LMFDB - Embedded newform 1148.2.n.d.57.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(57,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("1148.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.n (of order $5$, degree $4$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			57.6
Character	$\chi$	$=$	1148.57
Dual form			1148.2.n.d.141.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.97808 q^{3} +(0.835003 + 0.606666i) q^{5} +(0.309017 + 0.951057i) q^{7} +5.86899 q^{9} +O(q^{10})$	\(q+2.97808 q^{3} +(0.835003 + 0.606666i) q^{5} +(0.309017 + 0.951057i) q^{7} +5.86899 q^{9} +(2.06367 - 1.49934i) q^{11} +(-0.633449 + 1.94956i) q^{13} +(2.48671 + 1.80670i) q^{15} +(0.870400 - 0.632383i) q^{17} +(-0.670217 - 2.06272i) q^{19} +(0.920279 + 2.83233i) q^{21} +(-0.733436 + 2.25728i) q^{23} +(-1.21590 - 3.74215i) q^{25} +8.54409 q^{27} +(-1.01468 - 0.737207i) q^{29} +(-7.64454 + 5.55408i) q^{31} +(6.14578 - 4.46517i) q^{33} +(-0.318943 + 0.981605i) q^{35} +(0.810574 + 0.588917i) q^{37} +(-1.88646 + 5.80594i) q^{39} +(0.232860 + 6.39889i) q^{41} +(3.23255 - 9.94877i) q^{43} +(4.90063 + 3.56051i) q^{45} +(1.20916 - 3.72142i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(2.59212 - 1.88329i) q^{51} +(0.585206 + 0.425177i) q^{53} +2.63277 q^{55} +(-1.99596 - 6.14294i) q^{57} +(-2.87517 + 8.84888i) q^{59} +(-0.501913 - 1.54473i) q^{61} +(1.81362 + 5.58174i) q^{63} +(-1.71166 + 1.24359i) q^{65} +(4.74034 + 3.44406i) q^{67} +(-2.18424 + 6.72238i) q^{69} +(-0.581037 + 0.422148i) q^{71} +3.42292 q^{73} +(-3.62105 - 11.1444i) q^{75} +(2.06367 + 1.49934i) q^{77} +6.68234 q^{79} +7.83806 q^{81} -8.44938 q^{83} +1.11043 q^{85} +(-3.02180 - 2.19547i) q^{87} +(-5.24515 - 16.1429i) q^{89} -2.04988 q^{91} +(-22.7661 + 16.5405i) q^{93} +(0.691745 - 2.12897i) q^{95} +(-5.60863 - 4.07491i) q^{97} +(12.1116 - 8.79963i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9}+O(q^{10}) $ 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9	$ 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9} + 11 q^{11} - 4 q^{13} + 10 q^{15} + 9 q^{17} - 23 q^{19} + 5 q^{21} + 28 q^{23} - 10 q^{25} - 76 q^{27} + 28 q^{29} - 18 q^{31} - 27 q^{33} - q^{35} - 29 q^{37} - 6 q^{39} + 65 q^{41} - 15 q^{43} - 20 q^{45} - 11 q^{47} - 6 q^{49} - 18 q^{51} + 8 q^{53} - 50 q^{55} + 8 q^{57} + 55 q^{59} - 10 q^{61} - 2 q^{63} - 11 q^{65} + 65 q^{67} - 2 q^{69} - 14 q^{71} + 48 q^{73} - 77 q^{75} + 11 q^{77} + 22 q^{79} + 80 q^{81} - 22 q^{83} - 78 q^{85} - 4 q^{87} + 16 q^{89} - 4 q^{91} - 60 q^{93} + 56 q^{95} + 15 q^{97} + 80 q^{99}+O(q^{100}) $ 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9 + 11 * q^11 - 4 * q^13 + 10 * q^15 + 9 * q^17 - 23 * q^19 + 5 * q^21 + 28 * q^23 - 10 * q^25 - 76 * q^27 + 28 * q^29 - 18 * q^31 - 27 * q^33 - q^35 - 29 * q^37 - 6 * q^39 + 65 * q^41 - 15 * q^43 - 20 * q^45 - 11 * q^47 - 6 * q^49 - 18 * q^51 + 8 * q^53 - 50 * q^55 + 8 * q^57 + 55 * q^59 - 10 * q^61 - 2 * q^63 - 11 * q^65 + 65 * q^67 - 2 * q^69 - 14 * q^71 + 48 * q^73 - 77 * q^75 + 11 * q^77 + 22 * q^79 + 80 * q^81 - 22 * q^83 - 78 * q^85 - 4 * q^87 + 16 * q^89 - 4 * q^91 - 60 * q^93 + 56 * q^95 + 15 * q^97 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	2.97808			1.71940			0.859699	−	0.510801i	$-0.170651\pi$
$3$	2.97808			1.71940			0.859699	+	0.510801i	$0.170651\pi$
$4$		0			0
$5$	0.835003	+	0.606666i	0.373425	+	0.271309i	0.758630	−	0.651522i	$-0.225869\pi$
$5$	0.835003	+	0.606666i	0.373425	+	0.271309i	−0.385205	+	0.922831i	$0.625869\pi$
$6$		0			0
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$8$		0			0
$9$	5.86899			1.95633
$10$		0			0
$11$	2.06367	−	1.49934i	0.622219	−	0.452069i	−0.231477	−	0.972840i	$-0.574356\pi$
$11$	2.06367	−	1.49934i	0.622219	−	0.452069i	0.853696	+	0.520772i	$0.174356\pi$
$12$		0			0
$13$	−0.633449	+	1.94956i	−0.175687	+	0.540709i	−0.999664	−	0.0259138i	$-0.991750\pi$
$13$	−0.633449	+	1.94956i	−0.175687	+	0.540709i	0.823977	+	0.566623i	$0.191750\pi$
$14$		0			0
$15$	2.48671	+	1.80670i	0.642066	+	0.466488i
$16$		0			0
$17$	0.870400	−	0.632383i	0.211103	−	0.153375i	−0.477210	−	0.878790i	$-0.658352\pi$
$17$	0.870400	−	0.632383i	0.211103	−	0.153375i	0.688313	+	0.725414i	$0.258352\pi$
$18$		0			0
$19$	−0.670217	−	2.06272i	−0.153758	−	0.473220i	0.844275	−	0.535911i	$-0.180032\pi$
$19$	−0.670217	−	2.06272i	−0.153758	−	0.473220i	−0.998033	+	0.0626912i	$0.980032\pi$
$20$		0			0
$21$	0.920279	+	2.83233i	0.200821	+	0.618064i
$22$		0			0
$23$	−0.733436	+	2.25728i	−0.152932	+	0.470676i	−0.997945	−	0.0640686i	$-0.979592\pi$
$23$	−0.733436	+	2.25728i	−0.152932	+	0.470676i	0.845013	+	0.534745i	$0.179592\pi$
$24$		0			0
$25$	−1.21590	−	3.74215i	−0.243179	−	0.748429i
$26$		0			0
$27$	8.54409			1.64431
$28$		0			0
$29$	−1.01468	−	0.737207i	−0.188421	−	0.136896i	0.489576	−	0.871961i	$-0.337152\pi$
$29$	−1.01468	−	0.737207i	−0.188421	−	0.136896i	−0.677997	+	0.735065i	$0.737152\pi$
$30$		0			0
$31$	−7.64454	+	5.55408i	−1.37300	+	0.997543i	−0.375503	+	0.926821i	$0.622530\pi$
$31$	−7.64454	+	5.55408i	−1.37300	+	0.997543i	−0.997496	+	0.0707216i	$0.977470\pi$
$32$		0			0
$33$	6.14578	−	4.46517i	1.06984	−	0.777286i
$34$		0			0
$35$	−0.318943	+	0.981605i	−0.0539112	+	0.165922i
$36$		0			0
$37$	0.810574	+	0.588917i	0.133258	+	0.0968173i	0.652417	−	0.757860i	$-0.273755\pi$
$37$	0.810574	+	0.588917i	0.133258	+	0.0968173i	−0.519160	+	0.854677i	$0.673755\pi$
$38$		0			0
$39$	−1.88646	+	5.80594i	−0.302076	+	0.929695i
$40$		0			0
$41$	0.232860	+	6.39889i	0.0363666	+	0.999339i
$41$	0.232860	+	6.39889i	0.0363666	+	0.999339i
$42$		0			0
$43$	3.23255	−	9.94877i	0.492959	−	1.51717i	−0.327154	−	0.944971i	$-0.606089\pi$
$43$	3.23255	−	9.94877i	0.492959	−	1.51717i	0.820113	−	0.572202i	$-0.193911\pi$
$44$		0			0
$45$	4.90063	+	3.56051i	0.730542	+	0.530770i
$46$		0			0
$47$	1.20916	−	3.72142i	0.176374	−	0.542824i	−0.823319	−	0.567579i	$-0.807880\pi$
$47$	1.20916	−	3.72142i	0.176374	−	0.542824i	0.999694	+	0.0247542i	$0.00788031\pi$
$48$		0			0
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$		0			0
$51$	2.59212	−	1.88329i	0.362970	−	0.263713i
$52$		0			0
$53$	0.585206	+	0.425177i	0.0803842	+	0.0584025i	0.627252	−	0.778817i	$-0.284180\pi$
$53$	0.585206	+	0.425177i	0.0803842	+	0.0584025i	−0.546867	+	0.837219i	$0.684180\pi$
$54$		0			0
$55$	2.63277			0.355003
$56$		0			0
$57$	−1.99596	−	6.14294i	−0.264372	−	0.813653i
$58$		0			0
$59$	−2.87517	+	8.84888i	−0.374316	+	1.15203i	0.569623	+	0.821906i	$0.307089\pi$
$59$	−2.87517	+	8.84888i	−0.374316	+	1.15203i	−0.943939	+	0.330120i	$0.892911\pi$
$60$		0			0
$61$	−0.501913	−	1.54473i	−0.0642633	−	0.197782i	0.913770	−	0.406233i	$-0.133158\pi$
$61$	−0.501913	−	1.54473i	−0.0642633	−	0.197782i	−0.978033	+	0.208451i	$0.933158\pi$
$62$		0			0
