LMFDB - Embedded newform 1008.2.ca.c.257.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(257,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5, 5]))

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

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

chi := DirichletCharacter("1008.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.ca (of order $6$, degree $2$, 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.2
Root			$0.765614 + 1.55365i$ of defining polynomial
Character	$\chi$	$=$	1008.257
Dual form			1008.2.ca.c.353.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.52765 + 0.816261i) q^{3} +(-1.82207 - 3.15592i) q^{5} +(1.58246 - 2.12034i) q^{7} +(1.66744 - 2.49392i) q^{9} +O(q^{10})$	\(q+(-1.52765 + 0.816261i) q^{3} +(-1.82207 - 3.15592i) q^{5} +(1.58246 - 2.12034i) q^{7} +(1.66744 - 2.49392i) q^{9} +(-4.38809 - 2.53346i) q^{11} +(2.94391 + 1.69967i) q^{13} +(5.35954 + 3.33386i) q^{15} +(-0.774696 - 1.34181i) q^{17} +(0.707140 + 0.408267i) q^{19} +(-0.686700 + 4.53083i) q^{21} +(-1.47275 + 0.850294i) q^{23} +(-4.13989 + 7.17050i) q^{25} +(-0.511572 + 5.17091i) q^{27} +(-3.60693 + 2.08246i) q^{29} -2.16996i q^{31} +(8.77143 + 0.288426i) q^{33} +(-9.57497 - 1.13071i) q^{35} +(-3.39979 + 5.88860i) q^{37} +(-5.88465 - 0.193502i) q^{39} +(1.01681 - 1.76117i) q^{41} +(-3.06189 - 5.30335i) q^{43} +(-10.9088 - 0.718194i) q^{45} +6.74255 q^{47} +(-1.99165 - 6.71069i) q^{49} +(2.27874 + 1.41747i) q^{51} +(-11.4961 + 6.63726i) q^{53} +18.4646i q^{55} +(-1.41352 - 0.0464799i) q^{57} +2.17632 q^{59} -7.25382i q^{61} +(-2.64930 - 7.48206i) q^{63} -12.3877i q^{65} -2.45641 q^{67} +(1.55579 - 2.50110i) q^{69} +6.74272i q^{71} +(3.76912 - 2.17610i) q^{73} +(0.471313 - 14.3333i) q^{75} +(-12.3158 + 5.29511i) q^{77} -12.7530 q^{79} +(-3.43930 - 8.31692i) q^{81} +(-0.768040 - 1.33028i) q^{83} +(-2.82310 + 4.88976i) q^{85} +(3.81029 - 6.12546i) q^{87} +(-6.01679 + 10.4214i) q^{89} +(8.26249 - 3.55243i) q^{91} +(1.77125 + 3.31494i) q^{93} -2.97557i q^{95} +(-5.59509 + 3.23033i) q^{97} +(-13.6351 + 6.71916i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{7}+O(q^{10}) $ 16 * q - 2 * q^7	$ 16 q - 2 q^{7} - 12 q^{11} + 6 q^{13} + 18 q^{15} - 18 q^{17} - 12 q^{21} + 6 q^{23} - 8 q^{25} - 36 q^{27} + 6 q^{29} - 30 q^{35} - 2 q^{37} + 12 q^{39} - 6 q^{41} + 2 q^{43} - 30 q^{45} + 36 q^{47} - 8 q^{49} - 6 q^{51} - 36 q^{53} + 6 q^{57} - 60 q^{59} - 36 q^{63} + 28 q^{67} - 42 q^{69} - 60 q^{75} - 42 q^{77} - 32 q^{79} - 36 q^{81} - 12 q^{85} + 24 q^{87} - 24 q^{89} + 12 q^{91} - 42 q^{93} + 6 q^{97} - 18 q^{99}+O(q^{100}) $ 16 * q - 2 * q^7 - 12 * q^11 + 6 * q^13 + 18 * q^15 - 18 * q^17 - 12 * q^21 + 6 * q^23 - 8 * q^25 - 36 * q^27 + 6 * q^29 - 30 * q^35 - 2 * q^37 + 12 * q^39 - 6 * q^41 + 2 * q^43 - 30 * q^45 + 36 * q^47 - 8 * q^49 - 6 * q^51 - 36 * q^53 + 6 * q^57 - 60 * q^59 - 36 * q^63 + 28 * q^67 - 42 * q^69 - 60 * q^75 - 42 * q^77 - 32 * q^79 - 36 * q^81 - 12 * q^85 + 24 * q^87 - 24 * q^89 + 12 * q^91 - 42 * q^93 + 6 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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			0
$2$		0			0
$3$	−1.52765	+	0.816261i	−0.881990	+	0.471268i
$3$	−1.52765	+	0.816261i	−0.881990	+	0.471268i
$4$		0			0
$5$	−1.82207	−	3.15592i	−0.814855	−	1.41137i	−0.909432	−	0.415853i	$-0.863483\pi$
$5$	−1.82207	−	3.15592i	−0.814855	−	1.41137i	0.0945763	−	0.995518i	$-0.469850\pi$
$6$		0			0
$7$	1.58246	−	2.12034i	0.598113	−	0.801412i
$7$	1.58246	−	2.12034i	0.598113	−	0.801412i
$8$		0			0
$9$	1.66744	−	2.49392i	0.555812	−	0.831308i
$10$		0			0
$11$	−4.38809	−	2.53346i	−1.32306	−	0.763868i	−0.338843	−	0.940843i	$-0.610035\pi$
$11$	−4.38809	−	2.53346i	−1.32306	−	0.763868i	−0.984215	+	0.176975i	$0.943369\pi$
$12$		0			0
$13$	2.94391	+	1.69967i	0.816495	+	0.471404i	0.849206	−	0.528061i	$-0.177081\pi$
$13$	2.94391	+	1.69967i	0.816495	+	0.471404i	−0.0327114	+	0.999465i	$0.510414\pi$
$14$		0			0
$15$	5.35954	+	3.33386i	1.38383	+	0.860799i
$16$		0			0
$17$	−0.774696	−	1.34181i	−0.187891	−	0.325438i	0.756656	−	0.653814i	$-0.226832\pi$
$17$	−0.774696	−	1.34181i	−0.187891	−	0.325438i	−0.944547	+	0.328376i	$0.893499\pi$
$18$		0			0
$19$	0.707140	+	0.408267i	0.162229	+	0.0936629i	0.578916	−	0.815387i	$-0.303476\pi$
$19$	0.707140	+	0.408267i	0.162229	+	0.0936629i	−0.416687	+	0.909050i	$0.636809\pi$
$20$		0			0
$21$	−0.686700	+	4.53083i	−0.149850	+	0.988709i
$22$		0			0
$23$	−1.47275	+	0.850294i	−0.307090	+	0.177299i	−0.645624	−	0.763656i	$-0.723402\pi$
$23$	−1.47275	+	0.850294i	−0.307090	+	0.177299i	0.338533	+	0.940954i	$0.390069\pi$
$24$		0			0
$25$	−4.13989	+	7.17050i	−0.827979	+	1.43410i
$26$		0			0
$27$	−0.511572	+	5.17091i	−0.0984521	+	0.995142i
$28$		0			0
$29$	−3.60693	+	2.08246i	−0.669789	+	0.386703i	−0.795997	−	0.605301i	$-0.793053\pi$
$29$	−3.60693	+	2.08246i	−0.669789	+	0.386703i	0.126208	+	0.992004i	$0.459719\pi$
$30$		0			0
$31$		−	2.16996i		−	0.389736i	−0.980830	−	0.194868i	$-0.937572\pi$
$31$		−	2.16996i		−	0.389736i	0.980830	−	0.194868i	$-0.0624278\pi$
$32$		0			0
$33$	8.77143	+	0.288426i	1.52691	+	0.0502086i
$34$		0			0
$35$	−9.57497	−	1.13071i	−1.61846	−	0.191125i
$36$		0			0
$37$	−3.39979	+	5.88860i	−0.558921	+	0.968080i	0.438666	+	0.898650i	$0.355451\pi$
$37$	−3.39979	+	5.88860i	−0.558921	+	0.968080i	−0.997587	+	0.0694297i	$0.977882\pi$
$38$		0			0
$39$	−5.88465	−	0.193502i	−0.942298	−	0.0309851i
$40$		0			0
$41$	1.01681	−	1.76117i	0.158799	−	0.275049i	−0.775637	−	0.631180i	$-0.782571\pi$
$41$	1.01681	−	1.76117i	0.158799	−	0.275049i	0.934436	+	0.356131i	$0.115904\pi$
$42$		0			0
$43$	−3.06189	−	5.30335i	−0.466934	−	0.808753i	0.532353	−	0.846523i	$-0.321308\pi$
$43$	−3.06189	−	5.30335i	−0.466934	−	0.808753i	−0.999286	+	0.0377695i	$0.987975\pi$
$44$		0			0
$45$	−10.9088	−	0.718194i	−1.62619	−	0.107062i
$46$		0			0
$47$	6.74255			0.983502			0.491751	−	0.870736i	$-0.336357\pi$
$47$	6.74255			0.983502			0.491751	+	0.870736i	$0.336357\pi$
$48$		0			0
$49$	−1.99165	−	6.71069i	−0.284521	−	0.958670i
$50$		0			0
$51$	2.27874	+	1.41747i	0.319087	+	0.198485i
$52$		0			0
$53$	−11.4961	+	6.63726i	−1.57911	+	0.911698i	−0.584123	+	0.811665i	$0.698561\pi$
$53$	−11.4961	+	6.63726i	−1.57911	+	0.911698i	−0.994984	+	0.100032i	$0.968105\pi$
$54$		0			0
$55$			18.4646i			2.48977i
$56$		0			0
$57$	−1.41352	−	0.0464799i	−0.187225	−	0.00615641i
$58$		0			0
$59$	2.17632			0.283333			0.141666	−	0.989914i	$-0.454754\pi$
$59$	2.17632			0.283333			0.141666	+	0.989914i	$0.454754\pi$
$60$		0			0
$61$		−	7.25382i		−	0.928756i	−0.885637	−	0.464378i	$-0.846278\pi$
$61$		−	7.25382i		−	0.928756i	0.885637	−	0.464378i	$-0.153722\pi$
$62$		0			0
$63$	−2.64930	−	7.48206i	−0.333781	−	0.942651i
$64$		0			0
$65$		−	12.3877i		−	1.53650i
$66$		0			0
$67$	−2.45641			−0.300098			−0.150049	−	0.988679i	$-0.547943\pi$
$67$	−2.45641			−0.300098			−0.150049	+	0.988679i	$0.547943\pi$
$68$		0			0
$69$	1.55579	−	2.50110i	0.187295	−	0.301097i
$70$		0			0
$71$			6.74272i			0.800213i	0.916469	+	0.400107i	$0.131027\pi$
