LMFDB - Embedded newform 464.2.u.f.257.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [464,2,Mod(49,464)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(464, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([0, 0, 12])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("464.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 464 = 2^{4} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	464.u (of order $7$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,5,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$3.70505865379$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			257.1
Root			$0.900969 + 0.433884i$ of defining polynomial
Character	$\chi$	$=$	464.257
Dual form			464.2.u.f.65.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.62349 - 0.781831i) q^{3} +(0.900969 - 3.94740i) q^{5} +(0.623490 - 0.300257i) q^{7} +(0.153989 - 0.193096i) q^{9} +(1.77748 + 2.22889i) q^{11} +(0.914542 + 1.14680i) q^{13} +(-1.62349 - 7.11297i) q^{15} -1.60388 q^{17} +(-2.42543 - 1.16802i) q^{19} +(0.777479 - 0.974928i) q^{21} +(-1.14795 - 5.02949i) q^{23} +(-10.2654 - 4.94355i) q^{25} +(-1.10388 + 4.83639i) q^{27} +(3.71379 + 3.89971i) q^{29} +(-0.434157 + 1.90216i) q^{31} +(4.62833 + 2.22889i) q^{33} +(-0.623490 - 2.73169i) q^{35} +(1.77748 - 2.22889i) q^{37} +(2.38135 + 1.14680i) q^{39} +6.49396 q^{41} +(0.147948 + 0.648205i) q^{43} +(-0.623490 - 0.781831i) q^{45} +(2.96346 + 3.71606i) q^{47} +(-4.06584 + 5.09841i) q^{49} +(-2.60388 + 1.25396i) q^{51} +(-0.0108851 + 0.0476909i) q^{53} +(10.3998 - 5.00827i) q^{55} -4.85086 q^{57} +6.39612 q^{59} +(1.17845 - 0.567511i) q^{61} +(0.0380322 - 0.166630i) q^{63} +(5.35086 - 2.57684i) q^{65} +(-9.32036 + 11.6874i) q^{67} +(-5.79590 - 7.26782i) q^{69} +(1.40850 + 1.76621i) q^{71} +(-1.85205 - 8.11437i) q^{73} -20.5308 q^{75} +(1.77748 + 0.855989i) q^{77} +(6.07338 - 7.61577i) q^{79} +(2.15399 + 9.43724i) q^{81} +(-3.62349 - 1.74498i) q^{83} +(-1.44504 + 6.33114i) q^{85} +(9.07822 + 3.42758i) q^{87} +(-2.50484 + 10.9744i) q^{89} +(0.914542 + 0.440420i) q^{91} +(0.782323 + 3.42758i) q^{93} +(-6.79590 + 8.52179i) q^{95} +(4.11745 + 1.98286i) q^{97} +0.704103 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 5 q^{3} + q^{5} - q^{7} + 6 q^{9} + 11 q^{11} - 5 q^{13} - 5 q^{15} + 8 q^{17} - q^{19} + 5 q^{21} + 7 q^{23} - 24 q^{25} + 11 q^{27} + 6 q^{29} - 5 q^{31} + q^{33} + q^{35} + 11 q^{37} - 3 q^{39}+ \cdots + 32 q^{99}+O(q^{100}) $ 6 * q + 5 * q^3 + q^5 - q^7 + 6 * q^9 + 11 * q^11 - 5 * q^13 - 5 * q^15 + 8 * q^17 - q^19 + 5 * q^21 + 7 * q^23 - 24 * q^25 + 11 * q^27 + 6 * q^29 - 5 * q^31 + q^33 + q^35 + 11 * q^37 - 3 * q^39 + 20 * q^41 - 13 * q^43 + q^45 - 11 * q^47 - 22 * q^49 + 2 * q^51 + 3 * q^53 + 17 * q^55 - 2 * q^57 + 56 * q^59 + 3 * q^61 - 15 * q^63 + 5 * q^65 - 19 * q^67 - 7 * q^69 - 21 * q^71 - 25 * q^73 - 48 * q^75 + 11 * q^77 + 9 * q^79 + 18 * q^81 - 17 * q^83 - 8 * q^85 + 5 * q^87 + 7 * q^89 - 5 * q^91 - 17 * q^93 - 13 * q^95 + q^97 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/464\mathbb{Z}\right)^\times$.

$n$	$117$	$175$	$321$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{7}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.62349	−	0.781831i	0.937322	−	0.451391i	0.0980984	−	0.995177i	$-0.468724\pi$
$3$	1.62349	−	0.781831i	0.937322	−	0.451391i	0.839224	+	0.543786i	$0.183010\pi$
$4$		0			0
$5$	0.900969	−	3.94740i	0.402926	−	1.76533i	−0.212524	−	0.977156i	$-0.568168\pi$
$5$	0.900969	−	3.94740i	0.402926	−	1.76533i	0.615450	−	0.788176i	$-0.288974\pi$
$6$		0			0
$7$	0.623490	−	0.300257i	0.235657	−	0.113486i	−0.312329	−	0.949974i	$-0.601109\pi$
$7$	0.623490	−	0.300257i	0.235657	−	0.113486i	0.547986	+	0.836488i	$0.315395\pi$
$8$		0			0
$9$	0.153989	−	0.193096i	0.0513298	−	0.0643655i
$10$		0			0
$11$	1.77748	+	2.22889i	0.535930	+	0.672035i	0.973906	−	0.226952i	$-0.0728759\pi$
$11$	1.77748	+	2.22889i	0.535930	+	0.672035i	−0.437976	+	0.898987i	$0.644304\pi$
$12$		0			0
$13$	0.914542	+	1.14680i	0.253648	+	0.318065i	0.892310	−	0.451422i	$-0.149083\pi$
$13$	0.914542	+	1.14680i	0.253648	+	0.318065i	−0.638662	+	0.769487i	$0.720512\pi$
$14$		0			0
$15$	−1.62349	−	7.11297i	−0.419183	−	1.83656i
$16$		0			0
$17$	−1.60388			−0.388997			−0.194498	−	0.980903i	$-0.562308\pi$
$17$	−1.60388			−0.388997			−0.194498	+	0.980903i	$0.562308\pi$
$18$		0			0
$19$	−2.42543	−	1.16802i	−0.556431	−	0.267963i	0.134463	−	0.990919i	$-0.457069\pi$
$19$	−2.42543	−	1.16802i	−0.556431	−	0.267963i	−0.690895	+	0.722955i	$0.742783\pi$
$20$		0			0
$21$	0.777479	−	0.974928i	0.169660	−	0.212747i
$22$		0			0
$23$	−1.14795	−	5.02949i	−0.239364	−	1.04872i	−0.941588	−	0.336766i	$-0.890667\pi$
$23$	−1.14795	−	5.02949i	−0.239364	−	1.04872i	0.702225	−	0.711955i	$-0.252190\pi$
$24$		0			0
$25$	−10.2654	−	4.94355i	−2.05308	−	0.988711i
$26$		0			0
$27$	−1.10388	+	4.83639i	−0.212441	+	0.930765i
$28$		0			0
$29$	3.71379	+	3.89971i	0.689634	+	0.724158i
$29$	3.71379	+	3.89971i	0.689634	+	0.724158i
$30$		0			0
$31$	−0.434157	+	1.90216i	−0.0779769	+	0.341639i	−0.998835	−	0.0482592i	$-0.984633\pi$
$31$	−0.434157	+	1.90216i	−0.0779769	+	0.341639i	0.920858	+	0.389898i	$0.127490\pi$
$32$		0			0
$33$	4.62833	+	2.22889i	0.805690	+	0.388000i
$34$		0			0
$35$	−0.623490	−	2.73169i	−0.105389	−	0.461739i
$36$		0			0
$37$	1.77748	−	2.22889i	0.292216	−	0.366427i	−0.613953	−	0.789342i	$-0.710422\pi$
$37$	1.77748	−	2.22889i	0.292216	−	0.366427i	0.906169	+	0.422915i	$0.138993\pi$
$38$		0			0
$39$	2.38135	+	1.14680i	0.381322	+	0.183635i
$40$		0			0
$41$	6.49396			1.01419			0.507093	−	0.861891i	$-0.330720\pi$
$41$	6.49396			1.01419			0.507093	+	0.861891i	$0.330720\pi$
$42$		0			0
$43$	0.147948	+	0.648205i	0.0225619	+	0.0988503i	0.984955	−	0.172810i	$-0.0552846\pi$
$43$	0.147948	+	0.648205i	0.0225619	+	0.0988503i	−0.962393	+	0.271660i	$0.912427\pi$
$44$		0			0
$45$	−0.623490	−	0.781831i	−0.0929444	−	0.116549i
$46$		0			0
$47$	2.96346	+	3.71606i	0.432265	+	0.542043i	0.949486	−	0.313809i	$-0.101605\pi$
$47$	2.96346	+	3.71606i	0.432265	+	0.542043i	−0.517221	+	0.855852i	$0.673034\pi$
$48$		0			0
$49$	−4.06584	+	5.09841i	−0.580835	+	0.728344i
$50$		0			0
$51$	−2.60388	+	1.25396i	−0.364615	+	0.175590i
$52$		0			0
$53$	−0.0108851	+	0.0476909i	−0.00149519	+	0.00655085i	−0.975670	−	0.219244i	$-0.929641\pi$
$53$	−0.0108851	+	0.0476909i	−0.00149519	+	0.00655085i	0.974175	+	0.225795i	$0.0724980\pi$
$54$		0			0
$55$	10.3998	−	5.00827i	1.40231	−	0.675315i
$56$		0			0
$57$	−4.85086			−0.642511
$58$		0			0
$59$	6.39612			0.832704			0.416352	−	0.909203i	$-0.363308\pi$
$59$	6.39612			0.832704			0.416352	+	0.909203i	$0.363308\pi$
$60$		0			0
$61$	1.17845	−	0.567511i	0.150885	−	0.0726623i	−0.356918	−	0.934136i	$-0.616172\pi$
$61$	1.17845	−	0.567511i	0.150885	−	0.0726623i	0.507802	+	0.861474i	$0.330458\pi$
$62$		0			0
$63$	0.0380322	−	0.166630i	0.00479161	−	0.0209934i
$64$		0			0
$65$	5.35086	−	2.57684i	0.663692	−	0.319617i
$66$		0			0
$67$	−9.32036	+	11.6874i	−1.13866	+	1.42784i	−0.250615	+	0.968087i	$0.580633\pi$
$67$	−9.32036	+	11.6874i	−1.13866	+	1.42784i	−0.888048	+	0.459751i	$0.847939\pi$
$68$		0			0
$69$	−5.79590	−	7.26782i	−0.697744	−	0.874943i