$63$	1.81362	+	5.58174i	0.228494	+	0.703233i
$64$		0			0
$65$	−1.71166	+	1.24359i	−0.212305	+	0.154249i
$66$		0			0
$67$	4.74034	+	3.44406i	0.579124	+	0.420759i	0.838408	−	0.545043i	$-0.183487\pi$
$67$	4.74034	+	3.44406i	0.579124	+	0.420759i	−0.259284	+	0.965801i	$0.583487\pi$
$68$		0			0
$69$	−2.18424	+	6.72238i	−0.262951	+	0.809280i
$70$		0			0
$71$	−0.581037	+	0.422148i	−0.0689564	+	0.0500997i	−0.621729	−	0.783232i	$-0.713570\pi$
$71$	−0.581037	+	0.422148i	−0.0689564	+	0.0500997i	0.552773	+	0.833332i	$0.313570\pi$
$72$		0			0
$73$	3.42292			0.400622			0.200311	−	0.979732i	$-0.435805\pi$
$73$	3.42292			0.400622			0.200311	+	0.979732i	$0.435805\pi$
$74$		0			0
$75$	−3.62105	−	11.1444i	−0.418122	−	1.28685i
$76$		0			0
$77$	2.06367	+	1.49934i	0.235177	+	0.170866i
$78$		0			0
$79$	6.68234			0.751822			0.375911	−	0.926656i	$-0.377330\pi$
$79$	6.68234			0.751822			0.375911	+	0.926656i	$0.377330\pi$
$80$		0			0
$81$	7.83806			0.870896
$82$		0			0
$83$	−8.44938			−0.927440			−0.463720	−	0.885982i	$-0.653486\pi$
$83$	−8.44938			−0.927440			−0.463720	+	0.885982i	$0.653486\pi$
$84$		0			0
$85$	1.11043			0.120443
$86$		0			0
$87$	−3.02180	−	2.19547i	−0.323971	−	0.235379i
$88$		0			0
$89$	−5.24515	−	16.1429i	−0.555984	−	1.71114i	−0.693329	−	0.720621i	$-0.743857\pi$
$89$	−5.24515	−	16.1429i	−0.555984	−	1.71114i	0.137345	−	0.990523i	$-0.456143\pi$
$90$		0			0
$91$	−2.04988			−0.214886
$92$		0			0
$93$	−22.7661	+	16.5405i	−2.36073	+	1.71517i
$94$		0			0
$95$	0.691745	−	2.12897i	0.0709716	−	0.218428i
$96$		0			0
$97$	−5.60863	−	4.07491i	−0.569470	−	0.413744i	0.265443	−	0.964127i	$-0.414482\pi$
$97$	−5.60863	−	4.07491i	−0.569470	−	0.413744i	−0.834913	+	0.550383i	$0.814482\pi$
$98$		0			0
$99$	12.1116	−	8.79963i	1.21727	−	0.884396i
$100$		0			0
$101$	−3.31914	−	10.2153i	−0.330267	−	1.01646i	−0.969007	−	0.247035i	$-0.920544\pi$
$101$	−3.31914	−	10.2153i	−0.330267	−	1.01646i	0.638740	−	0.769423i	$-0.279456\pi$
$102$		0			0
$103$	−0.00357052	−	0.0109889i	−0.000351814	−	0.00108277i	0.950880	−	0.309558i	$-0.100181\pi$
$103$	−0.00357052	−	0.0109889i	−0.000351814	−	0.00108277i	−0.951232	+	0.308476i	$0.900181\pi$
$104$		0			0
$105$	−0.949839	+	2.92330i	−0.0926948	+	0.285285i
$106$		0			0
$107$	−1.11086	−	3.41889i	−0.107391	−	0.330516i	0.882893	−	0.469574i	$-0.155593\pi$
$107$	−1.11086	−	3.41889i	−0.107391	−	0.330516i	−0.990284	+	0.139058i	$0.955593\pi$
$108$		0			0
$109$	0.879767			0.0842664			0.0421332	−	0.999112i	$-0.486585\pi$
$109$	0.879767			0.0842664			0.0421332	+	0.999112i	$0.486585\pi$
$110$		0			0
$111$	2.41396	+	1.75384i	0.229123	+	0.166467i
$112$		0			0
$113$	−3.46104	+	2.51459i	−0.325587	+	0.236553i	−0.738556	−	0.674192i	$-0.764492\pi$
$113$	−3.46104	+	2.51459i	−0.325587	+	0.236553i	0.412969	+	0.910745i	$0.364492\pi$
$114$		0			0
$115$	−1.98184	+	1.43989i	−0.184807	+	0.134270i
$116$		0			0
$117$	−3.71770	+	11.4419i	−0.343702	+	1.05781i
$118$		0			0
$119$	0.870400	+	0.632383i	0.0797894	+	0.0579704i
$120$		0			0
$121$	−1.38849	+	4.27333i	−0.126226	+	0.388484i
$122$		0			0
$123$	0.693477	+	19.0564i	0.0625287	+	1.71826i
$124$		0			0
$125$	2.84967	−	8.77038i	0.254882	−	0.784446i
$126$		0			0
$127$	−14.9542	−	10.8649i	−1.32697	−	0.964101i	−0.999817	−	0.0191304i	$-0.993910\pi$
$127$	−14.9542	−	10.8649i	−1.32697	−	0.964101i	−0.327155	−	0.944971i	$-0.606090\pi$
$128$		0			0
$129$	9.62681	−	29.6283i	0.847593	−	2.60862i
$130$		0			0
$131$	−1.84511	+	1.34055i	−0.161208	+	0.117124i	−0.665465	−	0.746429i	$-0.731767\pi$
$131$	−1.84511	+	1.34055i	−0.161208	+	0.117124i	0.504257	+	0.863554i	$0.331767\pi$
$132$		0			0
$133$	1.75465	−	1.27483i	0.152148	−	0.110542i
$134$		0			0
$135$	7.13435	+	5.18341i	0.614027	+	0.446117i
$136$		0			0
$137$	−12.6908			−1.08425			−0.542126	−	0.840298i	$-0.682380\pi$
$137$	−12.6908			−1.08425			−0.542126	+	0.840298i	$0.682380\pi$
$138$		0			0
$139$	0.468566	+	1.44210i	0.0397433	+	0.122317i	0.968960	−	0.247219i	$-0.0795166\pi$
$139$	0.468566	+	1.44210i	0.0397433	+	0.122317i	−0.929216	+	0.369536i	$0.879517\pi$
$140$		0			0
$141$	3.60099	−	11.0827i	0.303258	−	0.933331i
$142$		0			0
$143$	1.61582	+	4.97299i	0.135122	+	0.415863i
$144$		0			0
$145$	−0.400022	−	1.23114i	−0.0332200	−	0.102241i
$146$		0			0
$147$	−2.40932	+	1.75047i	−0.198717	+	0.144377i
$148$		0			0
$149$	12.4004	+	9.00938i	1.01588	+	0.738077i	0.965433	−	0.260650i	$-0.0839367\pi$
$149$	12.4004	+	9.00938i	1.01588	+	0.738077i	0.0504429	+	0.998727i	$0.483937\pi$
$150$		0			0
$151$	−2.20902	+	6.79865i	−0.179767	+	0.553267i	−0.999819	−	0.0190227i	$-0.993945\pi$
$151$	−2.20902	+	6.79865i	−0.179767	+	0.553267i	0.820052	+	0.572289i	$0.193945\pi$
$152$		0			0
$153$	5.10837	−	3.71145i	0.412987	−	0.300053i
$154$		0			0
$155$	−9.75269			−0.783355
$156$		0			0
$157$	4.25435	+	13.0935i	0.339534	+	1.04498i	0.964445	+	0.264282i	$0.0851351\pi$
$157$	4.25435	+	13.0935i	0.339534	+	1.04498i	−0.624911	+	0.780696i	$0.714865\pi$
$158$		0			0
$159$	1.74279	+	1.26621i	0.138212	+	0.100417i
$160$		0			0
$161$	−2.37345			−0.187054
$162$		0			0
$163$	−1.07486			−0.0841897			−0.0420948	−	0.999114i	$-0.513403\pi$
$163$	−1.07486			−0.0841897			−0.0420948	+	0.999114i	$0.513403\pi$
$164$		0			0
$165$	7.84061			0.610391
$166$		0			0
$167$	−3.21340			−0.248660			−0.124330	−	0.992241i	$-0.539678\pi$
$167$	−3.21340			−0.248660			−0.124330	+	0.992241i	$0.539678\pi$
$168$		0			0
$169$	7.11771	+	5.17132i	0.547516	+	0.397794i
$170$		0			0
$171$	−3.93350	−	12.1061i	−0.300802	−	0.925774i
$172$		0			0
$173$	−1.67085			−0.127032			−0.0635162	−	0.997981i	$-0.520231\pi$
$173$	−1.67085			−0.127032			−0.0635162	+	0.997981i	$0.520231\pi$
$174$		0			0
$175$	3.18326	−	2.31277i	0.240632	−	0.174829i
$176$		0			0
$177$	−8.56251	+	26.3527i	−0.643598	+	1.98079i
$178$		0			0
$179$	−5.66057	−	4.11264i	−0.423091	−	0.307393i	0.355789	−	0.934566i	$-0.384212\pi$
$179$	−5.66057	−	4.11264i	−0.423091	−	0.307393i	−0.778880	+	0.627173i	$0.784212\pi$
$180$		0			0
$181$	17.5867	−	12.7775i	1.30721	−	0.949745i	0.307214	−	0.951641i	$-0.400603\pi$
$181$	17.5867	−	12.7775i	1.30721	−	0.949745i	0.999998	+	0.00189551i	$0.000603360\pi$
$182$		0			0
$183$	−1.49474	−	4.60033i	−0.110494	−	0.340066i
$184$		0			0
$185$	0.319557	+	0.983495i	0.0234943	+	0.0723080i
$186$		0			0
$187$	0.848059	−	2.61006i	0.0620162	−	0.190866i
$188$		0			0
$189$	2.64027	+	8.12591i	0.192051	+	0.591073i
$190$		0			0
$191$	4.32531			0.312969			0.156484	−	0.987680i	$-0.449984\pi$
$191$	4.32531			0.312969			0.156484	+	0.987680i	$0.449984\pi$
$192$		0			0
$193$	19.3295	+	14.0437i	1.39137	+	1.01089i	0.995714	+	0.0924874i	$0.0294818\pi$
$193$	19.3295	+	14.0437i	1.39137	+	1.01089i	0.395653	+	0.918400i	$0.370518\pi$
$194$		0			0
$195$	−5.09747	+	3.70353i	−0.365037	+	0.265215i
$196$		0			0