$71$			6.74272i			0.800213i	−0.916469	+	0.400107i	$0.868973\pi$
$72$		0			0
$73$	3.76912	−	2.17610i	0.441142	−	0.254694i	−0.262940	−	0.964812i	$-0.584692\pi$
$73$	3.76912	−	2.17610i	0.441142	−	0.254694i	0.704082	+	0.710119i	$0.251359\pi$
$74$		0			0
$75$	0.471313	−	14.3333i	0.0544225	−	1.65506i
$76$		0			0
$77$	−12.3158	+	5.29511i	−1.40351	+	0.603434i
$78$		0			0
$79$	−12.7530			−1.43483			−0.717414	−	0.696647i	$-0.754674\pi$
$79$	−12.7530			−1.43483			−0.717414	+	0.696647i	$0.754674\pi$
$80$		0			0
$81$	−3.43930	−	8.31692i	−0.382145	−	0.924102i
$82$		0			0
$83$	−0.768040	−	1.33028i	−0.0843034	−	0.146018i	0.820791	−	0.571229i	$-0.193533\pi$
$83$	−0.768040	−	1.33028i	−0.0843034	−	0.146018i	−0.905094	+	0.425211i	$0.860200\pi$
$84$		0			0
$85$	−2.82310	+	4.88976i	−0.306209	+	0.530369i
$86$		0			0
$87$	3.81029	−	6.12546i	0.408506	−	0.656718i
$88$		0			0
$89$	−6.01679	+	10.4214i	−0.637778	+	1.10466i	0.348141	+	0.937442i	$0.386813\pi$
$89$	−6.01679	+	10.4214i	−0.637778	+	1.10466i	−0.985919	+	0.167222i	$0.946520\pi$
$90$		0			0
$91$	8.26249	−	3.55243i	0.866145	−	0.372396i
$92$		0			0
$93$	1.77125	+	3.31494i	0.183670	+	0.343743i
$94$		0			0
$95$		−	2.97557i		−	0.305287i
$96$		0			0
$97$	−5.59509	+	3.23033i	−0.568095	+	0.327990i	−0.756388	−	0.654123i	$-0.773038\pi$
$97$	−5.59509	+	3.23033i	−0.568095	+	0.327990i	0.188293	+	0.982113i	$0.439705\pi$
$98$		0			0
$99$	−13.6351	+	6.71916i	−1.37038	+	0.675301i
$100$		0			0
$101$	5.95045	−	10.3065i	0.592092	−	1.02553i	−0.401858	−	0.915702i	$-0.631636\pi$
$101$	5.95045	−	10.3065i	0.592092	−	1.02553i	0.993950	−	0.109831i	$-0.0350311\pi$
$102$		0			0
$103$	−12.7174	+	7.34240i	−1.25308	+	0.723468i	−0.971721	−	0.236134i	$-0.924120\pi$
$103$	−12.7174	+	7.34240i	−1.25308	+	0.723468i	−0.281363	+	0.959601i	$0.590786\pi$
$104$		0			0
$105$	15.5502	−	6.08833i	1.51754	−	0.594161i
$106$		0			0
$107$	2.87453	+	1.65961i	0.277891	+	0.160440i	0.632468	−	0.774586i	$-0.282042\pi$
$107$	2.87453	+	1.65961i	0.277891	+	0.160440i	−0.354577	+	0.935027i	$0.615375\pi$
$108$		0			0
$109$	1.41837	+	2.45668i	0.135855	+	0.235308i	0.925924	−	0.377711i	$-0.123289\pi$
$109$	1.41837	+	2.45668i	0.135855	+	0.235308i	−0.790069	+	0.613018i	$0.789955\pi$
$110$		0			0
$111$	0.387054	−	11.7708i	0.0367376	−	1.11724i
$112$		0			0
$113$	−6.80465	−	3.92866i	−0.640127	−	0.369578i	0.144536	−	0.989500i	$-0.453831\pi$
$113$	−6.80465	−	3.92866i	−0.640127	−	0.369578i	−0.784664	+	0.619922i	$0.787164\pi$
$114$		0			0
$115$	5.36692	+	3.09859i	0.500468	+	0.288945i
$116$		0			0
$117$	9.14764	−	4.50780i	0.845699	−	0.416746i
$118$		0			0
$119$	−4.07102	−	0.480749i	−0.373190	−	0.0440702i
$120$		0			0
$121$	7.33687	+	12.7078i	0.666988	+	1.15526i
$122$		0			0
$123$	−0.115761	+	3.52044i	−0.0104378	+	0.317427i
$124$		0			0
$125$	11.9520			1.06902
$126$		0			0
$127$	17.4279			1.54647			0.773237	−	0.634117i	$-0.218636\pi$
$127$	17.4279			1.54647			0.773237	+	0.634117i	$0.218636\pi$
$128$		0			0
$129$	9.00642	+	5.60237i	0.792971	+	0.493261i
$130$		0			0
$131$	−1.61603	−	2.79904i	−0.141193	−	0.244554i	0.786753	−	0.617268i	$-0.211760\pi$
$131$	−1.61603	−	2.79904i	−0.141193	−	0.244554i	−0.927946	+	0.372714i	$0.878427\pi$
$132$		0			0
$133$	1.98468	−	0.853307i	0.172094	−	0.0739911i
$134$		0			0
$135$	17.2511	−	7.80729i	1.48474	−	0.671944i
$136$		0			0
$137$	12.6284	+	7.29101i	1.07892	+	0.622913i	0.930604	−	0.366027i	$-0.119282\pi$
$137$	12.6284	+	7.29101i	1.07892	+	0.622913i	0.148313	+	0.988940i	$0.452616\pi$
$138$		0			0
$139$	4.97814	+	2.87413i	0.422240	+	0.243780i	0.696035	−	0.718008i	$-0.254946\pi$
$139$	4.97814	+	2.87413i	0.422240	+	0.243780i	−0.273795	+	0.961788i	$0.588279\pi$
$140$		0			0
$141$	−10.3003	+	5.50368i	−0.867438	+	0.463493i
$142$		0			0
$143$	−8.61210	−	14.9166i	−0.720180	−	1.24739i
$144$		0			0
$145$	13.1442	+	7.58878i	1.09156	+	0.630214i
$146$		0			0
$147$	8.52021	+	8.62589i	0.702735	+	0.711451i
$148$		0			0
$149$	4.95904	−	2.86310i	0.406261	−	0.234555i	−0.282921	−	0.959143i	$-0.591303\pi$
$149$	4.95904	−	2.86310i	0.406261	−	0.234555i	0.689182	+	0.724589i	$0.257970\pi$
$150$		0			0
$151$	−6.38483	+	11.0589i	−0.519590	+	0.899957i	0.480151	+	0.877186i	$0.340582\pi$
$151$	−6.38483	+	11.0589i	−0.519590	+	0.899957i	−0.999741	+	0.0227705i	$0.992751\pi$
$152$		0			0
$153$	−4.63814	−	0.305357i	−0.374971	−	0.0246866i
$154$		0			0
$155$	−6.84821	+	3.95382i	−0.550062	+	0.317578i
$156$		0			0
$157$		−	12.7707i		−	1.01921i	−0.860407	−	0.509607i	$-0.829791\pi$
$157$		−	12.7707i		−	1.01921i	0.860407	−	0.509607i	$-0.170209\pi$
$158$		0			0
$159$	12.1443	−	19.5232i	0.963102	−	1.54829i
$160$		0			0
$161$	−0.527662	+	4.46829i	−0.0415856	+	0.352150i
$162$		0			0
$163$	1.51018	−	2.61570i	0.118286	−	0.204878i	−0.800802	−	0.598929i	$-0.795593\pi$
$163$	1.51018	−	2.61570i	0.118286	−	0.204878i	0.919089	+	0.394051i	$0.128927\pi$
$164$		0			0
$165$	−15.0719	−	28.2075i	−1.17335	−	2.19595i
$166$		0			0
$167$	7.14766	−	12.3801i	0.553103	−	0.958002i	−0.444946	−	0.895557i	$-0.646777\pi$
$167$	7.14766	−	12.3801i	0.553103	−	0.958002i	0.998048	−	0.0624443i	$-0.0198896\pi$
$168$		0			0
$169$	−0.722247	−	1.25097i	−0.0555575	−	0.0962284i
$170$		0			0
$171$	2.19730	−	1.08279i	0.168032	−	0.0828032i
$172$		0			0
$173$	2.19905			0.167191			0.0835954	−	0.996500i	$-0.473360\pi$
$173$	2.19905			0.167191			0.0835954	+	0.996500i	$0.473360\pi$
$174$		0			0
$175$	8.65267	+	20.1250i	0.654080	+	1.52131i
$176$		0			0
$177$	−3.32466	+	1.77644i	−0.249897	+	0.133526i
$178$		0			0
$179$	−9.30715	+	5.37349i	−0.695649	+	0.401633i	−0.805725	−	0.592290i	$-0.798224\pi$
$179$	−9.30715	+	5.37349i	−0.695649	+	0.401633i	0.110076	+	0.993923i	$0.464891\pi$
$180$		0			0
$181$			14.4710i			1.07562i	0.843065	+	0.537811i	$0.180749\pi$
$181$			14.4710i			1.07562i	−0.843065	+	0.537811i	$0.819251\pi$
$182$		0			0
$183$	5.92100	+	11.0813i	0.437693	+	0.819153i
$184$		0			0
$185$	24.7786			1.82176
$186$		0			0
$187$			7.85066i			0.574097i
$188$		0			0
$189$	10.1545	+	9.26746i	0.738633	+	0.674108i
$190$		0			0
$191$			8.33194i			0.602878i	0.953485	+	0.301439i	$0.0974670\pi$
$191$			8.33194i			0.602878i	−0.953485	+	0.301439i	$0.902533\pi$
$192$		0			0
$193$	−9.56786			−0.688710			−0.344355	−	0.938840i	$-0.611902\pi$
$193$	−9.56786			−0.688710			−0.344355	+	0.938840i	$0.611902\pi$
$194$		0			0
$195$	10.1116	+	18.9241i	0.724105	+	1.35518i
$196$		0			0
$197$		−	2.37228i		−	0.169018i	−0.996423	−	0.0845089i	$-0.973068\pi$
$197$		−	2.37228i		−	0.169018i	0.996423	−	0.0845089i	$-0.0269322\pi$
$198$		0			0
$199$	−19.4983	+	11.2573i	−1.38220	+	0.798011i	−0.992419	−	0.122898i	$-0.960781\pi$
$199$	−19.4983	+	11.2573i	−1.38220	+	0.798011i	−0.389777	+	0.920909i	$0.627448\pi$
$200$		0			0
$201$	3.75253	−	2.00507i	0.264683	−	0.141427i
$202$		0			0
$203$	−1.29230	+	10.9433i	−0.0907016	+	0.768069i
$204$		0			0
$205$	−7.41083			−0.517594
$206$		0			0
$207$	−0.335155	+	5.09074i	−0.0232949	+	0.353831i
$208$		0			0
$209$	−2.06866	−	3.58302i	−0.143092	−	0.247843i
