LMFDB - Embedded newform 1638.2.dm.c.415.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1638,2,Mod(415,1638)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1638, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1638.415"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.dm (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,6,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.752609431977984.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 15x^{10} + 90x^{8} - 247x^{6} + 270x^{4} + 21x^{2} + 49 $ x^12 - 15x^10 + 90x^8 - 247x^6 + 270x^4 + 21*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			415.5
Root			$-1.75780 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1638.415
Dual form			1638.2.dm.c.1117.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.294342 - 0.169938i) q^{5} +(0.420136 - 2.61218i) q^{7} +1.00000i q^{8} +(-0.169938 - 0.294342i) q^{10} +(0.571683 - 0.330062i) q^{11} +(0.660123 - 3.54461i) q^{13} +(1.66994 - 2.05215i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.27230 - 5.66780i) q^{17} +(-5.27341 - 3.04461i) q^{19} -0.339877i q^{20} +0.660123 q^{22} +(-3.71455 + 6.43378i) q^{23} +(-2.44224 - 4.23009i) q^{25} +(2.34399 - 2.73966i) q^{26} +(2.47228 - 0.942242i) q^{28} +3.56424 q^{29} +(3.46410 - 2.00000i) q^{31} +(-0.866025 + 0.500000i) q^{32} -6.54461i q^{34} +(-0.567573 + 0.697477i) q^{35} +(-3.06972 - 1.77230i) q^{37} +(-3.04461 - 5.27341i) q^{38} +(0.169938 - 0.294342i) q^{40} -0.864853i q^{41} -5.08921 q^{43} +(0.571683 + 0.330062i) q^{44} +(-6.43378 + 3.71455i) q^{46} +(8.18283 + 4.72436i) q^{47} +(-6.64697 - 2.19494i) q^{49} -4.88448i q^{50} +(3.39978 - 1.20062i) q^{52} +(1.50000 + 2.59808i) q^{53} -0.224361 q^{55} +(2.61218 + 0.420136i) q^{56} +(3.08672 + 1.78212i) q^{58} +(3.38106 - 1.95206i) q^{59} +(-0.932427 + 1.61501i) q^{61} +4.00000 q^{62} -1.00000 q^{64} +(-0.796667 + 0.931146i) q^{65} +(6.45078 - 3.72436i) q^{67} +(3.27230 - 5.66780i) q^{68} +(-0.840272 + 0.320246i) q^{70} +0.884484i q^{71} +(8.72051 - 5.03479i) q^{73} +(-1.77230 - 3.06972i) q^{74} -6.08921i q^{76} +(-0.621996 - 1.63201i) q^{77} +(6.22436 - 10.7809i) q^{79} +(0.294342 - 0.169938i) q^{80} +(0.432427 - 0.748985i) q^{82} -16.2939i q^{83} +2.22436i q^{85} +(-4.40739 - 2.54461i) q^{86} +(0.330062 + 0.571683i) q^{88} +(-3.85848 - 2.22770i) q^{89} +(-8.98181 - 3.21358i) q^{91} -7.42909 q^{92} +(4.72436 + 8.18283i) q^{94} +(1.03479 + 1.79231i) q^{95} +16.1088i q^{97} +(-4.65898 - 5.22436i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} + 12 q^{13} + 18 q^{14} - 6 q^{16} - 18 q^{17} + 12 q^{22} - 6 q^{25} - 12 q^{29} - 24 q^{35} + 6 q^{38} + 24 q^{43} - 18 q^{49} + 6 q^{52} + 18 q^{53} + 48 q^{55} + 6 q^{56} + 6 q^{61} + 48 q^{62}+ \cdots - 24 q^{95}+O(q^{100}) $ 12 * q + 6 * q^4 + 12 * q^13 + 18 * q^14 - 6 * q^16 - 18 * q^17 + 12 * q^22 - 6 * q^25 - 12 * q^29 - 24 * q^35 + 6 * q^38 + 24 * q^43 - 18 * q^49 + 6 * q^52 + 18 * q^53 + 48 * q^55 + 6 * q^56 + 6 * q^61 + 48 * q^62 - 12 * q^64 + 12 * q^65 + 18 * q^68 + 24 * q^77 + 24 * q^79 - 12 * q^82 + 6 * q^88 - 24 * q^91 + 6 * q^94 - 24 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.294342	−	0.169938i	−0.131634	−	0.0759988i	0.432737	−	0.901520i	$-0.357548\pi$
$5$	−0.294342	−	0.169938i	−0.131634	−	0.0759988i	−0.564371	+	0.825521i	$0.690881\pi$
$6$		0			0
$7$	0.420136	−	2.61218i	0.158796	−	0.987311i
$7$	0.420136	−	2.61218i	0.158796	−	0.987311i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−0.169938	−	0.294342i	−0.0537393	−	0.0930791i
$11$	0.571683	−	0.330062i	0.172369	−	0.0995173i	−0.411333	−	0.911485i	$-0.634937\pi$
$11$	0.571683	−	0.330062i	0.172369	−	0.0995173i	0.583702	+	0.811968i	$0.301603\pi$
$12$		0			0
$13$	0.660123	−	3.54461i	0.183085	−	0.983097i
$13$	0.660123	−	3.54461i	0.183085	−	0.983097i
$14$	1.66994	−	2.05215i	0.446310	−	0.548459i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.27230	−	5.66780i	−0.793650	−	1.37464i	−0.923693	−	0.383134i	$-0.874845\pi$
$17$	−3.27230	−	5.66780i	−0.793650	−	1.37464i	0.130043	−	0.991508i	$-0.458489\pi$
$18$		0			0
$19$	−5.27341	−	3.04461i	−1.20980	−	0.698481i	−0.247088	−	0.968993i	$-0.579474\pi$
$19$	−5.27341	−	3.04461i	−1.20980	−	0.698481i	−0.962716	+	0.270512i	$0.912807\pi$
$20$		−	0.339877i		−	0.0759988i
$21$		0			0
$22$	0.660123			0.140739
$23$	−3.71455	+	6.43378i	−0.774536	+	1.34154i	0.160519	+	0.987033i	$0.448683\pi$
$23$	−3.71455	+	6.43378i	−0.774536	+	1.34154i	−0.935055	+	0.354503i	$0.884650\pi$
$24$		0			0
$25$	−2.44224	−	4.23009i	−0.488448	−	0.846017i
$26$	2.34399	−	2.73966i	0.459694	−	0.537291i
$27$		0			0
$28$	2.47228	−	0.942242i	0.467217	−	0.178067i
$29$	3.56424			0.661862			0.330931	−	0.943655i	$-0.392637\pi$
$29$	3.56424			0.661862			0.330931	+	0.943655i	$0.392637\pi$
$30$		0			0
$31$	3.46410	−	2.00000i	0.622171	−	0.359211i	−0.155543	−	0.987829i	$-0.549713\pi$
$31$	3.46410	−	2.00000i	0.622171	−	0.359211i	0.777714	+	0.628619i	$0.216379\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$		−	6.54461i		−	1.12239i
$35$	−0.567573	+	0.697477i	−0.0959374	+	0.117895i
$36$		0			0
$37$	−3.06972	−	1.77230i	−0.504659	−	0.291365i	0.225977	−	0.974133i	$-0.427443\pi$
$37$	−3.06972	−	1.77230i	−0.504659	−	0.291365i	−0.730635	+	0.682768i	$0.760776\pi$
$38$	−3.04461	−	5.27341i	−0.493900	−	0.855461i
$39$		0			0
$40$	0.169938	−	0.294342i	0.0268696	−	0.0465396i
$41$		−	0.864853i		−	0.135067i	−0.997717	−	0.0675337i	$-0.978487\pi$
$41$		−	0.864853i		−	0.135067i	0.997717	−	0.0675337i	$-0.0215130\pi$
$42$		0			0
$43$	−5.08921			−0.776098			−0.388049	−	0.921639i	$-0.626851\pi$
$43$	−5.08921			−0.776098			−0.388049	+	0.921639i	$0.626851\pi$
$44$	0.571683	+	0.330062i	0.0861845	+	0.0497587i
$45$		0			0
$46$	−6.43378	+	3.71455i	−0.948609	+	0.547680i
$47$	8.18283	+	4.72436i	1.19359	+	0.689119i	0.959119	−	0.283004i	$-0.0913311\pi$
$47$	8.18283	+	4.72436i	1.19359	+	0.689119i	0.234470	+	0.972123i	$0.424664\pi$
$48$		0			0
$49$	−6.64697	−	2.19494i	−0.949567	−	0.313563i
$50$		−	4.88448i		−	0.690770i
$51$		0			0
$52$	3.39978	−	1.20062i	0.471465	−	0.166496i
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	0.950464	−	0.310835i	$-0.100609\pi$
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	−0.744423	+	0.667708i	$0.767275\pi$
$54$		0			0
$55$	−0.224361			−0.0302528
$56$	2.61218	+	0.420136i	0.349067	+	0.0561430i
$57$		0			0
$58$	3.08672	+	1.78212i	0.405306	+	0.234004i
$59$	3.38106	−	1.95206i	0.440177	−	0.254136i	−0.263496	−	0.964661i	$-0.584876\pi$
$59$	3.38106	−	1.95206i	0.440177	−	0.254136i	0.703673	+	0.710524i	$0.251542\pi$
$60$		0			0
$61$	−0.932427	+	1.61501i	−0.119385	+	0.206781i	−0.919524	−	0.393034i	$-0.871426\pi$
$61$	−0.932427	+	1.61501i	−0.119385	+	0.206781i	0.800139	+	0.599814i	$0.204759\pi$
$62$	4.00000			0.508001
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.796667	+	0.931146i	−0.0988144	+	0.115495i
$66$		0			0
$67$	6.45078	−	3.72436i	0.788088	−	0.455003i	−0.0512007	−	0.998688i	$-0.516305\pi$
$67$	6.45078	−	3.72436i	0.788088	−	0.455003i	0.839289	+	0.543685i	$0.182971\pi$
$68$	3.27230	−	5.66780i	0.396825	−	0.687321i
$69$		0			0
$70$	−0.840272	+	0.320246i	−0.100432	+	0.0382767i
$71$			0.884484i			0.104969i	0.998622	+	0.0524845i	$0.0167140\pi$
$71$			0.884484i			0.104969i	−0.998622	+	0.0524845i	$0.983286\pi$
$72$		0			0
