39.2735	−	8.34785i	1.71896	−	0.365375i
$523$	−12.7958	−	14.2111i	−0.559520	−	0.621410i	0.395315	−	0.918545i	$-0.370635\pi$
$523$	−12.7958	−	14.2111i	−0.559520	−	0.621410i	−0.954835	+	0.297136i	$0.903969\pi$
$524$	−6.47039	+	4.70101i	−0.282660	+	0.205365i
$525$		0			0
$526$	−4.49324	−	13.8288i	−0.195915	−	0.602963i
$527$	−0.276365	+	0.478679i	−0.0120387	+	0.0208516i
$528$	7.11652	−	7.30275i	0.309707	−	0.317812i
$529$	1.95114	+	3.37947i	0.0848322	+	0.146934i
$530$	18.8339	+	4.00326i	0.818091	+	0.173891i
$531$	18.1243	+	13.1681i	0.786527	+	0.571445i
$532$		0			0
$533$	−12.7450	+	39.2252i	−0.552049	+	1.69903i
$534$	−11.2492	−	12.4935i	−0.486799	−	0.540646i
$535$	8.23997	+	3.66867i	0.356245	+	0.158610i
$536$	−0.846055	+	8.04967i	−0.0365440	+	0.347693i
$537$	−2.24594	−	0.477390i	−0.0969196	−	0.0206009i
$538$	−22.8298			−0.984265
$539$		0			0
$540$	11.1815			0.481176
$541$	−10.6482	−	2.26333i	−0.457800	−	0.0973084i	−0.0267612	−	0.999642i	$-0.508519\pi$
$541$	−10.6482	−	2.26333i	−0.457800	−	0.0973084i	−0.431039	+	0.902333i	$0.641853\pi$
$542$	−4.09632	+	38.9739i	−0.175952	+	1.67407i
$543$	2.69418	+	1.19953i	0.115618	+	0.0514767i
$544$	−10.7940	−	11.9879i	−0.462787	−	0.513977i
$545$	10.8927	−	33.5243i	0.466592	−	1.43602i
$546$		0			0
$547$	10.4436	+	7.58775i	0.446538	+	0.324429i	0.788227	−	0.615384i	$-0.210999\pi$
$547$	10.4436	+	7.58775i	0.446538	+	0.324429i	−0.341689	+	0.939813i	$0.610999\pi$
$548$	2.96083	+	0.629343i	0.126480	+	0.0268842i
$549$	1.29411	+	2.24146i	0.0552311	+	0.0956630i
$550$	−2.29897	+	15.8362i	−0.0980285	+	0.675257i
$551$	8.36534	−	14.4892i	0.356376	−	0.617261i
$552$	1.24697	+	3.83777i	0.0530744	+	0.163346i
$553$		0			0
$554$	−34.6230	+	25.1551i	−1.47099	+	1.06874i
$555$	−1.18937	−	1.32093i	−0.0504859	−	0.0560703i
$556$	−1.13563	+	0.241385i	−0.0481614	+	0.0102370i
$557$	−0.696693	−	0.310188i	−0.0295198	−	0.0131431i	0.391924	−	0.919998i	$-0.371810\pi$
$557$	−0.696693	−	0.310188i	−0.0295198	−	0.0131431i	−0.421443	+	0.906855i	$0.638476\pi$
$558$	−0.852738	+	0.379663i	−0.0360993	+	0.0160724i
$559$	−6.24664	−	19.2252i	−0.264205	−	0.813139i
$560$		0			0
$561$	−1.53222	−	5.43651i	−0.0646906	−	0.229530i
$562$	−13.7238	+	23.7703i	−0.578904	+	1.00269i
$563$	14.8735	−	16.5187i	0.626844	−	0.696181i	−0.343158	−	0.939278i	$-0.611497\pi$
$563$	14.8735	−	16.5187i	0.626844	−	0.696181i	0.970002	+	0.243097i	$0.0781634\pi$
$564$	0.977149	−	9.29696i	0.0411454	−	0.391472i
$565$	5.35595	+	50.9585i	0.225327	+	2.14384i
$566$	1.84408	−	5.67551i	0.0775127	−	0.238559i
$567$		0			0
$568$	−2.43805	+	1.77135i	−0.102298	+	0.0743242i
$569$	−18.7397	+	8.34344i	−0.785608	+	0.349775i	−0.760022	−	0.649897i	$-0.774812\pi$
$569$	−18.7397	+	8.34344i	−0.785608	+	0.349775i	−0.0255863	+	0.999673i	$0.508145\pi$
$570$	3.95895	−	4.39686i	0.165822	−	0.184164i
$571$	9.78268	+	16.9441i	0.409393	+	0.709089i	0.994822	−	0.101635i	$-0.0324073\pi$
$571$	9.78268	+	16.9441i	0.409393	+	0.709089i	−0.585429	+	0.810724i	$0.699074\pi$
$572$	−1.07694	−	16.4752i	−0.0450292	−	0.688864i
$573$	0.512448			0.0214078
$574$		0			0
$575$	−9.59677	−	6.97246i	−0.400213	−	0.290772i
$576$	−0.124904	−	1.18838i	−0.00520434	−	0.0495160i
$577$	−19.1439	+	4.06916i	−0.796971	+	0.169401i	−0.588362	−	0.808598i	$-0.700227\pi$
$577$	−19.1439	+	4.06916i	−0.796971	+	0.169401i	−0.208609	+	0.977999i	$0.566894\pi$
$578$	16.3552	−	3.47642i	0.680289	−	0.144600i
$579$	−0.435291	−	4.14152i	−0.0180901	−	0.172116i
$580$	−22.4790	−	16.3319i	−0.933388	−	0.678146i
$581$		0			0
$582$	12.7609			0.528958
$583$	6.90435	−	10.9385i	0.285949	−	0.453025i
$584$	7.44871	+	12.9016i	0.308230	+	0.533870i
$585$	−20.8904	+	23.2011i	−0.863712	+	0.959249i
$586$	−11.1021	+	4.94297i	−0.458623	+	0.204192i
$587$	1.27071	−	0.923224i	0.0524477	−	0.0381055i	−0.561253	−	0.827645i	$-0.689680\pi$
$587$	1.27071	−	0.923224i	0.0524477	−	0.0381055i	0.613700	+	0.789539i	$0.289680\pi$
$588$		0			0
$589$	−0.120195	+	0.369922i	−0.00495254	+	0.0152424i
$590$	−4.41591	−	42.0146i	−0.181800	−	1.72971i
$591$	−0.705557	+	6.71292i	−0.0290227	+	0.276133i
$592$	−3.44674	+	3.82799i	−0.141660	+	0.157330i
$593$	−15.0615	+	26.0873i	−0.618502	+	1.07128i	0.371257	+	0.928530i	$0.378927\pi$
$593$	−15.0615	+	26.0873i	−0.618502	+	1.07128i	−0.989759	+	0.142747i	$0.954407\pi$
$594$	7.08807	−	19.2027i	0.290827	−	0.787896i
$595$		0			0
$596$	−5.33664	−	16.4245i	−0.218597	−	0.672773i
$597$	11.8423	−	5.27253i	0.484673	−	0.215790i
