LMFDB - Embedded newform 912.2.cc.d.257.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [912,2,Mod(257,912)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("912.257"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(912, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 9, 17])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.cc (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [18,0,0,0,0,0,0,0,0,0,0,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + \cdots + 19683 $ x^18 - x^15 - 18x^14 + 36x^13 + 10x^12 + 18x^11 + 90x^10 - 567x^9 + 270x^8 + 162x^7 + 270x^6 + 2916x^5 - 4374x^4 - 729x^3 + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			257.3
Root			$-1.72388 - 0.168030i$ of defining polynomial
Character	$\chi$	$=$	912.257
Dual form			912.2.cc.d.401.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.716422 - 1.57694i) q^{3} +(-1.14133 + 3.13578i) q^{5} +(1.07356 - 1.85947i) q^{7} +(-1.97348 - 2.25951i) q^{9} +(-5.41799 + 3.12808i) q^{11} +(-2.56208 + 3.05336i) q^{13} +(4.12726 + 4.04635i) q^{15} +(0.403611 - 0.0711674i) q^{17} +(-4.34640 - 0.329887i) q^{19} +(-2.16314 - 3.02511i) q^{21} +(-0.280411 - 0.770422i) q^{23} +(-4.70025 - 3.94398i) q^{25} +(-4.97695 + 1.49330i) q^{27} +(-0.805141 + 4.56618i) q^{29} +(2.02597 + 1.16970i) q^{31} +(1.05122 + 10.7849i) q^{33} +(4.60559 + 5.48872i) q^{35} -6.01346i q^{37} +(2.97944 + 6.22774i) q^{39} +(-0.926617 + 0.777524i) q^{41} +(-5.87377 - 2.13788i) q^{43} +(9.33771 - 3.60955i) q^{45} +(-7.59919 - 1.33994i) q^{47} +(1.19492 + 2.06967i) q^{49} +(0.176929 - 0.687455i) q^{51} +(0.220516 - 0.0802612i) q^{53} +(-3.62525 - 20.5598i) q^{55} +(-3.63407 + 6.61767i) q^{57} +(0.930375 + 5.27642i) q^{59} +(7.30705 - 2.65955i) q^{61} +(-6.32014 + 1.24389i) q^{63} +(-6.65050 - 11.5190i) q^{65} +(-3.48689 - 0.614832i) q^{67} +(-1.41580 - 0.109756i) q^{69} +(4.19799 + 1.52794i) q^{71} +(-4.33185 + 3.63485i) q^{73} +(-9.58679 + 4.58646i) q^{75} +13.4328i q^{77} +(8.05412 + 9.59853i) q^{79} +(-1.21076 + 8.91819i) q^{81} +(8.01579 + 4.62792i) q^{83} +(-0.237488 + 1.34686i) q^{85} +(6.62378 + 4.54097i) q^{87} +(5.61888 + 4.71480i) q^{89} +(2.92708 + 8.04207i) q^{91} +(3.29599 - 2.35684i) q^{93} +(5.99513 - 13.2528i) q^{95} +(-16.0734 + 2.83418i) q^{97} +(17.7602 + 6.06880i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 12 q^{13} + 24 q^{15} - 6 q^{17} + 6 q^{19} - 18 q^{25} + 3 q^{27} + 6 q^{29} - 27 q^{33} - 24 q^{35} - 6 q^{39} - 3 q^{41} + 6 q^{43} + 54 q^{45} + 30 q^{47} + 21 q^{49} + 33 q^{51} + 60 q^{53}+ \cdots + 30 q^{99}+O(q^{100}) $ 18 * q - 12 * q^13 + 24 * q^15 - 6 * q^17 + 6 * q^19 - 18 * q^25 + 3 * q^27 + 6 * q^29 - 27 * q^33 - 24 * q^35 - 6 * q^39 - 3 * q^41 + 6 * q^43 + 54 * q^45 + 30 * q^47 + 21 * q^49 + 33 * q^51 + 60 * q^53 - 30 * q^55 + 12 * q^57 + 3 * q^59 + 54 * q^61 - 84 * q^63 - 24 * q^65 + 15 * q^67 + 24 * q^69 + 36 * q^71 - 42 * q^73 + 6 * q^79 + 36 * q^83 + 54 * q^87 + 60 * q^89 + 18 * q^91 - 84 * q^93 + 6 * q^95 + 9 * q^97 + 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.716422	−	1.57694i	0.413626	−	0.910447i
$3$	0.716422	−	1.57694i	0.413626	−	0.910447i
$4$		0			0
$5$	−1.14133	+	3.13578i	−0.510418	+	1.40236i	0.370384	+	0.928879i	$0.379226\pi$
$5$	−1.14133	+	3.13578i	−0.510418	+	1.40236i	−0.880802	+	0.473484i	$0.842996\pi$
$6$		0			0
$7$	1.07356	−	1.85947i	0.405769	−	0.702812i	−0.588642	−	0.808394i	$-0.700337\pi$
$7$	1.07356	−	1.85947i	0.405769	−	0.702812i	0.994411	+	0.105582i	$0.0336704\pi$
$8$		0			0
$9$	−1.97348	−	2.25951i	−0.657826	−	0.753170i
$10$		0			0
$11$	−5.41799	+	3.12808i	−1.63359	+	0.943151i	−0.650611	+	0.759412i	$0.725487\pi$
$11$	−5.41799	+	3.12808i	−1.63359	+	0.943151i	−0.982975	+	0.183740i	$0.941180\pi$
$12$		0			0
$13$	−2.56208	+	3.05336i	−0.710592	+	0.846850i	−0.993681	−	0.112243i	$-0.964196\pi$
$13$	−2.56208	+	3.05336i	−0.710592	+	0.846850i	0.283089	+	0.959094i	$0.408641\pi$
$14$		0			0
$15$	4.12726	+	4.04635i	1.06565	+	1.04476i
$16$		0			0
$17$	0.403611	−	0.0711674i	0.0978899	−	0.0172606i	−0.124489	−	0.992221i	$-0.539729\pi$
$17$	0.403611	−	0.0711674i	0.0978899	−	0.0172606i	0.222379	+	0.974960i	$0.428618\pi$
$18$		0			0
$19$	−4.34640	−	0.329887i	−0.997132	−	0.0756812i
$19$	−4.34640	−	0.329887i	−0.997132	−	0.0756812i
$20$		0			0
$21$	−2.16314	−	3.02511i	−0.472037	−	0.660133i
$22$		0			0
$23$	−0.280411	−	0.770422i	−0.0584697	−	0.160644i	0.907019	−	0.421090i	$-0.138353\pi$
$23$	−0.280411	−	0.770422i	−0.0584697	−	0.160644i	−0.965488	+	0.260446i	$0.916130\pi$
$24$		0			0
$25$	−4.70025	−	3.94398i	−0.940051	−	0.788796i
$26$		0			0
$27$	−4.97695	+	1.49330i	−0.957815	+	0.287385i
$28$		0			0
$29$	−0.805141	+	4.56618i	−0.149511	+	0.847919i	0.814123	+	0.580693i	$0.197218\pi$
$29$	−0.805141	+	4.56618i	−0.149511	+	0.847919i	−0.963634	+	0.267226i	$0.913893\pi$
$30$		0			0
$31$	2.02597	+	1.16970i	0.363875	+	0.210084i	0.670779	−	0.741657i	$-0.265960\pi$
$31$	2.02597	+	1.16970i	0.363875	+	0.210084i	−0.306904	+	0.951740i	$0.599293\pi$
$32$		0			0
$33$	1.05122	+	10.7849i	0.182995	+	1.87740i
$34$		0			0
$35$	4.60559	+	5.48872i	0.778486	+	0.927764i
$36$		0			0
$37$		−	6.01346i		−	0.988607i	−0.869289	−	0.494303i	$-0.835423\pi$
$37$		−	6.01346i		−	0.988607i	0.869289	−	0.494303i	$-0.164577\pi$
$38$		0			0
$39$	2.97944	+	6.22774i	0.477093	+	0.997236i
$40$		0			0
$41$	−0.926617	+	0.777524i	−0.144713	+	0.121429i	−0.712270	−	0.701905i	$-0.752333\pi$
$41$	−0.926617	+	0.777524i	−0.144713	+	0.121429i	0.567557	+	0.823334i	$0.307889\pi$
$42$		0			0
$43$	−5.87377	−	2.13788i	−0.895741	−	0.326023i	−0.147196	−	0.989107i	$-0.547025\pi$
$43$	−5.87377	−	2.13788i	−0.895741	−	0.326023i	−0.748545	+	0.663084i	$0.769247\pi$
$44$		0			0
$45$	9.33771	−	3.60955i	1.39198	−	0.538080i
$46$		0			0
$47$	−7.59919	−	1.33994i	−1.10846	−	0.195451i	−0.410689	−	0.911776i	$-0.634712\pi$
$47$	−7.59919	−	1.33994i	−1.10846	−	0.195451i	−0.697767	+	0.716325i	$0.745823\pi$
$48$		0			0
$49$	1.19492	+	2.06967i	0.170703	+	0.295666i
$50$		0			0
$51$	0.176929	−	0.687455i	0.0247750	−	0.0962630i
$52$		0			0
$53$	0.220516	−	0.0802612i	0.0302902	−	0.0110247i	−0.326831	−	0.945083i	$-0.605981\pi$
$53$	0.220516	−	0.0802612i	0.0302902	−	0.0110247i	0.357121	+	0.934058i	$0.383758\pi$
$54$		0			0
$55$	−3.62525	−	20.5598i	−0.488828	−	2.77228i
$56$		0			0
$57$	−3.63407	+	6.61767i	−0.481344	+	0.876532i
$58$		0			0
$59$	0.930375	+	5.27642i	0.121124	+	0.686931i	0.983534	+	0.180721i	$0.0578430\pi$
$59$	0.930375	+	5.27642i	0.121124	+	0.686931i	−0.862410	+	0.506210i	$0.831046\pi$
$60$		0			0
$61$	7.30705	−	2.65955i	0.935572	−	0.340520i	0.171156	−	0.985244i	$-0.445250\pi$
$61$	7.30705	−	2.65955i	0.935572	−	0.340520i	0.764416	+	0.644723i	$0.223027\pi$
$62$		0			0
$63$	−6.32014	+	1.24389i	−0.796262	+	0.156716i
$64$		0			0
$65$	−6.65050	−	11.5190i	−0.824893	−	1.42876i
$66$		0			0
$67$	−3.48689	−	0.614832i	−0.425991	−	0.0751137i	−0.0434574	−	0.999055i	$-0.513837\pi$
