LMFDB - Embedded newform 496.2.bg.c.81.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [496,2,Mod(49,496)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("496.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(496, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([0, 0, 26])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 496 = 2^{4} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	496.bg (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.96057994026$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			81.1
Root			$-1.42343i$ of defining polynomial
Character	$\chi$	$=$	496.81
Dual form			496.2.bg.c.49.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.824384 + 0.367040i) q^{3} +(-1.85376 + 3.21080i) q^{5} +(-0.510810 + 0.567312i) q^{7} +(-1.46250 - 1.62427i) q^{9} +(-4.02569 - 0.855686i) q^{11} +(0.304152 + 2.89381i) q^{13} +(-2.70670 + 1.96653i) q^{15} +(-1.27993 + 0.272057i) q^{17} +(-0.397160 + 3.77873i) q^{19} +(-0.629330 + 0.280196i) q^{21} +(1.01449 - 3.12228i) q^{23} +(-4.37284 - 7.57398i) q^{25} +(-1.44606 - 4.45052i) q^{27} +(-3.96065 - 2.87758i) q^{29} +(1.63580 + 5.32204i) q^{31} +(-3.00464 - 2.18300i) q^{33} +(-0.874609 - 2.69177i) q^{35} +(5.20639 + 9.01773i) q^{37} +(-0.811405 + 2.49725i) q^{39} +(0.690591 - 0.307471i) q^{41} +(-0.748099 + 7.11768i) q^{43} +(7.92634 - 1.68480i) q^{45} +(-0.708753 + 0.514939i) q^{47} +(0.670783 + 6.38208i) q^{49} +(-1.15501 - 0.245505i) q^{51} +(2.39261 + 2.65727i) q^{53} +(10.2101 - 11.3395i) q^{55} +(-1.71435 + 2.96935i) q^{57} +(-0.847103 - 0.377155i) q^{59} +2.31704 q^{61} +1.66853 q^{63} +(-9.85528 - 4.38785i) q^{65} +(-1.04345 + 1.80731i) q^{67} +(1.98233 - 2.20160i) q^{69} +(5.17645 + 5.74903i) q^{71} +(5.53385 + 1.17626i) q^{73} +(-0.824950 - 7.84887i) q^{75} +(2.54180 - 1.84673i) q^{77} +(-13.7867 + 2.93046i) q^{79} +(-0.243989 + 2.32140i) q^{81} +(12.8880 - 5.73812i) q^{83} +(1.49916 - 4.61393i) q^{85} +(-2.20891 - 3.82595i) q^{87} +(-1.37043 - 4.21776i) q^{89} +(-1.79706 - 1.30564i) q^{91} +(-0.604868 + 4.98781i) q^{93} +(-11.3965 - 8.28005i) q^{95} +(-1.63088 - 5.01933i) q^{97} +(4.49770 + 7.79025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{3} - 3 q^{5} - 2 q^{7} - 10 q^{9} + 7 q^{11} - 7 q^{13} - 14 q^{15} - 6 q^{17} - 16 q^{19} + 9 q^{21} - q^{23} - 13 q^{25} - 9 q^{27} - 14 q^{29} - 15 q^{31} - 13 q^{33} + 9 q^{35} - 8 q^{37}+ \cdots - 6 q^{99}+O(q^{100}) $ 16 * q + 12 * q^3 - 3 * q^5 - 2 * q^7 - 10 * q^9 + 7 * q^11 - 7 * q^13 - 14 * q^15 - 6 * q^17 - 16 * q^19 + 9 * q^21 - q^23 - 13 * q^25 - 9 * q^27 - 14 * q^29 - 15 * q^31 - 13 * q^33 + 9 * q^35 - 8 * q^37 + 3 * q^39 - 8 * q^41 - 23 * q^43 + 65 * q^45 - 14 * q^47 + 2 * q^49 + 42 * q^51 + 6 * q^53 + 7 * q^55 - 17 * q^57 - 4 * q^59 - 60 * q^61 + 46 * q^63 - 12 * q^65 - 13 * q^67 + 38 * q^69 + 14 * q^71 + 2 * q^73 - 13 * q^75 + 18 * q^77 - 18 * q^79 + 23 * q^81 + 16 * q^83 + 37 * q^85 - 15 * q^87 + q^89 - 8 * q^91 + 17 * q^93 + 22 * q^95 + 3 * q^97 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/496\mathbb{Z}\right)^\times$.

$n$	$63$	$65$	$373$
$\chi(n)$	$1$	$e\left(\frac{2}{15}\right)$	$1$

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
$3$	0.824384	+	0.367040i	0.475958	+	0.211910i	0.630673	−	0.776049i	$-0.282779\pi$
$3$	0.824384	+	0.367040i	0.475958	+	0.211910i	−0.154714	+	0.987959i	$0.549446\pi$
$4$		0			0
$5$	−1.85376	+	3.21080i	−0.829026	+	1.43591i	0.0697774	+	0.997563i	$0.477771\pi$
$5$	−1.85376	+	3.21080i	−0.829026	+	1.43591i	−0.898803	+	0.438352i	$0.855562\pi$
$6$		0			0
$7$	−0.510810	+	0.567312i	−0.193068	+	0.214424i	−0.831905	−	0.554919i	$-0.812749\pi$
$7$	−0.510810	+	0.567312i	−0.193068	+	0.214424i	0.638836	+	0.769343i	$0.279416\pi$
$8$		0			0
$9$	−1.46250	−	1.62427i	−0.487500	−	0.541424i
$10$		0			0
$11$	−4.02569	−	0.855686i	−1.21379	−	0.257999i	−0.443842	−	0.896105i	$-0.646385\pi$
$11$	−4.02569	−	0.855686i	−1.21379	−	0.257999i	−0.769948	+	0.638106i	$0.779718\pi$
$12$		0			0
$13$	0.304152	+	2.89381i	0.0843565	+	0.802599i	0.952141	+	0.305658i	$0.0988766\pi$
$13$	0.304152	+	2.89381i	0.0843565	+	0.802599i	−0.867785	+	0.496940i	$0.834457\pi$
$14$		0			0
$15$	−2.70670	+	1.96653i	−0.698867	+	0.507757i
$16$		0			0
$17$	−1.27993	+	0.272057i	−0.310429	+	0.0659836i	−0.360492	−	0.932762i	$-0.617391\pi$
$17$	−1.27993	+	0.272057i	−0.310429	+	0.0659836i	0.0500631	+	0.998746i	$0.484058\pi$
$18$		0			0
$19$	−0.397160	+	3.77873i	−0.0911148	+	0.866900i	0.849538	+	0.527528i	$0.176881\pi$
$19$	−0.397160	+	3.77873i	−0.0911148	+	0.866900i	−0.940652	+	0.339371i	$0.889786\pi$
$20$		0			0
$21$	−0.629330	+	0.280196i	−0.137331	+	0.0611437i
$22$		0			0
$23$	1.01449	−	3.12228i	0.211536	−	0.651040i	−0.787846	−	0.615873i	$-0.788804\pi$
$23$	1.01449	−	3.12228i	0.211536	−	0.651040i	0.999381	−	0.0351674i	$-0.0111964\pi$
$24$		0			0
$25$	−4.37284	−	7.57398i	−0.874568	−	1.51480i
$26$		0			0
$27$	−1.44606	−	4.45052i	−0.278295	−	0.856503i
$28$		0			0
$29$	−3.96065	−	2.87758i	−0.735474	−	0.534353i	0.155816	−	0.987786i	$-0.450199\pi$
$29$	−3.96065	−	2.87758i	−0.735474	−	0.534353i	−0.891290	+	0.453433i	$0.850199\pi$
$30$		0			0
$31$	1.63580	+	5.32204i	0.293799	+	0.955867i
$31$	1.63580	+	5.32204i	0.293799	+	0.955867i
$32$		0			0
$33$	−3.00464	−	2.18300i	−0.523041	−	0.380012i
$34$		0			0
$35$	−0.874609	−	2.69177i	−0.147836	−	0.454992i
$36$		0			0
$37$	5.20639	+	9.01773i	0.855925	+	1.48251i	0.875784	+	0.482704i	$0.160345\pi$
$37$	5.20639	+	9.01773i	0.855925	+	1.48251i	−0.0198583	+	0.999803i	$0.506321\pi$
$38$		0			0
$39$	−0.811405	+	2.49725i	−0.129929	+	0.399880i
$40$		0			0
$41$	0.690591	−	0.307471i	0.107852	−	0.0480189i	−0.352101	−	0.935962i	$-0.614533\pi$
$41$	0.690591	−	0.307471i	0.107852	−	0.0480189i	0.459953	+	0.887943i	$0.347866\pi$
$42$		0			0
$43$	−0.748099	+	7.11768i	−0.114084	+	1.08544i	0.776343	+	0.630311i	$0.217072\pi$
$43$	−0.748099	+	7.11768i	−0.114084	+	1.08544i	−0.890427	+	0.455126i	$0.849594\pi$
$44$		0			0
$45$	7.92634	−	1.68480i	1.18159	−	0.251154i
$46$		0			0
$47$	−0.708753	+	0.514939i	−0.103382	+	0.0751116i	−0.638275	−	0.769808i	$-0.720352\pi$
$47$	−0.708753	+	0.514939i	−0.103382	+	0.0751116i	0.534893	+	0.844920i	$0.320352\pi$
$48$		0			0
$49$	0.670783	+	6.38208i	0.0958262	+	0.911725i
$50$		0			0
$51$	−1.15501	−	0.245505i	−0.161734	−	0.0343776i
$52$		0			0
$53$	2.39261	+	2.65727i	0.328651	+	0.365004i	0.884712	−	0.466138i	$-0.154355\pi$
$53$	2.39261	+	2.65727i	0.328651	+	0.365004i	−0.556062	+	0.831141i	$0.687688\pi$
$54$		0			0
$55$	10.2101	−	11.3395i	1.37673	−	1.52901i
$56$		0			0
$57$	−1.71435	+	2.96935i	−0.227072	+	0.393300i
$58$		0			0
$59$	−0.847103	−	0.377155i	−0.110283	−	0.0491014i	0.350853	−	0.936430i	$-0.385892\pi$
$59$	−0.847103	−	0.377155i	−0.110283	−	0.0491014i	−0.461137	+	0.887329i	$0.652558\pi$
$60$		0			0
$61$	2.31704			0.296666			0.148333	−	0.988937i	$-0.452609\pi$
$61$	2.31704			0.296666			0.148333	+	0.988937i	$0.452609\pi$
$62$		0			0
$63$	1.66853			0.210215
$64$		0			0
$65$	−9.85528	−	4.38785i	−1.22240	−	0.544246i
$66$		0			0
$67$	−1.04345	+	1.80731i	−0.127478	+	0.220798i	−0.922699	−	0.385522i	$-0.874021\pi$
$67$	−1.04345	+	1.80731i	−0.127478	+	0.220798i	0.795221	+	0.606320i	$0.207355\pi$
$68$		0			0
$69$	1.98233	−	2.20160i	0.238644	−	0.265041i
$70$		0			0
$71$	5.17645	+	5.74903i	0.614332	+	0.682284i	0.967383	−	0.253320i	$-0.0815224\pi$