$197$	1.31142	−	0.952804i	0.0934350	−	0.0678845i	−0.540087	−	0.841609i	$-0.681609\pi$
$197$	1.31142	−	0.952804i	0.0934350	−	0.0678845i	0.633522	+	0.773725i	$0.281609\pi$
$198$		0			0
$199$	−2.45000	+	7.54033i	−0.173676	+	0.534520i	−0.999571	−	0.0293048i	$-0.990671\pi$
$199$	−2.45000	+	7.54033i	−0.173676	+	0.534520i	0.825894	+	0.563825i	$0.190671\pi$
$200$		0			0
$201$	14.1171	+	10.2567i	0.995745	+	0.723451i
$202$		0			0
$203$	0.387573	−	1.19283i	0.0272023	−	0.0837200i
$204$		0			0
$205$	−3.68755	+	5.48436i	−0.257549	+	0.383044i
$206$		0			0
$207$	−4.30453	+	13.2480i	−0.299185	+	0.920798i
$208$		0			0
$209$	−4.47583	−	3.25188i	−0.309599	−	0.224937i
$210$		0			0
$211$	7.65784	−	23.5684i	0.527187	−	1.62252i	−0.232762	−	0.972534i	$-0.574776\pi$
$211$	7.65784	−	23.5684i	0.527187	−	1.62252i	0.759950	−	0.649982i	$-0.225224\pi$
$212$		0			0
$213$	−1.73038	+	1.25719i	−0.118563	+	0.0861414i
$214$		0			0
$215$	8.73477	−	6.34618i	0.595706	−	0.432806i
$216$		0			0
$217$	−7.64454	−	5.55408i	−0.518945	−	0.377036i
$218$		0			0
$219$	10.1937			0.688829
$220$		0			0
$221$	0.681511	+	2.09747i	0.0458434	+	0.141091i
$222$		0			0
$223$	−1.07506	+	3.30870i	−0.0719914	+	0.221567i	−0.980578	−	0.196130i	$-0.937163\pi$
$223$	−1.07506	+	3.30870i	−0.0719914	+	0.221567i	0.908587	+	0.417697i	$0.137163\pi$
$224$		0			0
$225$	−7.13609	−	21.9626i	−0.475739	−	1.46417i
$226$		0			0
$227$	−8.50725	−	26.1826i	−0.564646	−	1.73780i	−0.669000	−	0.743262i	$-0.733278\pi$
$227$	−8.50725	−	26.1826i	−0.564646	−	1.73780i	0.104354	−	0.994540i	$-0.466722\pi$
$228$		0			0
$229$	−23.3298	+	16.9501i	−1.54168	+	1.12009i	−0.592404	+	0.805641i	$0.701821\pi$
$229$	−23.3298	+	16.9501i	−1.54168	+	1.12009i	−0.949273	+	0.314453i	$0.898179\pi$
$230$		0			0
$231$	6.14578	+	4.46517i	0.404363	+	0.293787i
$232$		0			0
$233$	−6.79890	+	20.9248i	−0.445410	+	1.37083i	0.436623	+	0.899645i	$0.356175\pi$
$233$	−6.79890	+	20.9248i	−0.445410	+	1.37083i	−0.882033	+	0.471188i	$0.843825\pi$
$234$		0			0
$235$	3.26731	−	2.37384i	0.213136	−	0.154852i
$236$		0			0
$237$	19.9006			1.29268
$238$		0			0
$239$	−6.40423	−	19.7102i	−0.414255	−	1.27495i	−0.912915	−	0.408149i	$-0.866174\pi$
$239$	−6.40423	−	19.7102i	−0.414255	−	1.27495i	0.498660	−	0.866798i	$-0.333826\pi$
$240$		0			0
$241$	2.41095	+	1.75166i	0.155303	+	0.112834i	0.662723	−	0.748865i	$-0.269401\pi$
$241$	2.41095	+	1.75166i	0.155303	+	0.112834i	−0.507420	+	0.861699i	$0.669401\pi$
$242$		0			0
$243$	−2.28986			−0.146894
$244$		0			0
$245$	−1.03212			−0.0659398
$246$		0			0
$247$	4.44593			0.282888
$248$		0			0
$249$	−25.1630			−1.59464
$250$		0			0
$251$	−12.9592	−	9.41542i	−0.817978	−	0.594296i	0.0981543	−	0.995171i	$-0.468706\pi$
$251$	−12.9592	−	9.41542i	−0.817978	−	0.594296i	−0.916133	+	0.400875i	$0.868706\pi$
$252$		0			0
$253$	1.87087	+	5.75796i	0.117621	+	0.362000i
$254$		0			0
$255$	3.30696			0.207090
$256$		0			0
$257$	3.77424	−	2.74215i	0.235431	−	0.171050i	−0.463815	−	0.885932i	$-0.653520\pi$
$257$	3.77424	−	2.74215i	0.235431	−	0.171050i	0.699245	+	0.714882i	$0.253520\pi$
$258$		0			0
$259$	−0.309612	+	0.952887i	−0.0192383	+	0.0592095i
$260$		0			0
$261$	−5.95514	−	4.32666i	−0.368614	−	0.267814i
$262$		0			0
$263$	−7.09742	+	5.15658i	−0.437646	+	0.317968i	−0.784699	−	0.619877i	$-0.787182\pi$
$263$	−7.09742	+	5.15658i	−0.437646	+	0.317968i	0.347053	+	0.937846i	$0.387182\pi$
$264$		0			0
$265$	0.230709	+	0.710048i	0.0141723	+	0.0436179i
$266$		0			0
$267$	−15.6205	−	48.0749i	−0.955959	−	2.94214i
$268$		0			0
$269$	−2.26120	+	6.95926i	−0.137868	+	0.424314i	−0.996025	−	0.0890733i	$-0.971609\pi$
$269$	−2.26120	+	6.95926i	−0.137868	+	0.424314i	0.858157	+	0.513387i	$0.171609\pi$
$270$		0			0
$271$	−0.758249	−	2.33365i	−0.0460604	−	0.141759i	0.925381	−	0.379037i	$-0.123745\pi$
$271$	−0.758249	−	2.33365i	−0.0460604	−	0.141759i	−0.971442	+	0.237278i	$0.923745\pi$
$272$		0			0
$273$	−6.10473			−0.369475
$274$		0			0
$275$	−8.11997	−	5.89950i	−0.489653	−	0.355753i
$276$		0			0
$277$	0.592621	−	0.430564i	0.0356072	−	0.0258701i	−0.569839	−	0.821756i	$-0.692995\pi$
$277$	0.592621	−	0.430564i	0.0356072	−	0.0258701i	0.605446	+	0.795886i	$0.292995\pi$
$278$		0			0
$279$	−44.8657	+	32.5968i	−2.68604	+	1.95152i
$280$		0			0
$281$	5.51020	−	16.9587i	0.328711	−	1.01167i	−0.641027	−	0.767519i	$-0.721491\pi$
$281$	5.51020	−	16.9587i	0.328711	−	1.01167i	0.969738	−	0.244150i	$-0.0785088\pi$
$282$		0			0
$283$	−6.69337	−	4.86302i	−0.397879	−	0.289076i	0.370797	−	0.928714i	$-0.379084\pi$
$283$	−6.69337	−	4.86302i	−0.397879	−	0.289076i	−0.768677	+	0.639638i	$0.779084\pi$
$284$		0			0
$285$	2.06008	−	6.34026i	0.122028	−	0.375565i
$286$		0			0
$287$	−6.01375	+	2.19883i	−0.354980	+	0.129793i
$288$		0			0
$289$	−4.89560	+	15.0671i	−0.287977	+	0.886301i
$290$		0			0
$291$	−16.7030	−	12.1354i	−0.979145	−	0.711391i
$292$		0			0
$293$	−6.65969	+	20.4964i	−0.389063	+	1.19741i	0.544427	+	0.838808i	$0.316747\pi$
$293$	−6.65969	+	20.4964i	−0.389063	+	1.19741i	−0.933490	+	0.358604i	$0.883253\pi$
$294$		0			0
$295$	−7.76909	+	5.64457i	−0.452334	+	0.328640i
$296$		0			0
$297$	17.6322	−	12.8105i	1.02312	−	0.743342i
$298$		0			0
$299$	−3.93611	−	2.85975i	−0.227631	−	0.165384i
$300$		0			0
$301$	10.4608			0.602948
$302$		0			0
$303$	−9.88469	−	30.4220i	−0.567861	−	1.74770i
$304$		0			0
$305$	0.518035	−	1.59435i	0.0296626	−	0.0912920i
$306$		0			0
$307$	1.59917	+	4.92175i	0.0912697	+	0.280899i	0.986264	−	0.165179i	$-0.0528202\pi$
$307$	1.59917	+	4.92175i	0.0912697	+	0.280899i	−0.894994	+	0.446078i	$0.852820\pi$
$308$		0			0
$309$	−0.0106333	−	0.0327260i	−0.000604908	−	0.00186172i
$310$		0			0
$311$	−22.1458	+	16.0898i	−1.25577	+	0.912371i	−0.998542	−	0.0539797i	$-0.982809\pi$
$311$	−22.1458	+	16.0898i	−1.25577	+	0.912371i	−0.257229	+	0.966351i	$0.582809\pi$
$312$		0			0
$313$	20.3790	+	14.8062i	1.15189	+	0.836895i	0.988731	−	0.149706i	$-0.0478326\pi$
$313$	20.3790	+	14.8062i	1.15189	+	0.836895i	0.163156	+	0.986600i	$0.447833\pi$
$314$		0			0
$315$	−1.87187	+	5.76103i	−0.105468	+	0.324597i
$316$		0			0
$317$	0.332650	−	0.241684i	0.0186835	−	0.0135743i	−0.578404	−	0.815750i	$-0.696324\pi$
$317$	0.332650	−	0.241684i	0.0186835	−	0.0135743i	0.597088	+	0.802176i	$0.296324\pi$
$318$		0			0
$319$	−3.19929			−0.179126
$320$		0			0
$321$	−3.30825	−	10.1817i	−0.184648	−	0.568289i
$322$		0			0
$323$	−1.88778	−	1.37155i	−0.105039	−	0.0763153i
$324$		0			0
$325$	8.06573			0.447406
$326$		0			0
$327$	2.62002			0.144888
$328$		0			0
$329$	3.91293			0.215727
$330$		0			0
$331$	3.55749			0.195537			0.0977687	−	0.995209i	$-0.468829\pi$
$331$	3.55749			0.195537			0.0977687	+	0.995209i	$0.468829\pi$
$332$		0			0
$333$	4.75725	+	3.45635i	0.260696	+	0.189407i
$334$		0			0
$335$	1.86881	+	5.75160i	0.102104	+	0.314243i
$336$		0			0
$337$	−17.5822			−0.957763			−0.478882	−	0.877879i	$-0.658958\pi$