$210$		0			0
$211$	7.27211	−	12.5957i	0.500632	−	0.867121i	−0.499367	−	0.866390i	$-0.666434\pi$
$211$	7.27211	−	12.5957i	0.500632	−	0.867121i	1.00000		0.000730453i	$-0.000232511\pi$
$212$		0			0
$213$	−5.50381	−	10.3005i	−0.377115	−	0.705780i
$214$		0			0
$215$	−11.1580	+	19.3262i	−0.760967	+	1.31803i
$216$		0			0
$217$	−4.60104	−	3.43387i	−0.312339	−	0.233106i
$218$		0			0
$219$	−3.98163	+	6.40091i	−0.269054	+	0.432533i
$220$		0			0
$221$		−	5.26691i		−	0.354291i
$222$		0			0
$223$	22.5221	−	13.0031i	1.50819	−	0.870753i	0.508235	−	0.861219i	$-0.330298\pi$
$223$	22.5221	−	13.0031i	1.50819	−	0.870753i	0.999955	−	0.00953489i	$-0.00303510\pi$
$224$		0			0
$225$	10.9797	+	22.2809i	0.731978	+	1.48540i
$226$		0			0
$227$	11.4390	−	19.8129i	0.759231	−	1.31503i	−0.184012	−	0.982924i	$-0.558909\pi$
$227$	11.4390	−	19.8129i	0.759231	−	1.31503i	0.943243	−	0.332103i	$-0.107758\pi$
$228$		0			0
$229$	−23.3224	+	13.4652i	−1.54118	+	0.889803i	−0.542420	+	0.840107i	$0.682492\pi$
$229$	−23.3224	+	13.4652i	−1.54118	+	0.889803i	−0.998764	+	0.0496960i	$0.984175\pi$
$230$		0			0
$231$	14.4920	−	18.1420i	0.953503	−	1.19365i
$232$		0			0
$233$	−3.82003	−	2.20550i	−0.250259	−	0.144487i	0.369624	−	0.929181i	$-0.379486\pi$
$233$	−3.82003	−	2.20550i	−0.250259	−	0.144487i	−0.619883	+	0.784694i	$0.712820\pi$
$234$		0			0
$235$	−12.2854	−	21.2789i	−0.801412	−	1.38809i
$236$		0			0
$237$	19.4822	−	10.4098i	1.26550	−	0.676189i
$238$		0			0
$239$	−16.1660	−	9.33343i	−1.04569	−	0.603729i	−0.124250	−	0.992251i	$-0.539653\pi$
$239$	−16.1660	−	9.33343i	−1.04569	−	0.603729i	−0.921440	+	0.388522i	$0.872986\pi$
$240$		0			0
$241$	0.412458	+	0.238133i	0.0265688	+	0.0153395i	0.513226	−	0.858254i	$-0.328450\pi$
$241$	0.412458	+	0.238133i	0.0265688	+	0.0153395i	−0.486657	+	0.873593i	$0.661784\pi$
$242$		0			0
$243$	12.0428	+	9.89799i	0.772548	+	0.634956i
$244$		0			0
$245$	−17.5495	+	18.5128i	−1.12120	+	1.18274i
$246$		0			0
$247$	1.38784	+	2.40381i	0.0883061	+	0.152951i
$248$		0			0
$249$	2.25916	+	1.40529i	0.143168	+	0.0890566i
$250$		0			0
$251$	17.6939			1.11683			0.558415	−	0.829562i	$-0.311410\pi$
$251$	17.6939			1.11683			0.558415	+	0.829562i	$0.311410\pi$
$252$		0			0
$253$	8.61675			0.541731
$254$		0			0
$255$	0.321401	−	9.77424i	0.0201269	−	0.612087i
$256$		0			0
$257$	−11.5971	−	20.0867i	−0.723405	−	1.25297i	−0.959627	−	0.281275i	$-0.909243\pi$
$257$	−11.5971	−	20.0867i	−0.723405	−	1.25297i	0.236222	−	0.971699i	$-0.424091\pi$
$258$		0			0
$259$	7.10579	+	16.5272i	0.441532	+	1.02695i
$260$		0			0
$261$	−0.820829	+	12.4678i	−0.0508080	+	0.771735i
$262$		0			0
$263$	−2.98247	−	1.72193i	−0.183907	−	0.106179i	0.405220	−	0.914219i	$-0.367195\pi$
$263$	−2.98247	−	1.72193i	−0.183907	−	0.106179i	−0.589127	+	0.808040i	$0.700528\pi$
$264$		0			0
$265$	41.8933	+	24.1871i	2.57349	+	1.48580i
$266$		0			0
$267$	0.684991	−	20.8315i	0.0419208	−	1.27487i
$268$		0			0
$269$	−4.00690	−	6.94015i	−0.244305	−	0.423148i	0.717631	−	0.696423i	$-0.245226\pi$
$269$	−4.00690	−	6.94015i	−0.244305	−	0.423148i	−0.961936	+	0.273275i	$0.911893\pi$
$270$		0			0
$271$	1.55095	+	0.895442i	0.0942136	+	0.0543942i	0.546367	−	0.837546i	$-0.316011\pi$
$271$	1.55095	+	0.895442i	0.0942136	+	0.0543942i	−0.452153	+	0.891940i	$0.649344\pi$
$272$		0			0
$273$	−9.72250	+	12.1712i	−0.588433	+	0.736636i
$274$		0			0
$275$	36.3324	−	20.9765i	2.19093	−	1.26493i
$276$		0			0
$277$	12.2968	−	21.2986i	0.738841	−	1.27971i	−0.214176	−	0.976795i	$-0.568707\pi$
$277$	12.2968	−	21.2986i	0.738841	−	1.27971i	0.953017	−	0.302915i	$-0.0979599\pi$
$278$		0			0
$279$	−5.41170	−	3.61827i	−0.323990	−	0.216620i
$280$		0			0
$281$	18.6262	−	10.7539i	1.11115	−	0.641521i	0.172021	−	0.985093i	$-0.444970\pi$
$281$	18.6262	−	10.7539i	1.11115	−	0.641521i	0.939126	+	0.343572i	$0.111637\pi$
$282$		0			0
$283$		−	19.9480i		−	1.18579i	−0.805281	−	0.592894i	$-0.797985\pi$
$283$		−	19.9480i		−	1.18579i	0.805281	−	0.592894i	$-0.202015\pi$
$284$		0			0
$285$	2.42884	+	4.54563i	0.143872	+	0.269260i
$286$		0			0
$287$	−2.12521	−	4.94297i	−0.125447	−	0.291774i
$288$		0			0
$289$	7.29969	−	12.6434i	0.429394	−	0.743732i
$290$		0			0
$291$	5.91056	−	9.50186i	0.346483	−	0.557009i
$292$		0			0
$293$	−1.24656	+	2.15911i	−0.0728251	+	0.126137i	−0.900138	−	0.435604i	$-0.856535\pi$
$293$	−1.24656	+	2.15911i	−0.0728251	+	0.126137i	0.827313	+	0.561741i	$0.189868\pi$
$294$		0			0
$295$	−3.96541	−	6.86829i	−0.230875	−	0.399887i
$296$		0			0
$297$	15.3451	−	21.3943i	0.890415	−	1.24143i
$298$		0			0
$299$	−5.78088			−0.334317
$300$		0			0
$301$	−16.0902	−	1.90010i	−0.927423	−	0.109520i
$302$		0			0
$303$	−0.677439	+	20.6018i	−0.0389178	+	1.18354i
$304$		0			0
$305$	−22.8925	+	13.2170i	−1.31082	+	0.756802i
$306$		0			0
$307$			9.23124i			0.526854i	0.964679	+	0.263427i	$0.0848529\pi$
$307$			9.23124i			0.526854i	−0.964679	+	0.263427i	$0.915147\pi$
$308$		0			0
$309$	13.4345	−	21.5973i	0.764259	−	1.22863i
$310$		0			0
$311$	−22.9714			−1.30259			−0.651294	−	0.758826i	$-0.725773\pi$
$311$	−22.9714			−1.30259			−0.651294	+	0.758826i	$0.725773\pi$
$312$		0			0
$313$		−	6.43336i		−	0.363635i	−0.983332	−	0.181818i	$-0.941802\pi$
$313$		−	6.43336i		−	0.363635i	0.983332	−	0.181818i	$-0.0581980\pi$
$314$		0			0
$315$	−18.7856	+	21.9938i	−1.05845	+	1.23921i
$316$		0			0
$317$		−	8.73533i		−	0.490625i	−0.969444	−	0.245313i	$-0.921109\pi$
$317$		−	8.73533i		−	0.490625i	0.969444	−	0.245313i	$-0.0788906\pi$
$318$		0			0
$319$	21.1033			1.18156
$320$		0			0
$321$	−5.74595	−	0.188941i	−0.320708	−	0.0105457i
$322$		0			0
$323$		−	1.26513i		−	0.0703939i
$324$		0			0
$325$	−24.3750	+	14.0729i	−1.35208	+	0.780624i
$326$		0			0
$327$	−4.17207	−	2.59520i	−0.230716	−	0.143515i
$328$		0			0
$329$	10.6698	−	14.2965i	0.588245	−	0.788189i
$330$		0			0
$331$	−31.7007			−1.74243			−0.871215	−	0.490901i	$-0.836668\pi$
$331$	−31.7007			−1.74243			−0.871215	+	0.490901i	$0.836668\pi$
$332$		0			0
$333$	9.01679	+	18.2977i	0.494117	+	1.00271i
$334$		0			0
$335$	4.47575	+	7.75223i	0.244536	+	0.423549i
$336$		0			0
$337$	16.1308	−	27.9393i	0.878700	−	1.52195i	0.0259314	−	0.999664i	$-0.491745\pi$
$337$	16.1308	−	27.9393i	0.878700	−	1.52195i	0.852768	−	0.522289i	$-0.174922\pi$
$338$		0			0
$339$	13.6019	+	0.447265i	0.738756	+	0.0242921i
$340$		0			0
$341$	−5.49750	+	9.52196i	−0.297707	+	0.515643i
$342$		0			0
$343$	−17.3806	−	6.39643i	−0.938465	−	0.345375i
$344$		0			0
$345$	−10.7280	−	0.352765i	−0.577579	−	0.0189922i
$346$		0			0
$347$		−	6.82421i		−	0.366343i	−0.983081	−	0.183171i	$-0.941364\pi$
$347$		−	6.82421i		−	0.366343i	0.983081	−	0.183171i	$-0.0586363\pi$
$348$		0			0
$349$	−4.18379	+	2.41551i	−0.223953	+	0.129299i	−0.607779	−	0.794106i	$-0.707939\pi$
$349$	−4.18379	+	2.41551i	−0.223953	+	0.129299i	0.383826	+	0.923405i	$0.374606\pi$
$350$		0			0
$351$	−10.2949	+	14.3532i	−0.549499	+	0.766117i
$352$		0			0
$353$	−17.2922	+	29.9510i	−0.920371	+	1.59413i	−0.121529	+	0.992588i	$0.538780\pi$
$353$	−17.2922	+	29.9510i	−0.920371	+	1.59413i	−0.798842	+	0.601541i	$0.794554\pi$
