LMFDB - Embedded newform 820.2.bg.a.761.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(441,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.441"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bg (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			761.1
Character	$\chi$	$=$	820.761
Dual form			820.2.bg.a.681.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.16454i q^{3} +(0.809017 - 0.587785i) q^{5} +(2.82962 + 0.919400i) q^{7} -7.01429 q^{9} +(1.28943 - 1.77475i) q^{11} +(-2.68837 + 0.873505i) q^{13} +(-1.86007 - 2.56016i) q^{15} +(4.70595 - 6.47718i) q^{17} +(-3.09002 - 1.00401i) q^{19} +(2.90948 - 8.95445i) q^{21} +(-0.383756 - 1.18108i) q^{23} +(0.309017 - 0.951057i) q^{25} +12.7034i q^{27} +(-4.32569 - 5.95380i) q^{29} +(0.245929 + 0.178678i) q^{31} +(-5.61626 - 4.08045i) q^{33} +(2.82962 - 0.919400i) q^{35} +(-1.66076 + 1.20661i) q^{37} +(2.76424 + 8.50745i) q^{39} +(2.77462 + 5.77074i) q^{41} +(2.95741 + 9.10197i) q^{43} +(-5.67468 + 4.12290i) q^{45} +(-2.83949 + 0.922607i) q^{47} +(1.49835 + 1.08862i) q^{49} +(-20.4973 - 14.8921i) q^{51} +(4.26794 + 5.87431i) q^{53} -2.19371i q^{55} +(-3.17722 + 9.77849i) q^{57} +(3.86765 + 11.9034i) q^{59} +(4.37888 - 13.4768i) q^{61} +(-19.8478 - 6.44894i) q^{63} +(-1.66150 + 2.28686i) q^{65} +(-3.52615 - 4.85334i) q^{67} +(-3.73757 + 1.21441i) q^{69} +(5.09654 - 7.01479i) q^{71} -3.50440 q^{73} +(-3.00965 - 0.977896i) q^{75} +(5.28031 - 3.83637i) q^{77} +2.13307i q^{79} +19.1574 q^{81} -12.6863 q^{83} -8.00624i q^{85} +(-18.8410 + 13.6888i) q^{87} +(16.8438 + 5.47290i) q^{89} -8.41018 q^{91} +(0.565432 - 0.778250i) q^{93} +(-3.09002 + 1.00401i) q^{95} +(4.51451 + 6.21368i) q^{97} +(-9.04445 + 12.4486i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{5} + 5 q^{7} - 6 q^{9} + 5 q^{11} - 5 q^{13} - 5 q^{17} - 5 q^{19} - 6 q^{21} + 10 q^{23} - 6 q^{25} - 25 q^{29} + 7 q^{31} - 12 q^{33} + 5 q^{35} - 13 q^{37} + 4 q^{39} + 6 q^{41} + 14 q^{43}+ \cdots - 60 q^{99}+O(q^{100}) $ 24 * q + 6 * q^5 + 5 * q^7 - 6 * q^9 + 5 * q^11 - 5 * q^13 - 5 * q^17 - 5 * q^19 - 6 * q^21 + 10 * q^23 - 6 * q^25 - 25 * q^29 + 7 * q^31 - 12 * q^33 + 5 * q^35 - 13 * q^37 + 4 * q^39 + 6 * q^41 + 14 * q^43 + q^45 - 35 * q^47 + 23 * q^49 - 27 * q^51 + 35 * q^53 + 9 * q^57 - 14 * q^59 + 22 * q^61 - 10 * q^63 + 5 * q^65 - 20 * q^67 - 55 * q^71 + 8 * q^73 - 5 * q^75 + 6 * q^77 - 28 * q^81 - 82 * q^83 - 27 * q^87 + 50 * q^89 + 70 * q^91 - 80 * q^93 - 5 * q^95 - 20 * q^97 - 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$	$1$

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
$3$		−	3.16454i		−	1.82705i	−0.406787	−	0.913523i	$-0.633351\pi$
$3$		−	3.16454i		−	1.82705i	0.406787	−	0.913523i	$-0.366649\pi$
$4$		0			0
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$6$		0			0
$7$	2.82962	+	0.919400i	1.06950	+	0.347501i	0.790292	−	0.612731i	$-0.209929\pi$
$7$	2.82962	+	0.919400i	1.06950	+	0.347501i	0.279205	+	0.960231i	$0.409929\pi$
$8$		0			0
$9$	−7.01429			−2.33810
$10$		0			0
$11$	1.28943	−	1.77475i	0.388778	−	0.535107i	−0.569105	−	0.822265i	$-0.692710\pi$
$11$	1.28943	−	1.77475i	0.388778	−	0.535107i	0.957883	+	0.287157i	$0.0927103\pi$
$12$		0			0
$13$	−2.68837	+	0.873505i	−0.745620	+	0.242267i	−0.657095	−	0.753807i	$-0.728215\pi$
$13$	−2.68837	+	0.873505i	−0.745620	+	0.242267i	−0.0885244	+	0.996074i	$0.528215\pi$
$14$		0			0
$15$	−1.86007	−	2.56016i	−0.480267	−	0.661031i
$16$		0			0
$17$	4.70595	−	6.47718i	1.14136	−	1.57095i	0.376930	−	0.926242i	$-0.376980\pi$
$17$	4.70595	−	6.47718i	1.14136	−	1.57095i	0.764431	−	0.644706i	$-0.223020\pi$
$18$		0			0
$19$	−3.09002	−	1.00401i	−0.708900	−	0.230335i	−0.0676957	−	0.997706i	$-0.521565\pi$
$19$	−3.09002	−	1.00401i	−0.708900	−	0.230335i	−0.641204	+	0.767371i	$0.721565\pi$
$20$		0			0
$21$	2.90948	−	8.95445i	0.634900	−	1.95402i
$22$		0			0
$23$	−0.383756	−	1.18108i	−0.0800187	−	0.246272i	0.903042	−	0.429552i	$-0.141329\pi$
$23$	−0.383756	−	1.18108i	−0.0800187	−	0.246272i	−0.983061	+	0.183280i	$0.941329\pi$
$24$		0			0
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$		0			0
$27$			12.7034i			2.44477i
$28$		0			0
$29$	−4.32569	−	5.95380i	−0.803261	−	1.10559i	−0.992328	−	0.123630i	$-0.960547\pi$
$29$	−4.32569	−	5.95380i	−0.803261	−	1.10559i	0.189068	−	0.981964i	$-0.439453\pi$
$30$		0			0
$31$	0.245929	+	0.178678i	0.0441701	+	0.0320914i	0.609651	−	0.792670i	$-0.291310\pi$
$31$	0.245929	+	0.178678i	0.0441701	+	0.0320914i	−0.565481	+	0.824761i	$0.691310\pi$
$32$		0			0
$33$	−5.61626	−	4.08045i	−0.977666	−	0.710316i
$34$		0			0
$35$	2.82962	−	0.919400i	0.478294	−	0.155407i
$36$		0			0
$37$	−1.66076	+	1.20661i	−0.273027	+	0.198366i	−0.715870	−	0.698233i	$-0.753970\pi$
$37$	−1.66076	+	1.20661i	−0.273027	+	0.198366i	0.442843	+	0.896599i	$0.353970\pi$
$38$		0			0
$39$	2.76424	+	8.50745i	0.442632	+	1.36228i
$40$		0			0
$41$	2.77462	+	5.77074i	0.433323	+	0.901239i
$41$	2.77462	+	5.77074i	0.433323	+	0.901239i
$42$		0			0
$43$	2.95741	+	9.10197i	0.451001	+	1.38804i	0.875767	+	0.482734i	$0.160356\pi$
$43$	2.95741	+	9.10197i	0.451001	+	1.38804i	−0.424766	+	0.905303i	$0.639644\pi$
$44$		0			0
$45$	−5.67468	+	4.12290i	−0.845932	+	0.614605i
$46$		0			0
$47$	−2.83949	+	0.922607i	−0.414183	+	0.134576i	−0.508693	−	0.860948i	$-0.669871\pi$
$47$	−2.83949	+	0.922607i	−0.414183	+	0.134576i	0.0945108	+	0.995524i	$0.469871\pi$
$48$		0			0
$49$	1.49835	+	1.08862i	0.214050	+	0.155517i
$50$		0			0
$51$	−20.4973	−	14.8921i	−2.87019	−	2.08532i
$52$		0			0
$53$	4.26794	+	5.87431i	0.586246	+	0.806898i	0.994363	−	0.106031i	$-0.0338144\pi$
$53$	4.26794	+	5.87431i	0.586246	+	0.806898i	−0.408117	+	0.912930i	$0.633814\pi$
$54$		0			0
$55$		−	2.19371i		−	0.295800i
$56$		0			0
$57$	−3.17722	+	9.77849i	−0.420833	+	1.29519i
$58$		0			0
$59$	3.86765	+	11.9034i	0.503526	+	1.54969i	0.803235	+	0.595662i	$0.203110\pi$
$59$	3.86765	+	11.9034i	0.503526	+	1.54969i	−0.299709	+	0.954031i	$0.596890\pi$
$60$		0			0
$61$	4.37888	−	13.4768i	0.560659	−	1.72553i	−0.119852	−	0.992792i	$-0.538242\pi$
$61$	4.37888	−	13.4768i	0.560659	−	1.72553i	0.680511	−	0.732738i	$-0.261758\pi$
$62$		0			0
$63$	−19.8478	−	6.44894i	−2.50059	−	0.812490i
$64$		0			0
$65$	−1.66150	+	2.28686i	−0.206084	+	0.283651i
$66$		0			0
$67$	−3.52615	−	4.85334i	−0.430788	−	0.592929i	0.537346	−	0.843362i	$-0.319427\pi$
$67$	−3.52615	−	4.85334i	−0.430788	−	0.592929i	−0.968134	+	0.250433i	$0.919427\pi$
$68$		0			0
$69$	−3.73757	+	1.21441i	−0.449951	+	0.146198i
$70$		0			0
$71$	5.09654	−	7.01479i	0.604848	−	0.832502i	−0.391293	−	0.920266i	$-0.627972\pi$
$71$	5.09654	−	7.01479i	0.604848	−	0.832502i	0.996141	+	0.0877638i	$0.0279721\pi$