$337$	−17.5822			−0.957763			−0.478882	+	0.877879i	$0.658958\pi$
$338$		0			0
$339$	−10.3073	+	7.48866i	−0.559814	+	0.406728i
$340$		0			0
$341$	−7.44832	+	22.9236i	−0.403349	+	1.24138i
$342$		0			0
$343$	−0.809017	−	0.587785i	−0.0436828	−	0.0317374i
$344$		0			0
$345$	−5.90208	+	4.28811i	−0.317757	+	0.230864i
$346$		0			0
$347$	−8.10193	−	24.9352i	−0.434934	−	1.33859i	−0.893154	−	0.449751i	$-0.851513\pi$
$347$	−8.10193	−	24.9352i	−0.434934	−	1.33859i	0.458220	−	0.888839i	$-0.348487\pi$
$348$		0			0
$349$	2.14617	+	6.60523i	0.114882	+	0.353570i	0.991922	−	0.126847i	$-0.0404856\pi$
$349$	2.14617	+	6.60523i	0.114882	+	0.353570i	−0.877041	+	0.480416i	$0.840486\pi$
$350$		0			0
$351$	−5.41225	+	16.6572i	−0.288884	+	0.889095i
$352$		0			0
$353$	2.35964	+	7.26221i	0.125591	+	0.386529i	0.994008	−	0.109305i	$-0.0348626\pi$
$353$	2.35964	+	7.26221i	0.125591	+	0.386529i	−0.868418	+	0.495834i	$0.834863\pi$
$354$		0			0
$355$	−0.741270			−0.0393425
$356$		0			0
$357$	2.59212	+	1.88329i	0.137190	+	0.0996742i
$358$		0			0
$359$	2.99447	−	2.17561i	0.158042	−	0.114824i	−0.505954	−	0.862561i	$-0.668859\pi$
$359$	2.99447	−	2.17561i	0.158042	−	0.114824i	0.663996	+	0.747736i	$0.268859\pi$
$360$		0			0
$361$	11.5657	−	8.40298i	0.608722	−	0.442262i
$362$		0			0
$363$	−4.13504	+	12.7263i	−0.217033	+	0.667959i
$364$		0			0
$365$	2.85815	+	2.07657i	0.149602	+	0.108692i
$366$		0			0
$367$	4.76661	−	14.6701i	0.248815	−	0.765773i	−0.746171	−	0.665755i	$-0.768110\pi$
$367$	4.76661	−	14.6701i	0.248815	−	0.765773i	0.994986	−	0.100019i	$-0.0318903\pi$
$368$		0			0
$369$	1.36665	+	37.5550i	0.0711451	+	1.95504i
$370$		0			0
$371$	−0.223529	+	0.687951i	−0.0116050	+	0.0357166i
$372$		0			0
$373$	6.31601	+	4.58885i	0.327031	+	0.237602i	0.739170	−	0.673519i	$-0.235218\pi$
$373$	6.31601	+	4.58885i	0.327031	+	0.237602i	−0.412139	+	0.911121i	$0.635218\pi$
$374$		0			0
$375$	8.48655	−	26.1189i	0.438244	−	1.34878i
$376$		0			0
$377$	2.07997	−	1.51119i	0.107124	−	0.0778302i
$378$		0			0
$379$	10.4907	−	7.62191i	0.538869	−	0.391511i	−0.284796	−	0.958588i	$-0.591926\pi$
$379$	10.4907	−	7.62191i	0.538869	−	0.391511i	0.823665	+	0.567077i	$0.191926\pi$
$380$		0			0
$381$	−44.5349	−	32.3565i	−2.28159	−	1.65767i
$382$		0			0
$383$	−1.23706			−0.0632109			−0.0316055	−	0.999500i	$-0.510062\pi$
$383$	−1.23706			−0.0632109			−0.0316055	+	0.999500i	$0.510062\pi$
$384$		0			0
$385$	0.813571	+	2.50391i	0.0414634	+	0.127611i
$386$		0			0
$387$	18.9718	−	58.3892i	0.964391	−	2.96809i
$388$		0			0
$389$	−5.15023	−	15.8508i	−0.261127	−	0.803667i	−0.992560	−	0.121754i	$-0.961148\pi$
$389$	−5.15023	−	15.8508i	−0.261127	−	0.803667i	0.731433	−	0.681913i	$-0.238852\pi$
$390$		0			0
$391$	0.789085	+	2.42855i	0.0399057	+	0.122817i
$392$		0			0
$393$	−5.49489	+	3.99227i	−0.277181	+	0.201384i
$394$		0			0
$395$	5.57977	+	4.05394i	0.280749	+	0.203976i
$396$		0			0
$397$	−8.62747	+	26.5526i	−0.433000	+	1.33264i	0.462122	+	0.886817i	$0.347088\pi$
$397$	−8.62747	+	26.5526i	−0.433000	+	1.33264i	−0.895122	+	0.445821i	$0.852912\pi$
$398$		0			0
$399$	5.22550	−	3.79655i	0.261602	−	0.190065i
$400$		0			0
$401$	14.1065			0.704447			0.352223	−	0.935916i	$-0.385426\pi$
$401$	14.1065			0.704447			0.352223	+	0.935916i	$0.385426\pi$
$402$		0			0
$403$	−5.98557	−	18.4217i	−0.298162	−	0.917649i
$404$		0			0
$405$	6.54481	+	4.75508i	0.325214	+	0.236282i
$406$		0			0
$407$	2.55574			0.126684
$408$		0			0
$409$	31.2251			1.54398			0.771991	−	0.635633i	$-0.219261\pi$
$409$	31.2251			1.54398			0.771991	+	0.635633i	$0.219261\pi$
$410$		0			0
$411$	−37.7944			−1.86426
$412$		0			0
$413$	−9.30426			−0.457833
$414$		0			0
$415$	−7.05526	−	5.12595i	−0.346329	−	0.251623i
$416$		0			0
$417$	1.39543	+	4.29469i	0.0683345	+	0.210312i
$418$		0			0
$419$	−15.4211			−0.753371			−0.376685	−	0.926341i	$-0.622936\pi$
$419$	−15.4211			−0.753371			−0.376685	+	0.926341i	$0.622936\pi$
$420$		0			0
$421$	2.32957	−	1.69253i	0.113536	−	0.0824889i	−0.529568	−	0.848267i	$-0.677646\pi$
$421$	2.32957	−	1.69253i	0.113536	−	0.0824889i	0.643105	+	0.765778i	$0.277646\pi$
$422$		0			0
$423$	7.09656	−	21.8410i	0.345046	−	1.06194i
$424$		0			0
$425$	−3.42479	−	2.48825i	−0.166126	−	0.120698i
$426$		0			0
$427$	1.31402	−	0.954695i	0.0635901	−	0.0462009i
$428$		0			0
$429$	4.81206	+	14.8100i	0.232328	+	0.715033i
$430$		0			0
$431$	−5.61758	−	17.2891i	−0.270589	−	0.832789i	−0.990353	−	0.138569i	$-0.955750\pi$
$431$	−5.61758	−	17.2891i	−0.270589	−	0.832789i	0.719763	−	0.694219i	$-0.244250\pi$
$432$		0			0
$433$	1.07322	−	3.30302i	0.0515755	−	0.158733i	−0.921951	−	0.387306i	$-0.873406\pi$
$433$	1.07322	−	3.30302i	0.0515755	−	0.158733i	0.973527	+	0.228573i	$0.0734058\pi$
$434$		0			0
$435$	−1.19130	−	3.66644i	−0.0571184	−	0.175792i
$436$		0			0
$437$	5.14770			0.246248
$438$		0			0
$439$	10.9422	+	7.95000i	0.522245	+	0.379433i	0.817449	−	0.576001i	$-0.195388\pi$
$439$	10.9422	+	7.95000i	0.522245	+	0.379433i	−0.295204	+	0.955434i	$0.595388\pi$
$440$		0			0
$441$	−4.74811	+	3.44971i	−0.226101	+	0.164272i
$442$		0			0
$443$	−23.8897	+	17.3569i	−1.13503	+	0.824650i	−0.986420	−	0.164245i	$-0.947481\pi$
$443$	−23.8897	+	17.3569i	−1.13503	+	0.824650i	−0.148614	+	0.988895i	$0.547481\pi$
$444$		0			0
$445$	5.41363	−	16.6614i	0.256631	−	0.789828i
$446$		0			0
$447$	36.9293	+	26.8307i	1.74670	+	1.26905i
$448$		0			0
$449$	−12.8176	+	39.4485i	−0.604900	+	1.86169i	−0.107425	+	0.994213i	$0.534261\pi$
$449$	−12.8176	+	39.4485i	−0.604900	+	1.86169i	−0.497475	+	0.867478i	$0.665739\pi$
$450$		0			0
$451$	10.0747	+	12.8560i	0.474398	+	0.605368i
$452$		0			0
$453$	−6.57864	+	20.2470i	−0.309091	+	0.951285i
$454$		0			0
$455$	−1.71166	−	1.24359i	−0.0802439	−	0.0583006i
$456$		0			0
$457$	10.9300	−	33.6390i	0.511282	−	1.57356i	−0.278664	−	0.960389i	$-0.589892\pi$
$457$	10.9300	−	33.6390i	0.511282	−	1.57356i	0.789946	−	0.613176i	$-0.210108\pi$
$458$		0			0
$459$	7.43678	−	5.40313i	0.347119	−	0.252197i
$460$		0			0
$461$	31.8736	−	23.1575i	1.48450	−	1.07855i	0.508428	−	0.861105i	$-0.330227\pi$
$461$	31.8736	−	23.1575i	1.48450	−	1.07855i	0.976072	−	0.217447i	$-0.0697730\pi$
$462$		0			0
$463$	10.3368	+	7.51015i	0.480394	+	0.349026i	0.801478	−	0.598024i	$-0.204047\pi$
$463$	10.3368	+	7.51015i	0.480394	+	0.349026i	−0.321084	+	0.947051i	$0.604047\pi$
$464$		0			0
$465$	−29.0443			−1.34690
$466$		0			0
$467$	9.37315	+	28.8476i	0.433738	+	1.33491i	0.894375	+	0.447319i	$0.147621\pi$
$467$	9.37315	+	28.8476i	0.433738	+	1.33491i	−0.460637	+	0.887589i	$0.652379\pi$
$468$		0			0
$469$	−1.81065	+	5.57260i	−0.0836080	+	0.257319i
$470$		0			0
$471$	12.6698	+	38.9937i	0.583794	+	1.79673i
$472$		0			0
$473$	−8.24570	−	25.3777i	−0.379138	−	1.16687i
$474$		0			0
$475$	−6.90407	+	5.01610i	−0.316781	+	0.230155i
