LMFDB - Embedded newform 1140.2.bo.c.481.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1140,2,Mod(61,1140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1140, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("1140.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1140.bo (of order $9$, degree $6$, 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:	$9.10294583043$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			481.4
Character	$\chi$	$=$	1140.481
Dual form			1140.2.bo.c.301.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{5} +(2.18283 - 3.78077i) q^{7} +(0.766044 + 0.642788i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{5} +(2.18283 - 3.78077i) q^{7} +(0.766044 + 0.642788i) q^{9} +(-1.46083 - 2.53023i) q^{11} +(1.97460 - 0.718694i) q^{13} +(0.173648 - 0.984808i) q^{15} +(-4.23513 + 3.55370i) q^{17} +(-0.446215 - 4.33600i) q^{19} +(-3.34429 + 2.80619i) q^{21} +(-0.0427697 + 0.242559i) q^{23} +(-0.939693 + 0.342020i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(0.625678 + 0.525006i) q^{29} +(2.01506 - 3.49018i) q^{31} +(0.507341 + 2.87727i) q^{33} +(4.10237 + 1.49314i) q^{35} -2.56680 q^{37} -2.10132 q^{39} +(-4.20629 - 1.53097i) q^{41} +(1.07368 + 6.08916i) q^{43} +(-0.500000 + 0.866025i) q^{45} +(-4.38885 - 3.68268i) q^{47} +(-6.02947 - 10.4433i) q^{49} +(5.19516 - 1.89088i) q^{51} +(2.13735 - 12.1215i) q^{53} +(2.23812 - 1.87801i) q^{55} +(-1.06369 + 4.22712i) q^{57} +(3.22812 - 2.70872i) q^{59} +(2.03319 - 11.5308i) q^{61} +(4.10237 - 1.49314i) q^{63} +(1.05066 + 1.81980i) q^{65} +(-6.59198 - 5.53133i) q^{67} +(0.123150 - 0.213303i) q^{69} +(-0.186952 - 1.06026i) q^{71} +(9.27564 + 3.37606i) q^{73} +1.00000 q^{75} -12.7550 q^{77} +(2.05494 + 0.747937i) q^{79} +(0.173648 + 0.984808i) q^{81} +(0.598619 - 1.03684i) q^{83} +(-4.23513 - 3.55370i) q^{85} +(-0.408382 - 0.707339i) q^{87} +(-2.52306 + 0.918319i) q^{89} +(1.59299 - 9.03428i) q^{91} +(-3.08725 + 2.59051i) q^{93} +(4.19264 - 1.19237i) q^{95} +(-8.49885 + 7.13138i) q^{97} +(0.507341 - 2.87727i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{7}+O(q^{10}) $ 24 * q - 6 * q^7	$ 24 q - 6 q^{7} - 12 q^{11} - 12 q^{17} + 12 q^{19} - 6 q^{21} + 9 q^{23} - 12 q^{27} + 3 q^{29} - 3 q^{33} + 3 q^{35} - 12 q^{37} + 6 q^{39} - 15 q^{41} - 12 q^{45} + 15 q^{47} - 24 q^{49} - 3 q^{51} + 12 q^{53} + 6 q^{55} + 9 q^{57} + 3 q^{59} + 24 q^{61} + 3 q^{63} - 3 q^{65} - 15 q^{67} - 24 q^{71} + 57 q^{73} + 24 q^{75} + 36 q^{77} - 6 q^{79} - 33 q^{83} - 12 q^{85} - 15 q^{87} - 24 q^{89} - 15 q^{91} + 15 q^{93} - 9 q^{95} + 18 q^{97} - 3 q^{99}+O(q^{100}) $ 24 * q - 6 * q^7 - 12 * q^11 - 12 * q^17 + 12 * q^19 - 6 * q^21 + 9 * q^23 - 12 * q^27 + 3 * q^29 - 3 * q^33 + 3 * q^35 - 12 * q^37 + 6 * q^39 - 15 * q^41 - 12 * q^45 + 15 * q^47 - 24 * q^49 - 3 * q^51 + 12 * q^53 + 6 * q^55 + 9 * q^57 + 3 * q^59 + 24 * q^61 + 3 * q^63 - 3 * q^65 - 15 * q^67 - 24 * q^71 + 57 * q^73 + 24 * q^75 + 36 * q^77 - 6 * q^79 - 33 * q^83 - 12 * q^85 - 15 * q^87 - 24 * q^89 - 15 * q^91 + 15 * q^93 - 9 * q^95 + 18 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1140\mathbb{Z}\right)^\times$.

$n$	$457$	$571$	$761$	$781$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{7}{9}\right)$

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
$3$	−0.939693	−	0.342020i	−0.542532	−	0.197465i
$3$	−0.939693	−	0.342020i	−0.542532	−	0.197465i
$4$		0			0
$5$	0.173648	+	0.984808i	0.0776578	+	0.440419i
$5$	0.173648	+	0.984808i	0.0776578	+	0.440419i
$6$		0			0
$7$	2.18283	−	3.78077i	0.825031	−	1.42900i	−0.0768643	−	0.997042i	$-0.524491\pi$
$7$	2.18283	−	3.78077i	0.825031	−	1.42900i	0.901895	−	0.431954i	$-0.142176\pi$
$8$		0			0
$9$	0.766044	+	0.642788i	0.255348	+	0.214263i
$10$		0			0
$11$	−1.46083	−	2.53023i	−0.440457	−	0.762894i	0.557267	−	0.830334i	$-0.311850\pi$
$11$	−1.46083	−	2.53023i	−0.440457	−	0.762894i	−0.997723	+	0.0674401i	$0.978517\pi$
$12$		0			0
$13$	1.97460	−	0.718694i	0.547655	−	0.199330i	−0.0533495	−	0.998576i	$-0.516990\pi$
$13$	1.97460	−	0.718694i	0.547655	−	0.199330i	0.601004	+	0.799246i	$0.294768\pi$
$14$		0			0
$15$	0.173648	−	0.984808i	0.0448358	−	0.254276i
$16$		0			0
$17$	−4.23513	+	3.55370i	−1.02717	+	0.861899i	−0.990512	−	0.137429i	$-0.956116\pi$
$17$	−4.23513	+	3.55370i	−1.02717	+	0.861899i	−0.0366594	+	0.999328i	$0.511672\pi$
$18$		0			0
$19$	−0.446215	−	4.33600i	−0.102369	−	0.994747i
$19$	−0.446215	−	4.33600i	−0.102369	−	0.994747i
$20$		0			0
$21$	−3.34429	+	2.80619i	−0.729783	+	0.612361i
$22$		0			0
$23$	−0.0427697	+	0.242559i	−0.00891809	+	0.0505770i	−0.988942	−	0.148302i	$-0.952619\pi$
$23$	−0.0427697	+	0.242559i	−0.00891809	+	0.0505770i	0.980024	+	0.198879i	$0.0637302\pi$
$24$		0			0
$25$	−0.939693	+	0.342020i	−0.187939	+	0.0684040i
$26$		0			0
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$		0			0
$29$	0.625678	+	0.525006i	0.116186	+	0.0974912i	0.699029	−	0.715093i	$-0.253616\pi$
$29$	0.625678	+	0.525006i	0.116186	+	0.0974912i	−0.582844	+	0.812584i	$0.698060\pi$
$30$		0			0
$31$	2.01506	−	3.49018i	0.361915	−	0.626856i	−0.626361	−	0.779533i	$-0.715456\pi$
$31$	2.01506	−	3.49018i	0.361915	−	0.626856i	0.988276	+	0.152678i	$0.0487896\pi$
$32$		0			0
$33$	0.507341	+	2.87727i	0.0883167	+	0.500869i
$34$		0			0
$35$	4.10237	+	1.49314i	0.693428	+	0.252387i
$36$		0			0
$37$	−2.56680			−0.421979			−0.210990	−	0.977488i	$-0.567669\pi$
$37$	−2.56680			−0.421979			−0.210990	+	0.977488i	$0.567669\pi$
$38$		0			0
$39$	−2.10132			−0.336481
$40$		0			0
$41$	−4.20629	−	1.53097i	−0.656912	−	0.239097i	−0.00800969	−	0.999968i	$-0.502550\pi$
$41$	−4.20629	−	1.53097i	−0.656912	−	0.239097i	−0.648903	+	0.760871i	$0.724772\pi$
$42$		0			0
$43$	1.07368	+	6.08916i	0.163735	+	0.928588i	0.950359	+	0.311156i	$0.100716\pi$
$43$	1.07368	+	6.08916i	0.163735	+	0.928588i	−0.786624	+	0.617433i	$0.788173\pi$
$44$		0			0
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$		0			0
$47$	−4.38885	−	3.68268i	−0.640180	−	0.537175i	0.263894	−	0.964552i	$-0.414993\pi$
$47$	−4.38885	−	3.68268i	−0.640180	−	0.537175i	−0.904073	+	0.427377i	$0.859438\pi$
$48$		0			0
$49$	−6.02947	−	10.4433i	−0.861353	−	1.49191i
$50$		0			0
$51$	5.19516	−	1.89088i	0.727468	−	0.264777i
$52$		0			0
$53$	2.13735	−	12.1215i	0.293588	−	1.66502i	−0.379298	−	0.925275i	$-0.623834\pi$
$53$	2.13735	−	12.1215i	0.293588	−	1.66502i	0.672886	−	0.739746i	$-0.265055\pi$
$54$		0			0
$55$	2.23812	−	1.87801i	0.301788	−	0.253230i
$56$		0			0
$57$	−1.06369	+	4.22712i	−0.140890	+	0.559896i
$58$		0			0
$59$	3.22812	−	2.70872i	0.420266	−	0.352645i	−0.407999	−	0.912983i	$-0.633773\pi$
$59$	3.22812	−	2.70872i	0.420266	−	0.352645i	0.828264	+	0.560338i	$0.189329\pi$
$60$		0			0
$61$	2.03319	−	11.5308i	0.260323	−	1.47637i	−0.521707	−	0.853125i	$-0.674705\pi$
$61$	2.03319	−	11.5308i	0.260323	−	1.47637i	0.782030	−	0.623241i	$-0.214184\pi$
$62$		0			0
$63$	4.10237	−	1.49314i	0.516850	−	0.188118i