$71$	5.17645	+	5.74903i	0.614332	+	0.682284i	−0.353051	+	0.935604i	$0.614856\pi$
$72$		0			0
$73$	5.53385	+	1.17626i	0.647688	+	0.137670i	0.520030	−	0.854148i	$-0.325921\pi$
$73$	5.53385	+	1.17626i	0.647688	+	0.137670i	0.127658	+	0.991818i	$0.459254\pi$
$74$		0			0
$75$	−0.824950	−	7.84887i	−0.0952570	−	0.906310i
$76$		0			0
$77$	2.54180	−	1.84673i	0.289665	−	0.210454i
$78$		0			0
$79$	−13.7867	+	2.93046i	−1.55113	+	0.329702i	−0.902257	−	0.431198i	$-0.858091\pi$
$79$	−13.7867	+	2.93046i	−1.55113	+	0.329702i	−0.648869	+	0.760900i	$0.724758\pi$
$80$		0			0
$81$	−0.243989	+	2.32140i	−0.0271098	+	0.257933i
$82$		0			0
$83$	12.8880	−	5.73812i	1.41465	−	0.629841i	0.449913	−	0.893072i	$-0.351455\pi$
$83$	12.8880	−	5.73812i	1.41465	−	0.629841i	0.964733	+	0.263231i	$0.0847883\pi$
$84$		0			0
$85$	1.49916	−	4.61393i	0.162606	−	0.500451i
$86$		0			0
$87$	−2.20891	−	3.82595i	−0.236820	−	0.410184i
$88$		0			0
$89$	−1.37043	−	4.21776i	−0.145266	−	0.447081i	0.851780	−	0.523900i	$-0.175524\pi$
$89$	−1.37043	−	4.21776i	−0.145266	−	0.447081i	−0.997045	+	0.0768191i	$0.975524\pi$
$90$		0			0
$91$	−1.79706	−	1.30564i	−0.188383	−	0.136868i
$92$		0			0
$93$	−0.604868	+	4.98781i	−0.0627219	+	0.517212i
$94$		0			0
$95$	−11.3965	−	8.28005i	−1.16926	−	0.849515i
$96$		0			0
$97$	−1.63088	−	5.01933i	−0.165591	−	0.509636i	0.833489	−	0.552537i	$-0.186340\pi$
$97$	−1.63088	−	5.01933i	−0.165591	−	0.509636i	−0.999079	+	0.0429007i	$0.986340\pi$
$98$		0			0
$99$	4.49770	+	7.79025i	0.452036	+	0.782949i
$100$		0			0
$101$	1.17656	−	3.62108i	0.117072	−	0.360311i	−0.875301	−	0.483578i	$-0.839337\pi$
$101$	1.17656	−	3.62108i	0.117072	−	0.360311i	0.992374	+	0.123267i	$0.0393371\pi$
$102$		0			0
$103$	5.70573	−	2.54035i	0.562202	−	0.250308i	−0.105902	−	0.994377i	$-0.533773\pi$
$103$	5.70573	−	2.54035i	0.562202	−	0.250308i	0.668104	+	0.744068i	$0.267106\pi$
$104$		0			0
$105$	0.266972	−	2.54007i	0.0260538	−	0.247885i
$106$		0			0
$107$	2.27653	−	0.483890i	0.220080	−	0.0467795i	−0.0965518	−	0.995328i	$-0.530781\pi$
$107$	2.27653	−	0.483890i	0.220080	−	0.0467795i	0.316632	+	0.948548i	$0.397448\pi$
$108$		0			0
$109$	−1.19478	+	0.868057i	−0.114439	+	0.0831448i	−0.643533	−	0.765419i	$-0.722532\pi$
$109$	−1.19478	+	0.868057i	−0.114439	+	0.0831448i	0.529094	+	0.848563i	$0.322532\pi$
$110$		0			0
$111$	0.982202	+	9.34503i	0.0932265	+	0.886991i
$112$		0			0
$113$	−6.24112	−	1.32659i	−0.587115	−	0.124795i	−0.0952299	−	0.995455i	$-0.530359\pi$
$113$	−6.24112	−	1.32659i	−0.587115	−	0.124795i	−0.491885	+	0.870660i	$0.663692\pi$
$114$		0			0
$115$	8.14440	+	9.04528i	0.759470	+	0.843476i
$116$		0			0
$117$	4.25551	−	4.72623i	0.393422	−	0.436940i
$118$		0			0
$119$	0.499460	−	0.865089i	0.0457854	−	0.0793026i
$120$		0			0
$121$	5.42495	+	2.41534i	0.493178	+	0.219577i
$122$		0			0
$123$	0.682166			0.0615089
$124$		0			0
$125$	13.8872			1.24211
$126$		0			0
$127$	1.30821	+	0.582453i	0.116085	+	0.0516843i	0.463957	−	0.885858i	$-0.346429\pi$
$127$	1.30821	+	0.582453i	0.116085	+	0.0516843i	−0.347872	+	0.937542i	$0.613096\pi$
$128$		0			0
$129$	−3.22919	+	5.59312i	−0.284314	+	0.492447i
$130$		0			0
$131$	−4.21077	+	4.67654i	−0.367897	+	0.408591i	−0.898461	−	0.439054i	$-0.855314\pi$
$131$	−4.21077	+	4.67654i	−0.367897	+	0.408591i	0.530564	+	0.847645i	$0.321980\pi$
$132$		0			0
$133$	−1.94084	−	2.15553i	−0.168293	−	0.186908i
$134$		0			0
$135$	16.9704	+	3.60717i	1.46058	+	0.310456i
$136$		0			0
$137$	−1.33273	−	12.6801i	−0.113863	−	1.08333i	−0.891001	−	0.454001i	$-0.849996\pi$
$137$	−1.33273	−	12.6801i	−0.113863	−	1.08333i	0.777139	−	0.629330i	$-0.216670\pi$
$138$		0			0
$139$	15.1397	−	10.9997i	1.28414	−	0.932979i	0.284466	−	0.958686i	$-0.408184\pi$
$139$	15.1397	−	10.9997i	1.28414	−	0.932979i	0.999670	+	0.0257067i	$0.00818361\pi$
$140$		0			0
$141$	−0.773288	+	0.164367i	−0.0651226	+	0.0138422i
$142$		0			0
$143$	1.25177	−	11.9098i	0.104679	−	0.995950i
$144$		0			0
$145$	16.5814	−	7.38253i	1.37701	−	0.613086i
$146$		0			0
$147$	−1.78949	+	5.50749i	−0.147595	+	0.454250i
$148$		0			0
$149$	10.0677	+	17.4377i	0.824774	+	1.42855i	0.902092	+	0.431545i	$0.142031\pi$
$149$	10.0677	+	17.4377i	0.824774	+	1.42855i	−0.0773172	+	0.997007i	$0.524635\pi$
$150$		0			0
$151$	−4.75035	−	14.6201i	−0.386578	−	1.18977i	−0.935329	−	0.353779i	$-0.884896\pi$
$151$	−4.75035	−	14.6201i	−0.386578	−	1.18977i	0.548751	−	0.835986i	$-0.315104\pi$
$152$		0			0
$153$	2.31379	+	1.68107i	0.187059	+	0.135906i
$154$		0			0
$155$	−20.1204	−	4.61353i	−1.61611	−	0.370568i
$156$		0			0
$157$	−12.2544	−	8.90334i	−0.978008	−	0.710564i	−0.0207452	−	0.999785i	$-0.506604\pi$
$157$	−12.2544	−	8.90334i	−0.978008	−	0.710564i	−0.957262	+	0.289221i	$0.906604\pi$
$158$		0			0
$159$	0.997111	+	3.06879i	0.0790760	+	0.243371i
$160$		0			0
$161$	1.25310	+	2.17042i	0.0987577	+	0.171053i
$162$		0			0
$163$	0.322882	−	0.993730i	0.0252901	−	0.0778349i	−0.937615	−	0.347676i	$-0.886971\pi$
$163$	0.322882	−	0.993730i	0.0252901	−	0.0778349i	0.962905	+	0.269841i	$0.0869710\pi$
$164$		0			0
$165$	12.5791	−	5.60056i	0.979279	−	0.436003i
$166$		0			0
$167$	−1.18006	+	11.2276i	−0.0913161	+	0.868815i	0.848973	+	0.528437i	$0.177222\pi$
$167$	−1.18006	+	11.2276i	−0.0913161	+	0.868815i	−0.940289	+	0.340378i	$0.889445\pi$
$168$		0			0
$169$	4.43428	−	0.942536i	0.341099	−	0.0725028i
$170$		0			0
$171$	6.71853	−	4.88129i	0.513778	−	0.373282i
$172$		0			0
$173$	2.15879	+	20.5395i	0.164130	+	1.56159i	0.698045	+	0.716054i	$0.254054\pi$
$173$	2.15879	+	20.5395i	0.164130	+	1.56159i	−0.533915	+	0.845538i	$0.679280\pi$
$174$		0			0
$175$	6.53050	+	1.38810i	0.493660	+	0.104931i
$176$		0			0
$177$	−0.559908	−	0.621841i	−0.0420853	−	0.0467404i
$178$		0			0
$179$	0.0880993	−	0.0978442i	0.00658485	−	0.00731322i	−0.739843	−	0.672779i	$-0.765100\pi$
$179$	0.0880993	−	0.0978442i	0.00658485	−	0.00731322i	0.746428	+	0.665466i	$0.231767\pi$
$180$		0			0
$181$	−3.86599	+	6.69610i	−0.287357	+	0.497717i	−0.973178	−	0.230053i	$-0.926110\pi$
$181$	−3.86599	+	6.69610i	−0.287357	+	0.497717i	0.685821	+	0.727770i	$0.259443\pi$
$182$		0			0
$183$	1.91013	+	0.850445i	0.141201	+	0.0628667i
$184$		0			0
$185$	−38.6056			−2.83834
$186$		0			0
$187$	5.38539			0.393819
$188$		0			0
$189$	3.26350	+	1.45300i	0.237385	+	0.105690i
$190$		0			0
$191$	−10.5513	+	18.2755i	−0.763468	+	1.32237i	0.177585	+	0.984106i	$0.443172\pi$
$191$	−10.5513	+	18.2755i	−0.763468	+	1.32237i	−0.941053	+	0.338260i	$0.890162\pi$
$192$		0			0
$193$	3.78944	−	4.20860i	0.272770	−	0.302942i	−0.591159	−	0.806555i	$-0.701330\pi$
$193$	3.78944	−	4.20860i	0.272770	−	0.302942i	0.863929	+	0.503613i	$0.167996\pi$
$194$		0			0
$195$	−6.51402	−	7.23456i	−0.466479	−	0.518077i
$196$		0			0
$197$	−15.5670	−	3.30887i	−1.10910	−	0.235747i	−0.383283	−	0.923631i	$-0.625207\pi$
$197$	−15.5670	−	3.30887i	−1.10910	−	0.235747i	−0.725821	+	0.687883i	$0.758540\pi$
$198$		0			0
$199$	−0.445443	−	4.23811i	−0.0315766	−	0.300432i	−0.998900	−	0.0468866i	$-0.985070\pi$
$199$	−0.445443	−	4.23811i	−0.0315766	−	0.300432i	0.967324	−	0.253545i	$-0.0815966\pi$
$200$		0			0
$201$	−1.52356	+	1.10693i	−0.107463	+	0.0780767i
$202$		0			0
$203$	3.65563	−	0.777027i	0.256575	−	0.0545366i
$204$		0			0
$205$	−0.292960	+	2.78733i	−0.0204612	+	0.194675i
$206$		0			0
$207$	−6.55512	+	2.91853i	−0.455612	+	0.202852i