$73$	8.72051	−	5.03479i	1.02066	−	0.589278i	0.106364	−	0.994327i	$-0.466079\pi$
$73$	8.72051	−	5.03479i	1.02066	−	0.589278i	0.914295	+	0.405049i	$0.132746\pi$
$74$	−1.77230	−	3.06972i	−0.206026	−	0.356848i
$75$		0			0
$76$		−	6.08921i		−	0.698481i
$77$	−0.621996	−	1.63201i	−0.0708830	−	0.185985i
$78$		0			0
$79$	6.22436	−	10.7809i	0.700295	−	1.21295i	−0.268067	−	0.963400i	$-0.586385\pi$
$79$	6.22436	−	10.7809i	0.700295	−	1.21295i	0.968363	−	0.249547i	$-0.0802817\pi$
$80$	0.294342	−	0.169938i	0.0329084	−	0.0189997i
$81$		0			0
$82$	0.432427	−	0.748985i	0.0477535	−	0.0827115i
$83$		−	16.2939i		−	1.78849i	−0.447575	−	0.894246i	$-0.647712\pi$
$83$		−	16.2939i		−	1.78849i	0.447575	−	0.894246i	$-0.352288\pi$
$84$		0			0
$85$			2.22436i			0.241266i
$86$	−4.40739	−	2.54461i	−0.475261	−	0.274392i
$87$		0			0
$88$	0.330062	+	0.571683i	0.0351847	+	0.0609417i
$89$	−3.85848	−	2.22770i	−0.408998	−	0.236135i	0.281361	−	0.959602i	$-0.409214\pi$
$89$	−3.85848	−	2.22770i	−0.408998	−	0.236135i	−0.690359	+	0.723467i	$0.742548\pi$
$90$		0			0
$91$	−8.98181	−	3.21358i	−0.941550	−	0.336874i
$92$	−7.42909			−0.774536
$93$		0			0
$94$	4.72436	+	8.18283i	0.487281	+	0.843995i
$95$	1.03479	+	1.79231i	0.106167	+	0.183887i
$96$		0			0
$97$			16.1088i			1.63561i	0.575499	+	0.817803i	$0.304808\pi$
$97$			16.1088i			1.63561i	−0.575499	+	0.817803i	$0.695192\pi$
$98$	−4.65898	−	5.22436i	−0.470628	−	0.527740i
$99$		0			0
$100$	2.44224	−	4.23009i	0.244224	−	0.423009i
$101$	1.39764	+	2.42077i	0.139070	+	0.240876i	0.927145	−	0.374703i	$-0.122255\pi$
$101$	1.39764	+	2.42077i	0.139070	+	0.240876i	−0.788075	+	0.615579i	$0.788922\pi$
$102$		0			0
$103$	3.76897	−	6.52804i	0.371367	−	0.643227i	−0.618409	−	0.785857i	$-0.712222\pi$
$103$	3.76897	−	6.52804i	0.371367	−	0.643227i	0.989776	+	0.142629i	$0.0455557\pi$
$104$	3.54461	+	0.660123i	0.347577	+	0.0647304i
$105$		0			0
$106$			3.00000i			0.291386i
$107$	−1.86485	+	3.23002i	−0.180282	+	0.312258i	−0.941977	−	0.335679i	$-0.891034\pi$
$107$	−1.86485	+	3.23002i	−0.180282	+	0.312258i	0.761694	+	0.647936i	$0.224368\pi$
$108$		0			0
$109$	12.4790	−	7.20473i	1.19527	−	0.690088i	0.235771	−	0.971809i	$-0.424238\pi$
$109$	12.4790	−	7.20473i	1.19527	−	0.690088i	0.959496	+	0.281721i	$0.0909052\pi$
$110$	−0.194302	−	0.112180i	−0.0185260	−	0.0106960i
$111$		0			0
$112$	2.05215	+	1.66994i	0.193910	+	0.157794i
$113$	−15.5576			−1.46353			−0.731766	−	0.681556i	$-0.761304\pi$
$113$	−15.5576			−1.46353			−0.731766	+	0.681556i	$0.761304\pi$
$114$		0			0
$115$	2.18669	−	1.26249i	0.203910	−	0.117728i
$116$	1.78212	+	3.08672i	0.165466	+	0.286595i
$117$		0			0
$118$	3.90411			0.359403
$119$	−16.1801	+	6.16660i	−1.48323	+	0.565292i
$120$		0			0
$121$	−5.28212	+	9.14890i	−0.480193	+	0.831718i
$122$	−1.61501	+	0.932427i	−0.146216	+	0.0844179i
$123$		0			0
$124$	3.46410	+	2.00000i	0.311086	+	0.179605i
$125$			3.35951i			0.300483i
$126$		0			0
$127$	14.4028			1.27804			0.639020	−	0.769190i	$-0.279340\pi$
$127$	14.4028			1.27804			0.639020	+	0.769190i	$0.279340\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	−1.15551	+	0.408063i	−0.101345	+	0.0357895i
$131$	−10.3365	+	17.9034i	−0.903108	+	1.56423i	−0.0796705	+	0.996821i	$0.525387\pi$
$131$	−10.3365	+	17.9034i	−0.903108	+	1.56423i	−0.823437	+	0.567407i	$0.807947\pi$
$132$		0			0
$133$	−10.1686	+	12.4960i	−0.881730	+	1.08354i
$134$	7.44872			0.643472
$135$		0			0
$136$	5.66780	−	3.27230i	0.486009	−	0.280598i
$137$	12.3187	−	7.11218i	1.05245	−	0.607635i	0.129119	−	0.991629i	$-0.458785\pi$
$137$	12.3187	−	7.11218i	1.05245	−	0.607635i	0.923335	+	0.383995i	$0.125452\pi$
$138$		0			0
$139$	9.42909			0.799765			0.399883	−	0.916566i	$-0.369051\pi$
$139$	9.42909			0.799765			0.399883	+	0.916566i	$0.369051\pi$
$140$	−0.887820	−	0.142794i	−0.0750345	−	0.0120683i
$141$		0			0
$142$	−0.442242	+	0.765985i	−0.0371121	+	0.0642801i
$143$	−0.792557	−	2.24427i	−0.0662769	−	0.187676i
$144$		0			0
$145$	−1.04910	−	0.605701i	−0.0871234	−	0.0503007i
$146$	10.0696			0.833365
$147$		0			0
$148$		−	3.54461i		−	0.291365i
$149$	−7.02247	−	4.05442i	−0.575303	−	0.332151i	0.183962	−	0.982933i	$-0.441108\pi$
$149$	−7.02247	−	4.05442i	−0.575303	−	0.332151i	−0.759264	+	0.650782i	$0.774441\pi$
$150$		0			0
$151$	−4.59047	+	2.65031i	−0.373567	+	0.215679i	−0.675016	−	0.737803i	$-0.735863\pi$
$151$	−4.59047	+	2.65031i	−0.373567	+	0.215679i	0.301449	+	0.953482i	$0.402530\pi$
$152$	3.04461	−	5.27341i	0.246950	−	0.427730i
$153$		0			0
$154$	0.277341	−	1.72436i	0.0223488	−	0.138953i
$155$	−1.35951			−0.109198
$156$		0			0
$157$	11.5281	+	19.9673i	0.920044	+	1.59356i	0.799344	+	0.600874i	$0.205181\pi$
$157$	11.5281	+	19.9673i	0.920044	+	1.59356i	0.120700	+	0.992689i	$0.461486\pi$
$158$	10.7809	−	6.22436i	0.857683	−	0.495184i
$159$		0			0
$160$	0.339877			0.0268696
$161$	15.2456	+	12.4061i	1.20152	+	0.977740i
$162$		0			0
$163$	11.7470	+	6.78212i	0.920094	+	0.531217i	0.883665	−	0.468120i	$-0.155068\pi$
$163$	11.7470	+	6.78212i	0.920094	+	0.531217i	0.0364290	+	0.999336i	$0.488402\pi$
$164$	0.748985	−	0.432427i	0.0584859	−	0.0337668i
$165$		0			0
$166$	8.14697	−	14.1110i	0.632328	−	1.09522i
$167$		−	15.7034i		−	1.21517i	−0.794256	−	0.607583i	$-0.792139\pi$
$167$		−	15.7034i		−	1.21517i	0.794256	−	0.607583i	$-0.207861\pi$
$168$		0			0
$169$	−12.1285	−	4.67975i	−0.932960	−	0.359981i
$170$	−1.11218	+	1.92635i	−0.0853003	+	0.147745i
$171$		0			0
$172$	−2.54461	−	4.40739i	−0.194024	−	0.336060i
$173$	6.80175	−	11.7810i	0.517127	−	0.895691i	−0.482675	−	0.875800i	$-0.660335\pi$
$173$	6.80175	−	11.7810i	0.517127	−	0.895691i	0.999802	−	0.0198913i	$-0.00633201\pi$
$174$		0			0
$175$	−12.0758	+	4.60236i	−0.912846	+	0.347906i
$176$			0.660123i			0.0497587i
$177$		0			0
$178$	−2.22770	−	3.85848i	−0.166973	−	0.289206i
$179$	0.224361	+	0.388604i	0.0167695	+	0.0290456i	0.874288	−	0.485407i	$-0.161329\pi$
$179$	0.224361	+	0.388604i	0.0167695	+	0.0290456i	−0.857519	+	0.514453i	$0.827995\pi$
$180$		0			0
$181$	−15.9041			−1.18214			−0.591072	−	0.806619i	$-0.701295\pi$
$181$	−15.9041			−1.18214			−0.591072	+	0.806619i	$0.701295\pi$
$182$	−6.17169	−	7.27394i	−0.457476	−	0.539181i
$183$		0			0
$184$	−6.43378	−	3.71455i	−0.474305	−	0.273840i
$185$	0.602365	+	1.04333i	0.0442868	+	0.0767069i
$186$		0			0
$187$	−3.74144	−	2.16012i	−0.273601	−	0.157964i
$188$			9.44872i			0.689119i
$189$		0			0
$190$			2.06958i			0.150143i
$191$	−5.20473	+	9.01486i	−0.376601	+	0.652292i	−0.990565	−	0.137042i	$-0.956241\pi$
$191$	−5.20473	+	9.01486i	−0.376601	+	0.652292i	0.613964	+	0.789334i	$0.289574\pi$
$192$		0			0
$193$	−6.66786	+	3.84969i	−0.479963	+	0.277107i	−0.720401	−	0.693558i	$-0.756042\pi$
$193$	−6.66786	+	3.84969i	−0.479963	+	0.277107i	0.240438	+	0.970665i	$0.422709\pi$
$194$	−8.05442	+	13.9507i	−0.578274	+	1.00160i
$195$		0			0
$196$	−1.42261	−	6.85392i	−0.101615	−	0.489565i
$197$			8.98037i			0.639825i	0.947447	+	0.319912i	$0.103653\pi$
$197$			8.98037i			0.639825i	−0.947447	+	0.319912i	$0.896347\pi$
$198$		0			0
$199$	10.2973	+	17.8354i	0.729955	+	1.26432i	0.956902	+	0.290412i	$0.0937922\pi$
$199$	10.2973	+	17.8354i	0.729955	+	1.26432i	−0.226947	+	0.973907i	$0.572874\pi$
$200$	4.23009	−	2.44224i	0.299112	−	0.172693i
$201$		0			0
$202$			2.79527i			0.196675i
$203$	1.49746	−	9.31043i	0.105101	−	0.653464i
$204$		0			0