$354$		0			0
$355$	21.2795	−	12.2857i	1.12940	−	0.652058i
$356$		0			0
$357$	6.61152	−	2.58860i	0.349918	−	0.137003i
$358$		0			0
$359$	−23.5112	−	13.5742i	−1.24087	−	0.716417i	−0.271600	−	0.962410i	$-0.587553\pi$
$359$	−23.5112	−	13.5742i	−1.24087	−	0.716417i	−0.969272	+	0.245993i	$0.920886\pi$
$360$		0			0
$361$	−9.16664	−	15.8771i	−0.482455	−	0.835636i
$362$		0			0
$363$	−21.5811	−	13.4243i	−1.13271	−	0.704595i
$364$		0			0
$365$	−13.7352	−	7.93003i	−0.718934	−	0.415077i
$366$		0			0
$367$	10.3307	+	5.96444i	0.539259	+	0.311341i	0.744778	−	0.667312i	$-0.232555\pi$
$367$	10.3307	+	5.96444i	0.539259	+	0.311341i	−0.205520	+	0.978653i	$0.565888\pi$
$368$		0			0
$369$	−2.69675	−	5.47250i	−0.140387	−	0.284887i
$370$		0			0
$371$	−4.11884	+	34.8787i	−0.213840	+	1.81081i
$372$		0			0
$373$	−4.81925	−	8.34718i	−0.249531	−	0.432201i	0.713865	−	0.700284i	$-0.246943\pi$
$373$	−4.81925	−	8.34718i	−0.249531	−	0.432201i	−0.963396	+	0.268083i	$0.913610\pi$
$374$		0			0
$375$	−18.2585	+	9.75596i	−0.942865	+	0.503795i
$376$		0			0
$377$	−14.1580			−0.729173
$378$		0			0
$379$	16.0145			0.822612			0.411306	−	0.911497i	$-0.365073\pi$
$379$	16.0145			0.822612			0.411306	+	0.911497i	$0.365073\pi$
$380$		0			0
$381$	−26.6237	+	14.2257i	−1.36397	+	0.728804i
$382$		0			0
$383$	3.18472	+	5.51610i	0.162732	+	0.281860i	0.935847	−	0.352405i	$-0.114636\pi$
$383$	3.18472	+	5.51610i	0.162732	+	0.281860i	−0.773116	+	0.634265i	$0.781303\pi$
$384$		0			0
$385$	39.1512	+	29.2195i	1.99533	+	1.48916i
$386$		0			0
$387$	−18.3317	−	1.20688i	−0.931850	−	0.0613494i
$388$		0			0
$389$	−15.2013	−	8.77645i	−0.770735	−	0.444984i	0.0624020	−	0.998051i	$-0.480124\pi$
$389$	−15.2013	−	8.77645i	−0.770735	−	0.444984i	−0.833137	+	0.553067i	$0.813457\pi$
$390$		0			0
$391$	2.28187	+	1.31744i	0.115399	+	0.0666258i
$392$		0			0
$393$	4.75348	+	2.95686i	0.239781	+	0.149154i
$394$		0			0
$395$	23.2369	+	40.2476i	1.16918	+	2.02507i
$396$		0			0
$397$	11.5693	+	6.67955i	0.580647	+	0.335237i	0.761391	−	0.648293i	$-0.224517\pi$
$397$	11.5693	+	6.67955i	0.580647	+	0.335237i	−0.180743	+	0.983530i	$0.557850\pi$
$398$		0			0
$399$	−2.33538	+	2.92357i	−0.116915	+	0.146362i
$400$		0			0
$401$	3.66182	−	2.11415i	0.182863	−	0.105576i	−0.405774	−	0.913973i	$-0.632998\pi$
$401$	3.66182	−	2.11415i	0.182863	−	0.105576i	0.588637	+	0.808398i	$0.299665\pi$
$402$		0			0
$403$	3.68821	−	6.38817i	0.183723	−	0.318217i
$404$		0			0
$405$	−19.9809	+	26.0082i	−0.992858	+	1.29236i
$406$		0			0
$407$	29.8371	−	17.2265i	1.47897	−	0.853884i
$408$		0			0
$409$		−	38.4154i		−	1.89952i	−0.312982	−	0.949759i	$-0.601328\pi$
$409$		−	38.4154i		−	1.89952i	0.312982	−	0.949759i	$-0.398672\pi$
$410$		0			0
$411$	−25.2432	−	0.830057i	−1.24515	−	0.0409437i
$412$		0			0
$413$	3.44394	−	4.61453i	0.169465	−	0.227066i
$414$		0			0
$415$	−2.79885	+	4.84775i	−0.137390	+	0.237967i
$416$		0			0
$417$	−9.95089	−	0.327210i	−0.487297	−	0.0160235i
$418$		0			0
$419$	−7.03301	+	12.1815i	−0.343585	+	0.595107i	−0.985096	−	0.172007i	$-0.944975\pi$
$419$	−7.03301	+	12.1815i	−0.343585	+	0.595107i	0.641511	+	0.767114i	$0.278308\pi$
$420$		0			0
$421$	10.5504	+	18.2738i	0.514195	+	0.890612i	0.999864	+	0.0164691i	$0.00524252\pi$
$421$	10.5504	+	18.2738i	0.514195	+	0.890612i	−0.485670	+	0.874143i	$0.661424\pi$
$422$		0			0
$423$	11.2428	−	16.8154i	0.546642	−	0.817592i
$424$		0			0
$425$	12.8286			0.622280
$426$		0			0
$427$	−15.3805	−	11.4789i	−0.744316	−	0.555501i
$428$		0			0
$429$	25.3321	+	15.7576i	1.22305	+	0.760786i
$430$		0			0
$431$	−10.0928	+	5.82709i	−0.486154	+	0.280681i	−0.722977	−	0.690872i	$-0.757227\pi$
$431$	−10.0928	+	5.82709i	−0.486154	+	0.280681i	0.236824	+	0.971553i	$0.423894\pi$
$432$		0			0
$433$		−	17.9149i		−	0.860936i	−0.902606	−	0.430468i	$-0.858348\pi$
$433$		−	17.9149i		−	0.860936i	0.902606	−	0.430468i	$-0.141652\pi$
$434$		0			0
$435$	−26.2741	−	0.863957i	−1.25975	−	0.0414236i
$436$		0			0
$437$	−1.38859			−0.0664252
$438$		0			0
$439$			19.0275i			0.908135i	0.890967	+	0.454068i	$0.150028\pi$
$439$			19.0275i			0.908135i	−0.890967	+	0.454068i	$0.849972\pi$
$440$		0			0
$441$	−20.0569	−	6.22264i	−0.955090	−	0.296316i
$442$		0			0
$443$		−	7.67734i		−	0.364761i	−0.983228	−	0.182381i	$-0.941620\pi$
$443$		−	7.67734i		−	0.364761i	0.983228	−	0.182381i	$-0.0583803\pi$
$444$		0			0
$445$	43.8521			2.07879
$446$		0			0
$447$	−5.23865	+	8.42170i	−0.247780	+	0.398333i
$448$		0			0
$449$		−	30.1018i		−	1.42059i	−0.703903	−	0.710296i	$-0.748561\pi$
$449$		−	30.1018i		−	1.42059i	0.703903	−	0.710296i	$-0.251439\pi$
$450$		0			0
$451$	−8.92373	+	5.15212i	−0.420202	+	0.242604i
$452$		0			0
$453$	0.726892	−	22.1058i	0.0341523	−	1.03862i
$454$		0			0
$455$	−26.2660	−	19.6030i	−1.23137	−	0.919003i
$456$		0			0
$457$	−39.4876			−1.84715			−0.923576	−	0.383415i	$-0.874748\pi$
$457$	−39.4876			−1.84715			−0.923576	+	0.383415i	$0.874748\pi$
$458$		0			0
$459$	7.33471	−	3.31945i	0.342355	−	0.154939i
$460$		0			0
$461$	11.3776	+	19.7066i	0.529909	+	0.917830i	0.999391	+	0.0348879i	$0.0111074\pi$
$461$	11.3776	+	19.7066i	0.529909	+	0.917830i	−0.469482	+	0.882942i	$0.655559\pi$
$462$		0			0
$463$	−6.63866	+	11.4985i	−0.308525	+	0.534381i	−0.978040	−	0.208418i	$-0.933169\pi$
$463$	−6.63866	+	11.4985i	−0.308525	+	0.534381i	0.669515	+	0.742798i	$0.266502\pi$
$464$		0			0
$465$	7.23434	−	11.6300i	0.335484	−	0.539327i
$466$		0			0
$467$	11.5873	−	20.0698i	0.536195	−	0.928717i	−0.462909	−	0.886406i	$-0.653194\pi$
$467$	11.5873	−	20.0698i	0.536195	−	0.928717i	0.999104	−	0.0423116i	$-0.0134722\pi$
$468$		0			0
$469$	−3.88716	+	5.20841i	−0.179493	+	0.240502i
$470$		0			0
$471$	10.4242	+	19.5092i	0.480324	+	0.898937i
$472$		0			0
$473$			31.0287i			1.42670i
$474$		0			0
$475$	−5.85497	+	3.38037i	−0.268644	+	0.155102i
$476$		0			0
$477$	−2.61616	+	39.7375i	−0.119786	+	1.81946i
$478$		0			0
$479$	12.3567	−	21.4025i	0.564594	−	0.977905i	−0.432493	−	0.901637i	$-0.642366\pi$
$479$	12.3567	−	21.4025i	0.564594	−	0.977905i	0.997087	−	0.0762684i	$-0.0243006\pi$
$480$		0			0
$481$	−20.0174	+	11.5570i	−0.912713	+	0.526955i
$482$		0			0
$483$	−2.84120	−	7.25669i	−0.129279	−	0.330191i
$484$		0			0
$485$	20.3893	+	11.7718i	0.925831	+	0.534529i
$486$		0			0
$487$	−16.9877	−	29.4236i	−0.769788	−	1.33331i	−0.937678	−	0.347506i	$-0.887029\pi$
$487$	−16.9877	−	29.4236i	−0.769788	−	1.33331i	0.167889	−	0.985806i	$-0.446305\pi$
$488$		0			0
$489$	−0.171929	+	5.22858i	−0.00777488	+	0.236445i
$490$		0			0
$491$	25.5933	+	14.7763i	1.15501	+	0.666845i	0.950103	−	0.311937i	$-0.100978\pi$
$491$	25.5933	+	14.7763i	1.15501	+	0.666845i	0.204906	+	0.978782i	$0.434311\pi$
$492$		0			0
$493$	5.58854	+	3.22655i	0.251695	+	0.145316i
$494$		0			0
$495$	46.0493	+	30.7886i	2.06976	+	1.38384i
$496$		0			0
$497$	14.2968	+	10.6701i	0.641300	+	0.478618i
$498$		0			0
$499$	−5.38644	−	9.32959i	−0.241130	−	0.417650i	0.719906	−	0.694071i	$-0.244185\pi$
$499$	−5.38644	−	9.32959i	−0.241130	−	0.417650i	−0.961037	+	0.276421i	$0.910851\pi$