$64$		0			0
$65$	1.05066	+	1.81980i	0.130318	+	0.225718i
$66$		0			0
$67$	−6.59198	−	5.53133i	−0.805339	−	0.675760i	0.144152	−	0.989556i	$-0.453955\pi$
$67$	−6.59198	−	5.53133i	−0.805339	−	0.675760i	−0.949490	+	0.313796i	$0.898399\pi$
$68$		0			0
$69$	0.123150	−	0.213303i	0.0148256	−	0.0256786i
$70$		0			0
$71$	−0.186952	−	1.06026i	−0.0221872	−	0.125830i	0.971702	−	0.236208i	$-0.0759048\pi$
$71$	−0.186952	−	1.06026i	−0.0221872	−	0.125830i	−0.993890	+	0.110379i	$0.964794\pi$
$72$		0			0
$73$	9.27564	+	3.37606i	1.08563	+	0.395138i	0.822001	−	0.569486i	$-0.192858\pi$
$73$	9.27564	+	3.37606i	1.08563	+	0.395138i	0.263631	+	0.964624i	$0.415080\pi$
$74$		0			0
$75$	1.00000			0.115470
$76$		0			0
$77$	−12.7550			−1.45356
$78$		0			0
$79$	2.05494	+	0.747937i	0.231199	+	0.0841495i	0.455022	−	0.890480i	$-0.349632\pi$
$79$	2.05494	+	0.747937i	0.231199	+	0.0841495i	−0.223823	+	0.974630i	$0.571854\pi$
$80$		0			0
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$		0			0
$83$	0.598619	−	1.03684i	0.0657070	−	0.113808i	−0.831300	−	0.555823i	$-0.812403\pi$
$83$	0.598619	−	1.03684i	0.0657070	−	0.113808i	0.897007	+	0.442016i	$0.145736\pi$
$84$		0			0
$85$	−4.23513	−	3.55370i	−0.459365	−	0.385453i
$86$		0			0
$87$	−0.408382	−	0.707339i	−0.0437832	−	0.0758347i
$88$		0			0
$89$	−2.52306	+	0.918319i	−0.267444	+	0.0973416i	−0.472261	−	0.881459i	$-0.656562\pi$
$89$	−2.52306	+	0.918319i	−0.267444	+	0.0973416i	0.204817	+	0.978800i	$0.434340\pi$
$90$		0			0
$91$	1.59299	−	9.03428i	0.166990	−	0.947050i
$92$		0			0
$93$	−3.08725	+	2.59051i	−0.320133	+	0.268623i
$94$		0			0
$95$	4.19264	−	1.19237i	0.430156	−	0.122335i
$96$		0			0
$97$	−8.49885	+	7.13138i	−0.862928	+	0.724082i	−0.962597	−	0.270938i	$-0.912666\pi$
$97$	−8.49885	+	7.13138i	−0.862928	+	0.724082i	0.0996691	+	0.995021i	$0.468222\pi$
$98$		0			0
$99$	0.507341	−	2.87727i	0.0509897	−	0.289177i
$100$		0			0
$101$	9.90524	−	3.60521i	0.985608	−	0.358732i	0.201590	−	0.979470i	$-0.435389\pi$
$101$	9.90524	−	3.60521i	0.985608	−	0.358732i	0.784018	+	0.620738i	$0.213167\pi$
$102$		0			0
$103$	−2.66647	−	4.61847i	−0.262735	−	0.455071i	0.704232	−	0.709969i	$-0.251291\pi$
$103$	−2.66647	−	4.61847i	−0.262735	−	0.455071i	−0.966968	+	0.254898i	$0.917958\pi$
$104$		0			0
$105$	−3.34429	−	2.80619i	−0.326369	−	0.273856i
$106$		0			0
$107$	0.915087	−	1.58498i	0.0884648	−	0.153226i	−0.818398	−	0.574652i	$-0.805137\pi$
$107$	0.915087	−	1.58498i	0.0884648	−	0.153226i	0.906862	+	0.421427i	$0.138471\pi$
$108$		0			0
$109$	−2.37802	−	13.4864i	−0.227773	−	1.29176i	−0.857313	−	0.514796i	$-0.827868\pi$
$109$	−2.37802	−	13.4864i	−0.227773	−	1.29176i	0.629540	−	0.776968i	$-0.283243\pi$
$110$		0			0
$111$	2.41200	+	0.877897i	0.228937	+	0.0833263i
$112$		0			0
$113$	−4.73295			−0.445239			−0.222619	−	0.974905i	$-0.571461\pi$
$113$	−4.73295			−0.445239			−0.222619	+	0.974905i	$0.571461\pi$
$114$		0			0
$115$	−0.246301			−0.0229677
$116$		0			0
$117$	1.97460	+	0.718694i	0.182552	+	0.0664433i
$118$		0			0
$119$	4.19115	+	23.7692i	0.384202	+	2.17892i
$120$		0			0
$121$	1.23195	−	2.13380i	0.111996	−	0.193982i
$122$		0			0
$123$	3.42900	+	2.87727i	0.309183	+	0.259435i
$124$		0			0
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$		0			0
$127$	−3.36470	+	1.22465i	−0.298568	+	0.108670i	−0.486961	−	0.873424i	$-0.661895\pi$
$127$	−3.36470	+	1.22465i	−0.298568	+	0.108670i	0.188392	+	0.982094i	$0.439672\pi$
$128$		0			0
$129$	1.07368	−	6.08916i	0.0945326	−	0.536121i
$130$		0			0
$131$	1.50661	−	1.26419i	0.131633	−	0.110453i	−0.574594	−	0.818438i	$-0.694840\pi$
$131$	1.50661	−	1.26419i	0.131633	−	0.110453i	0.706227	+	0.707985i	$0.250396\pi$
$132$		0			0
$133$	−17.3674	−	7.77770i	−1.50595	−	0.674412i
$134$		0			0
$135$	0.766044	−	0.642788i	0.0659306	−	0.0553223i
$136$		0			0
$137$	−3.57785	+	20.2910i	−0.305677	+	1.73358i	0.314626	+	0.949216i	$0.398121\pi$
$137$	−3.57785	+	20.2910i	−0.305677	+	1.73358i	−0.620303	+	0.784363i	$0.712990\pi$
$138$		0			0
$139$	−5.57817	+	2.03029i	−0.473134	+	0.172207i	−0.567572	−	0.823324i	$-0.692117\pi$
$139$	−5.57817	+	2.03029i	−0.473134	+	0.172207i	0.0944374	+	0.995531i	$0.469895\pi$
$140$		0			0
$141$	2.86462	+	4.96167i	0.241245	+	0.417848i
$142$		0			0
$143$	−4.70301	−	3.94630i	−0.393286	−	0.330006i
$144$		0			0
$145$	−0.408382	+	0.707339i	−0.0339143	+	0.0587413i
$146$		0			0
$147$	2.09401	+	11.8757i	0.172711	+	0.979494i
$148$		0			0
$149$	5.42371	+	1.97407i	0.444327	+	0.161722i	0.554488	−	0.832192i	$-0.312914\pi$
$149$	5.42371	+	1.97407i	0.444327	+	0.161722i	−0.110160	+	0.993914i	$0.535136\pi$
$150$		0			0
$151$	18.9542			1.54247			0.771237	−	0.636549i	$-0.219639\pi$
$151$	18.9542			1.54247			0.771237	+	0.636549i	$0.219639\pi$
$152$		0			0
$153$	−5.52858			−0.446959
$154$		0			0
$155$	3.78707	+	1.37838i	0.304185	+	0.110714i
$156$		0			0
$157$	0.840399	+	4.76614i	0.0670711	+	0.380379i	0.999804	+	0.0198105i	$0.00630630\pi$
$157$	0.840399	+	4.76614i	0.0670711	+	0.380379i	−0.932733	+	0.360569i	$0.882583\pi$
$158$		0			0
$159$	−6.15427	+	10.6595i	−0.488065	+	0.845353i
$160$		0			0
$161$	0.823700	+	0.691166i	0.0649167	+	0.0544715i
$162$		0			0
$163$	−5.00126	−	8.66244i	−0.391729	−	0.678495i	0.600949	−	0.799288i	$-0.294790\pi$
$163$	−5.00126	−	8.66244i	−0.391729	−	0.678495i	−0.992678	+	0.120793i	$0.961456\pi$
$164$		0			0
$165$	−2.74546	+	0.999267i	−0.213734	+	0.0777928i
$166$		0			0
$167$	−0.854075	+	4.84370i	−0.0660903	+	0.374817i	0.933766	+	0.357883i	$0.116501\pi$
$167$	−0.854075	+	4.84370i	−0.0660903	+	0.374817i	−0.999857	+	0.0169334i	$0.994610\pi$
$168$		0			0
$169$	−6.57607	+	5.51798i	−0.505851	+	0.424460i
$170$		0			0
$171$	2.44531	−	3.60839i	0.186997	−	0.275940i
$172$		0			0
$173$	8.62430	−	7.23665i	0.655693	−	0.550192i	−0.253099	−	0.967440i	$-0.581450\pi$
$173$	8.62430	−	7.23665i	0.655693	−	0.550192i	0.908792	+	0.417248i	$0.137005\pi$
$174$		0			0
$175$	−0.758088	+	4.29933i	−0.0573061	+	0.324999i
$176$		0			0
$177$	−3.95988	+	1.44128i	−0.297643	+	0.108333i
$178$		0			0
$179$	11.0683	+	19.1709i	0.827287	+	1.43290i	0.900159	+	0.435561i	$0.143450\pi$
$179$	11.0683	+	19.1709i	0.827287	+	1.43290i	−0.0728723	+	0.997341i	$0.523217\pi$
$180$		0			0
$181$	13.5203	+	11.3449i	1.00495	+	0.843257i	0.987663	−	0.156594i	$-0.0500513\pi$
$181$	13.5203	+	11.3449i	1.00495	+	0.843257i	0.0172913	+	0.999850i	$0.494496\pi$
$182$		0			0
$183$	−5.85433	+	10.1400i	−0.432765	+	0.749570i
$184$		0			0
$185$	−0.445720	−	2.52780i	−0.0327700	−	0.185848i
$186$		0			0
$187$	15.1785	+	5.52452i	1.10996	+	0.403993i
$188$		0			0
$189$	−4.36565			−0.317555
$190$		0			0
$191$	16.9258			1.22471			0.612354	−	0.790584i	$-0.290223\pi$
$191$	16.9258			1.22471			0.612354	+	0.790584i	$0.290223\pi$
$192$		0			0
$193$	−19.6963	−	7.16888i	−1.41777	−	0.516028i	−0.484373	−	0.874862i	$-0.660952\pi$
$193$	−19.6963	−	7.16888i	−1.41777	−	0.516028i	−0.933401	+	0.358834i	$0.883174\pi$
$194$		0			0