$67$	−3.48689	−	0.614832i	−0.425991	−	0.0751137i	−0.382534	+	0.923942i	$0.624948\pi$
$68$		0			0
$69$	−1.41580	−	0.109756i	−0.170443	−	0.0132131i
$70$		0			0
$71$	4.19799	+	1.52794i	0.498210	+	0.181334i	0.578889	−	0.815407i	$-0.303487\pi$
$71$	4.19799	+	1.52794i	0.498210	+	0.181334i	−0.0806788	+	0.996740i	$0.525709\pi$
$72$		0			0
$73$	−4.33185	+	3.63485i	−0.507005	+	0.425427i	−0.860074	−	0.510170i	$-0.829583\pi$
$73$	−4.33185	+	3.63485i	−0.507005	+	0.425427i	0.353069	+	0.935597i	$0.385138\pi$
$74$		0			0
$75$	−9.58679	+	4.58646i	−1.10699	+	0.529599i
$76$		0			0
$77$			13.4328i			1.53081i
$78$		0			0
$79$	8.05412	+	9.59853i	0.906159	+	1.07992i	0.996465	+	0.0840047i	$0.0267711\pi$
$79$	8.05412	+	9.59853i	0.906159	+	1.07992i	−0.0903059	+	0.995914i	$0.528784\pi$
$80$		0			0
$81$	−1.21076	+	8.91819i	−0.134529	+	0.990910i
$82$		0			0
$83$	8.01579	+	4.62792i	0.879848	+	0.507980i	0.870608	−	0.491977i	$-0.163726\pi$
$83$	8.01579	+	4.62792i	0.879848	+	0.507980i	0.00923947	+	0.999957i	$0.497059\pi$
$84$		0			0
$85$	−0.237488	+	1.34686i	−0.0257591	+	0.146087i
$86$		0			0
$87$	6.62378	+	4.54097i	0.710143	+	0.486843i
$88$		0			0
$89$	5.61888	+	4.71480i	0.595600	+	0.499767i	0.890028	−	0.455906i	$-0.150685\pi$
$89$	5.61888	+	4.71480i	0.595600	+	0.499767i	−0.294428	+	0.955674i	$0.595129\pi$
$90$		0			0
$91$	2.92708	+	8.04207i	0.306841	+	0.843038i
$92$		0			0
$93$	3.29599	−	2.35684i	0.341778	−	0.244393i
$94$		0			0
$95$	5.99513	−	13.2528i	0.615087	−	1.35971i
$96$		0			0
$97$	−16.0734	+	2.83418i	−1.63201	+	0.287767i	−0.913221	−	0.407464i	$-0.866413\pi$
$97$	−16.0734	+	2.83418i	−1.63201	+	0.287767i	−0.718786	+	0.695231i	$0.755302\pi$
$98$		0			0
$99$	17.7602	+	6.06880i	1.78497	+	0.609937i
$100$		0			0
$101$	3.69207	−	4.40004i	0.367375	−	0.437820i	−0.550412	−	0.834893i	$-0.685529\pi$
$101$	3.69207	−	4.40004i	0.367375	−	0.437820i	0.917787	+	0.397073i	$0.129974\pi$
$102$		0			0
$103$	0.957127	−	0.552597i	0.0943085	−	0.0544490i	−0.452104	−	0.891965i	$-0.649326\pi$
$103$	0.957127	−	0.552597i	0.0943085	−	0.0544490i	0.546413	+	0.837516i	$0.315993\pi$
$104$		0			0
$105$	11.9549	−	3.33049i	1.16668	−	0.325023i
$106$		0			0
$107$	−3.47626	+	6.02105i	−0.336062	+	0.582077i	−0.983688	−	0.179881i	$-0.942429\pi$
$107$	−3.47626	+	6.02105i	−0.336062	+	0.582077i	0.647626	+	0.761958i	$0.275762\pi$
$108$		0			0
$109$	2.42887	−	6.67327i	0.232644	−	0.639183i	−0.767354	−	0.641223i	$-0.778427\pi$
$109$	2.42887	−	6.67327i	0.232644	−	0.639183i	0.999998	+	0.00204008i	$0.000649379\pi$
$110$		0			0
$111$	−9.48286	−	4.30817i	−0.900074	−	0.408914i
$112$		0			0
$113$	−2.33000			−0.219188			−0.109594	−	0.993976i	$-0.534955\pi$
$113$	−2.33000			−0.219188			−0.109594	+	0.993976i	$0.534955\pi$
$114$		0			0
$115$	2.73592			0.255125
$116$		0			0
$117$	11.9553	−	0.236716i	1.10527	−	0.0218844i
$118$		0			0
$119$	0.300968	−	0.826903i	0.0275897	−	0.0758021i
$120$		0			0
$121$	14.0697	−	24.3695i	1.27907	−	2.21541i
$122$		0			0
$123$	0.562260	+	2.01825i	0.0506973	+	0.181980i
$124$		0			0
$125$	3.28225	−	1.89501i	0.293573	−	0.169495i
$126$		0			0
$127$	−0.792153	+	0.944052i	−0.0702922	+	0.0837710i	−0.800045	−	0.599941i	$-0.795191\pi$
$127$	−0.792153	+	0.944052i	−0.0702922	+	0.0837710i	0.729752	+	0.683712i	$0.239635\pi$
$128$		0			0
$129$	−7.57940	+	7.73096i	−0.667329	+	0.680673i
$130$		0			0
$131$	6.34320	−	1.11848i	0.554208	−	0.0977218i	0.110472	−	0.993879i	$-0.464764\pi$
$131$	6.34320	−	1.11848i	0.554208	−	0.0977218i	0.443736	+	0.896157i	$0.353653\pi$
$132$		0			0
$133$	−5.27955	+	7.72783i	−0.457795	+	0.670088i
$134$		0			0
$135$	0.997698	−	17.3110i	0.0858682	−	1.48989i
$136$		0			0
$137$	−3.68452	−	10.1231i	−0.314790	−	0.864878i	−0.991672	−	0.128787i	$-0.958892\pi$
$137$	−3.68452	−	10.1231i	−0.314790	−	0.864878i	0.676882	−	0.736091i	$-0.263331\pi$
$138$		0			0
$139$	−6.45972	−	5.42035i	−0.547906	−	0.459748i	0.326325	−	0.945258i	$-0.394190\pi$
$139$	−6.45972	−	5.42035i	−0.547906	−	0.459748i	−0.874231	+	0.485510i	$0.838634\pi$
$140$		0			0
$141$	−7.55723	+	11.0235i	−0.636434	+	0.928346i
$142$		0			0
$143$	4.33014	−	24.5575i	0.362105	−	2.05360i
$144$		0			0
$145$	−13.3996	−	7.73627i	−1.11278	−	0.642462i
$146$		0			0
$147$	4.11981	−	0.401566i	0.339796	−	0.0331206i
$148$		0			0
$149$	3.41271	+	4.06711i	0.279580	+	0.333190i	0.887500	−	0.460808i	$-0.152440\pi$
$149$	3.41271	+	4.06711i	0.279580	+	0.333190i	−0.607920	+	0.793998i	$0.707996\pi$
$150$		0			0
$151$		−	2.55987i		−	0.208319i	−0.994561	−	0.104160i	$-0.966785\pi$
$151$		−	2.55987i		−	0.208319i	0.994561	−	0.104160i	$-0.0332153\pi$
$152$		0			0
$153$	−0.957320	−	0.771514i	−0.0773948	−	0.0623732i
$154$		0			0
$155$	−5.98021	+	5.01799i	−0.480342	+	0.403055i
$156$		0			0
$157$	15.7565	+	5.73489i	1.25750	+	0.457694i	0.882931	−	0.469503i	$-0.155567\pi$
$157$	15.7565	+	5.73489i	1.25750	+	0.457694i	0.374573	+	0.927197i	$0.377789\pi$
$158$		0			0
$159$	0.0314153	−	0.405241i	0.00249139	−	0.0321377i
$160$		0			0
$161$	−1.73361	−	0.305683i	−0.136628	−	0.0240912i
$162$		0			0
$163$	−5.28499	−	9.15387i	−0.413952	−	0.716987i	0.581365	−	0.813643i	$-0.302519\pi$
$163$	−5.28499	−	9.15387i	−0.413952	−	0.716987i	−0.995318	+	0.0966559i	$0.969185\pi$
$164$		0			0
$165$	−35.0188	−	9.01269i	−2.72621	−	0.701637i
$166$		0			0
$167$	−10.5199	+	3.82893i	−0.814054	+	0.296292i	−0.715298	−	0.698820i	$-0.753709\pi$
$167$	−10.5199	+	3.82893i	−0.814054	+	0.296292i	−0.0987568	+	0.995112i	$0.531487\pi$
$168$		0			0
$169$	−0.501366	−	2.84339i	−0.0385666	−	0.218722i
$170$		0			0
$171$	7.83214	+	10.4717i	0.598939	+	0.800795i
$172$		0			0
$173$	−3.80558	−	21.5825i	−0.289333	−	1.64089i	−0.689384	−	0.724396i	$-0.742119\pi$
$173$	−3.80558	−	21.5825i	−0.289333	−	1.64089i	0.400051	−	0.916493i	$-0.368993\pi$
$174$		0			0
$175$	−12.3797	+	4.50585i	−0.935819	+	0.340610i
$176$		0			0
$177$	8.98713	+	2.31300i	0.675514	+	0.173855i
$178$		0			0
$179$	−10.6934	−	18.5215i	−0.799263	−	1.38436i	−0.920097	−	0.391692i	$-0.871890\pi$
$179$	−10.6934	−	18.5215i	−0.799263	−	1.38436i	0.120833	−	0.992673i	$-0.461443\pi$
$180$		0			0
$181$	−18.0057	−	3.17489i	−1.33835	−	0.235988i	−0.541775	−	0.840523i	$-0.682248\pi$
$181$	−18.0057	−	3.17489i	−1.33835	−	0.235988i	−0.796578	+	0.604536i	$0.793359\pi$
$182$		0			0
$183$	1.04098	−	13.4281i	0.0769516	−	0.992637i
$184$		0			0
$185$	18.8569	+	6.86334i	1.38639	+	0.504603i
$186$		0			0
$187$	−1.96414	+	1.64811i	−0.143632	+	0.120522i
$188$		0			0
$189$	−2.56634	+	10.8576i	−0.186674	+	0.789776i
$190$		0			0
$191$		−	3.46116i		−	0.250441i	−0.992129	−	0.125220i	$-0.960036\pi$
$191$		−	3.46116i		−	0.250441i	0.992129	−	0.125220i	$-0.0399638\pi$
$192$		0			0
$193$	6.64414	+	7.91818i	0.478256	+	0.569963i	0.950190	−	0.311671i	$-0.100889\pi$
$193$	6.64414	+	7.91818i	0.478256	+	0.569963i	−0.471934	+	0.881634i	$0.656444\pi$
$194$		0			0
$195$	−22.9293	+	2.23497i	−1.64200	+	0.160050i
$196$		0			0
$197$	−10.2877	−	5.93959i	−0.732966	−	0.423178i	0.0865400	−	0.996248i	$-0.472419\pi$
