LMFDB - Embedded newform 1008.2.cz.i.607.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(367,1008)]

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([3, 0, 4, 1]))

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

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

chi := DirichletCharacter("1008.367");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.cz (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			607.7
Character	$\chi$	$=$	1008.607
Dual form			1008.2.cz.i.367.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.555316 - 1.64062i) q^{3} +(-3.72015 + 2.14783i) q^{5} +(-2.43997 - 1.02300i) q^{7} +(-2.38325 + 1.82212i) q^{9} +O(q^{10})$	\(q+(-0.555316 - 1.64062i) q^{3} +(-3.72015 + 2.14783i) q^{5} +(-2.43997 - 1.02300i) q^{7} +(-2.38325 + 1.82212i) q^{9} +(-3.12208 - 1.80254i) q^{11} +(4.45873 + 2.57425i) q^{13} +(5.58963 + 4.91062i) q^{15} +(-0.886675 + 0.511922i) q^{17} +(0.662930 - 1.14823i) q^{19} +(-0.323393 + 4.57115i) q^{21} +(2.72335 - 1.57233i) q^{23} +(6.72634 - 11.6504i) q^{25} +(4.31286 + 2.89814i) q^{27} +(-0.373020 - 0.646090i) q^{29} +9.29651 q^{31} +(-1.22353 + 6.12312i) q^{33} +(11.2743 - 1.43494i) q^{35} +(-0.761414 + 1.31881i) q^{37} +(1.74735 - 8.74459i) q^{39} +(-4.22328 - 2.43831i) q^{41} +(-6.14560 + 3.54817i) q^{43} +(4.95243 - 11.8974i) q^{45} +7.40975 q^{47} +(4.90694 + 4.99218i) q^{49} +(1.33225 + 1.17041i) q^{51} +(-0.0746200 - 0.129246i) q^{53} +15.4862 q^{55} +(-2.25194 - 0.449984i) q^{57} -1.99395 q^{59} +5.83639i q^{61} +(7.67909 - 2.00787i) q^{63} -22.1162 q^{65} +9.07752i q^{67} +(-4.09191 - 3.59484i) q^{69} +11.3710i q^{71} +(4.04560 - 2.33573i) q^{73} +(-22.8490 - 4.56571i) q^{75} +(5.77381 + 7.59203i) q^{77} -11.1787i q^{79} +(2.35974 - 8.68514i) q^{81} +(-6.90574 - 11.9611i) q^{83} +(2.19904 - 3.80885i) q^{85} +(-0.852841 + 0.970767i) q^{87} +(14.0722 + 8.12459i) q^{89} +(-8.24573 - 10.8424i) q^{91} +(-5.16250 - 15.2520i) q^{93} +5.69544i q^{95} +(6.25228 - 3.60975i) q^{97} +(10.7251 - 1.39293i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{9}+O(q^{10}) $ 32 * q - 4 * q^9	$ 32 q - 4 q^{9} + 6 q^{13} - 18 q^{17} + 4 q^{21} + 16 q^{25} - 12 q^{29} + 2 q^{37} - 36 q^{41} + 12 q^{45} + 2 q^{49} - 12 q^{53} - 46 q^{57} - 36 q^{65} + 42 q^{69} + 42 q^{77} + 20 q^{81} - 12 q^{85} - 18 q^{89} - 38 q^{93} + 6 q^{97}+O(q^{100}) $ 32 * q - 4 * q^9 + 6 * q^13 - 18 * q^17 + 4 * q^21 + 16 * q^25 - 12 * q^29 + 2 * q^37 - 36 * q^41 + 12 * q^45 + 2 * q^49 - 12 * q^53 - 46 * q^57 - 36 * q^65 + 42 * q^69 + 42 * q^77 + 20 * q^81 - 12 * q^85 - 18 * q^89 - 38 * q^93 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.555316	−	1.64062i	−0.320612	−	0.947211i
$3$	−0.555316	−	1.64062i	−0.320612	−	0.947211i
$4$		0			0
$5$	−3.72015	+	2.14783i	−1.66370	+	0.960539i	−0.692777	+	0.721151i	$0.743613\pi$
$5$	−3.72015	+	2.14783i	−1.66370	+	0.960539i	−0.970924	+	0.239387i	$0.923053\pi$
$6$		0			0
$7$	−2.43997	−	1.02300i	−0.922223	−	0.386658i
$7$	−2.43997	−	1.02300i	−0.922223	−	0.386658i
$8$		0			0
$9$	−2.38325	+	1.82212i	−0.794416	+	0.607374i
$10$		0			0
$11$	−3.12208	−	1.80254i	−0.941344	−	0.543485i	−0.0509625	−	0.998701i	$-0.516229\pi$
$11$	−3.12208	−	1.80254i	−0.941344	−	0.543485i	−0.890381	+	0.455215i	$0.849562\pi$
$12$		0			0
$13$	4.45873	+	2.57425i	1.23663	+	0.713968i	0.968404	−	0.249388i	$-0.0802295\pi$
$13$	4.45873	+	2.57425i	1.23663	+	0.713968i	0.268225	+	0.963356i	$0.413563\pi$
$14$		0			0
$15$	5.58963	+	4.91062i	1.44324	+	1.26792i
$16$		0			0
$17$	−0.886675	+	0.511922i	−0.215050	+	0.124159i	−0.603656	−	0.797245i	$-0.706290\pi$
$17$	−0.886675	+	0.511922i	−0.215050	+	0.124159i	0.388606	+	0.921404i	$0.372957\pi$
$18$		0			0
$19$	0.662930	−	1.14823i	0.152087	−	0.263422i	−0.779908	−	0.625894i	$-0.784734\pi$
$19$	0.662930	−	1.14823i	0.152087	−	0.263422i	0.931994	+	0.362473i	$0.118067\pi$
$20$		0			0
$21$	−0.323393	+	4.57115i	−0.0705702	+	0.997507i
$22$		0			0
$23$	2.72335	−	1.57233i	0.567858	−	0.327853i	−0.188435	−	0.982086i	$-0.560342\pi$
$23$	2.72335	−	1.57233i	0.567858	−	0.327853i	0.756293	+	0.654233i	$0.227008\pi$
$24$		0			0
$25$	6.72634	−	11.6504i	1.34527	−	2.33007i
$26$		0			0
$27$	4.31286	+	2.89814i	0.830011	+	0.557748i
$28$		0			0
$29$	−0.373020	−	0.646090i	−0.0692681	−	0.119976i	0.829311	−	0.558787i	$-0.188733\pi$
$29$	−0.373020	−	0.646090i	−0.0692681	−	0.119976i	−0.898579	+	0.438811i	$0.855400\pi$
$30$		0			0
$31$	9.29651			1.66970			0.834851	−	0.550475i	$-0.185554\pi$
$31$	9.29651			1.66970			0.834851	+	0.550475i	$0.185554\pi$
$32$		0			0
$33$	−1.22353	+	6.12312i	−0.212989	+	1.06590i
$34$		0			0
$35$	11.2743	−	1.43494i	1.90570	−	0.242548i
$36$		0			0
$37$	−0.761414	+	1.31881i	−0.125176	+	0.216811i	−0.921802	−	0.387662i	$-0.873283\pi$
$37$	−0.761414	+	1.31881i	−0.125176	+	0.216811i	0.796626	+	0.604473i	$0.206616\pi$
$38$		0			0
$39$	1.74735	−	8.74459i	0.279800	−	1.40025i
$40$		0			0
$41$	−4.22328	−	2.43831i	−0.659565	−	0.380800i	0.132546	−	0.991177i	$-0.457685\pi$
$41$	−4.22328	−	2.43831i	−0.659565	−	0.380800i	−0.792111	+	0.610377i	$0.791018\pi$
$42$		0			0
$43$	−6.14560	+	3.54817i	−0.937196	+	0.541090i	−0.889080	−	0.457752i	$-0.848655\pi$
$43$	−6.14560	+	3.54817i	−0.937196	+	0.541090i	−0.0481156	+	0.998842i	$0.515322\pi$
$44$		0			0
$45$	4.95243	−	11.8974i	0.738265	−	1.77356i
$46$		0			0
$47$	7.40975			1.08082			0.540411	−	0.841401i	$-0.318269\pi$
$47$	7.40975			1.08082			0.540411	+	0.841401i	$0.318269\pi$
$48$		0			0
$49$	4.90694	+	4.99218i	0.700992	+	0.713169i
$50$		0			0
$51$	1.33225	+	1.17041i	0.186553	+	0.163891i
$52$		0			0
$53$	−0.0746200	−	0.129246i	−0.0102499	−	0.0177533i	0.860855	−	0.508850i	$-0.169929\pi$
$53$	−0.0746200	−	0.129246i	−0.0102499	−	0.0177533i	−0.871105	+	0.491097i	$0.836596\pi$
$54$		0			0
$55$	15.4862			2.08815
$56$		0			0
$57$	−2.25194	−	0.449984i	−0.298277	−	0.0596019i
$58$		0			0
$59$	−1.99395			−0.259590			−0.129795	−	0.991541i	$-0.541432\pi$
$59$	−1.99395			−0.259590			−0.129795	+	0.991541i	$0.541432\pi$
$60$		0			0
$61$			5.83639i			0.747274i	0.927575	+	0.373637i	$0.121889\pi$
$61$			5.83639i			0.747274i	−0.927575	+	0.373637i	$0.878111\pi$
$62$		0			0
$63$	7.67909	−	2.00787i	0.967475	−	0.252968i
$64$		0			0
$65$	−22.1162			−2.74318
$66$		0			0
$67$			9.07752i			1.10900i	0.832185	+	0.554498i	$0.187090\pi$
$67$			9.07752i			1.10900i	−0.832185	+	0.554498i	$0.812910\pi$
$68$		0			0
$69$	−4.09191	−	3.59484i	−0.492608	−	0.432768i
$70$		0			0
$71$			11.3710i			1.34949i	0.738052	+	0.674743i	$0.235746\pi$
$71$			11.3710i			1.34949i	−0.738052	+	0.674743i	$0.764254\pi$
$72$		0			0
$73$	4.04560	−	2.33573i	0.473502	−	0.273377i	−0.244202	−	0.969724i	$-0.578526\pi$
$73$	4.04560	−	2.33573i	0.473502	−	0.273377i	0.717705	+	0.696348i	$0.245193\pi$