$195$	−0.364891	−	2.06940i	−0.0261304	−	0.148193i
$196$		0			0
$197$	−7.52147	+	13.0276i	−0.535883	+	0.928176i	0.463237	+	0.886234i	$0.346688\pi$
$197$	−7.52147	+	13.0276i	−0.535883	+	0.928176i	−0.999120	+	0.0419417i	$0.986646\pi$
$198$		0			0
$199$	8.34638	+	7.00345i	0.591659	+	0.496461i	0.888753	−	0.458387i	$-0.151573\pi$
$199$	8.34638	+	7.00345i	0.591659	+	0.496461i	−0.297093	+	0.954848i	$0.596017\pi$
$200$		0			0
$201$	4.30261	+	7.45234i	0.303483	+	0.525648i
$202$		0			0
$203$	3.35067	−	1.21955i	0.235171	−	0.0855953i
$204$		0			0
$205$	0.777291	−	4.40824i	0.0542884	−	0.307885i
$206$		0			0
$207$	−0.188677	+	0.158319i	−0.0131140	+	0.0110039i
$208$		0			0
$209$	−10.3192	+	7.46318i	−0.713797	+	0.516239i
$210$		0			0
$211$	4.40576	−	3.69687i	0.303305	−	0.254503i	−0.478413	−	0.878135i	$-0.658788\pi$
$211$	4.40576	−	3.69687i	0.303305	−	0.254503i	0.781718	+	0.623632i	$0.214343\pi$
$212$		0			0
$213$	−0.186952	+	1.06026i	−0.0128098	+	0.0726478i
$214$		0			0
$215$	−5.81021	+	2.11474i	−0.396253	+	0.144224i
$216$		0			0
$217$	−8.79705	−	15.2369i	−0.597183	−	1.03435i
$218$		0			0
$219$	−7.56157	−	6.34491i	−0.510964	−	0.428749i
$220$		0			0
$221$	−5.80866	+	10.0609i	−0.390733	+	0.676769i
$222$		0			0
$223$	1.36537	+	7.74342i	0.0914322	+	0.518538i	0.995782	+	0.0917464i	$0.0292449\pi$
$223$	1.36537	+	7.74342i	0.0914322	+	0.518538i	−0.904350	+	0.426791i	$0.859644\pi$
$224$		0			0
$225$	−0.939693	−	0.342020i	−0.0626462	−	0.0228013i
$226$		0			0
$227$	27.2584			1.80921			0.904603	−	0.426255i	$-0.140167\pi$
$227$	27.2584			1.80921			0.904603	+	0.426255i	$0.140167\pi$
$228$		0			0
$229$	18.8743			1.24725			0.623626	−	0.781723i	$-0.285659\pi$
$229$	18.8743			1.24725			0.623626	+	0.781723i	$0.285659\pi$
$230$		0			0
$231$	11.9857	+	4.36245i	0.788604	+	0.287028i
$232$		0			0
$233$	5.13387	+	29.1156i	0.336331	+	1.90743i	0.413677	+	0.910424i	$0.364244\pi$
$233$	5.13387	+	29.1156i	0.336331	+	1.90743i	−0.0773462	+	0.997004i	$0.524645\pi$
$234$		0			0
$235$	2.86462	−	4.96167i	0.186867	−	0.323663i
$236$		0			0
$237$	−1.67520	−	1.40566i	−0.108816	−	0.0913075i
$238$		0			0
$239$	−10.1532	−	17.5859i	−0.656756	−	1.13754i	−0.981450	−	0.191716i	$-0.938595\pi$
$239$	−10.1532	−	17.5859i	−0.656756	−	1.13754i	0.324694	−	0.945819i	$-0.394739\pi$
$240$		0			0
$241$	21.7901	−	7.93096i	1.40363	−	0.510878i	0.474373	−	0.880324i	$-0.342675\pi$
$241$	21.7901	−	7.93096i	1.40363	−	0.510878i	0.929252	+	0.369446i	$0.120453\pi$
$242$		0			0
$243$	0.173648	−	0.984808i	0.0111395	−	0.0631754i
$244$		0			0
$245$	9.23768	−	7.75134i	0.590174	−	0.495215i
$246$		0			0
$247$	−3.99735	−	8.24116i	−0.254345	−	0.524372i
$248$		0			0
$249$	−0.917138	+	0.769570i	−0.0581212	+	0.0487695i
$250$		0			0
$251$	−1.38627	+	7.86195i	−0.0875009	+	0.496242i	0.909288	+	0.416167i	$0.136627\pi$
$251$	−1.38627	+	7.86195i	−0.0875009	+	0.496242i	−0.996789	+	0.0800747i	$0.974484\pi$
$252$		0			0
$253$	0.676209	−	0.246120i	0.0425129	−	0.0154734i
$254$		0			0
$255$	2.76429	+	4.78789i	0.173106	+	0.299829i
$256$		0			0
$257$	−22.7462	−	19.0863i	−1.41887	−	1.19057i	−0.951942	−	0.306278i	$-0.900916\pi$
$257$	−22.7462	−	19.0863i	−1.41887	−	1.19057i	−0.466928	−	0.884296i	$-0.654639\pi$
$258$		0			0
$259$	−5.60288	+	9.70447i	−0.348146	+	0.603006i
$260$		0			0
$261$	0.141830	+	0.804356i	0.00877904	+	0.0497884i
$262$		0			0
$263$	2.41902	+	0.880451i	0.149163	+	0.0542909i	0.415523	−	0.909583i	$-0.363599\pi$
$263$	2.41902	+	0.880451i	0.149163	+	0.0542909i	−0.266360	+	0.963874i	$0.585821\pi$
$264$		0			0
$265$	12.3085			0.756107
$266$		0			0
$267$	2.68499			0.164318
$268$		0			0
$269$	−14.8625	−	5.40949i	−0.906180	−	0.329823i	−0.153454	−	0.988156i	$-0.549040\pi$
$269$	−14.8625	−	5.40949i	−0.906180	−	0.329823i	−0.752727	+	0.658333i	$0.771262\pi$
$270$		0			0
$271$	2.26975	+	12.8724i	0.137878	+	0.781943i	0.972812	+	0.231594i	$0.0743941\pi$
$271$	2.26975	+	12.8724i	0.137878	+	0.781943i	−0.834935	+	0.550349i	$0.814495\pi$
$272$		0			0
$273$	−4.58682	+	7.94461i	−0.277607	+	0.480830i
$274$		0			0
$275$	2.23812	+	1.87801i	0.134964	+	0.113248i
$276$		0			0
$277$	9.88982	+	17.1297i	0.594222	+	1.02922i	0.993656	+	0.112461i	$0.0358732\pi$
$277$	9.88982	+	17.1297i	0.594222	+	1.02922i	−0.399434	+	0.916762i	$0.630793\pi$
$278$		0			0
$279$	3.78707	−	1.37838i	0.226726	−	0.0825215i
$280$		0			0
$281$	0.581258	−	3.29648i	0.0346750	−	0.196652i	−0.962549	−	0.271106i	$-0.912611\pi$
$281$	0.581258	−	3.29648i	0.0346750	−	0.196652i	0.997224	+	0.0744547i	$0.0237216\pi$
$282$		0			0
$283$	17.3401	−	14.5501i	1.03076	−	0.864913i	0.0398216	−	0.999207i	$-0.487321\pi$
$283$	17.3401	−	14.5501i	1.03076	−	0.864913i	0.990942	+	0.134294i	$0.0428766\pi$
$284$		0			0
$285$	−4.34761	−	0.313503i	−0.257530	−	0.0185703i
$286$		0			0
$287$	−14.9698	+	12.5612i	−0.883641	+	0.741463i
$288$		0			0
$289$	2.35556	−	13.3591i	0.138563	−	0.785827i
$290$		0			0
$291$	10.4254	−	3.79453i	0.611147	−	0.222439i
$292$		0			0
$293$	−1.22130	−	2.11535i	−0.0713491	−	0.123580i	0.828144	−	0.560516i	$-0.189397\pi$
$293$	−1.22130	−	2.11535i	−0.0713491	−	0.123580i	−0.899493	+	0.436936i	$0.856064\pi$
$294$		0			0
$295$	3.22812	+	2.70872i	0.187948	+	0.157707i
$296$		0			0
$297$	−1.46083	+	2.53023i	−0.0847659	+	0.146819i
$298$		0			0
$299$	0.0898729	+	0.509694i	0.00519748	+	0.0294764i
$300$		0			0
$301$	25.3654	+	9.23224i	1.46204	+	0.532137i
$302$		0			0
$303$	−10.5409			−0.605561
$304$		0			0
$305$	11.7087			0.670436
$306$		0			0
$307$	−10.5476	−	3.83900i	−0.601982	−	0.219104i	0.0230093	−	0.999735i	$-0.492675\pi$
$307$	−10.5476	−	3.83900i	−0.601982	−	0.219104i	−0.624991	+	0.780632i	$0.714897\pi$
$308$		0			0
$309$	0.926056	+	5.25193i	0.0526815	+	0.298772i
$310$		0			0
$311$	−10.3352	+	17.9010i	−0.586053	+	1.01507i	0.408690	+	0.912673i	$0.365986\pi$
$311$	−10.3352	+	17.9010i	−0.586053	+	1.01507i	−0.994743	+	0.102401i	$0.967348\pi$
$312$		0			0
$313$	12.9886	+	10.8987i	0.734157	+	0.616031i	0.931261	−	0.364352i	$-0.118709\pi$
$313$	12.9886	+	10.8987i	0.734157	+	0.616031i	−0.197104	+	0.980382i	$0.563154\pi$
$314$		0			0
$315$	2.18283	+	3.78077i	0.122988	+	0.213022i
$316$		0			0
$317$	−15.3731	+	5.59536i	−0.863441	+	0.314267i	−0.735508	−	0.677516i	$-0.763056\pi$
$317$	−15.3731	+	5.59536i	−0.863441	+	0.314267i	−0.127933	+	0.991783i	$0.540834\pi$
$318$		0			0
$319$	0.414378	−	2.35006i	0.0232007	−	0.131578i
$320$		0			0
$321$	−1.40199	+	1.17641i	−0.0782517	+	0.0656610i
$322$		0			0
$323$	17.2986	+	16.7778i	0.962521	+	0.933543i
$324$		0			0
$325$	−1.60971	+	1.35070i	−0.0892904	+	0.0749236i
$326$		0			0
$327$	−2.37802	+	13.4864i	−0.131505	+	0.745800i
$328$		0			0
$329$	−23.5035	+	8.55457i	−1.29579	+	0.471629i
$330$		0			0
$331$	−17.1744	−	29.7470i	−0.943992	−	1.63504i	−0.757758	−	0.652536i	$-0.773705\pi$
$331$	−17.1744	−	29.7470i	−0.943992	−	1.63504i	−0.186234	−	0.982505i	$-0.559628\pi$
$332$		0			0
$333$	−1.96628	−	1.64991i	−0.107752	−	0.0904143i
$334$		0			0
$335$	4.30261	−	7.45234i	0.235077	−	0.407165i