$598$	30.4674	+	13.5650i	1.24591	+	0.554713i
$599$	−5.65166	+	1.20130i	−0.230920	+	0.0490837i	−0.321918	−	0.946767i	$-0.604328\pi$
$599$	−5.65166	+	1.20130i	−0.230920	+	0.0490837i	0.0909979	+	0.995851i	$0.470994\pi$
$600$	1.67714	+	1.86265i	0.0684689	+	0.0760425i
$601$	36.8625	−	26.7822i	1.50365	−	1.09247i	0.534754	−	0.845008i	$-0.320404\pi$
$601$	36.8625	−	26.7822i	1.50365	−	1.09247i	0.968898	−	0.247460i	$-0.0795958\pi$
$602$		0			0
$603$	4.38281	+	13.4889i	0.178482	+	0.549310i
$604$	−9.16232	+	15.8696i	−0.372809	+	0.645725i
$605$	26.8448	+	14.5877i	1.09140	+	0.593076i
$606$	−1.87400	−	3.24587i	−0.0761262	−	0.131854i
$607$	33.9623	+	7.21891i	1.37849	+	0.293007i	0.836770	−	0.547554i	$-0.184441\pi$
$607$	33.9623	+	7.21891i	1.37849	+	0.293007i	0.541718	+	0.840561i	$0.317774\pi$
$608$	−9.18369	−	6.67234i	−0.372448	−	0.270599i
$609$		0			0
$610$	1.50822	−	4.64182i	0.0610660	−	0.187942i
$611$	37.4785	+	41.6241i	1.51622	+	1.68393i
$612$	−7.64129	−	3.40212i	−0.308881	−	0.137523i
$613$	2.52355	−	24.0100i	0.101925	−	0.969755i	−0.817350	−	0.576141i	$-0.804558\pi$
$613$	2.52355	−	24.0100i	0.101925	−	0.969755i	0.919276	−	0.393614i	$-0.128775\pi$
$614$	−20.5108	−	4.35971i	−0.827750	−	0.175944i
$615$	16.4897			0.664931
$616$		0			0
$617$	−13.4967			−0.543358			−0.271679	−	0.962388i	$-0.587579\pi$
$617$	−13.4967			−0.543358			−0.271679	+	0.962388i	$0.587579\pi$
$618$	19.5379	+	4.15291i	0.785930	+	0.167055i
$619$	−4.54549	+	43.2474i	−0.182699	+	1.73826i	0.392062	+	0.919939i	$0.371762\pi$
$619$	−4.54549	+	43.2474i	−0.182699	+	1.73826i	−0.574761	+	0.818321i	$0.694905\pi$
$620$	0.590117	+	0.262737i	0.0236997	+	0.0105518i
$621$	10.1531	+	11.2762i	0.407430	+	0.452496i
$622$	−13.9042	+	42.7928i	−0.557509	+	1.71584i
$623$		0			0
$624$	−10.6791	−	7.75883i	−0.427507	−	0.310602i
$625$	30.5221	+	6.48768i	1.22089	+	0.259507i
$626$	−17.4676	−	30.2548i	−0.698147	−	1.20923i
$627$	−1.85008	−	3.51791i	−0.0738849	−	0.140492i
$628$	2.66165	−	4.61011i	0.106211	−	0.183964i
$629$	0.881726	+	2.71367i	0.0351567	+	0.108201i
$630$		0			0
$631$	−5.19398	+	3.77365i	−0.206769	+	0.150227i	−0.686351	−	0.727271i	$-0.740788\pi$
$631$	−5.19398	+	3.77365i	−0.206769	+	0.150227i	0.479581	+	0.877497i	$0.340788\pi$
$632$	−6.29174	−	6.98768i	−0.250272	−	0.277955i
$633$	−3.64144	+	0.774012i	−0.144734	+	0.0307642i
$634$	5.86287	+	2.61032i	0.232844	+	0.103669i
$635$	49.5021	−	22.0397i	1.96443	−	0.874620i
$636$	0.863624	+	2.65796i	0.0342449	+	0.105395i
$637$		0			0
$638$	−42.2974	+	28.2515i	−1.67457	+	1.11849i
$639$	−2.64035	+	4.57322i	−0.104451	+	0.180914i
$640$	20.2519	−	22.4920i	0.800528	−	0.889076i
$641$	0.668564	−	6.36096i	0.0264067	−	0.251243i	−0.973353	−	0.229313i	$-0.926352\pi$
$641$	0.668564	−	6.36096i	0.0264067	−	0.251243i	0.999760	−	0.0219302i	$-0.00698116\pi$
$642$	0.372903	+	3.54794i	0.0147173	+	0.140026i
$643$	−0.201683	+	0.620716i	−0.00795360	+	0.0244787i	−0.954955	−	0.296752i	$-0.904097\pi$
$643$	−0.201683	+	0.620716i	−0.00795360	+	0.0244787i	0.947001	+	0.321231i	$0.104097\pi$
$644$		0			0
$645$	−6.53848	+	4.75048i	−0.257452	+	0.187050i
$646$	−8.67650	+	3.86303i	−0.341372	+	0.151989i
$647$	−12.0190	+	13.3485i	−0.472516	+	0.524783i	−0.931539	−	0.363642i	$-0.881533\pi$
$647$	−12.0190	+	13.3485i	−0.472516	+	0.524783i	0.459022	+	0.888425i	$0.348200\pi$
$648$	4.26421	+	7.38583i	0.167514	+	0.290143i
$649$	−27.5063	−	6.99085i	−1.07972	−	0.274415i
$650$	20.7153			0.812522
$651$		0			0
$652$	−7.53943	−	5.47771i	−0.295267	−	0.214524i
$653$	1.76842	+	16.8254i	0.0692036	+	0.658428i	0.973054	+	0.230579i	$0.0740620\pi$
$653$	1.76842	+	16.8254i	0.0692036	+	0.658428i	−0.903850	+	0.427849i	$0.859271\pi$
$654$	13.6372	−	2.89867i	0.533255	−	0.113347i
$655$	−18.7403	+	3.98337i	−0.732244	+	0.155643i
$656$	−4.99506	−	47.5248i	−0.195024	−	1.85553i
$657$	21.1191	+	15.3439i	0.823934	+	0.598623i
$658$		0			0
$659$	23.6249			0.920297			0.460148	−	0.887842i	$-0.347796\pi$
$659$	23.6249			0.920297			0.460148	+	0.887842i	$0.347796\pi$
$660$	−6.13154	+	2.44499i	−0.238670	+	0.0951711i
$661$	−10.4910	−	18.1709i	−0.408051	−	0.706766i	0.586620	−	0.809862i	$-0.300458\pi$
$661$	−10.4910	−	18.1709i	−0.408051	−	0.706766i	−0.994671	+	0.103097i	$0.967125\pi$
$662$	−31.5581	+	35.0488i	−1.22654	+	1.36221i
$663$	−6.67976	+	2.97402i	−0.259420	+	0.115501i
$664$	2.08077	−	1.51177i	0.0807494	−	0.0586679i
$665$		0			0
$666$	−1.48904	+	4.58278i	−0.0576990	+	0.177579i
$667$	−3.94130	−	37.4990i	−0.152608	−	1.45197i