$70$		0			0
$71$	1.40850	+	1.76621i	0.167158	+	0.209610i	0.858354	−	0.513057i	$-0.171487\pi$
$71$	1.40850	+	1.76621i	0.167158	+	0.209610i	−0.691196	+	0.722667i	$0.742916\pi$
$72$		0			0
$73$	−1.85205	−	8.11437i	−0.216766	−	0.949715i	−0.959849	−	0.280516i	$-0.909494\pi$
$73$	−1.85205	−	8.11437i	−0.216766	−	0.949715i	0.743083	−	0.669199i	$-0.233363\pi$
$74$		0			0
$75$	−20.5308			−2.37069
$76$		0			0
$77$	1.77748	+	0.855989i	0.202563	+	0.0975490i
$78$		0			0
$79$	6.07338	−	7.61577i	0.683308	−	0.856841i	−0.312346	−	0.949968i	$-0.601115\pi$
$79$	6.07338	−	7.61577i	0.683308	−	0.856841i	0.995654	+	0.0931270i	$0.0296863\pi$
$80$		0			0
$81$	2.15399	+	9.43724i	0.239332	+	1.04858i
$82$		0			0
$83$	−3.62349	−	1.74498i	−0.397730	−	0.191537i	0.224318	−	0.974516i	$-0.427985\pi$
$83$	−3.62349	−	1.74498i	−0.397730	−	0.191537i	−0.622047	+	0.782980i	$0.713699\pi$
$84$		0			0
$85$	−1.44504	+	6.33114i	−0.156737	+	0.686709i
$86$		0			0
$87$	9.07822	+	3.42758i	0.973287	+	0.367475i
$88$		0			0
$89$	−2.50484	+	10.9744i	−0.265513	+	1.16329i	0.649659	+	0.760225i	$0.274912\pi$
$89$	−2.50484	+	10.9744i	−0.265513	+	1.16329i	−0.915172	+	0.403063i	$0.867946\pi$
$90$		0			0
$91$	0.914542	+	0.440420i	0.0958701	+	0.0461686i
$92$		0			0
$93$	0.782323	+	3.42758i	0.0811232	+	0.355424i
$94$		0			0
$95$	−6.79590	+	8.52179i	−0.697244	+	0.874317i
$96$		0			0
$97$	4.11745	+	1.98286i	0.418064	+	0.201329i	0.631077	−	0.775721i	$-0.282613\pi$
$97$	4.11745	+	1.98286i	0.418064	+	0.201329i	−0.213013	+	0.977049i	$0.568328\pi$
$98$		0			0
$99$	0.704103			0.0707650
$100$		0			0
$101$	−0.714988	−	3.13257i	−0.0711440	−	0.311702i	0.926818	−	0.375510i	$-0.122533\pi$
$101$	−0.714988	−	3.13257i	−0.0711440	−	0.311702i	−0.997962	+	0.0638082i	$0.979675\pi$
$102$		0			0
$103$	4.07338	+	5.10785i	0.401362	+	0.503292i	0.940907	−	0.338665i	$-0.109975\pi$
$103$	4.07338	+	5.10785i	0.401362	+	0.503292i	−0.539545	+	0.841957i	$0.681404\pi$
$104$		0			0
$105$	−3.14795	−	3.94740i	−0.307208	−	0.385227i
$106$		0			0
$107$	3.60656	−	4.52249i	0.348660	−	0.437205i	−0.576319	−	0.817225i	$-0.695511\pi$
$107$	3.60656	−	4.52249i	0.348660	−	0.437205i	0.924978	+	0.380020i	$0.124083\pi$
$108$		0			0
$109$	−8.27628	+	3.98565i	−0.792724	+	0.381756i	−0.786004	−	0.618222i	$-0.787853\pi$
$109$	−8.27628	+	3.98565i	−0.792724	+	0.381756i	−0.00672026	+	0.999977i	$0.502139\pi$
$110$		0			0
$111$	1.14310	−	5.00827i	0.108499	−	0.475364i
$112$		0			0
$113$	8.07822	−	3.89027i	0.759935	−	0.365965i	−0.0134437	−	0.999910i	$-0.504279\pi$
$113$	8.07822	−	3.89027i	0.759935	−	0.365965i	0.773379	+	0.633944i	$0.218565\pi$
$114$		0			0
$115$	−20.8877			−1.94779
$116$		0			0
$117$	0.362273			0.0334921
$118$		0			0
$119$	−1.00000	+	0.481575i	−0.0916698	+	0.0441459i
$120$		0			0
$121$	0.639219	−	2.80060i	0.0581108	−	0.254600i
$122$		0			0
$123$	10.5429	−	5.07718i	0.950619	−	0.457794i
$124$		0			0
$125$	−16.1407	+	20.2398i	−1.44367	+	1.81030i
$126$		0			0
$127$	−9.70440	−	12.1689i	−0.861126	−	1.07982i	−0.996035	−	0.0889600i	$-0.971646\pi$
$127$	−9.70440	−	12.1689i	−0.861126	−	1.07982i	0.134909	−	0.990858i	$-0.456926\pi$
$128$		0			0
$129$	0.746980	+	0.936683i	0.0657679	+	0.0824703i
$130$		0			0
$131$	2.98911	+	13.0962i	0.261160	+	1.14422i	0.919995	+	0.391930i	$0.128192\pi$
$131$	2.98911	+	13.0962i	0.261160	+	1.14422i	−0.658835	+	0.752288i	$0.728950\pi$
$132$		0			0
$133$	−1.86294			−0.161537
$134$		0			0
$135$	18.0966	+	8.71488i	1.55751	+	0.750058i
$136$		0			0
$137$	−10.5945	+	13.2851i	−0.905148	+	1.13502i	0.0851931	+	0.996364i	$0.472849\pi$
$137$	−10.5945	+	13.2851i	−0.905148	+	1.13502i	−0.990341	+	0.138655i	$0.955722\pi$
$138$		0			0
$139$	2.77359	+	12.1519i	0.235253	+	1.03071i	0.945209	+	0.326465i	$0.105858\pi$
$139$	2.77359	+	12.1519i	0.235253	+	1.03071i	−0.709956	+	0.704246i	$0.751285\pi$
$140$		0			0
$141$	7.71648	+	3.71606i	0.649845	+	0.312949i
$142$		0			0
$143$	−0.930509	+	4.07683i	−0.0778131	+	0.340921i
$144$		0			0
$145$	18.7397	−	11.1463i	1.55625	−	0.925651i
$146$		0			0
$147$	−2.61476	+	11.4560i	−0.215662	+	0.944876i
$148$		0			0
$149$	16.5015	+	7.94670i	1.35185	+	0.651019i	0.962805	−	0.270198i	$-0.0870890\pi$
$149$	16.5015	+	7.94670i	1.35185	+	0.651019i	0.389050	+	0.921217i	$0.372803\pi$
$150$		0			0
$151$	−4.23609	−	18.5595i	−0.344728	−	1.51035i	−0.788961	−	0.614443i	$-0.789381\pi$
$151$	−4.23609	−	18.5595i	−0.344728	−	1.51035i	0.444233	−	0.895911i	$-0.353476\pi$
$152$		0			0
$153$	−0.246980	+	0.309703i	−0.0199671	+	0.0250380i
$154$		0			0
$155$	7.11745	+	3.42758i	0.571687	+	0.275310i
$156$		0			0
$157$	−11.4383			−0.912879			−0.456439	−	0.889755i	$-0.650875\pi$
$157$	−11.4383			−0.912879			−0.456439	+	0.889755i	$0.650875\pi$
$158$		0			0
$159$	0.0196143	+	0.0859360i	0.00155552	+	0.00681517i
$160$		0			0
$161$	−2.22587	−	2.79116i	−0.175423	−	0.219974i
$162$		0			0
$163$	4.16152	+	5.21838i	0.325956	+	0.408735i	0.917626	−	0.397444i	$-0.130103\pi$
$163$	4.16152	+	5.21838i	0.325956	+	0.408735i	−0.591671	+	0.806180i	$0.701531\pi$
$164$		0			0
$165$	12.9683	−	16.2617i	1.00958	−	1.26597i
$166$		0			0
$167$	−13.2153	+	6.36415i	−1.02263	+	0.492472i	−0.868558	−	0.495587i	$-0.834953\pi$
$167$	−13.2153	+	6.36415i	−1.02263	+	0.492472i	−0.154071	+	0.988060i	$0.549239\pi$
$168$		0			0
$169$	2.41401	−	10.5765i	0.185693	−	0.813575i
$170$		0			0
$171$	−0.599031	+	0.288478i	−0.0458091	+	0.0220605i
$172$		0			0
$173$	−23.3599			−1.77602			−0.888009	−	0.459825i	$-0.847912\pi$
$173$	−23.3599			−1.77602			−0.888009	+	0.459825i	$0.847912\pi$
$174$		0			0
$175$	−7.88471			−0.596028
$176$		0			0
$177$	10.3840	−	5.00069i	0.780512	−	0.375875i
$178$		0			0
$179$	−0.147948	+	0.648205i	−0.0110582	+	0.0484491i	−0.980156	−	0.198228i	$-0.936481\pi$
$179$	−0.147948	+	0.648205i	−0.0110582	+	0.0484491i	0.969098	+	0.246677i	$0.0793386\pi$
$180$		0			0
$181$	−9.88016	+	4.75803i	−0.734386	+	0.353662i	−0.763408	−	0.645917i	$-0.776475\pi$
$181$	−9.88016	+	4.75803i	−0.734386	+	0.353662i	0.0290213	+	0.999579i	$0.490761\pi$
$182$		0			0
$183$	1.46950	−	1.84270i	0.108629	−	0.136216i
$184$		0			0
$185$	−7.19687	−	9.02458i	−0.529124	−	0.663501i
$186$		0			0
$187$	−2.85086	−	3.57486i	−0.208475	−	0.261420i
$188$		0			0
$189$	0.763906	+	3.34689i	0.0555660	+	0.243450i
$190$		0			0
$191$	0.518122			0.0374900			0.0187450	−	0.999824i	$-0.494033\pi$
$191$	0.518122			0.0374900			0.0187450	+	0.999824i	$0.494033\pi$
$192$		0			0
$193$	−1.24914	−	0.601552i	−0.0899147	−	0.0433007i	0.388386	−	0.921497i	$-0.373033\pi$
$193$	−1.24914	−	0.601552i	−0.0899147	−	0.0433007i	−0.478301	+	0.878196i	$0.658747\pi$
$194$		0			0
$195$	6.67241	−	8.36693i	0.477821	−	0.599169i
$196$		0			0
$197$	−2.88351	−	12.6335i	−0.205442	−	0.900099i	−0.967556	−	0.252656i	$-0.918696\pi$
$197$	−2.88351	−	12.6335i	−0.205442	−	0.900099i	0.762114	−	0.647442i	$-0.224161\pi$
$198$		0			0
$199$	−17.5722	−	8.46232i	−1.24566	−	0.599878i	−0.309314	−	0.950960i	$-0.600099\pi$
$199$	−17.5722	−	8.46232i	−1.24566	−	0.599878i	−0.936345	+	0.351082i	$0.885814\pi$
$200$		0			0
$201$	−5.99396	+	26.2613i	−0.422781	+	1.85233i
$202$		0			0
$203$	3.48643	+	1.31634i	0.244699	+	0.0923889i
$204$		0			0
$205$	5.85086	−	25.6343i	0.408641	−	1.79038i