$72$		0			0
$73$	−3.50440			−0.410159			−0.205080	−	0.978745i	$-0.565745\pi$
$73$	−3.50440			−0.410159			−0.205080	+	0.978745i	$0.565745\pi$
$74$		0			0
$75$	−3.00965	−	0.977896i	−0.347525	−	0.112918i
$76$		0			0
$77$	5.28031	−	3.83637i	0.601747	−	0.437195i
$78$		0			0
$79$			2.13307i			0.239989i	0.992775	+	0.119994i	$0.0382877\pi$
$79$			2.13307i			0.239989i	−0.992775	+	0.119994i	$0.961712\pi$
$80$		0			0
$81$	19.1574			2.12860
$82$		0			0
$83$	−12.6863			−1.39250			−0.696251	−	0.717798i	$-0.745150\pi$
$83$	−12.6863			−1.39250			−0.696251	+	0.717798i	$0.745150\pi$
$84$		0			0
$85$		−	8.00624i		−	0.868399i
$86$		0			0
$87$	−18.8410	+	13.6888i	−2.01997	+	1.46759i
$88$		0			0
$89$	16.8438	+	5.47290i	1.78544	+	0.580126i	0.999282	−	0.0378938i	$-0.0120648\pi$
$89$	16.8438	+	5.47290i	1.78544	+	0.580126i	0.786163	+	0.618020i	$0.212065\pi$
$90$		0			0
$91$	−8.41018			−0.881626
$92$		0			0
$93$	0.565432	−	0.778250i	0.0586325	−	0.0807008i
$94$		0			0
$95$	−3.09002	+	1.00401i	−0.317029	+	0.103009i
$96$		0			0
$97$	4.51451	+	6.21368i	0.458379	+	0.630904i	0.974172	−	0.225809i	$-0.0725026\pi$
$97$	4.51451	+	6.21368i	0.458379	+	0.630904i	−0.515793	+	0.856713i	$0.672503\pi$
$98$		0			0
$99$	−9.04445	+	12.4486i	−0.909002	+	1.25113i
$100$		0			0
$101$	2.10067	+	0.682549i	0.209025	+	0.0679162i	0.411658	−	0.911339i	$-0.364950\pi$
$101$	2.10067	+	0.682549i	0.209025	+	0.0679162i	−0.202633	+	0.979255i	$0.564950\pi$
$102$		0			0
$103$	1.99288	−	6.13345i	0.196364	−	0.604347i	−0.803594	−	0.595178i	$-0.797081\pi$
$103$	1.99288	−	6.13345i	0.196364	−	0.604347i	0.999958	−	0.00916862i	$-0.00291850\pi$
$104$		0			0
$105$	−2.90948	−	8.95445i	−0.283936	−	0.873864i
$106$		0			0
$107$	−0.436887	+	1.34460i	−0.0422354	+	0.129987i	−0.969951	−	0.243301i	$-0.921770\pi$
$107$	−0.436887	+	1.34460i	−0.0422354	+	0.129987i	0.927715	+	0.373288i	$0.121770\pi$
$108$		0			0
$109$		−	17.3087i		−	1.65788i	−0.559340	−	0.828938i	$-0.688945\pi$
$109$		−	17.3087i		−	1.65788i	0.559340	−	0.828938i	$-0.311055\pi$
$110$		0			0
$111$	3.81836	+	5.25553i	0.362423	+	0.498833i
$112$		0			0
$113$	9.99967	+	7.26519i	0.940690	+	0.683451i	0.948587	−	0.316518i	$-0.102514\pi$
$113$	9.99967	+	7.26519i	0.940690	+	0.683451i	−0.00789667	+	0.999969i	$0.502514\pi$
$114$		0			0
$115$	−1.00469	−	0.729948i	−0.0936875	−	0.0680680i
$116$		0			0
$117$	18.8570	−	6.12702i	1.74333	−	0.566443i
$118$		0			0
$119$	19.2712	−	14.0013i	1.76659	−	1.28350i
$120$		0			0
$121$	1.91208	+	5.88478i	0.173826	+	0.534980i
$122$		0			0
$123$	18.2617	−	8.78039i	1.64660	−	0.791701i
$124$		0			0
$125$	−0.309017	−	0.951057i	−0.0276393	−	0.0850651i
$126$		0			0
$127$	−0.608913	+	0.442402i	−0.0540323	+	0.0392568i	−0.614474	−	0.788937i	$-0.710632\pi$
$127$	−0.608913	+	0.442402i	−0.0540323	+	0.0392568i	0.560441	+	0.828194i	$0.310632\pi$
$128$		0			0
$129$	28.8035	−	9.35883i	2.53601	−	0.823999i
$130$		0			0
$131$	9.70588	+	7.05173i	0.848006	+	0.616113i	0.924596	−	0.380950i	$-0.124403\pi$
$131$	9.70588	+	7.05173i	0.848006	+	0.616113i	−0.0765892	+	0.997063i	$0.524403\pi$
$132$		0			0
$133$	−7.82051	−	5.68193i	−0.678124	−	0.492686i
$134$		0			0
$135$	7.46686	+	10.2772i	0.642645	+	0.884525i
$136$		0			0
$137$			1.62491i			0.138825i	0.997588	+	0.0694125i	$0.0221125\pi$
$137$			1.62491i			0.138825i	−0.997588	+	0.0694125i	$0.977888\pi$
$138$		0			0
$139$	−2.17198	+	6.68467i	−0.184225	+	0.566986i	−0.999934	−	0.0114759i	$-0.996347\pi$
$139$	−2.17198	+	6.68467i	−0.184225	+	0.566986i	0.815709	+	0.578462i	$0.196347\pi$
$140$		0			0
$141$	2.91962	+	8.98568i	0.245877	+	0.756731i
$142$		0			0
$143$	−1.91622	+	5.89751i	−0.160242	+	0.493175i
$144$		0			0
$145$	−6.99912	−	2.27415i	−0.581245	−	0.188858i
$146$		0			0
$147$	3.44497	−	4.74159i	0.284136	−	0.391080i
$148$		0			0
$149$	−11.4895	−	15.8140i	−0.941259	−	1.29553i	−0.955302	−	0.295631i	$-0.904470\pi$
$149$	−11.4895	−	15.8140i	−0.941259	−	1.29553i	0.0140430	−	0.999901i	$-0.495530\pi$
$150$		0			0
$151$	19.0866	−	6.20162i	1.55325	−	0.504681i	0.598254	−	0.801307i	$-0.295861\pi$
$151$	19.0866	−	6.20162i	1.55325	−	0.504681i	0.954994	+	0.296626i	$0.0958614\pi$
$152$		0			0
$153$	−33.0089	+	45.4329i	−2.66861	+	3.67303i
$154$		0			0
$155$	0.303984			0.0244166
$156$		0			0
$157$	−8.76077	−	2.84655i	−0.699185	−	0.227179i	−0.0622098	−	0.998063i	$-0.519815\pi$
$157$	−8.76077	−	2.84655i	−0.699185	−	0.227179i	−0.636976	+	0.770884i	$0.719815\pi$
$158$		0			0
$159$	18.5895	−	13.5060i	1.47424	−	1.07110i
$160$		0			0
$161$		−	3.69484i		−	0.291194i
$162$		0			0
$163$	6.19590			0.485300			0.242650	−	0.970114i	$-0.421983\pi$
$163$	6.19590			0.485300			0.242650	+	0.970114i	$0.421983\pi$
$164$		0			0
$165$	−6.94208			−0.540440
$166$		0			0
$167$			16.2195i			1.25510i	0.778577	+	0.627550i	$0.215942\pi$
$167$			16.2195i			1.25510i	−0.778577	+	0.627550i	$0.784058\pi$
$168$		0			0
$169$	−4.05290	+	2.94460i	−0.311761	+	0.226508i
$170$		0			0
$171$	21.6743	+	7.04241i	1.65748	+	0.538547i
$172$		0			0
$173$	19.5261			1.48455			0.742273	−	0.670098i	$-0.233748\pi$
$173$	19.5261			1.48455			0.742273	+	0.670098i	$0.233748\pi$
$174$		0			0
$175$	1.74880	−	2.40702i	0.132197	−	0.181954i
$176$		0			0
$177$	37.6688	−	12.2393i	2.83136	−	0.919965i
$178$		0			0
$179$	−8.65091	−	11.9070i	−0.646599	−	0.889967i	0.352347	−	0.935870i	$-0.385384\pi$
$179$	−8.65091	−	11.9070i	−0.646599	−	0.889967i	−0.998946	+	0.0459021i	$0.985384\pi$
$180$		0			0
$181$	12.6809	−	17.4538i	0.942567	−	1.29733i	−0.0121841	−	0.999926i	$-0.503878\pi$
$181$	12.6809	−	17.4538i	0.942567	−	1.29733i	0.954751	−	0.297406i	$-0.0961216\pi$
$182$		0			0
$183$	−42.6479	−	13.8571i	−3.15262	−	1.02435i
$184$		0			0
$185$	−0.634353	+	1.95234i	−0.0466385	+	0.143539i
$186$		0			0
$187$	−5.42738	−	16.7038i	−0.396890	−	1.22150i
$188$		0			0
$189$	−11.6795	+	35.9458i	−0.849558	+	2.61467i
$190$		0			0
$191$			11.0908i			0.802503i	0.915968	+	0.401251i	$0.131425\pi$
$191$			11.0908i			0.802503i	−0.915968	+	0.401251i	$0.868575\pi$
$192$		0			0
$193$	4.89110	+	6.73202i	0.352069	+	0.484581i	0.947918	−	0.318515i	$-0.103184\pi$
$193$	4.89110	+	6.73202i	0.352069	+	0.484581i	−0.595849	+	0.803097i	$0.703184\pi$
$194$		0			0
$195$	7.23687	+	5.25789i	0.518243	+	0.376525i
$196$		0			0
$197$	−9.31427	−	6.76721i	−0.663614	−	0.482144i	0.204267	−	0.978915i	$-0.434519\pi$
$197$	−9.31427	−	6.76721i	−0.663614	−	0.482144i	−0.867882	+	0.496771i	$0.834519\pi$
$198$		0			0
$199$	−6.22505	+	2.02264i	−0.441282	+	0.143381i	−0.521227	−	0.853418i	$-0.674525\pi$
$199$	−6.22505	+	2.02264i	−0.441282	+	0.143381i	0.0799452	+	0.996799i	$0.474525\pi$
$200$		0			0