$74$		0			0
$75$	−22.8490	−	4.56571i	−2.63838	−	0.527203i
$76$		0			0
$77$	5.77381	+	7.59203i	0.657987	+	0.865192i
$78$		0			0
$79$		−	11.1787i		−	1.25770i	−0.777527	−	0.628850i	$-0.783526\pi$
$79$		−	11.1787i		−	1.25770i	0.777527	−	0.628850i	$-0.216474\pi$
$80$		0			0
$81$	2.35974	−	8.68514i	0.262193	−	0.965015i
$82$		0			0
$83$	−6.90574	−	11.9611i	−0.758003	−	1.31290i	−0.943867	−	0.330324i	$-0.892842\pi$
$83$	−6.90574	−	11.9611i	−0.758003	−	1.31290i	0.185864	−	0.982575i	$-0.440492\pi$
$84$		0			0
$85$	2.19904	−	3.80885i	0.238520	−	0.413128i
$86$		0			0
$87$	−0.852841	+	0.970767i	−0.0914342	+	0.104077i
$88$		0			0
$89$	14.0722	+	8.12459i	1.49165	+	0.861205i	0.999954	−	0.00956141i	$-0.00304354\pi$
$89$	14.0722	+	8.12459i	1.49165	+	0.861205i	0.491697	+	0.870767i	$0.336377\pi$
$90$		0			0
$91$	−8.24573	−	10.8424i	−0.864387	−	1.13659i
$92$		0			0
$93$	−5.16250	−	15.2520i	−0.535327	−	1.58156i
$94$		0			0
$95$			5.69544i			0.584340i
$96$		0			0
$97$	6.25228	−	3.60975i	0.634822	−	0.366515i	−0.147795	−	0.989018i	$-0.547218\pi$
$97$	6.25228	−	3.60975i	0.634822	−	0.366515i	0.782617	+	0.622503i	$0.213884\pi$
$98$		0			0
$99$	10.7251	−	1.39293i	1.07792	−	0.139995i
$100$		0			0
$101$	7.79711	+	4.50166i	0.775842	+	0.447932i	0.834955	−	0.550319i	$-0.185494\pi$
$101$	7.79711	+	4.50166i	0.775842	+	0.447932i	−0.0591129	+	0.998251i	$0.518827\pi$
$102$		0			0
$103$	4.64765	+	8.04997i	0.457947	+	0.793187i	0.998852	−	0.0478964i	$-0.0152517\pi$
$103$	4.64765	+	8.04997i	0.457947	+	0.793187i	−0.540906	+	0.841083i	$0.681918\pi$
$104$		0			0
$105$	−8.61498	−	17.7000i	−0.840736	−	1.72734i
$106$		0			0
$107$	−4.62335	−	2.66929i	−0.446956	−	0.258050i	0.259588	−	0.965720i	$-0.416413\pi$
$107$	−4.62335	−	2.66929i	−0.446956	−	0.258050i	−0.706544	+	0.707669i	$0.749747\pi$
$108$		0			0
$109$	−2.66385	−	4.61393i	−0.255151	−	0.441934i	0.709786	−	0.704418i	$-0.248792\pi$
$109$	−2.66385	−	4.61393i	−0.255151	−	0.441934i	−0.964936	+	0.262484i	$0.915458\pi$
$110$		0			0
$111$	2.58648	+	0.516833i	0.245498	+	0.0490556i
$112$		0			0
$113$	5.83794	−	10.1116i	0.549187	−	0.951221i	−0.449143	−	0.893460i	$-0.648271\pi$
$113$	5.83794	−	10.1116i	0.549187	−	0.951221i	0.998330	−	0.0577607i	$-0.0183960\pi$
$114$		0			0
$115$	−6.75419	+	11.6986i	−0.629831	+	1.09090i
$116$		0			0
$117$	−15.3168	+	1.98928i	−1.41604	+	0.183909i
$118$		0			0
$119$	2.68716	−	0.342008i	0.246331	−	0.0313518i
$120$		0			0
$121$	0.998273	+	1.72906i	0.0907521	+	0.157187i
$122$		0			0
$123$	−1.65508	+	8.28281i	−0.149233	+	0.746836i
$124$		0			0
$125$			36.3099i			3.24765i
$126$		0			0
$127$		−	13.4887i		−	1.19693i	−0.801150	−	0.598463i	$-0.795778\pi$
$127$		−	13.4887i		−	1.19693i	0.801150	−	0.598463i	$-0.204222\pi$
$128$		0			0
$129$	9.23394	+	8.11223i	0.813003	+	0.714242i
$130$		0			0
$131$	8.29113	+	14.3607i	0.724399	+	1.25470i	0.959221	+	0.282658i	$0.0912161\pi$
$131$	8.29113	+	14.3607i	0.724399	+	1.25470i	−0.234821	+	0.972039i	$0.575451\pi$
$132$		0			0
$133$	−2.79217	+	2.12347i	−0.242112	+	0.184128i
$134$		0			0
$135$	−22.2692	−	1.51823i	−1.91663	−	0.130668i
$136$		0			0
$137$	−2.98951	+	5.17799i	−0.255411	+	0.442385i	−0.965007	−	0.262224i	$-0.915544\pi$
$137$	−2.98951	+	5.17799i	−0.255411	+	0.442385i	0.709596	+	0.704609i	$0.248878\pi$
$138$		0			0
$139$	8.75126	−	15.1576i	0.742272	−	1.28565i	−0.209187	−	0.977876i	$-0.567082\pi$
$139$	8.75126	−	15.1576i	0.742272	−	1.28565i	0.951459	−	0.307777i	$-0.0995850\pi$
$140$		0			0
$141$	−4.11475	−	12.1566i	−0.346525	−	1.02377i
$142$		0			0
$143$	−9.28035	−	16.0740i	−0.776062	−	1.34418i
$144$		0			0
$145$	2.77538	+	1.60237i	0.230483	+	0.133069i
$146$		0			0
$147$	5.46536	−	10.8227i	0.450775	−	0.892638i
$148$		0			0
$149$	7.58878	+	13.1441i	0.621697	+	1.07681i	0.989170	+	0.146776i	$0.0468897\pi$
$149$	7.58878	+	13.1441i	0.621697	+	1.07681i	−0.367473	+	0.930034i	$0.619777\pi$
$150$		0			0
$151$	−6.09784	−	3.52059i	−0.496235	−	0.286501i	0.230922	−	0.972972i	$-0.425826\pi$
$151$	−6.09784	−	3.52059i	−0.496235	−	0.286501i	−0.727157	+	0.686471i	$0.759159\pi$
$152$		0			0
$153$	1.18038	−	2.83567i	0.0954281	−	0.229250i
$154$		0			0
$155$	−34.5844	+	19.9673i	−2.77789	+	1.60381i
$156$		0			0
$157$			15.8267i			1.26311i	0.775330	+	0.631556i	$0.217583\pi$
$157$			15.8267i			1.26311i	−0.775330	+	0.631556i	$0.782417\pi$
$158$		0			0
$159$	−0.170605	+	0.194195i	−0.0135299	+	0.0154007i
$160$		0			0
$161$	−8.25340	+	1.05045i	−0.650459	+	0.0827871i
$162$		0			0
$163$	9.98202	+	5.76312i	0.781852	+	0.451403i	0.837086	−	0.547071i	$-0.184257\pi$
$163$	9.98202	+	5.76312i	0.781852	+	0.451403i	−0.0552341	+	0.998473i	$0.517591\pi$
$164$		0			0
$165$	−8.59972	−	25.4069i	−0.669487	−	1.97792i
$166$		0			0
$167$	−3.14269	+	5.44330i	−0.243189	+	0.421215i	−0.961621	−	0.274382i	$-0.911527\pi$
$167$	−3.14269	+	5.44330i	−0.243189	+	0.421215i	0.718432	+	0.695597i	$0.244860\pi$
$168$		0			0
$169$	6.75351	+	11.6974i	0.519500	+	0.899801i
$170$		0			0
$171$	0.512287	+	3.94445i	0.0391756	+	0.301640i
$172$		0			0
$173$			7.17579i			0.545565i	0.962076	+	0.272783i	$0.0879440\pi$
$173$			7.17579i			0.545565i	−0.962076	+	0.272783i	$0.912056\pi$
$174$		0			0
$175$	−28.3304	+	21.5455i	−2.14158	+	1.62869i
$176$		0			0
$177$	1.10727	+	3.27130i	0.0832276	+	0.245886i
$178$		0			0
$179$	17.9847	−	10.3835i	1.34424	−	0.776098i	0.356815	−	0.934175i	$-0.383863\pi$
$179$	17.9847	−	10.3835i	1.34424	−	0.776098i	0.987427	+	0.158077i	$0.0505293\pi$
$180$		0			0
$181$			13.7498i			1.02201i	0.859577	+	0.511005i	$0.170727\pi$
$181$			13.7498i			1.02201i	−0.859577	+	0.511005i	$0.829273\pi$
$182$		0			0
$183$	9.57529	−	3.24104i	0.707825	−	0.239585i
$184$		0			0
$185$		−	6.54155i		−	0.480944i
$186$		0			0
$187$	3.69103			0.269915
$188$		0			0
$189$	−7.55847	−	11.4834i	−0.549798	−	0.835298i
$190$		0			0
$191$			5.84765i			0.423121i	0.977365	+	0.211561i	$0.0678546\pi$
$191$			5.84765i			0.423121i	−0.977365	+	0.211561i	$0.932145\pi$
$192$		0			0
$193$	−2.27127			−0.163490			−0.0817448	−	0.996653i	$-0.526049\pi$
$193$	−2.27127			−0.163490			−0.0817448	+	0.996653i	$0.526049\pi$
$194$		0			0
$195$	12.2815	+	36.2842i	0.879495	+	2.59836i
$196$		0			0
$197$	−9.34192			−0.665584			−0.332792	−	0.943000i	$-0.607991\pi$
$197$	−9.34192			−0.665584			−0.332792	+	0.943000i	$0.607991\pi$
$198$		0			0
$199$	−1.05079	−	1.82002i	−0.0744883	−	0.129017i	0.826375	−	0.563120i	$-0.190399\pi$
$199$	−1.05079	−	1.82002i	−0.0744883	−	0.129017i	−0.900864	+	0.434102i	$0.857066\pi$
$200$		0			0
$201$	14.8927	−	5.04089i	1.05045	−	0.355557i
$202$		0			0
$203$	0.249210	+	1.95804i	0.0174911	+	0.137428i
$204$		0			0
$205$	20.9483			1.46309
$206$		0			0
$207$	−3.62545	+	8.70953i	−0.251986	+	0.605354i
