LMFDB - Embedded newform 855.2.k.f.676.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [855,2,Mod(406,855)] 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("855.406"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(855, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.k (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,2,0,-2,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 285)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			676.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	855.676
Dual form			855.2.k.f.406.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.207107 + 0.358719i) q^{2} +(0.914214 + 1.58346i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.82843 q^{7} -1.58579 q^{8} +(-0.207107 - 0.358719i) q^{10} +2.82843 q^{11} +(0.914214 + 1.58346i) q^{13} +(-0.378680 + 0.655892i) q^{14} +(-1.50000 + 2.59808i) q^{16} +(-0.585786 + 1.01461i) q^{17} +(4.00000 - 1.73205i) q^{19} -1.82843 q^{20} +(-0.585786 + 1.01461i) q^{22} +(-0.414214 - 0.717439i) q^{23} +(-0.500000 - 0.866025i) q^{25} -0.757359 q^{26} +(1.67157 + 2.89525i) q^{28} +(4.82843 + 8.36308i) q^{29} -5.00000 q^{31} +(-2.20711 - 3.82282i) q^{32} +(-0.242641 - 0.420266i) q^{34} +(-0.914214 + 1.58346i) q^{35} -2.17157 q^{37} +(-0.207107 + 1.79360i) q^{38} +(0.792893 - 1.37333i) q^{40} +(1.41421 - 2.44949i) q^{41} +(-3.91421 + 6.77962i) q^{43} +(2.58579 + 4.47871i) q^{44} +0.343146 q^{46} +(-1.58579 - 2.74666i) q^{47} -3.65685 q^{49} +0.414214 q^{50} +(-1.67157 + 2.89525i) q^{52} +(-1.00000 - 1.73205i) q^{53} +(-1.41421 + 2.44949i) q^{55} -2.89949 q^{56} -4.00000 q^{58} +(4.15685 + 7.19988i) q^{61} +(1.03553 - 1.79360i) q^{62} -4.17157 q^{64} -1.82843 q^{65} +(-2.74264 - 4.75039i) q^{67} -2.14214 q^{68} +(-0.378680 - 0.655892i) q^{70} +(5.00000 - 8.66025i) q^{71} +(-4.74264 + 8.21449i) q^{73} +(0.449747 - 0.778985i) q^{74} +(6.39949 + 4.75039i) q^{76} +5.17157 q^{77} +(1.67157 - 2.89525i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(0.585786 + 1.01461i) q^{82} +8.00000 q^{83} +(-0.585786 - 1.01461i) q^{85} +(-1.62132 - 2.80821i) q^{86} -4.48528 q^{88} +(6.24264 + 10.8126i) q^{89} +(1.67157 + 2.89525i) q^{91} +(0.757359 - 1.31178i) q^{92} +1.31371 q^{94} +(-0.500000 + 4.33013i) q^{95} +(3.00000 - 5.19615i) q^{97} +(0.757359 - 1.31178i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{7} - 12 q^{8} + 2 q^{10} - 2 q^{13} - 10 q^{14} - 6 q^{16} - 8 q^{17} + 16 q^{19} + 4 q^{20} - 8 q^{22} + 4 q^{23} - 2 q^{25} - 20 q^{26} + 18 q^{28} + 8 q^{29}+ \cdots + 20 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^7 - 12 * q^8 + 2 * q^10 - 2 * q^13 - 10 * q^14 - 6 * q^16 - 8 * q^17 + 16 * q^19 + 4 * q^20 - 8 * q^22 + 4 * q^23 - 2 * q^25 - 20 * q^26 + 18 * q^28 + 8 * q^29 - 20 * q^31 - 6 * q^32 + 16 * q^34 + 2 * q^35 - 20 * q^37 + 2 * q^38 + 6 * q^40 - 10 * q^43 + 16 * q^44 + 24 * q^46 - 12 * q^47 + 8 * q^49 - 4 * q^50 - 18 * q^52 - 4 * q^53 + 28 * q^56 - 16 * q^58 - 6 * q^61 - 10 * q^62 - 28 * q^64 + 4 * q^65 + 6 * q^67 + 48 * q^68 - 10 * q^70 + 20 * q^71 - 2 * q^73 - 18 * q^74 - 14 * q^76 + 32 * q^77 + 18 * q^79 - 6 * q^80 + 8 * q^82 + 32 * q^83 - 8 * q^85 + 2 * q^86 + 16 * q^88 + 8 * q^89 + 18 * q^91 + 20 * q^92 - 40 * q^94 - 2 * q^95 + 12 * q^97 + 20 * q^98

Character values

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

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.207107	+	0.358719i	−0.146447	+	0.253653i	−0.929912	−	0.367783i	$-0.880117\pi$
$2$	−0.207107	+	0.358719i	−0.146447	+	0.253653i	0.783465	+	0.621436i	$0.213450\pi$
$3$		0			0
$3$		0			0
$4$	0.914214	+	1.58346i	0.457107	+	0.791732i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	1.82843			0.691080			0.345540	−	0.938404i	$-0.387696\pi$
$7$	1.82843			0.691080			0.345540	+	0.938404i	$0.387696\pi$
$8$	−1.58579			−0.560660
$9$		0			0
$10$	−0.207107	−	0.358719i	−0.0654929	−	0.113437i
$11$	2.82843			0.852803			0.426401	−	0.904534i	$-0.359781\pi$
$11$	2.82843			0.852803			0.426401	+	0.904534i	$0.359781\pi$
$12$		0			0
$13$	0.914214	+	1.58346i	0.253557	+	0.439174i	0.964503	−	0.264073i	$-0.0850661\pi$
$13$	0.914214	+	1.58346i	0.253557	+	0.439174i	−0.710945	+	0.703247i	$0.751733\pi$
$14$	−0.378680	+	0.655892i	−0.101206	+	0.175295i
$15$		0			0
$16$	−1.50000	+	2.59808i	−0.375000	+	0.649519i
$17$	−0.585786	+	1.01461i	−0.142074	+	0.246080i	−0.928278	−	0.371888i	$-0.878710\pi$
$17$	−0.585786	+	1.01461i	−0.142074	+	0.246080i	0.786203	+	0.617968i	$0.212044\pi$
$18$		0			0
$19$	4.00000	−	1.73205i	0.917663	−	0.397360i
$19$	4.00000	−	1.73205i	0.917663	−	0.397360i
$20$	−1.82843			−0.408849
$21$		0			0
$22$	−0.585786	+	1.01461i	−0.124890	+	0.216316i
$23$	−0.414214	−	0.717439i	−0.0863695	−	0.149596i	0.819604	−	0.572930i	$-0.194193\pi$
$23$	−0.414214	−	0.717439i	−0.0863695	−	0.149596i	−0.905974	+	0.423333i	$0.860860\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.757359			−0.148530
$27$		0			0
$28$	1.67157	+	2.89525i	0.315898	+	0.547151i
$29$	4.82843	+	8.36308i	0.896616	+	1.55299i	0.831791	+	0.555089i	$0.187316\pi$
$29$	4.82843	+	8.36308i	0.896616	+	1.55299i	0.0648251	+	0.997897i	$0.479351\pi$
$30$		0			0
$31$	−5.00000			−0.898027			−0.449013	−	0.893525i	$-0.648224\pi$
$31$	−5.00000			−0.898027			−0.449013	+	0.893525i	$0.648224\pi$
$32$	−2.20711	−	3.82282i	−0.390165	−	0.675786i
$33$		0			0
$34$	−0.242641	−	0.420266i	−0.0416125	−	0.0720750i
$35$	−0.914214	+	1.58346i	−0.154530	+	0.267654i
$36$		0			0
$37$	−2.17157			−0.357004			−0.178502	−	0.983940i	$-0.557125\pi$
$37$	−2.17157			−0.357004			−0.178502	+	0.983940i	$0.557125\pi$
$38$	−0.207107	+	1.79360i	−0.0335972	+	0.290960i
$39$		0			0
$40$	0.792893	−	1.37333i	0.125367	−	0.217143i
$41$	1.41421	−	2.44949i	0.220863	−	0.382546i	−0.734207	−	0.678925i	$-0.762446\pi$
$41$	1.41421	−	2.44949i	0.220863	−	0.382546i	0.955070	+	0.296379i	$0.0957793\pi$
$42$		0			0
$43$	−3.91421	+	6.77962i	−0.596912	+	1.03388i	0.396362	+	0.918094i	$0.370273\pi$
$43$	−3.91421	+	6.77962i	−0.596912	+	1.03388i	−0.993274	+	0.115788i	$0.963061\pi$
$44$	2.58579	+	4.47871i	0.389822	+	0.675191i
$45$		0			0
$46$	0.343146			0.0505941
$47$	−1.58579	−	2.74666i	−0.231311	−	0.400642i	0.726883	−	0.686761i	$-0.240968\pi$
$47$	−1.58579	−	2.74666i	−0.231311	−	0.400642i	−0.958194	+	0.286119i	$0.907635\pi$
$48$		0			0
$49$	−3.65685			−0.522408
$50$	0.414214			0.0585786
$51$		0			0
$52$	−1.67157	+	2.89525i	−0.231805	+	0.401499i
$53$	−1.00000	−	1.73205i	−0.137361	−	0.237915i	0.789136	−	0.614218i	$-0.210529\pi$
$53$	−1.00000	−	1.73205i	−0.137361	−	0.237915i	−0.926497	+	0.376303i	$0.877195\pi$
$54$		0			0
$55$	−1.41421	+	2.44949i	−0.190693	+	0.330289i
$56$	−2.89949			−0.387461
$57$		0			0
$58$	−4.00000			−0.525226
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	4.15685	+	7.19988i	0.532231	+	0.921851i	0.999292	+	0.0376256i	$0.0119794\pi$
$61$	4.15685	+	7.19988i	0.532231	+	0.921851i	−0.467061	+	0.884225i	$0.654687\pi$
$62$	1.03553	−	1.79360i	0.131513	−	0.227787i
$63$		0			0
$64$	−4.17157			−0.521447
$65$	−1.82843			−0.226788
$66$		0			0
$67$	−2.74264	−	4.75039i	−0.335067	−	0.580353i	0.648431	−	0.761274i	$-0.275426\pi$