$205$	−0.146972	+	0.254563i	−0.0102650	+	0.0177794i
$206$	6.52804	−	3.76897i	0.454830	−	0.262596i
$207$		0			0
$208$	2.73966	+	2.34399i	0.189961	+	0.162526i
$209$	−4.01963			−0.278044
$210$		0			0
$211$	15.3898			1.05948			0.529740	−	0.848160i	$-0.322290\pi$
$211$	15.3898			1.05948			0.529740	+	0.848160i	$0.322290\pi$
$212$	−1.50000	+	2.59808i	−0.103020	+	0.178437i
$213$		0			0
$214$	−3.23002	+	1.86485i	−0.220800	+	0.127479i
$215$	1.49797	+	0.864853i	0.102161	+	0.0589825i
$216$		0			0
$217$	−3.76897	−	9.88913i	−0.255854	−	0.671318i
$218$	14.4095			0.975932
$219$		0			0
$220$	−0.112180	−	0.194302i	−0.00756319	−	0.0130998i
$221$	−22.2502	+	7.85759i	−1.49671	+	0.528558i
$222$		0			0
$223$		−	18.0196i		−	1.20668i	−0.797483	−	0.603342i	$-0.793835\pi$
$223$		−	18.0196i		−	1.20668i	0.797483	−	0.603342i	$-0.206165\pi$
$224$	0.942242	+	2.47228i	0.0629562	+	0.165186i
$225$		0			0
$226$	−13.4732	−	7.77878i	−0.896227	−	0.517437i
$227$	−0.200080	+	0.115516i	−0.0132798	+	0.00766709i	−0.506625	−	0.862166i	$-0.669107\pi$
$227$	−0.200080	+	0.115516i	−0.0132798	+	0.00766709i	0.493345	+	0.869833i	$0.335774\pi$
$228$		0			0
$229$	−5.75084	−	3.32025i	−0.380026	−	0.219408i	0.297804	−	0.954627i	$-0.403746\pi$
$229$	−5.75084	−	3.32025i	−0.380026	−	0.219408i	−0.677830	+	0.735219i	$0.737079\pi$
$230$	2.52498			0.166492
$231$		0			0
$232$			3.56424i			0.234004i
$233$	−14.7592	+	25.5636i	−0.966904	+	1.67473i	−0.262495	+	0.964933i	$0.584545\pi$
$233$	−14.7592	+	25.5636i	−0.966904	+	1.67473i	−0.704410	+	0.709794i	$0.748788\pi$
$234$		0			0
$235$	−1.60570	−	2.78116i	−0.104744	−	0.181423i
$236$	3.38106	+	1.95206i	0.220088	+	0.127068i
$237$		0			0
$238$	−17.0957	−	2.74962i	−1.10815	−	0.178232i
$239$			15.0236i			0.971799i	0.874015	+	0.485900i	$0.161508\pi$
$239$			15.0236i			0.971799i	−0.874015	+	0.485900i	$0.838492\pi$
$240$		0			0
$241$	−3.85271	+	2.22436i	−0.248175	+	0.143284i	−0.618928	−	0.785448i	$-0.712433\pi$
$241$	−3.85271	+	2.22436i	−0.248175	+	0.143284i	0.370754	+	0.928731i	$0.379099\pi$
$242$	−9.14890	+	5.28212i	−0.588113	+	0.339547i
$243$		0			0
$244$	−1.86485			−0.119385
$245$	1.58348	+	1.77564i	0.101165	+	0.113441i
$246$		0			0
$247$	−14.2730	+	16.6824i	−0.908172	+	1.06147i
$248$	2.00000	+	3.46410i	0.127000	+	0.219971i
$249$		0			0
$250$	−1.67975	+	2.90942i	−0.106237	+	0.184008i
$251$	24.3961			1.53987			0.769935	−	0.638123i	$-0.220289\pi$
$251$	24.3961			1.53987			0.769935	+	0.638123i	$0.220289\pi$
$252$		0			0
$253$			4.90411i			0.308319i
$254$	12.4732	+	7.20139i	0.782637	+	0.451856i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.22436	−	15.9771i	0.575400	−	0.996622i	−0.420598	−	0.907247i	$-0.638180\pi$
$257$	9.22436	−	15.9771i	0.575400	−	0.996622i	0.995998	−	0.0893747i	$-0.0284869\pi$
$258$		0			0
$259$	−5.91928	+	7.27405i	−0.367806	+	0.451988i
$260$	−1.20473	−	0.224361i	−0.0747142	−	0.0139143i
$261$		0			0
$262$	−17.9034	+	10.3365i	−1.10608	+	0.638594i
$263$	−3.15031	−	5.45649i	−0.194256	−	0.336462i	0.752400	−	0.658706i	$-0.228896\pi$
$263$	−3.15031	−	5.45649i	−0.194256	−	0.336462i	−0.946656	+	0.322245i	$0.895563\pi$
$264$		0			0
$265$		−	1.01963i		−	0.0626354i
$266$	−15.0543	+	5.73751i	−0.923036	+	0.351789i
$267$		0			0
$268$	6.45078	+	3.72436i	0.394044	+	0.227502i
$269$	−4.94759	−	8.56947i	−0.301660	−	0.522490i	0.674852	−	0.737953i	$-0.264207\pi$
$269$	−4.94759	−	8.56947i	−0.301660	−	0.522490i	−0.976512	+	0.215463i	$0.930874\pi$
$270$		0			0
$271$	10.9980	+	6.34969i	0.668080	+	0.385716i	0.795349	−	0.606152i	$-0.207288\pi$
$271$	10.9980	+	6.34969i	0.668080	+	0.385716i	−0.127269	+	0.991868i	$0.540621\pi$
$272$	6.54461			0.396825
$273$		0			0
$274$	14.2244			0.859325
$275$	−2.79238	−	1.61218i	−0.168387	−	0.0972181i
$276$		0			0
$277$	−14.0216	−	24.2862i	−0.842479	−	1.45922i	−0.887793	−	0.460243i	$-0.847762\pi$
$277$	−14.0216	−	24.2862i	−0.842479	−	1.45922i	0.0453142	−	0.998973i	$-0.485571\pi$
$278$	8.16583	+	4.71455i	0.489754	+	0.282760i
$279$		0			0
$280$	−0.697477	−	0.567573i	−0.0416822	−	0.0339190i
$281$		−	1.82157i		−	0.108666i	−0.998523	−	0.0543330i	$-0.982697\pi$
$281$		−	1.82157i		−	0.108666i	0.998523	−	0.0543330i	$-0.0173032\pi$
$282$		0			0
$283$	−4.49018	−	7.77723i	−0.266914	−	0.462308i	0.701149	−	0.713014i	$-0.252671\pi$
$283$	−4.49018	−	7.77723i	−0.266914	−	0.462308i	−0.968063	+	0.250706i	$0.919337\pi$
$284$	−0.765985	+	0.442242i	−0.0454529	+	0.0262422i
$285$		0			0
$286$	0.435763	−	2.33988i	0.0257672	−	0.138360i
$287$	−2.25915	−	0.363356i	−0.133354	−	0.0214482i
$288$		0			0
$289$	−12.9159	+	22.3711i	−0.759761	+	1.31594i
$290$	−0.605701	−	1.04910i	−0.0355680	−	0.0616056i
$291$		0			0
$292$	8.72051	+	5.03479i	0.510330	+	0.294639i
$293$		−	2.80194i		−	0.163691i	−0.996645	−	0.0818456i	$-0.973919\pi$
$293$		−	2.80194i		−	0.163691i	0.996645	−	0.0818456i	$-0.0260814\pi$
$294$		0			0
$295$	−1.32692			−0.0772562
$296$	1.77230	−	3.06972i	0.103013	−	0.178424i
$297$		0			0
$298$	−4.05442	−	7.02247i	−0.234866	−	0.406800i
$299$	20.3532	+	17.4137i	1.17705	+	1.00706i
$300$		0			0
$301$	−2.13816	+	13.2939i	−0.123242	+	0.766250i
$302$	−5.30062			−0.305016
$303$		0			0
$304$	5.27341	−	3.04461i	0.302451	−	0.174620i
$305$	0.548905	−	0.316910i	0.0314302	−	0.0181462i
$306$		0			0
$307$			9.21769i			0.526081i	0.964785	+	0.263041i	$0.0847253\pi$
$307$			9.21769i			0.526081i	−0.964785	+	0.263041i	$0.915275\pi$
$308$	1.10236	−	1.35467i	0.0628131	−	0.0771895i
$309$		0			0
$310$	−1.17737	−	0.679754i	−0.0668700	−	0.0386074i
$311$	−5.73418	−	9.93188i	−0.325155	−	0.563185i	0.656388	−	0.754423i	$-0.272083\pi$
$311$	−5.73418	−	9.93188i	−0.325155	−	0.563185i	−0.981544	+	0.191238i	$0.938750\pi$
$312$		0			0
$313$	11.2821	−	19.5412i	0.637703	−	1.10453i	−0.348233	−	0.937408i	$-0.613218\pi$
$313$	11.2821	−	19.5412i	0.637703	−	1.10453i	0.985936	−	0.167126i	$-0.0534486\pi$
$314$			23.0562i			1.30114i
$315$		0			0
$316$	12.4487			0.700295
$317$	−10.9354	−	6.31357i	−0.614195	−	0.354606i	0.160410	−	0.987050i	$-0.448718\pi$
$317$	−10.9354	−	6.31357i	−0.614195	−	0.354606i	−0.774605	+	0.632445i	$0.782052\pi$
$318$		0			0
$319$	2.03762	−	1.17642i	0.114085	−	0.0658667i
$320$	0.294342	+	0.169938i	0.0164542	+	0.00949985i
$321$		0			0
$322$	7.00000	+	18.3668i	0.390095	+	1.02354i
$323$			39.8515i			2.21740i
$324$		0			0
$325$	−16.6062	+	5.86441i	−0.921145	+	0.325299i
$326$	6.78212	+	11.7470i	0.375627	+	0.650605i
$327$		0			0
$328$	0.864853			0.0477535
$329$	15.7788	−	19.3902i	0.869912	−	1.06901i
$330$		0			0
$331$	−23.2278	−	13.4106i	−1.27672	−	0.737113i	−0.300474	−	0.953790i	$-0.597145\pi$
$331$	−23.2278	−	13.4106i	−1.27672	−	0.737113i	−0.976243	+	0.216677i	$0.930478\pi$
$332$	14.1110	−	8.14697i	0.774440	−	0.447123i
$333$		0			0
$334$	7.85170	−	13.5995i	0.429626	−	0.744134i
$335$	−2.53165			−0.138319
$336$		0			0
$337$	9.81892			0.534871			0.267435	−	0.963576i	$-0.413824\pi$
$337$	9.81892			0.534871			0.267435	+	0.963576i	$0.413824\pi$
$338$	−8.16369	−	10.1170i	−0.444046	−	0.550294i
$339$		0			0
$340$	−1.92635	+	1.11218i	−0.104471	+	0.0603164i
$341$	1.32025	−	2.28673i	0.0714953	−	0.123834i
$342$		0			0
$343$	−8.52621	+	16.4409i	−0.460372	+	0.887726i
$344$		−	5.08921i		−	0.274392i
$345$		0			0
$346$	11.7810	−	6.80175i	0.633349	−	0.365664i
$347$	9.54794	+	16.5375i	0.512560	+	0.887781i	0.999894	+	0.0145648i	$0.00463627\pi$