$201$	−15.3586	+	11.1586i	−1.08331	+	0.787070i
$202$		0			0
$203$	−6.76615	−	20.8241i	−0.474891	−	1.46156i
$204$		0			0
$205$	5.63667	+	3.03775i	0.393682	+	0.212166i
$206$		0			0
$207$	2.69178	+	8.28444i	0.187091	+	0.575808i
$208$		0			0
$209$	−5.76624	+	4.18942i	−0.398859	+	0.289788i
$210$		0			0
$211$	17.5034	−	5.68720i	1.20498	−	0.391523i	0.363391	−	0.931637i	$-0.381619\pi$
$211$	17.5034	−	5.68720i	1.20498	−	0.391523i	0.841592	+	0.540114i	$0.181619\pi$
$212$		0			0
$213$	−22.1986	−	16.1282i	−1.52102	−	1.10509i
$214$		0			0
$215$	7.74260	+	5.62533i	0.528041	+	0.383644i
$216$		0			0
$217$	0.531609	+	0.731697i	0.0360880	+	0.0496708i
$218$		0			0
$219$			11.0898i			0.749380i
$220$		0			0
$221$	−6.99349	+	21.5237i	−0.470433	+	1.44784i
$222$		0			0
$223$	1.06319	+	3.27216i	0.0711964	+	0.219120i	0.980323	−	0.197400i	$-0.0632497\pi$
$223$	1.06319	+	3.27216i	0.0711964	+	0.219120i	−0.909127	+	0.416520i	$0.863250\pi$
$224$		0			0
$225$	−2.16754	+	6.67099i	−0.144502	+	0.444733i
$226$		0			0
$227$	8.45819	+	2.74823i	0.561390	+	0.182407i	0.575946	−	0.817488i	$-0.304634\pi$
$227$	8.45819	+	2.74823i	0.561390	+	0.182407i	−0.0145567	+	0.999894i	$0.504634\pi$
$228$		0			0
$229$	−2.89652	+	3.98672i	−0.191408	+	0.263450i	−0.893925	−	0.448217i	$-0.852059\pi$
$229$	−2.89652	+	3.98672i	−0.191408	+	0.263450i	0.702517	+	0.711667i	$0.252059\pi$
$230$		0			0
$231$	−12.1403	−	16.7097i	−0.798776	−	1.09942i
$232$		0			0
$233$	13.3328	−	4.33208i	0.873459	−	0.283804i	0.162220	−	0.986755i	$-0.448135\pi$
$233$	13.3328	−	4.33208i	0.873459	−	0.283804i	0.711239	+	0.702951i	$0.248135\pi$
$234$		0			0
$235$	−1.75490	+	2.41542i	−0.114477	+	0.157564i
$236$		0			0
$237$	6.75017			0.438471
$238$		0			0
$239$	8.66332	+	2.81488i	0.560384	+	0.182080i	0.575494	−	0.817806i	$-0.304810\pi$
$239$	8.66332	+	2.81488i	0.560384	+	0.182080i	−0.0151102	+	0.999886i	$0.504810\pi$
$240$		0			0
$241$	−11.6975	+	8.49873i	−0.753502	+	0.547451i	−0.896910	−	0.442212i	$-0.854194\pi$
$241$	−11.6975	+	8.49873i	−0.753502	+	0.547451i	0.143408	+	0.989664i	$0.454194\pi$
$242$		0			0
$243$		−	22.5142i		−	1.44429i
$244$		0			0
$245$	1.85206			0.118324
$246$		0			0
$247$	9.18413			0.584372
$248$		0			0
$249$			40.1463i			2.54417i
$250$		0			0
$251$	−14.1964	+	10.3143i	−0.896071	+	0.651034i	−0.937454	−	0.348110i	$-0.886824\pi$
$251$	−14.1964	+	10.3143i	−0.896071	+	0.651034i	0.0413828	+	0.999143i	$0.486824\pi$
$252$		0			0
$253$	−2.59095	−	0.841851i	−0.162892	−	0.0529267i
$254$		0			0
$255$	−25.3360			−1.58660
$256$		0			0
$257$	12.9028	−	17.7591i	0.804853	−	1.10778i	−0.187245	−	0.982313i	$-0.559956\pi$
$257$	12.9028	−	17.7591i	0.804853	−	1.10778i	0.992097	−	0.125471i	$-0.0400443\pi$
$258$		0			0
$259$	−5.80867	+	1.88735i	−0.360933	+	0.117274i
$260$		0			0
$261$	30.3417	+	41.7617i	1.87810	+	2.58499i
$262$		0			0
$263$	−0.0309160	+	0.0425523i	−0.00190636	+	0.00262389i	−0.809969	−	0.586473i	$-0.800516\pi$
$263$	−0.0309160	+	0.0425523i	−0.00190636	+	0.00262389i	0.808063	+	0.589096i	$0.200516\pi$
$264$		0			0
$265$	6.90566	+	2.24379i	0.424212	+	0.137835i
$266$		0			0
$267$	17.3192	−	53.3030i	1.05992	−	3.26209i
$268$		0			0
$269$	−5.49344	−	16.9071i	−0.334941	−	1.03084i	−0.966751	−	0.255719i	$-0.917688\pi$
$269$	−5.49344	−	16.9071i	−0.334941	−	1.03084i	0.631810	−	0.775123i	$-0.282312\pi$
$270$		0			0
$271$	−9.79827	+	30.1560i	−0.595203	+	1.83185i	−0.0414874	+	0.999139i	$0.513210\pi$
$271$	−9.79827	+	30.1560i	−0.595203	+	1.83185i	−0.553715	+	0.832706i	$0.686790\pi$
$272$		0			0
$273$			26.6143i			1.61077i
$274$		0			0
$275$	−1.28943	−	1.77475i	−0.0777557	−	0.107021i
$276$		0			0
$277$	18.8854	+	13.7211i	1.13472	+	0.824419i	0.986374	−	0.164517i	$-0.0526067\pi$
$277$	18.8854	+	13.7211i	1.13472	+	0.824419i	0.148341	+	0.988936i	$0.452607\pi$
$278$		0			0
$279$	−1.72501	−	1.25330i	−0.103274	−	0.0750329i
$280$		0			0
$281$	9.31241	−	3.02579i	0.555532	−	0.180503i	−0.0177779	−	0.999842i	$-0.505659\pi$
$281$	9.31241	−	3.02579i	0.555532	−	0.180503i	0.573310	+	0.819339i	$0.305659\pi$
$282$		0			0
$283$	−20.4311	+	14.8440i	−1.21450	+	0.882386i	−0.995632	−	0.0933682i	$-0.970237\pi$
$283$	−20.4311	+	14.8440i	−1.21450	+	0.882386i	−0.218869	+	0.975754i	$0.570237\pi$
$284$		0			0
$285$	3.17722	+	9.77849i	0.188202	+	0.579228i
$286$		0			0
$287$	2.54550	+	18.8800i	0.150256	+	1.11445i
$288$		0			0
$289$	−14.5547	−	44.7946i	−0.856157	−	2.63498i
$290$		0			0
$291$	19.6634	−	14.2863i	1.15269	−	0.837479i
$292$		0			0
$293$	3.88808	−	1.26331i	0.227144	−	0.0738035i	−0.193234	−	0.981153i	$-0.561898\pi$
$293$	3.88808	−	1.26331i	0.227144	−	0.0738035i	0.420378	+	0.907349i	$0.361898\pi$
$294$		0			0
$295$	10.1256	+	7.35671i	0.589538	+	0.428325i
$296$		0			0
$297$	22.5453	+	16.3801i	1.30821	+	0.950472i
$298$		0			0
$299$	2.06336	+	2.83997i	0.119327	+	0.164240i
$300$		0			0
$301$			28.4742i			1.64122i
$302$		0			0
$303$	2.15995	−	6.64765i	0.124086	−	0.381898i
$304$		0			0
$305$	−4.37888	−	13.4768i	−0.250734	−	0.771680i
$306$		0			0
$307$	−2.11189	+	6.49972i	−0.120532	+	0.370958i	−0.993061	−	0.117604i	$-0.962479\pi$
$307$	−2.11189	+	6.49972i	−0.120532	+	0.370958i	0.872529	+	0.488563i	$0.162479\pi$
$308$		0			0
$309$	−19.4095	−	6.30654i	−1.10417	−	0.358766i
$310$		0			0
$311$	−5.58443	+	7.68631i	−0.316664	+	0.435851i	−0.937445	−	0.348133i	$-0.886816\pi$
$311$	−5.58443	+	7.68631i	−0.316664	+	0.435851i	0.620781	+	0.783984i	$0.286816\pi$
$312$		0			0
$313$	−0.791125	−	1.08889i	−0.0447170	−	0.0615477i	0.786073	−	0.618134i	$-0.212111\pi$
$313$	−0.791125	−	1.08889i	−0.0447170	−	0.0615477i	−0.830790	+	0.556586i	$0.812111\pi$
$314$		0			0
$315$	−19.8478	+	6.44894i	−1.11830	+	0.363357i
$316$		0			0
$317$	−8.35924	+	11.5055i	−0.469501	+	0.646213i	−0.976445	−	0.215766i	$-0.930775\pi$
$317$	−8.35924	+	11.5055i	−0.469501	+	0.646213i	0.506944	+	0.861979i	$0.330775\pi$
$318$		0			0
$319$	−16.1442			−0.903902
$320$		0			0
$321$	4.25503	+	1.38254i	0.237493	+	0.0771661i
$322$		0			0
$323$	−21.0446	+	15.2898i	−1.17095	+	0.850748i
$324$		0			0
$325$			2.82672i			0.156798i
$326$		0			0
$327$	−54.7742			−3.02902
$328$		0			0
$329$	−8.88294			−0.489732
$330$		0			0
$331$		−	9.29054i		−	0.510654i	−0.966855	−	0.255327i	$-0.917817\pi$
$331$		−	9.29054i		−	0.510654i	0.966855	−	0.255327i	$-0.0821832\pi$
$332$		0			0
$333$	11.6490	−	8.46352i	0.638363	−	0.463798i
$334$		0			0
$335$	−5.70544	−	1.85381i	−0.311721	−	0.101284i
$336$		0			0
$337$	−3.55075			−0.193421			−0.0967107	−	0.995313i	$-0.530832\pi$
$337$	−3.55075			−0.193421			−0.0967107	+	0.995313i	$0.530832\pi$
$338$		0			0
$339$	22.9909	−	31.6443i	1.24870	−	1.71868i
$340$		0			0