$67$	−2.74264	−	4.75039i	−0.335067	−	0.580353i	−0.983498	+	0.180921i	$0.942092\pi$
$68$	−2.14214			−0.259772
$69$		0			0
$70$	−0.378680	−	0.655892i	−0.0452609	−	0.0783941i
$71$	5.00000	−	8.66025i	0.593391	−	1.02778i	−0.400381	−	0.916349i	$-0.631122\pi$
$71$	5.00000	−	8.66025i	0.593391	−	1.02778i	0.993772	−	0.111434i	$-0.0355445\pi$
$72$		0			0
$73$	−4.74264	+	8.21449i	−0.555084	+	0.961434i	0.442813	+	0.896614i	$0.353981\pi$
$73$	−4.74264	+	8.21449i	−0.555084	+	0.961434i	−0.997897	+	0.0648198i	$0.979353\pi$
$74$	0.449747	−	0.778985i	0.0522821	−	0.0905552i
$75$		0			0
$76$	6.39949	+	4.75039i	0.734072	+	0.544907i
$77$	5.17157			0.589355
$78$		0			0
$79$	1.67157	−	2.89525i	0.188067	−	0.325741i	−0.756539	−	0.653949i	$-0.773111\pi$
$79$	1.67157	−	2.89525i	0.188067	−	0.325741i	0.944606	+	0.328208i	$0.106445\pi$
$80$	−1.50000	−	2.59808i	−0.167705	−	0.290474i
$81$		0			0
$82$	0.585786	+	1.01461i	0.0646893	+	0.112045i
$83$	8.00000			0.878114			0.439057	−	0.898459i	$-0.355313\pi$
$83$	8.00000			0.878114			0.439057	+	0.898459i	$0.355313\pi$
$84$		0			0
$85$	−0.585786	−	1.01461i	−0.0635375	−	0.110050i
$86$	−1.62132	−	2.80821i	−0.174831	−	0.302817i
$87$		0			0
$88$	−4.48528			−0.478133
$89$	6.24264	+	10.8126i	0.661719	+	1.14613i	0.980164	+	0.198189i	$0.0635060\pi$
$89$	6.24264	+	10.8126i	0.661719	+	1.14613i	−0.318445	+	0.947941i	$0.603161\pi$
$90$		0			0
$91$	1.67157	+	2.89525i	0.175228	+	0.303505i
$92$	0.757359	−	1.31178i	0.0789602	−	0.136763i
$93$		0			0
$94$	1.31371			0.135499
$95$	−0.500000	+	4.33013i	−0.0512989	+	0.444262i
$96$		0			0
$97$	3.00000	−	5.19615i	0.304604	−	0.527589i	−0.672569	−	0.740034i	$-0.734809\pi$
$97$	3.00000	−	5.19615i	0.304604	−	0.527589i	0.977173	+	0.212445i	$0.0681426\pi$
$98$	0.757359	−	1.31178i	0.0765048	−	0.132510i
$99$		0			0
$100$	0.914214	−	1.58346i	0.0914214	−	0.158346i
$101$	6.07107	+	10.5154i	0.604094	+	1.04632i	0.992194	+	0.124704i	$0.0397981\pi$
$101$	6.07107	+	10.5154i	0.604094	+	1.04632i	−0.388100	+	0.921617i	$0.626869\pi$
$102$		0			0
$103$	9.82843			0.968424			0.484212	−	0.874951i	$-0.339106\pi$
$103$	9.82843			0.968424			0.484212	+	0.874951i	$0.339106\pi$
$104$	−1.44975	−	2.51104i	−0.142159	−	0.246227i
$105$		0			0
$106$	0.828427			0.0804640
$107$	−14.0000			−1.35343			−0.676716	−	0.736245i	$-0.736597\pi$
$107$	−14.0000			−1.35343			−0.676716	+	0.736245i	$0.736597\pi$
$108$		0			0
$109$	8.65685	−	14.9941i	0.829176	−	1.43618i	−0.0695090	−	0.997581i	$-0.522143\pi$
$109$	8.65685	−	14.9941i	0.829176	−	1.43618i	0.898685	−	0.438594i	$-0.144523\pi$
$110$	−0.585786	−	1.01461i	−0.0558525	−	0.0967394i
$111$		0			0
$112$	−2.74264	+	4.75039i	−0.259155	+	0.448870i
$113$	−4.00000			−0.376288			−0.188144	−	0.982141i	$-0.560247\pi$
$113$	−4.00000			−0.376288			−0.188144	+	0.982141i	$0.560247\pi$
$114$		0			0
$115$	0.828427			0.0772512
$116$	−8.82843	+	15.2913i	−0.819699	+	1.41976i
$117$		0			0
$118$		0			0
$119$	−1.07107	+	1.85514i	−0.0981846	+	0.170061i
$120$		0			0
$121$	−3.00000			−0.272727
$122$	−3.44365			−0.311773
$123$		0			0
$124$	−4.57107	−	7.91732i	−0.410494	−	0.710996i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−6.48528	−	11.2328i	−0.575476	−	0.996753i	−0.995990	−	0.0894671i	$-0.971484\pi$
$127$	−6.48528	−	11.2328i	−0.575476	−	0.996753i	0.420514	−	0.907286i	$-0.361850\pi$
$128$	5.27817	−	9.14207i	0.466529	−	0.808052i
$129$		0			0
$130$	0.378680	−	0.655892i	0.0332124	−	0.0575256i
$131$	3.24264	−	5.61642i	0.283311	−	0.490709i	−0.688887	−	0.724868i	$-0.741901\pi$
$131$	3.24264	−	5.61642i	0.283311	−	0.490709i	0.972198	+	0.234160i	$0.0752339\pi$
$132$		0			0
$133$	7.31371	−	3.16693i	0.634179	−	0.274608i
$134$	2.27208			0.196278
$135$		0			0
$136$	0.928932	−	1.60896i	0.0796553	−	0.137967i
$137$	−5.24264	−	9.08052i	−0.447909	−	0.775801i	0.550341	−	0.834940i	$-0.314498\pi$
$137$	−5.24264	−	9.08052i	−0.447909	−	0.775801i	−0.998250	+	0.0591390i	$0.981164\pi$
$138$		0			0
$139$	8.15685	+	14.1281i	0.691855	+	1.19833i	0.971229	+	0.238146i	$0.0765398\pi$
$139$	8.15685	+	14.1281i	0.691855	+	1.19833i	−0.279374	+	0.960182i	$0.590127\pi$
$140$	−3.34315			−0.282547
$141$		0			0
$142$	2.07107	+	3.58719i	0.173800	+	0.301031i
$143$	2.58579	+	4.47871i	0.216234	+	0.374529i
$144$		0			0
$145$	−9.65685			−0.801958
$146$	−1.96447	−	3.40256i	−0.162580	−	0.281597i
$147$		0			0
$148$	−1.98528	−	3.43861i	−0.163189	−	0.282652i
$149$	−0.585786	+	1.01461i	−0.0479895	+	0.0831202i	−0.889022	−	0.457864i	$-0.848615\pi$
$149$	−0.585786	+	1.01461i	−0.0479895	+	0.0831202i	0.841033	+	0.540984i	$0.181948\pi$
$150$		0			0
$151$	10.3431			0.841713			0.420857	−	0.907127i	$-0.361730\pi$
$151$	10.3431			0.841713			0.420857	+	0.907127i	$0.361730\pi$
$152$	−6.34315	+	2.74666i	−0.514497	+	0.222784i
$153$		0			0
$154$	−1.07107	+	1.85514i	−0.0863091	+	0.149492i
$155$	2.50000	−	4.33013i	0.200805	−	0.347804i
$156$		0			0
$157$	9.91421	−	17.1719i	0.791240	−	1.37047i	−0.133959	−	0.990987i	$-0.542769\pi$
$157$	9.91421	−	17.1719i	0.791240	−	1.37047i	0.925199	−	0.379482i	$-0.123898\pi$
$158$	0.692388	+	1.19925i	0.0550834	+	0.0954073i
$159$		0			0
$160$	4.41421			0.348974
$161$	−0.757359	−	1.31178i	−0.0596883	−	0.103383i
$162$		0			0
$163$	15.1421			1.18602			0.593012	−	0.805194i	$-0.297939\pi$
$163$	15.1421			1.18602			0.593012	+	0.805194i	$0.297939\pi$
$164$	5.17157			0.403832
$165$		0			0
$166$	−1.65685	+	2.86976i	−0.128597	+	0.222736i
$167$	−12.4853	−	21.6251i	−0.966140	−	1.67340i	−0.706520	−	0.707693i	$-0.749736\pi$
$167$	−12.4853	−	21.6251i	−0.966140	−	1.67340i	−0.259620	−	0.965711i	$-0.583597\pi$
$168$		0			0
$169$	4.82843	−	8.36308i	0.371417	−	0.643314i
$170$	0.485281			0.0372194
$171$		0			0
$172$	−14.3137			−1.09141
$173$	3.65685	−	6.33386i	0.278025	−	0.481554i	−0.692868	−	0.721064i	$-0.743653\pi$
$173$	3.65685	−	6.33386i	0.278025	−	0.481554i	0.970894	+	0.239510i	$0.0769867\pi$
$174$		0			0
$175$	−0.914214	−	1.58346i	−0.0691080	−	0.119699i
$176$	−4.24264	+	7.34847i	−0.319801	+	0.553912i
$177$		0			0
$178$	−5.17157			−0.387626
$179$	−16.1421			−1.20652			−0.603260	−	0.797545i	$-0.706132\pi$
$179$	−16.1421			−1.20652			−0.603260	+	0.797545i	$0.706132\pi$
$180$		0			0
$181$	−12.6569	−	21.9223i	−0.940777	−	1.62947i	−0.763994	−	0.645223i	$-0.776765\pi$
$181$	−12.6569	−	21.9223i	−0.940777	−	1.62947i	−0.176782	−	0.984250i	$-0.556569\pi$
$182$	−1.38478			−0.102646
$183$		0			0
$184$	0.656854	+	1.13770i	0.0484239	+	0.0838727i
$185$	1.08579	−	1.88064i	0.0798286	−	0.138267i
$186$		0			0
$187$	−1.65685	+	2.86976i	−0.121161	+	0.209857i
$188$	2.89949	−	5.02207i	0.211467	−	0.366272i
$189$		0			0
$190$	−1.44975	−	1.07616i	−0.105176	−	0.0780727i
$191$	16.8284			1.21766			0.608831	−	0.793300i	$-0.291639\pi$
$191$	16.8284			1.21766			0.608831	+	0.793300i	$0.291639\pi$
$192$		0			0
$193$	12.3995	−	21.4766i	0.892535	−	1.54592i	0.0557094	−	0.998447i	$-0.482258\pi$
$193$	12.3995	−	21.4766i	0.892535	−	1.54592i	0.836826	−	0.547469i	$-0.184409\pi$
$194$	1.24264	+	2.15232i	0.0892164	+	0.154527i
$195$		0			0
$196$	−3.34315	−	5.79050i	−0.238796	−	0.413607i
$197$	−17.6569			−1.25800			−0.628999	−	0.777406i	$-0.716535\pi$
$197$	−17.6569			−1.25800			−0.628999	+	0.777406i	$0.716535\pi$