$208$		0			0
$209$	4.83225	−	14.8721i	0.334254	−	1.02873i
$210$		0			0
$211$	−5.75414	−	9.96646i	−0.396131	−	0.686120i	0.597113	−	0.802157i	$-0.296314\pi$
$211$	−5.75414	−	9.96646i	−0.396131	−	0.686120i	−0.993245	+	0.116037i	$0.962981\pi$
$212$		0			0
$213$	2.15726	+	6.63937i	0.147813	+	0.454922i
$214$		0			0
$215$	−21.4667	−	15.5965i	−1.46402	−	1.06367i
$216$		0			0
$217$	−3.85485	−	1.79054i	−0.261684	−	0.121550i
$218$		0			0
$219$	4.13028	+	3.00083i	0.279099	+	0.202777i
$220$		0			0
$221$	−1.17658	−	3.62113i	−0.0791450	−	0.243583i
$222$		0			0
$223$	4.71196	+	8.16135i	0.315536	+	0.546524i	0.979551	−	0.201195i	$-0.0644824\pi$
$223$	4.71196	+	8.16135i	0.315536	+	0.546524i	−0.664015	+	0.747719i	$0.731149\pi$
$224$		0			0
$225$	−5.90692	+	18.1796i	−0.393795	+	1.21197i
$226$		0			0
$227$	−19.8815	+	8.85182i	−1.31958	+	0.587516i	−0.941111	−	0.338097i	$-0.890217\pi$
$227$	−19.8815	+	8.85182i	−1.31958	+	0.587516i	−0.378471	+	0.925613i	$0.623550\pi$
$228$		0			0
$229$	−1.77237	+	16.8630i	−0.117122	+	1.11434i	0.765233	+	0.643754i	$0.222624\pi$
$229$	−1.77237	+	16.8630i	−0.117122	+	1.11434i	−0.882355	+	0.470585i	$0.844043\pi$
$230$		0			0
$231$	2.77324	−	0.589471i	0.182466	−	0.0387844i
$232$		0			0
$233$	7.95758	−	5.78152i	0.521318	−	0.378760i	−0.295782	−	0.955255i	$-0.595580\pi$
$233$	7.95758	−	5.78152i	0.521318	−	0.378760i	0.817100	+	0.576496i	$0.195580\pi$
$234$		0			0
$235$	−0.339512	−	3.23024i	−0.0221473	−	0.210718i
$236$		0			0
$237$	−12.4411	−	2.64445i	−0.808139	−	0.171775i
$238$		0			0
$239$	−0.395212	−	0.438927i	−0.0255641	−	0.0283919i	0.730227	−	0.683204i	$-0.239414\pi$
$239$	−0.395212	−	0.438927i	−0.0255641	−	0.0283919i	−0.755791	+	0.654813i	$0.772748\pi$
$240$		0			0
$241$	10.2848	−	11.4225i	0.662504	−	0.735786i	−0.314440	−	0.949277i	$-0.601817\pi$
$241$	10.2848	−	11.4225i	0.662504	−	0.735786i	0.976945	+	0.213491i	$0.0684836\pi$
$242$		0			0
$243$	−8.07252	+	13.9820i	−0.517852	+	0.896946i
$244$		0			0
$245$	−21.7351	−	9.67707i	−1.38860	−	0.618245i
$246$		0			0
$247$	−11.0557			−0.703459
$248$		0			0
$249$	12.7308			0.806783
$250$		0			0
$251$	5.52832	+	2.46137i	0.348945	+	0.155360i	0.573722	−	0.819050i	$-0.305499\pi$
$251$	5.52832	+	2.46137i	0.348945	+	0.155360i	−0.224778	+	0.974410i	$0.572166\pi$
$252$		0			0
$253$	−6.75571	+	11.7012i	−0.424728	+	0.735650i
$254$		0			0
$255$	2.92938	−	3.25340i	0.183445	−	0.203736i
$256$		0			0
$257$	−3.02972	−	3.36484i	−0.188988	−	0.209893i	0.641203	−	0.767371i	$-0.278436\pi$
$257$	−3.02972	−	3.36484i	−0.188988	−	0.209893i	−0.830192	+	0.557478i	$0.811769\pi$
$258$		0			0
$259$	−7.77535	−	1.65270i	−0.483137	−	0.102694i
$260$		0			0
$261$	1.11848	+	10.6416i	0.0692322	+	0.658700i
$262$		0			0
$263$	−2.02971	+	1.47467i	−0.125157	+	0.0909322i	−0.648603	−	0.761127i	$-0.724646\pi$
$263$	−2.02971	+	1.47467i	−0.125157	+	0.0909322i	0.523445	+	0.852059i	$0.324646\pi$
$264$		0			0
$265$	−12.9673	+	2.75628i	−0.796574	+	0.169317i
$266$		0			0
$267$	0.418321	−	3.98005i	0.0256008	−	0.243575i
$268$		0			0
$269$	12.1865	−	5.42577i	0.743023	−	0.330815i	−7.27860e−5	−	1.00000i	$-0.500023\pi$
$269$	12.1865	−	5.42577i	0.743023	−	0.330815i	0.743096	+	0.669185i	$0.233357\pi$
$270$		0			0
$271$	−4.27190	+	13.1476i	−0.259500	+	0.798658i	0.733410	+	0.679787i	$0.237928\pi$
$271$	−4.27190	+	13.1476i	−0.259500	+	0.798658i	−0.992910	+	0.118871i	$0.962072\pi$
$272$		0			0
$273$	−1.00225	−	1.73594i	−0.0606586	−	0.105064i
$274$		0			0
$275$	11.1227	+	34.2322i	0.670726	+	2.06428i
$276$		0			0
$277$	−9.36093	−	6.80111i	−0.562444	−	0.408639i	0.269909	−	0.962886i	$-0.413006\pi$
$277$	−9.36093	−	6.80111i	−0.562444	−	0.408639i	−0.832353	+	0.554247i	$0.813006\pi$
$278$		0			0
$279$	6.25208	−	10.4405i	0.374302	−	0.625055i
$280$		0			0
$281$	12.4583	+	9.05151i	0.743202	+	0.539968i	0.893712	−	0.448641i	$-0.148092\pi$
$281$	12.4583	+	9.05151i	0.743202	+	0.539968i	−0.150510	+	0.988608i	$0.548092\pi$
$282$		0			0
$283$	7.01336	+	21.5849i	0.416901	+	1.28309i	0.910539	+	0.413422i	$0.135667\pi$
$283$	7.01336	+	21.5849i	0.416901	+	1.28309i	−0.493638	+	0.869667i	$0.664333\pi$
$284$		0			0
$285$	−6.35600	−	11.0089i	−0.376497	−	0.652112i
$286$		0			0
$287$	−0.178329	+	0.548840i	−0.0105264	+	0.0323970i
$288$		0			0
$289$	−13.9661	+	6.21809i	−0.821533	+	0.365770i
$290$		0			0
$291$	0.497822	−	4.73646i	0.0291828	−	0.277656i
$292$		0			0
$293$	−12.1299	+	2.57828i	−0.708635	+	0.150625i	−0.548109	−	0.836407i	$-0.684652\pi$
$293$	−12.1299	+	2.57828i	−0.708635	+	0.150625i	−0.160525	+	0.987032i	$0.551319\pi$
$294$		0			0
$295$	2.78129	−	2.02073i	0.161933	−	0.117651i
$296$		0			0
$297$	2.01314	+	19.1538i	0.116814	+	1.11142i
$298$		0			0
$299$	9.34384	+	1.98610i	0.540368	+	0.114859i
$300$		0			0
$301$	−3.65581	−	4.06019i	−0.210718	−	0.234026i
$302$		0			0
$303$	2.29902	−	2.55332i	0.132075	−	0.146684i
$304$		0			0
$305$	−4.29523	+	7.43956i	−0.245944	+	0.425988i
$306$		0			0
$307$	−28.0641	−	12.4949i	−1.60170	−	0.713124i	−0.605152	−	0.796110i	$-0.706888\pi$
$307$	−28.0641	−	12.4949i	−1.60170	−	0.713124i	−0.996551	+	0.0829855i	$0.973554\pi$
$308$		0			0
$309$	5.63612			0.320628
$310$		0			0
$311$	−2.38141			−0.135037			−0.0675187	−	0.997718i	$-0.521508\pi$
$311$	−2.38141			−0.135037			−0.0675187	+	0.997718i	$0.521508\pi$
$312$		0			0
$313$	9.81659	+	4.37063i	0.554866	+	0.247042i	0.664960	−	0.746879i	$-0.268449\pi$
$313$	9.81659	+	4.37063i	0.554866	+	0.247042i	−0.110094	+	0.993921i	$0.535115\pi$
$314$		0			0
$315$	−3.09305	+	5.35732i	−0.174274	+	0.301851i
$316$		0			0
$317$	5.85245	−	6.49980i	0.328706	−	0.365065i	−0.556026	−	0.831165i	$-0.687674\pi$
$317$	5.85245	−	6.49980i	0.328706	−	0.365065i	0.884732	+	0.466100i	$0.154341\pi$
$318$		0			0
$319$	13.4820	+	14.9733i	0.754849	+	0.838344i
$320$		0			0
$321$	2.05434	+	0.436663i	0.114662	+	0.0243722i
$322$		0			0
$323$	−0.519694	−	4.94456i	−0.0289165	−	0.275122i
$324$		0			0
$325$	20.5877	−	14.9578i	1.14200	−	0.829710i
$326$		0			0
$327$	−1.30357	+	0.277082i	−0.0720874	+	0.0153227i
$328$		0			0
$329$	0.0699070	−	0.665120i	0.00385410	−	0.0366693i
$330$		0			0
$331$	29.5706	−	13.1657i	1.62535	−	0.723652i	0.626889	−	0.779109i	$-0.284328\pi$
$331$	29.5706	−	13.1657i	1.62535	−	0.723652i	0.998461	+	0.0554567i	$0.0176615\pi$
$332$		0			0
$333$	7.03290	−	21.6450i	0.385400	−	1.18614i
$334$		0			0
$335$	−3.86860	−	6.70062i	−0.211364	−	0.366094i
$336$		0			0
$337$	8.57021	+	26.3764i	0.466849	+	1.43681i	0.856642	+	0.515912i	$0.172547\pi$
$337$	8.57021	+	26.3764i	0.466849	+	1.43681i	−0.389792	+	0.920903i	$0.627453\pi$
$338$		0			0
$339$	−4.65817	−	3.38436i	−0.252997	−	0.183813i
$340$		0			0
$341$	−2.03124	−	22.8246i	−0.109998	−	1.23602i
$342$		0			0
$343$	−8.28646	−	6.02047i	−0.447427	−	0.325075i
$344$		0			0
$345$	3.39414	+	10.4461i	0.182735	+	0.562399i
$346$		0			0
$347$	−12.9580	−	22.4440i	−0.695624	−	1.20486i	−0.969970	−	0.243224i	$-0.921795\pi$
$347$	−12.9580	−	22.4440i	−0.695624	−	1.20486i	0.274347	−	0.961631i	$-0.411538\pi$
$348$		0			0
$349$	1.72862	−	5.32015i	0.0925309	−	0.284781i	−0.894071	−	0.447924i	$-0.852163\pi$
$349$	1.72862	−	5.32015i	0.0925309	−	0.284781i	0.986602	+	0.163144i	$0.0521634\pi$
$350$		0			0
$351$	12.4391	−	5.53827i	0.663953	−	0.295611i
$352$		0			0
$353$	−1.21974	+	11.6051i	−0.0649202	+	0.617675i	0.912893	+	0.408198i	$0.133843\pi$