$206$		0			0
$207$	−1.14795	−	0.552823i	−0.0797879	−	0.0384238i
$208$		0			0
$209$	−1.70775	−	7.48215i	−0.118128	−	0.517551i
$210$		0			0
$211$	12.8632	−	16.1300i	0.885541	−	1.11043i	−0.107679	−	0.994186i	$-0.534342\pi$
$211$	12.8632	−	16.1300i	0.885541	−	1.11043i	0.993220	−	0.116248i	$-0.0370868\pi$
$212$		0			0
$213$	3.66756	+	1.76621i	0.251297	+	0.121018i
$214$		0			0
$215$	2.69202			0.183594
$216$		0			0
$217$	0.300446	+	1.31634i	0.0203956	+	0.0893589i
$218$		0			0
$219$	−9.35086	−	11.7256i	−0.631872	−	0.792343i
$220$		0			0
$221$	−1.46681	−	1.83932i	−0.0986685	−	0.123726i
$222$		0			0
$223$	13.1561	−	16.4973i	0.881001	−	1.10474i	−0.112806	−	0.993617i	$-0.535984\pi$
$223$	13.1561	−	16.4973i	0.881001	−	1.10474i	0.993807	−	0.111123i	$-0.0354447\pi$
$224$		0			0
$225$	−2.53534	+	1.22096i	−0.169023	+	0.0813971i
$226$		0			0
$227$	1.58761	−	6.95579i	0.105374	−	0.461672i	−0.894519	−	0.447030i	$-0.852482\pi$
$227$	1.58761	−	6.95579i	0.105374	−	0.461672i	0.999893	−	0.0146424i	$-0.00466098\pi$
$228$		0			0
$229$	2.02930	−	0.977261i	0.134100	−	0.0645792i	−0.365631	−	0.930760i	$-0.619147\pi$
$229$	2.02930	−	0.977261i	0.134100	−	0.0645792i	0.499731	+	0.866181i	$0.333432\pi$
$230$		0			0
$231$	3.55496			0.233899
$232$		0			0
$233$	18.9095			1.23880			0.619400	−	0.785076i	$-0.287376\pi$
$233$	18.9095			1.23880			0.619400	+	0.785076i	$0.287376\pi$
$234$		0			0
$235$	17.3388	−	8.34991i	1.13106	−	0.544688i
$236$		0			0
$237$	3.90581	−	17.1125i	0.253710	−	1.11158i
$238$		0			0
$239$	−18.4448	+	8.88255i	−1.19310	+	0.574564i	−0.921700	−	0.387904i	$-0.873199\pi$
$239$	−18.4448	+	8.88255i	−1.19310	+	0.574564i	−0.271395	+	0.962468i	$0.587485\pi$
$240$		0			0
$241$	4.59448	−	5.76130i	0.295957	−	0.371118i	−0.611514	−	0.791234i	$-0.709439\pi$
$241$	4.59448	−	5.76130i	0.295957	−	0.371118i	0.907470	+	0.420116i	$0.138011\pi$
$242$		0			0
$243$	1.59634	+	2.00175i	0.102405	+	0.128412i
$244$		0			0
$245$	16.4623	+	20.6430i	1.05174	+	1.31883i
$246$		0			0
$247$	−0.878666	−	3.84969i	−0.0559082	−	0.244950i
$248$		0			0
$249$	−7.24698			−0.459259
$250$		0			0
$251$	11.6724	+	5.62114i	0.736756	+	0.354803i	0.764337	−	0.644817i	$-0.223066\pi$
$251$	11.6724	+	5.62114i	0.736756	+	0.354803i	−0.0275815	+	0.999620i	$0.508781\pi$
$252$		0			0
$253$	9.16972	−	11.4985i	0.576495	−	0.722902i
$254$		0			0
$255$	2.60388	+	11.4083i	0.163061	+	0.714417i
$256$		0			0
$257$	−15.0390	−	7.24240i	−0.938107	−	0.451768i	−0.0986056	−	0.995127i	$-0.531438\pi$
$257$	−15.0390	−	7.24240i	−0.938107	−	0.451768i	−0.839501	+	0.543358i	$0.817153\pi$
$258$		0			0
$259$	0.439001	−	1.92339i	0.0272782	−	0.119514i
$260$		0			0
$261$	1.32490	−	0.116606i	0.0820095	−	0.00721774i
$262$		0			0
$263$	3.91843	−	17.1678i	0.241621	−	1.05861i	−0.697921	−	0.716175i	$-0.745891\pi$
$263$	3.91843	−	17.1678i	0.241621	−	1.05861i	0.939542	−	0.342434i	$-0.111251\pi$
$264$		0			0
$265$	0.178448	+	0.0859360i	0.0109620	+	0.00527901i
$266$		0			0
$267$	4.51357	+	19.7753i	0.276226	+	1.21023i
$268$		0			0
$269$	4.18329	−	5.24568i	0.255060	−	0.319835i	−0.637772	−	0.770225i	$-0.720144\pi$
$269$	4.18329	−	5.24568i	0.255060	−	0.319835i	0.892832	+	0.450390i	$0.148715\pi$
$270$		0			0
$271$	11.4133	+	5.49638i	0.693311	+	0.333881i	0.747138	−	0.664669i	$-0.231427\pi$
$271$	11.4133	+	5.49638i	0.693311	+	0.333881i	−0.0538264	+	0.998550i	$0.517142\pi$
$272$		0			0
$273$	1.82908			0.110701
$274$		0			0
$275$	−7.22790	−	31.6675i	−0.435859	−	1.90962i
$276$		0			0
$277$	9.81431	+	12.3068i	0.589685	+	0.739442i	0.983731	−	0.179649i	$-0.0574963\pi$
$277$	9.81431	+	12.3068i	0.589685	+	0.739442i	−0.394046	+	0.919091i	$0.628925\pi$
$278$		0			0
$279$	0.300446	+	0.376747i	0.0179872	+	0.0225553i
$280$		0			0
$281$	7.36629	−	9.23703i	0.439436	−	0.551035i	−0.511959	−	0.859010i	$-0.671080\pi$
$281$	7.36629	−	9.23703i	0.439436	−	0.551035i	0.951394	+	0.307975i	$0.0996513\pi$
$282$		0			0
$283$	−1.98039	+	0.953703i	−0.117722	+	0.0566918i	−0.491818	−	0.870698i	$-0.663667\pi$
$283$	−1.98039	+	0.953703i	−0.117722	+	0.0566918i	0.374096	+	0.927390i	$0.377953\pi$
$284$		0			0
$285$	−4.37047	+	19.1483i	−0.258884	+	1.13425i
$286$		0			0
$287$	4.04892	−	1.94986i	0.239000	−	0.115096i
$288$		0			0
$289$	−14.4276			−0.848681
$290$		0			0
$291$	8.23490			0.482738
$292$		0			0
$293$	18.5993	−	8.95696i	1.08658	−	0.523271i	0.197168	−	0.980370i	$-0.436826\pi$
$293$	18.5993	−	8.95696i	1.08658	−	0.523271i	0.889416	+	0.457098i	$0.151111\pi$
$294$		0			0
$295$	5.76271	−	25.2481i	0.335518	−	1.47000i
$296$		0			0
$297$	−12.7419	+	6.13617i	−0.739360	+	0.356057i
$298$		0			0
$299$	4.71797	−	5.91615i	0.272847	−	0.342140i
$300$		0			0
$301$	0.286872	+	0.359726i	0.0165350	+	0.0207343i
$302$		0			0
$303$	−3.60992	−	4.52669i	−0.207384	−	0.260052i
$304$		0			0
$305$	−1.17845	−	5.16312i	−0.0674777	−	0.295639i
$306$		0			0
$307$	−22.8116			−1.30193			−0.650964	−	0.759108i	$-0.725635\pi$
$307$	−22.8116			−1.30193			−0.650964	+	0.759108i	$0.725635\pi$
$308$		0			0
$309$	10.6066	+	5.10785i	0.603386	+	0.290576i
$310$		0			0
$311$	−19.3843	+	24.3072i	−1.09918	+	1.37833i	−0.180392	+	0.983595i	$0.557737\pi$
$311$	−19.3843	+	24.3072i	−1.09918	+	1.37833i	−0.918793	+	0.394740i	$0.870835\pi$
$312$		0			0
$313$	2.49947	+	10.9509i	0.141278	+	0.618980i	0.995139	+	0.0984792i	$0.0313978\pi$
$313$	2.49947	+	10.9509i	0.141278	+	0.618980i	−0.853861	+	0.520501i	$0.825745\pi$
$314$		0			0
$315$	−0.623490	−	0.300257i	−0.0351297	−	0.0169176i
$316$		0			0
$317$	1.31886	−	5.77832i	0.0740748	−	0.324543i	−0.924291	−	0.381688i	$-0.875343\pi$
$317$	1.31886	−	5.77832i	0.0740748	−	0.324543i	0.998366	+	0.0571456i	$0.0181999\pi$
$318$		0			0
$319$	−2.09083	+	15.2093i	−0.117064	+	0.851556i
$320$		0			0
$321$	2.31940	−	10.1619i	0.129456	−	0.567184i
$322$		0			0
$323$	3.89008	+	1.87337i	0.216450	+	0.104237i
$324$		0			0
$325$	−3.71887	−	16.2934i	−0.206286	−	0.903798i
$326$		0			0
$327$	−10.3204	+	12.9413i	−0.570717	+	0.715656i
$328$		0			0
$329$	2.96346	+	1.42713i	0.163381	+	0.0786801i
$330$		0			0
$331$	−30.9095			−1.69894			−0.849469	−	0.527639i	$-0.823077\pi$
$331$	−30.9095			−1.69894			−0.849469	+	0.527639i	$0.823077\pi$
$332$		0			0
$333$	−0.156678	−	0.686450i	−0.00858588	−	0.0376172i
$334$		0			0
$335$	37.7373	+	47.3211i	2.06181	+	2.58543i
$336$		0			0
$337$	4.99731	+	6.26643i	0.272221	+	0.341354i	0.899085	−	0.437775i	$-0.144233\pi$
$337$	4.99731	+	6.26643i	0.272221	+	0.341354i	−0.626864	+	0.779129i	$0.715662\pi$
$338$		0			0
$339$	10.0734	−	12.6316i	0.547111	−	0.686055i
$340$		0			0
$341$	−5.01142	+	2.41337i	−0.271383	+	0.130691i
$342$		0			0
$343$	−2.08211	+	9.12230i	−0.112423	+	0.492558i
$344$		0			0
$345$	−33.9110	+	16.3307i	−1.82570	+	0.879213i
$346$		0			0
$347$	2.26337			0.121504			0.0607521	−	0.998153i	$-0.480650\pi$
$347$	2.26337			0.121504			0.0607521	+	0.998153i	$0.480650\pi$
$348$		0			0
$349$	−23.5690			−1.26162			−0.630809	−	0.775938i	$-0.717277\pi$
$349$	−23.5690			−1.26162			−0.630809	+	0.775938i	$0.717277\pi$
$350$		0			0
$351$	−6.55592	+	3.15716i	−0.349929	+	0.168517i
$352$		0			0
$353$	0.218636	−	0.957907i	0.0116368	−	0.0509843i	−0.968776	−	0.247937i	$-0.920247\pi$
