LMFDB - Embedded newform 912.2.cc.c.401.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(257,912)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			401.1
Root			$-1.72388 - 0.168030i$ of defining polynomial
Character	$\chi$	$=$	912.401
Dual form			912.2.cc.c.257.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.67739 - 0.431705i) q^{3} +(1.14133 + 3.13578i) q^{5} +(1.07356 + 1.85947i) q^{7} +(2.62726 + 1.44827i) q^{9} +O(q^{10})$	\(q+(-1.67739 - 0.431705i) q^{3} +(1.14133 + 3.13578i) q^{5} +(1.07356 + 1.85947i) q^{7} +(2.62726 + 1.44827i) q^{9} +(5.41799 + 3.12808i) q^{11} +(-2.56208 - 3.05336i) q^{13} +(-0.560722 - 5.75264i) q^{15} +(-0.403611 - 0.0711674i) q^{17} +(-4.34640 + 0.329887i) q^{19} +(-0.998042 - 3.58251i) q^{21} +(0.280411 - 0.770422i) q^{23} +(-4.70025 + 3.94398i) q^{25} +(-3.78171 - 3.56352i) q^{27} +(0.805141 + 4.56618i) q^{29} +(2.02597 - 1.16970i) q^{31} +(-7.73767 - 7.58597i) q^{33} +(-4.60559 + 5.48872i) q^{35} +6.01346i q^{37} +(2.97944 + 6.22774i) q^{39} +(0.926617 + 0.777524i) q^{41} +(-5.87377 + 2.13788i) q^{43} +(-1.54289 + 9.89147i) q^{45} +(7.59919 - 1.33994i) q^{47} +(1.19492 - 2.06967i) q^{49} +(0.646288 + 0.293616i) q^{51} +(-0.220516 - 0.0802612i) q^{53} +(-3.62525 + 20.5598i) q^{55} +(7.43301 + 1.32301i) q^{57} +(-0.930375 + 5.27642i) q^{59} +(7.30705 + 2.65955i) q^{61} +(0.127515 + 6.44012i) q^{63} +(6.65050 - 11.5190i) q^{65} +(-3.48689 + 0.614832i) q^{67} +(-0.802953 + 1.17124i) q^{69} +(-4.19799 + 1.52794i) q^{71} +(-4.33185 - 3.63485i) q^{73} +(9.58679 - 4.58646i) q^{75} +13.4328i q^{77} +(8.05412 - 9.59853i) q^{79} +(4.80501 + 7.60999i) q^{81} +(-8.01579 + 4.62792i) q^{83} +(-0.237488 - 1.34686i) q^{85} +(0.620710 - 8.00685i) q^{87} +(-5.61888 + 4.71480i) q^{89} +(2.92708 - 8.04207i) q^{91} +(-3.90331 + 1.08741i) q^{93} +(-5.99513 - 13.2528i) q^{95} +(-16.0734 - 2.83418i) q^{97} +(9.70416 + 16.0650i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{3} - 3 q^{9}+O(q^{10}) $ 18 * q - 3 * q^3 - 3 * q^9	$ 18 q - 3 q^{3} - 3 q^{9} - 12 q^{13} - 18 q^{15} + 6 q^{17} + 6 q^{19} - 18 q^{25} + 6 q^{27} - 6 q^{29} - 24 q^{33} + 24 q^{35} - 6 q^{39} + 3 q^{41} + 6 q^{43} - 54 q^{45} - 30 q^{47} + 21 q^{49} - 42 q^{51} - 60 q^{53} - 30 q^{55} + 12 q^{57} - 3 q^{59} + 54 q^{61} + 18 q^{63} + 24 q^{65} + 15 q^{67} + 30 q^{69} - 36 q^{71} - 42 q^{73} + 6 q^{79} - 3 q^{81} - 36 q^{83} - 60 q^{89} + 18 q^{91} - 66 q^{93} - 6 q^{95} + 9 q^{97} + 102 q^{99}+O(q^{100}) $ 18 * q - 3 * q^3 - 3 * q^9 - 12 * q^13 - 18 * q^15 + 6 * q^17 + 6 * q^19 - 18 * q^25 + 6 * q^27 - 6 * q^29 - 24 * q^33 + 24 * q^35 - 6 * q^39 + 3 * q^41 + 6 * q^43 - 54 * q^45 - 30 * q^47 + 21 * q^49 - 42 * q^51 - 60 * q^53 - 30 * q^55 + 12 * q^57 - 3 * q^59 + 54 * q^61 + 18 * q^63 + 24 * q^65 + 15 * q^67 + 30 * q^69 - 36 * q^71 - 42 * q^73 + 6 * q^79 - 3 * q^81 - 36 * q^83 - 60 * q^89 + 18 * q^91 - 66 * q^93 - 6 * q^95 + 9 * q^97 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−1.67739	−	0.431705i	−0.968440	−	0.249245i
$3$	−1.67739	−	0.431705i	−0.968440	−	0.249245i
$4$		0			0
$5$	1.14133	+	3.13578i	0.510418	+	1.40236i	0.880802	+	0.473484i	$0.157004\pi$
$5$	1.14133	+	3.13578i	0.510418	+	1.40236i	−0.370384	+	0.928879i	$0.620774\pi$
$6$		0			0
$7$	1.07356	+	1.85947i	0.405769	+	0.702812i	0.994411	−	0.105582i	$-0.0336704\pi$
$7$	1.07356	+	1.85947i	0.405769	+	0.702812i	−0.588642	+	0.808394i	$0.700337\pi$
$8$		0			0
$9$	2.62726	+	1.44827i	0.875754	+	0.482758i
$10$		0			0
$11$	5.41799	+	3.12808i	1.63359	+	0.943151i	0.982975	+	0.183740i	$0.0588203\pi$
$11$	5.41799	+	3.12808i	1.63359	+	0.943151i	0.650611	+	0.759412i	$0.274513\pi$
$12$		0			0
$13$	−2.56208	−	3.05336i	−0.710592	−	0.846850i	0.283089	−	0.959094i	$-0.408641\pi$
$13$	−2.56208	−	3.05336i	−0.710592	−	0.846850i	−0.993681	+	0.112243i	$0.964196\pi$
$14$		0			0
$15$	−0.560722	−	5.75264i	−0.144778	−	1.48532i
$16$		0			0
$17$	−0.403611	−	0.0711674i	−0.0978899	−	0.0172606i	0.124489	−	0.992221i	$-0.460271\pi$
$17$	−0.403611	−	0.0711674i	−0.0978899	−	0.0172606i	−0.222379	+	0.974960i	$0.571382\pi$
$18$		0			0
$19$	−4.34640	+	0.329887i	−0.997132	+	0.0756812i
$19$	−4.34640	+	0.329887i	−0.997132	+	0.0756812i
$20$		0			0
$21$	−0.998042	−	3.58251i	−0.217791	−	0.781768i
$22$		0			0
$23$	0.280411	−	0.770422i	0.0584697	−	0.160644i	−0.907019	−	0.421090i	$-0.861647\pi$
$23$	0.280411	−	0.770422i	0.0584697	−	0.160644i	0.965488	+	0.260446i	$0.0838697\pi$
$24$		0			0
$25$	−4.70025	+	3.94398i	−0.940051	+	0.788796i
$26$		0			0
$27$	−3.78171	−	3.56352i	−0.727790	−	0.685800i
$28$		0			0
$29$	0.805141	+	4.56618i	0.149511	+	0.847919i	0.963634	+	0.267226i	$0.0861071\pi$
$29$	0.805141	+	4.56618i	0.149511	+	0.847919i	−0.814123	+	0.580693i	$0.802782\pi$
$30$		0			0
$31$	2.02597	−	1.16970i	0.363875	−	0.210084i	−0.306904	−	0.951740i	$-0.599293\pi$