$353$	−1.21974	+	11.6051i	−0.0649202	+	0.617675i	−0.977814	+	0.209477i	$0.932824\pi$
$354$		0			0
$355$	−28.0549	+	5.96325i	−1.48900	+	0.316497i
$356$		0			0
$357$	0.729269	−	0.529845i	0.0385970	−	0.0280424i
$358$		0			0
$359$	2.73863	+	26.0563i	0.144539	+	1.37520i	0.790796	+	0.612080i	$0.209667\pi$
$359$	2.73863	+	26.0563i	0.144539	+	1.37520i	−0.646257	+	0.763120i	$0.723666\pi$
$360$		0			0
$361$	4.46376	+	0.948801i	0.234935	+	0.0499369i
$362$		0			0
$363$	3.58572	+	3.98234i	0.188201	+	0.209019i
$364$		0			0
$365$	−14.0351	+	15.5876i	−0.734633	+	0.815893i
$366$		0			0
$367$	13.5073	−	23.3953i	0.705076	−	1.22123i	−0.261589	−	0.965179i	$-0.584246\pi$
$367$	13.5073	−	23.3953i	0.705076	−	1.22123i	0.966664	−	0.256047i	$-0.0824203\pi$
$368$		0			0
$369$	−1.50941	−	0.672031i	−0.0785765	−	0.0349845i
$370$		0			0
$371$	−2.72967			−0.141717
$372$		0			0
$373$	−12.4058			−0.642351			−0.321175	−	0.947020i	$-0.604078\pi$
$373$	−12.4058			−0.642351			−0.321175	+	0.947020i	$0.604078\pi$
$374$		0			0
$375$	11.4484	+	5.09714i	0.591191	+	0.263215i
$376$		0			0
$377$	7.12253	−	12.3366i	0.366829	−	0.635367i
$378$		0			0
$379$	3.10411	−	3.44746i	0.159447	−	0.177084i	−0.658128	−	0.752906i	$-0.728651\pi$
$379$	3.10411	−	3.44746i	0.159447	−	0.177084i	0.817575	+	0.575822i	$0.195318\pi$
$380$		0			0
$381$	0.864685	+	0.960330i	0.0442991	+	0.0491992i
$382$		0			0
$383$	−4.91161	−	1.04399i	−0.250971	−	0.0533456i	0.0807080	−	0.996738i	$-0.474282\pi$
$383$	−4.91161	−	1.04399i	−0.250971	−	0.0533456i	−0.331679	+	0.943392i	$0.607615\pi$
$384$		0			0
$385$	1.21759	+	11.5846i	0.0620542	+	0.590407i
$386$		0			0
$387$	12.6551	−	9.19450i	0.643297	−	0.467383i
$388$		0			0
$389$	−18.1953	+	3.86754i	−0.922540	+	0.196092i	−0.644612	−	0.764510i	$-0.722981\pi$
$389$	−18.1953	+	3.86754i	−0.922540	+	0.196092i	−0.277928	+	0.960602i	$0.589648\pi$
$390$		0			0
$391$	−0.449036	+	4.27230i	−0.0227087	+	0.216059i
$392$		0			0
$393$	−5.18777	+	2.30974i	−0.261688	+	0.116511i
$394$		0			0
$395$	16.1481	−	49.6988i	0.812500	−	2.50062i
$396$		0			0
$397$	−16.2794	−	28.1968i	−0.817040	−	1.41515i	−0.907854	−	0.419287i	$-0.862280\pi$
$397$	−16.2794	−	28.1968i	−0.817040	−	1.41515i	0.0908142	−	0.995868i	$-0.471053\pi$
$398$		0			0
$399$	−0.808838	−	2.48935i	−0.0404926	−	0.124623i
$400$		0			0
$401$	10.0239	+	7.28282i	0.500572	+	0.363687i	0.809235	−	0.587485i	$-0.199882\pi$
$401$	10.0239	+	7.28282i	0.500572	+	0.363687i	−0.308664	+	0.951171i	$0.599882\pi$
$402$		0			0
$403$	−14.9035	+	6.35242i	−0.742394	+	0.316437i
$404$		0			0
$405$	−7.00125	−	5.08671i	−0.347895	−	0.252760i
$406$		0			0
$407$	−13.2429	−	40.7576i	−0.656429	−	2.02028i
$408$		0			0
$409$	1.72404	+	2.98613i	0.0852484	+	0.147654i	0.905497	−	0.424353i	$-0.139498\pi$
$409$	1.72404	+	2.98613i	0.0852484	+	0.147654i	−0.820249	+	0.572007i	$0.806165\pi$
$410$		0			0
$411$	3.55540	−	10.9424i	0.175375	−	0.539749i
$412$		0			0
$413$	0.646673	−	0.287918i	0.0318207	−	0.0141675i
$414$		0			0
$415$	−5.46732	+	52.0180i	−0.268380	+	2.55347i
$416$		0			0
$417$	16.5183	−	3.51107i	0.808903	−	0.171938i
$418$		0			0
$419$	−32.3988	+	23.5391i	−1.58279	+	1.14996i	−0.669374	+	0.742926i	$0.733437\pi$
$419$	−32.3988	+	23.5391i	−1.58279	+	1.14996i	−0.913412	+	0.407035i	$0.866563\pi$
$420$		0			0
$421$	−2.26664	−	21.5656i	−0.110469	−	1.05104i	−0.899569	−	0.436779i	$-0.856119\pi$
$421$	−2.26664	−	21.5656i	−0.110469	−	1.05104i	0.789100	−	0.614265i	$-0.210548\pi$
$422$		0			0
$423$	1.87295	+	0.398108i	0.0910660	+	0.0193567i
$424$		0			0
$425$	7.65748	+	8.50450i	0.371442	+	0.412529i
$426$		0			0
$427$	−1.18357	+	1.31448i	−0.0572768	+	0.0636124i
$428$		0			0
$429$	5.40332	−	9.35883i	0.260875	−	0.451849i
$430$		0			0
$431$	10.6160	+	4.72655i	0.511355	+	0.227670i	0.646160	−	0.763202i	$-0.276374\pi$
$431$	10.6160	+	4.72655i	0.511355	+	0.227670i	−0.134805	+	0.990872i	$0.543041\pi$
$432$		0			0
$433$	24.5964			1.18203			0.591015	−	0.806661i	$-0.298728\pi$
$433$	24.5964			1.18203			0.591015	+	0.806661i	$0.298728\pi$
$434$		0			0
$435$	16.3791			0.785320
$436$		0			0
$437$	11.3953	+	5.07353i	0.545112	+	0.242700i
$438$		0			0
$439$	9.09662	−	15.7558i	0.434158	−	0.751984i	−0.563068	−	0.826410i	$-0.690379\pi$
$439$	9.09662	−	15.7558i	0.434158	−	0.751984i	0.997227	+	0.0744265i	$0.0237126\pi$
$440$		0			0
$441$	9.38520	−	10.4233i	0.446914	−	0.496349i
$442$		0			0
$443$	−11.8840	−	13.1985i	−0.564625	−	0.627080i	0.391451	−	0.920199i	$-0.371973\pi$
$443$	−11.8840	−	13.1985i	−0.564625	−	0.627080i	−0.956076	+	0.293119i	$0.905307\pi$
$444$		0			0
$445$	16.0828	+	3.41851i	0.762400	+	0.162053i
$446$		0			0
$447$	1.89929	+	18.0706i	0.0898336	+	0.854709i
$448$		0			0
$449$	7.44180	−	5.40679i	0.351200	−	0.255162i	−0.398172	−	0.917311i	$-0.630355\pi$
$449$	7.44180	−	5.40679i	0.351200	−	0.255162i	0.749372	+	0.662149i	$0.230355\pi$
$450$		0			0
$451$	−3.04320	+	0.646852i	−0.143299	+	0.0304591i
$452$		0			0
$453$	1.45003	−	13.7961i	0.0681284	−	0.648199i
$454$		0			0
$455$	7.52346	−	3.34966i	0.352705	−	0.157035i
$456$		0			0
$457$	−9.64130	+	29.6729i	−0.451001	+	1.38804i	0.424766	+	0.905303i	$0.360356\pi$
$457$	−9.64130	+	29.6729i	−0.451001	+	1.38804i	−0.875767	+	0.482735i	$0.839644\pi$
$458$		0			0
$459$	3.06166	+	5.30294i	0.142906	+	0.247520i
$460$		0			0
$461$	−2.06067	−	6.34209i	−0.0959750	−	0.295381i	0.891532	−	0.452959i	$-0.149631\pi$
$461$	−2.06067	−	6.34209i	−0.0959750	−	0.295381i	−0.987507	+	0.157578i	$0.949631\pi$
$462$		0			0
$463$	28.5732	+	20.7597i	1.32791	+	0.964784i	0.999797	+	0.0201457i	$0.00641301\pi$
$463$	28.5732	+	20.7597i	1.32791	+	0.964784i	0.328114	+	0.944638i	$0.393587\pi$
$464$		0			0
$465$	−14.8936	−	11.1883i	−0.690675	−	0.518846i
$466$		0			0
$467$	29.0789	+	21.1270i	1.34561	+	0.977642i	0.999218	+	0.0395520i	$0.0125931\pi$
$467$	29.0789	+	21.1270i	1.34561	+	0.977642i	0.346391	+	0.938090i	$0.387407\pi$
$468$		0			0
$469$	−0.492303	−	1.51515i	−0.0227324	−	0.0699632i
$470$		0			0
$471$	−6.83446	−	11.8376i	−0.314915	−	0.545449i
$472$		0			0
$473$	9.10211	−	28.0134i	0.418516	−	1.28806i
$474$		0			0
$475$	30.3567	−	13.5157i	1.39286	−	0.620142i
$476$		0			0
$477$	0.816923	−	7.77251i	0.0374043	−	0.355879i
$478$		0			0
$479$	32.5179	−	6.91190i	1.48578	−	0.315813i	0.607640	−	0.794212i	$-0.292116\pi$
$479$	32.5179	−	6.91190i	1.48578	−	0.315813i	0.878142	+	0.478400i	$0.158783\pi$
$480$		0			0
$481$	−24.5121	+	17.8091i	−1.11765	+	0.812024i
$482$		0			0
$483$	0.236400	+	2.24920i	0.0107566	+	0.102342i
$484$		0			0
$485$	19.1393	+	4.06819i	0.869073	+	0.184727i
$486$		0			0
$487$	−19.0805	−	21.1910i	−0.864620	−	0.960258i	0.134912	−	0.990858i	$-0.456925\pi$
$487$	−19.0805	−	21.1910i	−0.864620	−	0.960258i	−0.999532	+	0.0305999i	$0.990258\pi$
$488$		0			0
$489$	0.630917	−	0.700705i	0.0285311	−	0.0316870i
$490$		0			0
$491$	−13.9818	+	24.2172i	−0.630991	+	1.09291i	0.356359	+	0.934349i	$0.384018\pi$
$491$	−13.9818	+	24.2172i	−0.630991	+	1.09291i	−0.987350	+	0.158559i	$0.949315\pi$
$492$		0			0
$493$	5.85222	+	2.60558i	0.263571	+	0.117349i
$494$		0			0
$495$	−33.3506			−1.49900
$496$		0			0
$497$	−5.90568			−0.264906
$498$		0			0
$499$	37.7340	+	16.8002i	1.68920	+	0.752082i	0.999611	+	0.0278849i	$0.00887720\pi$
$499$	37.7340	+	16.8002i	1.68920	+	0.752082i	0.689593	+	0.724197i	$0.257789\pi$
$500$		0			0
$501$	−5.09378	+	8.82269i	−0.227573	+	0.394169i