$353$	0.218636	−	0.957907i	0.0116368	−	0.0509843i	0.980413	+	0.196953i	$0.0631045\pi$
$354$		0			0
$355$	8.24094	−	3.96863i	0.437384	−	0.210633i
$356$		0			0
$357$	−1.24698	+	1.56366i	−0.0659972	+	0.0827578i
$358$		0			0
$359$	4.91454	+	6.16264i	0.259380	+	0.325252i	0.894421	−	0.447227i	$-0.147588\pi$
$359$	4.91454	+	6.16264i	0.259380	+	0.325252i	−0.635041	+	0.772478i	$0.719017\pi$
$360$		0			0
$361$	−7.32789	−	9.18888i	−0.385678	−	0.483625i
$362$		0			0
$363$	−1.15183	−	5.04651i	−0.0604556	−	0.264873i
$364$		0			0
$365$	−33.6993			−1.76390
$366$		0			0
$367$	−26.4056	−	12.7163i	−1.37836	−	0.663783i	−0.409711	−	0.912216i	$-0.634370\pi$
$367$	−26.4056	−	12.7163i	−1.37836	−	0.663783i	−0.968649	+	0.248432i	$0.920085\pi$
$368$		0			0
$369$	1.00000	−	1.25396i	0.0520579	−	0.0652786i
$370$		0			0
$371$	0.00753275	+	0.0330031i	0.000391081	+	0.00171344i
$372$		0			0
$373$	3.43512	+	1.65426i	0.177864	+	0.0856546i	0.520697	−	0.853742i	$-0.325672\pi$
$373$	3.43512	+	1.65426i	0.177864	+	0.0856546i	−0.342833	+	0.939396i	$0.611387\pi$
$374$		0			0
$375$	−10.3802	+	45.4784i	−0.536029	+	2.34850i
$376$		0			0
$377$	−1.07577	+	7.82543i	−0.0554049	+	0.403030i
$378$		0			0
$379$	2.00849	−	8.79978i	0.103169	−	0.452014i	−0.896785	−	0.442466i	$-0.854104\pi$
$379$	2.00849	−	8.79978i	0.103169	−	0.452014i	0.999954	−	0.00954794i	$-0.00303925\pi$
$380$		0			0
$381$	−25.2690	−	12.1689i	−1.29457	−	0.623433i
$382$		0			0
$383$	−7.38524	−	32.3568i	−0.377368	−	1.65336i	−0.705488	−	0.708722i	$-0.749272\pi$
$383$	−7.38524	−	32.3568i	−0.377368	−	1.65336i	0.328120	−	0.944636i	$-0.393585\pi$
$384$		0			0
$385$	4.98039	−	6.24521i	0.253824	−	0.318285i
$386$		0			0
$387$	0.147948	+	0.0712482i	0.00752064	+	0.00362175i
$388$		0			0
$389$	27.5362			1.39614			0.698070	−	0.716030i	$-0.254043\pi$
$389$	27.5362			1.39614			0.698070	+	0.716030i	$0.254043\pi$
$390$		0			0
$391$	1.84117	+	8.06668i	0.0931118	+	0.407949i
$392$		0			0
$393$	15.0918	+	18.9245i	0.761280	+	0.954615i
$394$		0			0
$395$	−24.5906	−	30.8356i	−1.23729	−	1.55151i
$396$		0			0
$397$	−11.9852	+	15.0290i	−0.601521	+	0.754284i	−0.985614	−	0.169010i	$-0.945943\pi$
$397$	−11.9852	+	15.0290i	−0.601521	+	0.754284i	0.384093	+	0.923294i	$0.374514\pi$
$398$		0			0
$399$	−3.02446	+	1.45650i	−0.151412	+	0.0729163i
$400$		0			0
$401$	−2.45353	+	10.7496i	−0.122524	+	0.536811i	0.875991	+	0.482327i	$0.160208\pi$
$401$	−2.45353	+	10.7496i	−0.122524	+	0.536811i	−0.998515	+	0.0544837i	$0.982649\pi$
$402$		0			0
$403$	−2.57846	+	1.24172i	−0.128442	+	0.0618545i
$404$		0			0
$405$	39.1933			1.94753
$406$		0			0
$407$	8.12737			0.402859
$408$		0			0
$409$	−30.4720	+	14.6745i	−1.50674	+	0.725608i	−0.991337	−	0.131339i	$-0.958072\pi$
$409$	−30.4720	+	14.6745i	−1.50674	+	0.725608i	−0.515404	+	0.856948i	$0.672358\pi$
$410$		0			0
$411$	−6.81336	+	29.8513i	−0.336078	+	1.47245i
$412$		0			0
$413$	3.98792	−	1.92048i	0.196233	−	0.0945007i
$414$		0			0
$415$	−10.1528	+	12.7312i	−0.498381	+	0.624950i
$416$		0			0
$417$	14.0036	+	17.5600i	0.685762	+	0.859918i
$418$		0			0
$419$	22.2080	+	27.8480i	1.08493	+	1.36046i	0.927882	+	0.372874i	$0.121628\pi$
$419$	22.2080	+	27.8480i	1.08493	+	1.36046i	0.157052	+	0.987590i	$0.449801\pi$
$420$		0			0
$421$	2.10441	+	9.22001i	0.102563	+	0.449356i	0.999967	+	0.00814670i	$0.00259320\pi$
$421$	2.10441	+	9.22001i	0.102563	+	0.449356i	−0.897404	+	0.441209i	$0.854550\pi$
$422$		0			0
$423$	1.17390			0.0570769
$424$		0			0
$425$	16.4644	+	7.92885i	0.798642	+	0.384606i
$426$		0			0
$427$	0.564351	−	0.707674i	0.0273109	−	0.0342468i
$428$		0			0
$429$	1.67672	+	7.34619i	0.0809528	+	0.354677i
$430$		0			0
$431$	0.887928	+	0.427603i	0.0427700	+	0.0205969i	0.455146	−	0.890417i	$-0.349587\pi$
$431$	0.887928	+	0.427603i	0.0427700	+	0.0205969i	−0.412377	+	0.911014i	$0.635301\pi$
$432$		0			0
$433$	6.38285	−	27.9651i	0.306740	−	1.34392i	−0.552999	−	0.833182i	$-0.686517\pi$
$433$	6.38285	−	27.9651i	0.306740	−	1.34392i	0.859739	−	0.510734i	$-0.170626\pi$
$434$		0			0
$435$	21.7092	−	32.7472i	1.04088	−	1.57011i
$436$		0			0
$437$	−3.09030	+	13.5395i	−0.147829	+	0.647682i
$438$		0			0
$439$	−5.94116	−	2.86111i	−0.283556	−	0.136553i	0.286700	−	0.958020i	$-0.407442\pi$
$439$	−5.94116	−	2.86111i	−0.283556	−	0.136553i	−0.570256	+	0.821467i	$0.693156\pi$
$440$		0			0
$441$	0.358388	+	1.57020i	0.0170661	+	0.0747714i
$442$		0			0
$443$	13.3354	−	16.7221i	0.633585	−	0.794490i	−0.356599	−	0.934257i	$-0.616064\pi$
$443$	13.3354	−	16.7221i	0.633585	−	0.794490i	0.990184	+	0.139767i	$0.0446353\pi$
$444$		0			0
$445$	41.0637	+	19.7753i	1.94661	+	0.937437i
$446$		0			0
$447$	33.0030			1.56099
$448$		0			0
$449$	−6.51022	−	28.5231i	−0.307236	−	1.34609i	−0.858951	−	0.512058i	$-0.828883\pi$
$449$	−6.51022	−	28.5231i	−0.307236	−	1.34609i	0.551715	−	0.834033i	$-0.313974\pi$
$450$		0			0
$451$	11.5429	+	14.4743i	0.543533	+	0.681569i
$452$		0			0
$453$	−21.3877	−	26.8193i	−1.00488	−	1.26008i
$454$		0			0
$455$	2.56249	−	3.21326i	0.120131	−	0.150640i
$456$		0			0
$457$	0.217677	−	0.104828i	0.0101825	−	0.00490362i	−0.428786	−	0.903406i	$-0.641058\pi$
$457$	0.217677	−	0.104828i	0.0101825	−	0.00490362i	0.438968	+	0.898503i	$0.355344\pi$
$458$		0			0
$459$	1.77048	−	7.75697i	0.0826389	−	0.362065i
$460$		0			0
$461$	−15.6211	+	7.52272i	−0.727547	+	0.350368i	−0.760719	−	0.649081i	$-0.775153\pi$
$461$	−15.6211	+	7.52272i	−0.727547	+	0.350368i	0.0331719	+	0.999450i	$0.489439\pi$
$462$		0			0
$463$	−4.24996			−0.197513			−0.0987563	−	0.995112i	$-0.531486\pi$
$463$	−4.24996			−0.197513			−0.0987563	+	0.995112i	$0.531486\pi$
$464$		0			0
$465$	14.2349			0.660128
$466$		0			0
$467$	−25.9780	+	12.5103i	−1.20212	+	0.578910i	−0.924279	−	0.381718i	$-0.875333\pi$
$467$	−25.9780	+	12.5103i	−1.20212	+	0.578910i	−0.277839	+	0.960628i	$0.589618\pi$
$468$		0			0
$469$	−2.30194	+	10.0854i	−0.106294	+	0.465703i
$470$		0			0
$471$	−18.5700	+	8.94285i	−0.855662	+	0.412065i
$472$		0			0
$473$	−1.18180	+	1.48193i	−0.0543392	+	0.0681392i
$474$		0			0
$475$	19.1238	+	23.9805i	0.877459	+	1.10030i
$476$		0			0
$477$	0.00753275	+	0.00944576i	0.000344901	+	0.000432492i
$478$		0			0
$479$	−5.37986	−	23.5707i	−0.245812	−	1.07697i	−0.935628	−	0.352988i	$-0.885166\pi$
$479$	−5.37986	−	23.5707i	−0.245812	−	1.07697i	0.689816	−	0.723985i	$-0.257692\pi$
$480$		0			0
$481$	4.18167			0.190668
$482$		0			0
$483$	−5.79590	−	2.79116i	−0.263722	−	0.127002i
$484$		0			0
$485$	11.5368	−	14.4667i	0.523861	−	0.656901i
$486$		0			0
$487$	4.29709	+	18.8268i	0.194720	+	0.853124i	0.974018	+	0.226470i	$0.0727186\pi$
$487$	4.29709	+	18.8268i	0.194720	+	0.853124i	−0.779298	+	0.626653i	$0.784424\pi$
$488$		0			0
$489$	10.8361	+	5.21838i	0.490025	+	0.235983i
$490$		0			0
$491$	8.20895	−	35.9657i	0.370465	−	1.62311i	−0.355010	−	0.934863i	$-0.615523\pi$
$491$	8.20895	−	35.9657i	0.370465	−	1.62311i	0.725475	−	0.688249i	$-0.241620\pi$
$492$		0			0
$493$	−5.95646	−	6.25465i	−0.268265	−	0.281695i
$494$		0			0
$495$	0.634375	−	2.77938i	0.0285130	−	0.124924i
$496$		0			0
$497$	1.40850	+	0.678299i	0.0631799	+	0.0304259i
$498$		0			0
$499$	8.39254	+	36.7701i	0.375701	+	1.64606i	0.710450	+	0.703748i	$0.248492\pi$
$499$	8.39254	+	36.7701i	0.375701	+	1.64606i	−0.334748	+	0.942308i	$0.608651\pi$