$197$	−10.2877	−	5.93959i	−0.732966	−	0.423178i	−0.819506	+	0.573070i	$0.805752\pi$
$198$		0			0
$199$	−4.24330	+	24.0650i	−0.300800	+	1.70592i	0.341845	+	0.939756i	$0.388948\pi$
$199$	−4.24330	+	24.0650i	−0.300800	+	1.70592i	−0.642645	+	0.766164i	$0.722163\pi$
$200$		0			0
$201$	−3.46764	+	5.05813i	−0.244588	+	0.356773i
$202$		0			0
$203$	7.62630	+	6.39922i	0.535261	+	0.449137i
$204$		0			0
$205$	−1.38057	−	3.79308i	−0.0964230	−	0.264920i
$206$		0			0
$207$	−1.18739	+	2.15400i	−0.0825294	+	0.149714i
$208$		0			0
$209$	24.5807	−	11.8085i	1.70028	−	0.816814i
$210$		0			0
$211$	16.3173	−	2.87718i	1.12333	−	0.198074i	0.419028	−	0.907973i	$-0.362371\pi$
$211$	16.3173	−	2.87718i	1.12333	−	0.198074i	0.704303	+	0.709900i	$0.251260\pi$
$212$		0			0
$213$	5.41701	−	5.52533i	0.371167	−	0.378589i
$214$		0			0
$215$	13.4078	−	15.9788i	0.914405	−	1.08975i
$216$		0			0
$217$	4.35002	−	2.51149i	0.295299	−	0.170491i
$218$		0			0
$219$	2.62851	+	9.43516i	0.177619	+	0.637569i
$220$		0			0
$221$	−0.816781	+	1.41471i	−0.0549426	+	0.0951634i
$222$		0			0
$223$	4.05122	−	11.1306i	0.271290	−	0.745362i	−0.726986	−	0.686653i	$-0.759079\pi$
$223$	4.05122	−	11.1306i	0.271290	−	0.745362i	0.998275	−	0.0587091i	$-0.0186984\pi$
$224$		0			0
$225$	0.364394	+	18.4036i	0.0242929	+	1.22691i
$226$		0			0
$227$	−23.0722			−1.53135			−0.765676	−	0.643226i	$-0.777595\pi$
$227$	−23.0722			−1.53135			−0.765676	+	0.643226i	$0.777595\pi$
$228$		0			0
$229$	14.0461			0.928192			0.464096	−	0.885785i	$-0.346379\pi$
$229$	14.0461			0.928192			0.464096	+	0.885785i	$0.346379\pi$
$230$		0			0
$231$	21.1827	+	9.62353i	1.39372	+	0.633182i
$232$		0			0
$233$	8.06779	−	22.1661i	0.528539	−	1.45215i	−0.332253	−	0.943190i	$-0.607809\pi$
$233$	8.06779	−	22.1661i	0.528539	−	1.45215i	0.860792	−	0.508958i	$-0.169969\pi$
$234$		0			0
$235$	12.8749	−	22.3001i	0.839869	−	1.45470i
$236$		0			0
$237$	20.9065	−	5.82427i	1.35802	−	0.378327i
$238$		0			0
$239$	−23.6023	+	13.6268i	−1.52670	+	0.881443i	−0.527206	+	0.849738i	$0.676760\pi$
$239$	−23.6023	+	13.6268i	−1.52670	+	0.881443i	−0.999497	+	0.0317050i	$0.989906\pi$
$240$		0			0
$241$	13.6728	−	16.2946i	0.880739	−	1.04962i	−0.117659	−	0.993054i	$-0.537539\pi$
$241$	13.6728	−	16.2946i	0.880739	−	1.04962i	0.998399	−	0.0565704i	$-0.0180165\pi$
$242$		0			0
$243$	13.1960	+	8.29848i	0.846526	+	0.532348i
$244$		0			0
$245$	−7.85381	+	1.38484i	−0.501762	+	0.0884741i
$246$		0			0
$247$	12.1431	−	12.4259i	0.772645	−	0.790643i
$248$		0			0
$249$	13.0406	−	9.32488i	0.826417	−	0.590940i
$250$		0			0
$251$	0.848967	+	2.33252i	0.0535863	+	0.147227i	0.963598	−	0.267355i	$-0.0861498\pi$
$251$	0.848967	+	2.33252i	0.0535863	+	0.147227i	−0.910012	+	0.414583i	$0.863928\pi$
$252$		0			0
$253$	3.92920	+	3.29699i	0.247027	+	0.207280i
$254$		0			0
$255$	1.95377	+	1.33942i	0.122350	+	0.0838779i
$256$		0			0
$257$	−1.95465	+	11.0854i	−0.121928	+	0.691488i	0.861157	+	0.508339i	$0.169740\pi$
$257$	−1.95465	+	11.0854i	−0.121928	+	0.691488i	−0.983085	+	0.183149i	$0.941371\pi$
$258$		0			0
$259$	−11.1818	−	6.45583i	−0.694805	−	0.401146i
$260$		0			0
$261$	11.9063	−	7.19205i	0.736979	−	0.445176i
$262$		0			0
$263$	7.57578	+	9.02847i	0.467143	+	0.556719i	0.947252	−	0.320490i	$-0.103847\pi$
$263$	7.57578	+	9.02847i	0.467143	+	0.556719i	−0.480109	+	0.877209i	$0.659403\pi$
$264$		0			0
$265$			0.783093i			0.0481050i
$266$		0			0
$267$	11.4604	−	5.48285i	0.701367	−	0.335545i
$268$		0			0
$269$	−8.96522	+	7.52271i	−0.546619	+	0.458668i	−0.873794	−	0.486296i	$-0.838348\pi$
$269$	−8.96522	+	7.52271i	−0.546619	+	0.458668i	0.327175	+	0.944964i	$0.393903\pi$
$270$		0			0
$271$	29.1999	+	10.6279i	1.77377	+	0.645598i	0.999925	+	0.0122180i	$0.00388921\pi$
$271$	29.1999	+	10.6279i	1.77377	+	0.645598i	0.773841	+	0.633380i	$0.218333\pi$
$272$		0			0
$273$	14.7789	+	1.14570i	0.894459	+	0.0693406i
$274$		0			0
$275$	37.8030	+	6.66569i	2.27961	+	0.401956i
$276$		0			0
$277$	1.91965	+	3.32494i	0.115341	+	0.199776i	0.917916	−	0.396775i	$-0.129871\pi$
$277$	1.91965	+	3.32494i	0.115341	+	0.199776i	−0.802575	+	0.596551i	$0.796537\pi$
$278$		0			0
$279$	−1.35528	−	6.88607i	−0.0811383	−	0.412258i
$280$		0			0
$281$	−23.0658	+	8.39528i	−1.37599	+	0.500820i	−0.920961	−	0.389655i	$-0.872594\pi$
$281$	−23.0658	+	8.39528i	−1.37599	+	0.500820i	−0.455031	+	0.890475i	$0.650372\pi$
$282$		0			0
$283$	4.03563	+	22.8872i	0.239894	+	1.36050i	0.832059	+	0.554688i	$0.187162\pi$
$283$	4.03563	+	22.8872i	0.239894	+	1.36050i	−0.592165	+	0.805817i	$0.701727\pi$
$284$		0			0
$285$	−16.6039	−	18.9486i	−0.983529	−	1.12242i
$286$		0			0
$287$	0.450998	+	2.55773i	0.0266215	+	0.150978i
$288$		0			0
$289$	−15.8169	+	5.75689i	−0.930408	+	0.338641i
$290$		0			0
$291$	−7.04602	+	27.3773i	−0.413045	+	1.60488i
$292$		0			0
$293$	−5.48661	−	9.50309i	−0.320531	−	0.555177i	0.660066	−	0.751207i	$-0.270528\pi$
$293$	−5.48661	−	9.50309i	−0.320531	−	0.555177i	−0.980598	+	0.196031i	$0.937195\pi$
$294$		0			0
$295$	−17.6075	−	3.10468i	−1.02515	−	0.180762i
$296$		0			0
$297$	22.2939	−	23.6590i	1.29363	−	1.37283i
$298$		0			0
$299$	3.07081	+	1.11768i	0.177590	+	0.0646374i
$300$		0			0
$301$	−10.2812	+	8.62693i	−0.592597	+	0.497248i
$302$		0			0
$303$	−4.29352	−	8.97446i	−0.246656	−	0.515569i
$304$		0			0
$305$			25.9487i			1.48582i
$306$		0			0
$307$	0.351542	+	0.418952i	0.0200636	+	0.0239108i	0.775983	−	0.630754i	$-0.217254\pi$
$307$	0.351542	+	0.418952i	0.0200636	+	0.0239108i	−0.755919	+	0.654665i	$0.772810\pi$
$308$		0			0
$309$	−0.185706	−	1.90522i	−0.0105645	−	0.108384i
$310$		0			0
$311$	12.1908	+	7.03836i	0.691277	+	0.399109i	0.804090	−	0.594507i	$-0.202653\pi$
$311$	12.1908	+	7.03836i	0.691277	+	0.399109i	−0.112813	+	0.993616i	$0.535986\pi$
$312$		0			0
$313$	−3.23018	+	18.3193i	−0.182580	+	1.03547i	0.746444	+	0.665448i	$0.231759\pi$
$313$	−3.23018	+	18.3193i	−0.182580	+	1.03547i	−0.929025	+	0.370018i	$0.879352\pi$
$314$		0			0
$315$	3.31279	−	21.2382i	0.186655	−	1.19664i
$316$		0			0
$317$	20.8301	+	17.4785i	1.16993	+	0.981690i	0.999993	−	0.00376423i	$-0.00119819\pi$
$317$	20.8301	+	17.4785i	1.16993	+	0.981690i	0.169940	+	0.985454i	$0.445643\pi$
$318$		0			0
$319$	−9.92113	−	27.2581i	−0.555477	−	1.52616i
$320$		0			0
$321$	7.00437	+	9.79546i	0.390946	+	0.546730i
$322$		0			0
$323$	−1.77773	+	0.176176i	−0.0989155	+	0.00980270i
$324$		0			0
$325$	24.0848	−	4.24680i	1.33598	−	0.235570i
$326$		0			0
$327$	−8.78325	−	8.61106i	−0.485715	−	0.476193i
$328$		0			0
$329$	−10.6498	+	12.6919i	−0.587142	+	0.699729i
$330$		0			0
$331$	−25.4221	+	14.6775i	−1.39733	+	0.806746i	−0.994112	−	0.108360i	$-0.965440\pi$
$331$	−25.4221	+	14.6775i	−1.39733	+	0.806746i	−0.403214	+	0.915106i	$0.632107\pi$
$332$		0			0
$333$	−13.5875	+	11.8674i	−0.744588	+	0.650332i
$334$		0			0
$335$	5.90767	−	10.2324i	0.322770	−	0.559055i
$336$		0			0
$337$	4.60842	−	12.6615i	0.251037	−	0.689717i	−0.748607	−	0.663014i	$-0.769277\pi$