$502$		0			0
$503$	17.1204	−	19.0141i	0.763361	−	0.847798i	−0.228708	−	0.973495i	$-0.573450\pi$
$503$	17.1204	−	19.0141i	0.763361	−	0.847798i	0.992069	+	0.125697i	$0.0401167\pi$
$504$		0			0
$505$	9.44552	+	10.4903i	0.420320	+	0.466813i
$506$		0			0
$507$	4.00150	+	0.850545i	0.177713	+	0.0377741i
$508$		0			0
$509$	2.55758	+	24.3337i	0.113363	+	1.07857i	0.892291	+	0.451461i	$0.149097\pi$
$509$	2.55758	+	24.3337i	0.113363	+	1.07857i	−0.778928	+	0.627113i	$0.784236\pi$
$510$		0			0
$511$	−3.49405	+	2.53858i	−0.154568	+	0.112300i
$512$		0			0
$513$	17.3916	−	3.69670i	0.767859	−	0.163213i
$514$		0			0
$515$	−2.42046	+	23.0292i	−0.106658	+	1.01479i
$516$		0			0
$517$	3.29384	−	1.46651i	0.144863	−	0.0644972i
$518$		0			0
$519$	−5.75915	+	17.7248i	−0.252799	+	0.778034i
$520$		0			0
$521$	−7.48279	−	12.9606i	−0.327827	−	0.567813i	0.654253	−	0.756275i	$-0.272983\pi$
$521$	−7.48279	−	12.9606i	−0.327827	−	0.567813i	−0.982080	+	0.188462i	$0.939650\pi$
$522$		0			0
$523$	6.47873	+	19.9395i	0.283295	+	0.871893i	0.986904	+	0.161306i	$0.0515706\pi$
$523$	6.47873	+	19.9395i	0.283295	+	0.871893i	−0.703609	+	0.710587i	$0.748429\pi$
$524$		0			0
$525$	4.87415	+	3.54128i	0.212726	+	0.154554i
$526$		0			0
$527$	−3.54162	−	6.36681i	−0.154275	−	0.277342i
$528$		0			0
$529$	9.88796	+	7.18402i	0.429911	+	0.312349i
$530$		0			0
$531$	0.626287	+	1.92751i	0.0271786	+	0.0836470i
$532$		0			0
$533$	1.09981	+	1.90492i	0.0476379	+	0.0825113i
$534$		0			0
$535$	−2.66645	+	8.20649i	−0.115281	+	0.354798i
$536$		0			0
$537$	0.108540	−	0.0483253i	0.00468386	−	0.00208539i
$538$		0			0
$539$	2.76069	−	26.2662i	0.118911	−	1.13137i
$540$		0			0
$541$	−1.69347	+	0.359958i	−0.0728079	+	0.0154758i	−0.244172	−	0.969732i	$-0.578516\pi$
$541$	−1.69347	+	0.359958i	−0.0728079	+	0.0154758i	0.171364	+	0.985208i	$0.445183\pi$
$542$		0			0
$543$	−5.64480	+	4.10118i	−0.242241	+	0.175999i
$544$		0			0
$545$	−0.572331	−	5.44536i	−0.0245160	−	0.233254i
$546$		0			0
$547$	−12.8347	−	2.72810i	−0.548772	−	0.116645i	−0.0748220	−	0.997197i	$-0.523839\pi$
$547$	−12.8347	−	2.72810i	−0.548772	−	0.116645i	−0.473950	+	0.880552i	$0.657172\pi$
$548$		0			0
$549$	−3.38867	−	3.76350i	−0.144625	−	0.160622i
$550$		0			0
$551$	12.4466	−	13.8234i	0.530243	−	0.588895i
$552$		0			0
$553$	5.37991	−	9.31828i	0.228777	−	0.396254i
$554$		0			0
$555$	−31.8258	−	14.1698i	−1.35093	−	0.601473i
$556$		0			0
$557$	−28.0246			−1.18744			−0.593721	−	0.804671i	$-0.702342\pi$
$557$	−28.0246			−1.18744			−0.593721	+	0.804671i	$0.702342\pi$
$558$		0			0
$559$	−20.8248			−0.880794
$560$		0			0
$561$	4.43963	+	1.97665i	0.187441	+	0.0834543i
$562$		0			0
$563$	11.3259	−	19.6171i	0.477331	−	0.826762i	−0.522331	−	0.852743i	$-0.674938\pi$
$563$	11.3259	−	19.6171i	0.477331	−	0.826762i	0.999662	+	0.0259808i	$0.00827088\pi$
$564$		0			0
$565$	15.8289	−	17.5798i	0.665928	−	0.739589i
$566$		0			0
$567$	−1.19232	−	1.32421i	−0.0500729	−	0.0556116i
$568$		0			0
$569$	45.4271	+	9.65584i	1.90441	+	0.404794i	0.999771	−	0.0213953i	$-0.00681086\pi$
$569$	45.4271	+	9.65584i	1.90441	+	0.404794i	0.904634	+	0.426189i	$0.140144\pi$
$570$		0			0
$571$	−1.30643	−	12.4299i	−0.0546726	−	0.520175i	−0.987247	−	0.159197i	$-0.949110\pi$
$571$	−1.30643	−	12.4299i	−0.0546726	−	0.520175i	0.932574	−	0.360978i	$-0.117557\pi$
$572$		0			0
$573$	−15.4062	+	11.1932i	−0.643602	+	0.467604i
$574$		0			0
$575$	−28.0843	+	5.96950i	−1.17120	+	0.248945i
$576$		0			0
$577$	3.18648	−	30.3173i	0.132655	−	1.26213i	−0.702330	−	0.711852i	$-0.747857\pi$
$577$	3.18648	−	30.3173i	0.132655	−	1.26213i	0.834984	−	0.550274i	$-0.185477\pi$
$578$		0			0
$579$	4.66868	−	2.07863i	0.194024	−	0.0863850i
$580$		0			0
$581$	−3.32803	+	10.2426i	−0.138070	+	0.424936i
$582$		0			0
$583$	−7.35812	−	12.7446i	−0.304742	−	0.527829i
$584$		0			0
$585$	7.28629	+	22.4249i	0.301251	+	0.927155i
$586$		0			0
$587$	27.2300	+	19.7837i	1.12390	+	0.816562i	0.984796	−	0.173716i	$-0.0555774\pi$
$587$	27.2300	+	19.7837i	1.12390	+	0.816562i	0.139105	+	0.990278i	$0.455577\pi$
$588$		0			0
$589$	−20.7602	+	4.06756i	−0.855410	+	0.167601i
$590$		0			0
$591$	−11.6187	−	8.44150i	−0.477930	−	0.347237i
$592$		0			0
$593$	−13.8711	−	42.6909i	−0.569619	−	1.75311i	−0.653812	−	0.756657i	$-0.726831\pi$
$593$	−13.8711	−	42.6909i	−0.569619	−	1.75311i	0.0841933	−	0.996449i	$-0.473169\pi$
$594$		0			0
$595$	1.85175	+	3.20733i	0.0759145	+	0.131488i
$596$		0			0
$597$	1.18834	−	3.65733i	0.0486354	−	0.149684i
$598$		0			0
$599$	17.8914	−	7.96578i	0.731024	−	0.325473i	−0.00724987	−	0.999974i	$-0.502308\pi$
$599$	17.8914	−	7.96578i	0.731024	−	0.325473i	0.738274	+	0.674501i	$0.235641\pi$
$600$		0			0
$601$	−3.18388	+	30.2926i	−0.129873	+	1.23566i	0.714396	+	0.699742i	$0.246702\pi$
$601$	−3.18388	+	30.2926i	−0.129873	+	1.23566i	−0.844269	+	0.535919i	$0.819965\pi$
$602$		0			0
$603$	4.46160	−	0.948342i	0.181690	−	0.0386195i
$604$		0			0
$605$	−17.8117	+	12.9410i	−0.724150	+	0.526126i
$606$		0			0
$607$	−1.39802	−	13.3013i	−0.0567440	−	0.539883i	−0.985558	−	0.169337i	$-0.945837\pi$
$607$	−1.39802	−	13.3013i	−0.0567440	−	0.539883i	0.928814	−	0.370546i	$-0.120829\pi$
$608$		0			0
$609$	3.29884	+	0.701190i	0.133676	+	0.0284137i
$610$		0			0
$611$	−1.70570	−	1.89438i	−0.0690054	−	0.0766383i
$612$		0			0
$613$	−3.47627	+	3.86079i	−0.140405	+	0.155936i	−0.809246	−	0.587470i	$-0.800124\pi$
$613$	−3.47627	+	3.86079i	−0.140405	+	0.155936i	0.668841	+	0.743406i	$0.266791\pi$
$614$		0			0
$615$	−1.26457	+	2.19030i	−0.0509924	+	0.0883215i
$616$		0			0
$617$	−27.4183	−	12.2074i	−1.10382	−	0.491452i	−0.227790	−	0.973710i	$-0.573150\pi$
$617$	−27.4183	−	12.2074i	−1.10382	−	0.491452i	−0.876029	+	0.482258i	$0.839817\pi$
$618$		0			0
$619$	−18.3260			−0.736584			−0.368292	−	0.929710i	$-0.620057\pi$
$619$	−18.3260			−0.736584			−0.368292	+	0.929710i	$0.620057\pi$
$620$		0			0
$621$	−15.3628			−0.616487
$622$		0			0
$623$	3.09282	+	1.37701i	0.123911	+	0.0551687i
$624$		0			0
$625$	−3.87924	+	6.71905i	−0.155170	+	0.268762i
$626$		0			0
$627$	9.44229	−	10.4867i	0.377089	−	0.418799i
$628$		0			0
$629$	−9.11716	−	10.1256i	−0.363525	−	0.403735i
$630$		0			0
$631$	10.1094	+	2.14881i	0.402447	+	0.0855428i	0.404688	−	0.914455i	$-0.367380\pi$
$631$	10.1094	+	2.14881i	0.402447	+	0.0855428i	−0.00224100	+	0.999997i	$0.500713\pi$
$632$		0			0
$633$	−1.08554	−	10.3282i	−0.0431462	−	0.410509i
$634$		0			0
$635$	−4.29525	+	3.12068i	−0.170452	+	0.123840i
$636$		0			0
$637$	−18.2645	+	3.88224i	−0.723666	+	0.153820i
$638$		0			0
$639$	1.76742	−	16.8159i	0.0699182	−	0.665228i
$640$		0			0
$641$	0.0924983	−	0.0411829i	0.00365346	−	0.00162663i	−0.404909	−	0.914357i	$-0.632697\pi$
$641$	0.0924983	−	0.0411829i	0.00365346	−	0.00162663i	0.408563	+	0.912730i	$0.366030\pi$
$642$		0			0
$643$	4.23719	−	13.0407i	0.167098	−	0.514276i	−0.832086	−	0.554646i	$-0.812854\pi$
$643$	4.23719	−	13.0407i	0.167098	−	0.514276i	0.999185	+	0.0403701i	$0.0128537\pi$
$644$		0			0
$645$	−11.9723	−	20.7366i	−0.471408	−	0.816503i
$646$		0			0
$647$	3.34800	+	10.3041i	0.131624	+	0.405096i	0.995050	−	0.0993798i	$-0.0316859\pi$
$647$	3.34800	+	10.3041i	0.131624	+	0.405096i	−0.863426	+	0.504476i	$0.831686\pi$
$648$		0			0
$649$	3.08745	+	2.24316i	0.121193	+	0.0880518i
$650$		0			0
$651$	−2.52067	−	2.89098i	−0.0987930	−	0.113306i
$652$		0			0