$500$		0			0
$501$	−16.4792	+	20.6642i	−0.736236	+	0.923211i
$502$		0			0
$503$	−6.31551	−	3.04139i	−0.281595	−	0.135609i	0.287756	−	0.957704i	$-0.407091\pi$
$503$	−6.31551	−	3.04139i	−0.281595	−	0.135609i	−0.569350	+	0.822095i	$0.692805\pi$
$504$		0			0
$505$	−13.0097			−0.578924
$506$		0			0
$507$	−4.34990	−	19.0581i	−0.193186	−	0.846402i
$508$		0			0
$509$	11.4641	+	14.3756i	0.508138	+	0.637185i	0.968043	−	0.250783i	$-0.0806880\pi$
$509$	11.4641	+	14.3756i	0.508138	+	0.637185i	−0.459905	+	0.887968i	$0.652117\pi$
$510$		0			0
$511$	−3.59113	−	4.50313i	−0.158862	−	0.199207i
$512$		0			0
$513$	8.32640	−	10.4410i	0.367619	−	0.460980i
$514$		0			0
$515$	23.8327	−	11.4772i	1.05020	−	0.505748i
$516$		0			0
$517$	−3.01520	+	13.2104i	−0.132608	+	0.580995i
$518$		0			0
$519$	−37.9245	+	18.2635i	−1.66470	+	0.801678i
$520$		0			0
$521$	3.94571			0.172865			0.0864323	−	0.996258i	$-0.472453\pi$
$521$	3.94571			0.172865			0.0864323	+	0.996258i	$0.472453\pi$
$522$		0			0
$523$	33.9952			1.48651			0.743253	−	0.669010i	$-0.233282\pi$
$523$	33.9952			1.48651			0.743253	+	0.669010i	$0.233282\pi$
$524$		0			0
$525$	−12.8007	+	6.16451i	−0.558670	+	0.269041i
$526$		0			0
$527$	0.696333	−	3.05084i	0.0303328	−	0.132896i
$528$		0			0
$529$	−3.25571	+	1.56787i	−0.141553	+	0.0681681i
$530$		0			0
$531$	0.984935	−	1.23507i	0.0427425	−	0.0535974i
$532$		0			0
$533$	5.93900	+	7.44727i	0.257247	+	0.322577i
$534$		0			0
$535$	−14.6027	−	18.3112i	−0.631329	−	0.791661i
$536$		0			0
$537$	0.266594	+	1.16802i	0.0115044	+	0.0504040i
$538$		0			0
$539$	−18.5907			−0.800759
$540$		0			0
$541$	−21.1151	−	10.1685i	−0.907807	−	0.437177i	−0.0791047	−	0.996866i	$-0.525206\pi$
$541$	−21.1151	−	10.1685i	−0.907807	−	0.437177i	−0.828702	+	0.559689i	$0.810920\pi$
$542$		0			0
$543$	−12.3204	+	15.4492i	−0.528717	+	0.662990i
$544$		0			0
$545$	8.27628	+	36.2608i	0.354517	+	1.55324i
$546$		0			0
$547$	29.0976	+	14.0127i	1.24412	+	0.599138i	0.935930	−	0.352186i	$-0.114561\pi$
$547$	29.0976	+	14.0127i	1.24412	+	0.599138i	0.308193	+	0.951324i	$0.400276\pi$
$548$		0			0
$549$	0.0718841	−	0.314945i	0.00306794	−	0.0134415i
$550$		0			0
$551$	−4.45257	−	13.7963i	−0.189686	−	0.587741i
$552$		0			0
$553$	1.50000	−	6.57193i	0.0637865	−	0.279467i
$554$		0			0
$555$	−18.7397	−	9.02458i	−0.795458	−	0.383072i
$556$		0			0
$557$	−3.61045	−	15.8184i	−0.152980	−	0.670248i	−0.992010	−	0.126162i	$-0.959734\pi$
$557$	−3.61045	−	15.8184i	−0.152980	−	0.670248i	0.839030	−	0.544085i	$-0.183123\pi$
$558$		0			0
$559$	−0.608056	+	0.762478i	−0.0257180	+	0.0322494i
$560$		0			0
$561$	−7.42327	−	3.57486i	−0.313411	−	0.150931i
$562$		0			0
$563$	21.9168			0.923681			0.461841	−	0.886963i	$-0.347189\pi$
$563$	21.9168			0.923681			0.461841	+	0.886963i	$0.347189\pi$
$564$		0			0
$565$	−8.07822	−	35.3930i	−0.339853	−	1.48899i
$566$		0			0
$567$	4.17659	+	5.23728i	0.175400	+	0.219945i
$568$		0			0
$569$	−23.3790	−	29.3163i	−0.980097	−	1.22900i	−0.973421	−	0.229025i	$-0.926446\pi$
$569$	−23.3790	−	29.3163i	−0.980097	−	1.22900i	−0.00667655	−	0.999978i	$-0.502125\pi$
$570$		0			0
$571$	−17.2201	+	21.5934i	−0.720640	+	0.903654i	−0.998374	−	0.0570041i	$-0.981845\pi$
$571$	−17.2201	+	21.5934i	−0.720640	+	0.903654i	0.277734	+	0.960658i	$0.410417\pi$
$572$		0			0
$573$	0.841166	−	0.405084i	0.0351402	−	0.0169226i
$574$		0			0
$575$	−13.0794	+	57.3047i	−0.545449	+	2.38977i
$576$		0			0
$577$	5.70387	−	2.74684i	0.237455	−	0.114352i	−0.311372	−	0.950288i	$-0.600789\pi$
$577$	5.70387	−	2.74684i	0.237455	−	0.114352i	0.548827	+	0.835936i	$0.315074\pi$
$578$		0			0
$579$	−2.49827			−0.103825
$580$		0			0
$581$	−2.78315			−0.115465
$582$		0			0
$583$	−0.125646	+	0.0605078i	−0.00520371	+	0.00250598i
$584$		0			0
$585$	0.326396	−	1.43004i	0.0134948	−	0.0591247i
$586$		0			0
$587$	−17.5939	+	8.47280i	−0.726180	+	0.349710i	−0.760180	−	0.649712i	$-0.774890\pi$
$587$	−17.5939	+	8.47280i	−0.726180	+	0.349710i	0.0340005	+	0.999422i	$0.489175\pi$
$588$		0			0
$589$	3.27479	−	4.10646i	0.134935	−	0.169204i
$590$		0			0
$591$	−14.5586	−	18.2559i	−0.598861	−	0.750948i
$592$		0			0
$593$	−1.53720	−	1.92759i	−0.0631254	−	0.0791568i	0.749266	−	0.662269i	$-0.230406\pi$
$593$	−1.53720	−	1.92759i	−0.0631254	−	0.0791568i	−0.812392	+	0.583112i	$0.801835\pi$
$594$		0			0
$595$	1.00000	+	4.38129i	0.0409960	+	0.179615i
$596$		0			0
$597$	−35.1444			−1.43836
$598$		0			0
$599$	−4.65064	−	2.23963i	−0.190020	−	0.0915087i	0.336455	−	0.941700i	$-0.390772\pi$
$599$	−4.65064	−	2.23963i	−0.190020	−	0.0915087i	−0.526474	+	0.850191i	$0.676486\pi$
$600$		0			0
$601$	−18.3723	+	23.0381i	−0.749420	+	0.939743i	−0.999595	−	0.0284577i	$-0.990940\pi$
$601$	−18.3723	+	23.0381i	−0.749420	+	0.939743i	0.250175	+	0.968201i	$0.419512\pi$
$602$		0			0
$603$	0.821552	+	3.59945i	0.0334562	+	0.146581i
$604$		0			0
$605$	−10.4792	−	5.04651i	−0.426040	−	0.205170i
$606$		0			0
$607$	7.71068	−	33.7827i	0.312967	−	1.37120i	−0.536654	−	0.843802i	$-0.680312\pi$
$607$	7.71068	−	33.7827i	0.312967	−	1.37120i	0.849621	−	0.527394i	$-0.176831\pi$
$608$		0			0
$609$	6.68933	−	0.588735i	0.271065	−	0.0238567i
$610$		0			0
$611$	−1.55137	+	6.79699i	−0.0627617	+	0.274977i
$612$		0			0
$613$	−24.7407	−	11.9145i	−0.999268	−	0.481222i	−0.138578	−	0.990352i	$-0.544253\pi$
$613$	−24.7407	−	11.9145i	−0.999268	−	0.481222i	−0.860690	+	0.509130i	$0.829967\pi$
$614$		0			0
$615$	−10.5429	−	46.1914i	−0.425130	−	1.86262i
$616$		0			0
$617$	21.3723	−	26.8000i	0.860415	−	1.07893i	−0.135690	−	0.990751i	$-0.543325\pi$
$617$	21.3723	−	26.8000i	0.860415	−	1.07893i	0.996105	−	0.0881746i	$-0.0281033\pi$
$618$		0			0
$619$	23.1247	+	11.1363i	0.929462	+	0.447605i	0.836440	−	0.548059i	$-0.184633\pi$
$619$	23.1247	+	11.1363i	0.929462	+	0.447605i	0.0930221	+	0.995664i	$0.470347\pi$
$620$		0			0
$621$	25.5918			1.02696
$622$		0			0
$623$	1.73341	+	7.59455i	0.0694474	+	0.304269i
$624$		0			0
$625$	29.8330	+	37.4094i	1.19332	+	1.49638i
$626$		0			0
$627$	−8.62229	−	10.8120i	−0.344341	−	0.431790i
$628$		0			0
$629$	−2.85086	+	3.57486i	−0.113671	+	0.142539i
$630$		0			0
$631$	−26.4894	+	12.7566i	−1.05453	+	0.507833i	−0.879089	−	0.476657i	$-0.841848\pi$
$631$	−26.4894	+	12.7566i	−1.05453	+	0.507833i	−0.175438	+	0.984491i	$0.556134\pi$
$632$		0			0
$633$	8.27240	−	36.2437i	0.328798	−	1.44056i
$634$		0			0
$635$	−56.7790	+	27.3433i	−2.25321	+	1.08509i
$636$		0			0
$637$	−9.56524			−0.378989
$638$		0			0
$639$	0.557942			0.0220718
$640$		0			0
$641$	9.43080	−	4.54164i	0.372494	−	0.179384i	−0.238265	−	0.971200i	$-0.576579\pi$
$641$	9.43080	−	4.54164i	0.372494	−	0.179384i	0.610759	+	0.791816i	$0.290864\pi$
$642$		0			0
$643$	0.678743	−	2.97377i	0.0267670	−	0.117274i	−0.959779	−	0.280755i	$-0.909415\pi$
$643$	0.678743	−	2.97377i	0.0267670	−	0.117274i	0.986546	+	0.163481i	$0.0522723\pi$
$644$		0			0
$645$	4.37047	−	2.10471i	0.172087	−	0.0828728i
$646$		0			0
$647$	18.5824	−	23.3016i	0.730550	−	0.916080i	−0.268334	−	0.963326i	$-0.586473\pi$
$647$	18.5824	−	23.3016i	0.730550	−	0.916080i	0.998883	+	0.0472458i	$0.0150444\pi$
$648$		0			0
$649$	11.3690	+	14.2562i	0.446271	+	0.559607i
$650$		0			0