$31$	2.02597	−	1.16970i	0.363875	−	0.210084i	0.670779	+	0.741657i	$0.265960\pi$
$32$		0			0
$33$	−7.73767	−	7.58597i	−1.34695	−	1.32055i
$34$		0			0
$35$	−4.60559	+	5.48872i	−0.778486	+	0.927764i
$36$		0			0
$37$			6.01346i			0.988607i	0.869289	+	0.494303i	$0.164577\pi$
$37$			6.01346i			0.988607i	−0.869289	+	0.494303i	$0.835423\pi$
$38$		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	$-0.247667\pi$
$41$	0.926617	+	0.777524i	0.144713	+	0.121429i	−0.567557	+	0.823334i	$0.692111\pi$
$42$		0			0
$43$	−5.87377	+	2.13788i	−0.895741	+	0.326023i	−0.748545	−	0.663084i	$-0.769247\pi$
$43$	−5.87377	+	2.13788i	−0.895741	+	0.326023i	−0.147196	+	0.989107i	$0.547025\pi$
$44$		0			0
$45$	−1.54289	+	9.89147i	−0.230001	+	1.47453i
$46$		0			0
$47$	7.59919	−	1.33994i	1.10846	−	0.195451i	0.410689	−	0.911776i	$-0.365288\pi$
$47$	7.59919	−	1.33994i	1.10846	−	0.195451i	0.697767	+	0.716325i	$0.254177\pi$
$48$		0			0
$49$	1.19492	−	2.06967i	0.170703	−	0.295666i
$50$		0			0
$51$	0.646288	+	0.293616i	0.0904984	+	0.0411145i
$52$		0			0
$53$	−0.220516	−	0.0802612i	−0.0302902	−	0.0110247i	0.326831	−	0.945083i	$-0.394019\pi$
$53$	−0.220516	−	0.0802612i	−0.0302902	−	0.0110247i	−0.357121	+	0.934058i	$0.616242\pi$
$54$		0			0
$55$	−3.62525	+	20.5598i	−0.488828	+	2.77228i
$56$		0			0
$57$	7.43301	+	1.32301i	0.984526	+	0.175237i
$58$		0			0
$59$	−0.930375	+	5.27642i	−0.121124	+	0.686931i	0.862410	+	0.506210i	$0.168954\pi$
$59$	−0.930375	+	5.27642i	−0.121124	+	0.686931i	−0.983534	+	0.180721i	$0.942157\pi$
$60$		0			0
$61$	7.30705	+	2.65955i	0.935572	+	0.340520i	0.764416	−	0.644723i	$-0.223027\pi$
$61$	7.30705	+	2.65955i	0.935572	+	0.340520i	0.171156	+	0.985244i	$0.445250\pi$
$62$		0			0
$63$	0.127515	+	6.44012i	0.0160654	+	0.811379i
$64$		0			0
$65$	6.65050	−	11.5190i	0.824893	−	1.42876i
$66$		0			0
$67$	−3.48689	+	0.614832i	−0.425991	+	0.0751137i	−0.382534	−	0.923942i	$-0.624948\pi$
$67$	−3.48689	+	0.614832i	−0.425991	+	0.0751137i	−0.0434574	+	0.999055i	$0.513837\pi$
$68$		0			0
$69$	−0.802953	+	1.17124i	−0.0966642	+	0.141001i
$70$		0			0
$71$	−4.19799	+	1.52794i	−0.498210	+	0.181334i	−0.578889	−	0.815407i	$-0.696513\pi$
$71$	−4.19799	+	1.52794i	−0.498210	+	0.181334i	0.0806788	+	0.996740i	$0.474291\pi$
$72$		0			0
$73$	−4.33185	−	3.63485i	−0.507005	−	0.425427i	0.353069	−	0.935597i	$-0.385138\pi$
$73$	−4.33185	−	3.63485i	−0.507005	−	0.425427i	−0.860074	+	0.510170i	$0.829583\pi$
$74$		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	−0.0903059	−	0.995914i	$-0.528784\pi$
$79$	8.05412	−	9.59853i	0.906159	−	1.07992i	0.996465	−	0.0840047i	$-0.0267711\pi$
$80$		0			0
$81$	4.80501	+	7.60999i	0.533889	+	0.845554i
$82$		0			0
$83$	−8.01579	+	4.62792i	−0.879848	+	0.507980i	−0.870608	−	0.491977i	$-0.836274\pi$
$83$	−8.01579	+	4.62792i	−0.879848	+	0.507980i	−0.00923947	+	0.999957i	$0.502941\pi$
$84$		0			0
$85$	−0.237488	−	1.34686i	−0.0257591	−	0.146087i
$86$		0			0
$87$	0.620710	−	8.00685i	0.0665471	−	0.858424i
$88$		0			0
$89$	−5.61888	+	4.71480i	−0.595600	+	0.499767i	−0.890028	−	0.455906i	$-0.849315\pi$
$89$	−5.61888	+	4.71480i	−0.595600	+	0.499767i	0.294428	+	0.955674i	$0.404871\pi$
$90$		0			0
$91$	2.92708	−	8.04207i	0.306841	−	0.843038i
$92$		0			0
$93$	−3.90331	+	1.08741i	−0.404754	+	0.112759i
$94$		0			0
$95$	−5.99513	−	13.2528i	−0.615087	−	1.35971i
$96$		0			0
$97$	−16.0734	−	2.83418i	−1.63201	−	0.287767i	−0.718786	−	0.695231i	$-0.755302\pi$
$97$	−16.0734	−	2.83418i	−1.63201	−	0.287767i	−0.913221	+	0.407464i	$0.866413\pi$
$98$		0			0
$99$	9.70416	+	16.0650i	0.975305	+	1.61459i
$100$		0			0
$101$	−3.69207	−	4.40004i	−0.367375	−	0.437820i	0.550412	−	0.834893i	$-0.314471\pi$
$101$	−3.69207	−	4.40004i	−0.367375	−	0.437820i	−0.917787	+	0.397073i	$0.870026\pi$
$102$		0			0
$103$	0.957127	+	0.552597i	0.0943085	+	0.0544490i	0.546413	−	0.837516i	$-0.315993\pi$
$103$	0.957127	+	0.552597i	0.0943085	+	0.0544490i	−0.452104	+	0.891965i	$0.649326\pi$
$104$		0			0
$105$	10.0949	−	7.21847i	0.985158	−	0.704450i
$106$		0			0
$107$	3.47626	+	6.02105i	0.336062	+	0.582077i	0.983688	−	0.179881i	$-0.0575713\pi$
$107$	3.47626	+	6.02105i	0.336062	+	0.582077i	−0.647626	+	0.761958i	$0.724238\pi$
$108$		0			0
$109$	2.42887	+	6.67327i	0.232644	+	0.639183i	0.999998	−	0.00204008i	$-0.000649379\pi$
$109$	2.42887	+	6.67327i	0.232644	+	0.639183i	−0.767354	+	0.641223i	$0.778427\pi$
$110$		0			0
$111$	2.59604	−	10.0869i	0.246405	−	0.957407i
$112$		0			0
$113$	2.33000			0.219188			0.109594	−	0.993976i	$-0.465045\pi$
$113$	2.33000			0.219188			0.109594	+	0.993976i	$0.465045\pi$
$114$		0			0
$115$	2.73592			0.255125
$116$		0			0
$117$	−2.30914	−	11.7326i	−0.213480	−	1.08468i
$118$		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
$123$	−1.21863	−	1.70423i	−0.109881	−	0.153666i
$124$		0			0