$198$		0			0
$199$	8.50000	+	14.7224i	0.602549	+	1.04365i	0.992434	+	0.122782i	$0.0391815\pi$
$199$	8.50000	+	14.7224i	0.602549	+	1.04365i	−0.389885	+	0.920864i	$0.627485\pi$
$200$	0.792893	+	1.37333i	0.0560660	+	0.0971092i
$201$		0			0
$202$	−5.02944			−0.353870
$203$	8.82843	+	15.2913i	0.619634	+	1.07324i
$204$		0			0
$205$	1.41421	+	2.44949i	0.0987730	+	0.171080i
$206$	−2.03553	+	3.52565i	−0.141822	+	0.245644i
$207$		0			0
$208$	−5.48528			−0.380336
$209$	11.3137	−	4.89898i	0.782586	−	0.338869i
$210$		0			0
$211$	0.156854	−	0.271680i	0.0107983	−	0.0187032i	−0.860576	−	0.509322i	$-0.829896\pi$
$211$	0.156854	−	0.271680i	0.0107983	−	0.0187032i	0.871374	+	0.490619i	$0.163229\pi$
$212$	1.82843	−	3.16693i	0.125577	−	0.217506i
$213$		0			0
$214$	2.89949	−	5.02207i	0.198205	−	0.343302i
$215$	−3.91421	−	6.77962i	−0.266947	−	0.462366i
$216$		0			0
$217$	−9.14214			−0.620609
$218$	3.58579	+	6.21076i	0.242860	+	0.420646i
$219$		0			0
$220$	−5.17157			−0.348667
$221$	−2.14214			−0.144096
$222$		0			0
$223$	−2.91421	+	5.04757i	−0.195150	+	0.338010i	−0.946950	−	0.321382i	$-0.895853\pi$
$223$	−2.91421	+	5.04757i	−0.195150	+	0.338010i	0.751800	+	0.659392i	$0.229186\pi$
$224$	−4.03553	−	6.98975i	−0.269635	−	0.467022i
$225$		0			0
$226$	0.828427	−	1.43488i	0.0551062	−	0.0954467i
$227$	18.9706			1.25912			0.629560	−	0.776952i	$-0.283235\pi$
$227$	18.9706			1.25912			0.629560	+	0.776952i	$0.283235\pi$
$228$		0			0
$229$	−4.65685			−0.307734			−0.153867	−	0.988092i	$-0.549173\pi$
$229$	−4.65685			−0.307734			−0.153867	+	0.988092i	$0.549173\pi$
$230$	−0.171573	+	0.297173i	−0.0113132	+	0.0195950i
$231$		0			0
$232$	−7.65685	−	13.2621i	−0.502697	−	0.870697i
$233$	−12.6569	+	21.9223i	−0.829178	+	1.43618i	0.0695057	+	0.997582i	$0.477858\pi$
$233$	−12.6569	+	21.9223i	−0.829178	+	1.43618i	−0.898684	+	0.438597i	$0.855476\pi$
$234$		0			0
$235$	3.17157			0.206891
$236$		0			0
$237$		0			0
$238$	−0.443651	−	0.768426i	−0.0287576	−	0.0498096i
$239$	24.6274			1.59302			0.796508	−	0.604629i	$-0.206678\pi$
$239$	24.6274			1.59302			0.796508	+	0.604629i	$0.206678\pi$
$240$		0			0
$241$	−2.50000	−	4.33013i	−0.161039	−	0.278928i	0.774202	−	0.632938i	$-0.218151\pi$
$241$	−2.50000	−	4.33013i	−0.161039	−	0.278928i	−0.935242	+	0.354010i	$0.884818\pi$
$242$	0.621320	−	1.07616i	0.0399400	−	0.0691781i
$243$		0			0
$244$	−7.60051	+	13.1645i	−0.486572	+	0.842768i
$245$	1.82843	−	3.16693i	0.116814	−	0.202328i
$246$		0			0
$247$	6.39949	+	4.75039i	0.407190	+	0.302260i
$248$	7.92893			0.503488
$249$		0			0
$250$	−0.207107	+	0.358719i	−0.0130986	+	0.0226874i
$251$	−8.17157	−	14.1536i	−0.515785	−	0.893366i	−0.999832	−	0.0183240i	$-0.994167\pi$
$251$	−8.17157	−	14.1536i	−0.515785	−	0.893366i	0.484047	−	0.875042i	$-0.339166\pi$
$252$		0			0
$253$	−1.17157	−	2.02922i	−0.0736562	−	0.127576i
$254$	5.37258			0.337106
$255$		0			0
$256$	−1.98528	−	3.43861i	−0.124080	−	0.214913i
$257$	−8.41421	−	14.5738i	−0.524864	−	0.909091i	−0.999581	−	0.0289528i	$-0.990783\pi$
$257$	−8.41421	−	14.5738i	−0.524864	−	0.909091i	0.474717	−	0.880139i	$-0.342551\pi$
$258$		0			0
$259$	−3.97056			−0.246719
$260$	−1.67157	−	2.89525i	−0.103667	−	0.179556i
$261$		0			0
$262$	1.34315	+	2.32640i	0.0829798	+	0.143725i
$263$	12.8995	−	22.3426i	0.795417	−	1.37770i	−0.127157	−	0.991883i	$-0.540585\pi$
$263$	12.8995	−	22.3426i	0.795417	−	1.37770i	0.922574	−	0.385820i	$-0.126081\pi$
$264$		0			0
$265$	2.00000			0.122859
$266$	−0.378680	+	3.27946i	−0.0232183	+	0.201077i
$267$		0			0
$268$	5.01472	−	8.68575i	0.306323	−	0.530566i
$269$	0.828427	−	1.43488i	0.0505101	−	0.0874860i	−0.839665	−	0.543105i	$-0.817249\pi$
$269$	0.828427	−	1.43488i	0.0505101	−	0.0874860i	0.890175	+	0.455619i	$0.150582\pi$
$270$		0			0
$271$	−6.82843	+	11.8272i	−0.414797	+	0.718450i	−0.995407	−	0.0957318i	$-0.969481\pi$
$271$	−6.82843	+	11.8272i	−0.414797	+	0.718450i	0.580610	+	0.814182i	$0.302814\pi$
$272$	−1.75736	−	3.04384i	−0.106556	−	0.184560i
$273$		0			0
$274$	4.34315			0.262379
$275$	−1.41421	−	2.44949i	−0.0852803	−	0.147710i
$276$		0			0
$277$	6.00000			0.360505			0.180253	−	0.983620i	$-0.442309\pi$
$277$	6.00000			0.360505			0.180253	+	0.983620i	$0.442309\pi$
$278$	−6.75736			−0.405279
$279$		0			0
$280$	1.44975	−	2.51104i	0.0866390	−	0.150063i
$281$	−3.48528	−	6.03668i	−0.207914	−	0.360118i	0.743143	−	0.669133i	$-0.233334\pi$
$281$	−3.48528	−	6.03668i	−0.207914	−	0.360118i	−0.951057	+	0.309014i	$0.900001\pi$
$282$		0			0
$283$	10.4853	−	18.1610i	0.623285	−	1.07956i	−0.365584	−	0.930778i	$-0.619131\pi$
$283$	10.4853	−	18.1610i	0.623285	−	1.07956i	0.988870	−	0.148784i	$-0.0475358\pi$
$284$	18.2843			1.08497
$285$		0			0
$286$	−2.14214			−0.126667
$287$	2.58579	−	4.47871i	0.152634	−	0.264370i
$288$		0			0
$289$	7.81371	+	13.5337i	0.459630	+	0.796102i
$290$	2.00000	−	3.46410i	0.117444	−	0.203419i
$291$		0			0
$292$	−17.3431			−1.01493
$293$	5.31371			0.310430			0.155215	−	0.987881i	$-0.450393\pi$
$293$	5.31371			0.310430			0.155215	+	0.987881i	$0.450393\pi$
$294$		0			0
$295$		0			0
$296$	3.44365			0.200158
$297$		0			0
$298$	−0.242641	−	0.420266i	−0.0140558	−	0.0243454i
$299$	0.757359	−	1.31178i	0.0437992	−	0.0758625i
$300$		0			0
$301$	−7.15685	+	12.3960i	−0.412514	+	0.714496i
$302$	−2.14214	+	3.71029i	−0.123266	+	0.213503i
$303$		0			0
$304$	−1.50000	+	12.9904i	−0.0860309	+	0.745049i
$305$	−8.31371			−0.476042
$306$		0			0
$307$	8.82843	−	15.2913i	0.503865	−	0.872720i	−0.496125	−	0.868251i	$-0.665244\pi$
$307$	8.82843	−	15.2913i	0.503865	−	0.872720i	0.999990	−	0.00446862i	$-0.00142241\pi$
$308$	4.72792	+	8.18900i	0.269398	+	0.466612i
$309$		0			0
$310$	1.03553	+	1.79360i	0.0588144	+	0.101869i
$311$	4.00000			0.226819			0.113410	−	0.993548i	$-0.463823\pi$
$311$	4.00000			0.226819			0.113410	+	0.993548i	$0.463823\pi$
$312$		0			0
$313$	3.00000	+	5.19615i	0.169570	+	0.293704i	0.938269	−	0.345907i	$-0.112429\pi$
$313$	3.00000	+	5.19615i	0.169570	+	0.293704i	−0.768699	+	0.639611i	$0.779095\pi$
$314$	4.10660	+	7.11284i	0.231749	+	0.401401i
$315$		0			0
$316$	6.11270			0.343866
$317$	2.65685	+	4.60181i	0.149224	+	0.258463i	0.930941	−	0.365170i	$-0.118989\pi$
$317$	2.65685	+	4.60181i	0.149224	+	0.258463i	−0.781717	+	0.623633i	$0.785656\pi$
$318$		0			0
$319$	13.6569	+	23.6544i	0.764637	+	1.32439i
$320$	2.08579	−	3.61269i	0.116599	−	0.201955i
$321$		0			0
$322$	0.627417			0.0349646
$323$	−0.585786	+	5.07306i	−0.0325940	+	0.282273i
$324$		0			0
$325$	0.914214	−	1.58346i	0.0507114	−	0.0878348i
$326$	−3.13604	+	5.43178i	−0.173689	+	0.300838i
$327$		0			0
$328$	−2.24264	+	3.88437i	−0.123829	+	0.214478i
$329$	−2.89949	−	5.02207i	−0.159854	−	0.276876i
$330$		0			0
$331$	−5.34315			−0.293686			−0.146843	−	0.989160i	$-0.546911\pi$
$331$	−5.34315			−0.293686			−0.146843	+	0.989160i	$0.546911\pi$
$332$	7.31371	+	12.6677i	0.401392	+	0.695231i
$333$		0			0
$334$	10.3431			0.565952
$335$	5.48528			0.299693
$336$		0			0
$337$	−8.74264	+	15.1427i	−0.476242	+	0.824875i	−0.999629	−	0.0272195i	$-0.991335\pi$
$337$	−8.74264	+	15.1427i	−0.476242	+	0.824875i	0.523387	+	0.852095i	$0.324668\pi$