$668$	−1.62486	+	15.4595i	−0.0628676	+	0.598146i
$669$	−1.91268	+	2.12424i	−0.0739484	+	0.0821280i
$670$	13.3728	−	23.1623i	0.516636	−	0.894840i
$671$	−2.57458	−	2.03036i	−0.0993904	−	0.0783813i
$672$		0			0
$673$	3.73868	+	11.5065i	0.144116	+	0.443542i	0.996896	−	0.0787272i	$-0.0250856\pi$
$673$	3.73868	+	11.5065i	0.144116	+	0.443542i	−0.852781	+	0.522269i	$0.825086\pi$
$674$	−1.11390	+	0.495941i	−0.0429059	+	0.0191029i
$675$	8.61001	+	3.83342i	0.331399	+	0.147549i
$676$	−6.16270	+	1.30992i	−0.237027	+	0.0503816i
$677$	6.30982	+	7.00776i	0.242506	+	0.269330i	0.852095	−	0.523388i	$-0.175332\pi$
$677$	6.30982	+	7.00776i	0.242506	+	0.269330i	−0.609589	+	0.792718i	$0.708665\pi$
$678$	−16.3956	+	11.9121i	−0.629668	+	0.457480i
$679$		0			0
$680$	−3.53356	−	10.8752i	−0.135506	−	0.417044i
$681$	−5.34610	+	9.25971i	−0.204863	+	0.354833i
$682$	0.825296	−	0.846893i	0.0316022	−	0.0324292i
$683$	7.64930	+	13.2490i	0.292692	+	0.506958i	0.974445	−	0.224624i	$-0.0721155\pi$
$683$	7.64930	+	13.2490i	0.292692	+	0.506958i	−0.681753	+	0.731582i	$0.738782\pi$
$684$	−5.75746	−	1.22379i	−0.220142	−	0.0467926i
$685$	5.86632	+	4.26213i	0.224141	+	0.162848i
$686$		0			0
$687$	−0.845314	+	2.60161i	−0.0322507	+	0.0992575i
$688$	15.6719	+	17.4054i	0.597486	+	0.663576i
$689$	−15.2974	−	6.81083i	−0.582784	−	0.259472i
$690$	1.39378	−	13.2610i	0.0530604	−	0.504836i
$691$	22.3206	+	4.74439i	0.849116	+	0.180485i	0.611864	−	0.790963i	$-0.290420\pi$
$691$	22.3206	+	4.74439i	0.849116	+	0.180485i	0.237252	+	0.971448i	$0.423753\pi$
$692$	23.8639			0.907169
$693$		0			0
$694$	38.2256			1.45102
$695$	−2.72042	−	0.578243i	−0.103191	−	0.0219340i
$696$	−0.832781	+	7.92338i	−0.0315665	+	0.300335i
$697$	−24.1818	−	10.7664i	−0.915953	−	0.407808i
$698$	−23.1247	−	25.6826i	−0.875285	−	0.972102i
$699$	2.01163	−	6.19117i	0.0760869	−	0.234171i
$700$		0			0
$701$	26.1508	+	18.9997i	0.987702	+	0.717607i	0.959417	−	0.281992i	$-0.0909953\pi$
$701$	26.1508	+	18.9997i	0.987702	+	0.717607i	0.0282853	+	0.999600i	$0.490995\pi$
$702$	−25.9189	−	5.50922i	−0.978244	−	0.207932i
$703$	1.00395	+	1.73889i	0.0378646	+	0.0655834i
$704$	0.704604	+	1.33980i	0.0265558	+	0.0504957i
$705$	11.1969	−	19.3935i	0.421698	−	0.730402i
$706$	11.4967	+	35.3831i	0.432683	+	1.33166i
$707$		0			0
$708$	4.96078	−	3.60422i	0.186438	−	0.135455i
$709$	9.74239	+	10.8200i	0.365883	+	0.406354i	0.897772	−	0.440460i	$-0.145184\pi$
$709$	9.74239	+	10.8200i	0.365883	+	0.406354i	−0.531889	+	0.846814i	$0.678518\pi$
$710$	9.74043	−	2.07039i	0.365552	−	0.0777004i
$711$	−15.0521	−	6.70161i	−0.564496	−	0.251330i
$712$	−20.8877	+	9.29981i	−0.782800	+	0.348525i
$713$	0.270880	+	0.833684i	0.0101446	+	0.0312217i
$714$		0			0
$715$	13.6958	−	37.1040i	0.512193	−	1.38761i
$716$	2.15379	−	3.73048i	0.0804910	−	0.139415i
$717$	4.03474	−	4.48103i	0.150680	−	0.167347i
$718$	−1.81548	+	17.2731i	−0.0677531	+	0.644628i
$719$	4.68917	+	44.6144i	0.174876	+	1.66384i	0.632401	+	0.774641i	$0.282069\pi$
$719$	4.68917	+	44.6144i	0.174876	+	1.66384i	−0.457525	+	0.889197i	$0.651264\pi$
$720$	11.1780	−	34.4024i	0.416581	−	1.28210i
$721$		0			0
$722$	21.9152	−	15.9223i	0.815600	−	0.592568i
$723$	7.08581	−	3.15480i	0.263524	−	0.117328i
$724$	−3.70210	+	4.11159i	−0.137587	+	0.152806i
$725$	−11.7101	−	20.2825i	−0.434903	−	0.753274i
$726$	0.312084	+	12.0800i	0.0115825	+	0.448330i
$727$	−28.3582			−1.05175			−0.525874	−	0.850562i	$-0.676262\pi$
$727$	−28.3582			−1.05175			−0.525874	+	0.850562i	$0.676262\pi$
$728$		0			0
$729$	6.88197	+	5.00004i	0.254888	+	0.185187i
$730$	−5.14558	−	48.9569i	−0.190446	−	1.81198i
$731$	12.6902	−	2.69739i	0.469365	−	0.0997665i
$732$	0.692936	−	0.147288i	0.0256117	−	0.00544393i
$733$	0.654030	+	6.22268i	0.0241572	+	0.229840i	0.999938	+	0.0110917i	$0.00353068\pi$
$733$	0.654030	+	6.22268i	0.0241572	+	0.229840i	−0.975781	+	0.218748i	$0.929803\pi$
$734$	14.2359	+	10.3430i	0.525456	+	0.381766i
$735$		0			0
$736$	−25.5830			−0.943001
$737$	−11.4868	−	13.8163i	−0.423121	−	0.508929i
$738$	−22.3512	−	38.7134i	−0.822759	−	1.42506i
$739$	6.25771	−	6.94990i	0.230194	−	0.255656i	−0.616972	−	0.786985i	$-0.711641\pi$
$739$	6.25771	−	6.94990i	0.230194	−	0.255656i	0.847165	+	0.531329i	$0.178307\pi$
$740$	3.04632	−	1.35631i	0.111985	−	0.0498589i
$741$	−4.16273	+	3.02440i	−0.152922	+	0.111104i
$742$		0			0
$743$	7.78926	−	23.9729i	0.285760	−	0.879480i	−0.700409	−	0.713741i	$-0.746999\pi$