$500$		0			0
$501$	−0.813737	+	24.7468i	−0.0363551	+	1.10561i
$502$		0			0
$503$	−20.2016			−0.900743			−0.450372	−	0.892841i	$-0.648708\pi$
$503$	−20.2016			−0.900743			−0.450372	+	0.892841i	$0.648708\pi$
$504$		0			0
$505$	−43.3686			−1.92988
$506$		0			0
$507$	2.12446	+	1.32150i	0.0943505	+	0.0586900i
$508$		0			0
$509$	−0.529272	−	0.916725i	−0.0234595	−	0.0406331i	0.854057	−	0.520179i	$-0.174135\pi$
$509$	−0.529272	−	0.916725i	−0.0234595	−	0.0406331i	−0.877517	+	0.479546i	$0.840801\pi$
$510$		0			0
$511$	1.35041	−	11.4354i	0.0597387	−	0.505872i
$512$		0			0
$513$	−2.47287	+	3.44770i	−0.109180	+	0.152220i
$514$		0			0
$515$	46.3441	+	26.7568i	2.04216	+	1.17904i
$516$		0			0
$517$	−29.5869	−	17.0820i	−1.30123	−	0.751265i
$518$		0			0
$519$	−3.35939	+	1.79500i	−0.147461	+	0.0787918i
$520$		0			0
$521$	5.05068	+	8.74804i	0.221275	+	0.383259i	0.955195	−	0.295976i	$-0.0956450\pi$
$521$	5.05068	+	8.74804i	0.221275	+	0.383259i	−0.733921	+	0.679235i	$0.762312\pi$
$522$		0			0
$523$	8.02992	+	4.63608i	0.351124	+	0.202722i	0.665180	−	0.746683i	$-0.268355\pi$
$523$	8.02992	+	4.63608i	0.351124	+	0.202722i	−0.314056	+	0.949404i	$0.601688\pi$
$524$		0			0
$525$	−29.6455	−	23.6811i	−1.29384	−	1.03353i
$526$		0			0
$527$	−2.91168	+	1.68106i	−0.126835	+	0.0732280i
$528$		0			0
$529$	−10.0540	+	17.4140i	−0.437130	+	0.757132i
$530$		0			0
$531$	3.62888	−	5.42757i	0.157480	−	0.235537i
$532$		0			0
$533$	5.98682	−	3.45649i	0.259318	−	0.149717i
$534$		0			0
$535$		−	12.0957i		−	0.522943i
$536$		0			0
$537$	9.83192	−	15.8059i	0.424278	−	0.682074i
$538$		0			0
$539$	−8.26177	+	34.4928i	−0.355859	+	1.48571i
$540$		0			0
$541$	−2.87498	+	4.97960i	−0.123605	+	0.214090i	−0.921187	−	0.389121i	$-0.872779\pi$
$541$	−2.87498	+	4.97960i	−0.123605	+	0.214090i	0.797582	+	0.603211i	$0.206112\pi$
$542$		0			0
$543$	−11.8121	−	22.1067i	−0.506907	−	0.948689i
$544$		0			0
$545$	5.16874	−	8.95251i	0.221404	−	0.383484i
$546$		0			0
$547$	−18.3094	−	31.7128i	−0.782853	−	1.35594i	−0.930273	−	0.366867i	$-0.880430\pi$
$547$	−18.3094	−	31.7128i	−0.782853	−	1.35594i	0.147421	−	0.989074i	$-0.452903\pi$
$548$		0			0
$549$	−18.0905	−	12.0953i	−0.772082	−	0.516214i
$550$		0			0
$551$	−3.40080			−0.144879
$552$		0			0
$553$	−20.1811	+	27.0407i	−0.858190	+	1.14989i
$554$		0			0
$555$	−37.8531	+	20.2258i	−1.60677	+	0.858538i
$556$		0			0
$557$	−0.323902	+	0.187005i	−0.0137242	+	0.00792365i	−0.506846	−	0.862036i	$-0.669189\pi$
$557$	−0.323902	+	0.187005i	−0.0137242	+	0.00792365i	0.493122	+	0.869960i	$0.335856\pi$
$558$		0			0
$559$		−	20.8168i		−	0.880457i
$560$		0			0
$561$	−6.40818	−	11.9931i	−0.270554	−	0.506348i
$562$		0			0
$563$	4.37923			0.184562			0.0922812	−	0.995733i	$-0.470584\pi$
$563$	4.37923			0.184562			0.0922812	+	0.995733i	$0.470584\pi$
$564$		0			0
$565$			28.6332i			1.20461i
$566$		0			0
$567$	−23.0772	−	5.86871i	−0.969152	−	0.246463i
$568$		0			0
$569$			36.8641i			1.54542i	0.634757	+	0.772712i	$0.281100\pi$
$569$			36.8641i			1.54542i	−0.634757	+	0.772712i	$0.718900\pi$
$570$		0			0
$571$	−31.6595			−1.32491			−0.662454	−	0.749103i	$-0.730485\pi$
$571$	−31.6595			−1.32491			−0.662454	+	0.749103i	$0.730485\pi$
$572$		0			0
$573$	−6.80104	−	12.7283i	−0.284117	−	0.531732i
$574$		0			0
$575$		−	14.0805i		−	0.587198i
$576$		0			0
$577$	12.2923	−	7.09699i	0.511737	−	0.295452i	−0.221810	−	0.975090i	$-0.571197\pi$
$577$	12.2923	−	7.09699i	0.511737	−	0.295452i	0.733547	+	0.679638i	$0.237863\pi$
$578$		0			0
$579$	14.6164	−	7.80987i	0.607435	−	0.324567i
$580$		0			0
$581$	−4.03604	−	0.476618i	−0.167443	−	0.0197734i
$582$		0			0
$583$	67.2610			2.78567
$584$		0			0
$585$	−30.8939	−	20.6557i	−1.27731	−	0.854007i
$586$		0			0
$587$	2.32227	+	4.02230i	0.0958505	+	0.166018i	0.909963	−	0.414689i	$-0.136110\pi$
$587$	2.32227	+	4.02230i	0.0958505	+	0.166018i	−0.814113	+	0.580707i	$0.802776\pi$
$588$		0			0
$589$	0.885922	−	1.53446i	0.0365038	−	0.0632264i
$590$		0			0
$591$	1.93640	+	3.62402i	0.0796528	+	0.149072i
$592$		0			0
$593$	11.5215	−	19.9558i	0.473132	−	0.819488i	−0.526395	−	0.850240i	$-0.676457\pi$
$593$	11.5215	−	19.9558i	0.473132	−	0.819488i	0.999527	+	0.0307518i	$0.00979014\pi$
$594$		0			0
$595$	5.90049	+	13.7238i	0.241896	+	0.562620i
$596$		0			0
$597$	20.5977	−	33.1130i	0.843006	−	1.35522i
$598$		0			0
$599$			28.9622i			1.18336i	0.806171	+	0.591682i	$0.201536\pi$
$599$			28.9622i			1.18336i	−0.806171	+	0.591682i	$0.798464\pi$
$600$		0			0
$601$	5.04993	−	2.91558i	0.205991	−	0.118929i	−0.393456	−	0.919344i	$-0.628721\pi$
$601$	5.04993	−	2.91558i	0.205991	−	0.118929i	0.599447	+	0.800414i	$0.295387\pi$
$602$		0			0
$603$	−4.09591	+	6.12609i	−0.166798	+	0.249474i
$604$		0			0
$605$	26.7366	−	46.3092i	1.08700	−	1.88273i
$606$		0			0
$607$	−16.3750	+	9.45411i	−0.664641	+	0.383731i	−0.794043	−	0.607862i	$-0.792028\pi$
$607$	−16.3750	+	9.45411i	−0.664641	+	0.383731i	0.129402	+	0.991592i	$0.458694\pi$
$608$		0			0
$609$	−6.95840	−	17.7724i	−0.281969	−	0.720174i
$610$		0			0
$611$	19.8495	+	11.4601i	0.803024	+	0.463626i
$612$		0			0
$613$	−16.5880	−	28.7313i	−0.669984	−	1.16045i	−0.977908	−	0.209036i	$-0.932967\pi$
$613$	−16.5880	−	28.7313i	−0.669984	−	1.16045i	0.307924	−	0.951411i	$-0.400366\pi$
$614$		0			0
$615$	11.3212	−	6.04916i	0.456513	−	0.243926i
$616$		0			0
$617$	34.0222	+	19.6427i	1.36968	+	0.790786i	0.990887	−	0.134695i	$-0.0430054\pi$
$617$	34.0222	+	19.6427i	1.36968	+	0.790786i	0.378794	+	0.925481i	$0.376339\pi$
$618$		0			0
$619$	8.46727	+	4.88858i	0.340329	+	0.196489i	0.660417	−	0.750899i	$-0.270379\pi$
$619$	8.46727	+	4.88858i	0.340329	+	0.196489i	−0.320089	+	0.947388i	$0.603713\pi$
$620$		0			0
$621$	−3.64337	−	8.05046i	−0.146204	−	0.323054i
$622$		0			0
$623$	12.5755	+	29.2490i	0.503827	+	1.17184i
$624$		0			0
$625$	−1.07796	−	1.86708i	−0.0431185	−	0.0746834i
$626$		0			0
$627$	6.08487	+	3.78505i	0.243006	+	0.151160i
$628$		0			0
$629$	10.5352			0.420066
$630$		0			0
$631$	−11.6364			−0.463237			−0.231618	−	0.972807i	$-0.574402\pi$
$631$	−11.6364			−0.463237			−0.231618	+	0.972807i	$0.574402\pi$
$632$		0			0
$633$	−0.827905	+	25.1777i	−0.0329063	+	1.00072i
$634$		0			0
$635$	−31.7549	−	55.0010i	−1.26015	−	2.18265i
$636$		0			0
$637$	5.54272	−	23.1408i	0.219610	−	0.916873i
$638$		0			0
$639$	16.8158	+	11.2431i	0.665223	+	0.444768i
$640$		0			0
$641$	25.2233	+	14.5627i	0.996262	+	0.575192i	0.907140	−	0.420828i	$-0.138261\pi$
$641$	25.2233	+	14.5627i	0.996262	+	0.575192i	0.0891220	+	0.996021i	$0.471594\pi$
$642$		0			0
$643$	−33.9410	−	19.5959i	−1.33850	−	0.772785i	−0.351918	−	0.936031i	$-0.614470\pi$
$643$	−33.9410	−	19.5959i	−1.33850	−	0.772785i	−0.986585	+	0.163245i	$0.947804\pi$
$644$		0			0
$645$	1.27030	−	38.6315i	0.0500179	−	1.52111i
$646$		0			0
$647$	−10.1800	−	17.6323i	−0.400218	−	0.693199i	0.593534	−	0.804809i	$-0.297732\pi$
$647$	−10.1800	−	17.6323i	−0.400218	−	0.693199i	−0.993752	+	0.111610i	$0.964399\pi$
$648$		0			0
$649$	−9.54988	−	5.51362i	−0.374865	−	0.216429i