$338$	2.00000	+	3.46410i	0.108786	+	0.188422i
$339$		0			0
$340$	1.07107	−	1.85514i	0.0580868	−	0.100609i
$341$	−14.1421			−0.765840
$342$		0			0
$343$	−19.4853			−1.05211
$344$	6.20711	−	10.7510i	0.334665	−	0.579656i
$345$		0			0
$346$	1.51472	+	2.62357i	0.0814318	+	0.141044i
$347$	−17.7279	+	30.7057i	−0.951685	+	1.64837i	−0.209906	+	0.977722i	$0.567316\pi$
$347$	−17.7279	+	30.7057i	−0.951685	+	1.64837i	−0.741779	+	0.670645i	$0.766018\pi$
$348$		0			0
$349$	−31.6274			−1.69298			−0.846488	−	0.532407i	$-0.821288\pi$
$349$	−31.6274			−1.69298			−0.846488	+	0.532407i	$0.821288\pi$
$350$	0.757359			0.0404826
$351$		0			0
$352$	−6.24264	−	10.8126i	−0.332734	−	0.576312i
$353$	1.31371			0.0699216			0.0349608	−	0.999389i	$-0.488869\pi$
$353$	1.31371			0.0699216			0.0349608	+	0.999389i	$0.488869\pi$
$354$		0			0
$355$	5.00000	+	8.66025i	0.265372	+	0.459639i
$356$	−11.4142	+	19.7700i	−0.604952	+	1.04781i
$357$		0			0
$358$	3.34315	−	5.79050i	0.176691	−	0.306037i
$359$	4.58579	−	7.94282i	0.242029	−	0.419206i	−0.719263	−	0.694737i	$-0.755521\pi$
$359$	4.58579	−	7.94282i	0.242029	−	0.419206i	0.961292	+	0.275532i	$0.0888539\pi$
$360$		0			0
$361$	13.0000	−	13.8564i	0.684211	−	0.729285i
$362$	10.4853			0.551094
$363$		0			0
$364$	−3.05635	+	5.29375i	−0.160196	+	0.277468i
$365$	−4.74264	−	8.21449i	−0.248241	−	0.429966i
$366$		0			0
$367$	17.0563	+	29.5425i	0.890334	+	1.54210i	0.839475	+	0.543398i	$0.182863\pi$
$367$	17.0563	+	29.5425i	0.890334	+	1.54210i	0.0508591	+	0.998706i	$0.483804\pi$
$368$	2.48528			0.129554
$369$		0			0
$370$	0.449747	+	0.778985i	0.0233813	+	0.0404975i
$371$	−1.82843	−	3.16693i	−0.0949272	−	0.164419i
$372$		0			0
$373$	−11.6569			−0.603569			−0.301785	−	0.953376i	$-0.597582\pi$
$373$	−11.6569			−0.603569			−0.301785	+	0.953376i	$0.597582\pi$
$374$	−0.686292	−	1.18869i	−0.0354873	−	0.0614658i
$375$		0			0
$376$	2.51472	+	4.35562i	0.129687	+	0.224624i
$377$	−8.82843	+	15.2913i	−0.454687	+	0.787541i
$378$		0			0
$379$	1.68629			0.0866190			0.0433095	−	0.999062i	$-0.486210\pi$
$379$	1.68629			0.0866190			0.0433095	+	0.999062i	$0.486210\pi$
$380$	−7.31371	+	3.16693i	−0.375185	+	0.162460i
$381$		0			0
$382$	−3.48528	+	6.03668i	−0.178323	+	0.308864i
$383$	−16.9706	+	29.3939i	−0.867155	+	1.50196i	−0.00226413	+	0.999997i	$0.500721\pi$
$383$	−16.9706	+	29.3939i	−0.867155	+	1.50196i	−0.864891	+	0.501960i	$0.832613\pi$
$384$		0			0
$385$	−2.58579	+	4.47871i	−0.131784	+	0.228256i
$386$	5.13604	+	8.89588i	0.261418	+	0.452788i
$387$		0			0
$388$	10.9706			0.556946
$389$	−7.72792	−	13.3852i	−0.391821	−	0.678654i	0.600869	−	0.799348i	$-0.294821\pi$
$389$	−7.72792	−	13.3852i	−0.391821	−	0.678654i	−0.992690	+	0.120694i	$0.961488\pi$
$390$		0			0
$391$	0.970563			0.0490835
$392$	5.79899			0.292893
$393$		0			0
$394$	3.65685	−	6.33386i	0.184230	−	0.319095i
$395$	1.67157	+	2.89525i	0.0841060	+	0.145676i
$396$		0			0
$397$	11.9142	−	20.6360i	0.597957	−	1.03569i	−0.395165	−	0.918610i	$-0.629313\pi$
$397$	11.9142	−	20.6360i	0.597957	−	1.03569i	0.993122	−	0.117082i	$-0.0373541\pi$
$398$	−7.04163			−0.352965
$399$		0			0
$400$	3.00000			0.150000
$401$	−11.3137	+	19.5959i	−0.564980	+	0.978573i	0.432072	+	0.901839i	$0.357783\pi$
$401$	−11.3137	+	19.5959i	−0.564980	+	0.978573i	−0.997052	+	0.0767343i	$0.975551\pi$
$402$		0			0
$403$	−4.57107	−	7.91732i	−0.227701	−	0.394390i
$404$	−11.1005	+	19.2266i	−0.552271	+	0.956561i
$405$		0			0
$406$	−7.31371			−0.362973
$407$	−6.14214			−0.304454
$408$		0			0
$409$	−3.00000	−	5.19615i	−0.148340	−	0.256933i	0.782274	−	0.622935i	$-0.214060\pi$
$409$	−3.00000	−	5.19615i	−0.148340	−	0.256933i	−0.930614	+	0.366002i	$0.880726\pi$
$410$	−1.17157			−0.0578599
$411$		0			0
$412$	8.98528	+	15.5630i	0.442673	+	0.766732i
$413$		0			0
$414$		0			0
$415$	−4.00000	+	6.92820i	−0.196352	+	0.340092i
$416$	4.03553	−	6.98975i	0.197858	−	0.342701i
$417$		0			0
$418$	−0.585786	+	5.07306i	−0.0286518	+	0.248131i
$419$	−3.31371			−0.161885			−0.0809426	−	0.996719i	$-0.525793\pi$
$419$	−3.31371			−0.161885			−0.0809426	+	0.996719i	$0.525793\pi$
$420$		0			0
$421$	3.82843	−	6.63103i	0.186586	−	0.323177i	−0.757524	−	0.652808i	$-0.773591\pi$
$421$	3.82843	−	6.63103i	0.186586	−	0.323177i	0.944110	+	0.329631i	$0.106924\pi$
$422$	0.0649712	+	0.112533i	0.00316275	+	0.00547804i
$423$		0			0
$424$	1.58579	+	2.74666i	0.0770126	+	0.133390i
$425$	1.17157			0.0568296
$426$		0			0
$427$	7.60051	+	13.1645i	0.367814	+	0.637073i
$428$	−12.7990	−	22.1685i	−0.618663	−	1.07155i
$429$		0			0
$430$	3.24264			0.156374
$431$	−1.24264	−	2.15232i	−0.0598559	−	0.103673i	0.834545	−	0.550940i	$-0.185731\pi$
$431$	−1.24264	−	2.15232i	−0.0598559	−	0.103673i	−0.894401	+	0.447267i	$0.852397\pi$
$432$		0			0
$433$	19.9142	+	34.4924i	0.957016	+	1.65760i	0.729686	+	0.683783i	$0.239666\pi$
$433$	19.9142	+	34.4924i	0.957016	+	1.65760i	0.227330	+	0.973818i	$0.427000\pi$
$434$	1.89340	−	3.27946i	0.0908860	−	0.157419i
$435$		0			0
$436$	31.6569			1.51609
$437$	−2.89949	−	2.15232i	−0.138702	−	0.102959i
$438$		0			0
$439$	−8.50000	+	14.7224i	−0.405683	+	0.702663i	−0.994401	−	0.105675i	$-0.966300\pi$
$439$	−8.50000	+	14.7224i	−0.405683	+	0.702663i	0.588718	+	0.808339i	$0.299633\pi$
$440$	2.24264	−	3.88437i	0.106914	−	0.185180i
$441$		0			0
$442$	0.443651	−	0.768426i	0.0211023	−	0.0365503i
$443$	9.07107	+	15.7116i	0.430979	+	0.746478i	0.996958	−	0.0779417i	$-0.0248348\pi$
$443$	9.07107	+	15.7116i	0.430979	+	0.746478i	−0.565978	+	0.824420i	$0.691501\pi$
$444$		0			0
$445$	−12.4853			−0.591859
$446$	−1.20711	−	2.09077i	−0.0571582	−	0.0990008i
$447$		0			0
$448$	−7.62742			−0.360362
$449$	−13.1716			−0.621605			−0.310802	−	0.950475i	$-0.600598\pi$
$449$	−13.1716			−0.621605			−0.310802	+	0.950475i	$0.600598\pi$
$450$		0			0
$451$	4.00000	−	6.92820i	0.188353	−	0.326236i
$452$	−3.65685	−	6.33386i	−0.172004	−	0.297920i
$453$		0			0
$454$	−3.92893	+	6.80511i	−0.184394	+	0.319380i
$455$	−3.34315			−0.156729
$456$		0			0
$457$	−4.17157			−0.195138			−0.0975690	−	0.995229i	$-0.531107\pi$
$457$	−4.17157			−0.195138			−0.0975690	+	0.995229i	$0.531107\pi$
$458$	0.964466	−	1.67050i	0.0450665	−	0.0780575i
$459$		0			0
$460$	0.757359	+	1.31178i	0.0353121	+	0.0611623i
$461$	15.0711	−	26.1039i	0.701930	−	1.21578i	−0.265859	−	0.964012i	$-0.585655\pi$
$461$	15.0711	−	26.1039i	0.701930	−	1.21578i	0.967788	−	0.251766i	$-0.0810112\pi$
$462$		0			0
$463$	−22.7990			−1.05956			−0.529779	−	0.848135i	$-0.677725\pi$
$463$	−22.7990			−1.05956			−0.529779	+	0.848135i	$0.677725\pi$
$464$	−28.9706			−1.34492
$465$		0			0
$466$	−5.24264	−	9.08052i	−0.242861	−	0.420647i
$467$	−23.7990			−1.10129			−0.550643	−	0.834741i	$-0.685617\pi$
$467$	−23.7990			−1.10129			−0.550643	+	0.834741i	$0.685617\pi$
$468$		0			0
$469$	−5.01472	−	8.68575i	−0.231558	−	0.401071i
$470$	−0.656854	+	1.13770i	−0.0302984	+	0.0524784i
$471$		0			0
$472$		0			0
$473$	−11.0711	+	19.1757i	−0.509048	+	0.881697i
$474$		0			0
$475$	−3.50000	−	2.59808i	−0.160591	−	0.119208i
$476$	−3.91674			−0.179523
$477$		0			0
$478$	−5.10051	+	8.83433i	−0.233292	+	0.404073i
$479$	1.24264	+	2.15232i	0.0567777	+	0.0983419i	0.893017	−	0.450022i	$-0.148584\pi$