$337$	4.60842	−	12.6615i	0.251037	−	0.689717i	0.999643	−	0.0267031i	$-0.00850087\pi$
$338$		0			0
$339$	−1.66926	+	3.67427i	−0.0906620	+	0.199559i
$340$		0			0
$341$	−14.6356			−0.792562
$342$		0			0
$343$	20.1612			1.08860
$344$		0			0
$345$	1.96007	−	4.31437i	0.105527	−	0.232278i
$346$		0			0
$347$	2.06013	−	5.66016i	0.110594	−	0.303854i	−0.872033	−	0.489447i	$-0.837199\pi$
$347$	2.06013	−	5.66016i	0.110594	−	0.303854i	0.982627	+	0.185594i	$0.0594208\pi$
$348$		0			0
$349$	−14.3065	+	24.7795i	−0.765808	+	1.32642i	0.174010	+	0.984744i	$0.444328\pi$
$349$	−14.3065	+	24.7795i	−0.765808	+	1.32642i	−0.939818	+	0.341675i	$0.889006\pi$
$350$		0			0
$351$	8.19175	−	19.0224i	0.437243	−	1.01534i
$352$		0			0
$353$	−14.6066	+	8.43315i	−0.777433	+	0.448851i	−0.835520	−	0.549460i	$-0.814833\pi$
$353$	−14.6066	+	8.43315i	−0.777433	+	0.448851i	0.0580867	+	0.998312i	$0.481500\pi$
$354$		0			0
$355$	−9.58259	+	11.4201i	−0.508591	+	0.606115i
$356$		0			0
$357$	−1.08836	−	1.06702i	−0.0576019	−	0.0564727i
$358$		0			0
$359$	−16.2813	+	2.87084i	−0.859295	+	0.151517i	−0.585898	−	0.810385i	$-0.699258\pi$
$359$	−16.2813	+	2.87084i	−0.859295	+	0.151517i	−0.273397	+	0.961901i	$0.588147\pi$
$360$		0			0
$361$	18.7823	+	2.86764i	0.988545	+	0.150928i
$362$		0			0
$363$	−28.3494	−	39.6460i	−1.48796	−	2.08088i
$364$		0			0
$365$	−6.45403	−	17.7323i	−0.337819	−	0.928151i
$366$		0			0
$367$	7.32428	+	6.14580i	0.382324	+	0.320808i	0.813614	−	0.581405i	$-0.197497\pi$
$367$	7.32428	+	6.14580i	0.382324	+	0.320808i	−0.431290	+	0.902213i	$0.641941\pi$
$368$		0			0
$369$	3.58548	+	0.559271i	0.186653	+	0.0291145i
$370$		0			0
$371$	0.0874947	−	0.496207i	0.00454250	−	0.0257618i
$372$		0			0
$373$	3.75197	+	2.16620i	0.194270	+	0.112162i	0.593980	−	0.804480i	$-0.297556\pi$
$373$	3.75197	+	2.16620i	0.194270	+	0.112162i	−0.399710	+	0.916642i	$0.630889\pi$
$374$		0			0
$375$	−0.636837	−	6.53353i	−0.0328861	−	0.337390i
$376$		0			0
$377$	−11.8794	−	14.1573i	−0.611819	−	0.729138i
$378$		0			0
$379$		−	5.96818i		−	0.306565i	−0.988182	−	0.153282i	$-0.951016\pi$
$379$		−	5.96818i		−	0.306565i	0.988182	−	0.153282i	$-0.0489844\pi$
$380$		0			0
$381$	0.921197	+	1.92552i	0.0471943	+	0.0986472i
$382$		0			0
$383$	3.37004	−	2.82780i	0.172201	−	0.144494i	−0.552614	−	0.833437i	$-0.686370\pi$
$383$	3.37004	−	2.82780i	0.172201	−	0.144494i	0.724815	+	0.688944i	$0.241925\pi$
$384$		0			0
$385$	−42.1222	−	15.3312i	−2.14675	−	0.781351i
$386$		0			0
$387$	6.76121	+	17.4909i	0.343692	+	0.889112i
$388$		0			0
$389$	14.5009	+	2.55689i	0.735223	+	0.129640i	0.528708	−	0.848804i	$-0.322677\pi$
$389$	14.5009	+	2.55689i	0.735223	+	0.129640i	0.206515	+	0.978443i	$0.433788\pi$
$390$		0			0
$391$	−0.168006	−	0.290994i	−0.00849641	−	0.0147162i
$392$		0			0
$393$	2.78064	−	10.8041i	0.140264	−	0.544997i
$394$		0			0
$395$	−39.2913	+	14.3009i	−1.97696	+	0.719554i
$396$		0			0
$397$	1.74751	+	9.91059i	0.0877048	+	0.497398i	0.996740	+	0.0806794i	$0.0257090\pi$
$397$	1.74751	+	9.91059i	0.0877048	+	0.497398i	−0.909035	+	0.416719i	$0.863180\pi$
$398$		0			0
$399$	8.40394	+	13.8619i	0.420723	+	0.693964i
$400$		0			0
$401$	2.58090	+	14.6370i	0.128884	+	0.730937i	0.978925	+	0.204221i	$0.0654660\pi$
$401$	2.58090	+	14.6370i	0.128884	+	0.730937i	−0.850041	+	0.526717i	$0.823423\pi$
$402$		0			0
$403$	−8.76220	+	3.18918i	−0.436476	+	0.158864i
$404$		0			0
$405$	−26.5836	−	13.9753i	−1.32095	−	0.694437i
$406$		0			0
$407$	18.8106	+	32.5809i	0.932405	+	1.61497i
$408$		0			0
$409$	−9.81162	−	1.73005i	−0.485153	−	0.0855456i	−0.0742787	−	0.997238i	$-0.523665\pi$
$409$	−9.81162	−	1.73005i	−0.485153	−	0.0855456i	−0.410874	+	0.911692i	$0.634777\pi$
$410$		0			0
$411$	−18.6033	−	1.44217i	−0.917631	−	0.0711370i
$412$		0			0
$413$	10.8101	+	3.93457i	0.531932	+	0.193607i
$414$		0			0
$415$	−23.6608	+	19.8538i	−1.16146	+	0.974583i
$416$		0			0
$417$	−13.1754	+	6.30333i	−0.645204	+	0.308676i
$418$		0			0
$419$		−	8.34847i		−	0.407849i	−0.978987	−	0.203925i	$-0.934630\pi$
$419$		−	8.34847i		−	0.407849i	0.978987	−	0.203925i	$-0.0653698\pi$
$420$		0			0
$421$	23.4446	+	27.9402i	1.14262	+	1.36172i	0.922384	+	0.386273i	$0.126238\pi$
$421$	23.4446	+	27.9402i	1.14262	+	1.36172i	0.220234	+	0.975447i	$0.429318\pi$
$422$		0			0
$423$	11.9692	+	19.8148i	0.581964	+	0.963428i
$424$		0			0
$425$	−2.17775	−	1.25733i	−0.105637	−	0.0609893i
$426$		0			0
$427$	2.89924	−	16.4424i	0.140304	−	0.795705i
$428$		0			0
$429$	−35.6234	−	24.4219i	−1.71992	−	1.17910i
$430$		0			0
$431$	8.05751	+	6.76105i	0.388116	+	0.325668i	0.815879	−	0.578223i	$-0.196254\pi$
$431$	8.05751	+	6.76105i	0.388116	+	0.325668i	−0.427762	+	0.903891i	$0.640698\pi$
$432$		0			0
$433$	−12.6127	−	34.6530i	−0.606126	−	1.66532i	−0.738611	−	0.674132i	$-0.764518\pi$
$433$	−12.6127	−	34.6530i	−0.606126	−	1.66532i	0.132485	−	0.991185i	$-0.457704\pi$
$434$		0			0
$435$	−21.7994	+	15.5879i	−1.04520	+	0.747385i
$436$		0			0
$437$	0.964625	+	3.44107i	0.0461443	+	0.164608i
$438$		0			0
$439$	−13.1107	+	2.31177i	−0.625739	+	0.110335i	−0.477522	−	0.878620i	$-0.658465\pi$
$439$	−13.1107	+	2.31177i	−0.625739	+	0.110335i	−0.148218	+	0.988955i	$0.547354\pi$
$440$		0			0
$441$	2.31827	−	6.78438i	0.110394	−	0.323066i
$442$		0			0
$443$	4.79891	−	5.71912i	0.228003	−	0.271724i	−0.639899	−	0.768459i	$-0.721024\pi$
$443$	4.79891	−	5.71912i	0.228003	−	0.271724i	0.867902	+	0.496736i	$0.165468\pi$
$444$		0			0
$445$	−21.1976	+	12.2384i	−1.00486	+	0.580156i
$446$		0			0
$447$	8.85852	−	2.46787i	0.418994	−	0.116726i
$448$		0			0
$449$	−12.1781	+	21.0931i	−0.574722	+	0.995447i	0.421350	+	0.906898i	$0.361556\pi$
$449$	−12.1781	+	21.0931i	−0.574722	+	0.995447i	−0.996072	+	0.0885490i	$0.971777\pi$
$450$		0			0
$451$	2.58825	−	7.11115i	0.121876	−	0.334851i
$452$		0			0
$453$	−4.03676	−	1.83395i	−0.189664	−	0.0861664i
$454$		0			0
$455$	−28.5589			−1.33886
$456$		0			0
$457$	−34.8127			−1.62847			−0.814236	−	0.580534i	$-0.802844\pi$
$457$	−34.8127			−1.62847			−0.814236	+	0.580534i	$0.802844\pi$
$458$		0			0
$459$	−1.90248	+	0.956907i	−0.0888000	+	0.0446646i
$460$		0			0
$461$	−0.765028	+	2.10190i	−0.0356309	+	0.0978951i	−0.956232	−	0.292608i	$-0.905477\pi$
$461$	−0.765028	+	2.10190i	−0.0356309	+	0.0978951i	0.920601	+	0.390503i	$0.127699\pi$
$462$		0			0
$463$	−1.84091	+	3.18854i	−0.0855541	+	0.148184i	−0.905627	−	0.424075i	$-0.860599\pi$
$463$	−1.84091	+	3.18854i	−0.0855541	+	0.148184i	0.820073	+	0.572259i	$0.193933\pi$
$464$		0			0
$465$	3.62872	+	13.0254i	0.168278	+	0.604040i
$466$		0			0
$467$	−11.3948	+	6.57879i	−0.527288	+	0.304430i	−0.739911	−	0.672704i	$-0.765133\pi$
$467$	−11.3948	+	6.57879i	−0.527288	+	0.304430i	0.212623	+	0.977134i	$0.431799\pi$
$468$		0			0
$469$	−4.88666	+	5.82369i	−0.225645	+	0.268913i
$470$		0			0
$471$	20.3319	−	20.7384i	0.936843	−	0.955576i
$472$		0			0
$473$	38.5115	−	6.79061i	1.77076	−	0.312233i
$474$		0			0
$475$	19.1281	+	18.6927i	0.877658	+	0.857678i
$476$		0			0
$477$	−0.616534	−	0.339864i	−0.0282292	−	0.0155613i