$476$		0			0
$477$	3.43457	+	2.49536i	0.157258	+	0.114255i
$478$		0			0
$479$	−9.48521	+	29.1925i	−0.433390	+	1.33384i	0.461337	+	0.887225i	$0.347370\pi$
$479$	−9.48521	+	29.1925i	−0.433390	+	1.33384i	−0.894727	+	0.446613i	$0.852630\pi$
$480$		0			0
$481$	−1.66158	+	1.20721i	−0.0757617	+	0.0550441i
$482$		0			0
$483$	−7.06833			−0.321620
$484$		0			0
$485$	−2.21112	−	6.80512i	−0.100402	−	0.309005i
$486$		0			0
$487$	−22.6851	−	16.4817i	−1.02796	−	0.746857i	−0.0600608	−	0.998195i	$-0.519129\pi$
$487$	−22.6851	−	16.4817i	−1.02796	−	0.746857i	−0.967899	+	0.251338i	$0.919129\pi$
$488$		0			0
$489$	−3.20103			−0.144756
$490$		0			0
$491$	26.1986			1.18233			0.591163	−	0.806552i	$-0.298669\pi$
$491$	26.1986			1.18233			0.591163	+	0.806552i	$0.298669\pi$
$492$		0			0
$493$	−1.34937			−0.0607727
$494$		0			0
$495$	15.4517			0.694502
$496$		0			0
$497$	−0.581037	−	0.422148i	−0.0260631	−	0.0189359i
$498$		0			0
$499$	−2.89839	−	8.92031i	−0.129750	−	0.399328i	0.864987	−	0.501794i	$-0.167327\pi$
$499$	−2.89839	−	8.92031i	−0.129750	−	0.399328i	−0.994736	+	0.102466i	$0.967327\pi$
$500$		0			0
$501$	−9.56976			−0.427546
$502$		0			0
$503$	−5.56658	+	4.04436i	−0.248201	+	0.180329i	−0.704929	−	0.709278i	$-0.749021\pi$
$503$	−5.56658	+	4.04436i	−0.248201	+	0.180329i	0.456728	+	0.889606i	$0.349021\pi$
$504$		0			0
$505$	3.42576	−	10.5434i	0.152444	−	0.469175i
$506$		0			0
$507$	21.1972	+	15.4006i	0.941399	+	0.683966i
$508$		0			0
$509$	2.93412	−	2.13176i	0.130052	−	0.0944886i	−0.520857	−	0.853644i	$-0.674388\pi$
$509$	2.93412	−	2.13176i	0.130052	−	0.0944886i	0.650910	+	0.759155i	$0.274388\pi$
$510$		0			0
$511$	1.05774	+	3.25539i	0.0467917	+	0.144010i
$512$		0			0
$513$	−5.72640	−	17.6240i	−0.252827	−	0.778120i
$514$		0			0
$515$	0.00368521	−	0.0113419i	0.000162390	−	0.000499784i
$516$		0			0
$517$	−3.08437	−	9.49272i	−0.135650	−	0.417489i
$518$		0			0
$519$	−4.97593			−0.218419
$520$		0			0
$521$	3.55969	+	2.58627i	0.155953	+	0.113306i	0.663025	−	0.748597i	$-0.269272\pi$
$521$	3.55969	+	2.58627i	0.155953	+	0.113306i	−0.507072	+	0.861904i	$0.669272\pi$
$522$		0			0
$523$	11.1971	−	8.13518i	0.489616	−	0.355727i	−0.315421	−	0.948952i	$-0.602146\pi$
$523$	11.1971	−	8.13518i	0.489616	−	0.355727i	0.805037	+	0.593225i	$0.202146\pi$
$524$		0			0
$525$	9.48002	−	6.88764i	0.413742	−	0.300601i
$526$		0			0
$527$	−3.14150	+	9.66855i	−0.136846	+	0.421168i
$528$		0			0
$529$	14.0500	+	10.2079i	0.610869	+	0.443822i
$530$		0			0
$531$	−16.8744	+	51.9340i	−0.732285	+	2.25374i
$532$		0			0
$533$	−12.6225	−	3.59940i	−0.546741	−	0.155907i
$534$		0			0
$535$	1.14655	−	3.52871i	0.0495695	−	0.152559i
$536$		0			0
$537$	−16.8577	−	12.2478i	−0.727461	−	0.528532i
$538$		0			0
$539$	−0.788251	+	2.42599i	−0.0339524	+	0.104495i
$540$		0			0
$541$	21.3326	−	15.4990i	0.917160	−	0.666356i	−0.0256554	−	0.999671i	$-0.508167\pi$
$541$	21.3326	−	15.4990i	0.917160	−	0.666356i	0.942816	+	0.333315i	$0.108167\pi$
$542$		0			0
$543$	52.3748	−	38.0525i	2.24762	−	1.63299i
$544$		0			0
$545$	0.734609	+	0.533725i	0.0314672	+	0.0228622i
$546$		0			0
$547$	27.5161			1.17650			0.588251	−	0.808679i	$-0.299817\pi$
$547$	27.5161			1.17650			0.588251	+	0.808679i	$0.299817\pi$
$548$		0			0
$549$	−2.94572	−	9.06599i	−0.125720	−	0.386927i
$550$		0			0
$551$	−0.840594	+	2.58708i	−0.0358105	+	0.110213i
$552$		0			0
$553$	2.06496	+	6.35528i	0.0878109	+	0.270254i
$554$		0			0
$555$	0.951667	+	2.92893i	0.0403960	+	0.124326i
$556$		0			0
$557$	32.0498	−	23.2855i	1.35799	−	0.986639i	0.359422	−	0.933175i	$-0.382974\pi$
$557$	32.0498	−	23.2855i	1.35799	−	0.986639i	0.998570	−	0.0534638i	$-0.0170262\pi$
$558$		0			0
$559$	17.3480	+	12.6041i	0.733743	+	0.533095i
$560$		0			0
$561$	2.52559	−	7.77297i	0.106631	−	0.328175i
$562$		0			0
$563$	14.4771	−	10.5183i	0.610139	−	0.443292i	−0.239324	−	0.970940i	$-0.576926\pi$
$563$	14.4771	−	10.5183i	0.610139	−	0.443292i	0.849463	+	0.527648i	$0.176926\pi$
$564$		0			0
$565$	−4.41549			−0.185761
$566$		0			0
$567$	2.42209	+	7.45444i	0.101718	+	0.313057i
$568$		0			0
$569$	21.2775	+	15.4590i	0.892000	+	0.648076i	0.936399	−	0.350938i	$-0.114137\pi$
$569$	21.2775	+	15.4590i	0.892000	+	0.648076i	−0.0443987	+	0.999014i	$0.514137\pi$
$570$		0			0
$571$	−9.60064			−0.401774			−0.200887	−	0.979614i	$-0.564382\pi$
$571$	−9.60064			−0.401774			−0.200887	+	0.979614i	$0.564382\pi$
$572$		0			0
$573$	12.8812			0.538118
$574$		0			0
$575$	9.33887			0.389458
$576$		0			0
$577$	27.6681			1.15184			0.575918	−	0.817507i	$-0.304645\pi$
$577$	27.6681			1.15184			0.575918	+	0.817507i	$0.304645\pi$
$578$		0			0
$579$	57.5649	+	41.8233i	2.39231	+	1.73812i
$580$		0			0
$581$	−2.61100	−	8.03584i	−0.108323	−	0.333383i
$582$		0			0
$583$	1.84516			0.0764186
$584$		0			0
$585$	−10.0457	+	7.29864i	−0.415339	+	0.301762i
$586$		0			0
$587$	−6.01580	+	18.5147i	−0.248299	+	0.764185i	0.746778	+	0.665074i	$0.231600\pi$
$587$	−6.01580	+	18.5147i	−0.248299	+	0.764185i	−0.995076	+	0.0991112i	$0.968400\pi$
$588$		0			0
$589$	16.5800	+	12.0461i	0.683167	+	0.496350i
$590$		0			0
$591$	3.90553	−	2.83753i	0.160652	−	0.116720i
$592$		0			0
$593$	10.4648	+	32.2073i	0.429738	+	1.32260i	0.898384	+	0.439211i	$0.144742\pi$
$593$	10.4648	+	32.2073i	0.429738	+	1.32260i	−0.468646	+	0.883386i	$0.655258\pi$
$594$		0			0
$595$	0.343142	+	1.05608i	0.0140675	+	0.0432952i
$596$		0			0
$597$	−7.29631	+	22.4557i	−0.298618	+	0.919052i
$598$		0			0
$599$	7.07789	+	21.7835i	0.289195	+	0.890050i	0.985110	+	0.171926i	$0.0549990\pi$
$599$	7.07789	+	21.7835i	0.289195	+	0.890050i	−0.695915	+	0.718124i	$0.745001\pi$
$600$		0			0
$601$	46.2319			1.88584			0.942920	−	0.333020i	$-0.108068\pi$
$601$	46.2319			1.88584			0.942920	+	0.333020i	$0.108068\pi$
$602$		0			0
$603$	27.8210	+	20.2131i	1.13296	+	0.823142i
$604$		0			0
$605$	−3.75187	+	2.72590i	−0.152535	+	0.110823i
$606$		0			0
$607$	24.2927	−	17.6497i	0.986012	−	0.716380i	0.0269679	−	0.999636i	$-0.491415\pi$
$607$	24.2927	−	17.6497i	0.986012	−	0.716380i	0.959044	+	0.283257i	$0.0914148\pi$
$608$		0			0
$609$	1.15422	−	3.55234i	0.0467715	−	0.143948i
$610$		0			0
$611$	6.48917	+	4.71465i	0.262524	+	0.190735i
$612$		0			0
$613$	−10.1812	+	31.3345i	−0.411215	+	1.26559i	0.504379	+	0.863483i	$0.331722\pi$
$613$	−10.1812	+	31.3345i	−0.411215	+	1.26559i	−0.915593	+	0.402106i	$0.868278\pi$
$614$		0			0
$615$	−10.9818	+	16.3329i	−0.442830	+	0.658606i
$616$		0			0
$617$	8.82638	−	27.1648i	0.355337	−	1.09361i	−0.600477	−	0.799642i	$-0.705023\pi$
$617$	8.82638	−	27.1648i	0.355337	−	1.09361i	0.955814	−	0.293972i	$-0.0949774\pi$
$618$		0			0
$619$	22.4518	+	16.3122i	0.902413	+	0.655642i	0.939085	−	0.343686i	$-0.111676\pi$
$619$	22.4518	+	16.3122i	0.902413	+	0.655642i	−0.0366715	+	0.999327i	$0.511676\pi$
$620$		0			0