$651$	1.51693	+	1.90216i	0.0594530	+	0.0745517i
$652$		0			0
$653$	−2.53438	−	11.1039i	−0.0991781	−	0.434528i	−1.00000		0.000338791i	$-0.999892\pi$
$653$	−2.53438	−	11.1039i	−0.0991781	−	0.434528i	0.900822	−	0.434189i	$-0.142965\pi$
$654$		0			0
$655$	54.3889			2.12515
$656$		0			0
$657$	−1.85205	−	0.891901i	−0.0722554	−	0.0347964i
$658$		0			0
$659$	2.86025	−	3.58664i	0.111419	−	0.139716i	−0.722995	−	0.690854i	$-0.757235\pi$
$659$	2.86025	−	3.58664i	0.111419	−	0.139716i	0.834414	+	0.551138i	$0.185806\pi$
$660$		0			0
$661$	2.86712	+	12.5617i	0.111518	+	0.488592i	0.999583	+	0.0288743i	$0.00919225\pi$
$661$	2.86712	+	12.5617i	0.111518	+	0.488592i	−0.888065	+	0.459718i	$0.847951\pi$
$662$		0			0
$663$	−3.81940	−	1.83932i	−0.148333	−	0.0714334i
$664$		0			0
$665$	−1.67845	+	7.35376i	−0.0650874	+	0.285167i
$666$		0			0
$667$	15.3503	−	23.1551i	0.594367	−	0.896571i
$668$		0			0
$669$	8.46077	−	37.0691i	0.327112	−	1.43317i
$670$		0			0
$671$	3.35958	+	1.61789i	0.129695	+	0.0624580i
$672$		0			0
$673$	−1.06518	−	4.66686i	−0.0410596	−	0.179894i	0.950240	−	0.311519i	$-0.100838\pi$
$673$	−1.06518	−	4.66686i	−0.0410596	−	0.179894i	−0.991300	+	0.131625i	$0.957981\pi$
$674$		0			0
$675$	35.2407	−	44.1904i	1.35642	−	1.70089i
$676$		0			0
$677$	27.5034	+	13.2449i	1.05704	+	0.509045i	0.879909	−	0.475142i	$-0.157603\pi$
$677$	27.5034	+	13.2449i	1.05704	+	0.509045i	0.177133	+	0.984187i	$0.443318\pi$
$678$		0			0
$679$	3.16255			0.121368
$680$		0			0
$681$	−2.86078	−	12.5339i	−0.109625	−	0.480300i
$682$		0			0
$683$	−5.95138	−	7.46279i	−0.227723	−	0.285556i	0.654822	−	0.755783i	$-0.272743\pi$
$683$	−5.95138	−	7.46279i	−0.227723	−	0.285556i	−0.882545	+	0.470227i	$0.844172\pi$
$684$		0			0
$685$	42.8962	+	53.7901i	1.63898	+	2.05521i
$686$		0			0
$687$	2.53050	−	3.17315i	0.0965446	−	0.121063i
$688$		0			0
$689$	−0.0646468	+	0.0311323i	−0.00246285	+	0.00118604i
$690$		0			0
$691$	−3.66799	+	16.0705i	−0.139537	+	0.611351i	0.856000	+	0.516976i	$0.172942\pi$
$691$	−3.66799	+	16.0705i	−0.139537	+	0.611351i	−0.995537	+	0.0943750i	$0.969915\pi$
$692$		0			0
$693$	0.439001	−	0.211412i	0.0166763	−	0.00803087i
$694$		0			0
$695$	50.4674			1.91434
$696$		0			0
$697$	−10.4155			−0.394515
$698$		0			0
$699$	30.6993	−	14.7840i	1.16115	−	0.559183i
$700$		0			0
$701$	−10.4288	+	45.6915i	−0.393890	+	1.72574i	0.256858	+	0.966449i	$0.417313\pi$
$701$	−10.4288	+	45.6915i	−0.393890	+	1.72574i	−0.650748	+	0.759294i	$0.725544\pi$
$702$		0			0
$703$	−6.91454	+	3.32987i	−0.260787	+	0.125588i
$704$		0			0
$705$	21.6211	−	27.1120i	0.814298	−	1.02110i
$706$		0			0
$707$	−1.38636	−	1.73844i	−0.0521395	−	0.0653809i
$708$		0			0
$709$	6.60955	+	8.28811i	0.248227	+	0.311267i	0.890298	−	0.455379i	$-0.150496\pi$
$709$	6.60955	+	8.28811i	0.248227	+	0.311267i	−0.642071	+	0.766645i	$0.721925\pi$
$710$		0			0
$711$	−0.535344	−	2.34549i	−0.0200770	−	0.0879629i
$712$		0			0
$713$	10.0653			0.376949
$714$		0			0
$715$	15.2545	+	7.34619i	0.570486	+	0.274732i
$716$		0			0
$717$	−23.0003	+	28.8415i	−0.858962	+	1.07710i
$718$		0			0
$719$	−2.96064	−	12.9714i	−0.110413	−	0.483752i	−0.999654	−	0.0263121i	$-0.991624\pi$
$719$	−2.96064	−	12.9714i	−0.110413	−	0.483752i	0.889241	−	0.457440i	$-0.151234\pi$
$720$		0			0
$721$	4.07338	+	1.96163i	0.151700	+	0.0730551i
$722$		0			0
$723$	2.95473	−	12.9455i	0.109888	−	0.481449i
$724$		0			0
$725$	−18.8451	−	58.3914i	−0.699890	−	2.16860i
$726$		0			0
$727$	7.34708	−	32.1896i	0.272488	−	1.19385i	−0.634578	−	0.772859i	$-0.718826\pi$
$727$	7.34708	−	32.1896i	0.272488	−	1.19385i	0.907066	−	0.420989i	$-0.138317\pi$
$728$		0			0
$729$	−22.0073	−	10.5982i	−0.815085	−	0.392524i
$730$		0			0
$731$	−0.237291	−	1.03964i	−0.00877652	−	0.0384525i
$732$		0			0
$733$	19.8240	−	24.8585i	0.732216	−	0.918170i	−0.266744	−	0.963768i	$-0.585948\pi$
$733$	19.8240	−	24.8585i	0.732216	−	0.918170i	0.998960	+	0.0455974i	$0.0145191\pi$
$734$		0			0
$735$	42.8657	+	20.6430i	1.58112	+	0.761429i
$736$		0			0
$737$	−42.6165			−1.56980
$738$		0			0
$739$	−5.32616	−	23.3354i	−0.195926	−	0.858408i	−0.973331	−	0.229407i	$-0.926321\pi$
$739$	−5.32616	−	23.3354i	−0.195926	−	0.858408i	0.777405	−	0.629001i	$-0.216536\pi$
$740$		0			0
$741$	−4.43631	−	5.56296i	−0.162972	−	0.204360i
$742$		0			0
$743$	4.62163	+	5.79534i	0.169551	+	0.212610i	0.859346	−	0.511394i	$-0.170871\pi$
$743$	4.62163	+	5.79534i	0.169551	+	0.212610i	−0.689795	+	0.724005i	$0.742299\pi$
$744$		0			0
$745$	46.2362	−	57.9783i	1.69396	−	2.12416i
$746$		0			0
$747$	−0.894928	+	0.430975i	−0.0327437	+	0.0157685i
$748$		0			0
$749$	0.890748	−	3.90262i	0.0325472	−	0.142599i
$750$		0			0
$751$	−17.4448	+	8.40098i	−0.636570	+	0.306556i	−0.724193	−	0.689598i	$-0.757787\pi$
$751$	−17.4448	+	8.40098i	−0.636570	+	0.306556i	0.0876226	+	0.996154i	$0.472073\pi$
$752$		0			0
$753$	23.3448			0.850732
$754$		0			0
$755$	−77.0786			−2.80518
$756$		0			0
$757$	30.8463	−	14.8548i	1.12113	−	0.539907i	0.220887	−	0.975299i	$-0.429105\pi$
$757$	30.8463	−	14.8548i	1.12113	−	0.539907i	0.900241	+	0.435393i	$0.143390\pi$
$758$		0			0
$759$	5.89708	−	25.8368i	0.214051	−	0.937817i
$760$		0			0
$761$	−13.1174	+	6.31703i	−0.475507	+	0.228992i	−0.656258	−	0.754537i	$-0.727862\pi$
$761$	−13.1174	+	6.31703i	−0.475507	+	0.228992i	0.180751	+	0.983529i	$0.442147\pi$
$762$		0			0
$763$	−3.96346	+	4.97002i	−0.143487	+	0.179927i
$764$		0			0
$765$	1.00000	+	1.25396i	0.0361551	+	0.0453370i
$766$		0			0
$767$	5.84953	+	7.33507i	0.211214	+	0.264854i
$768$		0			0
$769$	−2.57314	−	11.2737i	−0.0927898	−	0.406539i	0.907107	−	0.420900i	$-0.138286\pi$
$769$	−2.57314	−	11.2737i	−0.0927898	−	0.406539i	−0.999897	+	0.0143613i	$0.995428\pi$
$770$		0			0
$771$	−30.0780			−1.08323
$772$		0			0
$773$	−7.54503	−	3.63350i	−0.271376	−	0.130688i	0.293247	−	0.956037i	$-0.405264\pi$
$773$	−7.54503	−	3.63350i	−0.271376	−	0.130688i	−0.564623	+	0.825349i	$0.690978\pi$
$774$		0			0
$775$	13.8602	−	17.3802i	0.497875	−	0.624315i
$776$		0			0
$777$	−0.791053	−	3.46583i	−0.0283789	−	0.124336i
$778$		0			0
$779$	−15.7506	−	7.58510i	−0.564325	−	0.271764i
$780$		0			0
$781$	−1.43309	+	6.27879i	−0.0512801	+	0.224673i
$782$		0			0
$783$	−22.9601	+	13.6566i	−0.820527	+	0.488046i
$784$		0			0
$785$	−10.3056	+	45.1517i	−0.367822	+	1.61153i
$786$		0			0
$787$	−8.76055	−	4.21886i	−0.312280	−	0.150386i	0.271179	−	0.962529i	$-0.412587\pi$
$787$	−8.76055	−	4.21886i	−0.312280	−	0.150386i	−0.583458	+	0.812143i	$0.698301\pi$
$788$		0			0
$789$	−7.06076	−	30.9352i	−0.251370	−	1.10132i
$790$		0			0
$791$	3.86861	−	4.85108i	0.137552	−	0.172485i
$792$		0			0
$793$	1.72856	+	0.832431i	0.0613830	+	0.0295605i
$794$		0			0
$795$	0.356896			0.0126578
$796$		0			0
$797$	5.87681	+	25.7480i	0.208167	+	0.912040i	0.965786	+	0.259342i	$0.0835057\pi$
$797$	5.87681	+	25.7480i	0.208167	+	0.912040i	−0.757618	+	0.652698i	$0.773637\pi$
$798$		0			0
$799$	−4.75302	−	5.96010i	−0.168150	−	0.210853i
$800$		0			0
$801$	1.73341	+	2.17362i	0.0612469	+	0.0768012i
$802$		0			0
$803$	14.7940	−	18.5511i	0.522070	−	0.654655i
$804$		0			0
$805$	−13.0233	+	6.27167i	−0.459010	+	0.221047i
$806$		0			0
$807$	2.69029	−	11.7869i	0.0947028	−	0.414920i
$808$		0			0