$478$		0			0
$479$	−11.4643	−	31.4978i	−0.523816	−	1.43917i	−0.866240	−	0.499628i	$-0.833470\pi$
$479$	−11.4643	−	31.4978i	−0.523816	−	1.43917i	0.342424	−	0.939546i	$-0.388752\pi$
$480$		0			0
$481$	18.3613	+	15.4069i	0.837202	+	0.702496i
$482$		0			0
$483$	−1.72404	+	2.51481i	−0.0784466	+	0.114428i
$484$		0			0
$485$	9.45772	−	53.6374i	0.429453	−	2.43555i
$486$		0			0
$487$	15.2052	+	8.77875i	0.689015	+	0.397803i	0.803243	−	0.595651i	$-0.203106\pi$
$487$	15.2052	+	8.77875i	0.689015	+	0.397803i	−0.114228	+	0.993455i	$0.536439\pi$
$488$		0			0
$489$	−18.2214	+	1.77608i	−0.824000	+	0.0803171i
$490$		0			0
$491$	15.8204	+	18.8540i	0.713964	+	0.850869i	0.994030	−	0.109112i	$-0.0348006\pi$
$491$	15.8204	+	18.8540i	0.713964	+	0.850869i	−0.280065	+	0.959981i	$0.590356\pi$
$492$		0			0
$493$			1.90026i			0.0855834i
$494$		0			0
$495$	−39.3007	+	48.7656i	−1.76643	+	2.19185i
$496$		0			0
$497$	7.34797	−	6.16568i	0.329602	−	0.276569i
$498$		0			0
$499$	−13.8001	−	5.02282i	−0.617777	−	0.224852i	0.0141259	−	0.999900i	$-0.495503\pi$
$499$	−13.8001	−	5.02282i	−0.617777	−	0.224852i	−0.631902	+	0.775048i	$0.717726\pi$
$500$		0			0
$501$	−1.49869	+	19.3324i	−0.0669567	+	0.863707i
$502$		0			0
$503$	−4.24201	−	0.747980i	−0.189142	−	0.0333508i	0.0782748	−	0.996932i	$-0.475059\pi$
$503$	−4.24201	−	0.747980i	−0.189142	−	0.0333508i	−0.267417	+	0.963581i	$0.586170\pi$
$504$		0			0
$505$	9.58368	+	16.5994i	0.426468	+	0.738665i
$506$		0			0
$507$	−4.84305	−	1.24644i	−0.215087	−	0.0553564i
$508$		0			0
$509$	4.35756	−	1.58602i	0.193145	−	0.0702991i	−0.243637	−	0.969867i	$-0.578340\pi$
$509$	4.35756	−	1.58602i	0.193145	−	0.0702991i	0.436782	+	0.899567i	$0.356118\pi$
$510$		0			0
$511$	2.10837	+	11.9572i	0.0932690	+	0.528955i
$512$		0			0
$513$	22.1244	−	4.84863i	0.976818	−	0.214072i
$514$		0			0
$515$	0.640425	+	3.63203i	0.0282205	+	0.160047i
$516$		0			0
$517$	45.3638	−	16.5111i	1.99510	−	0.726156i
$518$		0			0
$519$	−36.7608	−	9.46102i	−1.61362	−	0.415293i
$520$		0			0
$521$	0.205968	+	0.356747i	0.00902363	+	0.0156294i	0.870502	−	0.492165i	$-0.163794\pi$
$521$	0.205968	+	0.356747i	0.00902363	+	0.0156294i	−0.861478	+	0.507794i	$0.830461\pi$
$522$		0			0
$523$	19.2248	+	3.38986i	0.840643	+	0.148228i	0.577359	−	0.816490i	$-0.304083\pi$
$523$	19.2248	+	3.38986i	0.840643	+	0.148228i	0.263284	+	0.964718i	$0.415194\pi$
$524$		0			0
$525$	−1.76365	+	22.7502i	−0.0769719	+	0.992899i
$526$		0			0
$527$	0.900948	+	0.327918i	0.0392459	+	0.0142843i
$528$		0			0
$529$	17.1041	−	14.3520i	0.743657	−	0.624002i
$530$		0			0
$531$	10.0860	−	12.5151i	0.437697	−	0.543109i
$532$		0			0
$533$		−	4.82137i		−	0.208837i
$534$		0			0
$535$	−14.9131	−	17.7728i	−0.644751	−	0.768385i
$536$		0			0
$537$	−36.8683	+	3.59364i	−1.59099	+	0.155077i
$538$		0			0
$539$	−12.9481	−	7.47562i	−0.557716	−	0.321998i
$540$		0			0
$541$	−3.15633	+	17.9005i	−0.135701	+	0.769601i	0.838667	+	0.544644i	$0.183335\pi$
$541$	−3.15633	+	17.9005i	−0.135701	+	0.769601i	−0.974369	+	0.224957i	$0.927776\pi$
$542$		0			0
$543$	−17.9063	+	26.1194i	−0.768433	+	1.12089i
$544$		0			0
$545$	18.1538	+	15.2328i	0.777622	+	0.652502i
$546$		0			0
$547$	−1.42436	−	3.91340i	−0.0609014	−	0.167325i	0.905510	−	0.424324i	$-0.139488\pi$
$547$	−1.42436	−	3.91340i	−0.0609014	−	0.167325i	−0.966412	+	0.256999i	$0.917266\pi$
$548$		0			0
$549$	−20.4296	−	11.2618i	−0.871914	−	0.480641i
$550$		0			0
$551$	5.00579	−	19.5808i	0.213254	−	0.834172i
$552$		0			0
$553$	26.4948	−	4.67174i	1.12667	−	0.198663i
$554$		0			0
$555$	24.3326	−	24.8191i	1.03286	−	1.05351i
$556$		0			0
$557$	−9.16196	+	10.9188i	−0.388205	+	0.462644i	−0.924386	−	0.381459i	$-0.875422\pi$
$557$	−9.16196	+	10.9188i	−0.388205	+	0.462644i	0.536181	+	0.844103i	$0.319866\pi$
$558$		0			0
$559$	21.5767	−	12.4573i	0.912599	−	0.526889i
$560$		0			0
$561$	1.19182	+	4.27807i	0.0503185	+	0.180620i
$562$		0			0
$563$	−3.28307	+	5.68645i	−0.138365	+	0.239655i	−0.926878	−	0.375363i	$-0.877518\pi$
$563$	−3.28307	+	5.68645i	−0.138365	+	0.239655i	0.788513	+	0.615018i	$0.210851\pi$
$564$		0			0
$565$	2.65930	−	7.30637i	0.111878	−	0.307381i
$566$		0			0
$567$	15.2832	+	11.8256i	0.641836	+	0.496629i
$568$		0			0
$569$	−45.7506			−1.91797			−0.958983	−	0.283465i	$-0.908516\pi$
$569$	−45.7506			−1.91797			−0.958983	+	0.283465i	$0.908516\pi$
$570$		0			0
$571$	−5.82547			−0.243788			−0.121894	−	0.992543i	$-0.538897\pi$
$571$	−5.82547			−0.243788			−0.121894	+	0.992543i	$0.538897\pi$
$572$		0			0
$573$	−5.45805	−	2.47965i	−0.228013	−	0.103589i
$574$		0			0
$575$	−1.72053	+	4.72712i	−0.0717510	+	0.197134i
$576$		0			0
$577$	−17.9425	+	31.0773i	−0.746956	+	1.29377i	0.202320	+	0.979319i	$0.435152\pi$
$577$	−17.9425	+	31.0773i	−0.746956	+	1.29377i	−0.949276	+	0.314446i	$0.898181\pi$
$578$		0			0
$579$	17.2465	−	4.80465i	0.716740	−	0.199675i
$580$		0			0
$581$	17.2109	−	9.93674i	0.714030	−	0.412245i
$582$		0			0
$583$	−0.943689	+	1.12464i	−0.0390836	+	0.0465780i
$584$		0			0
$585$	−12.9027	+	37.7594i	−0.533459	+	1.56116i
$586$		0			0
$587$	29.5771	−	5.21525i	1.22078	−	0.215256i	0.474118	−	0.880461i	$-0.342767\pi$
$587$	29.5771	−	5.21525i	1.22078	−	0.215256i	0.746661	+	0.665205i	$0.231656\pi$
$588$		0			0
$589$	−8.41982	−	5.75231i	−0.346932	−	0.237020i
$590$		0			0
$591$	−16.7367	+	11.9678i	−0.688456	+	0.492289i
$592$		0			0
$593$	0.268437	+	0.737526i	0.0110234	+	0.0302866i	0.945082	−	0.326832i	$-0.105981\pi$
$593$	0.268437	+	0.737526i	0.0110234	+	0.0302866i	−0.934059	+	0.357119i	$0.883759\pi$
$594$		0			0
$595$	2.24948	+	1.88754i	0.0922198	+	0.0773816i
$596$		0			0
$597$	34.9090	+	23.9321i	1.42873	+	0.979476i
$598$		0			0
$599$	−2.35948	+	13.3813i	−0.0964057	+	0.546744i	0.897902	+	0.440196i	$0.145091\pi$
$599$	−2.35948	+	13.3813i	−0.0964057	+	0.546744i	−0.994308	+	0.106548i	$0.966020\pi$
$600$		0			0
$601$	1.41283	+	0.815696i	0.0576304	+	0.0332729i	0.528538	−	0.848909i	$-0.322740\pi$
$601$	1.41283	+	0.815696i	0.0576304	+	0.0332729i	−0.470908	+	0.882182i	$0.656074\pi$
$602$		0			0
$603$	5.49208	+	9.09201i	0.223655	+	0.370255i
$604$		0			0
$605$	60.3592	+	71.9333i	2.45395	+	2.92450i
$606$		0			0
$607$			23.6670i			0.960615i	0.877100	+	0.480308i	$0.159475\pi$
$607$			23.6670i			0.960615i	−0.877100	+	0.480308i	$0.840525\pi$
$608$		0			0
$609$	15.5548	−	7.44167i	0.630314	−	0.301552i
$610$		0			0
$611$	23.5610	−	19.7700i	0.953177	−	0.799811i
$612$		0			0
$613$	14.7136	+	5.35532i	0.594278	+	0.216299i	0.621610	−	0.783327i	$-0.286479\pi$
$613$	14.7136	+	5.35532i	0.594278	+	0.216299i	−0.0273321	+	0.999626i	$0.508701\pi$
$614$		0			0
$615$	−6.97052	−	0.540372i	−0.281079	−	0.0217899i
$616$		0			0
$617$	−19.6258	−	3.46056i	−0.790105	−	0.139317i	−0.235988	−	0.971756i	$-0.575833\pi$
$617$	−19.6258	−	3.46056i	−0.790105	−	0.139317i	−0.554117	+	0.832439i	$0.686944\pi$
$618$		0			0
$619$	3.55524	+	6.15786i	0.142897	+	0.247505i	0.928587	−	0.371116i	$-0.121025\pi$
$619$	3.55524	+	6.15786i	0.142897	+	0.247505i	−0.785689	+	0.618621i	$0.787691\pi$