$621$	−6.26655	+	19.2864i	−0.251468	+	0.773938i
$622$		0			0
$623$	13.7320	−	9.97686i	0.550160	−	0.399715i
$624$		0			0
$625$	−8.21613	+	5.96937i	−0.328645	+	0.238775i
$626$		0			0
$627$	−13.3294	−	9.68437i	−0.532324	−	0.386756i
$628$		0			0
$629$	1.07794			0.0429805
$630$		0			0
$631$	−7.46850	−	22.9857i	−0.297316	−	0.915046i	−0.982434	−	0.186613i	$-0.940249\pi$
$631$	−7.46850	−	22.9857i	−0.297316	−	0.915046i	0.685117	−	0.728433i	$-0.259751\pi$
$632$		0			0
$633$	22.8057	−	70.1887i	0.906445	−	2.78975i
$634$		0			0
$635$	−5.89548	−	18.1444i	−0.233955	−	0.720039i
$636$		0			0
$637$	−0.633449	−	1.94956i	−0.0250982	−	0.0772442i
$638$		0			0
$639$	−3.41010	+	2.47758i	−0.134901	+	0.0980116i
$640$		0			0
$641$	−17.2706	−	12.5478i	−0.682148	−	0.495609i	0.191922	−	0.981410i	$-0.438528\pi$
$641$	−17.2706	−	12.5478i	−0.682148	−	0.495609i	−0.874069	+	0.485801i	$0.838528\pi$
$642$		0			0
$643$	0.0791116	−	0.243480i	0.00311986	−	0.00960193i	−0.949484	−	0.313814i	$-0.898393\pi$
$643$	0.0791116	−	0.243480i	0.00311986	−	0.00960193i	0.952604	+	0.304212i	$0.0983932\pi$
$644$		0			0
$645$	26.0129	−	18.8995i	1.02426	−	0.744165i
$646$		0			0
$647$	−18.7089			−0.735524			−0.367762	−	0.929920i	$-0.619876\pi$
$647$	−18.7089			−0.735524			−0.367762	+	0.929920i	$0.619876\pi$
$648$		0			0
$649$	7.33409	+	22.5720i	0.287888	+	0.886029i
$650$		0			0
$651$	−22.7661	−	16.5405i	−0.892273	−	0.648274i
$652$		0			0
$653$	−29.6478			−1.16021			−0.580103	−	0.814543i	$-0.696988\pi$
$653$	−29.6478			−1.16021			−0.580103	+	0.814543i	$0.696988\pi$
$654$		0			0
$655$	−2.35394			−0.0919760
$656$		0			0
$657$	20.0891			0.783749
$658$		0			0
$659$	24.9277			0.971047			0.485523	−	0.874224i	$-0.338629\pi$
$659$	24.9277			0.971047			0.485523	+	0.874224i	$0.338629\pi$
$660$		0			0
$661$	33.9441	+	24.6619i	1.32027	+	0.959235i	0.999929	+	0.0119338i	$0.00379875\pi$
$661$	33.9441	+	24.6619i	1.32027	+	0.959235i	0.320345	+	0.947301i	$0.396201\pi$
$662$		0			0
$663$	2.02960	+	6.24646i	0.0788230	+	0.242592i
$664$		0			0
$665$	2.23853			0.0868067
$666$		0			0
$667$	2.40829	−	1.74972i	0.0932493	−	0.0677496i
$668$		0			0
$669$	−3.20162	+	9.85358i	−0.123782	+	0.380961i
$670$		0			0
$671$	−3.35186	−	2.43527i	−0.129397	−	0.0940125i
$672$		0			0
$673$	−25.0123	+	18.1725i	−0.964154	+	0.700499i	−0.954112	−	0.299450i	$-0.903197\pi$
$673$	−25.0123	+	18.1725i	−0.964154	+	0.700499i	−0.0100425	+	0.999950i	$0.503197\pi$
$674$		0			0
$675$	−10.3887	−	31.9732i	−0.399863	−	1.23065i
$676$		0			0
$677$	10.0153	+	30.8239i	0.384919	+	1.18466i	0.936539	+	0.350563i	$0.114010\pi$
$677$	10.0153	+	30.8239i	0.384919	+	1.18466i	−0.551620	+	0.834095i	$0.685990\pi$
$678$		0			0
$679$	2.14230	−	6.59334i	0.0822141	−	0.253029i
$680$		0			0
$681$	−25.3353	−	77.9741i	−0.970852	−	2.98797i
$682$		0			0
$683$	49.8027			1.90565			0.952823	−	0.303526i	$-0.0981640\pi$
$683$	49.8027			1.90565			0.952823	+	0.303526i	$0.0981640\pi$
$684$		0			0
$685$	−10.5969	−	7.69909i	−0.404886	−	0.294167i
$686$		0			0
$687$	−69.4781	+	50.4788i	−2.65076	+	1.92589i
$688$		0			0
$689$	−1.19960	+	0.871563i	−0.0457013	+	0.0332039i
$690$		0			0
$691$	−7.80436	+	24.0194i	−0.296892	+	0.913739i	0.685688	+	0.727896i	$0.259502\pi$
$691$	−7.80436	+	24.0194i	−0.296892	+	0.913739i	−0.982579	+	0.185843i	$0.940498\pi$
$692$		0			0
$693$	12.1116	+	8.79963i	0.460083	+	0.334270i
$694$		0			0
$695$	−0.483617	+	1.48842i	−0.0183446	+	0.0564590i
$696$		0			0
$697$	4.24923	+	5.42234i	0.160951	+	0.205386i
$698$		0			0
$699$	−20.2477	+	62.3160i	−0.765838	+	2.35701i
$700$		0			0
$701$	−5.66768	−	4.11781i	−0.214065	−	0.155528i	0.475586	−	0.879669i	$-0.342236\pi$
$701$	−5.66768	−	4.11781i	−0.214065	−	0.155528i	−0.689651	+	0.724142i	$0.742236\pi$
$702$		0			0
$703$	0.671507	−	2.06669i	0.0253264	−	0.0779466i
$704$		0			0
$705$	9.73032	−	7.06949i	0.366465	−	0.266253i
$706$		0			0
$707$	8.68963	−	6.31339i	0.326807	−	0.237439i
$708$		0			0
$709$	13.9400	+	10.1280i	0.523530	+	0.380366i	0.817932	−	0.575315i	$-0.195121\pi$
$709$	13.9400	+	10.1280i	0.523530	+	0.380366i	−0.294402	+	0.955682i	$0.595121\pi$
$710$		0			0
$711$	39.2186			1.47081
$712$		0			0
$713$	−6.93036	−	21.3295i	−0.259544	−	0.798795i
$714$		0			0
$715$	−1.66773	+	5.13273i	−0.0623694	+	0.191953i
$716$		0			0
$717$	−19.0723	−	58.6986i	−0.712270	−	2.19214i
$718$		0			0
$719$	−7.43749	−	22.8903i	−0.277372	−	0.853662i	−0.988582	−	0.150683i	$-0.951853\pi$
$719$	−7.43749	−	22.8903i	−0.277372	−	0.853662i	0.711210	−	0.702979i	$-0.248147\pi$
$720$		0			0
$721$	0.00934775	−	0.00679154i	0.000348128	−	0.000252930i
$722$		0			0
$723$	7.18001	+	5.21658i	0.267027	+	0.194007i
$724$		0			0
$725$	−1.52499	+	4.69344i	−0.0566368	+	0.174310i
$726$		0			0
$727$	35.4020	−	25.7211i	1.31299	−	0.953942i	0.312997	−	0.949754i	$-0.398667\pi$
$727$	35.4020	−	25.7211i	1.31299	−	0.953942i	0.999991	−	0.00418726i	$-0.00133285\pi$
$728$		0			0
$729$	−30.3336			−1.12347
$730$		0			0
$731$	−3.47782	−	10.7036i	−0.128632	−	0.395888i
$732$		0			0
$733$	26.6210	+	19.3413i	0.983267	+	0.714386i	0.958436	−	0.285306i	$-0.0920953\pi$
$733$	26.6210	+	19.3413i	0.983267	+	0.714386i	0.0248309	+	0.999692i	$0.492095\pi$
$734$		0			0
$735$	−3.07374			−0.113377
$736$		0			0
$737$	14.9463			0.550554
$738$		0			0
$739$	22.2584			0.818787			0.409394	−	0.912358i	$-0.365740\pi$
$739$	22.2584			0.818787			0.409394	+	0.912358i	$0.365740\pi$
$740$		0			0
$741$	13.2404			0.486396
$742$		0			0
$743$	−23.5527	−	17.1121i	−0.864066	−	0.627780i	0.0649224	−	0.997890i	$-0.479320\pi$
$743$	−23.5527	−	17.1121i	−0.864066	−	0.627780i	−0.928988	+	0.370110i	$0.879320\pi$
$744$		0			0
$745$	4.88865	+	15.0457i	0.179106	+	0.551233i
$746$		0			0
$747$	−49.5893			−1.81438
$748$		0			0
$749$	2.90828	−	2.11299i	0.106266	−	0.0772069i
$750$		0			0
$751$	5.31686	−	16.3636i	0.194015	−	0.597117i	−0.805972	−	0.591954i	$-0.798357\pi$
$751$	5.31686	−	16.3636i	0.194015	−	0.597117i	0.999987	−	0.00516263i	$-0.00164332\pi$
$752$		0			0
$753$	−38.5936	−	28.0399i	−1.40643	−	1.02183i
$754$		0			0
$755$	−5.96904	+	4.33676i	−0.217236	+	0.157831i
$756$		0			0
$757$	9.35572	+	28.7939i	0.340039	+	1.04653i	0.964186	+	0.265227i	$0.0854467\pi$
$757$	9.35572	+	28.7939i	0.340039	+	1.04653i	−0.624147	+	0.781307i	$0.714553\pi$
$758$		0			0
$759$	5.57162	+	17.1477i	0.202237	+	0.622422i
$760$		0			0
$761$	−3.50217	+	10.7786i	−0.126954	+	0.390723i	−0.994252	−	0.107066i	$-0.965855\pi$
$761$	−3.50217	+	10.7786i	−0.126954	+	0.390723i	0.867298	+	0.497789i	$0.165855\pi$
$762$		0			0
$763$	0.271863	+	0.836708i	0.00984210	+	0.0302909i
$764$		0			0
$765$	6.51711			0.235627
$766$		0			0
$767$	−15.4301	−	11.2106i	−0.557148	−	0.404792i
$768$		0			0
$769$	−28.4317	+	20.6568i	−1.02527	+	0.744904i	−0.967357	−	0.253418i	$-0.918445\pi$