$125$	−3.28225	−	1.89501i	−0.293573	−	0.169495i
$126$		0			0
$127$	−0.792153	−	0.944052i	−0.0702922	−	0.0837710i	0.729752	−	0.683712i	$-0.239635\pi$
$127$	−0.792153	−	0.944052i	−0.0702922	−	0.0837710i	−0.800045	+	0.599941i	$0.795191\pi$
$128$		0			0
$129$	10.7755	−	1.05031i	0.948732	−	0.0924749i
$130$		0			0
$131$	−6.34320	−	1.11848i	−0.554208	−	0.0977218i	−0.110472	−	0.993879i	$-0.535236\pi$
$131$	−6.34320	−	1.11848i	−0.554208	−	0.0977218i	−0.443736	+	0.896157i	$0.646347\pi$
$132$		0			0
$133$	−5.27955	−	7.72783i	−0.457795	−	0.670088i
$134$		0			0
$135$	6.85823	−	15.9258i	0.590262	−	1.37067i
$136$		0			0
$137$	3.68452	−	10.1231i	0.314790	−	0.864878i	−0.676882	−	0.736091i	$-0.736669\pi$
$137$	3.68452	−	10.1231i	0.314790	−	0.864878i	0.991672	−	0.128787i	$-0.0411084\pi$
$138$		0			0
$139$	−6.45972	+	5.42035i	−0.547906	+	0.459748i	−0.874231	−	0.485510i	$-0.838634\pi$
$139$	−6.45972	+	5.42035i	−0.547906	+	0.459748i	0.326325	+	0.945258i	$0.394190\pi$
$140$		0			0
$141$	−13.3253	−	1.03301i	−1.12219	−	0.0869948i
$142$		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
$147$	−2.89783	+	2.95578i	−0.239009	+	0.243788i
$148$		0			0
$149$	−3.41271	+	4.06711i	−0.279580	+	0.333190i	−0.887500	−	0.460808i	$-0.847560\pi$
$149$	−3.41271	+	4.06711i	−0.279580	+	0.333190i	0.607920	+	0.793998i	$0.292004\pi$
$150$		0			0
$151$			2.55987i			0.208319i	0.994561	+	0.104160i	$0.0332153\pi$
$151$			2.55987i			0.208319i	−0.994561	+	0.104160i	$0.966785\pi$
$152$		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	0.374573	−	0.927197i	$-0.377789\pi$
$157$	15.7565	−	5.73489i	1.25750	−	0.457694i	0.882931	+	0.469503i	$0.155567\pi$
$158$		0			0
$159$	0.335241	+	0.229827i	0.0265864	+	0.0182265i
$160$		0			0
$161$	1.73361	−	0.305683i	0.136628	−	0.0240912i
$162$		0			0
$163$	−5.28499	+	9.15387i	−0.413952	+	0.716987i	−0.995318	−	0.0966559i	$-0.969185\pi$
$163$	−5.28499	+	9.15387i	−0.413952	+	0.716987i	0.581365	+	0.813643i	$0.302519\pi$
$164$		0			0
$165$	14.9567	−	32.9217i	1.16438	−	2.56295i
$166$		0			0
$167$	10.5199	+	3.82893i	0.814054	+	0.296292i	0.715298	−	0.698820i	$-0.246291\pi$
$167$	10.5199	+	3.82893i	0.814054	+	0.296292i	0.0987568	+	0.995112i	$0.468513\pi$
$168$		0			0
$169$	−0.501366	+	2.84339i	−0.0385666	+	0.218722i
$170$		0			0
$171$	−11.8969	−	5.42808i	−0.909778	−	0.415095i
$172$		0			0
$173$	3.80558	−	21.5825i	0.289333	−	1.64089i	−0.400051	−	0.916493i	$-0.631007\pi$
$173$	3.80558	−	21.5825i	0.289333	−	1.64089i	0.689384	−	0.724396i	$-0.257881\pi$
$174$		0			0
$175$	−12.3797	−	4.50585i	−0.935819	−	0.340610i
$176$		0			0
$177$	3.83846	−	8.44895i	0.288516	−	0.635062i
$178$		0			0
$179$	10.6934	−	18.5215i	0.799263	−	1.38436i	−0.120833	−	0.992673i	$-0.538557\pi$
$179$	10.6934	−	18.5215i	0.799263	−	1.38436i	0.920097	−	0.391692i	$-0.128110\pi$
$180$		0			0
$181$	−18.0057	+	3.17489i	−1.33835	+	0.235988i	−0.796578	−	0.604536i	$-0.793359\pi$
$181$	−18.0057	+	3.17489i	−1.33835	+	0.235988i	−0.541775	+	0.840523i	$0.682248\pi$
$182$		0			0
$183$	−11.1086	−	7.61559i	−0.821173	−	0.562961i
$184$		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	−0.471934	−	0.881634i	$-0.656444\pi$
$193$	6.64414	−	7.91818i	0.478256	−	0.569963i	0.950190	+	0.311671i	$0.100889\pi$
$194$		0			0
$195$	−16.1283	+	16.4508i	−1.15497	+	1.17806i
$196$		0			0
$197$	10.2877	−	5.93959i	0.732966	−	0.423178i	−0.0865400	−	0.996248i	$-0.527581\pi$
$197$	10.2877	−	5.93959i	0.732966	−	0.423178i	0.819506	+	0.573070i	$0.194248\pi$
$198$		0			0
$199$	−4.24330	−	24.0650i	−0.300800	−	1.70592i	−0.642645	−	0.766164i	$-0.722163\pi$
$199$	−4.24330	−	24.0650i	−0.300800	−	1.70592i	0.341845	−	0.939756i	$-0.388948\pi$
$200$		0			0
$201$	6.11429	+	0.473995i	0.431269	+	0.0334330i
$202$		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
$207$	1.85249	−	1.61799i	0.128757	−	0.112458i
$208$		0			0
$209$	−24.5807	−	11.8085i	−1.70028	−	0.816814i
$210$		0			0
$211$	16.3173	+	2.87718i	1.12333	+	0.198074i	0.704303	−	0.709900i	$-0.251260\pi$
$211$	16.3173	+	2.87718i	1.12333	+	0.198074i	0.419028	+	0.907973i	$0.362371\pi$
$212$		0			0
$213$	7.70128	−	0.750660i	0.527683	−	0.0514344i
$214$		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
$219$	5.69701	+	7.96714i	0.384968	+	0.538370i
$220$		0			0
$221$	0.816781	+	1.41471i	0.0549426	+	0.0951634i
$222$		0			0
$223$	4.05122	+	11.1306i	0.271290	+	0.745362i	0.998275	+	0.0587091i	$0.0186984\pi$
$223$	4.05122	+	11.1306i	0.271290	+	0.745362i	−0.726986	+	0.686653i	$0.759079\pi$
$224$		0			0
$225$	−18.0608	+	3.55461i	−1.20405	+	0.236974i
$226$		0			0
$227$	23.0722			1.53135			0.765676	−	0.643226i	$-0.222405\pi$
$227$	23.0722			1.53135			0.765676	+	0.643226i	$0.222405\pi$
$228$		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
$231$	5.79899	−	22.5320i	0.381546	−	1.48249i
$232$		0			0