$650$		0			0
$651$	9.83171	+	1.49011i	0.385335	+	0.0584019i
$652$		0			0
$653$	−13.1105	+	7.56933i	−0.513052	+	0.296211i	−0.734087	−	0.679055i	$-0.762390\pi$
$653$	−13.1105	+	7.56933i	−0.513052	+	0.296211i	0.221035	+	0.975266i	$0.429056\pi$
$654$		0			0
$655$	−5.88904	+	10.2001i	−0.230104	+	0.398552i
$656$		0			0
$657$	0.857740	−	13.0284i	0.0334636	−	0.508287i
$658$		0			0
$659$	9.17413	−	5.29668i	0.357373	−	0.206330i	−0.310555	−	0.950556i	$-0.600515\pi$
$659$	9.17413	−	5.29668i	0.357373	−	0.206330i	0.667928	+	0.744226i	$0.267181\pi$
$660$		0			0
$661$			17.0415i			0.662836i	0.943484	+	0.331418i	$0.107527\pi$
$661$			17.0415i			0.662836i	−0.943484	+	0.331418i	$0.892473\pi$
$662$		0			0
$663$	4.29917	+	8.04600i	0.166966	+	0.312481i
$664$		0			0
$665$	−6.30921	−	4.70872i	−0.244661	−	0.182596i
$666$		0			0
$667$	3.54141	−	6.13389i	0.137124	−	0.237505i
$668$		0			0
$669$	−23.7919	+	38.2481i	−0.919849	+	1.47876i
$670$		0			0
$671$	−18.3773	+	31.8304i	−0.709447	+	1.22880i
$672$		0			0
$673$	−12.5048	−	21.6590i	−0.482025	−	0.834891i	0.517762	−	0.855524i	$-0.326765\pi$
$673$	−12.5048	−	21.6590i	−0.482025	−	0.834891i	−0.999787	+	0.0206331i	$0.993432\pi$
$674$		0			0
$675$	−34.9602	−	25.0752i	−1.34562	−	0.965146i
$676$		0			0
$677$	39.7068			1.52606			0.763028	−	0.646365i	$-0.223712\pi$
$677$	39.7068			1.52606			0.763028	+	0.646365i	$0.223712\pi$
$678$		0			0
$679$	−2.00462	+	16.9753i	−0.0769304	+	0.651453i
$680$		0			0
$681$	−1.30229	+	39.6043i	−0.0499038	+	1.51764i
$682$		0			0
$683$	−2.31868	+	1.33869i	−0.0887218	+	0.0512236i	−0.543705	−	0.839277i	$-0.682979\pi$
$683$	−2.31868	+	1.33869i	−0.0887218	+	0.0512236i	0.454983	+	0.890500i	$0.349645\pi$
$684$		0			0
$685$		−	53.1390i		−	2.03034i
$686$		0			0
$687$	24.6373	−	39.6072i	0.939973	−	1.51111i
$688$		0			0
$689$	−45.1246			−1.71911
$690$		0			0
$691$		−	19.2080i		−	0.730706i	−0.930869	−	0.365353i	$-0.880948\pi$
$691$		−	19.2080i		−	0.730706i	0.930869	−	0.365353i	$-0.119052\pi$
$692$		0			0
$693$	−7.33015	+	39.5438i	−0.278449	+	1.50215i
$694$		0			0
$695$		−	20.9475i		−	0.794583i
$696$		0			0
$697$	−3.15088			−0.119348
$698$		0			0
$699$	7.63594	+	0.251088i	0.288818	+	0.00949704i
$700$		0			0
$701$			34.1916i			1.29140i	0.763591	+	0.645700i	$0.223434\pi$
$701$			34.1916i			1.29140i	−0.763591	+	0.645700i	$0.776566\pi$
$702$		0			0
$703$	−4.80825	+	2.77604i	−0.181346	+	0.104700i
$704$		0			0
$705$	36.1370	+	22.4787i	1.36100	+	0.846598i
$706$		0			0
$707$	−12.4369	−	28.9265i	−0.467736	−	1.08789i
$708$		0			0
$709$	−23.4568			−0.880937			−0.440468	−	0.897768i	$-0.645188\pi$
$709$	−23.4568			−0.880937			−0.440468	+	0.897768i	$0.645188\pi$
$710$		0			0
$711$	−21.2649	+	31.8051i	−0.797495	+	1.19278i
$712$		0			0
$713$	1.84510	+	3.19581i	0.0690996	+	0.119684i
$714$		0			0
$715$	−31.3837	+	54.3582i	−1.17368	+	2.03288i
$716$		0			0
$717$	32.3145	+	1.06258i	1.20681	+	0.0396828i
$718$		0			0
$719$	7.98801	−	13.8356i	0.297902	−	0.515982i	−0.677753	−	0.735289i	$-0.737046\pi$
$719$	7.98801	−	13.8356i	0.297902	−	0.515982i	0.975656	+	0.219307i	$0.0703796\pi$
$720$		0			0
$721$	−4.55643	+	38.5842i	−0.169690	+	1.43695i
$722$		0			0
$723$	−0.824471	−	0.0271106i	−0.0306624	−	0.00100826i
$724$		0			0
$725$		−	34.4846i		−	1.28073i
$726$		0			0
$727$	−21.6787	+	12.5162i	−0.804019	+	0.464201i	−0.844875	−	0.534964i	$-0.820325\pi$
$727$	−21.6787	+	12.5162i	−0.804019	+	0.464201i	0.0408555	+	0.999165i	$0.486992\pi$
$728$		0			0
$729$	−26.4766	−	5.29058i	−0.980614	−	0.195948i
$730$		0			0
$731$	−4.74407	+	8.21697i	−0.175466	+	0.303916i
$732$		0			0
$733$	10.1433	−	5.85625i	0.374652	−	0.216305i	−0.300837	−	0.953676i	$-0.597266\pi$
$733$	10.1433	−	5.85625i	0.374652	−	0.216305i	0.675489	+	0.737370i	$0.263933\pi$
$734$		0			0
$735$	11.6982	−	42.6061i	0.431494	−	1.57155i
$736$		0			0
$737$	10.7789	+	6.22322i	0.397047	+	0.229235i
$738$		0			0
$739$	8.20255	+	14.2072i	0.301736	+	0.522622i	0.976529	−	0.215385i	$-0.0691006\pi$
$739$	8.20255	+	14.2072i	0.301736	+	0.522622i	−0.674793	+	0.738007i	$0.735767\pi$
$740$		0			0
$741$	−4.08227	−	2.53934i	−0.149966	−	0.0932850i
$742$		0			0
$743$	−8.02860	−	4.63532i	−0.294541	−	0.170053i	0.345447	−	0.938438i	$-0.387727\pi$
$743$	−8.02860	−	4.63532i	−0.294541	−	0.170053i	−0.639988	+	0.768385i	$0.721061\pi$
$744$		0			0
$745$	−18.0715	−	10.4336i	−0.662087	−	0.382256i
$746$		0			0
$747$	−4.59829	−	0.302733i	−0.168242	−	0.0110764i
$748$		0			0
$749$	8.06775	−	3.46870i	0.294789	−	0.126744i
$750$		0			0
$751$	10.0756	+	17.4515i	0.367665	+	0.636815i	0.989200	−	0.146572i	$-0.0468239\pi$
$751$	10.0756	+	17.4515i	0.367665	+	0.636815i	−0.621535	+	0.783386i	$0.713491\pi$
$752$		0			0
$753$	−27.0301	+	14.4428i	−0.985032	+	0.526326i
$754$		0			0
$755$	46.5345			1.69356
$756$		0			0
$757$	47.4297			1.72386			0.861932	−	0.507024i	$-0.169255\pi$
$757$	47.4297			1.72386			0.861932	+	0.507024i	$0.169255\pi$
$758$		0			0
$759$	−13.1634	+	7.03352i	−0.477801	+	0.255300i
$760$		0			0
$761$	−24.0809	−	41.7094i	−0.872933	−	1.51196i	−0.858948	−	0.512063i	$-0.828882\pi$
$761$	−24.0809	−	41.7094i	−0.872933	−	1.51196i	−0.0139853	−	0.999902i	$-0.504452\pi$
$762$		0			0
$763$	7.45350	+	0.880188i	0.269835	+	0.0318649i
$764$		0			0
$765$	7.48734	+	15.1940i	0.270705	+	0.549339i
$766$		0			0
$767$	6.40690	+	3.69902i	0.231340	+	0.133564i
$768$		0			0
$769$	9.84984	+	5.68681i	0.355194	+	0.205071i	0.666971	−	0.745084i	$-0.267591\pi$
$769$	9.84984	+	5.68681i	0.355194	+	0.205071i	−0.311776	+	0.950155i	$0.600924\pi$
$770$		0			0
$771$	34.1123	+	21.2193i	1.22852	+	0.764193i
$772$		0			0
$773$	2.13778	+	3.70275i	0.0768906	+	0.133179i	0.901907	−	0.431931i	$-0.142167\pi$
$773$	2.13778	+	3.70275i	0.0768906	+	0.133179i	−0.825016	+	0.565109i	$0.808834\pi$
$774$		0			0
$775$	15.5597	+	8.98339i	0.558920	+	0.322693i
$776$		0			0
$777$	−24.3456	−	19.4476i	−0.873395	−	0.697677i
$778$		0			0
$779$	1.43806	−	0.830263i	0.0515238	−	0.0297473i
$780$		0			0
$781$	17.0824	−	29.5876i	0.611257	−	1.05873i
$782$		0			0
$783$	−8.92300	−	19.7164i	−0.318882	−	0.704607i
$784$		0			0
$785$	−40.3034	+	23.2692i	−1.43849	+	0.830513i
$786$		0			0
$787$		−	26.4016i		−	0.941115i	−0.882369	−	0.470557i	$-0.844053\pi$
$787$		−	26.4016i		−	0.941115i	0.882369	−	0.470557i	$-0.155947\pi$
$788$		0			0
$789$	5.96172	+	0.196036i	0.212243	+	0.00697906i
$790$		0			0
$791$	−19.0982	+	8.21118i	−0.679053	+	0.291956i
$792$		0			0
$793$	12.3291	−	21.3546i	0.437819	−	0.758324i
$794$		0			0
$795$	−83.7414	−	2.75362i	−2.97000	−	0.0976610i
$796$		0			0
$797$	−26.7253	+	46.2896i	−0.946660	+	1.63966i	−0.194267	+	0.980949i	$0.562233\pi$
$797$	−26.7253	+	46.2896i	−0.946660	+	1.63966i	−0.752393	+	0.658715i	$0.771100\pi$
$798$		0			0
$799$	−5.22343	−	9.04724i	−0.184792	−	0.320068i
$800$		0			0
$801$	15.9575	+	32.3824i	0.563831	+	1.14418i
$802$		0			0
$803$	−22.0523			−0.778209
$804$		0			0
$805$	15.0630	−	6.47628i	0.530901	−	0.228259i
$806$		0			0
$807$	11.7861	+	7.33145i	0.414891	+	0.258079i
$808$		0			0