$341$	0.634216	−	0.206069i	0.0343447	−	0.0111593i
$342$		0			0
$343$	−9.00273	−	12.3912i	−0.486102	−	0.669061i
$344$		0			0
$345$	−2.30995	+	3.17937i	−0.124363	+	0.171171i
$346$		0			0
$347$	12.1916	+	3.96128i	0.654477	+	0.212653i	0.617387	−	0.786659i	$-0.288191\pi$
$347$	12.1916	+	3.96128i	0.654477	+	0.212653i	0.0370900	+	0.999312i	$0.488191\pi$
$348$		0			0
$349$	2.63267	−	8.10253i	0.140924	−	0.433718i	−0.855541	−	0.517736i	$-0.826775\pi$
$349$	2.63267	−	8.10253i	0.140924	−	0.433718i	0.996464	+	0.0840172i	$0.0267751\pi$
$350$		0			0
$351$	−11.0965	−	34.1514i	−0.592285	−	1.82287i
$352$		0			0
$353$	−1.75156	+	5.39076i	−0.0932263	+	0.286921i	−0.986787	−	0.162021i	$-0.948199\pi$
$353$	−1.75156	+	5.39076i	−0.0932263	+	0.286921i	0.893561	+	0.448942i	$0.148199\pi$
$354$		0			0
$355$		−	8.67076i		−	0.460196i
$356$		0			0
$357$	−44.3077	−	60.9844i	−2.34501	−	3.22764i
$358$		0			0
$359$	20.5526	+	14.9324i	1.08473	+	0.788100i	0.978501	−	0.206242i	$-0.0661233\pi$
$359$	20.5526	+	14.9324i	1.08473	+	0.788100i	0.106226	+	0.994342i	$0.466123\pi$
$360$		0			0
$361$	−6.83112	−	4.96310i	−0.359533	−	0.261216i
$362$		0			0
$363$	18.6226	−	6.05085i	0.977433	−	0.317587i
$364$		0			0
$365$	−2.83512	+	2.05984i	−0.148397	+	0.107817i
$366$		0			0
$367$	−3.80008	−	11.6954i	−0.198362	−	0.610497i	−0.999921	−	0.0125802i	$-0.995995\pi$
$367$	−3.80008	−	11.6954i	−0.198362	−	0.610497i	0.801558	−	0.597916i	$-0.204005\pi$
$368$		0			0
$369$	−19.4620	−	40.4777i	−1.01315	−	2.10718i
$370$		0			0
$371$	6.67581	+	20.5460i	0.346591	+	1.06670i
$372$		0			0
$373$	8.88129	−	6.45264i	0.459856	−	0.334105i	−0.333619	−	0.942708i	$-0.608270\pi$
$373$	8.88129	−	6.45264i	0.459856	−	0.334105i	0.793475	+	0.608603i	$0.208270\pi$
$374$		0			0
$375$	−3.00965	+	0.977896i	−0.155418	+	0.0504983i
$376$		0			0
$377$	16.8297	+	12.2275i	0.866775	+	0.629749i
$378$		0			0
$379$	−15.1818	−	11.0302i	−0.779837	−	0.566585i	0.125093	−	0.992145i	$-0.460077\pi$
$379$	−15.1818	−	11.0302i	−0.779837	−	0.566585i	−0.904930	+	0.425560i	$0.860077\pi$
$380$		0			0
$381$	1.40000	+	1.92693i	0.0717240	+	0.0987196i
$382$		0			0
$383$			3.03691i			0.155179i	0.996985	+	0.0775895i	$0.0247224\pi$
$383$			3.03691i			0.155179i	−0.996985	+	0.0775895i	$0.975278\pi$
$384$		0			0
$385$	2.01690	−	6.20738i	0.102791	−	0.316357i
$386$		0			0
$387$	−20.7441	−	63.8439i	−1.05448	−	3.24537i
$388$		0			0
$389$	4.60916	−	14.1856i	0.233694	−	0.719236i	−0.763598	−	0.645692i	$-0.776569\pi$
$389$	4.60916	−	14.1856i	0.233694	−	0.719236i	0.997292	−	0.0735441i	$-0.0234310\pi$
$390$		0			0
$391$	−9.45601	−	3.07244i	−0.478211	−	0.155380i
$392$		0			0
$393$	22.3155	−	30.7146i	1.12567	−	1.54935i
$394$		0			0
$395$	1.25379	+	1.72569i	0.0630848	+	0.0868288i
$396$		0			0
$397$	−5.45496	+	1.77242i	−0.273776	+	0.0889553i	−0.442688	−	0.896676i	$-0.645975\pi$
$397$	−5.45496	+	1.77242i	−0.273776	+	0.0889553i	0.168911	+	0.985631i	$0.445975\pi$
$398$		0			0
$399$	−17.9807	+	24.7483i	−0.900160	+	1.23896i
$400$		0			0
$401$	−7.07000			−0.353059			−0.176530	−	0.984295i	$-0.556487\pi$
$401$	−7.07000			−0.353059			−0.176530	+	0.984295i	$0.556487\pi$
$402$		0			0
$403$	−0.817223	−	0.265532i	−0.0407088	−	0.0132271i
$404$		0			0
$405$	15.4987	−	11.2604i	0.770136	−	0.559536i
$406$		0			0
$407$			4.50327i			0.223219i
$408$		0			0
$409$	−20.2276			−1.00019			−0.500095	−	0.865971i	$-0.666702\pi$
$409$	−20.2276			−1.00019			−0.500095	+	0.865971i	$0.666702\pi$
$410$		0			0
$411$	5.14207			0.253640
$412$		0			0
$413$			37.2381i			1.83237i
$414$		0			0
$415$	−10.2634	+	7.45682i	−0.503812	+	0.366041i
$416$		0			0
$417$	21.1539	+	6.87332i	1.03591	+	0.336588i
$418$		0			0
$419$	32.5460			1.58998			0.794988	−	0.606625i	$-0.207477\pi$
$419$	32.5460			1.58998			0.794988	+	0.606625i	$0.207477\pi$
$420$		0			0
$421$	3.23010	−	4.44585i	0.157425	−	0.216677i	−0.723017	−	0.690830i	$-0.757245\pi$
$421$	3.23010	−	4.44585i	0.157425	−	0.216677i	0.880443	+	0.474152i	$0.157245\pi$
$422$		0			0
$423$	19.9170	−	6.47144i	0.968399	−	0.314652i
$424$		0			0
$425$	−4.70595	−	6.47718i	−0.228272	−	0.314190i
$426$		0			0
$427$	24.7812	−	34.1084i	1.19925	−	1.65062i
$428$		0			0
$429$	18.6629	+	6.06394i	0.901053	+	0.292770i
$430$		0			0
$431$	6.71019	−	20.6518i	0.323218	−	0.994764i	−0.649020	−	0.760771i	$-0.724821\pi$
$431$	6.71019	−	20.6518i	0.323218	−	0.994764i	0.972238	−	0.233992i	$-0.0751791\pi$
$432$		0			0
$433$	10.7893	+	33.2060i	0.518499	+	1.59578i	0.776823	+	0.629719i	$0.216830\pi$
$433$	10.7893	+	33.2060i	0.518499	+	1.59578i	−0.258324	+	0.966058i	$0.583170\pi$
$434$		0			0
$435$	−7.19663	+	22.1490i	−0.345052	+	1.06196i
$436$		0			0
$437$			4.03486i			0.193013i
$438$		0			0
$439$	−1.05527	−	1.45245i	−0.0503652	−	0.0693217i	0.783092	−	0.621906i	$-0.213642\pi$
$439$	−1.05527	−	1.45245i	−0.0503652	−	0.0693217i	−0.833457	+	0.552585i	$0.813642\pi$
$440$		0			0
$441$	−10.5099	−	7.63587i	−0.500470	−	0.363613i
$442$		0			0
$443$	27.6807	+	20.1112i	1.31515	+	0.955511i	0.999979	+	0.00647578i	$0.00206132\pi$
$443$	27.6807	+	20.1112i	1.31515	+	0.955511i	0.315169	+	0.949035i	$0.397939\pi$
$444$		0			0
$445$	16.8438	−	5.47290i	0.798475	−	0.259440i
$446$		0			0
$447$	−50.0439	+	36.3590i	−2.36700	+	1.71972i
$448$		0			0
$449$	1.73946	+	5.35350i	0.0820901	+	0.252647i	0.983675	−	0.179955i	$-0.0575953\pi$
$449$	1.73946	+	5.35350i	0.0820901	+	0.252647i	−0.901585	+	0.432603i	$0.857595\pi$
$450$		0			0
$451$	13.8193	+	2.51672i	0.650726	+	0.118508i
$452$		0			0
$453$	−19.6253	−	60.4003i	−0.922075	−	2.83785i
$454$		0			0
$455$	−6.80398	+	4.94338i	−0.318975	+	0.231749i
$456$		0			0
$457$	−18.6130	+	6.04772i	−0.870678	+	0.282900i	−0.710081	−	0.704120i	$-0.751342\pi$
$457$	−18.6130	+	6.04772i	−0.870678	+	0.282900i	−0.160597	+	0.987020i	$0.551342\pi$
$458$		0			0
$459$	82.2821	+	59.7814i	3.84060	+	2.79036i
$460$		0			0
$461$	−21.8628	−	15.8843i	−1.01825	−	0.739804i	−0.0523284	−	0.998630i	$-0.516664\pi$
$461$	−21.8628	−	15.8843i	−1.01825	−	0.739804i	−0.965924	+	0.258826i	$0.916664\pi$
$462$		0			0
$463$	−4.48519	−	6.17334i	−0.208445	−	0.286899i	0.691975	−	0.721921i	$-0.256741\pi$
$463$	−4.48519	−	6.17334i	−0.208445	−	0.286899i	−0.900420	+	0.435022i	$0.856741\pi$
$464$		0			0
$465$		−	0.961970i		−	0.0446103i
$466$		0			0
$467$	2.35319	−	7.24238i	0.108893	−	0.335138i	−0.881732	−	0.471751i	$-0.843622\pi$
$467$	2.35319	−	7.24238i	0.108893	−	0.335138i	0.990624	+	0.136614i	$0.0436220\pi$
$468$		0			0
$469$	−5.51553	−	16.9751i	−0.254684	−	0.783835i
$470$		0			0
$471$	−9.00800	+	27.7238i	−0.415067	+	1.27744i
$472$		0			0
$473$	19.9671	+	6.48771i	0.918088	+	0.298305i
$474$		0			0