$809$	−16.9291	+	8.15261i	−0.595195	+	0.286631i	−0.707129	−	0.707085i	$-0.750010\pi$
$809$	−16.9291	+	8.15261i	−0.595195	+	0.286631i	0.111934	+	0.993716i	$0.464296\pi$
$810$		0			0
$811$	−48.6983			−1.71003			−0.855013	−	0.518606i	$-0.826451\pi$
$811$	−48.6983			−1.71003			−0.855013	+	0.518606i	$0.826451\pi$
$812$		0			0
$813$	22.8267			0.800567
$814$		0			0
$815$	24.3485	−	11.7256i	0.852889	−	0.410730i
$816$		0			0
$817$	0.398280	−	1.74498i	0.0139341	−	0.0610491i
$818$		0			0
$819$	0.225873	−	0.108775i	0.00789265	−	0.00380090i
$820$		0			0
$821$	3.90246	−	4.89353i	0.136197	−	0.170785i	−0.709056	−	0.705152i	$-0.750879\pi$
$821$	3.90246	−	4.89353i	0.136197	−	0.170785i	0.845253	+	0.534367i	$0.179450\pi$
$822$		0			0
$823$	9.36257	+	11.7403i	0.326359	+	0.409241i	0.917759	−	0.397137i	$-0.129996\pi$
$823$	9.36257	+	11.7403i	0.326359	+	0.409241i	−0.591401	+	0.806378i	$0.701425\pi$
$824$		0			0
$825$	−36.4931	−	45.7608i	−1.27053	−	1.59319i
$826$		0			0
$827$	2.66069	+	11.6573i	0.0925214	+	0.405363i	0.999888	−	0.0149778i	$-0.00476776\pi$
$827$	2.66069	+	11.6573i	0.0925214	+	0.405363i	−0.907366	+	0.420341i	$0.861911\pi$
$828$		0			0
$829$	28.6305			0.994380			0.497190	−	0.867642i	$-0.334365\pi$
$829$	28.6305			0.994380			0.497190	+	0.867642i	$0.334365\pi$
$830$		0			0
$831$	25.5553	+	12.3068i	0.886502	+	0.426917i
$832$		0			0
$833$	6.52111	−	8.17721i	0.225943	−	0.283323i
$834$		0			0
$835$	13.2153	+	57.8999i	0.457334	+	2.00371i
$836$		0			0
$837$	−8.72037	−	4.19951i	−0.301420	−	0.145156i
$838$		0			0
$839$	−10.7529	+	47.1115i	−0.371231	+	1.62647i	0.352096	+	0.935964i	$0.385469\pi$
$839$	−10.7529	+	47.1115i	−0.371231	+	1.62647i	−0.723327	+	0.690505i	$0.757388\pi$
$840$		0			0
$841$	−1.41550	+	28.9654i	−0.0488104	+	0.998808i
$842$		0			0
$843$	4.73729	−	20.7554i	0.163161	−	0.714855i
$844$		0			0
$845$	−39.5746	−	19.0581i	−1.36141	−	0.655620i
$846$		0			0
$847$	−0.442353	−	1.93808i	−0.0151994	−	0.0665931i
$848$		0			0
$849$	−2.46950	+	3.09666i	−0.0847530	+	0.106277i
$850$		0			0
$851$	−13.2506	−	6.38117i	−0.454226	−	0.218744i
$852$		0			0
$853$	−6.40688			−0.219367			−0.109684	−	0.993967i	$-0.534984\pi$
$853$	−6.40688			−0.219367			−0.109684	+	0.993967i	$0.534984\pi$
$854$		0			0
$855$	0.599031	+	2.62453i	0.0204864	+	0.0897569i
$856$		0			0
$857$	−0.447730	−	0.561436i	−0.0152942	−	0.0191783i	0.774126	−	0.633032i	$-0.218190\pi$
$857$	−0.447730	−	0.561436i	−0.0152942	−	0.0191783i	−0.789420	+	0.613854i	$0.789618\pi$
$858$		0			0
$859$	9.72484	+	12.1946i	0.331807	+	0.416073i	0.919549	−	0.392975i	$-0.128554\pi$
$859$	9.72484	+	12.1946i	0.331807	+	0.416073i	−0.587742	+	0.809049i	$0.699983\pi$
$860$		0			0
$861$	5.04892	−	6.33114i	0.172067	−	0.215765i
$862$		0			0
$863$	12.1586	−	5.85527i	0.413883	−	0.199316i	−0.215342	−	0.976539i	$-0.569087\pi$
$863$	12.1586	−	5.85527i	0.413883	−	0.199316i	0.629225	+	0.777223i	$0.283372\pi$
$864$		0			0
$865$	−21.0465	+	92.2108i	−0.715603	+	3.13526i
$866$		0			0
$867$	−23.4230	+	11.2799i	−0.795488	+	0.383087i
$868$		0			0
$869$	27.7700			0.942033
$870$		0			0
$871$	−21.9269			−0.742965
$872$		0			0
$873$	1.01693	−	0.489726i	0.0344177	−	0.0165747i
$874$		0			0
$875$	−3.98643	+	17.4657i	−0.134766	+	0.590448i
$876$		0			0
$877$	14.1446	−	6.81168i	0.477629	−	0.230014i	−0.179550	−	0.983749i	$-0.557464\pi$
$877$	14.1446	−	6.81168i	0.477629	−	0.230014i	0.657179	+	0.753735i	$0.271750\pi$
$878$		0			0
$879$	23.1930	−	29.0831i	0.782280	−	0.980948i
$880$		0			0
$881$	−6.75332	−	8.46839i	−0.227525	−	0.285307i	0.654944	−	0.755677i	$-0.272692\pi$
$881$	−6.75332	−	8.46839i	−0.227525	−	0.285307i	−0.882469	+	0.470370i	$0.844121\pi$
$882$		0			0
$883$	10.2744	+	12.8837i	0.345762	+	0.433572i	0.924056	−	0.382257i	$-0.124853\pi$
$883$	10.2744	+	12.8837i	0.345762	+	0.433572i	−0.578294	+	0.815828i	$0.696281\pi$
$884$		0			0
$885$	−10.3840	−	45.4955i	−0.349056	−	1.52931i
$886$		0			0
$887$	28.5763			0.959497			0.479748	−	0.877406i	$-0.340728\pi$
$887$	28.5763			0.959497			0.479748	+	0.877406i	$0.340728\pi$
$888$		0			0
$889$	−9.70440	−	4.67339i	−0.325475	−	0.156741i
$890$		0			0
$891$	−17.2059	+	21.5755i	−0.576419	+	0.722807i
$892$		0			0
$893$	−2.84721	−	12.4744i	−0.0952782	−	0.417441i
$894$		0			0
$895$	2.42543	+	1.16802i	0.0810731	+	0.0390427i
$896$		0			0
$897$	3.03415	−	13.2935i	0.101307	−	0.443856i
$898$		0			0
$899$	−9.03026	+	5.37116i	−0.301176	+	0.179138i
$900$		0			0
$901$	0.0174584	−	0.0764902i	0.000581624	−	0.00254826i
$902$		0			0
$903$	0.746980	+	0.359726i	0.0248579	+	0.0119709i
$904$		0			0
$905$	9.88016	+	43.2878i	0.328428	+	1.43894i
$906$		0			0
$907$	−20.4875	+	25.6906i	−0.680278	+	0.853042i	−0.995380	−	0.0960163i	$-0.969390\pi$
$907$	−20.4875	+	25.6906i	−0.680278	+	0.853042i	0.315102	+	0.949058i	$0.397961\pi$
$908$		0			0
$909$	−0.714988	−	0.344320i	−0.0237147	−	0.0114204i
$910$		0			0
$911$	−10.9638			−0.363245			−0.181623	−	0.983368i	$-0.558135\pi$
$911$	−10.9638			−0.363245			−0.181623	+	0.983368i	$0.558135\pi$
$912$		0			0
$913$	−2.55131	−	11.1780i	−0.0844360	−	0.369938i
$914$		0			0
$915$	−5.94989	−	7.46092i	−0.196697	−	0.246650i
$916$		0			0
$917$	5.79590	+	7.26782i	0.191397	+	0.240005i
$918$		0			0
$919$	−4.77748	+	5.99077i	−0.157594	+	0.197617i	−0.854360	−	0.519682i	$-0.826050\pi$
$919$	−4.77748	+	5.99077i	−0.157594	+	0.197617i	0.696765	+	0.717299i	$0.254622\pi$
$920$		0			0
$921$	−37.0344	+	17.8348i	−1.22033	+	0.587678i
$922$		0			0
$923$	−0.737349	+	3.23054i	−0.0242702	+	0.106334i
$924$		0			0
$925$	−29.2652	+	14.0934i	−0.962233	+	0.463387i
$926$		0			0
$927$	1.61356			0.0529964
$928$		0			0
$929$	9.35988			0.307088			0.153544	−	0.988142i	$-0.450931\pi$
$929$	9.35988			0.307088			0.153544	+	0.988142i	$0.450931\pi$
$930$		0			0
$931$	15.8165	−	7.61681i	0.518364	−	0.249631i
$932$		0			0
$933$	−12.4661	+	54.6178i	−0.408123	+	1.78811i
$934$		0			0
$935$	−16.6799	+	8.03264i	−0.545492	+	0.262695i
$936$		0			0
$937$	4.86563	−	6.10130i	0.158953	−	0.199321i	−0.695977	−	0.718064i	$-0.745028\pi$
$937$	4.86563	−	6.10130i	0.158953	−	0.199321i	0.854930	+	0.518743i	$0.173600\pi$
$938$		0			0
$939$	12.6196	+	15.8245i	0.411825	+	0.516413i
$940$		0			0
$941$	−17.9242	−	22.4763i	−0.584313	−	0.732706i	0.398529	−	0.917156i	$-0.369521\pi$
$941$	−17.9242	−	22.4763i	−0.584313	−	0.732706i	−0.982842	+	0.184450i	$0.940950\pi$
$942$		0			0
$943$	−7.45473	−	32.6613i	−0.242759	−	1.06360i
$944$		0			0
$945$	13.8998			0.452160
$946$		0			0
$947$	−2.08061	−	1.00197i	−0.0676108	−	0.0325597i	0.399773	−	0.916614i	$-0.369089\pi$
$947$	−2.08061	−	1.00197i	−0.0676108	−	0.0325597i	−0.467384	+	0.884055i	$0.654803\pi$
$948$		0			0
$949$	7.61178	−	9.54487i	0.247089	−	0.309839i
$950$		0			0
$951$	−2.37651	−	10.4122i	−0.0770636	−	0.337638i
$952$		0			0
$953$	31.1107	+	14.9821i	1.00778	+	0.485319i	0.863570	−	0.504228i	$-0.168223\pi$
$953$	31.1107	+	14.9821i	1.00778	+	0.485319i	0.144206	+	0.989548i	$0.453937\pi$
$954$		0			0
$955$	0.466812	−	2.04524i	0.0151057	−	0.0661823i
$956$		0			0
$957$	8.49665	+	26.3268i	0.274658	+	0.851024i
$958$		0			0
$959$	−2.61662	+	11.4642i	−0.0844951	+	0.370197i
$960$		0			0
$961$	24.5003	+	11.7987i	0.790332	+	0.380604i
$962$		0			0