$809$	8.76550	−	5.06076i	0.308179	−	0.177927i	−0.337933	−	0.941170i	$-0.609728\pi$
$809$	8.76550	−	5.06076i	0.308179	−	0.177927i	0.646111	+	0.763243i	$0.276394\pi$
$810$		0			0
$811$		−	44.8854i		−	1.57614i	−0.615586	−	0.788070i	$-0.711080\pi$
$811$		−	44.8854i		−	1.57614i	0.615586	−	0.788070i	$-0.288920\pi$
$812$		0			0
$813$	−3.10023	−	0.101943i	−0.108730	−	0.00357530i
$814$		0			0
$815$	−11.0066			−0.385544
$816$		0			0
$817$		−	5.00028i		−	0.174938i
$818$		0			0
$819$	4.91771	−	26.5295i	0.171839	−	0.927015i
$820$		0			0
$821$		−	34.4709i		−	1.20304i	−0.798857	−	0.601521i	$-0.794562\pi$
$821$		−	34.4709i		−	1.20304i	0.798857	−	0.601521i	$-0.205438\pi$
$822$		0			0
$823$	28.9121			1.00781			0.503906	−	0.863758i	$-0.331896\pi$
$823$	28.9121			1.00781			0.503906	+	0.863758i	$0.331896\pi$
$824$		0			0
$825$	−38.3810	+	61.7015i	−1.33625	+	2.14817i
$826$		0			0
$827$			18.8795i			0.656506i	0.944590	+	0.328253i	$0.106460\pi$
$827$			18.8795i			0.656506i	−0.944590	+	0.328253i	$0.893540\pi$
$828$		0			0
$829$	15.6663	−	9.04494i	0.544113	−	0.314144i	−0.202631	−	0.979255i	$-0.564949\pi$
$829$	15.6663	−	9.04494i	0.544113	−	0.314144i	0.746744	+	0.665111i	$0.231616\pi$
$830$		0			0
$831$	−1.39995	+	42.5742i	−0.0485636	+	1.47688i
$832$		0			0
$833$	−7.46157	+	7.87116i	−0.258528	+	0.272720i
$834$		0			0
$835$	−52.0942			−1.80279
$836$		0			0
$837$	11.2206	+	1.11009i	0.387842	+	0.0383703i
$838$		0			0
$839$	−2.53049	−	4.38294i	−0.0873623	−	0.151316i	0.819033	−	0.573746i	$-0.194510\pi$
$839$	−2.53049	−	4.38294i	−0.0873623	−	0.151316i	−0.906395	+	0.422430i	$0.861177\pi$
$840$		0			0
$841$	−5.82673	+	10.0922i	−0.200922	+	0.348007i
$842$		0			0
$843$	−19.6764	+	31.6320i	−0.677692	+	1.08946i
$844$		0			0
$845$	−2.63197	+	4.55871i	−0.0905426	+	0.156824i
$846$		0			0
$847$	38.5552	+	4.55300i	1.32477	+	0.156443i
$848$		0			0
$849$	16.2828	+	30.4736i	0.558824	+	1.04585i
$850$		0			0
$851$		−	11.5633i		−	0.396384i
$852$		0			0
$853$	37.0163	−	21.3714i	1.26741	−	0.731742i	0.292916	−	0.956138i	$-0.405374\pi$
$853$	37.0163	−	21.3714i	1.26741	−	0.731742i	0.974498	+	0.224397i	$0.0720412\pi$
$854$		0			0
$855$	−7.42084	−	4.96158i	−0.253787	−	0.169682i
$856$		0			0
$857$	0.537523	−	0.931017i	0.0183614	−	0.0318030i	−0.856699	−	0.515817i	$-0.827488\pi$
$857$	0.537523	−	0.931017i	0.0183614	−	0.0318030i	0.875060	+	0.484014i	$0.160822\pi$
$858$		0			0
$859$	20.9983	−	12.1234i	0.716452	−	0.413644i	−0.0969931	−	0.995285i	$-0.530922\pi$
$859$	20.9983	−	12.1234i	0.716452	−	0.413644i	0.813446	+	0.581641i	$0.197589\pi$
$860$		0			0
$861$	7.28133	+	5.81640i	0.248147	+	0.198223i
$862$		0			0
$863$	38.7211	+	22.3556i	1.31808	+	0.760994i	0.983420	−	0.181344i	$-0.0580449\pi$
$863$	38.7211	+	22.3556i	1.31808	+	0.760994i	0.334661	+	0.942339i	$0.391378\pi$
$864$		0			0
$865$	−4.00683	−	6.94004i	−0.136236	−	0.235968i
$866$		0			0
$867$	−0.831045	+	25.2732i	−0.0282238	+	0.858323i
$868$		0			0
$869$	55.9614	+	32.3093i	1.89836	+	1.09602i
$870$		0			0
$871$	−7.23145	−	4.17508i	−0.245028	−	0.141467i
$872$		0			0
$873$	−1.27328	+	19.3401i	−0.0430939	+	0.654563i
$874$		0			0
$875$	18.9136	−	25.3423i	0.639395	−	0.856725i
$876$		0			0
$877$	2.08435	+	3.61020i	0.0703835	+	0.121908i	0.899069	−	0.437806i	$-0.144244\pi$
$877$	2.08435	+	3.61020i	0.0703835	+	0.121908i	−0.828686	+	0.559714i	$0.810911\pi$
$878$		0			0
$879$	0.141917	−	4.31589i	0.00478675	−	0.145571i
$880$		0			0
$881$	−32.0880			−1.08107			−0.540536	−	0.841321i	$-0.681779\pi$
$881$	−32.0880			−1.08107			−0.540536	+	0.841321i	$0.681779\pi$
$882$		0			0
$883$	29.5080			0.993022			0.496511	−	0.868031i	$-0.334614\pi$
$883$	29.5080			0.993022			0.496511	+	0.868031i	$0.334614\pi$
$884$		0			0
$885$	11.6641	+	7.25555i	0.392084	+	0.243893i
$886$		0			0
$887$	−12.4214	−	21.5145i	−0.417071	−	0.722387i	0.578573	−	0.815631i	$-0.303610\pi$
$887$	−12.4214	−	21.5145i	−0.417071	−	0.722387i	−0.995643	+	0.0932433i	$0.970277\pi$
$888$		0			0
$889$	27.5789	−	36.9530i	0.924967	−	1.23936i
$890$		0			0
$891$	−5.97865	+	45.2087i	−0.200292	+	1.51455i
$892$		0			0
$893$	4.76792	+	2.75276i	0.159552	+	0.0921176i
$894$		0			0
$895$	33.9166	+	19.5818i	1.13371	+	0.654546i
$896$		0			0
$897$	8.83116	−	4.71870i	0.294864	−	0.157553i
$898$		0			0
$899$	4.51885	+	7.82687i	0.150712	+	0.261041i
$900$		0			0
$901$	17.8119	+	10.2837i	0.593401	+	0.342600i
$902$		0			0
$903$	26.1312	−	10.2311i	0.869591	−	0.340470i
$904$		0			0
$905$	45.6694	−	26.3673i	1.51810	−	0.876477i
$906$		0			0
$907$	20.4561	−	35.4311i	0.679235	−	1.17647i	−0.295977	−	0.955195i	$-0.595645\pi$
$907$	20.4561	−	35.4311i	0.679235	−	1.17647i	0.975212	−	0.221274i	$-0.0710215\pi$
$908$		0			0
$909$	−15.7816	−	32.0254i	−0.523442	−	1.06221i
$910$		0			0
$911$	−2.21678	+	1.27986i	−0.0734452	+	0.0424036i	−0.536273	−	0.844045i	$-0.680168\pi$
$911$	−2.21678	+	1.27986i	−0.0734452	+	0.0424036i	0.462828	+	0.886448i	$0.346835\pi$
$912$		0			0
$913$			7.78320i			0.257586i
$914$		0			0
$915$	24.1832	−	38.8771i	0.799473	−	1.28524i
$916$		0			0
$917$	−8.49221	−	1.00285i	−0.280438	−	0.0331170i
$918$		0			0
$919$	−5.12246	+	8.87236i	−0.168974	+	0.292672i	−0.938060	−	0.346474i	$-0.887379\pi$
$919$	−5.12246	+	8.87236i	−0.168974	+	0.292672i	0.769085	+	0.639146i	$0.220712\pi$
$920$		0			0
$921$	−7.53509	−	14.1021i	−0.248290	−	0.464680i
$922$		0			0
$923$	−11.4604	+	19.8500i	−0.377223	+	0.653370i
$924$		0			0
$925$	−28.1495	−	48.7564i	−0.925550	−	1.60310i
$926$		0			0
$927$	−2.89410	+	43.9592i	−0.0950548	+	1.44381i
$928$		0			0
$929$	−29.5704			−0.970173			−0.485087	−	0.874466i	$-0.661212\pi$
$929$	−29.5704			−0.970173			−0.485087	+	0.874466i	$0.661212\pi$
$930$		0			0
$931$	1.33138	−	5.55852i	0.0436343	−	0.182173i
$932$		0			0
$933$	35.0923	−	18.7506i	1.14887	−	0.613868i
$934$		0			0
$935$	24.7761	−	14.3045i	0.810264	−	0.467806i
$936$		0			0
$937$			17.9991i			0.588005i	0.955805	+	0.294002i	$0.0949874\pi$
$937$			17.9991i			0.588005i	−0.955805	+	0.294002i	$0.905013\pi$
$938$		0			0
$939$	5.25130	+	9.82793i	0.171370	+	0.320722i
$940$		0			0
$941$	29.7237			0.968965			0.484483	−	0.874801i	$-0.339008\pi$
$941$	29.7237			0.968965			0.484483	+	0.874801i	$0.339008\pi$
$942$		0			0
$943$			3.45836i			0.112620i
$944$		0			0
$945$	10.7451	−	48.9328i	0.349538	−	1.59179i
$946$		0			0
$947$			22.1959i			0.721270i	0.932707	+	0.360635i	$0.117440\pi$
$947$			22.1959i			0.721270i	−0.932707	+	0.360635i	$0.882560\pi$
$948$		0			0
$949$	14.7946			0.480254
$950$		0			0
$951$	7.13031	+	13.3445i	0.231216	+	0.432726i
$952$		0			0
$953$		−	2.12319i		−	0.0687769i	−0.999409	−	0.0343884i	$-0.989052\pi$
$953$		−	2.12319i		−	0.0687769i	0.999409	−	0.0343884i	$-0.0109483\pi$
$954$		0			0
$955$	26.2950	−	15.1814i	0.850885	−	0.491258i
$956$		0			0
$957$	−32.2385	+	17.2258i	−1.04212	+	0.556832i
$958$		0			0
$959$	35.4433	−	15.2387i	1.14452	−	0.492084i
$960$		0			0
$961$	26.2913			0.848106
$962$		0			0
$963$	8.93203	−	4.40156i	0.287831	−	0.141838i
$964$		0			0
$965$	17.4333	+	30.1954i	0.561199	+	0.972025i
$966$		0			0