$208$		0			0
$209$	−4.13945	+	2.38991i	−0.286332	+	0.165314i
$210$		0			0
$211$	−8.07179	−	4.66025i	−0.555685	−	0.320825i	0.195727	−	0.980658i	$-0.437293\pi$
$211$	−8.07179	−	4.66025i	−0.555685	−	0.320825i	−0.751412	+	0.659834i	$0.770627\pi$
$212$		0			0
$213$	18.6554	−	6.31449i	1.27825	−	0.432662i
$214$		0			0
$215$	15.2417	−	26.3994i	1.03948	−	1.80043i
$216$		0			0
$217$	−22.6832	−	9.51033i	−1.53984	−	0.645603i
$218$		0			0
$219$	−6.07863	−	5.34022i	−0.410756	−	0.360858i
$220$		0			0
$221$	−5.27126			−0.354583
$222$		0			0
$223$	3.87550	+	6.71256i	0.259523	+	0.449506i	0.966114	−	0.258115i	$-0.0831014\pi$
$223$	3.87550	+	6.71256i	0.259523	+	0.449506i	−0.706591	+	0.707622i	$0.749768\pi$
$224$		0			0
$225$	5.19786	+	40.0219i	0.346524	+	2.66813i
$226$		0			0
$227$	9.15434	−	15.8558i	0.607595	−	1.05239i	−0.384041	−	0.923316i	$-0.625468\pi$
$227$	9.15434	−	15.8558i	0.607595	−	1.05239i	0.991636	−	0.129069i	$-0.0411990\pi$
$228$		0			0
$229$	19.2937	−	11.1392i	1.27496	−	0.736099i	0.299044	−	0.954239i	$-0.403332\pi$
$229$	19.2937	−	11.1392i	1.27496	−	0.736099i	0.975917	+	0.218140i	$0.0699990\pi$
$230$		0			0
$231$	9.24932	−	13.6886i	0.608561	−	0.900643i
$232$		0			0
$233$	2.35026	−	4.07076i	0.153970	−	0.266684i	−0.778713	−	0.627380i	$-0.784127\pi$
$233$	2.35026	−	4.07076i	0.153970	−	0.266684i	0.932684	+	0.360696i	$0.117461\pi$
$234$		0			0
$235$	−27.5654	+	15.9149i	−1.79817	+	1.03817i
$236$		0			0
$237$	−18.3399	+	6.20770i	−1.19131	+	0.403233i
$238$		0			0
$239$	9.76287	+	5.63659i	0.631507	+	0.364601i	0.781336	−	0.624111i	$-0.214539\pi$
$239$	9.76287	+	5.63659i	0.631507	+	0.364601i	−0.149828	+	0.988712i	$0.547872\pi$
$240$		0			0
$241$	−3.22948	−	1.86454i	−0.208029	−	0.120106i	0.392366	−	0.919809i	$-0.371657\pi$
$241$	−3.22948	−	1.86454i	−0.208029	−	0.120106i	−0.600395	+	0.799704i	$0.704990\pi$
$242$		0			0
$243$	−15.5594	+	0.951574i	−0.998135	+	0.0610435i
$244$		0			0
$245$	−28.9769	−	8.03240i	−1.85127	−	0.513171i
$246$		0			0
$247$	5.91165	−	3.41309i	0.376149	−	0.217170i
$248$		0			0
$249$	−15.7887	+	17.9719i	−1.00057	+	1.13892i
$250$		0			0
$251$	−12.5374			−0.791354			−0.395677	−	0.918390i	$-0.629490\pi$
$251$	−12.5374			−0.791354			−0.395677	+	0.918390i	$0.629490\pi$
$252$		0			0
$253$	−11.3367			−0.712733
$254$		0			0
$255$	−7.47003	−	1.49267i	−0.467791	−	0.0934745i
$256$		0			0
$257$	13.3822	−	7.72620i	0.834757	−	0.481947i	−0.0207217	−	0.999785i	$-0.506596\pi$
$257$	13.3822	−	7.72620i	0.834757	−	0.481947i	0.855479	+	0.517838i	$0.173263\pi$
$258$		0			0
$259$	3.20697	−	2.43893i	0.199271	−	0.151548i
$260$		0			0
$261$	2.06625	+	0.860103i	0.127898	+	0.0532391i
$262$		0			0
$263$	−14.9586	−	8.63636i	−0.922387	−	0.532541i	−0.0379915	−	0.999278i	$-0.512096\pi$
$263$	−14.9586	−	8.63636i	−0.922387	−	0.532541i	−0.884396	+	0.466737i	$0.845429\pi$
$264$		0			0
$265$	0.555196	+	0.320542i	0.0341054	+	0.0196908i
$266$		0			0
$267$	5.51482	−	27.5988i	0.337501	−	1.68902i
$268$		0			0
$269$	8.06706	−	4.65752i	0.491857	−	0.283974i	−0.233487	−	0.972360i	$-0.575014\pi$
$269$	8.06706	−	4.65752i	0.491857	−	0.283974i	0.725345	+	0.688386i	$0.241680\pi$
$270$		0			0
$271$	−10.1759	+	17.6251i	−0.618140	+	1.07065i	0.371685	+	0.928359i	$0.378780\pi$
$271$	−10.1759	+	17.6251i	−0.618140	+	1.07065i	−0.989825	+	0.142291i	$0.954553\pi$
$272$		0			0
$273$	−13.2092	+	19.5490i	−0.799457	+	1.18316i
$274$		0			0
$275$	−42.0004	+	24.2490i	−2.53272	+	1.46227i
$276$		0			0
$277$	16.3380	−	28.2983i	0.981657	−	1.70028i	0.325718	−	0.945467i	$-0.394394\pi$
$277$	16.3380	−	28.2983i	0.981657	−	1.70028i	0.655940	−	0.754813i	$-0.272273\pi$
$278$		0			0
$279$	−22.1559	+	16.9394i	−1.32644	+	1.01413i
$280$		0			0
$281$	10.8916	+	18.8647i	0.649736	+	1.12538i	0.983186	+	0.182609i	$0.0584541\pi$
$281$	10.8916	+	18.8647i	0.649736	+	1.12538i	−0.333449	+	0.942768i	$0.608213\pi$
$282$		0			0
$283$	3.44313			0.204673			0.102336	−	0.994750i	$-0.467368\pi$
$283$	3.44313			0.204673			0.102336	+	0.994750i	$0.467368\pi$
$284$		0			0
$285$	9.34404	−	3.16277i	0.553493	−	0.187347i
$286$		0			0
$287$	7.81029	+	10.2698i	0.461027	+	0.606208i
$288$		0			0
$289$	−7.97587	+	13.8146i	−0.469169	+	0.812624i
$290$		0			0
$291$	−9.39421	−	8.25303i	−0.550699	−	0.483801i
$292$		0			0
$293$	−17.0502	−	9.84397i	−0.996086	−	0.575091i	−0.0889983	−	0.996032i	$-0.528367\pi$
$293$	−17.0502	−	9.84397i	−0.996086	−	0.575091i	−0.907088	+	0.420941i	$0.861700\pi$
$294$		0			0
$295$	7.41778	−	4.28266i	0.431880	−	0.249346i
$296$		0			0
$297$	−8.24111	−	16.8223i	−0.478198	−	0.976131i
$298$		0			0
$299$	16.1903			0.936306
$300$		0			0
$301$	18.6249	−	2.37048i	1.07352	−	0.136632i
$302$		0			0
$303$	3.05564	−	15.2919i	0.175542	−	0.878498i
$304$		0			0
$305$	−12.5356	−	21.7123i	−0.717785	−	1.24324i
$306$		0			0
$307$	−12.5054			−0.713719			−0.356859	−	0.934158i	$-0.616152\pi$
$307$	−12.5054			−0.713719			−0.356859	+	0.934158i	$0.616152\pi$
$308$		0			0
$309$	10.6260	−	12.0953i	0.604492	−	0.688077i
$310$		0			0
$311$	−10.7105			−0.607335			−0.303668	−	0.952778i	$-0.598211\pi$
$311$	−10.7105			−0.607335			−0.303668	+	0.952778i	$0.598211\pi$
$312$		0			0
$313$		−	11.4987i		−	0.649946i	−0.945723	−	0.324973i	$-0.894645\pi$
$313$		−	11.4987i		−	0.649946i	0.945723	−	0.324973i	$-0.105355\pi$
$314$		0			0
$315$	−24.2548	+	23.9630i	−1.36660	+	1.35016i
$316$		0			0
$317$	17.4157			0.978162			0.489081	−	0.872238i	$-0.337332\pi$
$317$	17.4157			0.978162			0.489081	+	0.872238i	$0.337332\pi$
$318$		0			0
$319$			2.68953i			0.150585i
$320$		0			0
$321$	−1.81186	+	9.06745i	−0.101128	+	0.506096i
$322$		0			0
$323$			1.35747i			0.0755319i
$324$		0			0
$325$	59.9819	−	34.6306i	3.32720	−	1.92096i
$326$		0			0
$327$	−6.09041	+	6.93255i	−0.336800	+	0.383371i
$328$		0			0
$329$	−18.0796	−	7.58017i	−0.996760	−	0.417908i
$330$		0			0
$331$			11.7567i			0.646209i	0.946363	+	0.323105i	$0.104727\pi$
$331$			11.7567i			0.646209i	−0.946363	+	0.323105i	$0.895273\pi$
$332$		0			0
$333$	−0.588391	−	4.53043i	−0.0322436	−	0.248266i
$334$		0			0
$335$	−19.4970	−	33.7697i	−1.06523	−	1.84504i
$336$		0			0
$337$	9.72282	−	16.8404i	0.529636	−	0.917356i	−0.469767	−	0.882791i	$-0.655662\pi$
$337$	9.72282	−	16.8404i	0.529636	−	0.917356i	0.999402	−	0.0345655i	$-0.0110047\pi$
$338$		0			0
$339$	−19.8312	−	3.96268i	−1.07708	−	0.215223i
$340$		0			0
$341$	−29.0245	−	16.7573i	−1.57176	−	0.907459i
$342$		0			0
$343$	−6.86581	−	17.2006i	−0.370719	−	0.928745i
$344$		0			0
$345$	22.9436	+	4.58461i	1.23524	+	0.246827i
$346$		0			0
$347$		−	9.91629i		−	0.532334i	−0.963927	−	0.266167i	$-0.914243\pi$
$347$		−	9.91629i		−	0.532334i	0.963927	−	0.266167i	$-0.0857573\pi$
$348$		0			0
$349$	−8.22452	+	4.74843i	−0.440248	+	0.254178i	−0.703703	−	0.710494i	$-0.748471\pi$