$336$		0			0
$337$	4.62984	+	26.2571i	0.252203	+	1.43032i	0.803151	+	0.595776i	$0.203155\pi$
$337$	4.62984	+	26.2571i	0.252203	+	1.43032i	−0.550948	+	0.834540i	$0.685734\pi$
$338$		0			0
$339$	4.44752	+	1.61876i	0.241556	+	0.0879192i
$340$		0			0
$341$	−11.7746			−0.637632
$342$		0			0
$343$	−22.0856			−1.19251
$344$		0			0
$345$	0.231447	+	0.0842398i	0.0124607	+	0.00453532i
$346$		0			0
$347$	−4.95642	−	28.1093i	−0.266075	−	1.50898i	−0.765958	−	0.642891i	$-0.777735\pi$
$347$	−4.95642	−	28.1093i	−0.266075	−	1.50898i	0.499883	−	0.866093i	$-0.333376\pi$
$348$		0			0
$349$	−5.40242	+	9.35727i	−0.289185	+	0.500883i	−0.973615	−	0.228195i	$-0.926718\pi$
$349$	−5.40242	+	9.35727i	−0.289185	+	0.500883i	0.684431	+	0.729078i	$0.260051\pi$
$350$		0			0
$351$	−1.60971	−	1.35070i	−0.0859197	−	0.0720952i
$352$		0			0
$353$	15.4386	+	26.7404i	0.821712	+	1.42325i	0.904406	+	0.426673i	$0.140314\pi$
$353$	15.4386	+	26.7404i	0.821712	+	1.42325i	−0.0826937	+	0.996575i	$0.526352\pi$
$354$		0			0
$355$	1.01169	−	0.368224i	0.0536948	−	0.0195433i
$356$		0			0
$357$	4.19115	−	23.7692i	0.221819	−	1.25800i
$358$		0			0
$359$	−11.0600	+	9.28043i	−0.583724	+	0.489802i	−0.886168	−	0.463365i	$-0.846642\pi$
$359$	−11.0600	+	9.28043i	−0.583724	+	0.489802i	0.302444	+	0.953167i	$0.402197\pi$
$360$		0			0
$361$	−18.6018	+	3.86958i	−0.979041	+	0.203662i
$362$		0			0
$363$	−1.88746	+	1.58377i	−0.0990660	+	0.0831262i
$364$		0			0
$365$	−1.71407	+	9.72097i	−0.0897185	+	0.508819i
$366$		0			0
$367$	−23.3815	+	8.51019i	−1.22051	+	0.444228i	−0.870336	−	0.492458i	$-0.836099\pi$
$367$	−23.3815	+	8.51019i	−1.22051	+	0.444228i	−0.350171	+	0.936686i	$0.613876\pi$
$368$		0			0
$369$	−2.23812	−	3.87654i	−0.116512	−	0.201805i
$370$		0			0
$371$	−41.1632	−	34.5401i	−2.13709	−	1.79323i
$372$		0			0
$373$	−5.61818	+	9.73098i	−0.290899	+	0.503851i	−0.974022	−	0.226451i	$-0.927288\pi$
$373$	−5.61818	+	9.73098i	−0.290899	+	0.503851i	0.683124	+	0.730302i	$0.260621\pi$
$374$		0			0
$375$	0.173648	+	0.984808i	0.00896715	+	0.0508553i
$376$		0			0
$377$	1.61278	+	0.587004i	0.0830625	+	0.0302323i
$378$		0			0
$379$	−21.7635			−1.11792			−0.558958	−	0.829196i	$-0.688799\pi$
$379$	−21.7635			−1.11792			−0.558958	+	0.829196i	$0.688799\pi$
$380$		0			0
$381$	3.58063			0.183441
$382$		0			0
$383$	15.9299	+	5.79802i	0.813981	+	0.296265i	0.715267	−	0.698851i	$-0.246305\pi$
$383$	15.9299	+	5.79802i	0.813981	+	0.296265i	0.0987136	+	0.995116i	$0.468527\pi$
$384$		0			0
$385$	−2.21488	−	12.5612i	−0.112880	−	0.640177i
$386$		0			0
$387$	−3.09155	+	5.35472i	−0.157152	+	0.272196i
$388$		0			0
$389$	−2.11571	−	1.77529i	−0.107271	−	0.0900107i	0.587575	−	0.809170i	$-0.300083\pi$
$389$	−2.11571	−	1.77529i	−0.107271	−	0.0900107i	−0.694845	+	0.719159i	$0.744527\pi$
$390$		0			0
$391$	−0.680846	−	1.17926i	−0.0344319	−	0.0596378i
$392$		0			0
$393$	−1.84813	+	0.672663i	−0.0932256	+	0.0339313i
$394$		0			0
$395$	−0.379737	+	2.15360i	−0.0191067	+	0.108359i
$396$		0			0
$397$	16.1020	−	13.5112i	0.808138	−	0.678108i	−0.142025	−	0.989863i	$-0.545361\pi$
$397$	16.1020	−	13.5112i	0.808138	−	0.678108i	0.950162	+	0.311755i	$0.100917\pi$
$398$		0			0
$399$	13.6599	+	13.2487i	0.683850	+	0.663262i
$400$		0			0
$401$	25.3933	−	21.3075i	1.26808	−	1.06405i	0.273311	−	0.961926i	$-0.411881\pi$
$401$	25.3933	−	21.3075i	1.26808	−	1.06405i	0.994772	−	0.102122i	$-0.0325633\pi$
$402$		0			0
$403$	1.47055	−	8.33992i	0.0732534	−	0.415441i
$404$		0			0
$405$	−0.939693	+	0.342020i	−0.0466937	+	0.0169951i
$406$		0			0
$407$	3.74966	+	6.49460i	0.185864	+	0.321925i
$408$		0			0
$409$	16.5297	+	13.8700i	0.817339	+	0.685829i	0.952347	−	0.305015i	$-0.0986616\pi$
$409$	16.5297	+	13.8700i	0.817339	+	0.685829i	−0.135008	+	0.990844i	$0.543106\pi$
$410$		0			0
$411$	10.3020	−	17.8436i	0.508161	−	0.880161i
$412$		0			0
$413$	−3.19459	−	18.1174i	−0.157196	−	0.891501i
$414$		0			0
$415$	1.12504	+	0.409480i	0.0552258	+	0.0201006i
$416$		0			0
$417$	5.93616			0.290695
$418$		0			0
$419$	10.8458			0.529854			0.264927	−	0.964268i	$-0.414652\pi$
$419$	10.8458			0.529854			0.264927	+	0.964268i	$0.414652\pi$
$420$		0			0
$421$	−14.0341	−	5.10798i	−0.683978	−	0.248948i	−0.0234235	−	0.999726i	$-0.507457\pi$
$421$	−14.0341	−	5.10798i	−0.683978	−	0.248948i	−0.660555	+	0.750778i	$0.729679\pi$
$422$		0			0
$423$	−0.994872	−	5.64220i	−0.0483723	−	0.274333i
$424$		0			0
$425$	2.76429	−	4.78789i	0.134088	−	0.232247i
$426$		0			0
$427$	−39.1571	−	32.8567i	−1.89495	−	1.59005i
$428$		0			0
$429$	3.06967	+	5.31683i	0.148205	+	0.256699i
$430$		0			0
$431$	−4.95968	+	1.80518i	−0.238899	+	0.0869523i	−0.458695	−	0.888594i	$-0.651683\pi$
$431$	−4.95968	+	1.80518i	−0.238899	+	0.0869523i	0.219796	+	0.975546i	$0.429461\pi$
$432$		0			0
$433$	−3.23188	+	18.3289i	−0.155314	+	0.880830i	0.803184	+	0.595731i	$0.203138\pi$
$433$	−3.23188	+	18.3289i	−0.155314	+	0.880830i	−0.958498	+	0.285099i	$0.907974\pi$
$434$		0			0
$435$	0.625678	−	0.525006i	0.0299990	−	0.0251721i
$436$		0			0
$437$	1.07082	+	0.0772159i	0.0512243	+	0.00369374i
$438$		0			0
$439$	−5.51070	+	4.62403i	−0.263012	+	0.220693i	−0.764751	−	0.644326i	$-0.777138\pi$
$439$	−5.51070	+	4.62403i	−0.263012	+	0.220693i	0.501739	+	0.865019i	$0.332694\pi$
$440$		0			0
$441$	2.09401	−	11.8757i	0.0997149	−	0.565511i
$442$		0			0
$443$	23.9400	−	8.71345i	1.13742	−	0.413989i	0.296442	−	0.955051i	$-0.404200\pi$
$443$	23.9400	−	8.71345i	1.13742	−	0.413989i	0.840982	+	0.541062i	$0.181978\pi$
$444$		0			0
$445$	−1.34249	−	2.32527i	−0.0636402	−	0.110228i
$446$		0			0
$447$	−4.42145	−	3.71003i	−0.209127	−	0.175479i
$448$		0			0
$449$	16.4661	−	28.5201i	0.777082	−	1.34595i	−0.156535	−	0.987672i	$-0.550032\pi$
$449$	16.4661	−	28.5201i	0.777082	−	1.34595i	0.933617	−	0.358273i	$-0.116634\pi$
$450$		0			0
$451$	2.27098	+	12.8794i	0.106936	+	0.606466i
$452$		0			0
$453$	−17.8111	−	6.48273i	−0.836841	−	0.304585i
$454$		0			0
$455$	9.17365			0.430067
$456$		0			0
$457$	23.2180			1.08609			0.543047	−	0.839703i	$-0.317271\pi$
$457$	23.2180			1.08609			0.543047	+	0.839703i	$0.317271\pi$
$458$		0			0
$459$	5.19516	+	1.89088i	0.242489	+	0.0882589i
$460$		0			0
$461$	0.630169	+	3.57387i	0.0293499	+	0.166451i	0.995960	−	0.0898012i	$-0.0286232\pi$
$461$	0.630169	+	3.57387i	0.0293499	+	0.166451i	−0.966610	+	0.256253i	$0.917512\pi$
$462$		0			0
$463$	3.17651	−	5.50187i	0.147625	−	0.255694i	−0.782724	−	0.622369i	$-0.786171\pi$
$463$	3.17651	−	5.50187i	0.147625	−	0.255694i	0.930349	+	0.366675i	$0.119504\pi$
$464$		0			0
$465$	−3.08725	−	2.59051i	−0.143168	−	0.120132i
$466$		0			0
$467$	4.70538	+	8.14996i	0.217739	+	0.377135i	0.954116	−	0.299436i	$-0.0967984\pi$
$467$	4.70538	+	8.14996i	0.217739	+	0.377135i	−0.736377	+	0.676571i	$0.763465\pi$
$468$		0			0
$469$	−35.3018	+	12.8488i	−1.63009	+	0.593303i
$470$		0			0
$471$	0.840399	−	4.76614i	0.0387235	−	0.219612i
$472$		0			0
$473$	13.8385	−	11.6119i	0.636296	−	0.533916i