$743$	7.78926	−	23.9729i	0.285760	−	0.879480i	0.986170	−	0.165739i	$-0.0530008\pi$
$744$	−0.0193607	−	0.184205i	−0.000709797	−	0.00675327i
$745$	4.32434	−	41.1433i	0.158431	−	1.50737i
$746$	−5.08425	+	5.64663i	−0.186148	+	0.206738i
$747$	2.25342	−	3.90304i	0.0824483	−	0.142805i
$748$	10.5881	+	0.417870i	0.387141	+	0.0152788i
$749$		0			0
$750$	2.15501	+	6.63243i	0.0786897	+	0.242182i
$751$	−31.7450	+	14.1338i	−1.15839	+	0.515750i	−0.893736	−	0.448593i	$-0.851925\pi$
$751$	−31.7450	+	14.1338i	−1.15839	+	0.515750i	−0.264657	+	0.964343i	$0.585259\pi$
$752$	−59.2855	−	26.3956i	−2.16192	−	0.962548i
$753$	6.64449	−	1.41233i	0.242139	−	0.0514681i
$754$	44.0596	+	48.9331i	1.60456	+	1.78204i
$755$	−35.5134	+	25.8020i	−1.29247	+	0.939031i
$756$		0			0
$757$	10.7526	+	33.0930i	0.390808	+	1.20278i	0.932178	+	0.362000i	$0.117906\pi$
$757$	10.7526	+	33.0930i	0.390808	+	1.20278i	−0.541370	+	0.840784i	$0.682094\pi$
$758$	−3.84465	+	6.65912i	−0.139644	+	0.241870i
$759$	−8.03328	−	3.96333i	−0.291589	−	0.143860i
$760$	−4.02337	−	6.96868i	−0.145943	−	0.252781i
$761$	−11.9583	−	2.54181i	−0.433488	−	0.0921407i	−0.0140008	−	0.999902i	$-0.504457\pi$
$761$	−11.9583	−	2.54181i	−0.433488	−	0.0921407i	−0.419487	+	0.907761i	$0.637790\pi$
$762$	17.3387	+	12.5973i	0.628116	+	0.456353i
$763$		0			0
$764$	−0.297079	+	0.914315i	−0.0107479	+	0.0330788i
$765$	−13.4075	−	14.8905i	−0.484748	−	0.538368i
$766$	2.14684	+	0.955836i	0.0775686	+	0.0345358i
$767$	−3.84036	+	36.5386i	−0.138667	+	1.31933i
$768$	12.2610	+	2.60616i	0.442431	+	0.0940417i
$769$	2.61946			0.0944603			0.0472301	−	0.998884i	$-0.484961\pi$
$769$	2.61946			0.0944603			0.0472301	+	0.998884i	$0.484961\pi$
$770$		0			0
$771$	3.29585			0.118697
$772$	7.64169	+	1.62429i	0.275030	+	0.0584595i
$773$	−0.0222441	+	0.211639i	−0.000800066	+	0.00761212i	−0.994915	−	0.100722i	$-0.967885\pi$
$773$	−0.0222441	+	0.211639i	−0.000800066	+	0.00761212i	0.994115	+	0.108334i	$0.0345515\pi$
$774$	20.0155	+	8.91148i	0.719442	+	0.320316i
$775$	0.364328	+	0.404627i	0.0130870	+	0.0145346i
$776$	5.36310	−	16.5059i	0.192524	−	0.592529i
$777$		0			0
$778$	55.3767	+	40.2336i	1.98535	+	1.44244i
$779$	−18.2202	−	3.87283i	−0.652807	−	0.138758i
$780$	4.27263	+	7.40041i	0.152985	+	0.264977i
$781$	0.961097	−	6.62039i	0.0343908	−	0.236896i
$782$	−10.7023	+	18.5369i	−0.382712	+	0.662877i
$783$	9.25750	+	28.4917i	0.330836	+	1.01821i
$784$		0			0
$785$	10.3166	−	7.49547i	0.368216	−	0.267525i
$786$	−5.07049	−	5.63134i	−0.180858	−	0.200863i
$787$	28.5008	−	6.05803i	1.01594	−	0.215946i	0.330295	−	0.943878i	$-0.392852\pi$
$787$	28.5008	−	6.05803i	1.01594	−	0.215946i	0.685649	+	0.727932i	$0.259519\pi$
$788$	−11.5682	−	5.15051i	−0.412101	−	0.183479i
$789$	4.61864	−	2.05635i	0.164428	−	0.0732080i
$790$	9.60131	+	29.5498i	0.341599	+	1.05133i
$791$		0			0
$792$	−10.1865	−	8.03330i	−0.361962	−	0.285451i
$793$	−2.12228	+	3.67590i	−0.0753645	+	0.130535i
$794$	0.487771	−	0.541724i	0.0173103	−	0.0192251i
$795$	−0.699804	+	6.65819i	−0.0248195	+	0.236142i
$796$	2.54203	+	24.1858i	0.0900997	+	0.857241i
$797$	−9.95913	+	30.6510i	−0.352770	+	1.08572i	0.604521	+	0.796589i	$0.293365\pi$
$797$	−9.95913	+	30.6510i	−0.352770	+	1.08572i	−0.957291	+	0.289126i	$0.906635\pi$
$798$		0			0
$799$	−29.0823	+	21.1295i	−1.02886	+	0.747509i
$800$	−14.5167	+	6.46324i	−0.513242	+	0.228510i
$801$	−26.8088	+	29.7742i	−0.947243	+	1.05202i
$802$	1.39252	+	2.41191i	0.0491715	+	0.0851675i
$803$	−32.0514	−	8.14599i	−1.13107	−	0.287466i
$804$	3.88203			0.136909
$805$		0			0
$806$	−1.23845	−	0.899783i	−0.0436224	−	0.0316935i
$807$	−0.829744	−	7.89449i	−0.0292084	−	0.277899i
$808$	−4.98604	+	1.05982i	−0.175408	+	0.0372842i
$809$	28.7048	−	6.10140i	1.00921	−	0.214514i	0.326493	−	0.945199i	$-0.394133\pi$
$809$	28.7048	−	6.10140i	1.00921	−	0.214514i	0.682714	+	0.730686i	$0.260800\pi$
$810$	−2.94572	−	28.0267i	−0.103502	−	0.984756i
$811$	0.840891	+	0.610943i	0.0295277	+	0.0214531i	0.602451	−	0.798156i	$-0.294191\pi$
$811$	0.840891	+	0.610943i	0.0295277	+	0.0214531i	−0.572924	+	0.819609i	$0.694191\pi$
$812$		0			0
$813$	−13.6259			−0.477882
$814$	−0.398179	−	6.09141i	−0.0139562	−	0.213504i
$815$	−11.1622	−	19.3335i	−0.390995	−	0.677224i
$816$	5.66877	−	6.29580i	0.198447	−	0.220397i
$817$	8.34036	−	3.71337i	0.291792	−	0.129914i
$818$	−9.74762	+	7.08206i	−0.340817	+	0.247618i
$819$		0			0
$820$	−9.55952	+	29.4212i	−0.333833	+	1.02743i