$963$	−0.317904	−	1.39283i	−0.0102443	−	0.0448833i
$964$		0			0
$965$	−3.50000	+	4.38886i	−0.112669	+	0.141282i
$966$		0			0
$967$	46.4163	+	22.3529i	1.49265	+	0.718822i	0.989386	−	0.145312i	$-0.0464185\pi$
$967$	46.4163	+	22.3529i	1.49265	+	0.718822i	0.503263	+	0.864134i	$0.332133\pi$
$968$		0			0
$969$	7.78017			0.249935
$970$		0			0
$971$	1.76582	+	7.73658i	0.0566680	+	0.248279i	0.995326	−	0.0965703i	$-0.0307873\pi$
$971$	1.76582	+	7.73658i	0.0566680	+	0.248279i	−0.938658	+	0.344849i	$0.887930\pi$
$972$		0			0
$973$	5.37800	+	6.74380i	0.172411	+	0.216196i
$974$		0			0
$975$	−18.7763	−	23.5447i	−0.601322	−	0.754034i
$976$		0			0
$977$	17.2080	−	21.5782i	0.550534	−	0.690348i	−0.426242	−	0.904609i	$-0.640163\pi$
$977$	17.2080	−	21.5782i	0.550534	−	0.690348i	0.976776	+	0.214261i	$0.0687343\pi$
$978$		0			0
$979$	−28.9131	+	13.9238i	−0.924067	+	0.445007i
$980$		0			0
$981$	−0.504844	+	2.21187i	−0.0161184	+	0.0706195i
$982$		0			0
$983$	31.8288	−	15.3280i	1.01518	−	0.488886i	0.149119	−	0.988819i	$-0.452356\pi$
$983$	31.8288	−	15.3280i	1.01518	−	0.488886i	0.866064	+	0.499933i	$0.166642\pi$
$984$		0			0
$985$	−52.4674			−1.67175
$986$		0			0
$987$	5.92692			0.188656
$988$		0			0
$989$	3.09030	−	1.48821i	0.0982659	−	0.0473224i
$990$		0			0
$991$	−0.123194	+	0.539750i	−0.00391340	+	0.0171457i	−0.976847	−	0.213939i	$-0.931370\pi$
$991$	−0.123194	+	0.539750i	−0.00391340	+	0.0171457i	0.972934	+	0.231085i	$0.0742276\pi$
$992$		0			0
$993$	−50.1812	+	24.1660i	−1.59245	+	0.766885i
$994$		0			0
$995$	−49.2362	+	61.7402i	−1.56089	+	1.95730i
$996$		0			0
$997$	13.8699	+	17.3924i	0.439265	+	0.550821i	0.951349	−	0.308114i	$-0.0996978\pi$
$997$	13.8699	+	17.3924i	0.439265	+	0.550821i	−0.512084	+	0.858935i	$0.671126\pi$
$998$		0			0
$999$	8.81767	+	11.0570i	0.278979	+	0.349828i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	464.2.u.f.257.1		6
4.3	odd	2		29.2.d.a.25.1	yes	6
12.11	even	2		261.2.k.a.199.1		6
20.3	even	4		725.2.r.b.199.2		12
20.7	even	4		725.2.r.b.199.1		12
20.19	odd	2		725.2.l.b.576.1		6
29.7	even	7	inner	464.2.u.f.65.1		6
116.3	even	28		841.2.e.d.196.1		12
116.7	odd	14		29.2.d.a.7.1	✓	6
116.11	even	28		841.2.e.c.270.2		12
116.15	even	28		841.2.b.c.840.5		6
116.19	even	28		841.2.e.b.267.1		12
116.23	odd	14		841.2.a.e.1.3		3
116.27	even	28		841.2.e.c.651.2		12
116.31	even	28		841.2.e.c.651.1		12
116.35	odd	14		841.2.a.f.1.1		3
116.39	even	28		841.2.e.b.267.2		12
116.43	even	28		841.2.b.c.840.2		6
116.47	even	28		841.2.e.c.270.1		12
116.51	odd	14		841.2.d.d.645.1		6
116.55	even	28		841.2.e.d.196.2		12
116.63	odd	14		841.2.d.c.190.1		6
116.67	odd	14		841.2.d.a.778.1		6
116.71	odd	14		841.2.d.c.571.1		6
116.75	even	4		841.2.e.d.236.2		12
116.79	even	28		841.2.e.b.63.2		12
116.83	odd	14		841.2.d.e.574.1		6
116.91	odd	14		841.2.d.a.574.1		6
116.95	even	28		841.2.e.b.63.1		12
116.99	even	4		841.2.e.d.236.1		12
116.103	odd	14		841.2.d.b.571.1		6
116.107	odd	14		841.2.d.e.778.1		6
116.111	odd	14		841.2.d.b.190.1		6
116.115	odd	2		841.2.d.d.605.1		6
348.23	even	14		7569.2.a.r.1.1		3
348.35	even	14		7569.2.a.p.1.3		3
348.239	even	14		261.2.k.a.181.1		6
580.7	even	28		725.2.r.b.674.2		12
580.123	even	28		725.2.r.b.674.1		12
580.239	odd	14		725.2.l.b.326.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.7.1	✓	6	116.7	odd	14
29.2.d.a.25.1	yes	6	4.3	odd	2
261.2.k.a.181.1		6	348.239	even	14
261.2.k.a.199.1		6	12.11	even	2
464.2.u.f.65.1		6	29.7	even	7	inner
464.2.u.f.257.1		6	1.1	even	1	trivial
725.2.l.b.326.1		6	580.239	odd	14
725.2.l.b.576.1		6	20.19	odd	2
725.2.r.b.199.1		12	20.7	even	4
725.2.r.b.199.2		12	20.3	even	4
725.2.r.b.674.1		12	580.123	even	28
725.2.r.b.674.2		12	580.7	even	28
841.2.a.e.1.3		3	116.23	odd	14
841.2.a.f.1.1		3	116.35	odd	14
841.2.b.c.840.2		6	116.43	even	28
841.2.b.c.840.5		6	116.15	even	28
841.2.d.a.574.1		6	116.91	odd	14
841.2.d.a.778.1		6	116.67	odd	14
841.2.d.b.190.1		6	116.111	odd	14
841.2.d.b.571.1		6	116.103	odd	14
841.2.d.c.190.1		6	116.63	odd	14
841.2.d.c.571.1		6	116.71	odd	14
841.2.d.d.605.1		6	116.115	odd	2
841.2.d.d.645.1		6	116.51	odd	14
841.2.d.e.574.1		6	116.83	odd	14
841.2.d.e.778.1		6	116.107	odd	14
841.2.e.b.63.1		12	116.95	even	28
841.2.e.b.63.2		12	116.79	even	28
841.2.e.b.267.1		12	116.19	even	28
841.2.e.b.267.2		12	116.39	even	28
841.2.e.c.270.1		12	116.47	even	28
841.2.e.c.270.2		12	116.11	even	28
841.2.e.c.651.1		12	116.31	even	28
841.2.e.c.651.2		12	116.27	even	28
841.2.e.d.196.1		12	116.3	even	28
841.2.e.d.196.2		12	116.55	even	28
841.2.e.d.236.1		12	116.99	even	4
841.2.e.d.236.2		12	116.75	even	4
7569.2.a.p.1.3		3	348.35	even	14
7569.2.a.r.1.1		3	348.23	even	14

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:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	464.u (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.62349 - 0.781831i) q^{3} +(0.900969 - 3.94740i) q^{5} +(0.623490 - 0.300257i) q^{7} +(0.153989 - 0.193096i) q^{9} +(1.77748 + 2.22889i) q^{11} +(0.914542 + 1.14680i) q^{13} +(-1.62349 - 7.11297i) q^{15} -1.60388 q^{17} +(-2.42543 - 1.16802i) q^{19} +(0.777479 - 0.974928i) q^{21} +(-1.14795 - 5.02949i) q^{23} +(-10.2654 - 4.94355i) q^{25} +(-1.10388 + 4.83639i) q^{27} +(3.71379 + 3.89971i) q^{29} +(-0.434157 + 1.90216i) q^{31} +(4.62833 + 2.22889i) q^{33} +(-0.623490 - 2.73169i) q^{35} +(1.77748 - 2.22889i) q^{37} +(2.38135 + 1.14680i) q^{39} +6.49396 q^{41} +(0.147948 + 0.648205i) q^{43} +(-0.623490 - 0.781831i) q^{45} +(2.96346 + 3.71606i) q^{47} +(-4.06584 + 5.09841i) q^{49} +(-2.60388 + 1.25396i) q^{51} +(-0.0108851 + 0.0476909i) q^{53} +(10.3998 - 5.00827i) q^{55} -4.85086 q^{57} +6.39612 q^{59} +(1.17845 - 0.567511i) q^{61} +(0.0380322 - 0.166630i) q^{63} +(5.35086 - 2.57684i) q^{65} +(-9.32036 + 11.6874i) q^{67} +(-5.79590 - 7.26782i) q^{69} +(1.40850 + 1.76621i) q^{71} +(-1.85205 - 8.11437i) q^{73} -20.5308 q^{75} +(1.77748 + 0.855989i) q^{77} +(6.07338 - 7.61577i) q^{79} +(2.15399 + 9.43724i) q^{81} +(-3.62349 - 1.74498i) q^{83} +(-1.44504 + 6.33114i) q^{85} +(9.07822 + 3.42758i) q^{87} +(-2.50484 + 10.9744i) q^{89} +(0.914542 + 0.440420i) q^{91} +(0.782323 + 3.42758i) q^{93} +(-6.79590 + 8.52179i) q^{95} +(4.11745 + 1.98286i) q^{97} +0.704103 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 5 q^{3} + q^{5} - q^{7} + 6 q^{9} + 11 q^{11} - 5 q^{13} - 5 q^{15} + 8 q^{17} - q^{19} + 5 q^{21} + 7 q^{23} - 24 q^{25} + 11 q^{27} + 6 q^{29} - 5 q^{31} + q^{33} + q^{35} + 11 q^{37} - 3 q^{39}+ \cdots + 32 q^{99}+O(q^{100}) \) 6 * q + 5 * q^3 + q^5 - q^7 + 6 * q^9 + 11 * q^11 - 5 * q^13 - 5 * q^15 + 8 * q^17 - q^19 + 5 * q^21 + 7 * q^23 - 24 * q^25 + 11 * q^27 + 6 * q^29 - 5 * q^31 + q^33 + q^35 + 11 * q^37 - 3 * q^39 + 20 * q^41 - 13 * q^43 + q^45 - 11 * q^47 - 22 * q^49 + 2 * q^51 + 3 * q^53 + 17 * q^55 - 2 * q^57 + 56 * q^59 + 3 * q^61 - 15 * q^63 + 5 * q^65 - 19 * q^67 - 7 * q^69 - 21 * q^71 - 25 * q^73 - 48 * q^75 + 11 * q^77 + 9 * q^79 + 18 * q^81 - 17 * q^83 - 8 * q^85 + 5 * q^87 + 7 * q^89 - 5 * q^91 - 17 * q^93 - 13 * q^95 + q^97 + 32 * q^99

Introduction

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Varieties

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