$474$		0			0
$475$	1.90230	+	3.92189i	0.0872837	+	0.179949i
$476$		0			0
$477$	9.42888	−	7.91177i	0.431719	−	0.362255i
$478$		0			0
$479$	6.80362	−	38.5852i	0.310865	−	1.76300i	−0.283658	−	0.958926i	$-0.591548\pi$
$479$	6.80362	−	38.5852i	0.310865	−	1.76300i	0.594523	−	0.804079i	$-0.297341\pi$
$480$		0			0
$481$	−5.06839	+	1.84474i	−0.231099	+	0.0841131i
$482$		0			0
$483$	−0.537632	−	0.931206i	−0.0244631	−	0.0423713i
$484$		0			0
$485$	−8.49885	−	7.13138i	−0.385913	−	0.323819i
$486$		0			0
$487$	5.23247	−	9.06290i	0.237106	−	0.410679i	−0.722777	−	0.691082i	$-0.757135\pi$
$487$	5.23247	−	9.06290i	0.237106	−	0.410679i	0.959883	+	0.280402i	$0.0904679\pi$
$488$		0			0
$489$	1.73692	+	9.85056i	0.0785462	+	0.445458i
$490$		0			0
$491$	21.6644	+	7.88520i	0.977701	+	0.355854i	0.780946	−	0.624598i	$-0.214737\pi$
$491$	21.6644	+	7.88520i	0.977701	+	0.355854i	0.196755	+	0.980453i	$0.436960\pi$
$492$		0			0
$493$	−4.51555			−0.203370
$494$		0			0
$495$	2.92166			0.131319
$496$		0			0
$497$	−4.41668	−	1.60754i	−0.198115	−	0.0721080i
$498$		0			0
$499$	2.47567	+	14.0402i	0.110826	+	0.628526i	0.988732	+	0.149694i	$0.0478287\pi$
$499$	2.47567	+	14.0402i	0.110826	+	0.628526i	−0.877906	+	0.478832i	$0.841060\pi$
$500$		0			0
$501$	2.45921	−	4.25948i	0.109869	−	0.190299i
$502$		0			0
$503$	21.7179	+	18.2235i	0.968354	+	0.812546i	0.982292	−	0.187357i	$-0.0599922\pi$
$503$	21.7179	+	18.2235i	0.968354	+	0.812546i	−0.0139377	+	0.999903i	$0.504437\pi$
$504$		0			0
$505$	5.27047	+	9.12872i	0.234533	+	0.406223i
$506$		0			0
$507$	8.06674	−	2.93605i	0.358257	−	0.130395i
$508$		0			0
$509$	5.58532	−	31.6759i	0.247565	−	1.40401i	−0.566895	−	0.823790i	$-0.691855\pi$
$509$	5.58532	−	31.6759i	0.247565	−	1.40401i	0.814460	−	0.580220i	$-0.197034\pi$
$510$		0			0
$511$	33.0112	−	27.6997i	1.46033	−	1.22536i
$512$		0			0
$513$	−3.53198	+	2.55443i	−0.155941	+	0.112781i
$514$		0			0
$515$	4.08527	−	3.42795i	0.180019	−	0.151054i
$516$		0			0
$517$	−2.90668	+	16.4846i	−0.127836	+	0.724991i
$518$		0			0
$519$	−10.5793	+	3.85054i	−0.464378	+	0.169020i
$520$		0			0
$521$	−13.0265	−	22.5625i	−0.570700	−	0.988481i	−0.996494	−	0.0836608i	$-0.973339\pi$
$521$	−13.0265	−	22.5625i	−0.570700	−	0.988481i	0.425795	−	0.904820i	$-0.359995\pi$
$522$		0			0
$523$	−15.6305	−	13.1155i	−0.683473	−	0.573502i	0.233546	−	0.972346i	$-0.424967\pi$
$523$	−15.6305	−	13.1155i	−0.683473	−	0.573502i	−0.917019	+	0.398844i	$0.869412\pi$
$524$		0			0
$525$	2.18283	−	3.78077i	0.0952664	−	0.165006i
$526$		0			0
$527$	3.86902	+	21.9423i	0.168537	+	0.955822i
$528$		0			0
$529$	21.5559	+	7.84571i	0.937214	+	0.341118i
$530$		0			0
$531$	4.21401			0.182873
$532$		0			0
$533$	−9.40603			−0.407420
$534$		0			0
$535$	1.71980	+	0.625957i	0.0743535	+	0.0270625i
$536$		0			0
$537$	−3.84399	−	21.8004i	−0.165881	−	0.940756i
$538$		0			0
$539$	−17.6161	+	30.5119i	−0.758777	+	1.31424i
$540$		0			0
$541$	29.7236	+	24.9410i	1.27792	+	1.07230i	0.993528	+	0.113590i	$0.0362351\pi$
$541$	29.7236	+	24.9410i	1.27792	+	1.07230i	0.284389	+	0.958709i	$0.408209\pi$
$542$		0			0
$543$	−8.82474	−	15.2849i	−0.378706	−	0.655937i
$544$		0			0
$545$	12.8686	−	4.68378i	0.551230	−	0.200631i
$546$		0			0
$547$	−7.59324	+	43.0634i	−0.324664	+	1.84126i	0.187365	+	0.982290i	$0.440005\pi$
$547$	−7.59324	+	43.0634i	−0.324664	+	1.84126i	−0.512028	+	0.858968i	$0.671106\pi$
$548$		0			0
$549$	8.96936	−	7.52618i	0.382803	−	0.321210i
$550$		0			0
$551$	1.99724	−	2.94721i	0.0850853	−	0.125555i
$552$		0			0
$553$	7.31335	−	6.13663i	0.310995	−	0.260956i
$554$		0			0
$555$	−0.445720	+	2.52780i	−0.0189198	+	0.107299i
$556$		0			0
$557$	−38.5299	+	14.0237i	−1.63257	+	0.594205i	−0.985716	−	0.168413i	$-0.946136\pi$
$557$	−38.5299	+	14.0237i	−1.63257	+	0.594205i	−0.646849	+	0.762618i	$0.723913\pi$
$558$		0			0
$559$	6.49634	+	11.2520i	0.274766	+	0.475908i
$560$		0			0
$561$	−12.3736	−	10.3827i	−0.522415	−	0.438358i
$562$		0			0
$563$	12.9722	−	22.4685i	0.546713	−	0.946935i	−0.451784	−	0.892127i	$-0.649212\pi$
$563$	12.9722	−	22.4685i	0.546713	−	0.946935i	0.998497	−	0.0548075i	$-0.0174545\pi$
$564$		0			0
$565$	−0.821868	−	4.66105i	−0.0345763	−	0.196092i
$566$		0			0
$567$	4.10237	+	1.49314i	0.172283	+	0.0627061i
$568$		0			0
$569$	−46.2797			−1.94015			−0.970073	−	0.242814i	$-0.921929\pi$
$569$	−46.2797			−1.94015			−0.970073	+	0.242814i	$0.921929\pi$
$570$		0			0
$571$	−16.5746			−0.693626			−0.346813	−	0.937934i	$-0.612736\pi$
$571$	−16.5746			−0.693626			−0.346813	+	0.937934i	$0.612736\pi$
$572$		0			0
$573$	−15.9051	−	5.78897i	−0.664443	−	0.241838i
$574$		0			0
$575$	−0.0427697	−	0.242559i	−0.00178362	−	0.0101154i
$576$		0			0
$577$	21.2617	−	36.8264i	0.885137	−	1.53310i	0.0395795	−	0.999216i	$-0.487398\pi$
$577$	21.2617	−	36.8264i	0.885137	−	1.53310i	0.845557	−	0.533885i	$-0.179269\pi$
$578$		0			0
$579$	16.0566	+	13.4731i	0.667290	+	0.559923i
$580$		0			0
$581$	−2.61336	−	4.52648i	−0.108421	−	0.187790i
$582$		0			0
$583$	−33.7926	+	12.2995i	−1.39955	+	0.509393i
$584$		0			0
$585$	−0.364891	+	2.06940i	−0.0150864	+	0.0855591i
$586$		0			0
$587$	28.6451	−	24.0361i	1.18231	−	0.992075i	0.182348	−	0.983234i	$-0.441630\pi$
$587$	28.6451	−	24.0361i	1.18231	−	0.992075i	0.999961	−	0.00884143i	$-0.00281435\pi$
$588$		0			0
$589$	−16.0326	−	7.17992i	−0.660611	−	0.295844i
$590$		0			0
$591$	11.5236	−	9.66942i	0.474016	−	0.397747i
$592$		0			0
$593$	0.0514973	−	0.292056i	0.00211474	−	0.0119933i	−0.983732	−	0.179642i	$-0.942506\pi$
$593$	0.0514973	−	0.292056i	0.00211474	−	0.0119933i	0.985847	+	0.167648i	$0.0536173\pi$
$594$		0			0
$595$	−22.6803	+	8.25495i	−0.929801	+	0.338420i
$596$		0			0
$597$	−5.44771	−	9.43572i	−0.222960	−	0.386178i
$598$		0			0
$599$	−1.45990	−	1.22500i	−0.0596497	−	0.0500521i	0.612475	−	0.790490i	$-0.290174\pi$
$599$	−1.45990	−	1.22500i	−0.0596497	−	0.0500521i	−0.672125	+	0.740438i	$0.734618\pi$
$600$		0			0
$601$	11.8121	−	20.4591i	0.481824	−	0.834544i	−0.517958	−	0.855406i	$-0.673308\pi$
$601$	11.8121	−	20.4591i	0.481824	−	0.834544i	0.999782	+	0.0208617i	$0.00664096\pi$
$602$		0			0
$603$	−1.49428	−	8.47449i	−0.0608518	−	0.345108i
$604$		0			0
$605$	2.31531	+	0.842705i	0.0941308	+	0.0342608i
$606$		0			0
$607$	6.62158			0.268762			0.134381	−	0.990930i	$-0.457095\pi$
$607$	6.62158			0.268762			0.134381	+	0.990930i	$0.457095\pi$
$608$		0			0
$609$	−3.56571			−0.144490
$610$		0			0
$611$	−11.3129	−	4.11757i	−0.457672	−	0.166579i
$612$		0			0
$613$	5.13383	+	29.1154i	0.207353	+	1.17596i	0.893693	+	0.448678i	$0.148105\pi$
$613$	5.13383	+	29.1154i	0.207353	+	1.17596i	−0.686340	+	0.727281i	$0.740784\pi$
$614$		0			0
$615$	−2.23812	+	3.87654i	−0.0902498	+	0.156317i
$616$		0			0
$617$	−6.56626	−	5.50975i	−0.264348	−	0.221814i	0.500974	−	0.865463i	$-0.332975\pi$
$617$	−6.56626	−	5.50975i	−0.264348	−	0.221814i	−0.765321	+	0.643649i	$0.777420\pi$
$618$		0			0