$653$	19.6204	+	14.2551i	0.767807	+	0.557844i	0.901295	−	0.433206i	$-0.142618\pi$
$653$	19.6204	+	14.2551i	0.767807	+	0.557844i	−0.133488	+	0.991050i	$0.542618\pi$
$654$		0			0
$655$	−7.20968	−	22.1891i	−0.281706	−	0.867001i
$656$		0			0
$657$	−6.18270	−	10.7087i	−0.241210	−	0.417788i
$658$		0			0
$659$	2.63699	−	8.11583i	0.102723	−	0.316148i	−0.886467	−	0.462793i	$-0.846847\pi$
$659$	2.63699	−	8.11583i	0.102723	−	0.316148i	0.989189	+	0.146645i	$0.0468474\pi$
$660$		0			0
$661$	34.6089	−	15.4089i	1.34613	−	0.599337i	0.398050	−	0.917364i	$-0.369687\pi$
$661$	34.6089	−	15.4089i	1.34613	−	0.599337i	0.948082	+	0.318027i	$0.103020\pi$
$662$		0			0
$663$	0.359146	−	3.41705i	0.0139481	−	0.132707i
$664$		0			0
$665$	10.5188	−	2.23585i	0.407903	−	0.0867024i
$666$		0			0
$667$	−13.0026	+	9.44697i	−0.503464	+	0.365788i
$668$		0			0
$669$	0.888925	+	8.45756i	0.0343678	+	0.326988i
$670$		0			0
$671$	−9.32767	−	1.98266i	−0.360091	−	0.0765397i
$672$		0			0
$673$	4.76428	+	5.29127i	0.183650	+	0.203963i	0.827939	−	0.560818i	$-0.189513\pi$
$673$	4.76428	+	5.29127i	0.183650	+	0.203963i	−0.644289	+	0.764782i	$0.722847\pi$
$674$		0			0
$675$	−27.3848	+	30.4139i	−1.05404	+	1.17063i
$676$		0			0
$677$	−24.0305	+	41.6220i	−0.923567	+	1.59966i	−0.129716	+	0.991551i	$0.541407\pi$
$677$	−24.0305	+	41.6220i	−0.923567	+	1.59966i	−0.793850	+	0.608113i	$0.791927\pi$
$678$		0			0
$679$	3.68060	+	1.63871i	0.141248	+	0.0628879i
$680$		0			0
$681$	−19.6390			−0.752567
$682$		0			0
$683$	−32.5731			−1.24638			−0.623188	−	0.782072i	$-0.714163\pi$
$683$	−32.5731			−1.24638			−0.623188	+	0.782072i	$0.714163\pi$
$684$		0			0
$685$	43.1837	+	19.2266i	1.64997	+	0.734612i
$686$		0			0
$687$	−7.65051	+	13.2511i	−0.291885	+	0.505560i
$688$		0			0
$689$	−6.96191	+	7.73198i	−0.265228	+	0.294565i
$690$		0			0
$691$	−18.2359	−	20.2530i	−0.693725	−	0.770460i	0.288639	−	0.957438i	$-0.406797\pi$
$691$	−18.2359	−	20.2530i	−0.693725	−	0.770460i	−0.982364	+	0.186978i	$0.940131\pi$
$692$		0			0
$693$	−6.71698	−	1.42774i	−0.255157	−	0.0542353i
$694$		0			0
$695$	7.25234	+	69.0014i	0.275097	+	2.61737i
$696$		0			0
$697$	−0.800258	+	0.581421i	−0.0303119	+	0.0220229i
$698$		0			0
$699$	8.68215	−	1.84545i	0.328389	−	0.0698012i
$700$		0			0
$701$	−0.887358	+	8.44265i	−0.0335150	+	0.318874i	0.964901	+	0.262614i	$0.0845845\pi$
$701$	−0.887358	+	8.44265i	−0.0335150	+	0.318874i	−0.998416	+	0.0562607i	$0.982082\pi$
$702$		0			0
$703$	−36.1433	+	16.0920i	−1.36317	+	0.606923i
$704$		0			0
$705$	0.905737	−	2.78757i	0.0341120	−	0.104986i
$706$		0			0
$707$	1.45328	+	2.51716i	0.0546564	+	0.0946676i
$708$		0			0
$709$	−7.22670	−	22.2415i	−0.271404	−	0.835297i	−0.990148	−	0.140022i	$-0.955283\pi$
$709$	−7.22670	−	22.2415i	−0.271404	−	0.835297i	0.718744	−	0.695275i	$-0.244717\pi$
$710$		0			0
$711$	24.9229	+	18.1076i	0.934683	+	0.679087i
$712$		0			0
$713$	18.2764	+	0.291720i	0.684457	+	0.0109250i
$714$		0			0
$715$	35.9197	+	26.0972i	1.34332	+	0.975978i
$716$		0			0
$717$	−0.164703	−	0.506903i	−0.00615094	−	0.0189306i
$718$		0			0
$719$	6.48843	+	11.2383i	0.241978	+	0.419118i	0.961278	−	0.275582i	$-0.0888706\pi$
$719$	6.48843	+	11.2383i	0.241978	+	0.419118i	−0.719300	+	0.694700i	$0.755537\pi$
$720$		0			0
$721$	−1.47337	+	4.53457i	−0.0548712	+	0.168876i
$722$		0			0
$723$	12.6712	−	5.64156i	0.471245	−	0.209812i
$724$		0			0
$725$	−4.47545	+	42.5811i	−0.166214	+	1.58142i
$726$		0			0
$727$	−12.1515	+	2.58289i	−0.450676	+	0.0957941i	−0.427657	−	0.903941i	$-0.640661\pi$
$727$	−12.1515	+	2.58289i	−0.450676	+	0.0957941i	−0.0230186	+	0.999735i	$0.507328\pi$
$728$		0			0
$729$	−6.12163	+	4.44762i	−0.226727	+	0.164727i
$730$		0			0
$731$	−0.978905	−	9.31366i	−0.0362061	−	0.344478i
$732$		0			0
$733$	33.4109	+	7.10171i	1.23406	+	0.262308i	0.778356	−	0.627823i	$-0.216054\pi$
$733$	33.4109	+	7.10171i	1.23406	+	0.262308i	0.455705	+	0.890131i	$0.349387\pi$
$734$		0			0
$735$	−14.3662	−	15.9553i	−0.529904	−	0.588518i
$736$		0			0
$737$	5.74708	−	6.38278i	0.211697	−	0.235113i
$738$		0			0
$739$	−6.18747	+	10.7170i	−0.227610	+	0.394231i	−0.957099	−	0.289761i	$-0.906424\pi$
$739$	−6.18747	+	10.7170i	−0.227610	+	0.394231i	0.729490	+	0.683992i	$0.239758\pi$
$740$		0			0
$741$	−9.11416	−	4.05789i	−0.334817	−	0.149070i
$742$		0			0
$743$	16.2455			0.595990			0.297995	−	0.954567i	$-0.403682\pi$
$743$	16.2455			0.595990			0.297995	+	0.954567i	$0.403682\pi$
$744$		0			0
$745$	−74.6520			−2.73504
$746$		0			0
$747$	−28.1690	−	12.5417i	−1.03065	−	0.458875i
$748$		0			0
$749$	−0.888356	+	1.53868i	−0.0324598	+	0.0562220i
$750$		0			0
$751$	7.21876	−	8.01725i	0.263416	−	0.292554i	−0.596898	−	0.802317i	$-0.703600\pi$
$751$	7.21876	−	8.01725i	0.263416	−	0.292554i	0.860315	+	0.509763i	$0.170267\pi$
$752$		0			0
$753$	3.65404	+	4.05823i	0.133161	+	0.147890i
$754$		0			0
$755$	55.7482	+	11.8496i	2.02888	+	0.431253i
$756$		0			0
$757$	−4.29629	−	40.8765i	−0.156151	−	1.48568i	−0.739333	−	0.673340i	$-0.764859\pi$
$757$	−4.29629	−	40.8765i	−0.156151	−	1.48568i	0.583181	−	0.812342i	$-0.301808\pi$
$758$		0			0
$759$	−9.86411	+	7.16670i	−0.358045	+	0.260135i
$760$		0			0
$761$	−19.2309	+	4.08765i	−0.697119	+	0.148177i	−0.542823	−	0.839847i	$-0.682644\pi$
$761$	−19.2309	+	4.08765i	−0.697119	+	0.148177i	−0.154296	+	0.988025i	$0.549311\pi$
$762$		0			0
$763$	0.117845	−	1.12122i	0.00426629	−	0.0405911i
$764$		0			0
$765$	−9.68679	+	4.31284i	−0.350227	+	0.155931i
$766$		0			0
$767$	0.833766	−	2.56607i	0.0301056	−	0.0926554i
$768$		0			0
$769$	−1.89417	−	3.28080i	−0.0683055	−	0.118309i	0.829850	−	0.557986i	$-0.188426\pi$
$769$	−1.89417	−	3.28080i	−0.0683055	−	0.118309i	−0.898155	+	0.439678i	$0.855093\pi$
$770$		0			0
$771$	−1.26262	−	3.88595i	−0.0454722	−	0.139949i
$772$		0			0
$773$	20.5244	+	14.9119i	0.738212	+	0.536342i	0.892151	−	0.451738i	$-0.149196\pi$
$773$	20.5244	+	14.9119i	0.738212	+	0.536342i	−0.153939	+	0.988080i	$0.549196\pi$
$774$		0			0
$775$	33.1559	−	35.6620i	1.19100	−	1.28102i
$776$		0			0
$777$	−5.80327	−	4.21632i	−0.208191	−	0.151260i
$778$		0			0
$779$	0.887573	+	2.73167i	0.0318006	+	0.0978722i
$780$		0			0
$781$	−15.9194	−	27.5732i	−0.569641	−	0.986647i
$782$		0			0
$783$	−7.07939	+	21.7881i	−0.252997	+	0.778644i
$784$		0			0
$785$	51.3036	−	22.8418i	1.83110	−	0.815260i
$786$		0			0
$787$	−2.71216	+	25.8045i	−0.0966780	+	0.919829i	0.833450	+	0.552594i	$0.186362\pi$
$787$	−2.71216	+	25.8045i	−0.0966780	+	0.919829i	−0.930128	+	0.367235i	$0.880305\pi$
$788$		0			0
$789$	−2.21453	+	0.470712i	−0.0788392	+	0.0167578i
$790$		0			0
$791$	3.94062	−	2.86303i	0.140112	−	0.101797i
$792$		0			0
$793$	0.704732	+	6.70507i	0.0250258	+	0.238104i
$794$		0			0
$795$	−11.7017	−	2.48727i	−0.415016	−	0.0882144i
$796$		0			0
$797$	−12.3807	−	13.7501i	−0.438546	−	0.487054i	0.482837	−	0.875710i	$-0.339606\pi$
$797$	−12.3807	−	13.7501i	−0.438546	−	0.487054i	−0.921383	+	0.388656i	$0.872940\pi$
$798$		0			0
$799$	0.767061	−	0.851907i	0.0271367	−	0.0301383i
$800$		0			0
$801$	−4.84652	+	8.39442i	−0.171243	+	0.296602i
$802$		0			0
$803$	−21.2710	−	9.47047i	−0.750638	−	0.334206i
$804$		0			0
$805$	−9.29174			−0.327491
$806$		0			0
$807$	12.0378			0.423751
$808$		0			0
$809$	33.5708	+	14.9467i	1.18029	+	0.525498i	0.900623	−	0.434600i	$-0.143110\pi$
$809$	33.5708	+	14.9467i	1.18029	+	0.525498i	0.279664	+	0.960098i	$0.409777\pi$