$821$	−2.98244	−	28.3760i	−0.104088	−	0.990330i	−0.914532	−	0.404514i	$-0.867441\pi$
$821$	−2.98244	−	28.3760i	−0.104088	−	0.990330i	0.810444	−	0.585816i	$-0.199226\pi$
$822$	−0.299784	+	2.85226i	−0.0104562	+	0.0994839i
$823$	17.8375	−	19.8105i	0.621774	−	0.690550i	−0.347178	−	0.937799i	$-0.612860\pi$
$823$	17.8375	−	19.8105i	0.621774	−	0.690550i	0.968952	+	0.247249i	$0.0795265\pi$
$824$	13.5830	−	23.5264i	0.473185	−	0.819581i
$825$	−5.55965	−	0.219416i	−0.193562	−	0.00763909i
$826$		0			0
$827$	0.531399	+	1.63548i	0.0184785	+	0.0568711i	0.959871	−	0.280443i	$-0.0904815\pi$
$827$	0.531399	+	1.63548i	0.0184785	+	0.0568711i	−0.941392	+	0.337314i	$0.890481\pi$
$828$	−12.1185	+	5.39550i	−0.421146	+	0.187506i
$829$	−25.5432	−	11.3725i	−0.887150	−	0.394985i	−0.0880033	−	0.996120i	$-0.528049\pi$
$829$	−25.5432	−	11.3725i	−0.887150	−	0.394985i	−0.799147	+	0.601135i	$0.794715\pi$
$830$	−8.31301	+	1.76699i	−0.288549	+	0.0613330i
$831$	−9.95692	−	11.0583i	−0.345402	−	0.383607i
$832$	1.58538	−	1.15185i	0.0549632	−	0.0399331i
$833$		0			0
$834$	−0.339923	−	1.04617i	−0.0117706	−	0.0362261i
$835$	−18.6187	+	32.2486i	−0.644328	+	1.11601i
$836$	7.34923	−	1.26150i	0.254179	−	0.0436300i
$837$	−0.348234	−	0.603159i	−0.0120367	−	0.0208482i
$838$	49.9370	+	10.6144i	1.72504	+	0.366670i
$839$	29.0133	+	21.0794i	1.00165	+	0.727742i	0.962441	−	0.271489i	$-0.0875162\pi$
$839$	29.0133	+	21.0794i	1.00165	+	0.727742i	0.0392091	+	0.999231i	$0.487516\pi$
$840$		0			0
$841$	14.0429	−	43.2197i	0.484240	−	1.49034i
$842$	14.5407	+	16.1491i	0.501107	+	0.556535i
$843$	−8.71849	−	3.88172i	−0.300281	−	0.133694i
$844$	0.730035	−	6.94581i	0.0251288	−	0.239085i
$845$	−14.7629	−	3.13794i	−0.507858	−	0.107949i
$846$	−60.7076			−2.08717
$847$		0			0
$848$	19.4014			0.666248
$849$	2.02960	+	0.431404i	0.0696555	+	0.0148057i
$850$	−1.38972	+	13.2223i	−0.0476669	+	0.453520i
$851$	4.13393	+	1.84054i	0.141709	+	0.0630930i
$852$	0.967145	+	1.07412i	0.0331339	+	0.0367989i
$853$	4.67937	−	14.4016i	0.160218	−	0.493102i	−0.838434	−	0.545004i	$-0.816528\pi$
$853$	4.67937	−	14.4016i	0.160218	−	0.493102i	0.998652	+	0.0519019i	$0.0165283\pi$
$854$		0			0
$855$	−11.4073	−	8.28790i	−0.390122	−	0.283440i
$856$	4.74589	+	1.00877i	0.162211	+	0.0344790i
$857$	12.6633	+	21.9335i	0.432571	+	0.749235i	0.997094	−	0.0761824i	$-0.0242731\pi$
$857$	12.6633	+	21.9335i	0.432571	+	0.749235i	−0.564523	+	0.825417i	$0.690940\pi$
$858$	15.4176	−	2.64645i	0.526350	−	0.0903483i
$859$	20.7646	−	35.9653i	0.708478	−	1.22712i	−0.256943	−	0.966426i	$-0.582715\pi$
$859$	20.7646	−	35.9653i	0.708478	−	1.22712i	0.965422	−	0.260694i	$-0.0839513\pi$
$860$	−4.68534	−	14.4200i	−0.159769	−	0.491718i
$861$		0			0
$862$	−5.30813	+	3.85658i	−0.180796	+	0.131356i
$863$	−16.0928	−	17.8729i	−0.547807	−	0.608401i	0.404128	−	0.914702i	$-0.367575\pi$
$863$	−16.0928	−	17.8729i	−0.547807	−	0.608401i	−0.951935	+	0.306302i	$0.900908\pi$
$864$	19.8821	−	4.22606i	0.676401	−	0.143774i
$865$	52.2241	+	23.2517i	1.77567	+	0.790580i
$866$	−47.2122	+	21.0202i	−1.60433	+	0.714296i
$867$	1.79656	+	5.52924i	0.0610144	+	0.187783i
$868$		0			0
$869$	20.8569	+	0.823133i	0.707521	+	0.0279229i
$870$	13.1630	−	22.7990i	0.446267	−	0.772957i
$871$	−15.5638	+	17.2853i	−0.527358	+	0.585690i
$872$	1.98201	−	18.8575i	0.0671192	−	0.638596i
$873$	−3.17888	−	30.2451i	−0.107589	−	1.02364i
$874$	−4.65455	+	14.3252i	−0.157443	+	0.484559i
$875$		0			0
$876$	5.78049	−	4.19977i	0.195304	−	0.141897i
$877$	30.8826	−	13.7498i	1.04283	−	0.464298i	0.187437	−	0.982277i	$-0.439982\pi$
$877$	30.8826	−	13.7498i	1.04283	−	0.464298i	0.855394	+	0.517978i	$0.173315\pi$
$878$	16.8911	−	18.7594i	0.570046	−	0.633100i
$879$	−2.11277	−	3.65942i	−0.0712618	−	0.123429i
$880$	2.98909	+	45.7276i	0.100762	+	1.54148i
$881$	36.8296			1.24082			0.620410	−	0.784278i	$-0.286966\pi$
$881$	36.8296			1.24082			0.620410	+	0.784278i	$0.286966\pi$
$882$		0			0
$883$	−43.2099	−	31.3938i	−1.45413	−	1.05649i	−0.984845	−	0.173438i	$-0.944512\pi$
$883$	−43.2099	−	31.3938i	−1.45413	−	1.05649i	−0.469283	−	0.883048i	$-0.655488\pi$
$884$	−1.43385	−	13.6422i	−0.0482257	−	0.458837i
$885$	14.3680	−	3.05401i	0.482975	−	0.102660i
$886$	−47.3529	+	10.0652i	−1.59085	+	0.338146i
$887$	1.19806	+	11.3988i	0.0402270	+	0.382735i	0.996050	+	0.0887922i	$0.0283007\pi$
$887$	1.19806	+	11.3988i	0.0402270	+	0.382735i	−0.955823	+	0.293942i	$0.905033\pi$
$888$	−0.773537	−	0.562007i	−0.0259582	−	0.0188597i
$889$		0			0