$233$	−8.06779	−	22.1661i	−0.528539	−	1.45215i	−0.860792	−	0.508958i	$-0.830031\pi$
$233$	−8.06779	−	22.1661i	−0.528539	−	1.45215i	0.332253	−	0.943190i	$-0.392191\pi$
$234$		0			0
$235$	12.8749	+	22.3001i	0.839869	+	1.45470i
$236$		0			0
$237$	−17.6536	+	12.6235i	−1.14673	+	0.819981i
$238$		0			0
$239$	23.6023	+	13.6268i	1.52670	+	0.881443i	0.999497	+	0.0317050i	$0.0100937\pi$
$239$	23.6023	+	13.6268i	1.52670	+	0.881443i	0.527206	+	0.849738i	$0.323240\pi$
$240$		0			0
$241$	13.6728	+	16.2946i	0.880739	+	1.04962i	0.998399	+	0.0565704i	$0.0180165\pi$
$241$	13.6728	+	16.2946i	0.880739	+	1.04962i	−0.117659	+	0.993054i	$0.537539\pi$
$242$		0			0
$243$	−4.77459	−	14.8392i	−0.306290	−	0.951938i
$244$		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
$249$	15.4435	−	4.30236i	0.978692	−	0.272651i
$250$		0			0
$251$	−0.848967	+	2.33252i	−0.0535863	+	0.147227i	−0.963598	−	0.267355i	$-0.913850\pi$
$251$	−0.848967	+	2.33252i	−0.0535863	+	0.147227i	0.910012	+	0.414583i	$0.136072\pi$
$252$		0			0
$253$	3.92920	−	3.29699i	0.247027	−	0.207280i
$254$		0			0
$255$	−0.183087	+	2.36173i	−0.0114654	+	0.147897i
$256$		0			0
$257$	1.95465	+	11.0854i	0.121928	+	0.691488i	0.983085	+	0.183149i	$0.0586291\pi$
$257$	1.95465	+	11.0854i	0.121928	+	0.691488i	−0.861157	+	0.508339i	$0.830260\pi$
$258$		0			0
$259$	−11.1818	+	6.45583i	−0.694805	+	0.401146i
$260$		0			0
$261$	−4.49777	+	13.1626i	−0.278405	+	0.814746i
$262$		0			0
$263$	−7.57578	+	9.02847i	−0.467143	+	0.556719i	−0.947252	−	0.320490i	$-0.896153\pi$
$263$	−7.57578	+	9.02847i	−0.467143	+	0.556719i	0.480109	+	0.877209i	$0.340597\pi$
$264$		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	$-0.161652\pi$
$269$	8.96522	+	7.52271i	0.546619	+	0.458668i	−0.327175	+	0.944964i	$0.606097\pi$
$270$		0			0
$271$	29.1999	−	10.6279i	1.77377	−	0.645598i	0.773841	−	0.633380i	$-0.218333\pi$
$271$	29.1999	−	10.6279i	1.77377	−	0.645598i	0.999925	−	0.0122180i	$-0.00388921\pi$
$272$		0			0
$273$	−8.38165	+	12.2260i	−0.507280	+	0.739954i
$274$		0			0
$275$	−37.8030	+	6.66569i	−2.27961	+	0.401956i
$276$		0			0
$277$	1.91965	−	3.32494i	0.115341	−	0.199776i	−0.802575	−	0.596551i	$-0.796537\pi$
$277$	1.91965	−	3.32494i	0.115341	−	0.199776i	0.917916	+	0.396775i	$0.129871\pi$
$278$		0			0
$279$	7.01680	−	0.138933i	0.420085	−	0.00831773i
$280$		0			0
$281$	23.0658	+	8.39528i	1.37599	+	0.500820i	0.920961	−	0.389655i	$-0.127406\pi$
$281$	23.0658	+	8.39528i	1.37599	+	0.500820i	0.455031	+	0.890475i	$0.349628\pi$
$282$		0			0
$283$	4.03563	−	22.8872i	0.239894	−	1.36050i	−0.592165	−	0.805817i	$-0.701727\pi$
$283$	4.03563	−	22.8872i	0.239894	−	1.36050i	0.832059	−	0.554688i	$-0.187162\pi$
$284$		0			0
$285$	4.33484	+	24.8183i	0.256774	+	1.47011i
$286$		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
$291$	25.7378	+	11.6930i	1.50878	+	0.685455i
$292$		0			0
$293$	5.48661	−	9.50309i	0.320531	−	0.555177i	−0.660066	−	0.751207i	$-0.729472\pi$
$293$	5.48661	−	9.50309i	0.320531	−	0.555177i	0.980598	+	0.196031i	$0.0628052\pi$
$294$		0			0
$295$	−17.6075	+	3.10468i	−1.02515	+	0.180762i
$296$		0			0
$297$	−9.34230	−	31.1366i	−0.542095	−	1.80673i
$298$		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	−0.755919	−	0.654665i	$-0.772810\pi$
$307$	0.351542	−	0.418952i	0.0200636	−	0.0239108i	0.775983	+	0.630754i	$0.217254\pi$
$308$		0			0
$309$	−1.36691	−	1.34012i	−0.0777610	−	0.0762366i
$310$		0			0
$311$	−12.1908	+	7.03836i	−0.691277	+	0.399109i	−0.804090	−	0.594507i	$-0.797347\pi$
$311$	−12.1908	+	7.03836i	−0.691277	+	0.399109i	0.112813	+	0.993616i	$0.464014\pi$
$312$		0			0
$313$	−3.23018	−	18.3193i	−0.182580	−	1.03547i	−0.929025	−	0.370018i	$-0.879352\pi$
$313$	−3.23018	−	18.3193i	−0.182580	−	1.03547i	0.746444	−	0.665448i	$-0.231759\pi$
$314$		0			0
$315$	−20.0493	+	7.75016i	−1.12965	+	0.436672i
$316$		0			0
$317$	−20.8301	+	17.4785i	−1.16993	+	0.981690i	−0.999993	−	0.00376423i	$-0.998802\pi$
$317$	−20.8301	+	17.4785i	−1.16993	+	0.981690i	−0.169940	+	0.985454i	$0.554357\pi$
$318$		0			0
$319$	−9.92113	+	27.2581i	−0.555477	+	1.52616i
$320$		0			0
$321$	−3.23171	−	11.6004i	−0.180377	−	0.647469i
$322$		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
$327$	−1.19328	−	12.2422i	−0.0659883	−	0.676996i
$328$		0			0
$329$	10.6498	+	12.6919i	0.587142	+	0.699729i
$330$		0			0
$331$	−25.4221	−	14.6775i	−1.39733	−	0.806746i	−0.403214	−	0.915106i	$-0.632107\pi$
$331$	−25.4221	−	14.6775i	−1.39733	−	0.806746i	−0.994112	+	0.108360i	$0.965440\pi$
$332$		0			0
$333$	−8.70914	+	15.7989i	−0.477258	+	0.865776i
$334$		0			0
$335$	−5.90767	−	10.2324i	−0.322770	−	0.559055i
$336$		0			0
$337$	4.60842	+	12.6615i	0.251037	+	0.689717i	0.999643	+	0.0267031i	$0.00850087\pi$
$337$	4.60842	+	12.6615i	0.251037	+	0.689717i	−0.748607	+	0.663014i	$0.769277\pi$
$338$		0			0