$810$		0			0
$811$	−19.7151	+	34.1475i	−0.692289	+	1.19908i	0.278797	+	0.960350i	$0.410064\pi$
$811$	−19.7151	+	34.1475i	−0.692289	+	1.19908i	−0.971086	+	0.238730i	$0.923269\pi$
$812$		0			0
$813$	−8.34737	+	9.27069i	−0.292755	+	0.325137i
$814$		0			0
$815$	2.59213	+	2.87885i	0.0907982	+	0.100842i
$816$		0			0
$817$	−26.5987	−	5.65372i	−0.930570	−	0.197799i
$818$		0			0
$819$	0.507486	+	4.82841i	0.0177330	+	0.168718i
$820$		0			0
$821$	−1.19782	+	0.870264i	−0.0418041	+	0.0303724i	−0.608491	−	0.793561i	$-0.708225\pi$
$821$	−1.19782	+	0.870264i	−0.0418041	+	0.0303724i	0.566687	+	0.823933i	$0.308225\pi$
$822$		0			0
$823$	−38.0159	+	8.08053i	−1.32515	+	0.281670i	−0.815523	−	0.578725i	$-0.803551\pi$
$823$	−38.0159	+	8.08053i	−1.32515	+	0.281670i	−0.509629	+	0.860394i	$0.670217\pi$
$824$		0			0
$825$	−3.39518	+	32.3030i	−0.118205	+	1.12465i
$826$		0			0
$827$	−31.0023	+	13.8031i	−1.07806	+	0.479982i	−0.867417	−	0.497582i	$-0.834221\pi$
$827$	−31.0023	+	13.8031i	−1.07806	+	0.479982i	−0.210640	+	0.977564i	$0.567555\pi$
$828$		0			0
$829$	5.10827	−	15.7216i	0.177417	−	0.546035i	−0.822318	−	0.569028i	$-0.807320\pi$
$829$	5.10827	−	15.7216i	0.177417	−	0.546035i	0.999736	+	0.0229933i	$0.00731965\pi$
$830$		0			0
$831$	−5.22073	−	9.04256i	−0.181105	−	0.313683i
$832$		0			0
$833$	−2.59485	−	7.98612i	−0.0899061	−	0.276703i
$834$		0			0
$835$	−33.8619	−	24.6021i	−1.17184	−	0.851392i
$836$		0			0
$837$	21.3204	−	14.9762i	0.736941	−	0.517653i
$838$		0			0
$839$	−43.7501	−	31.7863i	−1.51042	−	1.09738i	−0.965990	−	0.258579i	$-0.916746\pi$
$839$	−43.7501	−	31.7863i	−1.51042	−	1.09738i	−0.544430	−	0.838806i	$-0.683254\pi$
$840$		0			0
$841$	−1.55522	−	4.78647i	−0.0536282	−	0.165051i
$842$		0			0
$843$	6.94819	+	12.0346i	0.239308	+	0.414494i
$844$		0			0
$845$	−5.19379	+	15.9848i	−0.178672	+	0.549896i
$846$		0			0
$847$	−4.14138	+	1.84386i	−0.142299	+	0.0633558i
$848$		0			0
$849$	−2.14081	+	20.3684i	−0.0734724	+	0.699043i
$850$		0			0
$851$	33.4377	−	7.10741i	1.14623	−	0.243639i
$852$		0			0
$853$	−32.0178	+	23.2623i	−1.09627	+	0.796487i	−0.980447	−	0.196783i	$-0.936950\pi$
$853$	−32.0178	+	23.2623i	−1.09627	+	0.796487i	−0.115823	+	0.993270i	$0.536950\pi$
$854$		0			0
$855$	3.21836	+	30.6206i	0.110065	+	1.04720i
$856$		0			0
$857$	−12.4470	−	2.64569i	−0.425180	−	0.0903749i	−0.00964843	−	0.999953i	$-0.503071\pi$
$857$	−12.4470	−	2.64569i	−0.425180	−	0.0903749i	−0.415532	+	0.909579i	$0.636405\pi$
$858$		0			0
$859$	14.1550	+	15.7207i	0.482963	+	0.536385i	0.934545	−	0.355845i	$-0.115807\pi$
$859$	14.1550	+	15.7207i	0.482963	+	0.536385i	−0.451582	+	0.892230i	$0.649140\pi$
$860$		0			0
$861$	−0.348457	+	0.387001i	−0.0118754	+	0.0131890i
$862$		0			0
$863$	4.66987	−	8.08845i	0.158964	−	0.275334i	−0.775531	−	0.631309i	$-0.782518\pi$
$863$	4.66987	−	8.08845i	0.158964	−	0.275334i	0.934495	+	0.355975i	$0.115851\pi$
$864$		0			0
$865$	−69.9503	−	31.1439i	−2.37838	−	1.05892i
$866$		0			0
$867$	−13.7957			−0.468526
$868$		0			0
$869$	58.0085			1.96780
$870$		0			0
$871$	−5.54737	−	2.46985i	−0.187965	−	0.0836876i
$872$		0			0
$873$	−5.76760	+	9.98977i	−0.195204	+	0.338102i
$874$		0			0
$875$	−7.09370	+	7.87836i	−0.239811	+	0.266337i
$876$		0			0
$877$	15.0121	+	16.6726i	0.506923	+	0.562995i	0.941228	−	0.337771i	$-0.109673\pi$
$877$	15.0121	+	16.6726i	0.506923	+	0.562995i	−0.434305	+	0.900766i	$0.643006\pi$
$878$		0			0
$879$	−10.9460	−	2.32665i	−0.369200	−	0.0784758i
$880$		0			0
$881$	4.85341	+	46.1771i	0.163516	+	1.55575i	0.701425	+	0.712744i	$0.252548\pi$
$881$	4.85341	+	46.1771i	0.163516	+	1.55575i	−0.537909	+	0.843003i	$0.680786\pi$
$882$		0			0
$883$	29.5611	−	21.4774i	0.994811	−	0.722773i	0.0338419	−	0.999427i	$-0.489226\pi$
$883$	29.5611	−	21.4774i	0.994811	−	0.722773i	0.960969	+	0.276654i	$0.0892257\pi$
$884$		0			0
$885$	3.03454	−	0.645012i	0.102005	−	0.0216818i
$886$		0			0
$887$	2.99840	−	28.5279i	0.100677	−	0.957873i	−0.821266	−	0.570546i	$-0.806732\pi$
$887$	2.99840	−	28.5279i	0.100677	−	0.957873i	0.921942	−	0.387327i	$-0.126602\pi$
$888$		0			0
$889$	−0.998680	+	0.444641i	−0.0334946	+	0.0149128i
$890$		0			0
$891$	2.96861	−	9.13643i	0.0994521	−	0.306082i
$892$		0			0
$893$	−1.66433	−	2.88270i	−0.0556945	−	0.0964658i
$894$		0			0
$895$	0.150844	+	0.464249i	0.00504215	+	0.0155181i
$896$		0			0
$897$	6.97394	+	5.06687i	0.232853	+	0.169178i
$898$		0			0
$899$	8.83576	−	25.7859i	0.294689	−	0.860008i
$900$		0			0
$901$	−3.78531	−	2.75019i	−0.126107	−	0.0916220i
$902$		0			0
$903$	−1.52354	−	4.68898i	−0.0507004	−	0.156040i
$904$		0			0
$905$	−14.3332	−	24.8259i	−0.476453	−	0.825240i
$906$		0			0
$907$	6.85697	−	21.1036i	0.227682	−	0.700733i	−0.770326	−	0.637650i	$-0.779907\pi$
$907$	6.85697	−	21.1036i	0.227682	−	0.700733i	0.998008	−	0.0630831i	$-0.0200933\pi$
$908$		0			0
$909$	−7.60234	+	3.38478i	−0.252154	+	0.112266i
$910$		0			0
$911$	−3.01381	+	28.6745i	−0.0998520	+	0.950028i	0.823822	+	0.566849i	$0.191838\pi$
$911$	−3.01381	+	28.6745i	−0.0998520	+	0.950028i	−0.923674	+	0.383179i	$0.874829\pi$
$912$		0			0
$913$	−56.7932	+	12.0718i	−1.87958	+	0.399517i
$914$		0			0
$915$	−6.27153	+	4.55653i	−0.207330	+	0.150634i
$916$		0			0
$917$	−0.502151	−	4.77764i	−0.0165825	−	0.157772i
$918$		0			0
$919$	47.0121	+	9.99272i	1.55078	+	0.329629i	0.902134	−	0.431456i	$-0.142000\pi$
$919$	47.0121	+	9.99272i	1.55078	+	0.329629i	0.648651	+	0.761086i	$0.275333\pi$
$920$		0			0
$921$	−18.5495	−	20.6013i	−0.611226	−	0.678835i
$922$		0			0
$923$	−15.0622	+	16.7282i	−0.495778	+	0.550617i
$924$		0			0
$925$	45.5334	−	78.8662i	1.49713	−	2.59310i
$926$		0			0
$927$	−12.4708	−	5.55238i	−0.409596	−	0.182364i
$928$		0			0
$929$	7.01617			0.230193			0.115097	−	0.993354i	$-0.463282\pi$
$929$	7.01617			0.230193			0.115097	+	0.993354i	$0.463282\pi$
$930$		0			0
$931$	−24.3825			−0.799105
$932$		0			0
$933$	−1.96320	−	0.874072i	−0.0642722	−	0.0286158i
$934$		0			0
$935$	−9.98321	+	17.2914i	−0.326486	+	0.565490i
$936$		0			0
$937$	−8.61884	+	9.57219i	−0.281565	+	0.312710i	−0.867293	−	0.497798i	$-0.834142\pi$
$937$	−8.61884	+	9.57219i	−0.281565	+	0.312710i	0.585728	+	0.810508i	$0.300809\pi$
$938$		0			0
$939$	6.48845	+	7.20615i	0.211742	+	0.235164i
$940$		0			0
$941$	48.9458	+	10.4037i	1.59559	+	0.339152i	0.918089	−	0.396373i	$-0.129731\pi$
$941$	48.9458	+	10.4037i	1.59559	+	0.339152i	0.677497	+	0.735526i	$0.263065\pi$
$942$		0			0
$943$	−0.259412	−	2.46814i	−0.00844763	−	0.0803738i
$944$		0			0
$945$	−10.7150	+	7.78494i	−0.348560	+	0.253244i
$946$		0			0
$947$	50.7345	−	10.7840i	1.64865	−	0.350431i	0.712402	−	0.701772i	$-0.247607\pi$
$947$	50.7345	−	10.7840i	1.64865	−	0.350431i	0.936248	+	0.351340i	$0.114274\pi$
$948$		0			0
$949$	−1.72073	+	16.3717i	−0.0558573	+	0.531447i
$950$		0			0
$951$	7.21035	−	3.21026i	0.233812	−	0.104100i
$952$		0			0
$953$	5.78950	−	17.8183i	0.187540	−	0.577190i	−0.812443	−	0.583041i	$-0.801863\pi$
$953$	5.78950	−	17.8183i	0.187540	−	0.577190i	0.999983	+	0.00585146i	$0.00186259\pi$
$954$		0			0
$955$	−39.1193	−	67.7565i	−1.26587	−	2.19255i
$956$		0			0
$957$	5.61857	+	17.2922i	0.181623	+	0.558977i
$958$		0			0
$959$	7.87432	+	5.72103i	0.254275	+	0.184742i
$960$		0			0
$961$	−25.6483	+	17.4116i	−0.827364	+	0.561666i
$962$		0			0
$963$	−4.11539	−	2.99001i	−0.132617	−	0.0963516i
$964$		0			0
$965$	6.48829	+	19.9689i	0.208865	+	0.642821i