$619$	−20.1836	−	34.9589i	−0.811246	−	1.40512i	−0.911993	−	0.410206i	$-0.865457\pi$
$619$	−20.1836	−	34.9589i	−0.811246	−	1.40512i	0.100747	−	0.994912i	$-0.467877\pi$
$620$		0			0
$621$	0.231447	−	0.0842398i	0.00928765	−	0.00338043i
$622$		0			0
$623$	−2.03545	+	11.5436i	−0.0815488	+	0.462486i
$624$		0			0
$625$	0.766044	−	0.642788i	0.0306418	−	0.0257115i
$626$		0			0
$627$	12.2495	−	3.48371i	0.489197	−	0.139126i
$628$		0			0
$629$	10.8707	−	9.12163i	0.433445	−	0.363703i
$630$		0			0
$631$	3.25558	−	18.4633i	0.129602	−	0.735012i	−0.848865	−	0.528610i	$-0.822713\pi$
$631$	3.25558	−	18.4633i	0.129602	−	0.735012i	0.978467	−	0.206402i	$-0.0661755\pi$
$632$		0			0
$633$	−5.40447	+	1.96707i	−0.214808	+	0.0781839i
$634$		0			0
$635$	−1.79032	−	3.10092i	−0.0710466	−	0.123056i
$636$		0			0
$637$	−19.4113	−	16.2881i	−0.769106	−	0.645356i
$638$		0			0
$639$	0.538308	−	0.932376i	0.0212951	−	0.0368842i
$640$		0			0
$641$	7.57274	+	42.9471i	0.299105	+	1.69631i	0.650032	+	0.759907i	$0.274755\pi$
$641$	7.57274	+	42.9471i	0.299105	+	1.69631i	−0.350927	+	0.936403i	$0.614133\pi$
$642$		0			0
$643$	−2.93291	−	1.06749i	−0.115663	−	0.0420977i	0.283541	−	0.958960i	$-0.408491\pi$
$643$	−2.93291	−	1.06749i	−0.115663	−	0.0420977i	−0.399203	+	0.916863i	$0.630713\pi$
$644$		0			0
$645$	6.18310			0.243459
$646$		0			0
$647$	−33.2521			−1.30727			−0.653637	−	0.756808i	$-0.726758\pi$
$647$	−33.2521			−1.30727			−0.653637	+	0.756808i	$0.726758\pi$
$648$		0			0
$649$	−11.5694	−	4.21092i	−0.454139	−	0.165293i
$650$		0			0
$651$	3.05518	+	17.3268i	0.119742	+	0.679091i
$652$		0			0
$653$	10.2072	−	17.6793i	0.399437	−	0.691845i	−0.594220	−	0.804303i	$-0.702539\pi$
$653$	10.2072	−	17.6793i	0.399437	−	0.691845i	0.993656	+	0.112458i	$0.0358724\pi$
$654$		0			0
$655$	1.50661	+	1.26419i	0.0588680	+	0.0493961i
$656$		0			0
$657$	4.93547	+	8.54848i	0.192551	+	0.333508i
$658$		0			0
$659$	0.882390	−	0.321164i	0.0343730	−	0.0125108i	−0.324776	−	0.945791i	$-0.605289\pi$
$659$	0.882390	−	0.321164i	0.0343730	−	0.0125108i	0.359149	+	0.933280i	$0.383067\pi$
$660$		0			0
$661$	−8.30957	+	47.1259i	−0.323205	+	1.83299i	0.198796	+	0.980041i	$0.436297\pi$
$661$	−8.30957	+	47.1259i	−0.323205	+	1.83299i	−0.522001	+	0.852945i	$0.674814\pi$
$662$		0			0
$663$	8.89938	−	7.46747i	0.345623	−	0.290012i
$664$		0			0
$665$	4.64372	−	18.4542i	0.180076	−	0.715621i
$666$		0			0
$667$	−0.154105	+	0.129309i	−0.00596697	+	0.00500688i
$668$		0			0
$669$	1.36537	−	7.74342i	0.0527884	−	0.299378i
$670$		0			0
$671$	−32.1457	+	11.7001i	−1.24097	+	0.451676i
$672$		0			0
$673$	5.98130	+	10.3599i	0.230562	+	0.399345i	0.957974	−	0.286856i	$-0.0926102\pi$
$673$	5.98130	+	10.3599i	0.230562	+	0.399345i	−0.727412	+	0.686201i	$0.759277\pi$
$674$		0			0
$675$	0.766044	+	0.642788i	0.0294851	+	0.0247409i
$676$		0			0
$677$	6.62515	−	11.4751i	0.254625	−	0.441024i	−0.710168	−	0.704032i	$-0.751381\pi$
$677$	6.62515	−	11.4751i	0.254625	−	0.441024i	0.964794	+	0.263008i	$0.0847145\pi$
$678$		0			0
$679$	8.41058	+	47.6988i	0.322768	+	1.83051i
$680$		0			0
$681$	−25.6146	−	9.32294i	−0.981552	−	0.357256i
$682$		0			0
$683$	−4.61429			−0.176561			−0.0882805	−	0.996096i	$-0.528137\pi$
$683$	−4.61429			−0.176561			−0.0882805	+	0.996096i	$0.528137\pi$
$684$		0			0
$685$	−20.6040			−0.787240
$686$		0			0
$687$	−17.7361	−	6.45540i	−0.676673	−	0.246289i
$688$		0			0
$689$	−4.49127	−	25.4713i	−0.171104	−	0.970377i
$690$		0			0
$691$	4.80539	−	8.32318i	0.182806	−	0.316629i	−0.760029	−	0.649889i	$-0.774815\pi$
$691$	4.80539	−	8.32318i	0.182806	−	0.316629i	0.942835	+	0.333260i	$0.108149\pi$
$692$		0			0
$693$	−9.77086	−	8.19873i	−0.371164	−	0.311444i
$694$		0			0
$695$	−2.96808	−	5.14087i	−0.112586	−	0.195004i
$696$		0			0
$697$	23.2548	−	8.46406i	0.880838	−	0.320599i
$698$		0			0
$699$	5.13387	−	29.1156i	0.194181	−	1.10125i
$700$		0			0
$701$	−18.4042	+	15.4430i	−0.695119	+	0.583274i	−0.920380	−	0.391024i	$-0.872121\pi$
$701$	−18.4042	+	15.4430i	−0.695119	+	0.583274i	0.225261	+	0.974298i	$0.427676\pi$
$702$		0			0
$703$	1.14534	+	11.1296i	0.0431975	+	0.419762i
$704$		0			0
$705$	−4.38885	+	3.68268i	−0.165294	+	0.138698i
$706$		0			0
$707$	7.99096	−	45.3190i	0.300531	−	1.70440i
$708$		0			0
$709$	2.76984	−	1.00814i	0.104024	−	0.0378615i	−0.289484	−	0.957183i	$-0.593484\pi$
$709$	2.76984	−	1.00814i	0.104024	−	0.0378615i	0.393508	+	0.919321i	$0.371262\pi$
$710$		0			0
$711$	1.09341	+	1.89384i	0.0410061	+	0.0710246i
$712$		0			0
$713$	0.760392	+	0.638045i	0.0284769	+	0.0238950i
$714$		0			0
$715$	3.06967	−	5.31683i	0.114799	−	0.198838i
$716$		0			0
$717$	3.52617	+	19.9979i	0.131687	+	0.746836i
$718$		0			0
$719$	−25.6042	−	9.31917i	−0.954876	−	0.347546i	−0.182852	−	0.983140i	$-0.558533\pi$
$719$	−25.6042	−	9.31917i	−0.954876	−	0.347546i	−0.772024	+	0.635594i	$0.780755\pi$
$720$		0			0
$721$	−23.2818			−0.867059
$722$		0			0
$723$	−23.1886			−0.862392
$724$		0			0
$725$	−0.767508	−	0.279350i	−0.0285045	−	0.0103748i
$726$		0			0
$727$	6.02788	+	34.1858i	0.223562	+	1.26788i	0.865416	+	0.501055i	$0.167054\pi$
$727$	6.02788	+	34.1858i	0.223562	+	1.26788i	−0.641854	+	0.766827i	$0.721834\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	−26.1862	−	21.9729i	−0.968533	−	0.812696i
$732$		0			0
$733$	−4.42174	−	7.65869i	−0.163321	−	0.282880i	0.772737	−	0.634727i	$-0.218887\pi$
$733$	−4.42174	−	7.65869i	−0.163321	−	0.282880i	−0.936058	+	0.351846i	$0.885554\pi$
$734$		0			0
$735$	−11.3317	+	4.12440i	−0.417976	+	0.152131i
$736$		0			0
$737$	−4.36578	+	24.7596i	−0.160816	+	0.912031i
$738$		0			0
$739$	35.3405	−	29.6542i	1.30002	−	1.09085i	0.309880	−	0.950776i	$-0.399711\pi$
$739$	35.3405	−	29.6542i	1.30002	−	1.09085i	0.990141	−	0.140072i	$-0.0447333\pi$
$740$		0			0
$741$	0.937641	+	9.11133i	0.0344451	+	0.334713i
$742$		0			0
$743$	36.4857	−	30.6151i	1.33853	−	1.12316i	0.356529	−	0.934284i	$-0.383960\pi$
$743$	36.4857	−	30.6151i	1.33853	−	1.12316i	0.982001	−	0.188875i	$-0.0604842\pi$
$744$		0			0
$745$	−1.00226	+	5.68410i	−0.0367200	+	0.208249i
$746$		0			0
$747$	1.12504	−	0.409480i	0.0411629	−	0.0149821i
$748$		0			0
$749$	−3.99495	−	6.91946i	−0.145972	−	0.252832i
$750$		0			0
$751$	13.3665	+	11.2158i	0.487751	+	0.409272i	0.853219	−	0.521552i	$-0.174647\pi$
$751$	13.3665	+	11.2158i	0.487751	+	0.409272i	−0.365468	+	0.930824i	$0.619091\pi$
$752$		0			0
$753$	3.99162	−	6.91369i	0.145463	−	0.251949i
$754$		0			0
$755$	3.29137	+	18.6663i	0.119785	+	0.679335i
$756$		0			0
$757$	46.9086	+	17.0733i	1.70492	+	0.620541i	0.996371	−	0.0851166i	$-0.0271263\pi$
$757$	46.9086	+	17.0733i	1.70492	+	0.620541i	0.708553	+	0.705658i	$0.249349\pi$
$758$		0			0
$759$	−0.719607			−0.0261201
$760$		0			0
$761$	37.0508			1.34309			0.671545	−	0.740964i	$-0.265631\pi$
$761$	37.0508			1.34309			0.671545	+	0.740964i	$0.265631\pi$
$762$		0			0
$763$	−56.1798	−	20.4478i	−2.03384	−	0.740259i
$764$		0			0
$765$	−0.960027	−	5.44458i	−0.0347099	−	0.196849i
$766$		0			0