$475$	−1.90974	+	2.62853i	−0.0876248	+	0.120605i
$476$		0			0
$477$	−29.9365	−	41.2041i	−1.37070	−	1.88661i
$478$		0			0
$479$	15.1632	−	4.92682i	0.692825	−	0.225112i	0.0586231	−	0.998280i	$-0.481329\pi$
$479$	15.1632	−	4.92682i	0.692825	−	0.225112i	0.634201	+	0.773168i	$0.281329\pi$
$480$		0			0
$481$	3.41075	−	4.69450i	0.155517	−	0.214051i
$482$		0			0
$483$	−11.6924			−0.532025
$484$		0			0
$485$	7.30462	+	2.37342i	0.331686	+	0.107771i
$486$		0			0
$487$	−31.6657	+	23.0065i	−1.43491	+	1.04252i	−0.445835	+	0.895115i	$0.647093\pi$
$487$	−31.6657	+	23.0065i	−1.43491	+	1.04252i	−0.989076	+	0.147409i	$0.952907\pi$
$488$		0			0
$489$		−	19.6071i		−	0.886666i
$490$		0			0
$491$	19.7081			0.889415			0.444707	−	0.895676i	$-0.353308\pi$
$491$	19.7081			0.889415			0.444707	+	0.895676i	$0.353308\pi$
$492$		0			0
$493$	−58.9204			−2.65364
$494$		0			0
$495$			15.3873i			0.691609i
$496$		0			0
$497$	20.8707	−	15.1634i	0.936179	−	0.680174i
$498$		0			0
$499$	6.05429	+	1.96716i	0.271027	+	0.0880621i	0.441378	−	0.897321i	$-0.354490\pi$
$499$	6.05429	+	1.96716i	0.271027	+	0.0880621i	−0.170350	+	0.985384i	$0.554490\pi$
$500$		0			0
$501$	51.3271			2.29312
$502$		0			0
$503$	−12.0351	+	16.5648i	−0.536616	+	0.738589i	−0.988121	−	0.153680i	$-0.950888\pi$
$503$	−12.0351	+	16.5648i	−0.536616	+	0.738589i	0.451504	+	0.892269i	$0.350888\pi$
$504$		0			0
$505$	2.10067	−	0.682549i	0.0934786	−	0.0303731i
$506$		0			0
$507$	9.31830	+	12.8255i	0.413840	+	0.569602i
$508$		0			0
$509$	−21.3304	+	29.3587i	−0.945452	+	1.30130i	0.00806615	+	0.999967i	$0.497432\pi$
$509$	−21.3304	+	29.3587i	−0.945452	+	1.30130i	−0.953518	+	0.301336i	$0.902568\pi$
$510$		0			0
$511$	−9.91613	−	3.22195i	−0.438664	−	0.142531i
$512$		0			0
$513$	12.7543	−	39.2537i	0.563116	−	1.73309i
$514$		0			0
$515$	−1.99288	−	6.13345i	−0.0878167	−	0.270272i
$516$		0			0
$517$	−2.02393	+	6.22903i	−0.0890126	+	0.273952i
$518$		0			0
$519$		−	61.7912i		−	2.71233i
$520$		0			0
$521$	3.90055	+	5.36865i	0.170886	+	0.235205i	0.885867	−	0.463940i	$-0.153565\pi$
$521$	3.90055	+	5.36865i	0.170886	+	0.235205i	−0.714981	+	0.699144i	$0.753565\pi$
$522$		0			0
$523$	−4.45967	−	3.24014i	−0.195008	−	0.141681i	0.485997	−	0.873961i	$-0.338457\pi$
$523$	−4.45967	−	3.24014i	−0.195008	−	0.141681i	−0.681005	+	0.732279i	$0.738457\pi$
$524$		0			0
$525$	−7.61711	−	5.53415i	−0.332438	−	0.241530i
$526$		0			0
$527$	2.31465	−	0.752077i	0.100828	−	0.0327610i
$528$		0			0
$529$	17.3597	−	12.6126i	0.754770	−	0.548373i
$530$		0			0
$531$	−27.1289	−	83.4940i	−1.17729	−	3.62333i
$532$		0			0
$533$	−12.5000	−	13.0903i	−0.541434	−	0.567002i
$534$		0			0
$535$	0.436887	+	1.34460i	0.0188883	+	0.0581321i
$536$		0			0
$537$	−37.6800	+	27.3761i	−1.62601	+	1.18137i
$538$		0			0
$539$	3.86404	−	1.25550i	0.166436	−	0.0540784i
$540$		0			0
$541$	−36.3956	−	26.4429i	−1.56477	−	1.13687i	−0.931959	−	0.362563i	$-0.881902\pi$
$541$	−36.3956	−	26.4429i	−1.56477	−	1.13687i	−0.632809	−	0.774308i	$-0.718098\pi$
$542$		0			0
$543$	−55.2332	−	40.1293i	−2.37029	−	1.72211i
$544$		0			0
$545$	−10.1738	−	14.0031i	−0.435799	−	0.599826i
$546$		0			0
$547$			37.8555i			1.61858i	0.587407	+	0.809292i	$0.300149\pi$
$547$			37.8555i			1.61858i	−0.587407	+	0.809292i	$0.699851\pi$
$548$		0			0
$549$	−30.7148	+	94.5303i	−1.31087	+	4.03446i
$550$		0			0
$551$	7.38881	+	22.7404i	0.314774	+	0.968774i
$552$		0			0
$553$	−1.96114	+	6.03578i	−0.0833963	+	0.256667i
$554$		0			0
$555$	6.17824	+	2.00743i	0.262252	+	0.0852108i
$556$		0			0
$557$	−26.1370	+	35.9745i	−1.10746	+	1.52429i	−0.282351	+	0.959311i	$0.591114\pi$
$557$	−26.1370	+	35.9745i	−1.10746	+	1.52429i	−0.825108	+	0.564976i	$0.808886\pi$
$558$		0			0
$559$	−15.9012	−	21.8862i	−0.672550	−	0.925686i
$560$		0			0
$561$	−52.8597	+	17.1752i	−2.23174	+	0.725136i
$562$		0			0
$563$	−7.07584	+	9.73906i	−0.298211	+	0.410453i	−0.931660	−	0.363332i	$-0.881639\pi$
$563$	−7.07584	+	9.73906i	−0.298211	+	0.410453i	0.633448	+	0.773785i	$0.281639\pi$
$564$		0			0
$565$	12.3603			0.520001
$566$		0			0
$567$	54.2083	+	17.6133i	2.27653	+	0.739691i
$568$		0			0
$569$	3.96836	−	2.88318i	0.166362	−	0.120869i	−0.501489	−	0.865164i	$-0.667214\pi$
$569$	3.96836	−	2.88318i	0.166362	−	0.120869i	0.667851	+	0.744295i	$0.267214\pi$
$570$		0			0
$571$			42.6054i			1.78298i	0.453038	+	0.891491i	$0.350340\pi$
$571$			42.6054i			1.78298i	−0.453038	+	0.891491i	$0.649660\pi$
$572$		0			0
$573$	35.0973			1.46621
$574$		0			0
$575$	−1.24186			−0.0517892
$576$		0			0
$577$		−	37.9464i		−	1.57973i	−0.613280	−	0.789866i	$-0.710150\pi$
$577$		−	37.9464i		−	1.57973i	0.613280	−	0.789866i	$-0.289850\pi$
$578$		0			0
$579$	21.3037	−	15.4781i	0.885352	−	0.643246i
$580$		0			0
$581$	−35.8975	−	11.6638i	−1.48928	−	0.483896i
$582$		0			0
$583$	15.9286			0.659697
$584$		0			0
$585$	11.6543	−	16.0407i	0.481845	−	0.663203i
$586$		0			0
$587$	−43.9893	+	14.2930i	−1.81563	+	0.589935i	−0.815699	+	0.578477i	$0.803647\pi$
$587$	−43.9893	+	14.2930i	−1.81563	+	0.589935i	−0.999934	+	0.0114576i	$0.996353\pi$
$588$		0			0
$589$	−0.580531	−	0.799032i	−0.0239204	−	0.0329235i
$590$		0			0
$591$	−21.4151	+	29.4753i	−0.880899	+	1.21245i
$592$		0			0
$593$	−22.3816	−	7.27221i	−0.919101	−	0.298634i	−0.189003	−	0.981976i	$-0.560526\pi$
$593$	−22.3816	−	7.27221i	−0.919101	−	0.298634i	−0.730098	+	0.683342i	$0.760526\pi$
$594$		0			0
$595$	7.36094	−	22.6546i	0.301769	−	0.928750i
$596$		0			0
$597$	6.40072	+	19.6994i	0.261964	+	0.806242i
$598$		0			0
$599$	13.1055	−	40.3345i	0.535475	−	1.64802i	−0.207146	−	0.978310i	$-0.566418\pi$
$599$	13.1055	−	40.3345i	0.535475	−	1.64802i	0.742621	−	0.669712i	$-0.233582\pi$
$600$		0			0
$601$			1.73427i			0.0707424i	0.999374	+	0.0353712i	$0.0112613\pi$
$601$			1.73427i			0.0707424i	−0.999374	+	0.0353712i	$0.988739\pi$
$602$		0			0
$603$	24.7335	+	34.0427i	1.00723	+	1.38633i
$604$		0			0
$605$	5.00589	+	3.63700i	0.203519	+	0.147865i
$606$		0			0
$607$	30.9392	+	22.4786i	1.25578	+	0.912380i	0.998543	−	0.0539680i	$-0.0171869\pi$
$607$	30.9392	+	22.4786i	1.25578	+	0.912380i	0.257240	+	0.966348i	$0.417187\pi$
$608$		0			0
$609$	−65.8985	+	21.4117i	−2.67034	+	0.867647i
$610$		0			0
$611$	6.82771	−	4.96062i	0.276219	−	0.200685i
$612$		0			0
$613$	10.3961	+	31.9960i	0.419896	+	1.29231i	0.907798	+	0.419407i	$0.137762\pi$
$613$	10.3961	+	31.9960i	0.419896	+	1.29231i	−0.487903	+	0.872898i	$0.662238\pi$
$614$		0			0
$615$	9.61307	−	17.8375i	0.387636	−	0.719276i
$616$		0			0
$617$	6.05776	+	18.6439i	0.243876	+	0.750574i	0.995819	+	0.0913457i	$0.0291168\pi$
$617$	6.05776	+	18.6439i	0.243876	+	0.750574i	−0.751943	+	0.659228i	$0.770883\pi$