$967$	2.23409	−	3.86955i	0.0718434	−	0.124436i	−0.827866	−	0.560926i	$-0.810445\pi$
$967$	2.23409	−	3.86955i	0.0718434	−	0.124436i	0.899709	+	0.436490i	$0.143778\pi$
$968$		0			0
$969$	1.03268	+	1.93268i	0.0331744	+	0.0620867i
$970$		0			0
$971$	0.916026	−	1.58660i	0.0293967	−	0.0509165i	−0.850953	−	0.525242i	$-0.823975\pi$
$971$	0.916026	−	1.58660i	0.0293967	−	0.0509165i	0.880349	+	0.474326i	$0.157308\pi$
$972$		0			0
$973$	13.9718	−	6.00713i	0.447916	−	0.192580i
$974$		0			0
$975$	25.7493	−	41.3948i	0.824638	−	1.32570i
$976$		0			0
$977$		−	30.9498i		−	0.990173i	−0.868844	−	0.495087i	$-0.835136\pi$
$977$		−	30.9498i		−	0.990173i	0.868844	−	0.495087i	$-0.164864\pi$
$978$		0			0
$979$	52.8044	−	30.4866i	1.68764	−	0.974357i
$980$		0			0
$981$	8.49182	+	0.559068i	0.271123	+	0.0178497i
$982$		0			0
$983$	−16.2825	+	28.2020i	−0.519330	+	0.899505i	0.480418	+	0.877040i	$0.340485\pi$
$983$	−16.2825	+	28.2020i	−0.519330	+	0.899505i	−0.999748	+	0.0224656i	$0.992848\pi$
$984$		0			0
$985$	−7.48673	+	4.32246i	−0.238547	+	0.137725i
$986$		0			0
$987$	−4.63010	+	30.5494i	−0.147378	+	0.972397i
$988$		0			0
$989$	9.01881	+	5.20701i	0.286782	+	0.165573i
$990$		0			0
$991$	−1.45730	−	2.52411i	−0.0462926	−	0.0801811i	0.841951	−	0.539555i	$-0.181407\pi$
$991$	−1.45730	−	2.52411i	−0.0462926	−	0.0801811i	−0.888243	+	0.459373i	$0.848074\pi$
$992$		0			0
$993$	48.4277	−	25.8761i	1.53681	−	0.821152i
$994$		0			0
$995$	71.0545	+	41.0234i	2.25258	+	1.30053i
$996$		0			0
$997$	39.9943	+	23.0907i	1.26663	+	0.731290i	0.974349	−	0.225042i	$-0.0722520\pi$
$997$	39.9943	+	23.0907i	1.26663	+	0.731290i	0.292282	+	0.956332i	$0.405585\pi$
$998$		0			0
$999$	−28.7102	−	20.5924i	−0.908350	−	0.651515i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.ca.c.257.2		16
3.2	odd	2		3024.2.ca.c.2609.8		16
4.3	odd	2		126.2.l.a.5.4	✓	16
7.3	odd	6		1008.2.df.c.689.1		16
9.2	odd	6		1008.2.df.c.929.1		16
9.7	even	3		3024.2.df.c.1601.8		16
12.11	even	2		378.2.l.a.341.8		16
21.17	even	6		3024.2.df.c.17.8		16
28.3	even	6		126.2.t.a.59.8	yes	16
28.11	odd	6		882.2.t.a.815.5		16
28.19	even	6		882.2.m.a.293.2		16
28.23	odd	6		882.2.m.b.293.3		16
28.27	even	2		882.2.l.b.509.1		16
36.7	odd	6		378.2.t.a.89.4		16
36.11	even	6		126.2.t.a.47.8	yes	16
36.23	even	6		1134.2.k.b.971.4		16
36.31	odd	6		1134.2.k.a.971.5		16
63.38	even	6	inner	1008.2.ca.c.353.2		16
63.52	odd	6		3024.2.ca.c.2033.8		16
84.11	even	6		2646.2.t.b.2285.1		16
84.23	even	6		2646.2.m.b.881.8		16
84.47	odd	6		2646.2.m.a.881.5		16
84.59	odd	6		378.2.t.a.17.4		16
84.83	odd	2		2646.2.l.a.1097.5		16
252.11	even	6		882.2.l.b.227.5		16
252.31	even	6		1134.2.k.b.647.4		16
252.47	odd	6		882.2.m.b.587.3		16
252.59	odd	6		1134.2.k.a.647.5		16
252.79	odd	6		2646.2.m.a.1763.5		16
252.83	odd	6		882.2.t.a.803.5		16
252.115	even	6		378.2.l.a.143.4		16
252.151	odd	6		2646.2.l.a.521.1		16
252.187	even	6		2646.2.m.b.1763.8		16
252.191	even	6		882.2.m.a.587.2		16
252.223	even	6		2646.2.t.b.1979.1		16
252.227	odd	6		126.2.l.a.101.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.4	✓	16	4.3	odd	2
126.2.l.a.101.8	yes	16	252.227	odd	6
126.2.t.a.47.8	yes	16	36.11	even	6
126.2.t.a.59.8	yes	16	28.3	even	6
378.2.l.a.143.4		16	252.115	even	6
378.2.l.a.341.8		16	12.11	even	2
378.2.t.a.17.4		16	84.59	odd	6
378.2.t.a.89.4		16	36.7	odd	6
882.2.l.b.227.5		16	252.11	even	6
882.2.l.b.509.1		16	28.27	even	2
882.2.m.a.293.2		16	28.19	even	6
882.2.m.a.587.2		16	252.191	even	6
882.2.m.b.293.3		16	28.23	odd	6
882.2.m.b.587.3		16	252.47	odd	6
882.2.t.a.803.5		16	252.83	odd	6
882.2.t.a.815.5		16	28.11	odd	6
1008.2.ca.c.257.2		16	1.1	even	1	trivial
1008.2.ca.c.353.2		16	63.38	even	6	inner
1008.2.df.c.689.1		16	7.3	odd	6
1008.2.df.c.929.1		16	9.2	odd	6
1134.2.k.a.647.5		16	252.59	odd	6
1134.2.k.a.971.5		16	36.31	odd	6
1134.2.k.b.647.4		16	252.31	even	6
1134.2.k.b.971.4		16	36.23	even	6
2646.2.l.a.521.1		16	252.151	odd	6
2646.2.l.a.1097.5		16	84.83	odd	2
2646.2.m.a.881.5		16	84.47	odd	6
2646.2.m.a.1763.5		16	252.79	odd	6
2646.2.m.b.881.8		16	84.23	even	6
2646.2.m.b.1763.8		16	252.187	even	6
2646.2.t.b.1979.1		16	252.223	even	6
2646.2.t.b.2285.1		16	84.11	even	6
3024.2.ca.c.2033.8		16	63.52	odd	6
3024.2.ca.c.2609.8		16	3.2	odd	2
3024.2.df.c.17.8		16	21.17	even	6
3024.2.df.c.1601.8		16	9.7	even	3

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.ca (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.52765 + 0.816261i) q^{3} +(-1.82207 - 3.15592i) q^{5} +(1.58246 - 2.12034i) q^{7} +(1.66744 - 2.49392i) q^{9} +O(q^{10})\)	\(q+(-1.52765 + 0.816261i) q^{3} +(-1.82207 - 3.15592i) q^{5} +(1.58246 - 2.12034i) q^{7} +(1.66744 - 2.49392i) q^{9} +(-4.38809 - 2.53346i) q^{11} +(2.94391 + 1.69967i) q^{13} +(5.35954 + 3.33386i) q^{15} +(-0.774696 - 1.34181i) q^{17} +(0.707140 + 0.408267i) q^{19} +(-0.686700 + 4.53083i) q^{21} +(-1.47275 + 0.850294i) q^{23} +(-4.13989 + 7.17050i) q^{25} +(-0.511572 + 5.17091i) q^{27} +(-3.60693 + 2.08246i) q^{29} -2.16996i q^{31} +(8.77143 + 0.288426i) q^{33} +(-9.57497 - 1.13071i) q^{35} +(-3.39979 + 5.88860i) q^{37} +(-5.88465 - 0.193502i) q^{39} +(1.01681 - 1.76117i) q^{41} +(-3.06189 - 5.30335i) q^{43} +(-10.9088 - 0.718194i) q^{45} +6.74255 q^{47} +(-1.99165 - 6.71069i) q^{49} +(2.27874 + 1.41747i) q^{51} +(-11.4961 + 6.63726i) q^{53} +18.4646i q^{55} +(-1.41352 - 0.0464799i) q^{57} +2.17632 q^{59} -7.25382i q^{61} +(-2.64930 - 7.48206i) q^{63} -12.3877i q^{65} -2.45641 q^{67} +(1.55579 - 2.50110i) q^{69} +6.74272i q^{71} +(3.76912 - 2.17610i) q^{73} +(0.471313 - 14.3333i) q^{75} +(-12.3158 + 5.29511i) q^{77} -12.7530 q^{79} +(-3.43930 - 8.31692i) q^{81} +(-0.768040 - 1.33028i) q^{83} +(-2.82310 + 4.88976i) q^{85} +(3.81029 - 6.12546i) q^{87} +(-6.01679 + 10.4214i) q^{89} +(8.26249 - 3.55243i) q^{91} +(1.77125 + 3.31494i) q^{93} -2.97557i q^{95} +(-5.59509 + 3.23033i) q^{97} +(-13.6351 + 6.71916i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{7}+O(q^{10}) \) 16 * q - 2 * q^7	\( 16 q - 2 q^{7} - 12 q^{11} + 6 q^{13} + 18 q^{15} - 18 q^{17} - 12 q^{21} + 6 q^{23} - 8 q^{25} - 36 q^{27} + 6 q^{29} - 30 q^{35} - 2 q^{37} + 12 q^{39} - 6 q^{41} + 2 q^{43} - 30 q^{45} + 36 q^{47} - 8 q^{49} - 6 q^{51} - 36 q^{53} + 6 q^{57} - 60 q^{59} - 36 q^{63} + 28 q^{67} - 42 q^{69} - 60 q^{75} - 42 q^{77} - 32 q^{79} - 36 q^{81} - 12 q^{85} + 24 q^{87} - 24 q^{89} + 12 q^{91} - 42 q^{93} + 6 q^{97} - 18 q^{99}+O(q^{100}) \) 16 * q - 2 * q^7 - 12 * q^11 + 6 * q^13 + 18 * q^15 - 18 * q^17 - 12 * q^21 + 6 * q^23 - 8 * q^25 - 36 * q^27 + 6 * q^29 - 30 * q^35 - 2 * q^37 + 12 * q^39 - 6 * q^41 + 2 * q^43 - 30 * q^45 + 36 * q^47 - 8 * q^49 - 6 * q^51 - 36 * q^53 + 6 * q^57 - 60 * q^59 - 36 * q^63 + 28 * q^67 - 42 * q^69 - 60 * q^75 - 42 * q^77 - 32 * q^79 - 36 * q^81 - 12 * q^85 + 24 * q^87 - 24 * q^89 + 12 * q^91 - 42 * q^93 + 6 * q^97 - 18 * q^99

Introduction

L-functions

Modular forms

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Database

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