$767$	4.42750	−	7.66865i	0.159868	−	0.276899i
$768$		0			0
$769$	23.9041	+	20.0579i	0.862005	+	0.723308i	0.962399	−	0.271640i	$-0.0875660\pi$
$769$	23.9041	+	20.0579i	0.862005	+	0.723308i	−0.100394	+	0.994948i	$0.532010\pi$
$770$		0			0
$771$	14.8465	+	25.7150i	0.534685	+	0.926102i
$772$		0			0
$773$	9.43819	−	3.43522i	0.339468	−	0.123556i	−0.166661	−	0.986014i	$-0.553298\pi$
$773$	9.43819	−	3.43522i	0.339468	−	0.123556i	0.506128	+	0.862458i	$0.331076\pi$
$774$		0			0
$775$	−0.699823	+	3.96889i	−0.0251384	+	0.142567i
$776$		0			0
$777$	8.58411	−	7.20292i	0.307953	−	0.258403i
$778$		0			0
$779$	−4.76135	+	18.9216i	−0.170593	+	0.677937i
$780$		0			0
$781$	−2.40960	+	2.02189i	−0.0862221	+	0.0723490i
$782$		0			0
$783$	0.141830	−	0.804356i	0.00506858	−	0.0287454i
$784$		0			0
$785$	−4.54780	+	1.65526i	−0.162318	+	0.0590789i
$786$		0			0
$787$	4.70175	+	8.14366i	0.167599	+	0.290290i	0.937575	−	0.347782i	$-0.113065\pi$
$787$	4.70175	+	8.14366i	0.167599	+	0.290290i	−0.769976	+	0.638073i	$0.779732\pi$
$788$		0			0
$789$	−1.97200	−	1.65471i	−0.0702051	−	0.0589091i
$790$		0			0
$791$	−10.3312	+	17.8942i	−0.367336	+	0.636244i
$792$		0			0
$793$	−4.27238	−	24.2299i	−0.151717	−	0.860428i
$794$		0			0
$795$	−11.5662	−	4.20977i	−0.410212	−	0.149305i
$796$		0			0
$797$	21.2320			0.752077			0.376038	−	0.926604i	$-0.377286\pi$
$797$	21.2320			0.752077			0.376038	+	0.926604i	$0.377286\pi$
$798$		0			0
$799$	31.6745			1.12056
$800$		0			0
$801$	−2.52306	−	0.918319i	−0.0891480	−	0.0324472i
$802$		0			0
$803$	−5.00793	−	28.4014i	−0.176726	−	1.00226i
$804$		0			0
$805$	−0.537632	+	0.931206i	−0.0189490	+	0.0328207i
$806$		0			0
$807$	12.1160	+	10.1665i	0.426503	+	0.357879i
$808$		0			0
$809$	−3.08212	−	5.33839i	−0.108362	−	0.187688i	0.806745	−	0.590900i	$-0.201227\pi$
$809$	−3.08212	−	5.33839i	−0.108362	−	0.187688i	−0.915107	+	0.403212i	$0.867894\pi$
$810$		0			0
$811$	15.0944	−	5.49392i	0.530036	−	0.192917i	−0.0631182	−	0.998006i	$-0.520105\pi$
$811$	15.0944	−	5.49392i	0.530036	−	0.192917i	0.593155	+	0.805089i	$0.297882\pi$
$812$		0			0
$813$	2.26975	−	12.8724i	0.0796037	−	0.451455i
$814$		0			0
$815$	7.66238	−	6.42950i	0.268401	−	0.225216i
$816$		0			0
$817$	25.9235	−	7.37257i	0.906949	−	0.257933i
$818$		0			0
$819$	7.02742	−	5.89671i	0.245558	−	0.206048i
$820$		0			0
$821$	1.11360	−	6.31555i	0.0388650	−	0.220414i	−0.959189	−	0.282765i	$-0.908748\pi$
$821$	1.11360	−	6.31555i	0.0388650	−	0.220414i	0.998054	+	0.0623503i	$0.0198596\pi$
$822$		0			0
$823$	−0.264409	+	0.0962371i	−0.00921673	+	0.00335462i	−0.346624	−	0.938004i	$-0.612672\pi$
$823$	−0.264409	+	0.0962371i	−0.00921673	+	0.00335462i	0.337408	+	0.941359i	$0.390450\pi$
$824$		0			0
$825$	−1.46083	−	2.53023i	−0.0508596	−	0.0880914i
$826$		0			0
$827$	−31.3818	−	26.3324i	−1.09125	−	0.915668i	−0.0944452	−	0.995530i	$-0.530108\pi$
$827$	−31.3818	−	26.3324i	−1.09125	−	0.915668i	−0.996806	+	0.0798616i	$0.974552\pi$
$828$		0			0
$829$	28.1141	−	48.6950i	0.976443	−	1.69125i	0.301353	−	0.953513i	$-0.402562\pi$
$829$	28.1141	−	48.6950i	0.976443	−	1.69125i	0.675090	−	0.737736i	$-0.264105\pi$
$830$		0			0
$831$	−3.43470	−	19.4791i	−0.119148	−	0.675724i
$832$		0			0
$833$	62.6481	+	22.8021i	2.17063	+	0.790044i
$834$		0			0
$835$	−4.91842			−0.170209
$836$		0			0
$837$	−4.03012			−0.139301
$838$		0			0
$839$	26.9164	+	9.79677i	0.929258	+	0.338222i	0.761915	−	0.647677i	$-0.224259\pi$
$839$	26.9164	+	9.79677i	0.929258	+	0.338222i	0.167342	+	0.985899i	$0.446481\pi$
$840$		0			0
$841$	−4.91996	−	27.9025i	−0.169654	−	0.962154i
$842$		0			0
$843$	−1.67367	+	2.89888i	−0.0576442	+	0.0998426i
$844$		0			0
$845$	−6.57607	−	5.51798i	−0.226224	−	0.189824i
$846$		0			0
$847$	−5.37828	−	9.31545i	−0.184800	−	0.320083i
$848$		0			0
$849$	−21.2708	+	7.74194i	−0.730012	+	0.265703i
$850$		0			0
$851$	0.109781	−	0.622600i	0.00376325	−	0.0213425i
$852$		0			0
$853$	−7.60752	+	6.38347i	−0.260476	+	0.218566i	−0.763668	−	0.645609i	$-0.776603\pi$
$853$	−7.60752	+	6.38347i	−0.260476	+	0.218566i	0.503191	+	0.864175i	$0.332159\pi$
$854$		0			0
$855$	3.97819	+	1.78157i	0.136051	+	0.0609283i
$856$		0			0
$857$	15.8077	−	13.2643i	0.539982	−	0.453099i	−0.331550	−	0.943438i	$-0.607571\pi$
$857$	15.8077	−	13.2643i	0.539982	−	0.453099i	0.871532	+	0.490339i	$0.163127\pi$
$858$		0			0
$859$	0.466734	−	2.64698i	0.0159247	−	0.0903137i	−0.975810	−	0.218622i	$-0.929844\pi$
$859$	0.466734	−	2.64698i	0.0159247	−	0.0903137i	0.991734	+	0.128309i	$0.0409548\pi$
$860$		0			0
$861$	18.3632	−	6.68366i	0.625817	−	0.227779i
$862$		0			0
$863$	0.434778	+	0.753058i	0.0148000	+	0.0256344i	0.873331	−	0.487128i	$-0.161956\pi$
$863$	0.434778	+	0.753058i	0.0148000	+	0.0256344i	−0.858531	+	0.512762i	$0.828622\pi$
$864$		0			0
$865$	8.62430	+	7.23665i	0.293235	+	0.246053i
$866$		0			0
$867$	−6.78257	+	11.7478i	−0.230348	+	0.398975i
$868$		0			0
$869$	−1.10946	−	6.29208i	−0.0376360	−	0.213444i
$870$		0			0
$871$	−16.9918	−	6.18453i	−0.575747	−	0.209555i
$872$		0			0
$873$	−11.0945			−0.375491
$874$		0			0
$875$	−4.36565			−0.147586
$876$		0			0
$877$	−28.9962	−	10.5538i	−0.979132	−	0.356375i	−0.197629	−	0.980277i	$-0.563324\pi$
$877$	−28.9962	−	10.5538i	−0.979132	−	0.356375i	−0.781503	+	0.623902i	$0.785547\pi$
$878$		0			0
$879$	0.424153	+	2.40549i	0.0143063	+	0.0811352i
$880$		0			0
$881$	−10.7423	+	18.6062i	−0.361918	+	0.626860i	−0.988276	−	0.152675i	$-0.951211\pi$
$881$	−10.7423	+	18.6062i	−0.361918	+	0.626860i	0.626358	+	0.779535i	$0.284545\pi$
$882$		0			0
$883$	−9.10902	−	7.64338i	−0.306543	−	0.257220i	0.476518	−	0.879165i	$-0.341899\pi$
$883$	−9.10902	−	7.64338i	−0.306543	−	0.257220i	−0.783061	+	0.621944i	$0.786343\pi$
$884$		0			0
$885$	−2.10701	−	3.64944i	−0.0708262	−	0.122675i
$886$		0			0
$887$	32.5745	−	11.8561i	1.09374	−	0.398090i	0.268738	−	0.963213i	$-0.413393\pi$
$887$	32.5745	−	11.8561i	1.09374	−	0.398090i	0.825007	+	0.565123i	$0.191171\pi$
$888$		0			0
$889$	−2.71444	+	15.3943i	−0.0910393	+	0.516309i
$890$		0			0
$891$	2.23812	−	1.87801i	0.0749799	−	0.0629156i
$892$		0			0
$893$	−14.0097	+	20.6733i	−0.468818	+	0.691807i
$894$		0			0
$895$	−16.9577	+	14.2292i	−0.566833	+	0.475629i
$896$		0			0
$897$	0.0898729	−	0.509694i	0.00300077	−	0.0170182i
$898$		0			0
$899$	3.09315	−	1.12581i	0.103162	−	0.0375480i
$900$		0			0
$901$	34.0243	+	58.9319i	1.13351	+	1.96330i
$902$		0			0
$903$	−20.6780	−	17.3509i	−0.688122	−	0.577403i
$904$		0			0
$905$	−8.82474	+	15.2849i	−0.293344	+	0.508087i
$906$		0			0
$907$	7.16207	+	40.6181i	0.237813	+	1.34870i	0.836609	+	0.547801i	$0.184535\pi$
$907$	7.16207	+	40.6181i	0.237813	+	1.34870i	−0.598796	+	0.800902i	$0.704354\pi$
$908$		0			0
$909$	9.90524	+	3.60521i	0.328536	+	0.119577i
$910$		0			0
$911$	−44.3462			−1.46926			−0.734628	−	0.678470i	$-0.762643\pi$
$911$	−44.3462			−1.46926			−0.734628	+	0.678470i	$0.762643\pi$
$912$		0			0
$913$	−3.49792			−0.115764
$914$		0			0
$915$	−11.0025	−	4.00460i	−0.363733	−	0.132388i