$347$	9.54794	+	16.5375i	0.512560	+	0.887781i	−0.487334	+	0.873216i	$0.662030\pi$
$348$		0			0
$349$		−	0.416132i		−	0.0222750i	−0.999938	−	0.0111375i	$-0.996455\pi$
$349$		−	0.416132i		−	0.0222750i	0.999938	−	0.0111375i	$-0.00354525\pi$
$350$	−12.7592	−	2.05215i	−0.682005	−	0.109692i
$351$		0			0
$352$	−0.330062	+	0.571683i	−0.0175923	+	0.0304708i
$353$	−14.2790	+	8.24399i	−0.759995	+	0.438783i	−0.829294	−	0.558813i	$-0.811257\pi$
$353$	−14.2790	+	8.24399i	−0.759995	+	0.438783i	0.0692989	+	0.997596i	$0.477924\pi$
$354$		0			0
$355$	0.150308	−	0.260341i	0.00797751	−	0.0138175i
$356$		−	4.45539i		−	0.236135i
$357$		0			0
$358$			0.448721i			0.0237157i
$359$	21.1937	+	12.2362i	1.11856	+	0.645801i	0.941033	−	0.338315i	$-0.109857\pi$
$359$	21.1937	+	12.2362i	1.11856	+	0.645801i	0.177527	+	0.984116i	$0.443190\pi$
$360$		0			0
$361$	9.03926	+	15.6565i	0.475751	+	0.824024i
$362$	−13.7734	−	7.95206i	−0.723912	−	0.417951i
$363$		0			0
$364$	−1.70787	−	9.38526i	−0.0895165	−	0.491922i
$365$	−3.42242			−0.179138
$366$		0			0
$367$	6.24399	+	10.8149i	0.325934	+	0.564534i	0.981701	−	0.190429i	$-0.0609880\pi$
$367$	6.24399	+	10.8149i	0.325934	+	0.564534i	−0.655767	+	0.754963i	$0.727655\pi$
$368$	−3.71455	−	6.43378i	−0.193634	−	0.335384i
$369$		0			0
$370$			1.20473i			0.0626309i
$371$	7.41685	−	2.82673i	0.385064	−	0.146756i
$372$		0			0
$373$	3.91393	−	6.77913i	0.202656	−	0.351010i	−0.746728	−	0.665130i	$-0.768376\pi$
$373$	3.91393	−	6.77913i	0.202656	−	0.351010i	0.949383	+	0.314120i	$0.101709\pi$
$374$	−2.16012	−	3.74144i	−0.111697	−	0.193465i
$375$		0			0
$376$	−4.72436	+	8.18283i	−0.243640	+	0.421997i
$377$	2.35284	−	12.6338i	0.121177	−	0.650675i
$378$		0			0
$379$			8.67975i			0.445849i	0.974836	+	0.222925i	$0.0715603\pi$
$379$			8.67975i			0.445849i	−0.974836	+	0.222925i	$0.928440\pi$
$380$	−1.03479	+	1.79231i	−0.0530837	+	0.0919436i
$381$		0			0
$382$	−9.01486	+	5.20473i	−0.461240	+	0.266297i
$383$	−20.2844	−	11.7112i	−1.03648	−	0.598415i	−0.117649	−	0.993055i	$-0.537536\pi$
$383$	−20.2844	−	11.7112i	−1.03648	−	0.598415i	−0.918836	+	0.394640i	$0.870869\pi$
$384$		0			0
$385$	−0.0942619	+	0.586070i	−0.00480403	+	0.0298689i
$386$	−7.69938			−0.391888
$387$		0			0
$388$	−13.9507	+	8.05442i	−0.708238	+	0.408901i
$389$	−15.0957	−	26.1465i	−0.765382	−	1.32568i	−0.940044	−	0.341052i	$-0.889217\pi$
$389$	−15.0957	−	26.1465i	−0.765382	−	1.32568i	0.174662	−	0.984628i	$-0.444117\pi$
$390$		0			0
$391$	48.6205			2.45884
$392$	2.19494	−	6.64697i	0.110861	−	0.335723i
$393$		0			0
$394$	−4.49018	+	7.77723i	−0.226212	+	0.391811i
$395$	−3.66418	+	2.11552i	−0.184365	+	0.106443i
$396$		0			0
$397$	−7.35659	−	4.24733i	−0.369216	−	0.213167i	0.303900	−	0.952704i	$-0.401711\pi$
$397$	−7.35659	−	4.24733i	−0.369216	−	0.213167i	−0.673116	+	0.739537i	$0.735045\pi$
$398$			20.5946i			1.03231i
$399$		0			0
$400$	4.88448			0.244224
$401$	−17.4693	−	10.0859i	−0.872373	−	0.503665i	−0.00423681	−	0.999991i	$-0.501349\pi$
$401$	−17.4693	−	10.0859i	−0.872373	−	0.503665i	−0.868136	+	0.496326i	$0.834682\pi$
$402$		0			0
$403$	−4.80248	−	13.5991i	−0.239229	−	0.677421i
$404$	−1.39764	+	2.42077i	−0.0695349	+	0.120438i
$405$		0			0
$406$	5.95206	−	7.31434i	0.295396	−	0.363004i
$407$	−2.33988			−0.115983
$408$		0			0
$409$	3.72444	−	2.15031i	0.184162	−	0.106326i	−0.405085	−	0.914279i	$-0.632758\pi$
$409$	3.72444	−	2.15031i	0.184162	−	0.106326i	0.589247	+	0.807953i	$0.299425\pi$
$410$	−0.254563	+	0.146972i	−0.0125720	+	0.00725842i
$411$		0			0
$412$	7.53793			0.371367
$413$	−3.67862	−	9.65207i	−0.181013	−	0.474947i
$414$		0			0
$415$	−2.76897	+	4.79599i	−0.135923	+	0.235426i
$416$	1.20062	+	3.39978i	0.0588652	+	0.166688i
$417$		0			0
$418$	−3.48110	−	2.00982i	−0.170266	−	0.0983033i
$419$	32.8974			1.60715			0.803573	−	0.595207i	$-0.202930\pi$
$419$	32.8974			1.60715			0.803573	+	0.595207i	$0.202930\pi$
$420$		0			0
$421$			21.7230i			1.05872i	0.848399	+	0.529358i	$0.177567\pi$
$421$			21.7230i			1.05872i	−0.848399	+	0.529358i	$0.822433\pi$
$422$	13.3280	+	7.69491i	0.648796	+	0.374583i
$423$		0			0
$424$	−2.59808	+	1.50000i	−0.126174	+	0.0728464i
$425$	−15.9835	+	27.6843i	−0.775314	+	1.34288i
$426$		0			0
$427$	3.82695	+	3.11419i	0.185199	+	0.150706i
$428$	−3.72971			−0.180282
$429$		0			0
$430$	0.864853	+	1.49797i	0.0417069	+	0.0722385i
$431$	5.25063	−	3.03146i	0.252914	−	0.146020i	−0.368184	−	0.929753i	$-0.620020\pi$
$431$	5.25063	−	3.03146i	0.252914	−	0.146020i	0.621098	+	0.783733i	$0.286687\pi$
$432$		0			0
$433$	11.1392			0.535314			0.267657	−	0.963514i	$-0.413751\pi$
$433$	11.1392			0.535314			0.267657	+	0.963514i	$0.413751\pi$
$434$	1.68054	−	10.4487i	0.0806687	−	0.501555i
$435$		0			0
$436$	12.4790	+	7.20473i	0.597634	+	0.345044i
$437$	39.1767	−	22.6187i	1.87407	−	1.08200i
$438$		0			0
$439$	−5.81156	+	10.0659i	−0.277371	+	0.480420i	−0.970731	−	0.240171i	$-0.922796\pi$
$439$	−5.81156	+	10.0659i	−0.277371	+	0.480420i	0.693360	+	0.720592i	$0.256130\pi$
$440$		−	0.224361i		−	0.0106960i
$441$		0			0
$442$	−23.1981	−	4.32025i	−1.10342	−	0.205493i
$443$	−2.33654	+	4.04701i	−0.111012	+	0.192279i	−0.916179	−	0.400770i	$-0.868743\pi$
$443$	−2.33654	+	4.04701i	−0.111012	+	0.192279i	0.805166	+	0.593049i	$0.202076\pi$
$444$		0			0
$445$	0.757143	+	1.31141i	0.0358920	+	0.0621668i
$446$	9.00982	−	15.6055i	0.426627	−	0.738940i
$447$		0			0
$448$	−0.420136	+	2.61218i	−0.0198496	+	0.123414i
$449$			36.6271i			1.72854i	0.503026	+	0.864271i	$0.332220\pi$
$449$			36.6271i			1.72854i	−0.503026	+	0.864271i	$0.667780\pi$
$450$		0			0
$451$	−0.285455	−	0.494422i	−0.0134415	−	0.0232814i
$452$	−7.77878	−	13.4732i	−0.365883	−	0.633728i
$453$		0			0
$454$	−0.231033			−0.0108429
$455$	2.09761	+	2.47225i	0.0983377	+	0.115901i
$456$		0			0
$457$	27.1388	+	15.6686i	1.26950	+	0.732947i	0.974894	−	0.222672i	$-0.0714778\pi$
$457$	27.1388	+	15.6686i	1.26950	+	0.732947i	0.294607	+	0.955618i	$0.404811\pi$
$458$	−3.32025	−	5.75084i	−0.155145	−	0.268719i
$459$		0			0
$460$	2.18669	+	1.26249i	0.101955	+	0.0588638i
$461$			0.601231i			0.0280021i	0.999902	+	0.0140011i	$0.00445682\pi$
$461$			0.601231i			0.0280021i	−0.999902	+	0.0140011i	$0.995543\pi$
$462$		0			0
$463$			10.5013i			0.488038i	0.969770	+	0.244019i	$0.0784659\pi$
$463$			10.5013i			0.488038i	−0.969770	+	0.244019i	$0.921534\pi$
$464$	−1.78212	+	3.08672i	−0.0827328	+	0.143297i
$465$		0			0
$466$	−25.5636	+	14.7592i	−1.18421	+	0.683705i
$467$	13.6109	−	23.5747i	0.629835	−	1.09091i	−0.357749	−	0.933818i	$-0.616456\pi$
$467$	13.6109	−	23.5747i	0.629835	−	1.09091i	0.987584	−	0.157089i	$-0.0502109\pi$
$468$		0			0
$469$	−7.01850	−	18.4153i	−0.324084	−	0.850341i
$470$		−	3.21140i		−	0.148131i
$471$		0			0
$472$	1.95206	+	3.38106i	0.0898507	+	0.155626i
$473$	−2.90942	+	1.67975i	−0.133775	+	0.0772352i
$474$		0			0
$475$			29.7427i			1.36469i
$476$	−13.4305	−	10.9291i	−0.615586	−	0.500934i
$477$		0			0
$478$	−7.51182	+	13.0109i	−0.343583	+	0.595103i
$479$	−25.0031	+	14.4356i	−1.14242	+	0.659578i	−0.947029	−	0.321147i	$-0.895932\pi$
$479$	−25.0031	+	14.4356i	−1.14242	+	0.659578i	−0.195393	+	0.980725i	$0.562598\pi$
$480$		0			0
$481$	−8.30851	+	9.71101i	−0.378836	+	0.442784i
$482$	−4.44872			−0.202634
$483$		0			0
$484$	−10.5642			−0.480193
$485$	2.73751	−	4.74151i	0.124304	−	0.215301i
$486$		0			0