$349$	−8.22452	+	4.74843i	−0.440248	+	0.254178i	0.263455	+	0.964672i	$0.415138\pi$
$350$		0			0
$351$	11.7693	+	24.0244i	0.628201	+	1.28233i
$352$		0			0
$353$	6.39394	+	3.69154i	0.340315	+	0.196481i	0.660411	−	0.750904i	$-0.270382\pi$
$353$	6.39394	+	3.69154i	0.340315	+	0.196481i	−0.320096	+	0.947385i	$0.603715\pi$
$354$		0			0
$355$	−24.4229	−	42.3017i	−1.29623	−	2.24514i
$356$		0			0
$357$	−2.05333	−	4.21868i	−0.108674	−	0.223276i
$358$		0			0
$359$	9.92939	+	5.73274i	0.524053	+	0.302562i	0.738591	−	0.674153i	$-0.235491\pi$
$359$	9.92939	+	5.73274i	0.524053	+	0.302562i	−0.214538	+	0.976716i	$0.568825\pi$
$360$		0			0
$361$	8.62105	+	14.9321i	0.453739	+	0.785900i
$362$		0			0
$363$	2.28237	−	2.59796i	0.119793	−	0.136357i
$364$		0			0
$365$	−10.0335	+	17.3785i	−0.525178	+	0.909634i
$366$		0			0
$367$	13.3883	−	23.1892i	0.698864	−	1.21047i	−0.269996	−	0.962861i	$-0.587023\pi$
$367$	13.3883	−	23.1892i	0.698864	−	1.21047i	0.968861	−	0.247607i	$-0.0796441\pi$
$368$		0			0
$369$	14.5080	−	1.88423i	0.755257	−	0.0980892i
$370$		0			0
$371$	0.0498526	+	0.391692i	0.00258822	+	0.0203357i
$372$		0			0
$373$	6.83034	+	11.8305i	0.353662	+	0.612560i	0.986888	−	0.161407i	$-0.0516031\pi$
$373$	6.83034	+	11.8305i	0.353662	+	0.612560i	−0.633226	+	0.773967i	$0.718270\pi$
$374$		0			0
$375$	59.5706	−	20.1635i	3.07621	−	1.04124i
$376$		0			0
$377$		−	3.84098i		−	0.197821i
$378$		0			0
$379$		−	1.70006i		−	0.0873261i	−0.999046	−	0.0436630i	$-0.986097\pi$
$379$		−	1.70006i		−	0.0873261i	0.999046	−	0.0436630i	$-0.0139028\pi$
$380$		0			0
$381$	−22.1297	+	7.49048i	−1.13374	+	0.383749i
$382$		0			0
$383$	10.3029	+	17.8452i	0.526455	+	0.911847i	0.999525	+	0.0308220i	$0.00981249\pi$
$383$	10.3029	+	17.8452i	0.526455	+	0.911847i	−0.473070	+	0.881025i	$0.656854\pi$
$384$		0			0
$385$	−37.7858	−	15.8423i	−1.92574	−	0.807400i
$386$		0			0
$387$	8.18130	−	19.6542i	0.415879	−	0.999079i
$388$		0			0
$389$	6.72374	−	11.6459i	0.340907	−	0.590468i	−0.643694	−	0.765283i	$-0.722599\pi$
$389$	6.72374	−	11.6459i	0.340907	−	0.590468i	0.984601	+	0.174814i	$0.0559326\pi$
$390$		0			0
$391$	−1.60982	+	2.78829i	−0.0814120	+	0.141010i
$392$		0			0
$393$	18.9561	−	21.5773i	0.956211	−	1.08843i
$394$		0			0
$395$	24.0099	+	41.5863i	1.20807	+	2.09244i
$396$		0			0
$397$	−10.9040	−	6.29540i	−0.547254	−	0.315957i	0.200760	−	0.979641i	$-0.435659\pi$
$397$	−10.9040	−	6.29540i	−0.547254	−	0.315957i	−0.748014	+	0.663683i	$0.768992\pi$
$398$		0			0
$399$	5.03434	+	3.40168i	0.252032	+	0.170297i
$400$		0			0
$401$	−2.30449	−	3.99150i	−0.115081	−	0.199326i	0.802731	−	0.596341i	$-0.203379\pi$
$401$	−2.30449	−	3.99150i	−0.115081	−	0.199326i	−0.917812	+	0.397015i	$0.870046\pi$
$402$		0			0
$403$	41.4506	+	23.9315i	2.06480	+	1.19211i
$404$		0			0
$405$	9.87562	+	37.3783i	0.490724	+	1.85734i
$406$		0			0
$407$	4.75439	−	2.74495i	0.235667	−	0.136062i
$408$		0			0
$409$			20.5778i			1.01751i	0.860912	+	0.508754i	$0.169894\pi$
$409$			20.5778i			1.01751i	−0.860912	+	0.508754i	$0.830106\pi$
$410$		0			0
$411$	10.1552	+	2.02922i	0.500920	+	0.100094i
$412$		0			0
$413$	4.86518	+	2.03981i	0.239400	+	0.100372i
$414$		0			0
$415$	51.3808	+	29.6647i	2.52218	+	1.45618i
$416$		0			0
$417$	−29.7276	−	5.94018i	−1.45577	−	0.290892i
$418$		0			0
$419$	−3.93303	+	6.81221i	−0.192141	+	0.332798i	−0.945960	−	0.324284i	$-0.894877\pi$
$419$	−3.93303	+	6.81221i	−0.192141	+	0.332798i	0.753818	+	0.657083i	$0.228210\pi$
$420$		0			0
$421$	10.8367	+	18.7697i	0.528149	+	0.914781i	0.999461	+	0.0328148i	$0.0104471\pi$
$421$	10.8367	+	18.7697i	0.528149	+	0.914781i	−0.471312	+	0.881966i	$0.656220\pi$
$422$		0			0
$423$	−17.6593	+	13.5015i	−0.858623	+	0.656464i
$424$		0			0
$425$			13.7734i			0.668110i
$426$		0			0
$427$	5.97063	−	14.2406i	0.288939	−	0.689153i
$428$		0			0
$429$	−21.2178	+	24.1517i	−1.02441	+	1.16605i
$430$		0			0
$431$	−0.640472	+	0.369776i	−0.0308504	+	0.0178115i	−0.515346	−	0.856982i	$-0.672337\pi$
$431$	−0.640472	+	0.369776i	−0.0308504	+	0.0178115i	0.484495	+	0.874794i	$0.339003\pi$
$432$		0			0
$433$			26.1089i			1.25471i	0.778732	+	0.627357i	$0.215863\pi$
$433$			26.1089i			1.25471i	−0.778732	+	0.627357i	$0.784137\pi$
$434$		0			0
$435$	1.08766	−	5.44316i	0.0521491	−	0.260979i
$436$		0			0
$437$		−	4.16938i		−	0.199448i
$438$		0			0
$439$	14.8276			0.707684			0.353842	−	0.935305i	$-0.384875\pi$
$439$	14.8276			0.707684			0.353842	+	0.935305i	$0.384875\pi$
$440$		0			0
$441$	−20.7908	−	2.95656i	−0.990040	−	0.140788i
$442$		0			0
$443$		−	10.1466i		−	0.482080i	−0.970515	−	0.241040i	$-0.922511\pi$
$443$		−	10.1466i		−	0.482080i	0.970515	−	0.241040i	$-0.0774886\pi$
$444$		0			0
$445$	−69.8010			−3.30888
$446$		0			0
$447$	17.3503	−	19.7494i	0.820643	−	0.934116i
$448$		0			0
$449$	25.0880			1.18397			0.591987	−	0.805948i	$-0.298344\pi$
$449$	25.0880			1.18397			0.591987	+	0.805948i	$0.298344\pi$
$450$		0			0
$451$	8.79028	+	15.2252i	0.413918	+	0.716927i
$452$		0			0
$453$	−2.38971	+	11.9593i	−0.112278	+	0.561895i
$454$		0			0
$455$	53.9629	+	22.6248i	2.52982	+	1.06067i
$456$		0			0
$457$	−23.9975			−1.12256			−0.561279	−	0.827627i	$-0.689690\pi$
$457$	−23.9975			−1.12256			−0.561279	+	0.827627i	$0.689690\pi$
$458$		0			0
$459$	−5.30773	−	0.361861i	−0.247743	−	0.0168902i
$460$		0			0
$461$	12.2178	−	7.05393i	0.569038	−	0.328534i	−0.187727	−	0.982221i	$-0.560112\pi$
$461$	12.2178	−	7.05393i	0.569038	−	0.328534i	0.756765	+	0.653687i	$0.226779\pi$
$462$		0			0
$463$	−12.0911	−	6.98080i	−0.561921	−	0.324425i	0.191995	−	0.981396i	$-0.438504\pi$
$463$	−12.0911	−	6.98080i	−0.561921	−	0.324425i	−0.753916	+	0.656971i	$0.771837\pi$
$464$		0			0
$465$	51.9640	+	45.6516i	2.40977	+	2.11704i
$466$		0			0
$467$	13.2526	−	22.9542i	0.613258	−	1.06219i	−0.377429	−	0.926038i	$-0.623192\pi$
$467$	13.2526	−	22.9542i	0.613258	−	1.06219i	0.990687	−	0.136156i	$-0.0434748\pi$
$468$		0			0
$469$	9.28630	−	22.1489i	0.428801	−	1.02274i
$470$		0			0
$471$	25.9656	−	8.78885i	1.19643	−	0.404969i
$472$		0			0
$473$	25.5828			1.17630
$474$		0			0
$475$	−8.91819	−	15.4468i	−0.409195	−	0.708746i
$476$		0			0
$477$	0.413340	+	0.172058i	0.0189255	+	0.00787798i
$478$		0			0
$479$	−19.5447	+	33.8524i	−0.893019	+	1.54676i	−0.0567827	+	0.998387i	$0.518084\pi$
$479$	−19.5447	+	33.8524i	−0.893019	+	1.54676i	−0.836237	+	0.548369i	$0.815249\pi$
$480$		0			0
$481$	−6.78987	+	3.92013i	−0.309592	+	0.178743i
$482$		0			0
$483$	6.30664	+	12.9573i	0.286962	+	0.589579i
$484$		0			0
$485$	−15.5063	+	26.8576i	−0.704103	+	1.21954i
$486$		0			0
$487$	−6.79167	+	3.92117i	−0.307760	+	0.177685i	−0.645924	−	0.763402i	$-0.723528\pi$
$487$	−6.79167	+	3.92117i	−0.307760	+	0.177685i	0.338164	+	0.941087i	$0.390194\pi$