$339$	−3.90832	−	1.00587i	−0.212271	−	0.0546316i
$340$		0			0
$341$	14.6356			0.792562
$342$		0			0
$343$	20.1612			1.08860
$344$		0			0
$345$	−4.58919	−	1.18111i	−0.247074	−	0.0635888i
$346$		0			0
$347$	−2.06013	−	5.66016i	−0.110594	−	0.303854i	0.872033	−	0.489447i	$-0.162801\pi$
$347$	−2.06013	−	5.66016i	−0.110594	−	0.303854i	−0.982627	+	0.185594i	$0.940579\pi$
$348$		0			0
$349$	−14.3065	−	24.7795i	−0.765808	−	1.32642i	−0.939818	−	0.341675i	$-0.889006\pi$
$349$	−14.3065	−	24.7795i	−0.765808	−	1.32642i	0.174010	−	0.984744i	$-0.444328\pi$
$350$		0			0
$351$	−1.19169	+	20.6769i	−0.0636078	+	1.10365i
$352$		0			0
$353$	14.6066	+	8.43315i	0.777433	+	0.448851i	0.835520	−	0.549460i	$-0.185167\pi$
$353$	14.6066	+	8.43315i	0.777433	+	0.448851i	−0.0580867	+	0.998312i	$0.518500\pi$
$354$		0			0
$355$	−9.58259	−	11.4201i	−0.508591	−	0.606115i
$356$		0			0
$357$	0.147862	+	1.51697i	0.00782569	+	0.0802864i
$358$		0			0
$359$	16.2813	+	2.87084i	0.859295	+	0.151517i	0.585898	−	0.810385i	$-0.300742\pi$
$359$	16.2813	+	2.87084i	0.859295	+	0.151517i	0.273397	+	0.961901i	$0.411853\pi$
$360$		0			0
$361$	18.7823	−	2.86764i	0.988545	−	0.150928i
$362$		0			0
$363$	−13.0800	−	46.9511i	−0.686521	−	2.46429i
$364$		0			0
$365$	6.45403	−	17.7323i	0.337819	−	0.928151i
$366$		0			0
$367$	7.32428	−	6.14580i	0.382324	−	0.320808i	−0.431290	−	0.902213i	$-0.641941\pi$
$367$	7.32428	−	6.14580i	0.382324	−	0.320808i	0.813614	+	0.581405i	$0.197497\pi$
$368$		0			0
$369$	1.30840	+	3.38475i	0.0681124	+	0.176203i
$370$		0			0
$371$	−0.0874947	−	0.496207i	−0.00454250	−	0.0257618i
$372$		0			0
$373$	3.75197	−	2.16620i	0.194270	−	0.112162i	−0.399710	−	0.916642i	$-0.630889\pi$
$373$	3.75197	−	2.16620i	0.194270	−	0.112162i	0.593980	+	0.804480i	$0.297556\pi$
$374$		0			0
$375$	4.68752	+	4.59562i	0.242062	+	0.237317i
$376$		0			0
$377$	11.8794	−	14.1573i	0.611819	−	0.729138i
$378$		0			0
$379$			5.96818i			0.306565i	0.988182	+	0.153282i	$0.0489844\pi$
$379$			5.96818i			0.306565i	−0.988182	+	0.153282i	$0.951016\pi$
$380$		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	$-0.313630\pi$
$383$	−3.37004	−	2.82780i	−0.172201	−	0.144494i	−0.724815	+	0.688944i	$0.758075\pi$
$384$		0			0
$385$	−42.1222	+	15.3312i	−2.14675	+	0.781351i
$386$		0			0
$387$	−18.5282	−	2.89006i	−0.941839	−	0.146910i
$388$		0			0
$389$	−14.5009	+	2.55689i	−0.735223	+	0.129640i	−0.528708	−	0.848804i	$-0.677323\pi$
$389$	−14.5009	+	2.55689i	−0.735223	+	0.129640i	−0.206515	+	0.978443i	$0.566212\pi$
$390$		0			0
$391$	−0.168006	+	0.290994i	−0.00849641	+	0.0147162i
$392$		0			0
$393$	10.1572	+	4.61451i	0.512361	+	0.232771i
$394$		0			0
$395$	39.2913	+	14.3009i	1.97696	+	0.719554i
$396$		0			0
$397$	1.74751	−	9.91059i	0.0877048	−	0.497398i	−0.909035	−	0.416719i	$-0.863180\pi$
$397$	1.74751	−	9.91059i	0.0877048	−	0.497398i	0.996740	−	0.0806794i	$-0.0257090\pi$
$398$		0			0
$399$	5.51971	+	15.2418i	0.276331	+	0.763043i
$400$		0			0
$401$	−2.58090	+	14.6370i	−0.128884	+	0.730937i	0.850041	+	0.526717i	$0.176577\pi$
$401$	−2.58090	+	14.6370i	−0.128884	+	0.730937i	−0.978925	+	0.204221i	$0.934534\pi$
$402$		0			0
$403$	−8.76220	−	3.18918i	−0.436476	−	0.158864i
$404$		0			0
$405$	−18.3791	+	23.7529i	−0.913267	+	1.18029i
$406$		0			0
$407$	−18.8106	+	32.5809i	−0.932405	+	1.61497i
$408$		0			0
$409$	−9.81162	+	1.73005i	−0.485153	+	0.0855456i	−0.410874	−	0.911692i	$-0.634777\pi$
$409$	−9.81162	+	1.73005i	−0.485153	+	0.0855456i	−0.0742787	+	0.997238i	$0.523665\pi$
$410$		0			0
$411$	−10.5506	+	15.3898i	−0.520422	+	0.759123i
$412$		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	0.220234	−	0.975447i	$-0.429318\pi$
$421$	23.4446	−	27.9402i	1.14262	−	1.36172i	0.922384	−	0.386273i	$-0.126238\pi$
$422$		0			0
$423$	21.9057	+	7.48533i	1.06509	+	0.363949i
$424$		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
$429$	−3.33825	+	43.0617i	−0.161172	+	2.07904i
$430$		0			0
$431$	−8.05751	+	6.76105i	−0.388116	+	0.325668i	−0.815879	−	0.578223i	$-0.803746\pi$
$431$	−8.05751	+	6.76105i	−0.388116	+	0.325668i	0.427762	+	0.903891i	$0.359302\pi$
$432$		0			0
$433$	−12.6127	+	34.6530i	−0.606126	+	1.66532i	0.132485	+	0.991185i	$0.457704\pi$
$433$	−12.6127	+	34.6530i	−0.606126	+	1.66532i	−0.738611	+	0.674132i	$0.764518\pi$
$434$		0			0
$435$	25.8161	−	7.19205i	1.23779	−	0.344832i
$436$		0			0
$437$	−0.964625	+	3.44107i	−0.0461443	+	0.164608i
$438$		0			0
$439$	−13.1107	−	2.31177i	−0.625739	−	0.110335i	−0.148218	−	0.988955i	$-0.547354\pi$
$439$	−13.1107	−	2.31177i	−0.625739	−	0.110335i	−0.477522	+	0.878620i	$0.658465\pi$
$440$		0			0
$441$	6.13681	−	3.70698i	0.292229	−	0.176523i
$442$		0			0
$443$	−4.79891	−	5.71912i	−0.228003	−	0.271724i	0.639899	−	0.768459i	$-0.278976\pi$
$443$	−4.79891	−	5.71912i	−0.228003	−	0.271724i	−0.867902	+	0.496736i	$0.834532\pi$