$479$	1.24264	+	2.15232i	0.0567777	+	0.0983419i	−0.836240	+	0.548364i	$0.815251\pi$
$480$		0			0
$481$	−1.98528	−	3.43861i	−0.0905210	−	0.156787i
$482$	2.07107			0.0943346
$483$		0			0
$484$	−2.74264	−	4.75039i	−0.124665	−	0.215927i
$485$	3.00000	+	5.19615i	0.136223	+	0.235945i
$486$		0			0
$487$	−6.34315			−0.287435			−0.143718	−	0.989619i	$-0.545906\pi$
$487$	−6.34315			−0.287435			−0.143718	+	0.989619i	$0.545906\pi$
$488$	−6.59188	−	11.4175i	−0.298401	−	0.516845i
$489$		0			0
$490$	0.757359	+	1.31178i	0.0342140	+	0.0592604i
$491$	11.8284	−	20.4874i	0.533809	−	0.924585i	−0.465411	−	0.885095i	$-0.654093\pi$
$491$	11.8284	−	20.4874i	0.533809	−	0.924585i	0.999220	−	0.0394901i	$-0.0125734\pi$
$492$		0			0
$493$	−11.3137			−0.509544
$494$	−3.02944	+	1.31178i	−0.136301	+	0.0590200i
$495$		0			0
$496$	7.50000	−	12.9904i	0.336760	−	0.583285i
$497$	9.14214	−	15.8346i	0.410081	−	0.710281i
$498$		0			0
$499$	3.67157	−	6.35935i	0.164362	−	0.284684i	−0.772066	−	0.635542i	$-0.780777\pi$
$499$	3.67157	−	6.35935i	0.164362	−	0.284684i	0.936429	+	0.350858i	$0.114110\pi$
$500$	0.914214	+	1.58346i	0.0408849	+	0.0708147i
$501$		0			0
$502$	6.76955			0.302140
$503$	6.92893	+	12.0013i	0.308946	+	0.535110i	0.978132	−	0.207985i	$-0.0666905\pi$
$503$	6.92893	+	12.0013i	0.308946	+	0.535110i	−0.669186	+	0.743095i	$0.733357\pi$
$504$		0			0
$505$	−12.1421			−0.540318
$506$	0.970563			0.0431468
$507$		0			0
$508$	11.8579	−	20.5384i	0.526108	−	0.911245i
$509$	16.5563	+	28.6764i	0.733847	+	1.27106i	0.955227	+	0.295873i	$0.0956106\pi$
$509$	16.5563	+	28.6764i	0.733847	+	1.27106i	−0.221380	+	0.975188i	$0.571056\pi$
$510$		0			0
$511$	−8.67157	+	15.0196i	−0.383608	+	0.664428i
$512$	22.7574			1.00574
$513$		0			0
$514$	6.97056			0.307458
$515$	−4.91421	+	8.51167i	−0.216546	+	0.375069i
$516$		0			0
$517$	−4.48528	−	7.76874i	−0.197262	−	0.341669i
$518$	0.822330	−	1.42432i	0.0361311	−	0.0625809i
$519$		0			0
$520$	2.89949			0.127151
$521$	−6.34315			−0.277898			−0.138949	−	0.990300i	$-0.544372\pi$
$521$	−6.34315			−0.277898			−0.138949	+	0.990300i	$0.544372\pi$
$522$		0			0
$523$	14.8848	+	25.7812i	0.650866	+	1.12733i	0.982913	+	0.184070i	$0.0589273\pi$
$523$	14.8848	+	25.7812i	0.650866	+	1.12733i	−0.332047	+	0.943263i	$0.607739\pi$
$524$	11.8579			0.518013
$525$		0			0
$526$	5.34315	+	9.25460i	0.232972	+	0.403520i
$527$	2.92893	−	5.07306i	0.127586	−	0.220986i
$528$		0			0
$529$	11.1569	−	19.3242i	0.485081	−	0.840184i
$530$	−0.414214	+	0.717439i	−0.0179923	+	0.0311636i
$531$		0			0
$532$	11.7010	+	8.68575i	0.507303	+	0.376575i
$533$	5.17157			0.224006
$534$		0			0
$535$	7.00000	−	12.1244i	0.302636	−	0.524182i
$536$	4.34924	+	7.53311i	0.187859	+	0.325381i
$537$		0			0
$538$	0.343146	+	0.594346i	0.0147941	+	0.0256241i
$539$	−10.3431			−0.445511
$540$		0			0
$541$	−8.15685	−	14.1281i	−0.350691	−	0.607414i	0.635680	−	0.771953i	$-0.280720\pi$
$541$	−8.15685	−	14.1281i	−0.350691	−	0.607414i	−0.986371	+	0.164539i	$0.947386\pi$
$542$	−2.82843	−	4.89898i	−0.121491	−	0.210429i
$543$		0			0
$544$	5.17157			0.221729
$545$	8.65685	+	14.9941i	0.370819	+	0.642277i
$546$		0			0
$547$	6.57107	+	11.3814i	0.280959	+	0.486635i	0.971621	−	0.236543i	$-0.0760143\pi$
$547$	6.57107	+	11.3814i	0.280959	+	0.486635i	−0.690663	+	0.723177i	$0.742681\pi$
$548$	9.58579	−	16.6031i	0.409485	−	0.709248i
$549$		0			0
$550$	1.17157			0.0499560
$551$	33.7990	+	25.0892i	1.43989	+	1.06884i
$552$		0			0
$553$	3.05635	−	5.29375i	0.129969	−	0.225113i
$554$	−1.24264	+	2.15232i	−0.0527947	+	0.0914432i
$555$		0			0
$556$	−14.9142	+	25.8322i	−0.632504	+	1.09553i
$557$	−4.51472	−	7.81972i	−0.191295	−	0.331332i	0.754385	−	0.656432i	$-0.227935\pi$
$557$	−4.51472	−	7.81972i	−0.191295	−	0.331332i	−0.945680	+	0.325100i	$0.894602\pi$
$558$		0			0
$559$	−14.3137			−0.605405
$560$	−2.74264	−	4.75039i	−0.115898	−	0.200741i
$561$		0			0
$562$	2.88730			0.121793
$563$	12.1421			0.511730			0.255865	−	0.966713i	$-0.417640\pi$
$563$	12.1421			0.511730			0.255865	+	0.966713i	$0.417640\pi$
$564$		0			0
$565$	2.00000	−	3.46410i	0.0841406	−	0.145736i
$566$	4.34315	+	7.52255i	0.182556	+	0.316196i
$567$		0			0
$568$	−7.92893	+	13.7333i	−0.332691	+	0.576237i
$569$	−4.97056			−0.208377			−0.104188	−	0.994558i	$-0.533224\pi$
$569$	−4.97056			−0.208377			−0.104188	+	0.994558i	$0.533224\pi$
$570$		0			0
$571$	14.3137			0.599010			0.299505	−	0.954095i	$-0.403178\pi$
$571$	14.3137			0.599010			0.299505	+	0.954095i	$0.403178\pi$
$572$	−4.72792	+	8.18900i	−0.197684	+	0.342399i
$573$		0			0
$574$	1.07107	+	1.85514i	0.0447055	+	0.0774322i
$575$	−0.414214	+	0.717439i	−0.0172739	+	0.0299193i
$576$		0			0
$577$	−36.3431			−1.51298			−0.756492	−	0.654002i	$-0.773089\pi$
$577$	−36.3431			−1.51298			−0.756492	+	0.654002i	$0.773089\pi$
$578$	−6.47309			−0.269245
$579$		0			0
$580$	−8.82843	−	15.2913i	−0.366580	−	0.634936i
$581$	14.6274			0.606848
$582$		0			0
$583$	−2.82843	−	4.89898i	−0.117141	−	0.202895i
$584$	7.52082	−	13.0264i	0.311214	−	0.539038i
$585$		0			0
$586$	−1.10051	+	1.90613i	−0.0454614	+	0.0787415i
$587$	5.31371	−	9.20361i	0.219320	−	0.379874i	−0.735280	−	0.677763i	$-0.762949\pi$
$587$	5.31371	−	9.20361i	0.219320	−	0.379874i	0.954600	+	0.297890i	$0.0962827\pi$
$588$		0			0
$589$	−20.0000	+	8.66025i	−0.824086	+	0.356840i
$590$		0			0
$591$		0			0
$592$	3.25736	−	5.64191i	0.133877	−	0.231881i
$593$	−4.92893	−	8.53716i	−0.202407	−	0.350579i	0.746896	−	0.664940i	$-0.231543\pi$
$593$	−4.92893	−	8.53716i	−0.202407	−	0.350579i	−0.949303	+	0.314361i	$0.898210\pi$
$594$		0			0
$595$	−1.07107	−	1.85514i	−0.0439095	−	0.0760535i
$596$	−2.14214			−0.0877453
$597$		0			0
$598$	0.313708	+	0.543359i	0.0128285	+	0.0222196i
$599$	−8.48528	−	14.6969i	−0.346699	−	0.600501i	0.638962	−	0.769238i	$-0.279364\pi$
$599$	−8.48528	−	14.6969i	−0.346699	−	0.600501i	−0.985661	+	0.168738i	$0.946031\pi$
$600$		0			0
$601$	−35.3431			−1.44168			−0.720838	−	0.693103i	$-0.756243\pi$
$601$	−35.3431			−1.44168			−0.720838	+	0.693103i	$0.756243\pi$
$602$	−2.96447	−	5.13461i	−0.120823	−	0.209271i
$603$		0			0
$604$	9.45584	+	16.3780i	0.384753	+	0.666411i
$605$	1.50000	−	2.59808i	0.0609837	−	0.105627i
$606$		0			0
$607$	−6.17157			−0.250496			−0.125248	−	0.992125i	$-0.539973\pi$
$607$	−6.17157			−0.250496			−0.125248	+	0.992125i	$0.539973\pi$
$608$	−15.4497	−	11.4685i	−0.626570	−	0.465108i
$609$		0			0
$610$	1.72183	−	2.98229i	0.0697147	−	0.120749i
$611$	2.89949	−	5.02207i	0.117301	−	0.203171i
$612$		0			0
$613$	−16.7990	+	29.0967i	−0.678505	+	1.17520i	0.296926	+	0.954900i	$0.404038\pi$
$613$	−16.7990	+	29.0967i	−0.678505	+	1.17520i	−0.975431	+	0.220304i	$0.929295\pi$
$614$	3.65685	+	6.33386i	0.147579	+	0.255614i
$615$		0			0
$616$	−8.20101			−0.330428
$617$	12.8284	+	22.2195i	0.516453	+	0.894523i	0.999818	+	0.0191037i	$0.00608126\pi$
$617$	12.8284	+	22.2195i	0.516453	+	0.894523i	−0.483364	+	0.875419i	$0.660585\pi$
$618$		0			0
$619$	15.6863			0.630485			0.315243	−	0.949011i	$-0.397914\pi$
$619$	15.6863			0.630485			0.315243	+	0.949011i	$0.397914\pi$
$620$	9.14214			0.367157
$621$		0			0
$622$	−0.828427	+	1.43488i	−0.0332169	+	0.0575334i