$488$		0			0
$489$	3.91190	−	19.5770i	0.176902	−	0.885304i
$490$		0			0
$491$	−17.8659	−	10.3149i	−0.806278	−	0.465505i	0.0393839	−	0.999224i	$-0.487460\pi$
$491$	−17.8659	−	10.3149i	−0.806278	−	0.465505i	−0.845662	+	0.533720i	$0.820794\pi$
$492$		0			0
$493$	0.661495	+	0.381914i	0.0297922	+	0.0172005i
$494$		0			0
$495$	−36.9074	+	28.2177i	−1.65886	+	1.26829i
$496$		0			0
$497$	11.6325	−	27.7449i	0.521789	−	1.24453i
$498$		0			0
$499$	29.8075	−	17.2094i	1.33437	−	0.770397i	0.348401	−	0.937346i	$-0.386725\pi$
$499$	29.8075	−	17.2094i	1.33437	−	0.770397i	0.985966	+	0.166949i	$0.0533916\pi$
$500$		0			0
$501$	10.6756	+	2.13320i	0.476949	+	0.0953043i
$502$		0			0
$503$	25.7268			1.14710			0.573552	−	0.819169i	$-0.305565\pi$
$503$	25.7268			1.14710			0.573552	+	0.819169i	$0.305565\pi$
$504$		0			0
$505$	−38.6752			−1.72103
$506$		0			0
$507$	15.4406	−	17.5757i	0.685743	−	0.780563i
$508$		0			0
$509$	20.9343	−	12.0864i	0.927897	−	0.535722i	0.0417513	−	0.999128i	$-0.486706\pi$
$509$	20.9343	−	12.0864i	0.927897	−	0.535722i	0.886146	+	0.463406i	$0.153373\pi$
$510$		0			0
$511$	−12.2606	+	1.56047i	−0.542378	+	0.0690311i
$512$		0			0
$513$	6.18686	−	3.03089i	0.273156	−	0.133817i
$514$		0			0
$515$	−34.5799	−	19.9647i	−1.52377	−	0.879751i
$516$		0			0
$517$	−23.1339	−	13.3563i	−1.01743	−	0.587411i
$518$		0			0
$519$	11.7727	−	3.98483i	0.516765	−	0.174915i
$520$		0			0
$521$	31.1079	−	17.9602i	1.36286	−	0.786849i	0.372858	−	0.927888i	$-0.378378\pi$
$521$	31.1079	−	17.9602i	1.36286	−	0.786849i	0.990004	+	0.141040i	$0.0450445\pi$
$522$		0			0
$523$	7.02897	−	12.1745i	0.307355	−	0.532355i	−0.670428	−	0.741975i	$-0.733889\pi$
$523$	7.02897	−	12.1745i	0.307355	−	0.532355i	0.977783	+	0.209620i	$0.0672226\pi$
$524$		0			0
$525$	51.0803	+	34.5148i	2.22933	+	1.50635i
$526$		0			0
$527$	−8.24298	+	4.75909i	−0.359070	+	0.207309i
$528$		0			0
$529$	−6.55557	+	11.3546i	−0.285025	+	0.493677i
$530$		0			0
$531$	4.75207	−	3.63322i	0.206222	−	0.157668i
$532$		0			0
$533$	−12.5536	−	21.7435i	−0.543758	−	0.941816i
$534$		0			0
$535$	22.9327			0.991469
$536$		0			0
$537$	−27.0225	−	23.7399i	−1.16611	−	1.02445i
$538$		0			0
$539$	−6.32130	−	24.4310i	−0.272278	−	1.05232i
$540$		0			0
$541$	−2.60496	+	4.51193i	−0.111996	+	0.193983i	−0.916575	−	0.399863i	$-0.869058\pi$
$541$	−2.60496	+	4.51193i	−0.111996	+	0.193983i	0.804579	+	0.593846i	$0.202391\pi$
$542$		0			0
$543$	22.5581	−	7.63546i	0.968060	−	0.327669i
$544$		0			0
$545$	19.8199	+	11.4430i	0.848989	+	0.490164i
$546$		0			0
$547$	11.1833	−	6.45666i	0.478162	−	0.276067i	−0.241488	−	0.970404i	$-0.577635\pi$
$547$	11.1833	−	6.45666i	0.478162	−	0.276067i	0.719650	+	0.694337i	$0.244302\pi$
$548$		0			0
$549$	−10.6346	−	13.9096i	−0.453875	−	0.593646i
$550$		0			0
$551$	−0.989145			−0.0421390
$552$		0			0
$553$	−11.4358	+	27.2757i	−0.486299	+	1.15988i
$554$		0			0
$555$	−10.7322	+	3.63263i	−0.455555	+	0.154196i
$556$		0			0
$557$	−12.6086	−	21.8388i	−0.534245	−	0.925339i	−0.999199	−	0.0400045i	$-0.987263\pi$
$557$	−12.6086	−	21.8388i	−0.534245	−	0.925339i	0.464955	−	0.885334i	$-0.346071\pi$
$558$		0			0
$559$	−36.5354			−1.54528
$560$		0			0
$561$	−2.04969	−	6.05557i	−0.0865380	−	0.255666i
$562$		0			0
$563$	33.9850			1.43230			0.716148	−	0.697949i	$-0.245904\pi$
$563$	33.9850			1.43230			0.716148	+	0.697949i	$0.245904\pi$
$564$		0			0
$565$			50.1556i			2.11006i
$566$		0			0
$567$	−14.6426	+	18.7775i	−0.614931	+	0.788581i
$568$		0			0
$569$	26.7036			1.11947			0.559736	−	0.828671i	$-0.310903\pi$
$569$	26.7036			1.11947			0.559736	+	0.828671i	$0.310903\pi$
$570$		0			0
$571$			28.2741i			1.18324i	0.806218	+	0.591618i	$0.201511\pi$
$571$			28.2741i			1.18324i	−0.806218	+	0.591618i	$0.798489\pi$
$572$		0			0
$573$	9.59376	−	3.24730i	0.400785	−	0.135658i
$574$		0			0
$575$		−	42.3041i		−	1.76420i
$576$		0			0
$577$	−8.61528	+	4.97403i	−0.358659	+	0.207072i	−0.668492	−	0.743719i	$-0.733060\pi$
$577$	−8.61528	+	4.97403i	−0.358659	+	0.207072i	0.309833	+	0.950791i	$0.399727\pi$
$578$		0			0
$579$	1.26127	+	3.72629i	0.0524168	+	0.154859i
$580$		0			0
$581$	4.61363	+	36.2493i	0.191406	+	1.50387i
$582$		0			0
$583$			0.538021i			0.0222826i
$584$		0			0
$585$	52.7083	−	40.2984i	2.17922	−	1.66613i
$586$		0			0
$587$	0.00256306	+	0.00443935i	0.000105789	+	0.000183231i	0.866078	−	0.499908i	$-0.166633\pi$
$587$	0.00256306	+	0.00443935i	0.000105789	+	0.000183231i	−0.865973	+	0.500092i	$0.833300\pi$
$588$		0			0
$589$	6.16294	−	10.6745i	0.253939	−	0.439836i
$590$		0			0
$591$	5.18772	+	15.3265i	0.213394	+	0.630448i
$592$		0			0
$593$	9.34883	+	5.39755i	0.383910	+	0.221651i	0.679518	−	0.733659i	$-0.262189\pi$
$593$	9.34883	+	5.39755i	0.383910	+	0.221651i	−0.295608	+	0.955309i	$0.595522\pi$
$594$		0			0
$595$	−9.26206	+	7.04388i	−0.379707	+	0.288771i
$596$		0			0
$597$	−2.40243	+	2.73462i	−0.0983249	+	0.111921i
$598$		0			0
$599$		−	18.7335i		−	0.765429i	−0.923867	−	0.382714i	$-0.874989\pi$
$599$		−	18.7335i		−	0.765429i	0.923867	−	0.382714i	$-0.125011\pi$
$600$		0			0
$601$	−37.3269	+	21.5507i	−1.52260	+	0.879072i	−0.522954	+	0.852361i	$0.675170\pi$
$601$	−37.3269	+	21.5507i	−1.52260	+	0.879072i	−0.999643	+	0.0267107i	$0.991497\pi$
$602$		0			0
$603$	−16.5404	−	21.6340i	−0.673575	−	0.881003i
$604$		0			0
$605$	−7.42745	−	4.28824i	−0.301969	−	0.174342i
$606$		0			0
$607$	−15.4804	−	26.8129i	−0.628331	−	1.08830i	−0.987887	−	0.155178i	$-0.950405\pi$
$607$	−15.4804	−	26.8129i	−0.628331	−	1.08830i	0.359555	−	0.933124i	$-0.382928\pi$
$608$		0			0
$609$	3.07400	−	1.49619i	0.124565	−	0.0606287i
$610$		0			0
$611$	33.0380	+	19.0745i	1.33658	+	0.771673i
$612$		0			0
$613$	15.9145	+	27.5646i	0.642779	+	1.11333i	0.984810	+	0.173637i	$0.0555519\pi$
$613$	15.9145	+	27.5646i	0.642779	+	1.11333i	−0.342031	+	0.939689i	$0.611115\pi$
$614$		0			0
$615$	−11.6329	−	34.3681i	−0.469085	−	1.38586i
$616$		0			0
$617$	−8.34757	+	14.4584i	−0.336060	+	0.582074i	−0.983688	−	0.179883i	$-0.942428\pi$
$617$	−8.34757	+	14.4584i	−0.336060	+	0.582074i	0.647627	+	0.761957i	$0.275761\pi$
$618$		0			0
$619$	−4.04394	+	7.00430i	−0.162539	+	0.281527i	−0.935779	−	0.352588i	$-0.885302\pi$
$619$	−4.04394	+	7.00430i	−0.162539	+	0.281527i	0.773239	+	0.634114i	$0.218635\pi$
$620$		0			0
$621$	16.3023	+	1.11143i	0.654188	+	0.0446000i
$622$		0			0
$623$	−26.0244	−	34.2197i	−1.04264	−	1.37098i
$624$		0			0
$625$	−44.3557	−	76.8263i	−1.77423	−	3.07305i
$626$		0			0
$627$	6.21963	+	5.46409i	0.248388	+	0.218215i
$628$		0			0
$629$		−	1.55914i		−	0.0621669i
$630$		0			0
$631$			46.7312i			1.86034i	0.367130	+	0.930170i	$0.380340\pi$
$631$			46.7312i			1.86034i	−0.367130	+	0.930170i	$0.619660\pi$
$632$		0			0