$620$		0			0
$621$	2.54606	+	3.41562i	0.102170	+	0.137064i
$622$		0			0
$623$	14.7992	−	5.38648i	0.592919	−	0.215805i
$624$		0			0
$625$	−3.13111	−	17.7574i	−0.125244	−	0.710297i
$626$		0			0
$627$	−1.01125	−	47.2221i	−0.0403856	−	1.88587i
$628$		0			0
$629$	−0.427962	−	2.42710i	−0.0170640	−	0.0967746i
$630$		0			0
$631$	1.16675	−	0.424661i	0.0464474	−	0.0169055i	−0.318692	−	0.947858i	$-0.603244\pi$
$631$	1.16675	−	0.424661i	0.0464474	−	0.0169055i	0.365139	+	0.930953i	$0.381021\pi$
$632$		0			0
$633$	7.15294	−	27.7927i	0.284304	−	1.10466i
$634$		0			0
$635$	−2.05623	−	3.56149i	−0.0815989	−	0.141334i
$636$		0			0
$637$	−9.38092	−	1.65411i	−0.371685	−	0.0655382i
$638$		0			0
$639$	−4.83225	−	12.5008i	−0.191161	−	0.494522i
$640$		0			0
$641$	7.06477	+	2.57137i	0.279042	+	0.101563i	0.477750	−	0.878496i	$-0.341452\pi$
$641$	7.06477	+	2.57137i	0.279042	+	0.101563i	−0.198708	+	0.980059i	$0.563675\pi$
$642$		0			0
$643$	9.31005	−	7.81206i	0.367153	−	0.308078i	−0.440481	−	0.897762i	$-0.645192\pi$
$643$	9.31005	−	7.81206i	0.367153	−	0.308078i	0.807634	+	0.589684i	$0.200748\pi$
$644$		0			0
$645$	−15.5920	−	32.5909i	−0.613933	−	1.28327i
$646$		0			0
$647$			38.1298i			1.49904i	0.661983	+	0.749519i	$0.269715\pi$
$647$			38.1298i			1.49904i	−0.661983	+	0.749519i	$0.730285\pi$
$648$		0			0
$649$	−21.5458	−	25.6773i	−0.845747	−	1.00792i
$650$		0			0
$651$	−0.844012	−	8.65901i	−0.0330794	−	0.339373i
$652$		0			0
$653$	−39.7547	−	22.9524i	−1.55572	−	0.898196i	−0.997658	−	0.0683980i	$-0.978211\pi$
$653$	−39.7547	−	22.9524i	−1.55572	−	0.898196i	−0.558063	−	0.829798i	$-0.688455\pi$
$654$		0			0
$655$	−3.73239	+	21.1674i	−0.145836	+	0.827080i
$656$		0			0
$657$	16.7618	+	2.61454i	0.653940	+	0.102003i
$658$		0			0
$659$	−14.3577	−	12.0475i	−0.559295	−	0.469304i	0.318779	−	0.947829i	$-0.396727\pi$
$659$	−14.3577	−	12.0475i	−0.559295	−	0.469304i	−0.878074	+	0.478525i	$0.841172\pi$
$660$		0			0
$661$	4.05073	+	11.1293i	0.157555	+	0.432879i	0.993204	−	0.116385i	$-0.0371306\pi$
$661$	4.05073	+	11.1293i	0.157555	+	0.432879i	−0.835649	+	0.549263i	$0.814908\pi$
$662$		0			0
$663$	1.64575	+	2.30154i	0.0639155	+	0.0893844i
$664$		0			0
$665$	−18.2071	−	25.3755i	−0.706039	−	0.984020i
$666$		0			0
$667$	3.74366	−	0.660108i	0.144955	−	0.0255595i
$668$		0			0
$669$	−14.6499	−	14.3627i	−0.566400	−	0.555296i
$670$		0			0
$671$	−31.2703	+	37.2665i	−1.20718	+	1.43866i
$672$		0			0
$673$	−9.02264	+	5.20922i	−0.347797	+	0.200801i	−0.663715	−	0.747986i	$-0.731021\pi$
$673$	−9.02264	+	5.20922i	−0.347797	+	0.200801i	0.315917	+	0.948787i	$0.397688\pi$
$674$		0			0
$675$	29.2825	+	12.6101i	1.12708	+	0.485364i
$676$		0			0
$677$	−10.3670	+	17.9562i	−0.398437	+	0.690112i	−0.993533	−	0.113542i	$-0.963780\pi$
$677$	−10.3670	+	17.9562i	−0.398437	+	0.690112i	0.595097	+	0.803654i	$0.297114\pi$
$678$		0			0
$679$	−11.9858	+	32.9306i	−0.459972	+	1.26376i
$680$		0			0
$681$	−16.5294	+	36.3834i	−0.633408	+	1.39421i
$682$		0			0
$683$	−2.79983			−0.107132			−0.0535662	−	0.998564i	$-0.517059\pi$
$683$	−2.79983			−0.107132			−0.0535662	+	0.998564i	$0.517059\pi$
$684$		0			0
$685$	35.9492			1.37355
$686$		0			0
$687$	10.0629	−	22.1499i	0.383925	−	0.845070i
$688$		0			0
$689$	−0.319912	+	0.878950i	−0.0121877	+	0.0334853i
$690$		0			0
$691$	4.20182	−	7.27776i	0.159845	−	0.276859i	−0.774968	−	0.632001i	$-0.782234\pi$
$691$	4.20182	−	7.27776i	0.159845	−	0.276859i	0.934813	+	0.355142i	$0.115567\pi$
$692$		0			0
$693$	30.3514	−	26.5093i	1.15296	−	1.00700i
$694$		0			0
$695$	24.3697	−	14.0698i	0.924395	−	0.533700i
$696$		0			0
$697$	−0.318658	+	0.379762i	−0.0120700	+	0.0143845i
$698$		0			0
$699$	−29.1746	−	28.6027i	−1.10349	−	1.08185i
$700$		0			0
$701$	−14.9472	+	2.63560i	−0.564549	+	0.0995451i	−0.448636	−	0.893714i	$-0.648090\pi$
$701$	−14.9472	+	2.63560i	−0.564549	+	0.0995451i	−0.115912	+	0.993259i	$0.536979\pi$
$702$		0			0
$703$	−1.98376	+	26.1369i	−0.0748190	+	0.985771i
$704$		0			0
$705$	−25.9420	−	36.2793i	−0.977031	−	1.36636i
$706$		0			0
$707$	−4.21806	−	11.5890i	−0.158636	−	0.435850i
$708$		0			0
$709$	−29.3000	−	24.5857i	−1.10039	−	0.923334i	−0.102935	−	0.994688i	$-0.532823\pi$
$709$	−29.3000	−	24.5857i	−1.10039	−	0.923334i	−0.997451	+	0.0713544i	$0.977268\pi$
$710$		0			0
$711$	5.79331	−	37.1409i	0.217266	−	1.39289i
$712$		0			0
$713$	0.333055	−	1.88885i	0.0124730	−	0.0707380i
$714$		0			0
$715$	72.0647	+	41.6065i	2.69507	+	1.55600i
$716$		0			0
$717$	4.57942	+	46.9819i	0.171022	+	1.75457i
$718$		0			0
$719$	24.9620	+	29.7485i	0.930924	+	1.10943i	0.993775	+	0.111410i	$0.0355365\pi$
$719$	24.9620	+	29.7485i	0.930924	+	1.10943i	−0.0628501	+	0.998023i	$0.520019\pi$
$720$		0			0
$721$		−	2.37299i		−	0.0883749i
$722$		0			0
$723$	−15.9001	−	33.2349i	−0.591330	−	1.23602i
$724$		0			0
$725$	21.7933	−	18.2868i	0.809383	−	0.679153i
$726$		0			0
$727$	−35.9582	−	13.0877i	−1.33361	−	0.485396i	−0.425818	−	0.904809i	$-0.640014\pi$
$727$	−35.9582	−	13.0877i	−1.33361	−	0.485396i	−0.907796	+	0.419413i	$0.862236\pi$
$728$		0			0
$729$	22.5401	−	14.8641i	0.834820	−	0.550524i
$730$		0			0
$731$	−2.52286	−	0.444849i	−0.0933114	−	0.0164533i
$732$		0			0
$733$	−7.71039	−	13.3548i	−0.284790	−	0.493270i	0.687768	−	0.725930i	$-0.258590\pi$
$733$	−7.71039	−	13.3548i	−0.284790	−	0.493270i	−0.972558	+	0.232660i	$0.925257\pi$
$734$		0			0
$735$	−3.44284	+	13.3771i	−0.126991	+	0.493423i
$736$		0			0
$737$	20.8152	−	7.57610i	0.766736	−	0.279069i
$738$		0			0
$739$	4.98207	+	28.2547i	0.183268	+	1.03937i	0.928160	+	0.372181i	$0.121390\pi$
$739$	4.98207	+	28.2547i	0.183268	+	1.03937i	−0.744892	+	0.667185i	$0.767499\pi$
$740$		0			0
$741$	−10.8954	−	28.0511i	−0.400252	−	1.03048i
$742$		0			0
$743$	−4.95784	−	28.1173i	−0.181886	−	1.03152i	−0.929892	−	0.367833i	$-0.880100\pi$
$743$	−4.95784	−	28.1173i	−0.181886	−	1.03152i	0.748006	−	0.663691i	$-0.231011\pi$
$744$		0			0
$745$	−16.6486	+	6.05959i	−0.609957	+	0.222006i
$746$		0			0
$747$	−5.36218	−	27.2449i	−0.196192	−	0.996837i
$748$		0			0
$749$	7.46397	+	12.9280i	0.272727	+	0.472378i
$750$		0			0
$751$	−12.4716	−	2.19908i	−0.455096	−	0.0802457i	−0.0585987	−	0.998282i	$-0.518663\pi$
$751$	−12.4716	−	2.19908i	−0.455096	−	0.0802457i	−0.396497	+	0.918036i	$0.629774\pi$
$752$		0			0
$753$	4.28646	+	0.332297i	0.156207	+	0.0121096i
$754$		0			0
$755$	8.02719	+	2.92166i	0.292139	+	0.106330i
$756$		0			0
$757$	38.4432	−	32.2577i	1.39724	−	1.17243i	0.434934	−	0.900462i	$-0.356772\pi$
$757$	38.4432	−	32.2577i	1.39724	−	1.17243i	0.962308	−	0.271963i	$-0.0876729\pi$
$758$		0			0
$759$	8.01413	−	3.83408i	0.290894	−	0.139168i
$760$		0			0
$761$		−	26.6803i		−	0.967159i	−0.875300	−	0.483580i	$-0.839336\pi$
$761$		−	26.6803i		−	0.967159i	0.875300	−	0.483580i	$-0.160664\pi$
$762$		0			0
$763$	−9.80118	−	11.6806i	−0.354826	−	0.422866i
$764$		0			0
$765$	3.51192	−	2.12139i	0.126974	−	0.0766991i
$766$		0			0
$767$	−18.4945	−	10.6778i	−0.667798	−	0.385553i