$623$	11.4142	+	19.7700i	0.457301	+	0.792068i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−2.48528			−0.0993318
$627$		0			0
$628$	36.2548			1.44673
$629$	1.27208	−	2.20330i	0.0507211	−	0.0878515i
$630$		0			0
$631$	6.64214	+	11.5045i	0.264419	+	0.457988i	0.967411	−	0.253210i	$-0.0814864\pi$
$631$	6.64214	+	11.5045i	0.264419	+	0.457988i	−0.702992	+	0.711198i	$0.748153\pi$
$632$	−2.65076	+	4.59125i	−0.105441	+	0.182630i
$633$		0			0
$634$	−2.20101			−0.0874133
$635$	12.9706			0.514721
$636$		0			0
$637$	−3.34315	−	5.79050i	−0.132460	−	0.229428i
$638$	−11.3137			−0.447914
$639$		0			0
$640$	5.27817	+	9.14207i	0.208638	+	0.361372i
$641$	14.0711	−	24.3718i	0.555774	−	0.962628i	−0.442069	−	0.896981i	$-0.645755\pi$
$641$	14.0711	−	24.3718i	0.555774	−	0.962628i	0.997843	−	0.0656474i	$-0.0209113\pi$
$642$		0			0
$643$	−2.91421	+	5.04757i	−0.114925	+	0.199057i	−0.917750	−	0.397159i	$-0.869996\pi$
$643$	−2.91421	+	5.04757i	−0.114925	+	0.199057i	0.802825	+	0.596215i	$0.203330\pi$
$644$	1.38478	−	2.39850i	0.0545678	−	0.0945143i
$645$		0			0
$646$	−1.69848	−	1.26080i	−0.0668260	−	0.0496054i
$647$	32.2843			1.26923			0.634613	−	0.772830i	$-0.281160\pi$
$647$	32.2843			1.26923			0.634613	+	0.772830i	$0.281160\pi$
$648$		0			0
$649$		0			0
$650$	0.378680	+	0.655892i	0.0148530	+	0.0257262i
$651$		0			0
$652$	13.8431	+	23.9770i	0.542139	+	0.939013i
$653$	−39.9411			−1.56302			−0.781509	−	0.623895i	$-0.785549\pi$
$653$	−39.9411			−1.56302			−0.781509	+	0.623895i	$0.785549\pi$
$654$		0			0
$655$	3.24264	+	5.61642i	0.126700	+	0.219452i
$656$	4.24264	+	7.34847i	0.165647	+	0.286910i
$657$		0			0
$658$	2.40202			0.0936405
$659$	3.75736	+	6.50794i	0.146366	+	0.253513i	0.929882	−	0.367859i	$-0.119909\pi$
$659$	3.75736	+	6.50794i	0.146366	+	0.253513i	−0.783516	+	0.621372i	$0.786576\pi$
$660$		0			0
$661$	3.48528	+	6.03668i	0.135562	+	0.234800i	0.925812	−	0.377985i	$-0.123383\pi$
$661$	3.48528	+	6.03668i	0.135562	+	0.234800i	−0.790250	+	0.612784i	$0.790049\pi$
$662$	1.10660	−	1.91669i	0.0430093	−	0.0744943i
$663$		0			0
$664$	−12.6863			−0.492324
$665$	−0.914214	+	7.91732i	−0.0354517	+	0.307021i
$666$		0			0
$667$	4.00000	−	6.92820i	0.154881	−	0.268261i
$668$	22.8284	−	39.5400i	0.883258	−	1.52985i
$669$		0			0
$670$	−1.13604	+	1.96768i	−0.0438890	+	0.0760180i
$671$	11.7574	+	20.3643i	0.453888	+	0.786157i
$672$		0			0
$673$	−23.8284			−0.918518			−0.459259	−	0.888302i	$-0.651885\pi$
$673$	−23.8284			−0.918518			−0.459259	+	0.888302i	$0.651885\pi$
$674$	−3.62132	−	6.27231i	−0.139488	−	0.241600i
$675$		0			0
$676$	17.6569			0.679110
$677$	23.4558			0.901481			0.450741	−	0.892655i	$-0.351160\pi$
$677$	23.4558			0.901481			0.450741	+	0.892655i	$0.351160\pi$
$678$		0			0
$679$	5.48528	−	9.50079i	0.210506	−	0.364607i
$680$	0.928932	+	1.60896i	0.0356229	+	0.0617007i
$681$		0			0
$682$	2.92893	−	5.07306i	0.112155	−	0.194257i
$683$	−44.1421			−1.68905			−0.844526	−	0.535515i	$-0.820118\pi$
$683$	−44.1421			−1.68905			−0.844526	+	0.535515i	$0.820118\pi$
$684$		0			0
$685$	10.4853			0.400622
$686$	4.03553	−	6.98975i	0.154077	−	0.266870i
$687$		0			0
$688$	−11.7426	−	20.3389i	−0.447684	−	0.775411i
$689$	1.82843	−	3.16693i	0.0696575	−	0.120650i
$690$		0			0
$691$	31.3137			1.19123			0.595615	−	0.803270i	$-0.296908\pi$
$691$	31.3137			1.19123			0.595615	+	0.803270i	$0.296908\pi$
$692$	13.3726			0.508349
$693$		0			0
$694$	−7.34315	−	12.7187i	−0.278742	−	0.482795i
$695$	−16.3137			−0.618814
$696$		0			0
$697$	1.65685	+	2.86976i	0.0627578	+	0.108700i
$698$	6.55025	−	11.3454i	0.247931	−	0.429429i
$699$		0			0
$700$	1.67157	−	2.89525i	0.0631795	−	0.109430i
$701$	16.0711	−	27.8359i	0.606996	−	1.05135i	−0.384737	−	0.923026i	$-0.625708\pi$
$701$	16.0711	−	27.8359i	0.606996	−	1.05135i	0.991733	−	0.128321i	$-0.0409589\pi$
$702$		0			0
$703$	−8.68629	+	3.76127i	−0.327610	+	0.141859i
$704$	−11.7990			−0.444691
$705$		0			0
$706$	−0.272078	+	0.471253i	−0.0102398	+	0.0177358i
$707$	11.1005	+	19.2266i	0.417477	+	0.723092i
$708$		0			0
$709$	−15.8137	−	27.3901i	−0.593896	−	1.02866i	−0.993702	−	0.112058i	$-0.964256\pi$
$709$	−15.8137	−	27.3901i	−0.593896	−	1.02866i	0.399805	−	0.916600i	$-0.369078\pi$
$710$	−4.14214			−0.155452
$711$		0			0
$712$	−9.89949	−	17.1464i	−0.370999	−	0.642590i
$713$	2.07107	+	3.58719i	0.0775621	+	0.134341i
$714$		0			0
$715$	−5.17157			−0.193406
$716$	−14.7574	−	25.5605i	−0.551508	−	0.955241i
$717$		0			0
$718$	1.89949	+	3.29002i	0.0708885	+	0.122783i
$719$	−11.5858	+	20.0672i	−0.432077	+	0.748379i	−0.997052	−	0.0767288i	$-0.975552\pi$
$719$	−11.5858	+	20.0672i	−0.432077	+	0.748379i	0.564975	+	0.825108i	$0.308886\pi$
$720$		0			0
$721$	17.9706			0.669259
$722$	2.27817	+	7.53311i	0.0847849	+	0.280353i
$723$		0			0
$724$	23.1421	−	40.0834i	0.860071	−	1.48969i
$725$	4.82843	−	8.36308i	0.179323	−	0.310597i
$726$		0			0
$727$	−18.0858	+	31.3255i	−0.670765	+	1.16180i	0.306923	+	0.951734i	$0.400701\pi$
$727$	−18.0858	+	31.3255i	−0.670765	+	1.16180i	−0.977688	+	0.210064i	$0.932633\pi$
$728$	−2.65076	−	4.59125i	−0.0982436	−	0.170163i
$729$		0			0
$730$	3.92893			0.145416
$731$	−4.58579	−	7.94282i	−0.169611	−	0.293776i
$732$		0			0
$733$	3.65685			0.135069			0.0675345	−	0.997717i	$-0.478487\pi$
$733$	3.65685			0.135069			0.0675345	+	0.997717i	$0.478487\pi$
$734$	−14.1299			−0.521546
$735$		0			0
$736$	−1.82843	+	3.16693i	−0.0673967	+	0.116735i
$737$	−7.75736	−	13.4361i	−0.285746	−	0.494927i
$738$		0			0
$739$	20.8137	−	36.0504i	0.765645	−	1.32614i	−0.174260	−	0.984700i	$-0.555753\pi$
$739$	20.8137	−	36.0504i	0.765645	−	1.32614i	0.939905	−	0.341436i	$-0.110913\pi$
$740$	3.97056			0.145961
$741$		0			0
$742$	1.51472			0.0556071
$743$	17.0711	−	29.5680i	0.626277	−	1.08474i	−0.362016	−	0.932172i	$-0.617911\pi$
$743$	17.0711	−	29.5680i	0.626277	−	1.08474i	0.988292	−	0.152571i	$-0.0487553\pi$
$744$		0			0
$745$	−0.585786	−	1.01461i	−0.0214616	−	0.0371725i
$746$	2.41421	−	4.18154i	0.0883906	−	0.153097i
$747$		0			0
$748$	−6.05887			−0.221534
$749$	−25.5980			−0.935330
$750$		0			0
$751$	−13.1569	−	22.7883i	−0.480100	−	0.831558i	0.519639	−	0.854386i	$-0.326066\pi$
$751$	−13.1569	−	22.7883i	−0.480100	−	0.831558i	−0.999739	+	0.0228276i	$0.992733\pi$
$752$	9.51472			0.346966
$753$		0			0
$754$	−3.65685	−	6.33386i	−0.133175	−	0.230665i
$755$	−5.17157	+	8.95743i	−0.188213	+	0.325994i
$756$		0			0
$757$	16.5711	−	28.7019i	0.602286	−	1.04319i	−0.390188	−	0.920735i	$-0.627590\pi$
$757$	16.5711	−	28.7019i	0.602286	−	1.04319i	0.992474	−	0.122454i	$-0.0390765\pi$
$758$	−0.349242	+	0.604906i	−0.0126851	+	0.0219712i
$759$		0			0
$760$	0.792893	−	6.86666i	0.0287613	−	0.249080i
$761$	−51.5980			−1.87043			−0.935213	−	0.354087i	$-0.884792\pi$
$761$	−51.5980			−1.87043			−0.935213	+	0.354087i	$0.884792\pi$
$762$		0			0
$763$	15.8284	−	27.4156i	0.573028	−	0.992513i
$764$	15.3848	+	26.6472i	0.556602	+	0.964062i
$765$		0			0
$766$	−7.02944	−	12.1753i	−0.253984	−	0.439913i
$767$		0			0
$768$		0			0
$769$	−7.15685	−	12.3960i	−0.258083	−	0.447012i	0.707646	−	0.706568i	$-0.249757\pi$
$769$	−7.15685	−	12.3960i	−0.258083	−	0.447012i	−0.965728	+	0.259555i	$0.916424\pi$