$487$	−3.39262	+	1.95873i	−0.153734	+	0.0887585i	−0.574894	−	0.818228i	$-0.694957\pi$
$487$	−3.39262	+	1.95873i	−0.153734	+	0.0887585i	0.421159	+	0.906987i	$0.361623\pi$
$488$	−1.61501	−	0.932427i	−0.0731081	−	0.0422090i
$489$		0			0
$490$	0.483513	+	2.32949i	0.0218429	+	0.105236i
$491$	13.4202			0.605643			0.302821	−	0.953047i	$-0.402071\pi$
$491$	13.4202			0.605643			0.302821	+	0.953047i	$0.402071\pi$
$492$		0			0
$493$	−11.6633	−	20.2014i	−0.525287	−	0.909824i
$494$	−20.7020	+	7.31083i	−0.931427	+	0.328930i
$495$		0			0
$496$			4.00000i			0.179605i
$497$	2.31043	+	0.371603i	0.103637	+	0.0166687i
$498$		0			0
$499$	28.3900	+	16.3910i	1.27091	+	0.733760i	0.975159	−	0.221505i	$-0.0710969\pi$
$499$	28.3900	+	16.3910i	1.27091	+	0.733760i	0.295751	+	0.955265i	$0.404430\pi$
$500$	−2.90942	+	1.67975i	−0.130113	+	0.0751209i
$501$		0			0
$502$	21.1277	+	12.1981i	0.942973	+	0.544426i
$503$	−22.8582			−1.01920			−0.509598	−	0.860413i	$-0.670206\pi$
$503$	−22.8582			−1.01920			−0.509598	+	0.860413i	$0.670206\pi$
$504$		0			0
$505$		−	0.950048i		−	0.0422766i
$506$	−2.45206	+	4.24709i	−0.109007	+	0.188806i
$507$		0			0
$508$	7.20139	+	12.4732i	0.319510	+	0.553408i
$509$	−28.4445	−	16.4224i	−1.26078	−	0.727911i	−0.287553	−	0.957765i	$-0.592842\pi$
$509$	−28.4445	−	16.4224i	−1.26078	−	0.727911i	−0.973225	+	0.229854i	$0.926175\pi$
$510$		0			0
$511$	−9.48798	−	24.8949i	−0.419724	−	1.10128i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	15.9771	−	9.22436i	0.704718	−	0.406869i
$515$	−2.21873	+	1.28098i	−0.0977690	+	0.0564469i
$516$		0			0
$517$	6.23732			0.274317
$518$	−8.76327	+	3.33988i	−0.385036	+	0.146746i
$519$		0			0
$520$	−0.931146	−	0.796667i	−0.0408335	−	0.0349362i
$521$	1.40946	+	2.44126i	0.0617496	+	0.106953i	0.895248	−	0.445569i	$-0.146999\pi$
$521$	1.40946	+	2.44126i	0.0617496	+	0.106953i	−0.833498	+	0.552523i	$0.813665\pi$
$522$		0			0
$523$	2.81490	−	4.87555i	0.123087	−	0.213193i	−0.797897	−	0.602794i	$-0.794054\pi$
$523$	2.81490	−	4.87555i	0.123087	−	0.213193i	0.920984	+	0.389601i	$0.127387\pi$
$524$	−20.6731			−0.903108
$525$		0			0
$526$		−	6.30062i		−	0.274720i
$527$	−22.6712	−	13.0892i	−0.987572	−	0.570175i
$528$		0			0
$529$	−16.0957	−	27.8786i	−0.699813	−	1.21211i
$530$	0.509815	−	0.883026i	0.0221450	−	0.0383562i
$531$		0			0
$532$	−15.9061	−	2.55830i	−0.689618	−	0.110916i
$533$	−3.06556	−	0.570909i	−0.132784	−	0.0247288i
$534$		0			0
$535$	1.09781	−	0.633820i	0.0474624	−	0.0274024i
$536$	3.72436	+	6.45078i	0.160868	+	0.278631i
$537$		0			0
$538$		−	9.89517i		−	0.426611i
$539$	−4.52443	+	0.939099i	−0.194881	+	0.0404498i
$540$		0			0
$541$	−21.4015	−	12.3562i	−0.920123	−	0.531233i	−0.0364488	−	0.999336i	$-0.511605\pi$
$541$	−21.4015	−	12.3562i	−0.920123	−	0.531233i	−0.883674	+	0.468102i	$0.844938\pi$
$542$	6.34969	+	10.9980i	0.272743	+	0.472404i
$543$		0			0
$544$	5.66780	+	3.27230i	0.243005	+	0.140299i
$545$	−4.89744			−0.209783
$546$		0			0
$547$	18.1874			0.777636			0.388818	−	0.921315i	$-0.372884\pi$
$547$	18.1874			0.777636			0.388818	+	0.921315i	$0.372884\pi$
$548$	12.3187	+	7.11218i	0.526227	+	0.303817i
$549$		0			0
$550$	−1.61218	−	2.79238i	−0.0687436	−	0.119067i
$551$	−18.7957	−	10.8517i	−0.800724	−	0.462298i
$552$		0			0
$553$	−25.5466	−	20.7886i	−1.08635	−	0.884021i
$554$		−	28.0433i		−	1.19144i
$555$		0			0
$556$	4.71455	+	8.16583i	0.199941	+	0.346308i
$557$	23.0713	−	13.3202i	0.977564	−	0.564397i	0.0760303	−	0.997106i	$-0.475775\pi$
$557$	23.0713	−	13.3202i	0.977564	−	0.564397i	0.901534	+	0.432709i	$0.142442\pi$
$558$		0			0
$559$	−3.35951	+	18.0393i	−0.142092	+	0.762979i
$560$	−0.320246	−	0.840272i	−0.0135329	−	0.0355080i
$561$		0			0
$562$	0.910786	−	1.57753i	0.0384192	−	0.0665440i
$563$	13.8386	+	23.9691i	0.583225	+	1.01018i	0.995094	+	0.0989328i	$0.0315429\pi$
$563$	13.8386	+	23.9691i	0.583225	+	1.01018i	−0.411869	+	0.911243i	$0.635124\pi$
$564$		0			0
$565$	4.57925	+	2.64383i	0.192650	+	0.111227i
$566$		−	8.98037i		−	0.377473i
$567$		0			0
$568$	−0.884484			−0.0371121
$569$	−10.1949	+	17.6581i	−0.427393	+	0.740266i	−0.996641	−	0.0818997i	$-0.973901\pi$
$569$	−10.1949	+	17.6581i	−0.427393	+	0.740266i	0.569248	+	0.822166i	$0.307235\pi$
$570$		0			0
$571$	−19.1022	−	33.0859i	−0.799401	−	1.38460i	−0.920007	−	0.391903i	$-0.871817\pi$
$571$	−19.1022	−	33.0859i	−0.799401	−	1.38460i	0.120606	−	0.992700i	$-0.461516\pi$
$572$	1.54732	−	1.80851i	0.0646967	−	0.0756177i
$573$		0			0
$574$	−1.77481	−	1.44425i	−0.0740789	−	0.0602819i
$575$	36.2873			1.51328
$576$		0			0
$577$	9.83762	−	5.67975i	0.409546	−	0.236451i	−0.281049	−	0.959693i	$-0.590682\pi$
$577$	9.83762	−	5.67975i	0.409546	−	0.236451i	0.690594	+	0.723242i	$0.257349\pi$
$578$	−22.3711	+	12.9159i	−0.930514	+	0.537232i
$579$		0			0
$580$		−	1.21140i		−	0.0503007i
$581$	−42.5627	−	6.84567i	−1.76580	−	0.284006i
$582$		0			0
$583$	1.71505	+	0.990185i	0.0710301	+	0.0410093i
$584$	5.03479	+	8.72051i	0.208341	+	0.360857i
$585$		0			0
$586$	1.40097	−	2.42655i	0.0578736	−	0.100240i
$587$		−	37.2347i		−	1.53684i	−0.639946	−	0.768420i	$-0.721043\pi$
$587$		−	37.2347i		−	1.53684i	0.639946	−	0.768420i	$-0.278957\pi$
$588$		0			0
$589$	−24.3569			−1.00361
$590$	−1.14914	−	0.663459i	−0.0473095	−	0.0273142i
$591$		0			0
$592$	3.06972	−	1.77230i	0.126165	−	0.0728412i
$593$	20.9674	+	12.1055i	0.861026	+	0.497114i	0.864356	−	0.502881i	$-0.167727\pi$
$593$	20.9674	+	12.1055i	0.861026	+	0.497114i	−0.00332968	+	0.999994i	$0.501060\pi$
$594$		0			0
$595$	5.81043	+	0.934534i	0.238204	+	0.0383121i
$596$		−	8.10884i		−	0.332151i
$597$		0			0
$598$	8.91951	+	25.2573i	0.364746	+	1.03285i
$599$	−3.23952	−	5.61102i	−0.132363	−	0.229260i	0.792224	−	0.610231i	$-0.208923\pi$
$599$	−3.23952	−	5.61102i	−0.132363	−	0.229260i	−0.924587	+	0.380971i	$0.875590\pi$
$600$		0			0
$601$	41.4354			1.69018			0.845092	−	0.534621i	$-0.179546\pi$
$601$	41.4354			1.69018			0.845092	+	0.534621i	$0.179546\pi$
$602$	−8.49867	+	10.4438i	−0.346380	+	0.425658i
$603$		0			0
$604$	−4.59047	−	2.65031i	−0.186783	−	0.107839i
$605$	3.10950	−	1.79527i	0.126419	−	0.0729881i
$606$		0			0
$607$	4.20139	−	7.27703i	0.170529	−	0.295365i	−0.768076	−	0.640359i	$-0.778786\pi$
$607$	4.20139	−	7.27703i	0.170529	−	0.295365i	0.938605	+	0.344994i	$0.112119\pi$
$608$	6.08921			0.246950
$609$		0			0
$610$	0.633820			0.0256626
$611$	22.1477	−	25.8863i	0.895999	−	1.04725i
$612$		0			0
$613$	40.6144	−	23.4487i	1.64040	−	0.947085i	0.659708	−	0.751522i	$-0.270680\pi$
$613$	40.6144	−	23.4487i	1.64040	−	0.947085i	0.980691	−	0.195563i	$-0.0626534\pi$
$614$	−4.60884	+	7.98275i	−0.185998	+	0.322158i
$615$		0			0
$616$	1.63201	−	0.621996i	0.0657556	−	0.0250609i
$617$		−	32.6271i		−	1.31352i	−0.754100	−	0.656760i	$-0.771927\pi$
$617$		−	32.6271i		−	1.31352i	0.754100	−	0.656760i	$-0.228073\pi$
$618$		0			0
$619$	−4.72995	+	2.73084i	−0.190113	+	0.109762i	−0.592035	−	0.805912i	$-0.701675\pi$
$619$	−4.72995	+	2.73084i	−0.190113	+	0.109762i	0.401923	+	0.915674i	$0.368342\pi$
$620$	−0.679754	−	1.17737i	−0.0272996	−	0.0472842i
$621$		0			0
$622$		−	11.4684i		−	0.459839i
$623$	−7.44023	+	9.14312i	−0.298087	+	0.366311i
$624$		0			0
$625$	−11.6403	+	20.1616i	−0.465612	+	0.806464i
$626$	19.5412	−	11.2821i	0.781024	−	0.450924i
$627$		0			0
$628$	−11.5281	+	19.9673i	−0.460022	+	0.796782i