$633$	−3.16329	+	15.8306i	−0.125729	+	0.629211i
$634$		0			0
$635$	28.9714	+	50.1799i	1.14969	+	1.99133i
$636$		0			0
$637$	9.02761	+	34.8905i	0.357687	+	1.38241i
$638$		0			0
$639$	−20.7193	−	27.0999i	−0.819643	−	1.07205i
$640$		0			0
$641$	16.1777	−	28.0207i	0.638982	−	1.10675i	−0.346675	−	0.937985i	$-0.612689\pi$
$641$	16.1777	−	28.0207i	0.638982	−	1.10675i	0.985657	−	0.168764i	$-0.0539775\pi$
$642$		0			0
$643$	−7.92549	+	13.7273i	−0.312551	+	0.541354i	−0.978914	−	0.204274i	$-0.934517\pi$
$643$	−7.92549	+	13.7273i	−0.312551	+	0.541354i	0.666363	+	0.745627i	$0.267850\pi$
$644$		0			0
$645$	−51.7753	−	10.3458i	−2.03865	−	0.407365i
$646$		0			0
$647$	−22.9784	−	39.7997i	−0.903373	−	1.56469i	−0.823087	−	0.567916i	$-0.807750\pi$
$647$	−22.9784	−	39.7997i	−0.903373	−	1.56469i	−0.0802858	−	0.996772i	$-0.525583\pi$
$648$		0			0
$649$	6.22527	+	3.59416i	0.244363	+	0.141083i
$650$		0			0
$651$	−3.00643	+	42.4958i	−0.117831	+	1.66554i
$652$		0			0
$653$	−14.2265	−	24.6410i	−0.556725	−	0.964275i	−0.997767	−	0.0667891i	$-0.978725\pi$
$653$	−14.2265	−	24.6410i	−0.556725	−	0.964275i	0.441043	−	0.897486i	$-0.354609\pi$
$654$		0			0
$655$	−61.6885	−	35.6159i	−2.41037	−	1.39163i
$656$		0			0
$657$	−5.38569	+	12.9382i	−0.210116	+	0.504768i
$658$		0			0
$659$	24.8634	−	14.3549i	0.968539	−	0.559186i	0.0697486	−	0.997565i	$-0.477780\pi$
$659$	24.8634	−	14.3549i	0.968539	−	0.559186i	0.898791	+	0.438378i	$0.144447\pi$
$660$		0			0
$661$		−	21.0760i		−	0.819763i	−0.912139	−	0.409881i	$-0.865570\pi$
$661$		−	21.0760i		−	0.819763i	0.912139	−	0.409881i	$-0.134430\pi$
$662$		0			0
$663$	2.92721	+	8.64811i	0.113684	+	0.335865i
$664$		0			0
$665$	5.82644	−	13.8967i	0.225940	−	0.538892i
$666$		0			0
$667$	−2.03173	−	1.17302i	−0.0786689	−	0.0454195i
$668$		0			0
$669$	8.86062	−	10.0858i	0.342571	−	0.389940i
$670$		0			0
$671$	10.5203	−	18.2217i	0.406132	−	0.703441i
$672$		0			0
$673$	−1.51490	−	2.62388i	−0.0583950	−	0.101143i	0.835350	−	0.549718i	$-0.185265\pi$
$673$	−1.51490	−	2.62388i	−0.0583950	−	0.101143i	−0.893745	+	0.448575i	$0.851932\pi$
$674$		0			0
$675$	62.7742	−	30.7525i	2.41618	−	1.18367i
$676$		0			0
$677$			35.6707i			1.37094i	0.728103	+	0.685468i	$0.240402\pi$
$677$			35.6707i			1.37094i	−0.728103	+	0.685468i	$0.759598\pi$
$678$		0			0
$679$	−18.9482	+	2.41163i	−0.727164	+	0.0925498i
$680$		0			0
$681$	−31.0968	−	6.21379i	−1.19163	−	0.238113i
$682$		0			0
$683$	14.7745	−	8.53004i	0.565329	−	0.326393i	−0.189952	−	0.981793i	$-0.560833\pi$
$683$	14.7745	−	8.53004i	0.565329	−	0.326393i	0.755282	+	0.655400i	$0.227500\pi$
$684$		0			0
$685$		−	25.6839i		−	0.981330i
$686$		0			0
$687$	−28.9893	−	25.4677i	−1.10601	−	0.971655i
$688$		0			0
$689$		−	0.768362i		−	0.0292723i
$690$		0			0
$691$	−4.06264			−0.154550			−0.0772750	−	0.997010i	$-0.524622\pi$
$691$	−4.06264			−0.154550			−0.0772750	+	0.997010i	$0.524622\pi$
$692$		0			0
$693$	−27.5940	−	7.57310i	−1.04821	−	0.287678i
$694$		0			0
$695$			75.1848i			2.85192i
$696$		0			0
$697$	4.99289			0.189119
$698$		0			0
$699$	−7.98370	−	1.59531i	−0.301971	−	0.0603401i
$700$		0			0
$701$	40.4912			1.52933			0.764666	−	0.644427i	$-0.222904\pi$
$701$	40.4912			1.52933			0.764666	+	0.644427i	$0.222904\pi$
$702$		0			0
$703$	1.00953	+	1.74855i	0.0380751	+	0.0659480i
$704$		0			0
$705$	41.4177	+	36.3864i	1.55988	+	1.37039i
$706$		0			0
$707$	−14.4195	−	18.9604i	−0.542303	−	0.713079i
$708$		0			0
$709$	−17.6241			−0.661888			−0.330944	−	0.943650i	$-0.607367\pi$
$709$	−17.6241			−0.661888			−0.330944	+	0.943650i	$0.607367\pi$
$710$		0			0
$711$	20.3689	+	26.6415i	0.763894	+	0.999136i
$712$		0			0
$713$	25.3177	−	14.6172i	0.948155	−	0.547417i
$714$		0			0
$715$	69.0486	+	39.8652i	2.58227	+	1.49087i
$716$		0			0
$717$	3.82601	−	19.1472i	0.142885	−	0.715066i
$718$		0			0
$719$	−20.7748	+	35.9829i	−0.774768	+	1.34194i	0.160157	+	0.987092i	$0.448800\pi$
$719$	−20.7748	+	35.9829i	−0.774768	+	1.34194i	−0.934925	+	0.354846i	$0.884533\pi$
$720$		0			0
$721$	−3.10503	−	24.3963i	−0.115637	−	0.908564i
$722$		0			0
$723$	−1.26561	+	6.33375i	−0.0470687	+	0.235555i
$724$		0			0
$725$	−10.0362			−0.372737
$726$		0			0
$727$	19.2047	+	33.2636i	0.712264	+	1.23368i	0.964005	+	0.265884i	$0.0856637\pi$
$727$	19.2047	+	33.2636i	0.712264	+	1.23368i	−0.251741	+	0.967795i	$0.581003\pi$
$728$		0			0
$729$	10.2016	+	24.9986i	0.377835	+	0.925873i
$730$		0			0
$731$	3.63277	−	6.29214i	0.134363	−	0.232723i
$732$		0			0
$733$	−30.4497	+	17.5801i	−1.12468	+	0.649336i	−0.942592	−	0.333945i	$-0.891620\pi$
$733$	−30.4497	+	17.5801i	−1.12468	+	0.649336i	−0.182091	+	0.983282i	$0.558287\pi$
$734$		0			0
$735$	2.91328	+	52.0006i	0.107458	+	1.91807i
$736$		0			0
$737$	16.3626	−	28.3408i	0.602722	−	1.04395i
$738$		0			0
$739$	14.6816	−	8.47640i	0.540070	−	0.311809i	−0.205037	−	0.978754i	$-0.565732\pi$
$739$	14.6816	−	8.47640i	0.540070	−	0.311809i	0.745107	+	0.666945i	$0.232398\pi$
$740$		0			0
$741$	−8.88241	−	7.80341i	−0.326304	−	0.286665i
$742$		0			0
$743$	−23.2333	−	13.4138i	−0.852349	−	0.492104i	0.00909404	−	0.999959i	$-0.497105\pi$
$743$	−23.2333	−	13.4138i	−0.852349	−	0.492104i	−0.861443	+	0.507855i	$0.830439\pi$
$744$		0			0
$745$	−56.4628	−	32.5988i	−2.06864	−	1.19433i
$746$		0			0
$747$	38.2527	+	15.9231i	1.39959	+	0.582597i
$748$		0			0
$749$	8.55017	+	11.2427i	0.312416	+	0.410799i
$750$		0			0
$751$	19.4745	−	11.2436i	0.710634	−	0.410285i	−0.100662	−	0.994921i	$-0.532096\pi$
$751$	19.4745	−	11.2436i	0.710634	−	0.410285i	0.811296	+	0.584636i	$0.198763\pi$
$752$		0			0
$753$	6.96222	+	20.5691i	0.253718	+	0.749579i
$754$		0			0
$755$	30.2465			1.10078
$756$		0			0
$757$	27.2088			0.988921			0.494460	−	0.869200i	$-0.335366\pi$
$757$	27.2088			0.988921			0.494460	+	0.869200i	$0.335366\pi$
$758$		0			0
$759$	6.29546	+	18.5992i	0.228511	+	0.675108i
$760$		0			0
$761$	−2.39357	+	1.38193i	−0.0867669	+	0.0500949i	−0.542756	−	0.839891i	$-0.682619\pi$
$761$	−2.39357	+	1.38193i	−0.0867669	+	0.0500949i	0.455989	+	0.889986i	$0.349286\pi$
$762$		0			0
$763$	1.77968	+	13.9830i	0.0644289	+	0.506218i
$764$		0			0
$765$	1.69934	+	13.0844i	0.0614396	+	0.473066i
$766$		0			0
$767$	−8.89047	−	5.13291i	−0.321016	−	0.185339i
$768$		0			0
$769$	13.4636	+	7.77321i	0.485510	+	0.280309i	0.722710	−	0.691152i	$-0.242896\pi$
$769$	13.4636	+	7.77321i	0.485510	+	0.280309i	−0.237200	+	0.971461i	$0.576230\pi$
$770$		0			0
$771$	−20.1071	−	17.6645i	−0.724138	−	0.636172i
$772$		0			0
$773$	−2.21399	+	1.27825i	−0.0796317	+	0.0459754i	−0.539287	−	0.842122i	$-0.681306\pi$
$773$	−2.21399	+	1.27825i	−0.0796317	+	0.0459754i	0.459655	+	0.888097i	$0.347973\pi$
$774$		0			0
$775$	62.5315	−	108.308i	2.24620	−	3.89053i
$776$		0			0
$777$	−5.78223	−	3.90703i	−0.207436	−	0.140164i