$618$		0			0
$619$	−9.16339	+	6.65759i	−0.368308	+	0.267591i	−0.756509	−	0.653983i	$-0.773097\pi$
$619$	−9.16339	+	6.65759i	−0.368308	+	0.267591i	0.388201	+	0.921575i	$0.373097\pi$
$620$		0			0
$621$	15.0037	−	4.87500i	0.602078	−	0.195627i
$622$		0			0
$623$	42.6300	+	30.9725i	1.70793	+	1.24089i
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$		0			0
$627$	13.2576	+	18.2475i	0.529456	+	0.728734i
$628$		0			0
$629$			16.4353i			0.655317i
$630$		0			0
$631$	−7.37426	+	22.6956i	−0.293564	+	0.903499i	0.690135	+	0.723680i	$0.257551\pi$
$631$	−7.37426	+	22.6956i	−0.293564	+	0.903499i	−0.983700	+	0.179818i	$0.942449\pi$
$632$		0			0
$633$	−17.9973	−	55.3901i	−0.715330	−	2.20156i
$634$		0			0
$635$	−0.232584	+	0.715821i	−0.00922982	+	0.0284065i
$636$		0			0
$637$	−4.97903	−	1.61779i	−0.197277	−	0.0640990i
$638$		0			0
$639$	−35.7486	+	49.2038i	−1.41419	+	1.94647i
$640$		0			0
$641$	−4.32237	−	5.94923i	−0.170723	−	0.234980i	0.715079	−	0.699044i	$-0.246391\pi$
$641$	−4.32237	−	5.94923i	−0.170723	−	0.234980i	−0.885802	+	0.464064i	$0.846391\pi$
$642$		0			0
$643$	−45.2700	+	14.7091i	−1.78527	+	0.580070i	−0.999272	−	0.0381547i	$-0.987852\pi$
$643$	−45.2700	+	14.7091i	−1.78527	+	0.580070i	−0.786001	+	0.618225i	$0.787852\pi$
$644$		0			0
$645$	17.8016	−	24.5017i	0.700935	−	0.964755i
$646$		0			0
$647$	36.1774			1.42228			0.711140	−	0.703050i	$-0.248179\pi$
$647$	36.1774			1.42228			0.711140	+	0.703050i	$0.248179\pi$
$648$		0			0
$649$	26.1127	+	8.48452i	1.02501	+	0.333047i
$650$		0			0
$651$	2.31548	−	1.68230i	0.0907509	−	0.0659344i
$652$		0			0
$653$			34.7924i			1.36153i	0.732500	+	0.680767i	$0.238353\pi$
$653$			34.7924i			1.36153i	−0.732500	+	0.680767i	$0.761647\pi$
$654$		0			0
$655$	11.9971			0.468766
$656$		0			0
$657$	24.5809			0.958992
$658$		0			0
$659$			28.6866i			1.11747i	0.829346	+	0.558736i	$0.188713\pi$
$659$			28.6866i			1.11747i	−0.829346	+	0.558736i	$0.811287\pi$
$660$		0			0
$661$	5.06027	−	3.67650i	0.196822	−	0.142999i	−0.485009	−	0.874509i	$-0.661184\pi$
$661$	5.06027	−	3.67650i	0.196822	−	0.142999i	0.681831	+	0.731509i	$0.261184\pi$
$662$		0			0
$663$	68.1127	+	22.1311i	2.64528	+	0.859502i
$664$		0			0
$665$	−9.66668			−0.374858
$666$		0			0
$667$	−5.37191	+	7.39380i	−0.208001	+	0.286289i
$668$		0			0
$669$	10.3549	−	3.36450i	0.400342	−	0.130079i
$670$		0			0
$671$	−18.2717	−	25.1489i	−0.705372	−	0.970861i
$672$		0			0
$673$	−6.14804	+	8.46205i	−0.236989	+	0.326188i	−0.910902	−	0.412623i	$-0.864613\pi$
$673$	−6.14804	+	8.46205i	−0.236989	+	0.326188i	0.673912	+	0.738811i	$0.264613\pi$
$674$		0			0
$675$	12.0816	+	3.92556i	0.465022	+	0.151095i
$676$		0			0
$677$	−3.56548	+	10.9734i	−0.137032	+	0.421743i	−0.995901	−	0.0904542i	$-0.971168\pi$
$677$	−3.56548	+	10.9734i	−0.137032	+	0.421743i	0.858868	+	0.512197i	$0.171168\pi$
$678$		0			0
$679$	7.06149	+	21.7330i	0.270995	+	0.834037i
$680$		0			0
$681$	8.69688	−	26.7662i	0.333265	−	1.02568i
$682$		0			0
$683$			5.51994i			0.211215i	0.994408	+	0.105607i	$0.0336787\pi$
$683$			5.51994i			0.211215i	−0.994408	+	0.105607i	$0.966321\pi$
$684$		0			0
$685$	0.955096	+	1.31458i	0.0364923	+	0.0502274i
$686$		0			0
$687$	12.6161	+	9.16615i	0.481335	+	0.349710i
$688$		0			0
$689$	−16.6050	−	12.0643i	−0.632601	−	0.459612i
$690$		0			0
$691$	−14.9586	+	4.86034i	−0.569052	+	0.184896i	−0.579390	−	0.815050i	$-0.696709\pi$
$691$	−14.9586	+	4.86034i	−0.569052	+	0.184896i	0.0103382	+	0.999947i	$0.496709\pi$
$692$		0			0
$693$	−37.0377	+	26.9094i	−1.40694	+	1.02220i
$694$		0			0
$695$	2.17198	+	6.68467i	0.0823880	+	0.253564i
$696$		0			0
$697$	50.4354	+	9.18511i	1.91038	+	0.347911i
$698$		0			0
$699$	−13.7090	−	42.1920i	−0.518523	−	1.59585i
$700$		0			0
$701$	38.0569	−	27.6500i	1.43739	−	1.04433i	0.448811	−	0.893627i	$-0.351848\pi$
$701$	38.0569	−	27.6500i	1.43739	−	1.04433i	0.988580	−	0.150699i	$-0.0481525\pi$
$702$		0			0
$703$	6.34322	−	2.06104i	0.239239	−	0.0777335i
$704$		0			0
$705$	7.64368	+	5.55346i	0.287877	+	0.209155i
$706$		0			0
$707$	5.31657	+	3.86272i	0.199950	+	0.145272i
$708$		0			0
$709$	15.0123	+	20.6627i	0.563800	+	0.776005i	0.991803	−	0.127773i	$-0.0407828\pi$
$709$	15.0123	+	20.6627i	0.563800	+	0.776005i	−0.428003	+	0.903777i	$0.640783\pi$
$710$		0			0
$711$		−	14.9620i		−	0.561117i
$712$		0			0
$713$	0.116656	−	0.359030i	0.00436880	−	0.0134458i
$714$		0			0
$715$	1.91622	+	5.89751i	0.0716625	+	0.220554i
$716$		0			0
$717$	8.90780	−	27.4154i	0.332668	−	1.02385i
$718$		0			0
$719$	9.82347	+	3.19184i	0.366353	+	0.119035i	0.486408	−	0.873732i	$-0.338307\pi$
$719$	9.82347	+	3.19184i	0.366353	+	0.119035i	−0.120054	+	0.992767i	$0.538307\pi$
$720$		0			0
$721$	11.2782	−	15.5231i	0.420022	−	0.578110i
$722$		0			0
$723$	26.8945	+	37.0172i	1.00022	+	1.37668i
$724$		0			0
$725$	−6.99912	+	2.27415i	−0.259941	+	0.0844598i
$726$		0			0
$727$	−10.7748	+	14.8302i	−0.399613	+	0.550021i	−0.960647	−	0.277772i	$-0.910404\pi$
$727$	−10.7748	+	14.8302i	−0.399613	+	0.550021i	0.561034	+	0.827793i	$0.310404\pi$
$728$		0			0
$729$	−13.7749			−0.510180
$730$		0			0
$731$	72.8726	+	23.6777i	2.69529	+	0.875752i
$732$		0			0
$733$	24.4671	−	17.7764i	0.903712	−	0.656585i	−0.0357047	−	0.999362i	$-0.511368\pi$
$733$	24.4671	−	17.7764i	0.903712	−	0.656585i	0.939417	+	0.342777i	$0.111368\pi$
$734$		0			0
$735$		−	5.86093i		−	0.216183i
$736$		0			0
$737$	−13.1602			−0.484762
$738$		0			0
$739$	−41.5903			−1.52992			−0.764962	−	0.644076i	$-0.777242\pi$
$739$	−41.5903			−1.52992			−0.764962	+	0.644076i	$0.777242\pi$
$740$		0			0
$741$		−	29.0635i		−	1.06767i
$742$		0			0
$743$	25.1654	−	18.2837i	0.923229	−	0.670765i	−0.0210968	−	0.999777i	$-0.506716\pi$
$743$	25.1654	−	18.2837i	0.923229	−	0.670765i	0.944326	+	0.329012i	$0.106716\pi$
$744$		0			0
$745$	−18.5905	−	6.04041i	−0.681102	−	0.221303i
$746$		0			0
$747$	88.9855			3.25581
$748$		0			0
$749$	−2.47245	+	3.40304i	−0.0903414	+	0.124344i
$750$		0			0
$751$	−24.4640	+	7.94885i	−0.892706	+	0.290058i	−0.719223	−	0.694779i	$-0.755502\pi$
$751$	−24.4640	+	7.94885i	−0.892706	+	0.290058i	−0.173483	+	0.984837i	$0.555502\pi$
$752$		0			0
$753$	32.6400	+	44.9251i	1.18947	+	1.63716i
$754$		0			0
$755$	11.7962	−	16.2361i	0.429307	−	0.590890i
$756$		0			0
$757$	14.5464	+	4.72641i	0.528698	+	0.171784i	0.561189	−	0.827688i	$-0.310344\pi$
$757$	14.5464	+	4.72641i	0.528698	+	0.171784i	−0.0324911	+	0.999472i	$0.510344\pi$
$758$		0			0
$759$	−2.66407	+	8.19915i	−0.0966995	+	0.297610i
$760$		0			0
$761$	−13.3501	−	41.0873i	−0.483940	−	1.48941i	−0.833511	−	0.552504i	$-0.813673\pi$
$761$	−13.3501	−	41.0873i	−0.483940	−	1.48941i	0.349571	−	0.936910i	$-0.386327\pi$