$629$			23.1981i			0.924967i
$630$		0			0
$631$		−	41.8845i		−	1.66739i	−0.552221	−	0.833697i	$-0.686220\pi$
$631$		−	41.8845i		−	1.66739i	0.552221	−	0.833697i	$-0.313780\pi$
$632$	10.7809	+	6.22436i	0.428842	+	0.247592i
$633$		0			0
$634$	−6.31357	−	10.9354i	−0.250744	−	0.434301i
$635$	−4.23935	−	2.44759i	−0.168233	−	0.0971295i
$636$		0			0
$637$	−12.1680	+	22.1120i	−0.482115	+	0.876108i
$638$	2.35284			0.0931497
$639$		0			0
$640$	0.169938	+	0.294342i	0.00671741	+	0.0116349i
$641$	3.30842	+	5.73035i	0.130675	+	0.226335i	0.923937	−	0.382545i	$-0.124952\pi$
$641$	3.30842	+	5.73035i	0.130675	+	0.226335i	−0.793262	+	0.608880i	$0.791619\pi$
$642$		0			0
$643$		−	23.7427i		−	0.936319i	−0.883644	−	0.468160i	$-0.844917\pi$
$643$		−	23.7427i		−	0.936319i	0.883644	−	0.468160i	$-0.155083\pi$
$644$	−3.12123	+	19.4061i	−0.122994	+	0.764708i
$645$		0			0
$646$	−19.9258	+	34.5124i	−0.783968	+	1.35787i
$647$	19.5642	+	33.8863i	0.769150	+	1.33221i	0.938025	+	0.346569i	$0.112653\pi$
$647$	19.5642	+	33.8863i	0.769150	+	1.33221i	−0.168875	+	0.985637i	$0.554013\pi$
$648$		0			0
$649$	1.28860	−	2.23192i	0.0505819	−	0.0876104i
$650$	−17.3136	−	3.22436i	−0.679094	−	0.126470i
$651$		0			0
$652$			13.5642i			0.531217i
$653$	2.75714	−	4.77551i	0.107895	−	0.186880i	−0.807022	−	0.590521i	$-0.798922\pi$
$653$	2.75714	−	4.77551i	0.107895	−	0.186880i	0.914917	+	0.403641i	$0.132256\pi$
$654$		0			0
$655$	6.08496	−	3.51315i	0.237759	−	0.137270i
$656$	0.748985	+	0.432427i	0.0292429	+	0.0168834i
$657$		0			0
$658$	23.3599	−	8.90298i	0.910664	−	0.347074i
$659$	49.2217			1.91741			0.958703	−	0.284410i	$-0.0917977\pi$
$659$	49.2217			1.91741			0.958703	+	0.284410i	$0.0917977\pi$
$660$		0			0
$661$	−10.6731	+	6.16213i	−0.415137	+	0.239679i	−0.692994	−	0.720943i	$-0.743709\pi$
$661$	−10.6731	+	6.16213i	−0.415137	+	0.239679i	0.277858	+	0.960622i	$0.410376\pi$
$662$	−13.4106	−	23.2278i	−0.521218	−	0.902775i
$663$		0			0
$664$	16.2939			0.632328
$665$	5.11659	−	1.95005i	0.198413	−	0.0756196i
$666$		0			0
$667$	−13.2395	+	22.9315i	−0.512636	+	0.887912i
$668$	13.5995	−	7.85170i	0.526182	−	0.303791i
$669$		0			0
$670$	−2.19247	−	1.26582i	−0.0847026	−	0.0489031i
$671$			1.23103i			0.0475235i
$672$		0			0
$673$	6.79527			0.261938			0.130969	−	0.991386i	$-0.458191\pi$
$673$	6.79527			0.261938			0.130969	+	0.991386i	$0.458191\pi$
$674$	8.50343	+	4.90946i	0.327540	+	0.189105i
$675$		0			0
$676$	−2.01145	−	12.8434i	−0.0773635	−	0.493979i
$677$	8.34636	−	14.4563i	0.320777	−	0.555601i	−0.659872	−	0.751378i	$-0.729389\pi$
$677$	8.34636	−	14.4563i	0.320777	−	0.555601i	0.980648	+	0.195777i	$0.0627228\pi$
$678$		0			0
$679$	42.0792	+	6.76790i	1.61485	+	0.259728i
$680$	−2.22436			−0.0853003
$681$		0			0
$682$	2.28673	−	1.32025i	0.0875636	−	0.0505548i
$683$	18.8069	−	10.8582i	0.719627	−	0.415477i	−0.0949885	−	0.995478i	$-0.530281\pi$
$683$	18.8069	−	10.8582i	0.719627	−	0.415477i	0.814615	+	0.580002i	$0.196948\pi$
$684$		0			0
$685$	−4.83453			−0.184718
$686$	−15.6044	+	9.97514i	−0.595778	+	0.380853i
$687$		0			0
$688$	2.54461	−	4.40739i	0.0970122	−	0.168030i
$689$	10.1993	−	3.60186i	0.388564	−	0.137220i
$690$		0			0
$691$	−40.6461	−	23.4670i	−1.54625	−	0.892728i	−0.998423	−	0.0561358i	$-0.982122\pi$
$691$	−40.6461	−	23.4670i	−1.54625	−	0.892728i	−0.547827	−	0.836592i	$-0.684545\pi$
$692$	13.6035			0.517127
$693$		0			0
$694$			19.0959i			0.724870i
$695$	−2.77538	−	1.60236i	−0.105276	−	0.0607812i
$696$		0			0
$697$	−4.90181	+	2.83006i	−0.185669	+	0.107196i
$698$	0.208066	−	0.360381i	0.00787541	−	0.0136406i
$699$		0			0
$700$	−10.0237	−	8.15679i	−0.378859	−	0.308298i
$701$	7.32251			0.276568			0.138284	−	0.990393i	$-0.455841\pi$
$701$	7.32251			0.276568			0.138284	+	0.990393i	$0.455841\pi$
$702$		0			0
$703$	10.7919	+	18.6922i	0.407026	+	0.704989i
$704$	−0.571683	+	0.330062i	−0.0215461	+	0.0124397i
$705$		0			0
$706$	−16.4880			−0.620533
$707$	6.91070	−	2.63382i	0.259904	−	0.0990550i
$708$		0			0
$709$	5.75661	+	3.32358i	0.216194	+	0.124820i	0.604187	−	0.796843i	$-0.293498\pi$
$709$	5.75661	+	3.32358i	0.216194	+	0.124820i	−0.387993	+	0.921662i	$0.626831\pi$
$710$	0.260341	−	0.150308i	0.00977041	−	0.00564095i
$711$		0			0
$712$	2.22770	−	3.85848i	0.0834865	−	0.144603i
$713$			29.7164i			1.11289i
$714$		0			0
$715$	−0.148106	+	0.795270i	−0.00553884	+	0.0297414i
$716$	−0.224361	+	0.388604i	−0.00838475	+	0.0145228i
$717$		0			0
$718$	12.2362	+	21.1937i	0.456650	+	0.790942i
$719$	−2.43576	+	4.21886i	−0.0908386	+	0.157337i	−0.907864	−	0.419264i	$-0.862288\pi$
$719$	−2.43576	+	4.21886i	−0.0908386	+	0.157337i	0.817026	+	0.576601i	$0.195621\pi$
$720$		0			0
$721$	−15.4689	−	12.5879i	−0.576094	−	0.468797i
$722$			18.0785i			0.672813i
$723$		0			0
$724$	−7.95206	−	13.7734i	−0.295536	−	0.511883i
$725$	−8.70473	−	15.0770i	−0.323286	−	0.559947i
$726$		0			0
$727$	−4.98931			−0.185043			−0.0925216	−	0.995711i	$-0.529493\pi$
$727$	−4.98931			−0.185043			−0.0925216	+	0.995711i	$0.529493\pi$
$728$	3.21358	−	8.98181i	0.119103	−	0.332888i
$729$		0			0
$730$	−2.96390	−	1.71121i	−0.109699	−	0.0633347i
$731$	16.6535	+	28.8446i	0.615950	+	1.06686i
$732$		0			0
$733$	−6.46582	−	3.73304i	−0.238820	−	0.137883i	0.375814	−	0.926695i	$-0.377363\pi$
$733$	−6.46582	−	3.73304i	−0.238820	−	0.137883i	−0.614634	+	0.788812i	$0.710696\pi$
$734$			12.4880i			0.460940i
$735$		0			0
$736$		−	7.42909i		−	0.273840i
$737$	2.45854	−	4.25831i	0.0905614	−	0.156857i
$738$		0			0
$739$	1.26585	−	0.730840i	0.0465651	−	0.0268844i	−0.476537	−	0.879155i	$-0.658108\pi$
$739$	1.26585	−	0.730840i	0.0465651	−	0.0268844i	0.523102	+	0.852270i	$0.324775\pi$
$740$	−0.602365	+	1.04333i	−0.0221434	+	0.0383535i
$741$		0			0
$742$	7.83654	+	1.26041i	0.287688	+	0.0462710i
$743$		−	5.67975i		−	0.208370i	−0.994558	−	0.104185i	$-0.966777\pi$
$743$		−	5.67975i		−	0.208370i	0.994558	−	0.104185i	$-0.0332234\pi$
$744$		0			0
$745$	1.37800	+	2.38677i	0.0504862	+	0.0874446i
$746$	6.77913	−	3.91393i	0.248201	−	0.143299i
$747$		0			0
$748$		−	4.32025i		−	0.157964i
$749$	7.65390	+	6.22838i	0.279668	+	0.227580i
$750$		0			0
$751$	−2.19806	+	3.80715i	−0.0802083	+	0.138925i	−0.903339	−	0.428927i	$-0.858892\pi$
$751$	−2.19806	+	3.80715i	−0.0802083	+	0.138925i	0.823131	+	0.567851i	$0.192225\pi$
$752$	−8.18283	+	4.72436i	−0.298397	+	0.172280i
$753$		0			0
$754$	8.35453	−	9.76479i	0.304254	−	0.355613i
$755$	1.80156			0.0655654
$756$		0			0
$757$	21.0326			0.764442			0.382221	−	0.924071i	$-0.375159\pi$
$757$	21.0326			0.764442			0.382221	+	0.924071i	$0.375159\pi$
$758$	−4.33988	+	7.51689i	−0.157631	+	0.273026i
$759$		0			0
$760$	−1.79231	+	1.03479i	−0.0650140	+	0.0375358i
$761$	−10.9130	−	6.30062i	−0.395595	−	0.228397i	0.288986	−	0.957333i	$-0.406682\pi$
$761$	−10.9130	−	6.30062i	−0.395595	−	0.228397i	−0.684582	+	0.728936i	$0.740015\pi$
$762$		0			0
$763$	−13.5772	−	35.6243i	−0.491528	−	1.28968i
$764$	−10.4095			−0.376601
$765$		0			0
$766$	−11.7112	−	20.2844i	−0.423143	−	0.732906i
$767$	−4.68736	−	13.2731i	−0.169251	−	0.479265i
$768$		0			0
$769$		−	34.4398i		−	1.24193i	−0.783838	−	0.620965i	$-0.786741\pi$
$769$		−	34.4398i		−	1.24193i	0.783838	−	0.620965i	$-0.213259\pi$
$770$	−0.374668	+	0.460421i	−0.0135021	+	0.0165924i
$771$		0			0
$772$	−6.66786	−	3.84969i	−0.239982	−	0.138553i