$966$		0			0
$967$	−23.8923	−	41.3827i	−0.768324	−	1.33078i	−0.938471	−	0.345358i	$-0.887757\pi$
$967$	−23.8923	−	41.3827i	−0.768324	−	1.33078i	0.170146	−	0.985419i	$-0.445576\pi$
$968$		0			0
$969$	1.38642	−	4.26696i	0.0445382	−	0.137075i
$970$		0			0
$971$	28.4119	−	12.6498i	0.911780	−	0.405951i	0.103419	−	0.994638i	$-0.467022\pi$
$971$	28.4119	−	12.6498i	0.911780	−	0.405951i	0.808361	+	0.588687i	$0.200355\pi$
$972$		0			0
$973$	−1.49329	+	14.2077i	−0.0478727	+	0.455478i
$974$		0			0
$975$	22.4622	−	4.77450i	0.719368	−	0.152906i
$976$		0			0
$977$	17.8624	−	12.9778i	0.571469	−	0.415197i	−0.264170	−	0.964476i	$-0.585098\pi$
$977$	17.8624	−	12.9778i	0.571469	−	0.415197i	0.835639	+	0.549280i	$0.185098\pi$
$978$		0			0
$979$	1.90785	+	18.1520i	0.0609753	+	0.580141i
$980$		0			0
$981$	3.15732	+	0.671110i	0.100806	+	0.0214269i
$982$		0			0
$983$	25.1438	+	27.9251i	0.801964	+	0.890671i	0.995911	−	0.0903411i	$-0.0287957\pi$
$983$	25.1438	+	27.9251i	0.801964	+	0.890671i	−0.193947	+	0.981012i	$0.562129\pi$
$984$		0			0
$985$	39.4816	−	43.8488i	1.25799	−	1.39714i
$986$		0			0
$987$	0.301756	−	0.522656i	0.00960499	−	0.0166363i
$988$		0			0
$989$	21.4645	+	9.55659i	0.682530	+	0.303882i
$990$		0			0
$991$	6.77397			0.215182			0.107591	−	0.994195i	$-0.465686\pi$
$991$	6.77397			0.215182			0.107591	+	0.994195i	$0.465686\pi$
$992$		0			0
$993$	29.2099			0.926948
$994$		0			0
$995$	14.4335	+	6.42620i	0.457572	+	0.203724i
$996$		0			0
$997$	14.7866	−	25.6112i	0.468298	−	0.811115i	−0.531046	−	0.847343i	$-0.678201\pi$
$997$	14.7866	−	25.6112i	0.468298	−	0.811115i	0.999344	+	0.0362278i	$0.0115342\pi$
$998$		0			0
$999$	32.6049	−	36.2114i	1.03157	−	1.14568i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	496.2.bg.c.81.1		16
4.3	odd	2		31.2.g.a.19.2	yes	16
12.11	even	2		279.2.y.c.19.1		16
20.3	even	4		775.2.ck.a.174.3		32
20.7	even	4		775.2.ck.a.174.2		32
20.19	odd	2		775.2.bl.a.701.1		16
31.18	even	15	inner	496.2.bg.c.49.1		16
124.3	even	30		961.2.d.n.388.4		16
124.7	odd	30		961.2.a.i.1.3		8
124.11	even	30		961.2.c.i.439.3		16
124.15	even	10		961.2.g.j.338.2		16
124.19	odd	30		961.2.d.p.628.1		16
124.23	even	10		961.2.g.m.844.1		16
124.27	even	10		961.2.c.i.521.3		16
124.35	odd	10		961.2.c.j.521.3		16
124.39	odd	10		961.2.g.s.844.1		16
124.43	even	30		961.2.d.q.628.1		16
124.47	odd	10		961.2.g.k.338.2		16
124.51	odd	30		961.2.c.j.439.3		16
124.55	even	30		961.2.a.j.1.3		8
124.59	odd	30		961.2.d.o.388.4		16
124.67	odd	6		961.2.g.k.816.2		16
124.71	odd	30		961.2.g.t.547.1		16
124.75	even	30		961.2.g.l.235.2		16
124.79	even	30		961.2.d.q.531.1		16
124.83	even	30		961.2.g.m.846.1		16
124.87	odd	6		961.2.d.o.374.4		16
124.91	even	10		961.2.g.n.448.1		16
124.95	odd	10		961.2.g.t.448.1		16
124.99	even	6		961.2.d.n.374.4		16
124.103	odd	30		961.2.g.s.846.1		16
124.107	odd	30		961.2.d.p.531.1		16
124.111	odd	30		31.2.g.a.18.2	✓	16
124.115	even	30		961.2.g.n.547.1		16
124.119	even	6		961.2.g.j.816.2		16
124.123	even	2		961.2.g.l.732.2		16
372.131	even	30		8649.2.a.bf.1.6		8
372.179	odd	30		8649.2.a.be.1.6		8
372.359	even	30		279.2.y.c.235.1		16
620.359	odd	30		775.2.bl.a.576.1		16
620.483	even	60		775.2.ck.a.49.2		32
620.607	even	60		775.2.ck.a.49.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.18.2	✓	16	124.111	odd	30
31.2.g.a.19.2	yes	16	4.3	odd	2
279.2.y.c.19.1		16	12.11	even	2
279.2.y.c.235.1		16	372.359	even	30
496.2.bg.c.49.1		16	31.18	even	15	inner
496.2.bg.c.81.1		16	1.1	even	1	trivial
775.2.bl.a.576.1		16	620.359	odd	30
775.2.bl.a.701.1		16	20.19	odd	2
775.2.ck.a.49.2		32	620.483	even	60
775.2.ck.a.49.3		32	620.607	even	60
775.2.ck.a.174.2		32	20.7	even	4
775.2.ck.a.174.3		32	20.3	even	4
961.2.a.i.1.3		8	124.7	odd	30
961.2.a.j.1.3		8	124.55	even	30
961.2.c.i.439.3		16	124.11	even	30
961.2.c.i.521.3		16	124.27	even	10
961.2.c.j.439.3		16	124.51	odd	30
961.2.c.j.521.3		16	124.35	odd	10
961.2.d.n.374.4		16	124.99	even	6
961.2.d.n.388.4		16	124.3	even	30
961.2.d.o.374.4		16	124.87	odd	6
961.2.d.o.388.4		16	124.59	odd	30
961.2.d.p.531.1		16	124.107	odd	30
961.2.d.p.628.1		16	124.19	odd	30
961.2.d.q.531.1		16	124.79	even	30
961.2.d.q.628.1		16	124.43	even	30
961.2.g.j.338.2		16	124.15	even	10
961.2.g.j.816.2		16	124.119	even	6
961.2.g.k.338.2		16	124.47	odd	10
961.2.g.k.816.2		16	124.67	odd	6
961.2.g.l.235.2		16	124.75	even	30
961.2.g.l.732.2		16	124.123	even	2
961.2.g.m.844.1		16	124.23	even	10
961.2.g.m.846.1		16	124.83	even	30
961.2.g.n.448.1		16	124.91	even	10
961.2.g.n.547.1		16	124.115	even	30
961.2.g.s.844.1		16	124.39	odd	10
961.2.g.s.846.1		16	124.103	odd	30
961.2.g.t.448.1		16	124.95	odd	10
961.2.g.t.547.1		16	124.71	odd	30
8649.2.a.be.1.6		8	372.179	odd	30
8649.2.a.bf.1.6		8	372.131	even	30

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:	\( N \)	\(=\)	\( 496 = 2^{4} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	496.bg (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.824384 + 0.367040i) q^{3} +(-1.85376 + 3.21080i) q^{5} +(-0.510810 + 0.567312i) q^{7} +(-1.46250 - 1.62427i) q^{9} +(-4.02569 - 0.855686i) q^{11} +(0.304152 + 2.89381i) q^{13} +(-2.70670 + 1.96653i) q^{15} +(-1.27993 + 0.272057i) q^{17} +(-0.397160 + 3.77873i) q^{19} +(-0.629330 + 0.280196i) q^{21} +(1.01449 - 3.12228i) q^{23} +(-4.37284 - 7.57398i) q^{25} +(-1.44606 - 4.45052i) q^{27} +(-3.96065 - 2.87758i) q^{29} +(1.63580 + 5.32204i) q^{31} +(-3.00464 - 2.18300i) q^{33} +(-0.874609 - 2.69177i) q^{35} +(5.20639 + 9.01773i) q^{37} +(-0.811405 + 2.49725i) q^{39} +(0.690591 - 0.307471i) q^{41} +(-0.748099 + 7.11768i) q^{43} +(7.92634 - 1.68480i) q^{45} +(-0.708753 + 0.514939i) q^{47} +(0.670783 + 6.38208i) q^{49} +(-1.15501 - 0.245505i) q^{51} +(2.39261 + 2.65727i) q^{53} +(10.2101 - 11.3395i) q^{55} +(-1.71435 + 2.96935i) q^{57} +(-0.847103 - 0.377155i) q^{59} +2.31704 q^{61} +1.66853 q^{63} +(-9.85528 - 4.38785i) q^{65} +(-1.04345 + 1.80731i) q^{67} +(1.98233 - 2.20160i) q^{69} +(5.17645 + 5.74903i) q^{71} +(5.53385 + 1.17626i) q^{73} +(-0.824950 - 7.84887i) q^{75} +(2.54180 - 1.84673i) q^{77} +(-13.7867 + 2.93046i) q^{79} +(-0.243989 + 2.32140i) q^{81} +(12.8880 - 5.73812i) q^{83} +(1.49916 - 4.61393i) q^{85} +(-2.20891 - 3.82595i) q^{87} +(-1.37043 - 4.21776i) q^{89} +(-1.79706 - 1.30564i) q^{91} +(-0.604868 + 4.98781i) q^{93} +(-11.3965 - 8.28005i) q^{95} +(-1.63088 - 5.01933i) q^{97} +(4.49770 + 7.79025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{3} - 3 q^{5} - 2 q^{7} - 10 q^{9} + 7 q^{11} - 7 q^{13} - 14 q^{15} - 6 q^{17} - 16 q^{19} + 9 q^{21} - q^{23} - 13 q^{25} - 9 q^{27} - 14 q^{29} - 15 q^{31} - 13 q^{33} + 9 q^{35} - 8 q^{37}+ \cdots - 6 q^{99}+O(q^{100}) \) 16 * q + 12 * q^3 - 3 * q^5 - 2 * q^7 - 10 * q^9 + 7 * q^11 - 7 * q^13 - 14 * q^15 - 6 * q^17 - 16 * q^19 + 9 * q^21 - q^23 - 13 * q^25 - 9 * q^27 - 14 * q^29 - 15 * q^31 - 13 * q^33 + 9 * q^35 - 8 * q^37 + 3 * q^39 - 8 * q^41 - 23 * q^43 + 65 * q^45 - 14 * q^47 + 2 * q^49 + 42 * q^51 + 6 * q^53 + 7 * q^55 - 17 * q^57 - 4 * q^59 - 60 * q^61 + 46 * q^63 - 12 * q^65 - 13 * q^67 + 38 * q^69 + 14 * q^71 + 2 * q^73 - 13 * q^75 + 18 * q^77 - 18 * q^79 + 23 * q^81 + 16 * q^83 + 37 * q^85 - 15 * q^87 + q^89 - 8 * q^91 + 17 * q^93 + 22 * q^95 + 3 * q^97 - 6 * q^99

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