$890$	75.5525			2.53253
$891$	−18.3486	−	4.66339i	−0.614702	−	0.156229i
$892$	−2.68127	−	4.64410i	−0.0897756	−	0.155496i
$893$	−16.9267	+	18.7990i	−0.566430	+	0.629084i
$894$	14.9480	−	6.65526i	0.499934	−	0.222585i
$895$	8.34817	−	6.06530i	0.279048	−	0.202741i
$896$		0			0
$897$	−3.58339	+	11.0286i	−0.119646	+	0.368233i
$898$	7.78788	+	74.0967i	0.259885	+	2.47264i
$899$	−0.180906	+	1.72121i	−0.00603356	+	0.0574055i
$900$	−5.51334	+	6.12319i	−0.183778	+	0.204106i
$901$	5.37350	−	9.30717i	0.179017	−	0.310067i
$902$	44.4669	+	35.0675i	1.48059	+	1.16762i
$903$		0			0
$904$	8.51730	+	26.2136i	0.283281	+	0.871850i
$905$	−12.1078	+	5.39075i	−0.402478	+	0.179195i
$906$	−15.8610	−	7.06179i	−0.526948	−	0.234612i
$907$	−55.8113	+	11.8631i	−1.85318	+	0.393906i	−0.993201	−	0.116415i	$-0.962860\pi$
$907$	−55.8113	+	11.8631i	−1.85318	+	0.393906i	−0.859984	+	0.510322i	$0.829526\pi$
$908$	−13.4220	−	14.9066i	−0.445425	−	0.494695i
$909$	−7.22628	+	5.25020i	−0.239681	+	0.174138i
$910$		0			0
$911$	2.06289	+	6.34893i	0.0683467	+	0.210350i	0.979396	−	0.201947i	$-0.0647268\pi$
$911$	2.06289	+	6.34893i	0.0683467	+	0.210350i	−0.911050	+	0.412296i	$0.864727\pi$
$912$	2.98083	−	5.16295i	0.0987052	−	0.170962i
$913$	−0.820253	+	5.65021i	−0.0271464	+	0.186994i
$914$	−17.3284	−	30.0137i	−0.573173	−	0.992765i
$915$	1.65994	+	0.352831i	0.0548760	+	0.0116642i
$916$	−4.15177	−	3.01643i	−0.137178	−	0.0996658i
$917$		0			0
$918$	5.25526	−	16.1740i	0.173449	−	0.533822i
$919$	−19.4944	−	21.6507i	−0.643060	−	0.714191i	0.330196	−	0.943912i	$-0.392885\pi$
$919$	−19.4944	−	21.6507i	−0.643060	−	0.714191i	−0.973256	+	0.229722i	$0.926218\pi$
$920$	−16.5669	−	7.37607i	−0.546195	−	0.243182i
$921$	0.762114	−	7.25103i	0.0251125	−	0.238930i
$922$	21.2551	+	4.51790i	0.699998	+	0.148789i
$923$	−8.66015			−0.285052
$924$		0			0
$925$	2.81073			0.0924161
$926$	−24.0888	−	5.12023i	−0.791607	−	0.168261i
$927$	4.97583	−	47.3418i	0.163428	−	1.55491i
$928$	−46.1429	−	20.5442i	−1.51472	−	0.674395i
$929$	−1.56892	−	1.74246i	−0.0514747	−	0.0571684i	0.716858	−	0.697220i	$-0.245580\pi$
$929$	−1.56892	−	1.74246i	−0.0514747	−	0.0571684i	−0.768332	+	0.640051i	$0.778913\pi$
$930$	−0.189128	+	0.582077i	−0.00620176	+	0.0190871i
$931$		0			0
$932$	9.88015	+	7.17835i	0.323635	+	0.235135i
$933$	−15.3030	−	3.25275i	−0.500997	−	0.106490i
$934$	−14.5938	−	25.2772i	−0.477524	−	0.827095i
$935$	22.7641	+	11.2310i	0.744466	+	0.367292i
$936$	−8.39699	+	14.5440i	−0.274464	+	0.475386i
$937$	−2.71558	−	8.35769i	−0.0887141	−	0.273034i	0.896850	−	0.442334i	$-0.145849\pi$
$937$	−2.71558	−	8.35769i	−0.0887141	−	0.273034i	−0.985565	+	0.169300i	$0.945849\pi$
$938$		0			0
$939$	9.82717	−	7.13986i	0.320698	−	0.233000i
$940$	28.1110	+	31.2204i	0.916880	+	1.01830i
$941$	8.69447	−	1.84807i	0.283432	−	0.0602452i	−0.0640022	−	0.997950i	$-0.520386\pi$
$941$	8.69447	−	1.84807i	0.283432	−	0.0602452i	0.347434	+	0.937705i	$0.387053\pi$
$942$	4.60762	+	2.05145i	0.150124	+	0.0668397i
$943$	−38.3505	+	17.0747i	−1.24886	+	0.556030i
$944$	−13.1543	−	40.4847i	−0.428135	−	1.31766i
$945$		0			0
$946$	−27.7344	−	1.09456i	−0.901724	−	0.0355873i
$947$	3.93137	−	6.80934i	0.127752	−	0.221274i	−0.795053	−	0.606540i	$-0.792557\pi$
$947$	3.93137	−	6.80934i	0.127752	−	0.221274i	0.922805	+	0.385266i	$0.125890\pi$
$948$	−3.01763	+	3.35142i	−0.0980081	+	0.108849i
$949$	−4.47493	+	42.5761i	−0.145262	+	1.38208i
$950$	0.977949	+	9.30457i	0.0317289	+	0.301880i
$951$	−0.689556	+	2.12223i	−0.0223604	+	0.0688182i
$952$		0			0
$953$	14.1290	−	10.2653i	0.457683	−	0.332526i	−0.334939	−	0.942240i	$-0.608716\pi$
$953$	14.1290	−	10.2653i	0.457683	−	0.332526i	0.792622	+	0.609714i	$0.208716\pi$
$954$	16.5802	−	7.38197i	0.536803	−	0.239000i
$955$	−1.54099	+	1.71144i	−0.0498653	+	0.0553810i
$956$	5.65606	+	9.79659i	0.182930	+	0.316844i
$957$	−11.3066	−	13.5995i	−0.365489	−	0.439610i
$958$	44.0663			1.42372
$959$		0			0
$960$	−0.633854	−	0.460522i	−0.0204575	−	0.0148633i
$961$	3.23618	+	30.7902i	0.104393	+	0.993231i
$962$	−7.72967	+	1.64299i	−0.249215	+	0.0529722i
$963$	8.31617	−	1.76766i	0.267985	−	0.0569619i
$964$	1.52102	+	14.4715i	0.0489886	+	0.466095i
$965$	15.1406	+	11.0003i	0.487392	+	0.354111i
$966$		0			0
$967$	−45.6122			−1.46679			−0.733395	−	0.679802i	$-0.762066\pi$
$967$	−45.6122			−1.46679			−0.733395	+	0.679802i	$0.762066\pi$
$968$	15.7563	+	4.67324i	0.506426	+	0.150204i
$969$	−1.65117	−	2.85990i	−0.0530431	−	0.0918734i