$773$	−14.5471	+	8.39877i	−0.523223	+	0.302083i	−0.738252	−	0.674525i	$-0.764349\pi$
$773$	−14.5471	+	8.39877i	−0.523223	+	0.302083i	0.215030	+	0.976608i	$0.431015\pi$
$774$		0			0
$775$	−16.9203	−	9.76897i	−0.607797	−	0.350912i
$776$	−16.1088			−0.578274
$777$		0			0
$778$		−	30.1914i		−	1.08241i
$779$	−2.63314	+	4.56073i	−0.0943419	+	0.163405i
$780$		0			0
$781$	0.291934	+	0.505645i	0.0104462	+	0.0180934i
$782$	42.1066	+	24.3102i	1.50573	+	0.869332i
$783$		0			0
$784$	5.22436	−	4.65898i	0.186584	−	0.166392i
$785$		−	7.83628i		−	0.279689i
$786$		0			0
$787$	31.9974	−	18.4737i	1.14058	−	0.658516i	0.194008	−	0.981000i	$-0.437851\pi$
$787$	31.9974	−	18.4737i	1.14058	−	0.658516i	0.946575	+	0.322484i	$0.104518\pi$
$788$	−7.77723	+	4.49018i	−0.277052	+	0.159956i
$789$		0			0
$790$	−4.23103			−0.150533
$791$	−6.53629	+	40.6392i	−0.232404	+	1.44496i
$792$		0			0
$793$	5.10906	+	4.37119i	0.181428	+	0.155226i
$794$	−4.24733	−	7.35659i	−0.150732	−	0.261075i
$795$		0			0
$796$	−10.2973	+	17.8354i	−0.364977	+	0.632159i
$797$	−38.7819			−1.37373			−0.686863	−	0.726787i	$-0.741013\pi$
$797$	−38.7819			−1.37373			−0.686863	+	0.726787i	$0.741013\pi$
$798$		0			0
$799$		−	61.8382i		−	2.18768i
$800$	4.23009	+	2.44224i	0.149556	+	0.0863463i
$801$		0			0
$802$	−10.0859	−	17.4693i	−0.356145	−	0.616861i
$803$	3.32358	−	5.75661i	0.117287	−	0.203146i
$804$		0			0
$805$	−2.37914	−	6.24245i	−0.0838536	−	0.220018i
$806$	2.64049	−	14.1784i	0.0930074	−	0.499414i
$807$		0			0
$808$	−2.42077	+	1.39764i	−0.0851626	+	0.0491686i
$809$	1.06090	+	1.83754i	0.0372993	+	0.0646043i	0.884072	−	0.467350i	$-0.154791\pi$
$809$	1.06090	+	1.83754i	0.0372993	+	0.0646043i	−0.846773	+	0.531954i	$0.821458\pi$
$810$		0			0
$811$		−	3.66680i		−	0.128759i	−0.997926	−	0.0643793i	$-0.979493\pi$
$811$		−	3.66680i		−	0.128759i	0.997926	−	0.0643793i	$-0.0205067\pi$
$812$	8.81180	−	3.35837i	0.309234	−	0.117856i
$813$		0			0
$814$	−2.02639	−	1.16994i	−0.0710250	−	0.0410063i
$815$	−2.30509	−	3.99253i	−0.0807436	−	0.139852i
$816$		0			0
$817$	26.8375	+	15.4947i	0.938926	+	0.542089i
$818$	4.30062			0.150367
$819$		0			0
$820$	−0.293944			−0.0102650
$821$	−18.6261	−	10.7538i	−0.650057	−	0.375310i	0.138421	−	0.990373i	$-0.455797\pi$
$821$	−18.6261	−	10.7538i	−0.650057	−	0.375310i	−0.788478	+	0.615063i	$0.789131\pi$
$822$		0			0
$823$	17.9770	+	31.1371i	0.626640	+	1.08537i	0.988221	+	0.153032i	$0.0489037\pi$
$823$	17.9770	+	31.1371i	0.626640	+	1.08537i	−0.361581	+	0.932341i	$0.617763\pi$
$824$	6.52804	+	3.76897i	0.227415	+	0.131298i
$825$		0			0
$826$	1.64026	−	10.1983i	0.0570719	−	0.354843i
$827$		−	32.8778i		−	1.14327i	−0.820507	−	0.571637i	$-0.806309\pi$
$827$		−	32.8778i		−	1.14327i	0.820507	−	0.571637i	$-0.193691\pi$
$828$		0			0
$829$	4.91280	+	8.50921i	0.170628	+	0.295537i	0.938640	−	0.344899i	$-0.112087\pi$
$829$	4.91280	+	8.50921i	0.170628	+	0.295537i	−0.768011	+	0.640436i	$0.778754\pi$
$830$	−4.79599	+	2.76897i	−0.166471	+	0.0961123i
$831$		0			0
$832$	−0.660123	+	3.54461i	−0.0228857	+	0.122887i
$833$	9.31043	+	44.8562i	0.322587	+	1.55417i
$834$		0			0
$835$	−2.66861	+	4.62217i	−0.0923511	+	0.159957i
$836$	−2.00982	−	3.48110i	−0.0695109	−	0.120396i
$837$		0			0
$838$	28.4900	+	16.4487i	0.984171	+	0.568212i
$839$		−	42.6008i		−	1.47074i	−0.677663	−	0.735372i	$-0.737007\pi$
$839$		−	42.6008i		−	1.47074i	0.677663	−	0.735372i	$-0.262993\pi$
$840$		0			0
$841$	−16.2962			−0.561938
$842$	−10.8615	+	18.8127i	−0.374313	+	0.648328i
$843$		0			0
$844$	7.69491	+	13.3280i	0.264870	+	0.458768i
$845$	2.77465	+	3.43854i	0.0954509	+	0.118289i
$846$		0			0
$847$	21.6794	+	17.6416i	0.744912	+	0.606173i
$848$	−3.00000			−0.103020
$849$		0			0
$850$	−27.6843	+	15.9835i	−0.949562	+	0.548230i
$851$	22.8052	−	13.1666i	0.781753	−	0.451345i
$852$		0			0
$853$		−	47.7490i		−	1.63489i	−0.576005	−	0.817446i	$-0.695389\pi$
$853$		−	47.7490i		−	1.63489i	0.576005	−	0.817446i	$-0.304611\pi$
$854$	1.75714	+	4.61044i	0.0601282	+	0.157766i
$855$		0			0
$856$	−3.23002	−	1.86485i	−0.110400	−	0.0637394i
$857$	−3.44671	−	5.96988i	−0.117737	−	0.203927i	0.801133	−	0.598486i	$-0.204231\pi$
$857$	−3.44671	−	5.96988i	−0.117737	−	0.203927i	−0.918871	+	0.394559i	$0.870897\pi$
$858$		0			0
$859$	−14.3898	+	24.9239i	−0.490975	+	0.850393i	−0.999946	−	0.0103904i	$-0.996693\pi$
$859$	−14.3898	+	24.9239i	−0.490975	+	0.850393i	0.508971	+	0.860783i	$0.330026\pi$
$860$			1.72971i			0.0589825i
$861$		0			0
$862$	6.06291			0.206504
$863$	42.0668	+	24.2873i	1.43197	+	0.826748i	0.997271	−	0.0738274i	$-0.0235214\pi$
$863$	42.0668	+	24.2873i	1.43197	+	0.826748i	0.434699	+	0.900576i	$0.356855\pi$
$864$		0			0
$865$	−4.00408	+	2.31176i	−0.136143	+	0.0786021i
$866$	9.64680	+	5.56958i	0.327812	+	0.189262i
$867$		0			0
$868$	6.67975	−	8.20859i	0.226726	−	0.278618i
$869$		−	8.21769i		−	0.278766i
$870$		0			0
$871$	−8.94308	−	25.3240i	−0.303025	−	0.858072i
$872$	7.20473	+	12.4790i	0.243983	+	0.422591i
$873$		0			0
$874$	45.2373			1.53018
$875$	8.77564	+	1.41145i	0.296671	+	0.0477157i
$876$		0			0
$877$	7.99779	+	4.61753i	0.270066	+	0.155923i	0.628918	−	0.777472i	$-0.283498\pi$
$877$	7.99779	+	4.61753i	0.270066	+	0.155923i	−0.358852	+	0.933395i	$0.616832\pi$
$878$	−10.0659	+	5.81156i	−0.339709	+	0.196131i
$879$		0			0
$880$	0.112180	−	0.194302i	0.00378160	−	0.00654992i
$881$	14.9108			0.502357			0.251179	−	0.967941i	$-0.419182\pi$
$881$	14.9108			0.502357			0.251179	+	0.967941i	$0.419182\pi$
$882$		0			0
$883$	−37.9171			−1.27601			−0.638006	−	0.770032i	$-0.720240\pi$
$883$	−37.9171			−1.27601			−0.638006	+	0.770032i	$0.720240\pi$
$884$	−17.9300	−	15.3405i	−0.603051	−	0.515956i
$885$		0			0
$886$	−4.04701	+	2.33654i	−0.135962	+	0.0784976i
$887$	5.56424	−	9.63754i	0.186829	−	0.323597i	−0.757362	−	0.652995i	$-0.773512\pi$
$887$	5.56424	−	9.63754i	0.186829	−	0.323597i	0.944191	+	0.329398i	$0.106846\pi$
$888$		0			0
$889$	6.05113	−	37.6227i	0.202948	−	1.26182i
$890$			1.51429i			0.0507590i
$891$		0			0
$892$	15.6055	−	9.00982i	0.522509	−	0.301671i
$893$	−28.7676	−	49.8270i	−0.962672	−	1.66740i
$894$		0			0
$895$		−	0.152510i		−	0.00509785i
$896$	−1.66994	+	2.05215i	−0.0557887	+	0.0685574i
$897$		0			0
$898$	−18.3136	+	31.7200i	−0.611132	+	1.05851i
$899$	12.3469	−	7.12847i	0.411792	−	0.237748i
$900$		0			0
$901$	9.81691	−	17.0034i	0.327049	−	0.566465i
$902$		−	0.570909i		−	0.0190092i
$903$		0			0
$904$		−	15.5576i		−	0.517437i
$905$	4.68125	+	2.70272i	0.155610	+	0.0898415i
$906$		0			0
$907$	6.05442	+	10.4866i	0.201034	+	0.348201i	0.948862	−	0.315692i	$-0.102237\pi$
$907$	6.05442	+	10.4866i	0.201034	+	0.348201i	−0.747828	+	0.663893i	$0.768903\pi$
$908$	−0.200080	−	0.115516i	−0.00663989	−	0.00383354i
$909$		0			0
$910$	0.580464	+	3.18983i	0.0192422	+	0.105742i
$911$	46.4354			1.53847			0.769236	−	0.638964i	$-0.220637\pi$
$911$	46.4354			1.53847			0.769236	+	0.638964i	$0.220637\pi$
$912$		0			0
$913$	−5.37800	−	9.31498i	−0.177986	−	0.308281i
$914$	15.6686	+	27.1388i	0.518272	+	0.897673i
$915$		0			0
$916$		−	6.64049i		−	0.219408i
$917$	42.4242	+	34.5228i	1.40097	+	1.14004i
$918$		0			0
$919$	−18.3898	+	31.8521i	−0.606624	+	1.05070i	0.385168	+	0.922846i	$0.374143\pi$
$919$	−18.3898	+	31.8521i	−0.606624	+	1.05070i	−0.991792	+	0.127858i	$0.959190\pi$
$920$	1.26249	+	2.18669i	0.0416230	+	0.0720931i
$921$		0			0