$770$	−1.07107	−	1.85514i	−0.0385986	−	0.0668547i
$771$		0			0
$772$	45.3431			1.63194
$773$	−11.0000	−	19.0526i	−0.395643	−	0.685273i	0.597540	−	0.801839i	$-0.296145\pi$
$773$	−11.0000	−	19.0526i	−0.395643	−	0.685273i	−0.993183	+	0.116566i	$0.962811\pi$
$774$		0			0
$775$	2.50000	+	4.33013i	0.0898027	+	0.155543i
$776$	−4.75736	+	8.23999i	−0.170779	+	0.295798i
$777$		0			0
$778$	6.40202			0.229524
$779$	1.41421	−	12.2474i	0.0506695	−	0.438810i
$780$		0			0
$781$	14.1421	−	24.4949i	0.506045	−	0.876496i
$782$	−0.201010	+	0.348160i	−0.00718811	+	0.0124502i
$783$		0			0
$784$	5.48528	−	9.50079i	0.195903	−	0.339314i
$785$	9.91421	+	17.1719i	0.353853	+	0.612892i
$786$		0			0
$787$	−5.48528			−0.195529			−0.0977646	−	0.995210i	$-0.531169\pi$
$787$	−5.48528			−0.195529			−0.0977646	+	0.995210i	$0.531169\pi$
$788$	−16.1421	−	27.9590i	−0.575040	−	0.995998i
$789$		0			0
$790$	−1.38478			−0.0492681
$791$	−7.31371			−0.260046
$792$		0			0
$793$	−7.60051	+	13.1645i	−0.269902	+	0.467484i
$794$	4.93503	+	8.54772i	0.175138	+	0.303347i
$795$		0			0
$796$	−15.5416	+	26.9189i	−0.550858	+	0.954115i
$797$	53.1127			1.88135			0.940674	−	0.339311i	$-0.110194\pi$
$797$	53.1127			1.88135			0.940674	+	0.339311i	$0.110194\pi$
$798$		0			0
$799$	3.71573			0.131453
$800$	−2.20711	+	3.82282i	−0.0780330	+	0.135157i
$801$		0			0
$802$	−4.68629	−	8.11689i	−0.165479	−	0.286618i
$803$	−13.4142	+	23.2341i	−0.473377	+	0.819914i
$804$		0			0
$805$	1.51472			0.0533868
$806$	3.78680			0.133384
$807$		0			0
$808$	−9.62742	−	16.6752i	−0.338691	−	0.586631i
$809$	−3.37258			−0.118574			−0.0592869	−	0.998241i	$-0.518883\pi$
$809$	−3.37258			−0.118574			−0.0592869	+	0.998241i	$0.518883\pi$
$810$		0			0
$811$	−15.3137	−	26.5241i	−0.537737	−	0.931388i	−0.999025	−	0.0441376i	$-0.985946\pi$
$811$	−15.3137	−	26.5241i	−0.537737	−	0.931388i	0.461288	−	0.887250i	$-0.347387\pi$
$812$	−16.1421	+	27.9590i	−0.566478	+	0.981169i
$813$		0			0
$814$	1.27208	−	2.20330i	0.0445863	−	0.0772258i
$815$	−7.57107	+	13.1135i	−0.265203	+	0.459345i
$816$		0			0
$817$	−3.91421	+	33.8981i	−0.136941	+	1.18594i
$818$	2.48528			0.0868958
$819$		0			0
$820$	−2.58579	+	4.47871i	−0.0902996	+	0.156403i
$821$	−26.0000	−	45.0333i	−0.907406	−	1.57167i	−0.817654	−	0.575710i	$-0.804726\pi$
$821$	−26.0000	−	45.0333i	−0.907406	−	1.57167i	−0.0897520	−	0.995964i	$-0.528607\pi$
$822$		0			0
$823$	−12.9706	−	22.4657i	−0.452125	−	0.783104i	0.546392	−	0.837529i	$-0.316001\pi$
$823$	−12.9706	−	22.4657i	−0.452125	−	0.783104i	−0.998518	+	0.0544251i	$0.982667\pi$
$824$	−15.5858			−0.542957
$825$		0			0
$826$		0			0
$827$	−1.65685	−	2.86976i	−0.0576145	−	0.0997912i	0.835780	−	0.549065i	$-0.185016\pi$
$827$	−1.65685	−	2.86976i	−0.0576145	−	0.0997912i	−0.893394	+	0.449274i	$0.851683\pi$
$828$		0			0
$829$	−22.0294			−0.765114			−0.382557	−	0.923932i	$-0.624956\pi$
$829$	−22.0294			−0.765114			−0.382557	+	0.923932i	$0.624956\pi$
$830$	−1.65685	−	2.86976i	−0.0575103	−	0.0996107i
$831$		0			0
$832$	−3.81371	−	6.60554i	−0.132217	−	0.229006i
$833$	2.14214	−	3.71029i	0.0742206	−	0.128554i
$834$		0			0
$835$	24.9706			0.864142
$836$	18.1005	+	13.4361i	0.626019	+	0.464699i
$837$		0			0
$838$	0.686292	−	1.18869i	0.0237075	−	0.0410627i
$839$	−2.89949	+	5.02207i	−0.100102	+	0.173381i	−0.911726	−	0.410798i	$-0.865250\pi$
$839$	−2.89949	+	5.02207i	−0.100102	+	0.173381i	0.811625	+	0.584179i	$0.198583\pi$
$840$		0			0
$841$	−32.1274	+	55.6463i	−1.10784	+	1.91884i
$842$	1.58579	+	2.74666i	0.0546498	+	0.0946562i
$843$		0			0
$844$	0.573593			0.0197439
$845$	4.82843	+	8.36308i	0.166103	+	0.287699i
$846$		0			0
$847$	−5.48528			−0.188476
$848$	6.00000			0.206041
$849$		0			0
$850$	−0.242641	+	0.420266i	−0.00832251	+	0.0144150i
$851$	0.899495	+	1.55797i	0.0308343	+	0.0534066i
$852$		0			0
$853$	−2.22792	+	3.85887i	−0.0762826	+	0.132125i	−0.901643	−	0.432480i	$-0.857638\pi$
$853$	−2.22792	+	3.85887i	−0.0762826	+	0.132125i	0.825361	+	0.564606i	$0.190972\pi$
$854$	−6.29646			−0.215461
$855$		0			0
$856$	22.2010			0.758815
$857$	21.2426	−	36.7933i	0.725635	−	1.25684i	−0.233077	−	0.972458i	$-0.574880\pi$
$857$	21.2426	−	36.7933i	0.725635	−	1.25684i	0.958712	−	0.284378i	$-0.0917871\pi$
$858$		0			0
$859$	−17.4706	−	30.2599i	−0.596088	−	1.03245i	−0.993392	−	0.114768i	$-0.963388\pi$
$859$	−17.4706	−	30.2599i	−0.596088	−	1.03245i	0.397304	−	0.917687i	$-0.369946\pi$
$860$	7.15685	−	12.3960i	0.244047	−	0.422701i
$861$		0			0
$862$	1.02944			0.0350628
$863$	25.3137			0.861689			0.430844	−	0.902426i	$-0.358216\pi$
$863$	25.3137			0.861689			0.430844	+	0.902426i	$0.358216\pi$
$864$		0			0
$865$	3.65685	+	6.33386i	0.124337	+	0.215358i
$866$	−16.4975			−0.560607
$867$		0			0
$868$	−8.35786	−	14.4762i	−0.283684	−	0.491356i
$869$	4.72792	−	8.18900i	0.160384	−	0.277793i
$870$		0			0
$871$	5.01472	−	8.68575i	0.169917	−	0.294305i
$872$	−13.7279	+	23.7775i	−0.464886	+	0.805206i
$873$		0			0
$874$	1.37258	−	0.594346i	0.0464283	−	0.0201040i
$875$	1.82843			0.0618121
$876$		0			0
$877$	22.3995	−	38.7971i	0.756377	−	1.31008i	−0.188310	−	0.982110i	$-0.560301\pi$
$877$	22.3995	−	38.7971i	0.756377	−	1.31008i	0.944687	−	0.327974i	$-0.106366\pi$
$878$	−3.52082	−	6.09823i	−0.118822	−	0.205805i
$879$		0			0
$880$	−4.24264	−	7.34847i	−0.143019	−	0.247717i
$881$	−42.9706			−1.44772			−0.723858	−	0.689949i	$-0.757633\pi$
$881$	−42.9706			−1.44772			−0.723858	+	0.689949i	$0.757633\pi$
$882$		0			0
$883$	16.5711	+	28.7019i	0.557661	+	0.965897i	0.997691	+	0.0679140i	$0.0216343\pi$
$883$	16.5711	+	28.7019i	0.557661	+	0.965897i	−0.440030	+	0.897983i	$0.645032\pi$
$884$	−1.95837	−	3.39200i	−0.0658671	−	0.114085i
$885$		0			0
$886$	−7.51472			−0.252462
$887$	14.7279	+	25.5095i	0.494515	+	0.856525i	0.999980	−	0.00632174i	$-0.00201228\pi$
$887$	14.7279	+	25.5095i	0.494515	+	0.856525i	−0.505465	+	0.862847i	$0.668679\pi$
$888$		0			0
$889$	−11.8579	−	20.5384i	−0.397700	−	0.688837i
$890$	2.58579	−	4.47871i	0.0866758	−	0.150127i
$891$		0			0
$892$	−10.6569			−0.356818
$893$	−11.1005	−	8.23999i	−0.371464	−	0.275741i
$894$		0			0
$895$	8.07107	−	13.9795i	0.269786	−	0.467283i
$896$	9.65076	−	16.7156i	0.322409	−	0.558429i
$897$		0			0
$898$	2.72792	−	4.72490i	0.0910319	−	0.157672i
$899$	−24.1421	−	41.8154i	−0.805185	−	1.39462i
$900$		0			0
$901$	2.34315			0.0780615
$902$	1.65685	+	2.86976i	0.0551672	+	0.0955524i
$903$		0			0
$904$	6.34315			0.210970
$905$	25.3137			0.841456
$906$		0			0
$907$	15.1716	−	26.2779i	0.503764	−	0.872545i	−0.496227	−	0.868193i	$-0.665282\pi$
$907$	15.1716	−	26.2779i	0.503764	−	0.872545i	0.999991	−	0.00435154i	$-0.00138514\pi$
$908$	17.3431	+	30.0392i	0.575553	+	0.996886i
$909$		0			0
$910$	0.692388	−	1.19925i	0.0229524	−	0.0397548i
$911$	−38.1421			−1.26371			−0.631853	−	0.775089i	$-0.717705\pi$
$911$	−38.1421			−1.26371			−0.631853	+	0.775089i	$0.717705\pi$
$912$		0			0
$913$	22.6274			0.748858
$914$	0.863961	−	1.49642i	0.0285773	−	0.0494973i
$915$		0			0
$916$	−4.25736	−	7.37396i	−0.140667	−	0.243643i
$917$	5.92893	−	10.2692i	0.195791	−	0.339119i
$918$		0			0
$919$	−3.00000			−0.0989609			−0.0494804	−	0.998775i	$-0.515757\pi$