$444$		0			0
$445$	−21.1976	−	12.2384i	−1.00486	−	0.580156i
$446$		0			0
$447$	7.48023	−	5.34883i	0.353803	−	0.252991i
$448$		0			0
$449$	12.1781	+	21.0931i	0.574722	+	0.995447i	0.996072	+	0.0885490i	$0.0282230\pi$
$449$	12.1781	+	21.0931i	0.574722	+	0.995447i	−0.421350	+	0.906898i	$0.638444\pi$
$450$		0			0
$451$	2.58825	+	7.11115i	0.121876	+	0.334851i
$452$		0			0
$453$	1.10511	−	4.29390i	0.0519226	−	0.201745i
$454$		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
$459$	1.27273	+	1.70741i	0.0594060	+	0.0796950i
$460$		0			0
$461$	0.765028	+	2.10190i	0.0356309	+	0.0978951i	0.956232	−	0.292608i	$-0.0945232\pi$
$461$	0.765028	+	2.10190i	0.0356309	+	0.0978951i	−0.920601	+	0.390503i	$0.872301\pi$
$462$		0			0
$463$	−1.84091	−	3.18854i	−0.0855541	−	0.148184i	0.820073	−	0.572259i	$-0.193933\pi$
$463$	−1.84091	−	3.18854i	−0.0855541	−	0.148184i	−0.905627	+	0.424075i	$0.860599\pi$
$464$		0			0
$465$	−7.86484	−	10.9988i	−0.364723	−	0.510058i
$466$		0			0
$467$	11.3948	+	6.57879i	0.527288	+	0.304430i	0.739911	−	0.672704i	$-0.234867\pi$
$467$	11.3948	+	6.57879i	0.527288	+	0.304430i	−0.212623	+	0.977134i	$0.568201\pi$
$468$		0			0
$469$	−4.88666	−	5.82369i	−0.225645	−	0.268913i
$470$		0			0
$471$	−28.9055	+	2.81748i	−1.33190	+	0.129823i
$472$		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
$477$	−0.463112	−	0.530234i	−0.0212045	−	0.0242778i
$478$		0			0
$479$	11.4643	−	31.4978i	0.523816	−	1.43917i	−0.342424	−	0.939546i	$-0.611248\pi$
$479$	11.4643	−	31.4978i	0.523816	−	1.43917i	0.866240	−	0.499628i	$-0.166530\pi$
$480$		0			0
$481$	18.3613	−	15.4069i	0.837202	−	0.702496i
$482$		0			0
$483$	−3.03991	−	0.235661i	−0.138321	−	0.0107229i
$484$		0			0
$485$	−9.45772	−	53.6374i	−0.429453	−	2.43555i
$486$		0			0
$487$	15.2052	−	8.77875i	0.689015	−	0.397803i	−0.114228	−	0.993455i	$-0.536439\pi$
$487$	15.2052	−	8.77875i	0.689015	−	0.397803i	0.803243	+	0.595651i	$0.203106\pi$
$488$		0			0
$489$	12.8168	−	13.0730i	0.579594	−	0.591183i
$490$		0			0
$491$	−15.8204	+	18.8540i	−0.713964	+	0.850869i	−0.994030	−	0.109112i	$-0.965199\pi$
$491$	−15.8204	+	18.8540i	−0.713964	+	0.850869i	0.280065	+	0.959981i	$0.409644\pi$
$492$		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	−0.631902	−	0.775048i	$-0.717726\pi$
$499$	−13.8001	+	5.02282i	−0.617777	+	0.224852i	0.0141259	+	0.999900i	$0.495503\pi$
$500$		0			0
$501$	−15.9930	−	10.9641i	−0.714514	−	0.489840i
$502$		0			0
$503$	4.24201	−	0.747980i	0.189142	−	0.0333508i	−0.0782748	−	0.996932i	$-0.524941\pi$
$503$	4.24201	−	0.747980i	0.189142	−	0.0333508i	0.267417	+	0.963581i	$0.413830\pi$
$504$		0			0
$505$	9.58368	−	16.5994i	0.426468	−	0.738665i
$506$		0			0
$507$	2.06849	−	4.55303i	0.0918650	−	0.202207i
$508$		0			0
$509$	−4.35756	−	1.58602i	−0.193145	−	0.0702991i	0.243637	−	0.969867i	$-0.421660\pi$
$509$	−4.35756	−	1.58602i	−0.193145	−	0.0702991i	−0.436782	+	0.899567i	$0.643882\pi$
$510$		0			0
$511$	2.10837	−	11.9572i	0.0932690	−	0.528955i
$512$		0			0
$513$	17.6124	+	14.2409i	0.777605	+	0.628753i
$514$		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
$519$	−15.7007	+	34.5594i	−0.689185	+	1.51699i
$520$		0			0
$521$	−0.205968	+	0.356747i	−0.00902363	+	0.0156294i	−0.870502	−	0.492165i	$-0.836206\pi$
$521$	−0.205968	+	0.356747i	−0.00902363	+	0.0156294i	0.861478	+	0.507794i	$0.169539\pi$
$522$		0			0
$523$	19.2248	−	3.38986i	0.840643	−	0.148228i	0.263284	−	0.964718i	$-0.415194\pi$
$523$	19.2248	−	3.38986i	0.840643	−	0.148228i	0.577359	+	0.816490i	$0.304083\pi$
$524$		0			0
$525$	18.8204	+	12.9025i	0.821390	+	0.563109i
$526$		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
$537$	−25.9328	+	26.4514i	−1.11908	+	1.14146i
$538$		0			0
$539$	12.9481	−	7.47562i	0.557716	−	0.321998i
$540$		0			0
$541$	−3.15633	−	17.9005i	−0.135701	−	0.769601i	−0.974369	−	0.224957i	$-0.927776\pi$
$541$	−3.15633	−	17.9005i	−0.135701	−	0.769601i	0.838667	−	0.544644i	$-0.183335\pi$
$542$		0			0
$543$	31.5732	+	2.44763i	1.35493	+	0.105038i
$544$		0			0
$545$	−18.1538	+	15.2328i	−0.777622	+	0.652502i
$546$		0			0
$547$	−1.42436	+	3.91340i	−0.0609014	+	0.167325i	−0.966412	−	0.256999i	$-0.917266\pi$
$547$	−1.42436	+	3.91340i	−0.0609014	+	0.167325i	0.905510	+	0.424324i	$0.139488\pi$
$548$		0			0
$549$	15.3458	+	17.5699i	0.654942	+	0.749867i
$550$		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
$555$	34.5932	−	3.37188i	1.46840	−	0.143128i
$556$		0			0
$557$	9.16196	+	10.9188i	0.388205	+	0.462644i	0.924386	−	0.381459i	$-0.124578\pi$
$557$	9.16196	+	10.9188i	0.388205	+	0.462644i	−0.536181	+	0.844103i	$0.680134\pi$
$558$		0			0
$559$	21.5767	+	12.4573i	0.912599	+	0.526889i
$560$		0			0
$561$	2.58313	+	3.61245i	0.109060	+	0.152518i
$562$		0			0
$563$	3.28307	+	5.68645i	0.138365	+	0.239655i	0.926878	−	0.375363i	$-0.122482\pi$