$916$		0			0
$917$	−1.49096	−	8.45564i	−0.0492357	−	0.279230i
$918$		0			0
$919$	−24.8265	+	43.0007i	−0.818950	+	1.41846i	0.0875062	+	0.996164i	$0.472110\pi$
$919$	−24.8265	+	43.0007i	−0.818950	+	1.41846i	−0.906456	+	0.422299i	$0.861223\pi$
$920$		0			0
$921$	8.59846	+	7.21497i	0.283329	+	0.237741i
$922$		0			0
$923$	−1.13116	−	1.95922i	−0.0372325	−	0.0644886i
$924$		0			0
$925$	2.41200	−	0.877897i	0.0793061	−	0.0288651i
$926$		0			0
$927$	0.926056	−	5.25193i	0.0304157	−	0.172496i
$928$		0			0
$929$	8.09809	−	6.79510i	0.265690	−	0.222940i	−0.500204	−	0.865908i	$-0.666742\pi$
$929$	8.09809	−	6.79510i	0.265690	−	0.222940i	0.765893	+	0.642968i	$0.222297\pi$
$930$		0			0
$931$	−42.5919	+	30.8038i	−1.39589	+	1.00955i
$932$		0			0
$933$	15.8344	−	13.2866i	0.518395	−	0.434985i
$934$		0			0
$935$	−2.80487	+	15.9072i	−0.0917291	+	0.520222i
$936$		0			0
$937$	−18.5858	+	6.76467i	−0.607171	+	0.220992i	−0.627265	−	0.778806i	$-0.715826\pi$
$937$	−18.5858	+	6.76467i	−0.607171	+	0.220992i	0.0200938	+	0.999798i	$0.493604\pi$
$938$		0			0
$939$	−8.47768	−	14.6838i	−0.276659	−	0.479187i
$940$		0			0
$941$	−18.3896	−	15.4307i	−0.599482	−	0.503025i	0.291797	−	0.956480i	$-0.405747\pi$
$941$	−18.3896	−	15.4307i	−0.599482	−	0.503025i	−0.891279	+	0.453455i	$0.850191\pi$
$942$		0			0
$943$	0.551251	−	0.954795i	0.0179512	−	0.0310924i
$944$		0			0
$945$	−0.758088	−	4.29933i	−0.0246606	−	0.139857i
$946$		0			0
$947$	−52.6097	−	19.1484i	−1.70958	−	0.622238i	−0.712726	−	0.701443i	$-0.752540\pi$
$947$	−52.6097	−	19.1484i	−1.70958	−	0.622238i	−0.996858	+	0.0792047i	$0.974762\pi$
$948$		0			0
$949$	20.7420			0.673314
$950$		0			0
$951$	16.3597			0.530501
$952$		0			0
$953$	−18.6150	−	6.77529i	−0.602998	−	0.219473i	0.0224387	−	0.999748i	$-0.492857\pi$
$953$	−18.6150	−	6.77529i	−0.602998	−	0.219473i	−0.625437	+	0.780275i	$0.715079\pi$
$954$		0			0
$955$	2.93914	+	16.6687i	0.0951082	+	0.539385i
$956$		0			0
$957$	−1.19315	+	2.06660i	−0.0385692	+	0.0668038i
$958$		0			0
$959$	68.9058	+	57.8188i	2.22508	+	1.86707i
$960$		0			0
$961$	7.37908	+	12.7809i	0.238035	+	0.412288i
$962$		0			0
$963$	1.71980	−	0.625957i	0.0554198	−	0.0201712i
$964$		0			0
$965$	3.63974	−	20.6420i	0.117167	−	0.664489i
$966$		0			0
$967$	−17.4260	+	14.6221i	−0.560381	+	0.470215i	−0.878438	−	0.477856i	$-0.841414\pi$
$967$	−17.4260	+	14.6221i	−0.560381	+	0.470215i	0.318057	+	0.948072i	$0.396970\pi$
$968$		0			0
$969$	−10.5170	−	21.6825i	−0.337856	−	0.696542i
$970$		0			0
$971$	−28.8417	+	24.2010i	−0.925573	+	0.776648i	−0.975017	−	0.222129i	$-0.928699\pi$
$971$	−28.8417	+	24.2010i	−0.925573	+	0.776648i	0.0494446	+	0.998777i	$0.484255\pi$
$972$		0			0
$973$	−4.50014	+	25.5215i	−0.144268	+	0.818183i
$974$		0			0
$975$	1.97460	−	0.718694i	0.0632377	−	0.0230166i
$976$		0			0
$977$	25.8024	+	44.6910i	0.825491	+	1.42979i	0.901543	+	0.432688i	$0.142435\pi$
$977$	25.8024	+	44.6910i	0.825491	+	1.42979i	−0.0760525	+	0.997104i	$0.524232\pi$
$978$		0			0
$979$	6.00932	+	5.04242i	0.192059	+	0.161156i
$980$		0			0
$981$	6.84723	−	11.8598i	0.218615	−	0.378653i
$982$		0			0
$983$	1.03287	+	5.85772i	0.0329436	+	0.186832i	0.996839	−	0.0794490i	$-0.0253161\pi$
$983$	1.03287	+	5.85772i	0.0329436	+	0.186832i	−0.963895	+	0.266281i	$0.914205\pi$
$984$		0			0
$985$	−14.1357	−	5.14499i	−0.450402	−	0.163933i
$986$		0			0
$987$	25.0119			0.796137
$988$		0			0
$989$	−1.52290			−0.0484254
$990$		0			0
$991$	17.5494	+	6.38747i	0.557476	+	0.202905i	0.605365	−	0.795948i	$-0.293027\pi$
$991$	17.5494	+	6.38747i	0.557476	+	0.202905i	−0.0478892	+	0.998853i	$0.515249\pi$
$992$		0			0
$993$	5.96461	+	33.8270i	0.189281	+	1.07347i
$994$		0			0
$995$	−5.44771	+	9.43572i	−0.172704	+	0.299132i
$996$		0			0
$997$	3.57428	+	2.99917i	0.113198	+	0.0949848i	0.697630	−	0.716458i	$-0.254238\pi$
$997$	3.57428	+	2.99917i	0.113198	+	0.0949848i	−0.584431	+	0.811443i	$0.698682\pi$
$998$		0			0
$999$	1.28340	+	2.22291i	0.0406050	+	0.0703299i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1140.2.bo.c.481.4	yes	24
19.16	even	9	inner	1140.2.bo.c.301.4	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1140.2.bo.c.301.4	✓	24	19.16	even	9	inner
1140.2.bo.c.481.4	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1140.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{5} +(2.18283 - 3.78077i) q^{7} +(0.766044 + 0.642788i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{5} +(2.18283 - 3.78077i) q^{7} +(0.766044 + 0.642788i) q^{9} +(-1.46083 - 2.53023i) q^{11} +(1.97460 - 0.718694i) q^{13} +(0.173648 - 0.984808i) q^{15} +(-4.23513 + 3.55370i) q^{17} +(-0.446215 - 4.33600i) q^{19} +(-3.34429 + 2.80619i) q^{21} +(-0.0427697 + 0.242559i) q^{23} +(-0.939693 + 0.342020i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(0.625678 + 0.525006i) q^{29} +(2.01506 - 3.49018i) q^{31} +(0.507341 + 2.87727i) q^{33} +(4.10237 + 1.49314i) q^{35} -2.56680 q^{37} -2.10132 q^{39} +(-4.20629 - 1.53097i) q^{41} +(1.07368 + 6.08916i) q^{43} +(-0.500000 + 0.866025i) q^{45} +(-4.38885 - 3.68268i) q^{47} +(-6.02947 - 10.4433i) q^{49} +(5.19516 - 1.89088i) q^{51} +(2.13735 - 12.1215i) q^{53} +(2.23812 - 1.87801i) q^{55} +(-1.06369 + 4.22712i) q^{57} +(3.22812 - 2.70872i) q^{59} +(2.03319 - 11.5308i) q^{61} +(4.10237 - 1.49314i) q^{63} +(1.05066 + 1.81980i) q^{65} +(-6.59198 - 5.53133i) q^{67} +(0.123150 - 0.213303i) q^{69} +(-0.186952 - 1.06026i) q^{71} +(9.27564 + 3.37606i) q^{73} +1.00000 q^{75} -12.7550 q^{77} +(2.05494 + 0.747937i) q^{79} +(0.173648 + 0.984808i) q^{81} +(0.598619 - 1.03684i) q^{83} +(-4.23513 - 3.55370i) q^{85} +(-0.408382 - 0.707339i) q^{87} +(-2.52306 + 0.918319i) q^{89} +(1.59299 - 9.03428i) q^{91} +(-3.08725 + 2.59051i) q^{93} +(4.19264 - 1.19237i) q^{95} +(-8.49885 + 7.13138i) q^{97} +(0.507341 - 2.87727i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{7}+O(q^{10}) \) 24 * q - 6 * q^7	\( 24 q - 6 q^{7} - 12 q^{11} - 12 q^{17} + 12 q^{19} - 6 q^{21} + 9 q^{23} - 12 q^{27} + 3 q^{29} - 3 q^{33} + 3 q^{35} - 12 q^{37} + 6 q^{39} - 15 q^{41} - 12 q^{45} + 15 q^{47} - 24 q^{49} - 3 q^{51} + 12 q^{53} + 6 q^{55} + 9 q^{57} + 3 q^{59} + 24 q^{61} + 3 q^{63} - 3 q^{65} - 15 q^{67} - 24 q^{71} + 57 q^{73} + 24 q^{75} + 36 q^{77} - 6 q^{79} - 33 q^{83} - 12 q^{85} - 15 q^{87} - 24 q^{89} - 15 q^{91} + 15 q^{93} - 9 q^{95} + 18 q^{97} - 3 q^{99}+O(q^{100}) \) 24 * q - 6 * q^7 - 12 * q^11 - 12 * q^17 + 12 * q^19 - 6 * q^21 + 9 * q^23 - 12 * q^27 + 3 * q^29 - 3 * q^33 + 3 * q^35 - 12 * q^37 + 6 * q^39 - 15 * q^41 - 12 * q^45 + 15 * q^47 - 24 * q^49 - 3 * q^51 + 12 * q^53 + 6 * q^55 + 9 * q^57 + 3 * q^59 + 24 * q^61 + 3 * q^63 - 3 * q^65 - 15 * q^67 - 24 * q^71 + 57 * q^73 + 24 * q^75 + 36 * q^77 - 6 * q^79 - 33 * q^83 - 12 * q^85 - 15 * q^87 - 24 * q^89 - 15 * q^91 + 15 * q^93 - 9 * q^95 + 18 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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