$778$		0			0
$779$	−5.59947	+	3.23286i	−0.200622	+	0.115829i
$780$		0			0
$781$	20.4966	−	35.5011i	0.733426	−	1.27033i
$782$		0			0
$783$	0.263676	−	3.86756i	0.00942299	−	0.138215i
$784$		0			0
$785$	−33.9932	−	58.8779i	−1.21327	−	2.10144i
$786$		0			0
$787$	−50.9562			−1.81639			−0.908196	−	0.418544i	$-0.862540\pi$
$787$	−50.9562			−1.81639			−0.908196	+	0.418544i	$0.862540\pi$
$788$		0			0
$789$	−5.86219	+	29.3373i	−0.208700	+	1.04443i
$790$		0			0
$791$	−24.5886	+	18.6999i	−0.874270	+	0.664890i
$792$		0			0
$793$	−15.0243	+	26.0229i	−0.533529	+	0.924100i
$794$		0			0
$795$	0.217578	−	1.08887i	0.00771669	−	0.0386181i
$796$		0			0
$797$	−12.2946	−	7.09827i	−0.435496	−	0.251434i	0.266189	−	0.963921i	$-0.414235\pi$
$797$	−12.2946	−	7.09827i	−0.435496	−	0.251434i	−0.701685	+	0.712487i	$0.747569\pi$
$798$		0			0
$799$	−6.57003	+	3.79321i	−0.232431	+	0.134194i
$800$		0			0
$801$	−48.3416	+	6.27837i	−1.70806	+	0.221835i
$802$		0			0
$803$	−16.8410			−0.594305
$804$		0			0
$805$	28.4477	−	21.6347i	1.00265	−	0.762524i
$806$		0			0
$807$	−12.1210	−	10.6486i	−0.426678	−	0.374847i
$808$		0			0
$809$	−8.76155	−	15.1755i	−0.308040	−	0.533541i	0.669894	−	0.742457i	$-0.266340\pi$
$809$	−8.76155	−	15.1755i	−0.308040	−	0.533541i	−0.977933	+	0.208916i	$0.933006\pi$
$810$		0			0
$811$	−21.5806			−0.757796			−0.378898	−	0.925438i	$-0.623697\pi$
$811$	−21.5806			−0.757796			−0.378898	+	0.925438i	$0.623697\pi$
$812$		0			0
$813$	34.5669	+	6.90718i	1.21231	+	0.242246i
$814$		0			0
$815$	−49.5128			−1.73436
$816$		0			0
$817$			9.40874i			0.329170i
$818$		0			0
$819$	39.4077	+	10.8153i	1.37702	+	0.377919i
$820$		0			0
$821$	7.39538			0.258100			0.129050	−	0.991638i	$-0.458807\pi$
$821$	7.39538			0.258100			0.129050	+	0.991638i	$0.458807\pi$
$822$		0			0
$823$		−	8.75390i		−	0.305142i	−0.988293	−	0.152571i	$-0.951245\pi$
$823$		−	8.75390i		−	0.305142i	0.988293	−	0.152571i	$-0.0487553\pi$
$824$		0			0
$825$	63.1068	+	55.4408i	2.19710	+	1.93020i
$826$		0			0
$827$			10.9322i			0.380150i	0.981770	+	0.190075i	$0.0608732\pi$
$827$			10.9322i			0.380150i	−0.981770	+	0.190075i	$0.939127\pi$
$828$		0			0
$829$	2.09152	−	1.20754i	0.0726415	−	0.0419396i	−0.463239	−	0.886233i	$-0.653313\pi$
$829$	2.09152	−	1.20754i	0.0726415	−	0.0419396i	0.535881	+	0.844294i	$0.319980\pi$
$830$		0			0
$831$	−55.4995	−	11.0899i	−1.92525	−	0.384706i
$832$		0			0
$833$	−6.90647	−	1.91447i	−0.239295	−	0.0663325i
$834$		0			0
$835$		−	26.9999i		−	0.934369i
$836$		0			0
$837$	40.0946	+	26.9426i	1.38587	+	0.931273i
$838$		0			0
$839$	17.1615	+	29.7246i	0.592481	+	1.02621i	0.993897	+	0.110311i	$0.0351847\pi$
$839$	17.1615	+	29.7246i	0.592481	+	1.02621i	−0.401416	+	0.915896i	$0.631482\pi$
$840$		0			0
$841$	14.2217	−	24.6327i	0.490404	−	0.849404i
$842$		0			0
$843$	24.9016	−	28.3448i	0.857655	−	0.976247i
$844$		0			0
$845$	−50.2481	−	29.0108i	−1.72859	−	0.998001i
$846$		0			0
$847$	−0.666933	−	5.24009i	−0.0229161	−	0.180052i
$848$		0			0
$849$	−1.91203	−	5.64886i	−0.0656206	−	0.193868i
$850$		0			0
$851$			4.78877i			0.164157i
$852$		0			0
$853$	35.5925	−	20.5493i	1.21866	−	0.703596i	0.254032	−	0.967196i	$-0.418243\pi$
$853$	35.5925	−	20.5493i	1.21866	−	0.703596i	0.964632	+	0.263600i	$0.0849098\pi$
$854$		0			0
$855$	−10.3778	−	13.5737i	−0.354913	−	0.464209i
$856$		0			0
$857$	18.1214	+	10.4624i	0.619017	+	0.357390i	0.776486	−	0.630134i	$-0.217000\pi$
$857$	18.1214	+	10.4624i	0.619017	+	0.357390i	−0.157469	+	0.987524i	$0.550334\pi$
$858$		0			0
$859$	−8.28508	−	14.3502i	−0.282683	−	0.489622i	0.689362	−	0.724417i	$-0.257891\pi$
$859$	−8.28508	−	14.3502i	−0.282683	−	0.489622i	−0.972045	+	0.234796i	$0.924558\pi$
$860$		0			0
$861$	12.5117	−	18.5167i	0.426396	−	0.631047i
$862$		0			0
$863$	−7.89280	−	4.55691i	−0.268674	−	0.155119i	0.359611	−	0.933102i	$-0.382909\pi$
$863$	−7.89280	−	4.55691i	−0.268674	−	0.155119i	−0.628285	+	0.777983i	$0.716243\pi$
$864$		0			0
$865$	−15.4124	−	26.6950i	−0.524036	−	0.907658i
$866$		0			0
$867$	27.0936	+	5.41387i	0.920148	+	0.183865i
$868$		0			0
$869$	−20.1500	+	34.9008i	−0.683541	+	1.18393i
$870$		0			0
$871$	−23.3678	+	40.4742i	−0.791787	+	1.37142i
$872$		0			0
$873$	−8.32331	+	19.9954i	−0.281701	+	0.676740i
$874$		0			0
$875$	37.1450	−	88.5951i	1.25573	−	2.99506i
$876$		0			0
$877$	11.5430	+	19.9931i	0.389779	+	0.675117i	0.992420	−	0.122895i	$-0.0392180\pi$
$877$	11.5430	+	19.9931i	0.389779	+	0.675117i	−0.602640	+	0.798013i	$0.705885\pi$
$878$		0			0
$879$	−6.68190	+	33.4394i	−0.225375	+	1.12788i
$880$		0			0
$881$		−	17.9457i		−	0.604606i	−0.953212	−	0.302303i	$-0.902245\pi$
$881$		−	17.9457i		−	0.604606i	0.953212	−	0.302303i	$-0.0977554\pi$
$882$		0			0
$883$			12.6165i			0.424580i	0.977207	+	0.212290i	$0.0680922\pi$
$883$			12.6165i			0.424580i	−0.977207	+	0.212290i	$0.931908\pi$
$884$		0			0
$885$	−11.1454	−	9.79151i	−0.374649	−	0.329138i
$886$		0			0
$887$	14.2816	+	24.7365i	0.479530	+	0.830570i	0.999724	−	0.0234780i	$-0.00747398\pi$
$887$	14.2816	+	24.7365i	0.479530	+	0.830570i	−0.520195	+	0.854048i	$0.674141\pi$
$888$		0			0
$889$	−13.7989	+	32.9120i	−0.462800	+	1.10383i
$890$		0			0
$891$	−23.0226	+	22.8622i	−0.771285	+	0.765913i
$892$		0			0
$893$	4.91214	−	8.50808i	0.164379	−	0.284712i
$894$		0			0
$895$	−44.6039	+	77.2563i	−1.49094	+	2.58239i
$896$		0			0
$897$	−8.99071	−	26.5620i	−0.300191	−	0.886879i
$898$		0			0
$899$	−3.46778	−	6.00638i	−0.115657	−	0.200324i
$900$		0			0
$901$	0.132327	+	0.0763993i	0.00440846	+	0.00254523i
$902$		0			0
$903$	−14.2318	−	29.2399i	−0.473603	−	0.973044i
$904$		0			0
$905$	−29.5321	−	51.1511i	−0.981681	−	1.70032i
$906$		0			0
$907$	12.8967	+	7.44589i	0.428227	+	0.247237i	0.698591	−	0.715521i	$-0.253811\pi$
$907$	12.8967	+	7.44589i	0.428227	+	0.247237i	−0.270364	+	0.962758i	$0.587144\pi$
$908$		0			0
$909$	−26.7850	+	3.47871i	−0.888403	+	0.115382i
$910$		0			0
$911$	−16.3355	+	9.43130i	−0.541219	+	0.312473i	−0.745573	−	0.666424i	$-0.767824\pi$
$911$	−16.3355	+	9.43130i	−0.541219	+	0.312473i	0.204354	+	0.978897i	$0.434491\pi$
$912$		0			0
$913$			49.7914i			1.64785i
$914$		0			0
$915$	−28.6603	+	32.6233i	−0.947480	+	1.07849i
$916$		0			0
$917$	−5.53919	−	43.5214i	−0.182920	−	1.43720i
$918$		0			0
$919$	−23.9314	−	13.8168i	−0.789424	−	0.455774i	0.0503355	−	0.998732i	$-0.483971\pi$
$919$	−23.9314	−	13.8168i	−0.789424	−	0.455774i	−0.839760	+	0.542958i	$0.817304\pi$
$920$		0			0
$921$	6.94443	+	20.5165i	0.228827	+	0.676042i
$922$		0			0
$923$	−29.2717	+	50.7001i	−0.963490	+	1.66881i
$924$		0			0
$925$	10.2431	+	17.7415i	0.336790	+	0.583337i
$926$		0			0
$927$	−25.7445	−	10.7165i	−0.845561	−	0.351975i
$928$		0			0
$929$		−	17.4565i		−	0.572729i	−0.958121	−	0.286365i	$-0.907553\pi$