$563$	3.28307	+	5.68645i	0.138365	+	0.239655i	−0.788513	+	0.615018i	$0.789149\pi$
$564$		0			0
$565$	2.65930	+	7.30637i	0.111878	+	0.307381i
$566$		0			0
$567$	−8.99204	+	17.1046i	−0.377630	+	0.718324i
$568$		0			0
$569$	45.7506			1.91797			0.958983	−	0.283465i	$-0.0914840\pi$
$569$	45.7506			1.91797			0.958983	+	0.283465i	$0.0914840\pi$
$570$		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
$573$	−1.49420	+	5.80571i	−0.0624212	+	0.242537i
$574$		0			0
$575$	1.72053	+	4.72712i	0.0717510	+	0.197134i
$576$		0			0
$577$	−17.9425	−	31.0773i	−0.746956	−	1.29377i	−0.949276	−	0.314446i	$-0.898181\pi$
$577$	−17.9425	−	31.0773i	−0.746956	−	1.29377i	0.202320	−	0.979319i	$-0.435152\pi$
$578$		0			0
$579$	−14.5631	+	10.4135i	−0.605223	+	0.432772i
$580$		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
$585$	34.1553	−	20.6317i	1.41215	−	0.853015i
$586$		0			0
$587$	−29.5771	−	5.21525i	−1.22078	−	0.215256i	−0.474118	−	0.880461i	$-0.657233\pi$
$587$	−29.5771	−	5.21525i	−1.22078	−	0.215256i	−0.746661	+	0.665205i	$0.768344\pi$
$588$		0			0
$589$	−8.41982	+	5.75231i	−0.346932	+	0.237020i
$590$		0			0
$591$	−19.8206	+	5.52176i	−0.815309	+	0.227135i
$592$		0			0
$593$	−0.268437	+	0.737526i	−0.0110234	+	0.0302866i	−0.945082	−	0.326832i	$-0.894019\pi$
$593$	−0.268437	+	0.737526i	−0.0110234	+	0.0302866i	0.934059	+	0.357119i	$0.116241\pi$
$594$		0			0
$595$	2.24948	−	1.88754i	0.0922198	−	0.0773816i
$596$		0			0
$597$	−3.27130	+	42.1981i	−0.133886	+	1.72706i
$598$		0			0
$599$	2.35948	+	13.3813i	0.0964057	+	0.546744i	0.994308	+	0.106548i	$0.0339798\pi$
$599$	2.35948	+	13.3813i	0.0964057	+	0.546744i	−0.897902	+	0.440196i	$0.854909\pi$
$600$		0			0
$601$	1.41283	−	0.815696i	0.0576304	−	0.0332729i	−0.470908	−	0.882182i	$-0.656074\pi$
$601$	1.41283	−	0.815696i	0.0576304	−	0.0332729i	0.528538	+	0.848909i	$0.322740\pi$
$602$		0			0
$603$	−10.0514	−	3.43464i	−0.409325	−	0.139869i
$604$		0			0
$605$	−60.3592	+	71.9333i	−2.45395	+	2.92450i
$606$		0			0
$607$		−	23.6670i		−	0.960615i	−0.877100	−	0.480308i	$-0.840525\pi$
$607$		−	23.6670i		−	0.960615i	0.877100	−	0.480308i	$-0.159475\pi$
$608$		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	−0.0273321	−	0.999626i	$-0.508701\pi$
$613$	14.7136	−	5.35532i	0.594278	−	0.216299i	0.621610	+	0.783327i	$0.286479\pi$
$614$		0			0
$615$	3.95324	−	5.76646i	0.159410	−	0.232526i
$616$		0			0
$617$	19.6258	−	3.46056i	0.790105	−	0.139317i	0.235988	−	0.971756i	$-0.424167\pi$
$617$	19.6258	−	3.46056i	0.790105	−	0.139317i	0.554117	+	0.832439i	$0.313056\pi$
$618$		0			0
$619$	3.55524	−	6.15786i	0.142897	−	0.247505i	−0.785689	−	0.618621i	$-0.787691\pi$
$619$	3.55524	−	6.15786i	0.142897	−	0.247505i	0.928587	+	0.371116i	$0.121025\pi$
$620$		0			0
$621$	−3.80585	+	1.91426i	−0.152723	+	0.0768168i
$622$		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
$627$	36.1335	+	30.4191i	1.44303	+	1.21482i
$628$		0			0
$629$	0.427962	−	2.42710i	0.0170640	−	0.0967746i
$630$		0			0
$631$	1.16675	+	0.424661i	0.0464474	+	0.0169055i	0.365139	−	0.930953i	$-0.381021\pi$
$631$	1.16675	+	0.424661i	0.0464474	+	0.0169055i	−0.318692	+	0.947858i	$0.603244\pi$
$632$		0			0
$633$	−26.1284	−	11.8704i	−1.03851	−	0.471807i
$634$		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
$639$	−13.2421	−	2.06553i	−0.523849	−	0.0817112i
$640$		0			0
$641$	−7.06477	+	2.57137i	−0.279042	+	0.101563i	−0.477750	−	0.878496i	$-0.658548\pi$
$641$	−7.06477	+	2.57137i	−0.279042	+	0.101563i	0.198708	+	0.980059i	$0.436325\pi$
$642$		0			0
$643$	9.31005	+	7.81206i	0.367153	+	0.308078i	0.807634	−	0.589684i	$-0.200748\pi$
$643$	9.31005	+	7.81206i	0.367153	+	0.308078i	−0.440481	+	0.897762i	$0.645192\pi$
$644$		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
$651$	−6.21245	−	6.09066i	−0.243485	−	0.238712i
$652$		0			0
$653$	39.7547	−	22.9524i	1.55572	−	0.898196i	0.558063	−	0.829798i	$-0.311545\pi$
$653$	39.7547	−	22.9524i	1.55572	−	0.898196i	0.997658	−	0.0683980i	$-0.0217888\pi$
$654$		0			0
$655$	−3.73239	−	21.1674i	−0.145836	−	0.827080i
$656$		0			0
$657$	−6.11664	−	15.8234i	−0.238633	−	0.617330i
$658$		0			0
$659$	14.3577	−	12.0475i	0.559295	−	0.469304i	−0.318779	−	0.947829i	$-0.603273\pi$
$659$	14.3577	−	12.0475i	0.559295	−	0.469304i	0.878074	+	0.478525i	$0.158828\pi$
$660$		0			0
$661$	4.05073	−	11.1293i	0.157555	−	0.432879i	−0.835649	−	0.549263i	$-0.814908\pi$
$661$	4.05073	−	11.1293i	0.157555	−	0.432879i	0.993204	+	0.116385i	$0.0371306\pi$
$662$		0			0
$663$	−0.759323	−	2.72562i	−0.0294896	−	0.105854i
$664$		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
$669$	−1.99031	−	20.4193i	−0.0769500	−	0.789456i
$670$		0			0
$671$	31.2703	+	37.2665i	1.20718	+	1.43866i
$672$		0			0
$673$	−9.02264	−	5.20922i	−0.347797	−	0.200801i	0.315917	−	0.948787i	$-0.397688\pi$