$769$	−28.4317	+	20.6568i	−1.02527	+	0.744904i	−0.0579149	+	0.998322i	$0.518445\pi$
$770$		0			0
$771$	11.2400	−	8.16634i	0.404799	−	0.294104i
$772$		0			0
$773$	−7.18182	+	22.1034i	−0.258312	+	0.795003i	0.734847	+	0.678233i	$0.237254\pi$
$773$	−7.18182	+	22.1034i	−0.258312	+	0.795003i	−0.993159	+	0.116770i	$0.962746\pi$
$774$		0			0
$775$	30.0792	+	21.8538i	1.08048	+	0.785011i
$776$		0			0
$777$	−0.922050	+	2.83778i	−0.0330784	+	0.101805i
$778$		0			0
$779$	13.0430	−	4.76897i	0.467315	−	0.170866i
$780$		0			0
$781$	−0.566123	+	1.74235i	−0.0202575	+	0.0623461i
$782$		0			0
$783$	−8.66951	−	6.29877i	−0.309823	−	0.225100i
$784$		0			0
$785$	−4.39100	+	13.5141i	−0.156722	+	0.482340i
$786$		0			0
$787$	−29.1412	+	21.1723i	−1.03877	+	0.754711i	−0.970045	−	0.242924i	$-0.921893\pi$
$787$	−29.1412	+	21.1723i	−1.03877	+	0.754711i	−0.0687258	+	0.997636i	$0.521893\pi$
$788$		0			0
$789$	−21.1367	+	15.3567i	−0.752488	+	0.546714i
$790$		0			0
$791$	−3.46104	−	2.51459i	−0.123060	−	0.0894085i
$792$		0			0
$793$	3.32947			0.118233
$794$		0			0
$795$	0.687070	+	2.11458i	0.0243679	+	0.0749966i
$796$		0			0
$797$	7.21595	−	22.2084i	0.255602	−	0.786662i	−0.738108	−	0.674682i	$-0.764281\pi$
$797$	7.21595	−	22.2084i	0.255602	−	0.786662i	0.993710	−	0.111980i	$-0.0357193\pi$
$798$		0			0
$799$	−1.30090	−	4.00377i	−0.0460227	−	0.141643i
$800$		0			0
$801$	−30.7837	−	94.7425i	−1.08769	−	3.34756i
$802$		0			0
$803$	7.06377	−	5.13213i	0.249275	−	0.181109i
$804$		0			0
$805$	−1.98184	−	1.43989i	−0.0698506	−	0.0507495i
$806$		0			0
$807$	−6.73405	+	20.7253i	−0.237050	+	0.729564i
$808$		0			0
$809$	10.1519	−	7.37576i	0.356920	−	0.259318i	−0.394846	−	0.918747i	$-0.629202\pi$
$809$	10.1519	−	7.37576i	0.356920	−	0.259318i	0.751766	+	0.659430i	$0.229202\pi$
$810$		0			0
$811$	−14.7980			−0.519629			−0.259814	−	0.965659i	$-0.583661\pi$
$811$	−14.7980			−0.519629			−0.259814	+	0.965659i	$0.583661\pi$
$812$		0			0
$813$	−2.25813	−	6.94981i	−0.0791961	−	0.243741i
$814$		0			0
$815$	−0.897513	−	0.652082i	−0.0314385	−	0.0228414i
$816$		0			0
$817$	−22.6880			−0.793753
$818$		0			0
$819$	−12.0307			−0.420388
$820$		0			0
$821$	−40.0259			−1.39691			−0.698457	−	0.715652i	$-0.746130\pi$
$821$	−40.0259			−1.39691			−0.698457	+	0.715652i	$0.746130\pi$
$822$		0			0
$823$	5.01359			0.174763			0.0873814	−	0.996175i	$-0.472150\pi$
$823$	5.01359			0.174763			0.0873814	+	0.996175i	$0.472150\pi$
$824$		0			0
$825$	−24.1820	−	17.5692i	−0.841908	−	0.611682i
$826$		0			0
$827$	1.07640	+	3.31283i	0.0374302	+	0.115198i	0.968026	−	0.250851i	$-0.0807103\pi$
$827$	1.07640	+	3.31283i	0.0374302	+	0.115198i	−0.930596	+	0.366049i	$0.880710\pi$
$828$		0			0
$829$	−28.9345			−1.00494			−0.502468	−	0.864596i	$-0.667575\pi$
$829$	−28.9345			−1.00494			−0.502468	+	0.864596i	$0.667575\pi$
$830$		0			0
$831$	1.76488	−	1.28226i	0.0612229	−	0.0444810i
$832$		0			0
$833$	−0.332463	+	1.02322i	−0.0115192	+	0.0354524i
$834$		0			0
$835$	−2.68320	−	1.94946i	−0.0928558	−	0.0674637i
$836$		0			0
$837$	−65.3156	+	47.4546i	−2.25764	+	1.64027i
$838$		0			0
$839$	−1.70145	−	5.23652i	−0.0587406	−	0.180785i	0.917381	−	0.398011i	$-0.130299\pi$
$839$	−1.70145	−	5.23652i	−0.0587406	−	0.180785i	−0.976121	+	0.217226i	$0.930299\pi$
$840$		0			0
$841$	−8.47539	−	26.0846i	−0.292255	−	0.899468i
$842$		0			0
$843$	16.4098	−	50.5043i	0.565185	−	1.73946i
$844$		0			0
$845$	2.80605	+	8.63614i	0.0965311	+	0.297092i
$846$		0			0
$847$	−4.49324			−0.154390
$848$		0			0
$849$	−19.9334	−	14.4825i	−0.684113	−	0.497037i
$850$		0			0
$851$	−1.92386	+	1.39776i	−0.0659490	+	0.0479147i
$852$		0			0
$853$	21.6283	−	15.7139i	0.740540	−	0.538034i	−0.152340	−	0.988328i	$-0.548681\pi$
$853$	21.6283	−	15.7139i	0.740540	−	0.538034i	0.892880	+	0.450295i	$0.148681\pi$
$854$		0			0
$855$	4.05985	−	12.4949i	0.138844	−	0.427317i
$856$		0			0
$857$	−15.6519	−	11.3717i	−0.534657	−	0.388451i	0.287440	−	0.957799i	$-0.407196\pi$
$857$	−15.6519	−	11.3717i	−0.534657	−	0.388451i	−0.822097	+	0.569348i	$0.807196\pi$
$858$		0			0
$859$	−0.601764	+	1.85204i	−0.0205319	+	0.0631908i	−0.960798	−	0.277251i	$-0.910577\pi$
$859$	−0.601764	+	1.85204i	−0.0205319	+	0.0631908i	0.940266	+	0.340442i	$0.110577\pi$
$860$		0			0
$861$	−17.9094	+	6.54830i	−0.610352	+	0.223165i
$862$		0			0
$863$	−16.6727	+	51.3133i	−0.567546	+	1.74673i	0.0927180	+	0.995692i	$0.470444\pi$
$863$	−16.6727	+	51.3133i	−0.567546	+	1.74673i	−0.660264	+	0.751034i	$0.729556\pi$
$864$		0			0
$865$	−1.39517	−	1.01365i	−0.0474371	−	0.0344650i
$866$		0			0
$867$	−14.5795	+	44.8711i	−0.495146	+	1.52390i
$868$		0			0
$869$	13.7901	−	10.0191i	0.467798	−	0.339875i
$870$		0			0
$871$	−9.71714	+	7.05992i	−0.329253	+	0.239216i
$872$		0			0
$873$	−32.9170	−	23.9156i	−1.11407	−	0.809420i
$874$		0			0
$875$	9.22172			0.311751
$876$		0			0
$877$	2.00066	+	6.15741i	0.0675576	+	0.207921i	0.979136	−	0.203205i	$-0.0651357\pi$
$877$	2.00066	+	6.15741i	0.0675576	+	0.207921i	−0.911579	+	0.411126i	$0.865136\pi$
$878$		0			0
$879$	−19.8331	+	61.0400i	−0.668954	+	2.05883i
$880$		0			0
$881$	−15.2097	−	46.8107i	−0.512429	−	1.57709i	−0.787912	−	0.615788i	$-0.788838\pi$
$881$	−15.2097	−	46.8107i	−0.512429	−	1.57709i	0.275483	−	0.961306i	$-0.411162\pi$
$882$		0			0
$883$	−4.10544	−	12.6352i	−0.138159	−	0.425210i	0.857909	−	0.513802i	$-0.171763\pi$
$883$	−4.10544	−	12.6352i	−0.138159	−	0.425210i	−0.996068	+	0.0885921i	$0.971763\pi$
$884$		0			0
$885$	−23.1370	+	16.8100i	−0.777742	+	0.565063i
$886$		0			0
$887$	20.6495	+	15.0027i	0.693341	+	0.503742i	0.877757	−	0.479107i	$-0.159039\pi$
$887$	20.6495	+	15.0027i	0.693341	+	0.503742i	−0.184416	+	0.982848i	$0.559039\pi$
$888$		0			0
$889$	5.71200	−	17.5797i	0.191574	−	0.589605i
$890$		0			0
$891$	16.1752	−	11.7519i	0.541888	−	0.393705i
$892$		0			0
$893$	−8.48663			−0.283994
$894$		0			0
$895$	−2.23160	−	6.86814i	−0.0745940	−	0.229577i
$896$		0			0
$897$	−11.7221	−	8.51658i	−0.391388	−	0.284360i
$898$		0			0
$899$	11.8513			0.395262
$900$		0			0
$901$	0.778237			0.0259268
$902$		0			0
$903$	31.1530			1.03671
$904$		0			0
$905$	22.4367			0.745820
$906$		0			0
$907$	25.4037	+	18.4569i	0.843516	+	0.612850i	0.923351	−	0.383958i	$-0.125439\pi$
$907$	25.4037	+	18.4569i	0.843516	+	0.612850i	−0.0798345	+	0.996808i	$0.525439\pi$
$908$		0			0
$909$	−19.4800	−	59.9533i	−0.646111	−	1.98853i
$910$		0			0
$911$	−29.1646			−0.966267			−0.483134	−	0.875547i	$-0.660501\pi$
$911$	−29.1646			−0.966267			−0.483134	+	0.875547i	$0.660501\pi$
$912$		0			0
$913$	−17.4367	+	12.6685i	−0.577071	+	0.419267i
$914$		0			0
$915$	1.54275	−	4.74810i	0.0510018	−	0.156967i
$916$		0			0
$917$	−1.84511	−	1.34055i	−0.0609309	−	0.0442689i
$918$		0			0
$919$	16.1409	−	11.7271i	0.532440	−	0.386840i	−0.288830	−	0.957381i	$-0.593266\pi$
$919$	16.1409	−	11.7271i	0.532440	−	0.386840i	0.821270	+	0.570540i	$0.193266\pi$