$919$	−3.00000			−0.0989609			−0.0494804	+	0.998775i	$0.515757\pi$
$920$	−1.31371			−0.0433117
$921$		0			0
$922$	6.24264	+	10.8126i	0.205590	+	0.356093i
$923$	18.2843			0.601834
$924$		0			0
$925$	1.08579	+	1.88064i	0.0357004	+	0.0618350i
$926$	4.72183	−	8.17844i	0.155169	−	0.268760i
$927$		0			0
$928$	21.3137	−	36.9164i	0.699657	−	1.21184i
$929$	−11.2426	+	19.4728i	−0.368859	+	0.638883i	−0.989387	−	0.145301i	$-0.953585\pi$
$929$	−11.2426	+	19.4728i	−0.368859	+	0.638883i	0.620528	+	0.784184i	$0.286918\pi$
$930$		0			0
$931$	−14.6274	+	6.33386i	−0.479394	+	0.207584i
$932$	−46.2843			−1.51609
$933$		0			0
$934$	4.92893	−	8.53716i	0.161280	−	0.279344i
$935$	−1.65685	−	2.86976i	−0.0541849	−	0.0938510i
$936$		0			0
$937$	17.9142	+	31.0283i	0.585232	+	1.01365i	0.994846	+	0.101393i	$0.0323298\pi$
$937$	17.9142	+	31.0283i	0.585232	+	1.01365i	−0.409615	+	0.912259i	$0.634337\pi$
$938$	4.15433			0.135644
$939$		0			0
$940$	2.89949	+	5.02207i	0.0945711	+	0.163802i
$941$	−5.41421	−	9.37769i	−0.176498	−	0.305704i	0.764180	−	0.645002i	$-0.223144\pi$
$941$	−5.41421	−	9.37769i	−0.176498	−	0.305704i	−0.940679	+	0.339298i	$0.889810\pi$
$942$		0			0
$943$	−2.34315			−0.0763033
$944$		0			0
$945$		0			0
$946$	−4.58579	−	7.94282i	−0.149097	−	0.258243i
$947$	−28.5563	+	49.4610i	−0.927957	+	1.60727i	−0.141221	+	0.989978i	$0.545103\pi$
$947$	−28.5563	+	49.4610i	−0.927957	+	1.60727i	−0.786736	+	0.617290i	$0.788231\pi$
$948$		0			0
$949$	−17.3431			−0.562982
$950$	1.65685	−	0.717439i	0.0537555	−	0.0232768i
$951$		0			0
$952$	1.69848	−	2.94186i	0.0550482	−	0.0953463i
$953$	15.7990	−	27.3647i	0.511779	−	0.886428i	−0.488127	−	0.872772i	$-0.662320\pi$
$953$	15.7990	−	27.3647i	0.511779	−	0.886428i	0.999907	−	0.0136556i	$-0.00434685\pi$
$954$		0			0
$955$	−8.41421	+	14.5738i	−0.272278	+	0.471599i
$956$	22.5147	+	38.9966i	0.728178	+	1.26124i
$957$		0			0
$958$	−1.02944			−0.0332596
$959$	−9.58579	−	16.6031i	−0.309541	−	0.536141i
$960$		0			0
$961$	−6.00000			−0.193548
$962$	1.64466			0.0530260
$963$		0			0
$964$	4.57107	−	7.91732i	0.147224	−	0.255000i
$965$	12.3995	+	21.4766i	0.399154	+	0.691355i
$966$		0			0
$967$	−8.39949	+	14.5484i	−0.270110	+	0.467843i	−0.968890	−	0.247493i	$-0.920393\pi$
$967$	−8.39949	+	14.5484i	−0.270110	+	0.467843i	0.698780	+	0.715337i	$0.253727\pi$
$968$	4.75736			0.152907
$969$		0			0
$970$	−2.48528			−0.0797976
$971$	−10.4142	+	18.0379i	−0.334208	+	0.578865i	−0.983332	−	0.181817i	$-0.941802\pi$
$971$	−10.4142	+	18.0379i	−0.334208	+	0.578865i	0.649124	+	0.760682i	$0.275135\pi$
$972$		0			0
$973$	14.9142	+	25.8322i	0.478128	+	0.828142i
$974$	1.31371	−	2.27541i	0.0420939	−	0.0729088i
$975$		0			0
$976$	−24.9411			−0.798346
$977$	34.2843			1.09685			0.548426	−	0.836199i	$-0.315227\pi$
$977$	34.2843			1.09685			0.548426	+	0.836199i	$0.315227\pi$
$978$		0			0
$979$	17.6569	+	30.5826i	0.564316	+	0.977423i
$980$	6.68629			0.213586
$981$		0			0
$982$	4.89949	+	8.48617i	0.156349	+	0.270805i
$983$	−18.4853	+	32.0174i	−0.589589	+	1.02120i	0.404697	+	0.914451i	$0.367377\pi$
$983$	−18.4853	+	32.0174i	−0.589589	+	1.02120i	−0.994286	+	0.106747i	$0.965956\pi$
$984$		0			0
$985$	8.82843	−	15.2913i	0.281297	−	0.487221i
$986$	2.34315	−	4.05845i	0.0746210	−	0.129247i
$987$		0			0
$988$	−1.67157	+	14.4762i	−0.0531798	+	0.460551i
$989$	6.48528			0.206220
$990$		0			0
$991$	20.3284	−	35.2099i	0.645754	−	1.11848i	−0.338373	−	0.941012i	$-0.609877\pi$
$991$	20.3284	−	35.2099i	0.645754	−	1.11848i	0.984127	−	0.177466i	$-0.0567901\pi$
$992$	11.0355	+	19.1141i	0.350379	+	0.606873i
$993$		0			0
$994$	3.78680	+	6.55892i	0.120110	+	0.208036i
$995$	−17.0000			−0.538936
$996$		0			0
$997$	14.7426	+	25.5350i	0.466904	+	0.808702i	0.999285	−	0.0378031i	$-0.0120360\pi$
$997$	14.7426	+	25.5350i	0.466904	+	0.808702i	−0.532381	+	0.846505i	$0.678703\pi$
$998$	1.52082	+	2.63413i	0.0481406	+	0.0833819i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.k.f.676.1		4
3.2	odd	2		285.2.i.d.106.2	✓	4
19.7	even	3	inner	855.2.k.f.406.1		4
57.8	even	6		5415.2.a.o.1.2		2
57.11	odd	6		5415.2.a.u.1.1		2
57.26	odd	6		285.2.i.d.121.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.i.d.106.2	✓	4	3.2	odd	2
285.2.i.d.121.2	yes	4	57.26	odd	6
855.2.k.f.406.1		4	19.7	even	3	inner
855.2.k.f.676.1		4	1.1	even	1	trivial
5415.2.a.o.1.2		2	57.8	even	6
5415.2.a.u.1.1		2	57.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.207107 + 0.358719i) q^{2} +(0.914214 + 1.58346i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.82843 q^{7} -1.58579 q^{8} +(-0.207107 - 0.358719i) q^{10} +2.82843 q^{11} +(0.914214 + 1.58346i) q^{13} +(-0.378680 + 0.655892i) q^{14} +(-1.50000 + 2.59808i) q^{16} +(-0.585786 + 1.01461i) q^{17} +(4.00000 - 1.73205i) q^{19} -1.82843 q^{20} +(-0.585786 + 1.01461i) q^{22} +(-0.414214 - 0.717439i) q^{23} +(-0.500000 - 0.866025i) q^{25} -0.757359 q^{26} +(1.67157 + 2.89525i) q^{28} +(4.82843 + 8.36308i) q^{29} -5.00000 q^{31} +(-2.20711 - 3.82282i) q^{32} +(-0.242641 - 0.420266i) q^{34} +(-0.914214 + 1.58346i) q^{35} -2.17157 q^{37} +(-0.207107 + 1.79360i) q^{38} +(0.792893 - 1.37333i) q^{40} +(1.41421 - 2.44949i) q^{41} +(-3.91421 + 6.77962i) q^{43} +(2.58579 + 4.47871i) q^{44} +0.343146 q^{46} +(-1.58579 - 2.74666i) q^{47} -3.65685 q^{49} +0.414214 q^{50} +(-1.67157 + 2.89525i) q^{52} +(-1.00000 - 1.73205i) q^{53} +(-1.41421 + 2.44949i) q^{55} -2.89949 q^{56} -4.00000 q^{58} +(4.15685 + 7.19988i) q^{61} +(1.03553 - 1.79360i) q^{62} -4.17157 q^{64} -1.82843 q^{65} +(-2.74264 - 4.75039i) q^{67} -2.14214 q^{68} +(-0.378680 - 0.655892i) q^{70} +(5.00000 - 8.66025i) q^{71} +(-4.74264 + 8.21449i) q^{73} +(0.449747 - 0.778985i) q^{74} +(6.39949 + 4.75039i) q^{76} +5.17157 q^{77} +(1.67157 - 2.89525i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(0.585786 + 1.01461i) q^{82} +8.00000 q^{83} +(-0.585786 - 1.01461i) q^{85} +(-1.62132 - 2.80821i) q^{86} -4.48528 q^{88} +(6.24264 + 10.8126i) q^{89} +(1.67157 + 2.89525i) q^{91} +(0.757359 - 1.31178i) q^{92} +1.31371 q^{94} +(-0.500000 + 4.33013i) q^{95} +(3.00000 - 5.19615i) q^{97} +(0.757359 - 1.31178i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{7} - 12 q^{8} + 2 q^{10} - 2 q^{13} - 10 q^{14} - 6 q^{16} - 8 q^{17} + 16 q^{19} + 4 q^{20} - 8 q^{22} + 4 q^{23} - 2 q^{25} - 20 q^{26} + 18 q^{28} + 8 q^{29}+ \cdots + 20 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^7 - 12 * q^8 + 2 * q^10 - 2 * q^13 - 10 * q^14 - 6 * q^16 - 8 * q^17 + 16 * q^19 + 4 * q^20 - 8 * q^22 + 4 * q^23 - 2 * q^25 - 20 * q^26 + 18 * q^28 + 8 * q^29 - 20 * q^31 - 6 * q^32 + 16 * q^34 + 2 * q^35 - 20 * q^37 + 2 * q^38 + 6 * q^40 - 10 * q^43 + 16 * q^44 + 24 * q^46 - 12 * q^47 + 8 * q^49 - 4 * q^50 - 18 * q^52 - 4 * q^53 + 28 * q^56 - 16 * q^58 - 6 * q^61 - 10 * q^62 - 28 * q^64 + 4 * q^65 + 6 * q^67 + 48 * q^68 - 10 * q^70 + 20 * q^71 - 2 * q^73 - 18 * q^74 - 14 * q^76 + 32 * q^77 + 18 * q^79 - 6 * q^80 + 8 * q^82 + 32 * q^83 - 8 * q^85 + 2 * q^86 + 16 * q^88 + 8 * q^89 + 18 * q^91 + 20 * q^92 - 40 * q^94 - 2 * q^95 + 12 * q^97 + 20 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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