$768$		0			0
$769$	−6.83201	+	38.7463i	−0.246369	+	1.39723i	0.570924	+	0.821003i	$0.306585\pi$
$769$	−6.83201	+	38.7463i	−0.246369	+	1.39723i	−0.817292	+	0.576223i	$0.804526\pi$
$770$		0			0
$771$	16.0806	+	11.0242i	0.579130	+	0.397026i
$772$		0			0
$773$	2.48012	+	2.08107i	0.0892039	+	0.0748509i	0.686299	−	0.727319i	$-0.259234\pi$
$773$	2.48012	+	2.08107i	0.0892039	+	0.0748509i	−0.597095	+	0.802170i	$0.703679\pi$
$774$		0			0
$775$	−4.90933	−	13.4883i	−0.176348	−	0.484513i
$776$		0			0
$777$	−18.1914	+	13.0080i	−0.652612	+	0.466658i
$778$		0			0
$779$	4.28394	−	3.07375i	0.153488	−	0.110128i
$780$		0			0
$781$	−27.5242	+	4.85326i	−0.984893	+	0.173663i
$782$		0			0
$783$	−2.81152	−	23.9280i	−0.100475	−	0.855117i
$784$		0			0
$785$	−35.9667	+	42.8634i	−1.28371	+	1.52986i
$786$		0			0
$787$	22.8624	−	13.1996i	0.814956	−	0.470515i	−0.0337179	−	0.999431i	$-0.510735\pi$
$787$	22.8624	−	13.1996i	0.814956	−	0.470515i	0.848674	+	0.528916i	$0.177401\pi$
$788$		0			0
$789$	19.6648	−	5.47836i	0.700086	−	0.195035i
$790$		0			0
$791$	−2.50141	+	4.33256i	−0.0889397	+	0.154048i
$792$		0			0
$793$	−10.6007	+	29.1251i	−0.376440	+	1.03426i
$794$		0			0
$795$	1.23489	+	0.561025i	0.0437971	+	0.0198975i
$796$		0			0
$797$	−9.50783			−0.336785			−0.168392	−	0.985720i	$-0.553858\pi$
$797$	−9.50783			−0.336785			−0.168392	+	0.985720i	$0.553858\pi$
$798$		0			0
$799$	−3.16247			−0.111880
$800$		0			0
$801$	−0.435612	−	22.0005i	−0.0153916	−	0.777348i
$802$		0			0
$803$	12.0998	−	33.2440i	0.426993	−	1.17315i
$804$		0			0
$805$	2.93718	−	5.08734i	0.103522	−	0.179305i
$806$		0			0
$807$	5.43998	+	19.5270i	0.191497	+	0.687384i
$808$		0			0
$809$	−31.3018	+	18.0721i	−1.10051	+	0.635380i	−0.936355	−	0.351054i	$-0.885823\pi$
$809$	−31.3018	+	18.0721i	−1.10051	+	0.635380i	−0.164156	+	0.986434i	$0.552490\pi$
$810$		0			0
$811$	−16.3764	+	19.5167i	−0.575054	+	0.685323i	−0.972660	−	0.232233i	$-0.925397\pi$
$811$	−16.3764	+	19.5167i	−0.575054	+	0.685323i	0.397606	+	0.917556i	$0.369841\pi$
$812$		0			0
$813$	37.6790	−	38.4324i	1.32146	−	1.34788i
$814$		0			0
$815$	34.7364	−	6.12497i	1.21676	−	0.214548i
$816$		0			0
$817$	24.8245	+	11.2297i	0.868498	+	0.392879i
$818$		0			0
$819$	12.3946	−	22.4846i	0.433103	−	0.785676i
$820$		0			0
$821$	−3.53702	−	9.71788i	−0.123443	−	0.339156i	0.862543	−	0.505983i	$-0.168870\pi$
$821$	−3.53702	−	9.71788i	−0.123443	−	0.339156i	−0.985986	+	0.166827i	$0.946648\pi$
$822$		0			0
$823$	−11.1336	−	9.34221i	−0.388093	−	0.325649i	0.427776	−	0.903885i	$-0.359297\pi$
$823$	−11.1336	−	9.34221i	−0.388093	−	0.325649i	−0.815870	+	0.578235i	$0.803741\pi$
$824$		0			0
$825$	37.5943	−	54.8376i	1.30887	−	1.90920i
$826$		0			0
$827$	4.21974	−	23.9313i	0.146735	−	0.832174i	−0.819223	−	0.573475i	$-0.805595\pi$
$827$	4.21974	−	23.9313i	0.146735	−	0.832174i	0.965958	−	0.258699i	$-0.0832938\pi$
$828$		0			0
$829$	43.3587	+	25.0331i	1.50591	+	0.869437i	0.999976	+	0.00686327i	$0.00218466\pi$
$829$	43.3587	+	25.0331i	1.50591	+	0.869437i	0.505932	+	0.862573i	$0.331149\pi$
$830$		0			0
$831$	6.61851	−	0.645121i	0.229594	−	0.0223790i
$832$		0			0
$833$	0.629576	+	0.750299i	0.0218135	+	0.0259963i
$834$		0			0
$835$		−	37.3582i		−	1.29283i
$836$		0			0
$837$	−11.8299	−	2.79614i	−0.408900	−	0.0966488i
$838$		0			0
$839$	−25.2797	+	21.2122i	−0.872752	+	0.732326i	−0.964676	−	0.263440i	$-0.915143\pi$
$839$	−25.2797	+	21.2122i	−0.872752	+	0.732326i	0.0919238	+	0.995766i	$0.470698\pi$
$840$		0			0
$841$	7.04931	+	2.56574i	0.243080	+	0.0884737i
$842$		0			0
$843$	−3.28602	+	42.3880i	−0.113177	+	1.45992i
$844$		0			0
$845$	9.48847	+	1.67307i	0.326413	+	0.0575555i
$846$		0			0
$847$	−30.2095	−	52.3245i	−1.03801	−	1.79789i
$848$		0			0
$849$	38.9830	+	10.0330i	1.33789	+	0.344330i
$850$		0			0
$851$	−4.63290	+	1.68624i	−0.158814	+	0.0578035i
$852$		0			0
$853$	5.13243	+	29.1074i	0.175731	+	0.996620i	0.937297	+	0.348532i	$0.113320\pi$
$853$	5.13243	+	29.1074i	0.175731	+	0.996620i	−0.761566	+	0.648088i	$0.775569\pi$
$854$		0			0
$855$	−41.7762	+	12.6082i	−1.42871	+	0.431190i
$856$		0			0
$857$	−8.49473	−	48.1760i	−0.290175	−	1.64566i	−0.686193	−	0.727419i	$-0.740720\pi$
$857$	−8.49473	−	48.1760i	−0.290175	−	1.64566i	0.396019	−	0.918242i	$-0.370392\pi$
$858$		0			0
$859$	36.8403	−	13.4088i	1.25698	−	0.457502i	0.374222	−	0.927339i	$-0.377910\pi$
$859$	36.8403	−	13.4088i	1.25698	−	0.457502i	0.882753	+	0.469837i	$0.155687\pi$
$860$		0			0
$861$	4.35650	+	1.12122i	0.148469	+	0.0382111i
$862$		0			0
$863$	17.6337	+	30.5424i	0.600257	+	1.03967i	0.992782	+	0.119934i	$0.0382682\pi$
$863$	17.6337	+	30.5424i	0.600257	+	1.03967i	−0.392525	+	0.919741i	$0.628398\pi$
$864$		0			0
$865$	72.0215	+	12.6993i	2.44880	+	0.431790i
$866$		0			0
$867$	−2.25332	+	29.0667i	−0.0765269	+	0.987158i
$868$		0			0
$869$	−73.6621	−	26.8108i	−2.49882	−	0.909494i
$870$		0			0
$871$	10.8110	−	9.07148i	0.366316	−	0.307375i
$872$		0			0
$873$	38.1244	+	30.7248i	1.29031	+	1.03988i
$874$		0			0
$875$		−	8.13764i		−	0.275102i
$876$		0			0
$877$	14.4779	+	17.2541i	0.488883	+	0.582628i	0.952933	−	0.303181i	$-0.0980486\pi$
$877$	14.4779	+	17.2541i	0.488883	+	0.582628i	−0.464050	+	0.885809i	$0.653604\pi$
$878$		0			0
$879$	−18.9165	+	1.84384i	−0.638039	+	0.0621910i
$880$		0			0
$881$	47.0165	+	27.1450i	1.58403	+	0.914539i	0.994263	+	0.106964i	$0.0341129\pi$
$881$	47.0165	+	27.1450i	1.58403	+	0.914539i	0.589765	+	0.807575i	$0.299220\pi$
$882$		0			0
$883$	−4.51473	+	25.6043i	−0.151933	+	0.861653i	0.809604	+	0.586977i	$0.199682\pi$
$883$	−4.51473	+	25.6043i	−0.151933	+	0.861653i	−0.961537	+	0.274677i	$0.911429\pi$
$884$		0			0
$885$	−17.5103	+	25.5418i	−0.588603	+	0.858577i
$886$		0			0
$887$	−4.19836	−	3.52284i	−0.140967	−	0.118286i	0.569577	−	0.821938i	$-0.307107\pi$
$887$	−4.19836	−	3.52284i	−0.140967	−	0.118286i	−0.710545	+	0.703652i	$0.751551\pi$
$888$		0			0
$889$	0.905006	+	2.48648i	0.0303529	+	0.0833939i
$890$		0			0
$891$	−21.3369	−	52.1060i	−0.714813	−	1.74562i
$892$		0			0
$893$	32.5871	+	8.33079i	1.09048	+	0.278779i
$894$		0			0
$895$	70.2842	−	12.3930i	2.34934	−	0.414252i
$896$		0			0
$897$	3.96252	−	4.04175i	0.132305	−	0.134950i
$898$		0			0
$899$	−6.97224	+	8.30919i	−0.232537	+	0.277127i
$900$		0			0
$901$	0.0832905	−	0.0480878i	0.00277481	−	0.00160204i
$902$		0			0
$903$	6.23849	+	22.3933i	0.207604	+	0.745203i
$904$		0			0
$905$	30.5062	−	52.8383i	1.01406	−	1.75640i
$906$		0			0
$907$	−20.0545	+	55.0993i	−0.665899	+	1.82954i	−0.117971	+	0.993017i	$0.537639\pi$
$907$	−20.0545	+	55.0993i	−0.665899	+	1.82954i	−0.547928	+	0.836526i	$0.684583\pi$
$908$		0			0
$909$	−17.2282	+	0.341120i	−0.571422	+	0.0113142i
$910$		0			0
$911$	−2.91388			−0.0965412			−0.0482706	−	0.998834i	$-0.515371\pi$
$911$	−2.91388			−0.0965412			−0.0482706	+	0.998834i	$0.515371\pi$
$912$		0			0
$913$	−57.9060			−1.91641
$914$		0			0
$915$	40.9196	+	18.5902i	1.35276	+	0.614574i
$916$		0			0