$920$		0			0
$921$	4.76248	+	14.6574i	0.156929	+	0.482978i
$922$		0			0
$923$	−0.454944	−	1.40017i	−0.0149747	−	0.0460872i
$924$		0			0
$925$	1.21824	−	3.74935i	0.0400554	−	0.123278i
$926$		0			0
$927$	−0.0209554	−	0.0644940i	−0.000688264	−	0.00211826i
$928$		0			0
$929$	−25.2337			−0.827889			−0.413945	−	0.910302i	$-0.635849\pi$
$929$	−25.2337			−0.827889			−0.413945	+	0.910302i	$0.635849\pi$
$930$		0			0
$931$	1.75465	+	1.27483i	0.0575064	+	0.0417808i
$932$		0			0
$933$	−65.9519	+	47.9169i	−2.15917	+	1.56873i
$934$		0			0
$935$	2.29156	−	1.66492i	0.0749421	−	0.0544486i
$936$		0			0
$937$	11.0159	−	33.9034i	0.359873	−	1.10758i	−0.593256	−	0.805014i	$-0.702158\pi$
$937$	11.0159	−	33.9034i	0.359873	−	1.10758i	0.953130	−	0.302562i	$-0.0978420\pi$
$938$		0			0
$939$	60.6903	+	44.0941i	1.98055	+	1.43896i
$940$		0			0
$941$	0.361585	−	1.11285i	0.0117873	−	0.0362777i	−0.944990	−	0.327100i	$-0.893929\pi$
$941$	0.361585	−	1.11285i	0.0117873	−	0.0362777i	0.956777	+	0.290822i	$0.0939287\pi$
$942$		0			0
$943$	−14.6149	−	4.16755i	−0.475927	−	0.135714i
$944$		0			0
$945$	−2.72508	+	8.38693i	−0.0886468	+	0.272827i
$946$		0			0
$947$	−2.91530	−	2.11809i	−0.0947346	−	0.0688287i	0.539410	−	0.842044i	$-0.318647\pi$
$947$	−2.91530	−	2.11809i	−0.0947346	−	0.0688287i	−0.634144	+	0.773215i	$0.718647\pi$
$948$		0			0
$949$	−2.16824	+	6.67317i	−0.0703842	+	0.216620i
$950$		0			0
$951$	0.990659	−	0.719756i	0.0321243	−	0.0233397i
$952$		0			0
$953$	6.54621	−	4.75610i	0.212053	−	0.154065i	−0.476689	−	0.879072i	$-0.658163\pi$
$953$	6.54621	−	4.75610i	0.212053	−	0.154065i	0.688742	+	0.725007i	$0.258163\pi$
$954$		0			0
$955$	3.61165	+	2.62402i	0.116870	+	0.0849113i
$956$		0			0
$957$	−9.52775			−0.307988
$958$		0			0
$959$	−3.92168	−	12.0697i	−0.126638	−	0.389751i
$960$		0			0
$961$	18.0116	−	55.4340i	0.581020	−	1.78819i
$962$		0			0
$963$	−6.51965	−	20.0654i	−0.210093	−	0.646599i
$964$		0			0
$965$	7.62036	+	23.4531i	0.245308	+	0.754981i
$966$		0			0
$967$	47.3072	−	34.3707i	1.52130	−	1.10529i	0.560455	−	0.828185i	$-0.310626\pi$
$967$	47.3072	−	34.3707i	1.52130	−	1.10529i	0.960841	−	0.277101i	$-0.0893736\pi$
$968$		0			0
$969$	−5.62198	−	4.08461i	−0.180604	−	0.131216i
$970$		0			0
$971$	0.299642	−	0.922205i	0.00961598	−	0.0295950i	−0.946133	−	0.323777i	$-0.895047\pi$
$971$	0.299642	−	0.922205i	0.00961598	−	0.0295950i	0.955749	+	0.294182i	$0.0950472\pi$
$972$		0			0
$973$	−1.22672	+	0.891266i	−0.0393269	+	0.0285727i
$974$		0			0
$975$	24.0204			0.769269
$976$		0			0
$977$	11.0565	+	34.0283i	0.353728	+	1.08866i	0.956744	+	0.290932i	$0.0939655\pi$
$977$	11.0565	+	34.0283i	0.353728	+	1.08866i	−0.603016	+	0.797729i	$0.706035\pi$
$978$		0			0
$979$	−35.0280	−	25.4493i	−1.11950	−	0.813364i
$980$		0			0
$981$	5.16334			0.164853
$982$		0			0
$983$	56.4112			1.79924			0.899619	−	0.436676i	$-0.143844\pi$
$983$	56.4112			1.79924			0.899619	+	0.436676i	$0.143844\pi$
$984$		0			0
$985$	1.67308			0.0533086
$986$		0			0
$987$	11.6530			0.370920
$988$		0			0
$989$	20.0863	+	14.5936i	0.638708	+	0.464049i
$990$		0			0
$991$	−10.1614	−	31.2737i	−0.322789	−	0.993441i	−0.972429	−	0.233199i	$-0.925081\pi$
$991$	−10.1614	−	31.2737i	−0.322789	−	0.993441i	0.649640	−	0.760242i	$-0.274919\pi$
$992$		0			0
$993$	10.5945			0.336206
$994$		0			0
$995$	−6.62022	+	4.80987i	−0.209875	+	0.152483i
$996$		0			0
$997$	−18.1664	+	55.9104i	−0.575336	+	1.77070i	0.0596976	+	0.998217i	$0.480986\pi$
$997$	−18.1664	+	55.9104i	−0.575336	+	1.77070i	−0.635033	+	0.772485i	$0.719014\pi$
$998$		0			0
$999$	6.92562	+	5.03176i	0.219117	+	0.159198i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.n.d.57.6	✓	24
41.18	even	5	inner	1148.2.n.d.141.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.n.d.57.6	✓	24	1.1	even	1	trivial
1148.2.n.d.141.6	yes	24	41.18	even	5	inner

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+2.97808 q^{3} +(0.835003 + 0.606666i) q^{5} +(0.309017 + 0.951057i) q^{7} +5.86899 q^{9} +O(q^{10})\)	\(q+2.97808 q^{3} +(0.835003 + 0.606666i) q^{5} +(0.309017 + 0.951057i) q^{7} +5.86899 q^{9} +(2.06367 - 1.49934i) q^{11} +(-0.633449 + 1.94956i) q^{13} +(2.48671 + 1.80670i) q^{15} +(0.870400 - 0.632383i) q^{17} +(-0.670217 - 2.06272i) q^{19} +(0.920279 + 2.83233i) q^{21} +(-0.733436 + 2.25728i) q^{23} +(-1.21590 - 3.74215i) q^{25} +8.54409 q^{27} +(-1.01468 - 0.737207i) q^{29} +(-7.64454 + 5.55408i) q^{31} +(6.14578 - 4.46517i) q^{33} +(-0.318943 + 0.981605i) q^{35} +(0.810574 + 0.588917i) q^{37} +(-1.88646 + 5.80594i) q^{39} +(0.232860 + 6.39889i) q^{41} +(3.23255 - 9.94877i) q^{43} +(4.90063 + 3.56051i) q^{45} +(1.20916 - 3.72142i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(2.59212 - 1.88329i) q^{51} +(0.585206 + 0.425177i) q^{53} +2.63277 q^{55} +(-1.99596 - 6.14294i) q^{57} +(-2.87517 + 8.84888i) q^{59} +(-0.501913 - 1.54473i) q^{61} +(1.81362 + 5.58174i) q^{63} +(-1.71166 + 1.24359i) q^{65} +(4.74034 + 3.44406i) q^{67} +(-2.18424 + 6.72238i) q^{69} +(-0.581037 + 0.422148i) q^{71} +3.42292 q^{73} +(-3.62105 - 11.1444i) q^{75} +(2.06367 + 1.49934i) q^{77} +6.68234 q^{79} +7.83806 q^{81} -8.44938 q^{83} +1.11043 q^{85} +(-3.02180 - 2.19547i) q^{87} +(-5.24515 - 16.1429i) q^{89} -2.04988 q^{91} +(-22.7661 + 16.5405i) q^{93} +(0.691745 - 2.12897i) q^{95} +(-5.60863 - 4.07491i) q^{97} +(12.1116 - 8.79963i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9}+O(q^{10}) \) 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9	\( 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9} + 11 q^{11} - 4 q^{13} + 10 q^{15} + 9 q^{17} - 23 q^{19} + 5 q^{21} + 28 q^{23} - 10 q^{25} - 76 q^{27} + 28 q^{29} - 18 q^{31} - 27 q^{33} - q^{35} - 29 q^{37} - 6 q^{39} + 65 q^{41} - 15 q^{43} - 20 q^{45} - 11 q^{47} - 6 q^{49} - 18 q^{51} + 8 q^{53} - 50 q^{55} + 8 q^{57} + 55 q^{59} - 10 q^{61} - 2 q^{63} - 11 q^{65} + 65 q^{67} - 2 q^{69} - 14 q^{71} + 48 q^{73} - 77 q^{75} + 11 q^{77} + 22 q^{79} + 80 q^{81} - 22 q^{83} - 78 q^{85} - 4 q^{87} + 16 q^{89} - 4 q^{91} - 60 q^{93} + 56 q^{95} + 15 q^{97} + 80 q^{99}+O(q^{100}) \) 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9 + 11 * q^11 - 4 * q^13 + 10 * q^15 + 9 * q^17 - 23 * q^19 + 5 * q^21 + 28 * q^23 - 10 * q^25 - 76 * q^27 + 28 * q^29 - 18 * q^31 - 27 * q^33 - q^35 - 29 * q^37 - 6 * q^39 + 65 * q^41 - 15 * q^43 - 20 * q^45 - 11 * q^47 - 6 * q^49 - 18 * q^51 + 8 * q^53 - 50 * q^55 + 8 * q^57 + 55 * q^59 - 10 * q^61 - 2 * q^63 - 11 * q^65 + 65 * q^67 - 2 * q^69 - 14 * q^71 + 48 * q^73 - 77 * q^75 + 11 * q^77 + 22 * q^79 + 80 * q^81 - 22 * q^83 - 78 * q^85 - 4 * q^87 + 16 * q^89 - 4 * q^91 - 60 * q^93 + 56 * q^95 + 15 * q^97 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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