$762$		0			0
$763$	15.9137	−	48.9772i	0.576113	−	1.77309i
$764$		0			0
$765$			56.1581i			2.03040i
$766$		0			0
$767$	−20.7954	−	28.6224i	−0.750877	−	1.03349i
$768$		0			0
$769$	−9.60956	−	6.98176i	−0.346530	−	0.251769i	0.400882	−	0.916130i	$-0.368704\pi$
$769$	−9.60956	−	6.98176i	−0.346530	−	0.251769i	−0.747412	+	0.664361i	$0.768704\pi$
$770$		0			0
$771$	−56.1994	−	40.8313i	−2.02397	−	1.47050i
$772$		0			0
$773$	3.03975	−	0.987675i	0.109332	−	0.0355242i	−0.253840	−	0.967246i	$-0.581694\pi$
$773$	3.03975	−	0.987675i	0.109332	−	0.0355242i	0.363172	+	0.931722i	$0.381694\pi$
$774$		0			0
$775$	0.245929	−	0.178678i	0.00883402	−	0.00641829i
$776$		0			0
$777$	5.97260	+	18.3818i	0.214266	+	0.659442i
$778$		0			0
$779$	−2.77976	−	20.6175i	−0.0995951	−	0.738697i
$780$		0			0
$781$	−5.87786	−	18.0902i	−0.210326	−	0.647318i
$782$		0			0
$783$	75.6334	−	54.9509i	2.70292	−	1.96378i
$784$		0			0
$785$	−8.76077	+	2.84655i	−0.312685	+	0.101598i
$786$		0			0
$787$	35.3175	+	25.6596i	1.25893	+	0.914667i	0.998705	−	0.0508800i	$-0.0162026\pi$
$787$	35.3175	+	25.6596i	1.25893	+	0.914667i	0.260227	+	0.965547i	$0.416203\pi$
$788$		0			0
$789$	0.134658	+	0.0978349i	0.00479396	+	0.00348302i
$790$		0			0
$791$	21.6157	+	29.7514i	0.768565	+	1.05784i
$792$		0			0
$793$			40.0557i			1.42242i
$794$		0			0
$795$	7.10054	−	21.8532i	0.251830	−	0.775054i
$796$		0			0
$797$	−8.95729	−	27.5677i	−0.317284	−	0.976498i	−0.974804	−	0.223062i	$-0.928395\pi$
$797$	−8.95729	−	27.5677i	−0.317284	−	0.976498i	0.657521	−	0.753436i	$-0.271605\pi$
$798$		0			0
$799$	−7.38661	+	22.7337i	−0.261320	+	0.804259i
$800$		0			0
$801$	−118.148	−	38.3885i	−4.17454	−	1.35639i
$802$		0			0
$803$	−4.51869	+	6.21944i	−0.159461	+	0.219479i
$804$		0			0
$805$	−2.17177	−	2.98919i	−0.0765448	−	0.105355i
$806$		0			0
$807$	−53.5030	+	17.3842i	−1.88340	+	0.611952i
$808$		0			0
$809$	19.4093	−	26.7147i	0.682396	−	0.939237i	−0.317564	−	0.948237i	$-0.602865\pi$
$809$	19.4093	−	26.7147i	0.682396	−	0.939237i	0.999960	+	0.00899957i	$0.00286469\pi$
$810$		0			0
$811$	−35.2643			−1.23830			−0.619149	−	0.785273i	$-0.712522\pi$
$811$	−35.2643			−1.23830			−0.619149	+	0.785273i	$0.712522\pi$
$812$		0			0
$813$	95.4297	+	31.0070i	3.34687	+	1.08746i
$814$		0			0
$815$	5.01259	−	3.64186i	0.175583	−	0.127569i
$816$		0			0
$817$		−	31.0945i		−	1.08786i
$818$		0			0
$819$	58.9914			2.06133
$820$		0			0
$821$	−22.0569			−0.769791			−0.384896	−	0.922960i	$-0.625763\pi$
$821$	−22.0569			−0.769791			−0.384896	+	0.922960i	$0.625763\pi$
$822$		0			0
$823$			0.685749i			0.0239037i	0.999929	+	0.0119518i	$0.00380448\pi$
$823$			0.685749i			0.0239037i	−0.999929	+	0.0119518i	$0.996196\pi$
$824$		0			0
$825$	−5.61626	+	4.08045i	−0.195533	+	0.142063i
$826$		0			0
$827$	−40.2411	−	13.0751i	−1.39932	−	0.454666i	−0.490349	−	0.871526i	$-0.663131\pi$
$827$	−40.2411	−	13.0751i	−1.39932	−	0.454666i	−0.908971	+	0.416860i	$0.863131\pi$
$828$		0			0
$829$	−12.7449			−0.442648			−0.221324	−	0.975200i	$-0.571038\pi$
$829$	−12.7449			−0.442648			−0.221324	+	0.975200i	$0.571038\pi$
$830$		0			0
$831$	43.4208	−	59.7636i	1.50625	−	2.07318i
$832$		0			0
$833$	14.1023	−	4.58213i	0.488617	−	0.158761i
$834$		0			0
$835$	9.53356	+	13.1218i	0.329922	+	0.454099i
$836$		0			0
$837$	−2.26981	+	3.12412i	−0.0784561	+	0.107985i
$838$		0			0
$839$	−12.9553	−	4.20944i	−0.447268	−	0.145326i	0.0767185	−	0.997053i	$-0.475556\pi$
$839$	−12.9553	−	4.20944i	−0.447268	−	0.145326i	−0.523986	+	0.851727i	$0.675556\pi$
$840$		0			0
$841$	−7.77468	+	23.9280i	−0.268092	+	0.825103i
$842$		0			0
$843$	−9.57521	−	29.4695i	−0.329788	−	1.01498i
$844$		0			0
$845$	−1.54807	+	4.76446i	−0.0532552	+	0.163903i
$846$		0			0
$847$			18.4097i			0.632564i
$848$		0			0
$849$	46.9745	+	64.6548i	1.61216	+	2.21895i
$850$		0			0
$851$	2.06243	+	1.49844i	0.0706992	+	0.0513659i
$852$		0			0
$853$	−34.7614	−	25.2556i	−1.19021	−	0.864735i	−0.196920	−	0.980420i	$-0.563094\pi$
$853$	−34.7614	−	25.2556i	−1.19021	−	0.864735i	−0.993286	+	0.115684i	$0.963094\pi$
$854$		0			0
$855$	21.6743	−	7.04241i	0.741246	−	0.240845i
$856$		0			0
$857$	−36.0701	+	26.2065i	−1.23213	+	0.895196i	−0.997048	−	0.0767796i	$-0.975536\pi$
$857$	−36.0701	+	26.2065i	−1.23213	+	0.895196i	−0.235083	+	0.971975i	$0.575536\pi$
$858$		0			0
$859$	−15.7800	−	48.5658i	−0.538406	−	1.65704i	−0.736172	−	0.676794i	$-0.763369\pi$
$859$	−15.7800	−	48.5658i	−0.538406	−	1.65704i	0.197766	−	0.980249i	$-0.436631\pi$
$860$		0			0
$861$	59.7465	−	8.05534i	2.03616	−	0.274525i
$862$		0			0
$863$	−5.05231	−	15.5494i	−0.171983	−	0.529308i	0.827500	−	0.561466i	$-0.189762\pi$
$863$	−5.05231	−	15.5494i	−0.171983	−	0.529308i	−0.999483	+	0.0321571i	$0.989762\pi$
$864$		0			0
$865$	15.7970	−	11.4772i	0.537114	−	0.390236i
$866$		0			0
$867$	−141.754	+	46.0588i	−4.81423	+	1.56424i
$868$		0			0
$869$	3.78566	+	2.75045i	0.128420	+	0.0933025i
$870$		0			0
$871$	13.7190	+	9.96745i	0.464851	+	0.337734i
$872$		0			0
$873$	−31.6661	−	43.5846i	−1.07173	−	1.47512i
$874$		0			0
$875$		−	2.97524i		−	0.100582i
$876$		0			0
$877$	5.81522	−	17.8974i	0.196366	−	0.604352i	−0.803592	−	0.595181i	$-0.797081\pi$
$877$	5.81522	−	17.8974i	0.196366	−	0.604352i	0.999958	−	0.00917171i	$-0.00291949\pi$
$878$		0			0
$879$	−3.99780	−	12.3040i	−0.134842	−	0.415002i
$880$		0			0
$881$	−9.99386	+	30.7580i	−0.336702	+	1.03626i	0.629176	+	0.777263i	$0.283393\pi$
$881$	−9.99386	+	30.7580i	−0.336702	+	1.03626i	−0.965878	+	0.258999i	$0.916607\pi$
$882$		0			0
$883$	17.7169	+	5.75656i	0.596220	+	0.193724i	0.591554	−	0.806266i	$-0.298515\pi$
$883$	17.7169	+	5.75656i	0.596220	+	0.193724i	0.00466609	+	0.999989i	$0.498515\pi$
$884$		0			0
$885$	23.2806	−	32.0430i	0.782569	−	1.07711i
$886$		0			0
$887$	−17.1712	−	23.6342i	−0.576553	−	0.793557i	0.416759	−	0.909017i	$-0.363166\pi$
$887$	−17.1712	−	23.6342i	−0.576553	−	0.793557i	−0.993312	+	0.115460i	$0.963166\pi$
$888$		0			0
$889$	−2.12974	+	0.691994i	−0.0714292	+	0.0232087i
$890$		0			0
$891$	24.7022	−	33.9996i	0.827554	−	1.13903i
$892$		0			0
$893$	9.70040			0.324612
$894$		0			0
$895$	−13.9975	−	4.54805i	−0.467884	−	0.152025i
$896$		0			0
$897$	8.98718	−	6.52957i	0.300073	−	0.218016i
$898$		0			0
$899$		−	2.23711i		−	0.0746119i
$900$		0			0
$901$	58.1337			1.93671
$902$		0			0
$903$	90.1076			2.99859
$904$		0			0
$905$		−	21.5741i		−	0.717148i
$906$		0			0
$907$	38.8020	−	28.1913i	1.28840	−	0.936076i	0.288627	−	0.957442i	$-0.406801\pi$
$907$	38.8020	−	28.1913i	1.28840	−	0.936076i	0.999772	+	0.0213656i	$0.00680141\pi$
$908$		0			0
$909$	−14.7347	−	4.78760i	−0.488720	−	0.158795i