$917$	4.73006	−	12.9957i	0.156200	−	0.429157i
$918$		0			0
$919$	−2.94881	+	5.10749i	−0.0972722	+	0.168480i	−0.910555	−	0.413389i	$-0.864345\pi$
$919$	−2.94881	+	5.10749i	−0.0972722	+	0.168480i	0.813282	+	0.581869i	$0.197678\pi$
$920$		0			0
$921$	0.912514	−	0.254215i	0.0300684	−	0.00837666i
$922$		0			0
$923$	−15.4209	+	8.90328i	−0.507586	+	0.293055i
$924$		0			0
$925$	−23.7170	+	28.2648i	−0.779809	+	0.929340i
$926$		0			0
$927$	−3.13747	−	1.07210i	−0.103048	−	0.0352123i
$928$		0			0
$929$	22.4137	−	3.95214i	0.735369	−	0.129665i	0.206593	−	0.978427i	$-0.433762\pi$
$929$	22.4137	−	3.95214i	0.735369	−	0.129665i	0.528776	+	0.848762i	$0.322651\pi$
$930$		0			0
$931$	−4.51085	−	9.38978i	−0.147837	−	0.307738i
$932$		0			0
$933$	19.8328	−	14.1817i	0.649298	−	0.464289i
$934$		0			0
$935$	−2.92637	−	8.04015i	−0.0957027	−	0.262941i
$936$		0			0
$937$	−33.5028	−	28.1122i	−1.09449	−	0.918384i	−0.0974452	−	0.995241i	$-0.531067\pi$
$937$	−33.5028	−	28.1122i	−1.09449	−	0.918384i	−0.997042	+	0.0768570i	$0.975512\pi$
$938$		0			0
$939$	26.5742	+	18.2181i	0.867216	+	0.594526i
$940$		0			0
$941$	−1.06108	+	6.01769i	−0.0345903	+	0.196171i	−0.997206	−	0.0746992i	$-0.976200\pi$
$941$	−1.06108	+	6.01769i	−0.0345903	+	0.196171i	0.962616	+	0.270870i	$0.0873115\pi$
$942$		0			0
$943$	0.858855	+	0.495860i	0.0279682	+	0.0161474i
$944$		0			0
$945$	−31.1181	−	20.4396i	−1.01227	−	0.664901i
$946$		0			0
$947$	−19.9420	−	23.7660i	−0.648029	−	0.772291i	0.337586	−	0.941295i	$-0.390389\pi$
$947$	−19.9420	−	23.7660i	−0.648029	−	0.772291i	−0.985615	+	0.169004i	$0.945945\pi$
$948$		0			0
$949$		−	22.5395i		−	0.731662i
$950$		0			0
$951$	42.4857	−	20.3258i	1.37769	−	0.659109i
$952$		0			0
$953$	38.1684	−	32.0271i	1.23640	−	1.03746i	0.238599	−	0.971118i	$-0.423312\pi$
$953$	38.1684	−	32.0271i	1.23640	−	1.03746i	0.997797	−	0.0663415i	$-0.0211327\pi$
$954$		0			0
$955$	10.8534	+	3.95033i	0.351209	+	0.127830i
$956$		0			0
$957$	−50.0921	−	3.88326i	−1.61925	−	0.125528i
$958$		0			0
$959$	−22.7792	−	4.01659i	−0.735579	−	0.129702i
$960$		0			0
$961$	−12.7636	−	22.1072i	−0.411730	−	0.713137i
$962$		0			0
$963$	20.4649	−	4.02779i	0.659474	−	0.129794i
$964$		0			0
$965$	−32.4128	+	11.7973i	−1.04341	+	0.379769i
$966$		0			0
$967$	1.94625	+	11.0377i	0.0625873	+	0.354950i	0.999978	+	0.00666987i	$0.00212310\pi$
$967$	1.94625	+	11.0377i	0.0625873	+	0.354950i	−0.937390	+	0.348280i	$0.886766\pi$
$968$		0			0
$969$	−0.995785	+	2.92959i	−0.0319892	+	0.0941119i
$970$		0			0
$971$	−8.32593	−	47.2187i	−0.267192	−	1.51532i	−0.762720	−	0.646729i	$-0.776137\pi$
$971$	−8.32593	−	47.2187i	−0.267192	−	1.51532i	0.495528	−	0.868592i	$-0.334974\pi$
$972$		0			0
$973$	−17.0139	+	6.19254i	−0.545440	+	0.198524i
$974$		0			0
$975$	10.5579	−	41.0228i	0.338124	−	1.31378i
$976$		0			0
$977$	5.39563	+	9.34550i	0.172621	+	0.298989i	0.939336	−	0.343000i	$-0.111443\pi$
$977$	5.39563	+	9.34550i	0.172621	+	0.298989i	−0.766714	+	0.641989i	$0.778110\pi$
$978$		0			0
$979$	−45.1913	−	7.96844i	−1.44432	−	0.254672i
$980$		0			0
$981$	−19.8716	+	7.68150i	−0.634453	+	0.245252i
$982$		0			0
$983$	34.3549	+	12.5042i	1.09575	+	0.398821i	0.825748	−	0.564039i	$-0.190753\pi$
$983$	34.3549	+	12.5042i	1.09575	+	0.398821i	0.270003	+	0.962860i	$0.412975\pi$
$984$		0			0
$985$	30.3669	−	25.4808i	0.967569	−	0.811887i
$986$		0			0
$987$	12.3847	+	25.8869i	0.394208	+	0.823988i
$988$		0			0
$989$			5.12476i			0.162958i
$990$		0			0
$991$	3.96786	+	4.72871i	0.126043	+	0.150213i	0.825375	−	0.564584i	$-0.190964\pi$
$991$	3.96786	+	4.72871i	0.126043	+	0.150213i	−0.699332	+	0.714797i	$0.746519\pi$
$992$		0			0
$993$	4.93252	+	50.6044i	0.156529	+	1.60588i
$994$		0			0
$995$	−70.6194	−	40.7721i	−2.23879	−	1.29256i
$996$		0			0
$997$	3.18227	−	18.0475i	0.100783	−	0.571571i	−0.892038	−	0.451961i	$-0.850725\pi$
$997$	3.18227	−	18.0475i	0.100783	−	0.571571i	0.992821	−	0.119610i	$-0.0381643\pi$
$998$		0			0
$999$	8.97988	+	29.9287i	0.284111	+	0.946902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.cc.d.257.3		18
3.2	odd	2		912.2.cc.c.257.1		18
4.3	odd	2		114.2.l.a.29.1	✓	18
12.11	even	2		114.2.l.b.29.3	yes	18
19.2	odd	18		912.2.cc.c.401.1		18
57.2	even	18	inner	912.2.cc.d.401.3		18
76.59	even	18		114.2.l.b.59.3	yes	18
228.59	odd	18		114.2.l.a.59.1	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.29.1	✓	18	4.3	odd	2
114.2.l.a.59.1	yes	18	228.59	odd	18
114.2.l.b.29.3	yes	18	12.11	even	2
114.2.l.b.59.3	yes	18	76.59	even	18
912.2.cc.c.257.1		18	3.2	odd	2
912.2.cc.c.401.1		18	19.2	odd	18
912.2.cc.d.257.3		18	1.1	even	1	trivial
912.2.cc.d.401.3		18	57.2	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.cc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.716422 - 1.57694i) q^{3} +(-1.14133 + 3.13578i) q^{5} +(1.07356 - 1.85947i) q^{7} +(-1.97348 - 2.25951i) q^{9} +(-5.41799 + 3.12808i) q^{11} +(-2.56208 + 3.05336i) q^{13} +(4.12726 + 4.04635i) q^{15} +(0.403611 - 0.0711674i) q^{17} +(-4.34640 - 0.329887i) q^{19} +(-2.16314 - 3.02511i) q^{21} +(-0.280411 - 0.770422i) q^{23} +(-4.70025 - 3.94398i) q^{25} +(-4.97695 + 1.49330i) q^{27} +(-0.805141 + 4.56618i) q^{29} +(2.02597 + 1.16970i) q^{31} +(1.05122 + 10.7849i) q^{33} +(4.60559 + 5.48872i) q^{35} -6.01346i q^{37} +(2.97944 + 6.22774i) q^{39} +(-0.926617 + 0.777524i) q^{41} +(-5.87377 - 2.13788i) q^{43} +(9.33771 - 3.60955i) q^{45} +(-7.59919 - 1.33994i) q^{47} +(1.19492 + 2.06967i) q^{49} +(0.176929 - 0.687455i) q^{51} +(0.220516 - 0.0802612i) q^{53} +(-3.62525 - 20.5598i) q^{55} +(-3.63407 + 6.61767i) q^{57} +(0.930375 + 5.27642i) q^{59} +(7.30705 - 2.65955i) q^{61} +(-6.32014 + 1.24389i) q^{63} +(-6.65050 - 11.5190i) q^{65} +(-3.48689 - 0.614832i) q^{67} +(-1.41580 - 0.109756i) q^{69} +(4.19799 + 1.52794i) q^{71} +(-4.33185 + 3.63485i) q^{73} +(-9.58679 + 4.58646i) q^{75} +13.4328i q^{77} +(8.05412 + 9.59853i) q^{79} +(-1.21076 + 8.91819i) q^{81} +(8.01579 + 4.62792i) q^{83} +(-0.237488 + 1.34686i) q^{85} +(6.62378 + 4.54097i) q^{87} +(5.61888 + 4.71480i) q^{89} +(2.92708 + 8.04207i) q^{91} +(3.29599 - 2.35684i) q^{93} +(5.99513 - 13.2528i) q^{95} +(-16.0734 + 2.83418i) q^{97} +(17.7602 + 6.06880i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 12 q^{13} + 24 q^{15} - 6 q^{17} + 6 q^{19} - 18 q^{25} + 3 q^{27} + 6 q^{29} - 27 q^{33} - 24 q^{35} - 6 q^{39} - 3 q^{41} + 6 q^{43} + 54 q^{45} + 30 q^{47} + 21 q^{49} + 33 q^{51} + 60 q^{53}+ \cdots + 30 q^{99}+O(q^{100}) \) 18 * q - 12 * q^13 + 24 * q^15 - 6 * q^17 + 6 * q^19 - 18 * q^25 + 3 * q^27 + 6 * q^29 - 27 * q^33 - 24 * q^35 - 6 * q^39 - 3 * q^41 + 6 * q^43 + 54 * q^45 + 30 * q^47 + 21 * q^49 + 33 * q^51 + 60 * q^53 - 30 * q^55 + 12 * q^57 + 3 * q^59 + 54 * q^61 - 84 * q^63 - 24 * q^65 + 15 * q^67 + 24 * q^69 + 36 * q^71 - 42 * q^73 + 6 * q^79 + 36 * q^83 + 54 * q^87 + 60 * q^89 + 18 * q^91 - 84 * q^93 + 6 * q^95 + 9 * q^97 + 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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