$929$		−	17.4565i		−	0.572729i	0.958121	−	0.286365i	$-0.0924469\pi$
$930$		0			0
$931$	8.98513	−	2.32482i	0.294476	−	0.0761930i
$932$		0			0
$933$	5.94770	+	17.5718i	0.194719	+	0.575274i
$934$		0			0
$935$	−13.7312	+	7.92770i	−0.449058	+	0.259264i
$936$		0			0
$937$			6.00080i			0.196038i	0.995185	+	0.0980189i	$0.0312505\pi$
$937$			6.00080i			0.196038i	−0.995185	+	0.0980189i	$0.968749\pi$
$938$		0			0
$939$	−18.8650	+	6.38543i	−0.615636	+	0.208381i
$940$		0			0
$941$			17.4183i			0.567819i	0.958851	+	0.283909i	$0.0916315\pi$
$941$			17.4183i			0.567819i	−0.958851	+	0.283909i	$0.908368\pi$
$942$		0			0
$943$	−15.3353			−0.499386
$944$		0			0
$945$	52.7831	+	26.4858i	1.71704	+	0.861584i
$946$		0			0
$947$			13.5404i			0.440005i	0.975499	+	0.220002i	$0.0706065\pi$
$947$			13.5404i			0.440005i	−0.975499	+	0.220002i	$0.929393\pi$
$948$		0			0
$949$	24.0510			0.780729
$950$		0			0
$951$	−9.67121	−	28.5724i	−0.313610	−	0.926525i
$952$		0			0
$953$	−4.27802			−0.138579			−0.0692893	−	0.997597i	$-0.522073\pi$
$953$	−4.27802			−0.138579			−0.0692893	+	0.997597i	$0.522073\pi$
$954$		0			0
$955$	−12.5598	−	21.7541i	−0.406424	−	0.703948i
$956$		0			0
$957$	4.41249	−	1.49354i	0.142635	−	0.0482793i
$958$		0			0
$959$	12.5914	−	9.57588i	0.406598	−	0.309221i
$960$		0			0
$961$	55.4251			1.78791
$962$		0			0
$963$	15.8824	−	2.06273i	0.511802	−	0.0664705i
$964$		0			0
$965$	8.44947	−	4.87830i	0.271998	−	0.157038i
$966$		0			0
$967$	40.6804	+	23.4868i	1.30819	+	0.755285i	0.981794	−	0.189947i	$-0.0608317\pi$
$967$	40.6804	+	23.4868i	1.30819	+	0.755285i	0.326398	+	0.945232i	$0.394165\pi$
$968$		0			0
$969$	2.22709	−	0.753827i	0.0715446	−	0.0242164i
$970$		0			0
$971$	−28.9103	+	50.0741i	−0.927776	+	1.60695i	−0.140740	+	0.990047i	$0.544948\pi$
$971$	−28.9103	+	50.0741i	−0.927776	+	1.60695i	−0.787035	+	0.616908i	$0.788385\pi$
$972$		0			0
$973$	−36.8591	+	28.0317i	−1.18165	+	0.898654i
$974$		0			0
$975$	−90.1244	−	79.1764i	−2.88629	−	2.53567i
$976$		0			0
$977$	−11.0796			−0.354466			−0.177233	−	0.984169i	$-0.556715\pi$
$977$	−11.0796			−0.354466			−0.177233	+	0.984169i	$0.556715\pi$
$978$		0			0
$979$	−29.2897	−	50.7313i	−0.936104	−	1.62138i
$980$		0			0
$981$	14.7558	+	6.14226i	0.471115	+	0.196107i
$982$		0			0
$983$	−11.0527	+	19.1438i	−0.352525	+	0.610591i	−0.986691	−	0.162606i	$-0.948010\pi$
$983$	−11.0527	+	19.1438i	−0.352525	+	0.610591i	0.634166	+	0.773197i	$0.281344\pi$
$984$		0			0
$985$	34.7533	−	20.0648i	1.10733	−	0.639319i
$986$		0			0
$987$	−2.39626	+	33.8711i	−0.0762738	+	1.07813i
$988$		0			0
$989$	−11.1578	+	19.3258i	−0.354796	+	0.614525i
$990$		0			0
$991$	−0.396571	+	0.228961i	−0.0125975	+	0.00727317i	−0.506286	−	0.862366i	$-0.668982\pi$
$991$	−0.396571	+	0.228961i	−0.0125975	+	0.00727317i	0.493688	+	0.869639i	$0.335648\pi$
$992$		0			0
$993$	19.2883	−	6.52871i	0.612096	−	0.207182i
$994$		0			0
$995$	7.81817	+	4.51382i	0.247853	+	0.143098i
$996$		0			0
$997$	−29.7479	−	17.1749i	−0.942124	−	0.543936i	−0.0514986	−	0.998673i	$-0.516400\pi$
$997$	−29.7479	−	17.1749i	−0.942124	−	0.543936i	−0.890626	+	0.454737i	$0.849733\pi$
$998$		0			0
$999$	−7.10596	+	3.48115i	−0.224823	+	0.110139i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cz.i.607.7	yes	32
3.2	odd	2		3024.2.cz.i.1279.15		32
4.3	odd	2	inner	1008.2.cz.i.607.10	yes	32
7.3	odd	6		1008.2.bf.i.31.13	yes	32
9.2	odd	6		3024.2.bf.i.2287.15		32
9.7	even	3		1008.2.bf.i.943.4	yes	32
12.11	even	2		3024.2.cz.i.1279.16		32
21.17	even	6		3024.2.bf.i.1711.1		32
28.3	even	6		1008.2.bf.i.31.4	✓	32
36.7	odd	6		1008.2.bf.i.943.13	yes	32
36.11	even	6		3024.2.bf.i.2287.16		32
63.38	even	6		3024.2.cz.i.2719.16		32
63.52	odd	6	inner	1008.2.cz.i.367.10	yes	32
84.59	odd	6		3024.2.bf.i.1711.2		32
252.115	even	6	inner	1008.2.cz.i.367.7	yes	32
252.227	odd	6		3024.2.cz.i.2719.15		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.i.31.4	✓	32	28.3	even	6
1008.2.bf.i.31.13	yes	32	7.3	odd	6
1008.2.bf.i.943.4	yes	32	9.7	even	3
1008.2.bf.i.943.13	yes	32	36.7	odd	6
1008.2.cz.i.367.7	yes	32	252.115	even	6	inner
1008.2.cz.i.367.10	yes	32	63.52	odd	6	inner
1008.2.cz.i.607.7	yes	32	1.1	even	1	trivial
1008.2.cz.i.607.10	yes	32	4.3	odd	2	inner
3024.2.bf.i.1711.1		32	21.17	even	6
3024.2.bf.i.1711.2		32	84.59	odd	6
3024.2.bf.i.2287.15		32	9.2	odd	6
3024.2.bf.i.2287.16		32	36.11	even	6
3024.2.cz.i.1279.15		32	3.2	odd	2
3024.2.cz.i.1279.16		32	12.11	even	2
3024.2.cz.i.2719.15		32	252.227	odd	6
3024.2.cz.i.2719.16		32	63.38	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.555316 - 1.64062i) q^{3} +(-3.72015 + 2.14783i) q^{5} +(-2.43997 - 1.02300i) q^{7} +(-2.38325 + 1.82212i) q^{9} +O(q^{10})\)	\(q+(-0.555316 - 1.64062i) q^{3} +(-3.72015 + 2.14783i) q^{5} +(-2.43997 - 1.02300i) q^{7} +(-2.38325 + 1.82212i) q^{9} +(-3.12208 - 1.80254i) q^{11} +(4.45873 + 2.57425i) q^{13} +(5.58963 + 4.91062i) q^{15} +(-0.886675 + 0.511922i) q^{17} +(0.662930 - 1.14823i) q^{19} +(-0.323393 + 4.57115i) q^{21} +(2.72335 - 1.57233i) q^{23} +(6.72634 - 11.6504i) q^{25} +(4.31286 + 2.89814i) q^{27} +(-0.373020 - 0.646090i) q^{29} +9.29651 q^{31} +(-1.22353 + 6.12312i) q^{33} +(11.2743 - 1.43494i) q^{35} +(-0.761414 + 1.31881i) q^{37} +(1.74735 - 8.74459i) q^{39} +(-4.22328 - 2.43831i) q^{41} +(-6.14560 + 3.54817i) q^{43} +(4.95243 - 11.8974i) q^{45} +7.40975 q^{47} +(4.90694 + 4.99218i) q^{49} +(1.33225 + 1.17041i) q^{51} +(-0.0746200 - 0.129246i) q^{53} +15.4862 q^{55} +(-2.25194 - 0.449984i) q^{57} -1.99395 q^{59} +5.83639i q^{61} +(7.67909 - 2.00787i) q^{63} -22.1162 q^{65} +9.07752i q^{67} +(-4.09191 - 3.59484i) q^{69} +11.3710i q^{71} +(4.04560 - 2.33573i) q^{73} +(-22.8490 - 4.56571i) q^{75} +(5.77381 + 7.59203i) q^{77} -11.1787i q^{79} +(2.35974 - 8.68514i) q^{81} +(-6.90574 - 11.9611i) q^{83} +(2.19904 - 3.80885i) q^{85} +(-0.852841 + 0.970767i) q^{87} +(14.0722 + 8.12459i) q^{89} +(-8.24573 - 10.8424i) q^{91} +(-5.16250 - 15.2520i) q^{93} +5.69544i q^{95} +(6.25228 - 3.60975i) q^{97} +(10.7251 - 1.39293i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{9}+O(q^{10}) \) 32 * q - 4 * q^9	\( 32 q - 4 q^{9} + 6 q^{13} - 18 q^{17} + 4 q^{21} + 16 q^{25} - 12 q^{29} + 2 q^{37} - 36 q^{41} + 12 q^{45} + 2 q^{49} - 12 q^{53} - 46 q^{57} - 36 q^{65} + 42 q^{69} + 42 q^{77} + 20 q^{81} - 12 q^{85} - 18 q^{89} - 38 q^{93} + 6 q^{97}+O(q^{100}) \) 32 * q - 4 * q^9 + 6 * q^13 - 18 * q^17 + 4 * q^21 + 16 * q^25 - 12 * q^29 + 2 * q^37 - 36 * q^41 + 12 * q^45 + 2 * q^49 - 12 * q^53 - 46 * q^57 - 36 * q^65 + 42 * q^69 + 42 * q^77 + 20 * q^81 - 12 * q^85 - 18 * q^89 - 38 * q^93 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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