$910$		0			0
$911$	−31.4179			−1.04092			−0.520460	−	0.853886i	$-0.674239\pi$
$911$	−31.4179			−1.04092			−0.520460	+	0.853886i	$0.674239\pi$
$912$		0			0
$913$	−16.3581	+	22.5150i	−0.541375	+	0.745139i
$914$		0			0
$915$	−42.6479	+	13.8571i	−1.40990	+	0.458103i
$916$		0			0
$917$	20.9806	+	28.8773i	0.692841	+	0.953614i
$918$		0			0
$919$	−3.38412	+	4.65784i	−0.111632	+	0.153648i	−0.861177	−	0.508305i	$-0.830272\pi$
$919$	−3.38412	+	4.65784i	−0.111632	+	0.153648i	0.749545	+	0.661953i	$0.230272\pi$
$920$		0			0
$921$	20.5686	+	6.68314i	0.677758	+	0.220217i
$922$		0			0
$923$	−7.57395	+	23.3102i	−0.249299	+	0.767265i
$924$		0			0
$925$	0.634353	+	1.95234i	0.0208574	+	0.0641924i
$926$		0			0
$927$	−13.9786	+	43.0218i	−0.459119	+	1.41302i
$928$		0			0
$929$			27.2914i			0.895402i	0.894183	+	0.447701i	$0.147757\pi$
$929$			27.2914i			0.895402i	−0.894183	+	0.447701i	$0.852243\pi$
$930$		0			0
$931$	−3.53696	−	4.86820i	−0.115919	−	0.159549i
$932$		0			0
$933$	24.3236	+	17.6721i	0.796319	+	0.578560i
$934$		0			0
$935$	−14.2091	−	10.3235i	−0.464687	−	0.337615i
$936$		0			0
$937$	35.7966	−	11.6310i	1.16942	−	0.379969i	0.340996	−	0.940065i	$-0.389236\pi$
$937$	35.7966	−	11.6310i	1.16942	−	0.379969i	0.828428	+	0.560096i	$0.189236\pi$
$938$		0			0
$939$	−3.44583	+	2.50354i	−0.112451	+	0.0817001i
$940$		0			0
$941$	8.39656	+	25.8420i	0.273720	+	0.842424i	0.989555	+	0.144154i	$0.0460462\pi$
$941$	8.39656	+	25.8420i	0.273720	+	0.842424i	−0.715835	+	0.698269i	$0.753954\pi$
$942$		0			0
$943$	5.75093	−	5.49161i	0.187276	−	0.178831i
$944$		0			0
$945$	11.6795	+	35.9458i	0.379934	+	1.16932i
$946$		0			0
$947$	−12.7537	+	9.26614i	−0.414441	+	0.301109i	−0.775397	−	0.631474i	$-0.782450\pi$
$947$	−12.7537	+	9.26614i	−0.414441	+	0.301109i	0.360956	+	0.932583i	$0.382450\pi$
$948$		0			0
$949$	9.42113	−	3.06111i	0.305823	−	0.0993678i
$950$		0			0
$951$	36.4096	+	26.4531i	1.18066	+	0.857801i
$952$		0			0
$953$	−9.45357	−	6.86842i	−0.306231	−	0.222490i	0.424047	−	0.905640i	$-0.360609\pi$
$953$	−9.45357	−	6.86842i	−0.306231	−	0.222490i	−0.730278	+	0.683150i	$0.760609\pi$
$954$		0			0
$955$	6.51902	+	8.97265i	0.210950	+	0.290348i
$956$		0			0
$957$			51.0889i			1.65147i
$958$		0			0
$959$	−1.49394	+	4.59787i	−0.0482418	+	0.148473i
$960$		0			0
$961$	−9.55097	−	29.3949i	−0.308096	−	0.948222i
$962$		0			0
$963$	3.06445	−	9.43141i	0.0987506	−	0.303923i
$964$		0			0
$965$	7.91396	+	2.57140i	0.254759	+	0.0827763i
$966$		0			0
$967$	−6.61976	+	9.11132i	−0.212877	+	0.293000i	−0.902081	−	0.431568i	$-0.857961\pi$
$967$	−6.61976	+	9.11132i	−0.212877	+	0.293000i	0.689203	+	0.724568i	$0.257961\pi$
$968$		0			0
$969$	48.3852	+	66.5965i	1.55436	+	2.13939i
$970$		0			0
$971$	−29.9278	+	9.72413i	−0.960429	+	0.312062i	−0.746946	−	0.664884i	$-0.768481\pi$
$971$	−29.9278	+	9.72413i	−0.960429	+	0.312062i	−0.213483	+	0.976947i	$0.568481\pi$
$972$		0			0
$973$	−12.2918	+	16.9182i	−0.394056	+	0.542372i
$974$		0			0
$975$	8.94526			0.286478
$976$		0			0
$977$	−30.9923	−	10.0700i	−0.991530	−	0.322168i	−0.232054	−	0.972703i	$-0.574545\pi$
$977$	−30.9923	−	10.0700i	−0.991530	−	0.322168i	−0.759476	+	0.650535i	$0.774545\pi$
$978$		0			0
$979$	31.4320	−	22.8367i	1.00457	−	0.729864i
$980$		0			0
$981$			121.409i			3.87628i
$982$		0			0
$983$	5.38234			0.171670			0.0858350	−	0.996309i	$-0.472644\pi$
$983$	5.38234			0.171670			0.0858350	+	0.996309i	$0.472644\pi$
$984$		0			0
$985$	−11.5131			−0.366837
$986$		0			0
$987$			28.1104i			0.894764i
$988$		0			0
$989$	9.61523	−	6.98587i	0.305747	−	0.222138i
$990$		0			0
$991$	−5.15949	−	1.67642i	−0.163897	−	0.0532533i	0.225919	−	0.974146i	$-0.427461\pi$
$991$	−5.15949	−	1.67642i	−0.163897	−	0.0532533i	−0.389816	+	0.920893i	$0.627461\pi$
$992$		0			0
$993$	−29.4003			−0.932989
$994$		0			0
$995$	−3.84729	+	5.29534i	−0.121967	+	0.167874i
$996$		0			0
$997$	8.50629	−	2.76386i	0.269397	−	0.0875324i	−0.171204	−	0.985236i	$-0.554766\pi$
$997$	8.50629	−	2.76386i	0.269397	−	0.0875324i	0.440600	+	0.897703i	$0.354766\pi$
$998$		0			0
$999$	−15.3280	−	21.0972i	−0.484957	−	0.667487i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bg.a.761.1	yes	24
41.25	even	10	inner	820.2.bg.a.681.6	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bg.a.681.6	✓	24	41.25	even	10	inner
820.2.bg.a.761.1	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bg (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-3.16454i q^{3} +(0.809017 - 0.587785i) q^{5} +(2.82962 + 0.919400i) q^{7} -7.01429 q^{9} +(1.28943 - 1.77475i) q^{11} +(-2.68837 + 0.873505i) q^{13} +(-1.86007 - 2.56016i) q^{15} +(4.70595 - 6.47718i) q^{17} +(-3.09002 - 1.00401i) q^{19} +(2.90948 - 8.95445i) q^{21} +(-0.383756 - 1.18108i) q^{23} +(0.309017 - 0.951057i) q^{25} +12.7034i q^{27} +(-4.32569 - 5.95380i) q^{29} +(0.245929 + 0.178678i) q^{31} +(-5.61626 - 4.08045i) q^{33} +(2.82962 - 0.919400i) q^{35} +(-1.66076 + 1.20661i) q^{37} +(2.76424 + 8.50745i) q^{39} +(2.77462 + 5.77074i) q^{41} +(2.95741 + 9.10197i) q^{43} +(-5.67468 + 4.12290i) q^{45} +(-2.83949 + 0.922607i) q^{47} +(1.49835 + 1.08862i) q^{49} +(-20.4973 - 14.8921i) q^{51} +(4.26794 + 5.87431i) q^{53} -2.19371i q^{55} +(-3.17722 + 9.77849i) q^{57} +(3.86765 + 11.9034i) q^{59} +(4.37888 - 13.4768i) q^{61} +(-19.8478 - 6.44894i) q^{63} +(-1.66150 + 2.28686i) q^{65} +(-3.52615 - 4.85334i) q^{67} +(-3.73757 + 1.21441i) q^{69} +(5.09654 - 7.01479i) q^{71} -3.50440 q^{73} +(-3.00965 - 0.977896i) q^{75} +(5.28031 - 3.83637i) q^{77} +2.13307i q^{79} +19.1574 q^{81} -12.6863 q^{83} -8.00624i q^{85} +(-18.8410 + 13.6888i) q^{87} +(16.8438 + 5.47290i) q^{89} -8.41018 q^{91} +(0.565432 - 0.778250i) q^{93} +(-3.09002 + 1.00401i) q^{95} +(4.51451 + 6.21368i) q^{97} +(-9.04445 + 12.4486i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{5} + 5 q^{7} - 6 q^{9} + 5 q^{11} - 5 q^{13} - 5 q^{17} - 5 q^{19} - 6 q^{21} + 10 q^{23} - 6 q^{25} - 25 q^{29} + 7 q^{31} - 12 q^{33} + 5 q^{35} - 13 q^{37} + 4 q^{39} + 6 q^{41} + 14 q^{43}+ \cdots - 60 q^{99}+O(q^{100}) \) 24 * q + 6 * q^5 + 5 * q^7 - 6 * q^9 + 5 * q^11 - 5 * q^13 - 5 * q^17 - 5 * q^19 - 6 * q^21 + 10 * q^23 - 6 * q^25 - 25 * q^29 + 7 * q^31 - 12 * q^33 + 5 * q^35 - 13 * q^37 + 4 * q^39 + 6 * q^41 + 14 * q^43 + q^45 - 35 * q^47 + 23 * q^49 - 27 * q^51 + 35 * q^53 + 9 * q^57 - 14 * q^59 + 22 * q^61 - 10 * q^63 + 5 * q^65 - 20 * q^67 - 55 * q^71 + 8 * q^73 - 5 * q^75 + 6 * q^77 - 28 * q^81 - 82 * q^83 - 27 * q^87 + 50 * q^89 + 70 * q^91 - 80 * q^93 - 5 * q^95 - 20 * q^97 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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