$970$	−38.3736	+	42.6182i	−1.23210	+	1.36839i
$971$	−2.17769	+	0.969572i	−0.0698855	+	0.0311150i	−0.441382	−	0.897319i	$-0.645512\pi$
$971$	−2.17769	+	0.969572i	−0.0698855	+	0.0311150i	0.371496	+	0.928434i	$0.378845\pi$
$972$	13.0799	−	9.50313i	0.419539	−	0.304813i
$973$		0			0
$974$	−7.87338	+	24.2318i	−0.252279	+	0.776436i
$975$	0.752892	+	7.16329i	0.0241118	+	0.229409i
$976$	0.514061	−	4.89097i	0.0164547	−	0.156556i
$977$	−12.8916	+	14.3176i	−0.412439	+	0.458060i	−0.913191	−	0.407531i	$-0.866390\pi$
$977$	−12.8916	+	14.3176i	−0.412439	+	0.458060i	0.500753	+	0.865590i	$0.333057\pi$
$978$	4.41486	−	7.64676i	0.141172	−	0.244516i
$979$	17.5759	−	47.6158i	0.561728	−	1.52181i
$980$		0			0
$981$	−10.2674	−	31.5997i	−0.327812	−	1.00890i
$982$	−35.7553	+	15.9193i	−1.14100	+	0.508004i
$983$	14.8228	+	6.59956i	0.472775	+	0.210493i	0.629272	−	0.777185i	$-0.283353\pi$
$983$	14.8228	+	6.59956i	0.472775	+	0.210493i	−0.156496	+	0.987679i	$0.550020\pi$
$984$	8.67633	−	1.84421i	0.276591	−	0.0587913i
$985$	−20.2977	−	22.5429i	−0.646739	−	0.718277i
$986$	−34.1891	+	24.8398i	−1.08880	+	0.791061i
$987$		0			0
$988$	−2.98293	−	9.18051i	−0.0948996	−	0.292071i
$989$	10.2876	−	17.8187i	0.327128	−	0.566603i
$990$	19.9531	+	37.9408i	0.634152	+	1.20584i
$991$	25.2607	+	43.7528i	0.802433	+	1.38985i	0.918011	+	0.396556i	$0.129795\pi$
$991$	25.2607	+	43.7528i	0.802433	+	1.38985i	−0.115578	+	0.993298i	$0.536872\pi$
$992$	1.14860	+	0.244143i	0.0364681	+	0.00775154i
$993$	−13.2667	−	9.63884i	−0.421007	−	0.305879i
$994$		0			0
$995$	−18.0023	+	55.4053i	−0.570710	+	1.75647i
$996$	−0.825414	−	0.916716i	−0.0261543	−	0.0290472i
$997$	41.1284	+	18.3115i	1.30255	+	0.579932i	0.936501	−	0.350664i	$-0.114044\pi$
$997$	41.1284	+	18.3115i	1.30255	+	0.579932i	0.366048	+	0.930596i	$0.380711\pi$
$998$	4.70286	−	44.7447i	0.148866	−	1.41637i
$999$	−3.51676	−	0.747511i	−0.111265	−	0.0236502i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.q.b.324.1		16
7.2	even	3		539.2.f.d.148.2		8
7.3	odd	6		539.2.q.c.214.2		16
7.4	even	3	inner	539.2.q.b.214.2		16
7.5	odd	6		77.2.f.a.71.2	yes	8
7.6	odd	2		539.2.q.c.324.1		16
11.9	even	5	inner	539.2.q.b.471.2		16
21.5	even	6		693.2.m.g.379.1		8
77.5	odd	30		847.2.f.p.323.1		8
77.9	even	15		539.2.f.d.295.2		8
77.19	even	30		847.2.a.k.1.2		4
77.20	odd	10		539.2.q.c.471.2		16
77.26	odd	30		847.2.f.p.729.1		8
77.30	odd	30		5929.2.a.bb.1.2		4
77.31	odd	30		539.2.q.c.361.1		16
77.40	even	30		847.2.f.s.729.2		8
77.47	odd	30		847.2.a.l.1.3		4
77.53	even	15	inner	539.2.q.b.361.1		16
77.54	even	6		847.2.f.q.148.1		8
77.58	even	15		5929.2.a.bi.1.3		4
77.61	even	30		847.2.f.s.323.2		8
77.68	even	30		847.2.f.q.372.1		8
77.75	odd	30		77.2.f.a.64.2	✓	8
231.47	even	30		7623.2.a.ch.1.2		4
231.152	even	30		693.2.m.g.64.1		8
231.173	odd	30		7623.2.a.co.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.a.64.2	✓	8	77.75	odd	30
77.2.f.a.71.2	yes	8	7.5	odd	6
539.2.f.d.148.2		8	7.2	even	3
539.2.f.d.295.2		8	77.9	even	15
539.2.q.b.214.2		16	7.4	even	3	inner
539.2.q.b.324.1		16	1.1	even	1	trivial
539.2.q.b.361.1		16	77.53	even	15	inner
539.2.q.b.471.2		16	11.9	even	5	inner
539.2.q.c.214.2		16	7.3	odd	6
539.2.q.c.324.1		16	7.6	odd	2
539.2.q.c.361.1		16	77.31	odd	30
539.2.q.c.471.2		16	77.20	odd	10
693.2.m.g.64.1		8	231.152	even	30
693.2.m.g.379.1		8	21.5	even	6
847.2.a.k.1.2		4	77.19	even	30
847.2.a.l.1.3		4	77.47	odd	30
847.2.f.p.323.1		8	77.5	odd	30
847.2.f.p.729.1		8	77.26	odd	30
847.2.f.q.148.1		8	77.54	even	6
847.2.f.q.372.1		8	77.68	even	30
847.2.f.s.323.2		8	77.61	even	30
847.2.f.s.729.2		8	77.40	even	30
5929.2.a.bb.1.2		4	77.30	odd	30
5929.2.a.bi.1.3		4	77.58	even	15
7623.2.a.ch.1.2		4	231.47	even	30
7623.2.a.co.1.3		4	231.173	odd	30

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:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.q (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.73864 - 0.369560i) q^{2} +(0.0646021 - 0.614648i) q^{3} +(1.05921 + 0.471591i) q^{4} +(1.85850 + 2.06407i) q^{5} +(-0.339469 + 1.04478i) q^{6} +(1.20872 + 0.878189i) q^{8} +(2.56082 + 0.544320i) q^{9} +O(q^{10})\)	\(q+(-1.73864 - 0.369560i) q^{2} +(0.0646021 - 0.614648i) q^{3} +(1.05921 + 0.471591i) q^{4} +(1.85850 + 2.06407i) q^{5} +(-0.339469 + 1.04478i) q^{6} +(1.20872 + 0.878189i) q^{8} +(2.56082 + 0.544320i) q^{9} +(-2.46847 - 4.27551i) q^{10} +(-3.26882 + 0.561095i) q^{11} +(0.358290 - 0.620576i) q^{12} +(1.32676 + 4.08334i) q^{13} +(1.38874 - 1.00898i) q^{15} +(-3.32864 - 3.69683i) q^{16} +(-2.69534 + 0.572912i) q^{17} +(-4.25120 - 1.89275i) q^{18} +(-1.77145 + 0.788701i) q^{19} +(0.995144 + 3.06274i) q^{20} +(5.89066 + 0.232480i) q^{22} +(-2.18505 + 3.78461i) q^{23} +(0.617863 - 0.686207i) q^{24} +(-0.283734 + 2.69955i) q^{25} +(-0.797718 - 7.58978i) q^{26} +(1.07295 - 3.30220i) q^{27} +(-6.98027 + 5.07146i) q^{29} +(-2.78740 + 1.24103i) q^{30} +(0.134219 - 0.149066i) q^{31} +(2.92705 + 5.06980i) q^{32} +(0.133704 + 2.04542i) q^{33} +4.89796 q^{34} +(2.45576 + 1.78421i) q^{36} +(-0.108237 - 1.02981i) q^{37} +(3.37139 - 0.716612i) q^{38} +(2.59553 - 0.551697i) q^{39} +(0.433766 + 4.12701i) q^{40} +(7.77155 + 5.64636i) q^{41} -4.70820 q^{43} +(-3.72697 - 0.947227i) q^{44} +(3.63577 + 6.29735i) q^{45} +(5.19765 - 5.77258i) q^{46} +(11.9177 - 5.30610i) q^{47} +(-2.48729 + 1.80712i) q^{48} +(1.49096 - 4.58869i) q^{50} +(0.178015 + 1.69370i) q^{51} +(-0.520350 + 4.95080i) q^{52} +(-2.60969 + 2.89835i) q^{53} +(-3.08583 + 5.34482i) q^{54} +(-7.23324 - 5.70428i) q^{55} +(0.370334 + 1.13977i) q^{57} +(14.0104 - 6.23783i) q^{58} +(7.81733 + 3.48050i) q^{59} +(1.94680 - 0.413804i) q^{60} +(0.661508 + 0.734679i) q^{61} +(-0.288448 + 0.209570i) q^{62} +(-0.141042 - 0.434084i) q^{64} +(-5.96253 + 10.3274i) q^{65} +(0.523443 - 3.60567i) q^{66} +(2.70872 + 4.69165i) q^{67} +(-3.12511 - 0.664263i) q^{68} +(2.18505 + 1.58753i) q^{69} +(-0.623302 + 1.91833i) q^{71} +(2.61731 + 2.90682i) q^{72} +(9.10903 + 4.05560i) q^{73} +(-0.192390 + 1.83047i) q^{74} +(1.64094 + 0.348793i) q^{75} -2.24828 q^{76} -4.71658 q^{78} +(-6.15595 - 1.30849i) q^{79} +(1.44425 - 13.7411i) q^{80} +(5.21470 + 2.32174i) q^{81} +(-11.4253 - 12.6891i) q^{82} +(0.531960 - 1.63720i) q^{83} +(-6.19182 - 4.49862i) q^{85} +(8.18588 + 1.73996i) q^{86} +(2.66623 + 4.61804i) q^{87} +(-4.44384 - 2.19243i) q^{88} +(-7.65177 + 13.2532i) q^{89} +(-3.99406 - 12.2925i) q^{90} +(-4.09921 + 2.97825i) q^{92} +(-0.0829522 - 0.0921277i) q^{93} +(-22.6815 + 4.82111i) q^{94} +(-4.92018 - 2.19061i) q^{95} +(3.30524 - 1.47159i) q^{96} +(-3.58961 - 11.0477i) q^{97} +(-8.67628 - 0.342417i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} - 4 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q + q^2 - 4 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 + 6 * q^8 + 2 * q^9	\( 16 q + q^{2} - 4 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} + 6 q^{8} + 2 q^{9} - 28 q^{10} - 5 q^{11} - 14 q^{12} - 10 q^{13} + 12 q^{15} + 3 q^{16} - 11 q^{17} - 4 q^{18} - 9 q^{19} - 42 q^{20} - 2 q^{22} + 16 q^{23} + 21 q^{24} - 5 q^{25} + 21 q^{26} + 44 q^{27} - 18 q^{29} - 14 q^{30} - 11 q^{31} + 20 q^{32} + 10 q^{33} + 48 q^{34} - 4 q^{36} - 6 q^{37} + 35 q^{38} + 5 q^{39} - 16 q^{40} + 44 q^{41} + 32 q^{43} - 29 q^{44} + 18 q^{45} - 29 q^{46} + 7 q^{47} - 8 q^{48} - 68 q^{50} - 3 q^{51} + 21 q^{52} - 2 q^{53} + 4 q^{54} - 52 q^{55} - 6 q^{57} + 39 q^{58} + 25 q^{59} + 38 q^{60} + 7 q^{61} + 10 q^{62} + 2 q^{64} - 24 q^{65} + 18 q^{66} + 30 q^{67} + 8 q^{68} - 16 q^{69} - 28 q^{71} - 3 q^{72} + 3 q^{73} + 9 q^{74} + 5 q^{75} + 104 q^{76} - 36 q^{78} + 9 q^{79} - 33 q^{80} + 28 q^{81} + 31 q^{82} - 46 q^{83} - 20 q^{85} + 17 q^{86} + 12 q^{87} + 7 q^{88} - 34 q^{89} - 4 q^{90} - 68 q^{92} - 8 q^{93} - 30 q^{94} - 24 q^{95} + 10 q^{96} - 60 q^{97}+O(q^{100}) \) 16 * q + q^2 - 4 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 + 6 * q^8 + 2 * q^9 - 28 * q^10 - 5 * q^11 - 14 * q^12 - 10 * q^13 + 12 * q^15 + 3 * q^16 - 11 * q^17 - 4 * q^18 - 9 * q^19 - 42 * q^20 - 2 * q^22 + 16 * q^23 + 21 * q^24 - 5 * q^25 + 21 * q^26 + 44 * q^27 - 18 * q^29 - 14 * q^30 - 11 * q^31 + 20 * q^32 + 10 * q^33 + 48 * q^34 - 4 * q^36 - 6 * q^37 + 35 * q^38 + 5 * q^39 - 16 * q^40 + 44 * q^41 + 32 * q^43 - 29 * q^44 + 18 * q^45 - 29 * q^46 + 7 * q^47 - 8 * q^48 - 68 * q^50 - 3 * q^51 + 21 * q^52 - 2 * q^53 + 4 * q^54 - 52 * q^55 - 6 * q^57 + 39 * q^58 + 25 * q^59 + 38 * q^60 + 7 * q^61 + 10 * q^62 + 2 * q^64 - 24 * q^65 + 18 * q^66 + 30 * q^67 + 8 * q^68 - 16 * q^69 - 28 * q^71 - 3 * q^72 + 3 * q^73 + 9 * q^74 + 5 * q^75 + 104 * q^76 - 36 * q^78 + 9 * q^79 - 33 * q^80 + 28 * q^81 + 31 * q^82 - 46 * q^83 - 20 * q^85 + 17 * q^86 + 12 * q^87 + 7 * q^88 - 34 * q^89 - 4 * q^90 - 68 * q^92 - 8 * q^93 - 30 * q^94 - 24 * q^95 + 10 * q^96 - 60 * q^97

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