$922$	−0.300616	+	0.520681i	−0.00990025	+	0.0171477i
$923$	3.13515	+	0.583868i	0.103195	+	0.0192183i
$924$		0			0
$925$			17.3136i			0.569267i
$926$	−5.25066	+	9.09442i	−0.172548	+	0.298861i
$927$		0			0
$928$	−3.08672	+	1.78212i	−0.101327	+	0.0585009i
$929$	3.58462	+	2.06958i	0.117608	+	0.0679008i	0.557650	−	0.830076i	$-0.311703\pi$
$929$	3.58462	+	2.06958i	0.117608	+	0.0679008i	−0.440042	+	0.897977i	$0.645037\pi$
$930$		0			0
$931$	28.3695	+	31.8122i	0.929773	+	1.04260i
$932$	−29.5183			−0.966904
$933$		0			0
$934$	23.5747	−	13.6109i	0.771387	−	0.445361i
$935$	0.734176	+	1.27163i	0.0240101	+	0.0415867i
$936$		0			0
$937$	45.2939			1.47969			0.739844	−	0.672778i	$-0.234899\pi$
$937$	45.2939			1.47969			0.739844	+	0.672778i	$0.234899\pi$
$938$	3.12947	−	19.4574i	0.102181	−	0.635307i
$939$		0			0
$940$	1.60570	−	2.78116i	0.0523722	−	0.0907113i
$941$	−41.4781	+	23.9474i	−1.35215	+	0.780663i	−0.988550	−	0.150893i	$-0.951785\pi$
$941$	−41.4781	+	23.9474i	−1.35215	+	0.780663i	−0.363598	+	0.931556i	$0.618452\pi$
$942$		0			0
$943$	5.56428	+	3.21254i	0.181198	+	0.104615i
$944$			3.90411i			0.127068i
$945$		0			0
$946$	−3.35951			−0.109227
$947$	18.5809	+	10.7277i	0.603799	+	0.348603i	0.770534	−	0.637398i	$-0.219989\pi$
$947$	18.5809	+	10.7277i	0.603799	+	0.348603i	−0.166736	+	0.986002i	$0.553323\pi$
$948$		0			0
$949$	−12.0897	−	34.2344i	−0.392450	−	1.11129i
$950$	−14.8713	+	25.7579i	−0.482490	+	0.835697i
$951$		0			0
$952$	−6.16660	−	16.1801i	−0.199861	−	0.524401i
$953$	−48.0433			−1.55627			−0.778137	−	0.628094i	$-0.783835\pi$
$953$	−48.0433			−1.55627			−0.778137	+	0.628094i	$0.783835\pi$
$954$		0			0
$955$	3.06394	−	1.76897i	0.0991468	−	0.0572424i
$956$	−13.0109	+	7.51182i	−0.420801	+	0.242950i
$957$		0			0
$958$	−28.8711			−0.932784
$959$	−13.4028	−	35.1666i	−0.432799	−	1.13559i
$960$		0			0
$961$	−7.50000	+	12.9904i	−0.241935	+	0.419045i
$962$	−12.0509	+	4.25573i	−0.388536	+	0.137210i
$963$		0			0
$964$	−3.85271	−	2.22436i	−0.124087	−	0.0716418i
$965$	2.61684			0.0842392
$966$		0			0
$967$		−	4.91481i		−	0.158049i	−0.996873	−	0.0790247i	$-0.974819\pi$
$967$		−	4.91481i		−	0.158049i	0.996873	−	0.0790247i	$-0.0251806\pi$
$968$	−9.14890	−	5.28212i	−0.294057	−	0.169774i
$969$		0			0
$970$	4.74151	−	2.73751i	0.152241	−	0.0878962i
$971$	15.0792	−	26.1180i	0.483915	−	0.838165i	−0.515915	−	0.856640i	$-0.672548\pi$
$971$	15.0792	−	26.1180i	0.483915	−	0.838165i	0.999829	+	0.0184751i	$0.00588115\pi$
$972$		0			0
$973$	3.96150	−	24.6305i	0.127000	−	0.789617i
$974$	−3.91746			−0.125523
$975$		0			0
$976$	−0.932427	−	1.61501i	−0.0298462	−	0.0516952i
$977$	−29.7995	+	17.2047i	−0.953369	+	0.550428i	−0.894126	−	0.447815i	$-0.852202\pi$
$977$	−29.7995	+	17.2047i	−0.953369	+	0.550428i	−0.0592434	+	0.998244i	$0.518869\pi$
$978$		0			0
$979$	−2.94111			−0.0939982
$980$	−0.746010	+	2.25915i	−0.0238304	+	0.0721660i
$981$		0			0
$982$	11.6222	+	6.71008i	0.370879	+	0.214127i
$983$	17.2772	−	9.97502i	0.551059	−	0.318154i	−0.198490	−	0.980103i	$-0.563604\pi$
$983$	17.2772	−	9.97502i	0.551059	−	0.318154i	0.749549	+	0.661949i	$0.230270\pi$
$984$		0			0
$985$	1.52611	−	2.64330i	0.0486259	−	0.0842225i
$986$		−	23.3265i		−	0.742868i
$987$		0			0
$988$	−21.5839	−	4.01963i	−0.686674	−	0.127881i
$989$	18.9041	−	32.7429i	0.601116	−	1.04116i
$990$		0			0
$991$	11.9474	+	20.6935i	0.379521	+	0.657351i	0.990993	−	0.133916i	$-0.0427553\pi$
$991$	11.9474	+	20.6935i	0.379521	+	0.657351i	−0.611471	+	0.791267i	$0.709422\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$		0			0
$994$	1.81509	+	1.47703i	0.0575712	+	0.0468487i
$995$		−	6.99961i		−	0.221903i
$996$		0			0
$997$	−3.07273	−	5.32212i	−0.0973142	−	0.168553i	0.813258	−	0.581903i	$-0.197692\pi$
$997$	−3.07273	−	5.32212i	−0.0973142	−	0.168553i	−0.910572	+	0.413350i	$0.864359\pi$
$998$	16.3910	+	28.3900i	0.518847	+	0.898669i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.dm.c.415.5		12
3.2	odd	2		546.2.bk.b.415.2	yes	12
7.4	even	3	inner	1638.2.dm.c.1117.2		12
13.12	even	2	inner	1638.2.dm.c.415.2		12
21.2	odd	6		3822.2.c.k.883.5		6
21.5	even	6		3822.2.c.j.883.5		6
21.11	odd	6		546.2.bk.b.25.5	yes	12
39.38	odd	2		546.2.bk.b.415.5	yes	12
91.25	even	6	inner	1638.2.dm.c.1117.5		12
273.116	odd	6		546.2.bk.b.25.2	✓	12
273.194	even	6		3822.2.c.j.883.2		6
273.233	odd	6		3822.2.c.k.883.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bk.b.25.2	✓	12	273.116	odd	6
546.2.bk.b.25.5	yes	12	21.11	odd	6
546.2.bk.b.415.2	yes	12	3.2	odd	2
546.2.bk.b.415.5	yes	12	39.38	odd	2
1638.2.dm.c.415.2		12	13.12	even	2	inner
1638.2.dm.c.415.5		12	1.1	even	1	trivial
1638.2.dm.c.1117.2		12	7.4	even	3	inner
1638.2.dm.c.1117.5		12	91.25	even	6	inner
3822.2.c.j.883.2		6	273.194	even	6
3822.2.c.j.883.5		6	21.5	even	6
3822.2.c.k.883.2		6	273.233	odd	6
3822.2.c.k.883.5		6	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.dm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.294342 - 0.169938i) q^{5} +(0.420136 - 2.61218i) q^{7} +1.00000i q^{8} +(-0.169938 - 0.294342i) q^{10} +(0.571683 - 0.330062i) q^{11} +(0.660123 - 3.54461i) q^{13} +(1.66994 - 2.05215i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.27230 - 5.66780i) q^{17} +(-5.27341 - 3.04461i) q^{19} -0.339877i q^{20} +0.660123 q^{22} +(-3.71455 + 6.43378i) q^{23} +(-2.44224 - 4.23009i) q^{25} +(2.34399 - 2.73966i) q^{26} +(2.47228 - 0.942242i) q^{28} +3.56424 q^{29} +(3.46410 - 2.00000i) q^{31} +(-0.866025 + 0.500000i) q^{32} -6.54461i q^{34} +(-0.567573 + 0.697477i) q^{35} +(-3.06972 - 1.77230i) q^{37} +(-3.04461 - 5.27341i) q^{38} +(0.169938 - 0.294342i) q^{40} -0.864853i q^{41} -5.08921 q^{43} +(0.571683 + 0.330062i) q^{44} +(-6.43378 + 3.71455i) q^{46} +(8.18283 + 4.72436i) q^{47} +(-6.64697 - 2.19494i) q^{49} -4.88448i q^{50} +(3.39978 - 1.20062i) q^{52} +(1.50000 + 2.59808i) q^{53} -0.224361 q^{55} +(2.61218 + 0.420136i) q^{56} +(3.08672 + 1.78212i) q^{58} +(3.38106 - 1.95206i) q^{59} +(-0.932427 + 1.61501i) q^{61} +4.00000 q^{62} -1.00000 q^{64} +(-0.796667 + 0.931146i) q^{65} +(6.45078 - 3.72436i) q^{67} +(3.27230 - 5.66780i) q^{68} +(-0.840272 + 0.320246i) q^{70} +0.884484i q^{71} +(8.72051 - 5.03479i) q^{73} +(-1.77230 - 3.06972i) q^{74} -6.08921i q^{76} +(-0.621996 - 1.63201i) q^{77} +(6.22436 - 10.7809i) q^{79} +(0.294342 - 0.169938i) q^{80} +(0.432427 - 0.748985i) q^{82} -16.2939i q^{83} +2.22436i q^{85} +(-4.40739 - 2.54461i) q^{86} +(0.330062 + 0.571683i) q^{88} +(-3.85848 - 2.22770i) q^{89} +(-8.98181 - 3.21358i) q^{91} -7.42909 q^{92} +(4.72436 + 8.18283i) q^{94} +(1.03479 + 1.79231i) q^{95} +16.1088i q^{97} +(-4.65898 - 5.22436i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} + 12 q^{13} + 18 q^{14} - 6 q^{16} - 18 q^{17} + 12 q^{22} - 6 q^{25} - 12 q^{29} - 24 q^{35} + 6 q^{38} + 24 q^{43} - 18 q^{49} + 6 q^{52} + 18 q^{53} + 48 q^{55} + 6 q^{56} + 6 q^{61} + 48 q^{62}+ \cdots - 24 q^{95}+O(q^{100}) \) 12 * q + 6 * q^4 + 12 * q^13 + 18 * q^14 - 6 * q^16 - 18 * q^17 + 12 * q^22 - 6 * q^25 - 12 * q^29 - 24 * q^35 + 6 * q^38 + 24 * q^43 - 18 * q^49 + 6 * q^52 + 18 * q^53 + 48 * q^55 + 6 * q^56 + 6 * q^61 + 48 * q^62 - 12 * q^64 + 12 * q^65 + 18 * q^68 + 24 * q^77 + 24 * q^79 - 12 * q^82 + 6 * q^88 - 24 * q^91 + 6 * q^94 - 24 * q^95

Introduction

L-functions

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