$673$	−9.02264	−	5.20922i	−0.347797	−	0.200801i	−0.663715	+	0.747986i	$0.731021\pi$
$674$		0			0
$675$	31.8294	+	1.83445i	1.22512	+	0.0706082i
$676$		0			0
$677$	10.3670	+	17.9562i	0.398437	+	0.690112i	0.993533	−	0.113542i	$-0.0362196\pi$
$677$	10.3670	+	17.9562i	0.398437	+	0.690112i	−0.595097	+	0.803654i	$0.702886\pi$
$678$		0			0
$679$	−11.9858	−	32.9306i	−0.459972	−	1.26376i
$680$		0			0
$681$	−38.7009	−	9.96036i	−1.48302	−	0.381682i
$682$		0			0
$683$	2.79983			0.107132			0.0535662	−	0.998564i	$-0.482941\pi$
$683$	2.79983			0.107132			0.0535662	+	0.998564i	$0.482941\pi$
$684$		0			0
$685$	35.9492			1.37355
$686$		0			0
$687$	−23.5608	−	6.06377i	−0.898899	−	0.231347i
$688$		0			0
$689$	0.319912	+	0.878950i	0.0121877	+	0.0334853i
$690$		0			0
$691$	4.20182	+	7.27776i	0.159845	+	0.276859i	0.934813	−	0.355142i	$-0.115567\pi$
$691$	4.20182	+	7.27776i	0.159845	+	0.276859i	−0.774968	+	0.632001i	$0.782234\pi$
$692$		0			0
$693$	−19.4543	+	35.2914i	−0.739009	+	1.34061i
$694$		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
$699$	3.96361	+	40.6640i	0.149918	+	1.53805i
$700$		0			0
$701$	14.9472	+	2.63560i	0.564549	+	0.0995451i	0.448636	−	0.893714i	$-0.351910\pi$
$701$	14.9472	+	2.63560i	0.564549	+	0.0995451i	0.115912	+	0.993259i	$0.463021\pi$
$702$		0			0
$703$	−1.98376	−	26.1369i	−0.0748190	−	0.985771i
$704$		0			0
$705$	−11.9692	−	42.9640i	−0.450787	−	1.61812i
$706$		0			0
$707$	4.21806	−	11.5890i	0.158636	−	0.435850i
$708$		0			0
$709$	−29.3000	+	24.5857i	−1.10039	+	0.923334i	−0.997451	−	0.0713544i	$-0.977268\pi$
$709$	−29.3000	+	24.5857i	−1.10039	+	0.923334i	−0.102935	+	0.994688i	$0.532823\pi$
$710$		0			0
$711$	35.0616	−	13.5533i	1.31491	−	0.508287i
$712$		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
$717$	−33.7074	−	33.0466i	−1.25883	−	1.23415i
$718$		0			0
$719$	−24.9620	+	29.7485i	−0.930924	+	1.10943i	0.0628501	+	0.998023i	$0.479981\pi$
$719$	−24.9620	+	29.7485i	−0.930924	+	1.10943i	−0.993775	+	0.111410i	$0.964463\pi$
$720$		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	−0.907796	−	0.419413i	$-0.862236\pi$
$727$	−35.9582	+	13.0877i	−1.33361	+	0.485396i	−0.425818	+	0.904809i	$0.640014\pi$
$728$		0			0
$729$	1.60266	+	26.9524i	0.0593577	+	0.998237i
$730$		0			0
$731$	2.52286	−	0.444849i	0.0933114	−	0.0164533i
$732$		0			0
$733$	−7.71039	+	13.3548i	−0.284790	+	0.493270i	−0.972558	−	0.232660i	$-0.925257\pi$
$733$	−7.71039	+	13.3548i	−0.284790	+	0.493270i	0.687768	+	0.725930i	$0.258590\pi$
$734$		0			0
$735$	−12.5761	−	5.71344i	−0.463875	−	0.210744i
$736$		0			0
$737$	−20.8152	−	7.57610i	−0.766736	−	0.279069i
$738$		0			0
$739$	4.98207	−	28.2547i	0.183268	−	1.03937i	−0.744892	−	0.667185i	$-0.767499\pi$
$739$	4.98207	−	28.2547i	0.183268	−	1.03937i	0.928160	−	0.372181i	$-0.121390\pi$
$740$		0			0
$741$	−15.0043	−	26.0853i	−0.551196	−	0.958269i
$742$		0			0
$743$	4.95784	−	28.1173i	0.181886	−	1.03152i	−0.748006	−	0.663691i	$-0.768989\pi$
$743$	4.95784	−	28.1173i	0.181886	−	1.03152i	0.929892	−	0.367833i	$-0.119900\pi$
$744$		0			0
$745$	−16.6486	−	6.05959i	−0.609957	−	0.222006i
$746$		0			0
$747$	−27.7621	+	0.549693i	−1.01576	+	0.0201122i
$748$		0			0
$749$	−7.46397	+	12.9280i	−0.272727	+	0.472378i
$750$		0			0
$751$	−12.4716	+	2.19908i	−0.455096	+	0.0802457i	−0.396497	−	0.918036i	$-0.629774\pi$
$751$	−12.4716	+	2.19908i	−0.455096	+	0.0802457i	−0.0585987	+	0.998282i	$0.518663\pi$
$752$		0			0
$753$	2.43101	−	3.54603i	0.0885908	−	0.129225i
$754$		0			0
$755$	−8.02719	+	2.92166i	−0.292139	+	0.106330i
$756$		0			0
$757$	38.4432	+	32.2577i	1.39724	+	1.17243i	0.962308	+	0.271963i	$0.0876729\pi$
$757$	38.4432	+	32.2577i	1.39724	+	1.17243i	0.434934	+	0.900462i	$0.356772\pi$
$758$		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
$765$	1.32668	−	3.88250i	0.0479662	−	0.140372i
$766$		0			0
$767$	18.4945	−	10.6778i	0.667798	−	0.385553i
$768$		0			0
$769$	−6.83201	−	38.7463i	−0.246369	−	1.39723i	−0.817292	−	0.576223i	$-0.804526\pi$
$769$	−6.83201	−	38.7463i	−0.246369	−	1.39723i	0.570924	−	0.821003i	$-0.306585\pi$
$770$		0			0
$771$	1.50691	−	19.4383i	0.0542699	−	0.700054i
$772$		0			0
$773$	−2.48012	+	2.08107i	−0.0892039	+	0.0748509i	−0.686299	−	0.727319i	$-0.740766\pi$
$773$	−2.48012	+	2.08107i	−0.0892039	+	0.0748509i	0.597095	+	0.802170i	$0.296321\pi$
$774$		0			0
$775$	−4.90933	+	13.4883i	−0.176348	+	0.484513i
$776$		0			0
$777$	21.5433	−	6.00168i	0.772861	−	0.215309i
$778$		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
$783$	13.2269	−	20.1371i	0.472690	−	0.719642i
$784$		0			0
$785$	35.9667	+	42.8634i	1.28371	+	1.52986i
$786$		0			0
$787$	22.8624	+	13.1996i	0.814956	+	0.470515i	0.848674	−	0.528916i	$-0.177401\pi$
$787$	22.8624	+	13.1996i	0.814956	+	0.470515i	−0.0337179	+	0.999431i	$0.510735\pi$
$788$		0			0
$789$	16.6052	−	11.8737i	0.591160	−	0.422716i
$790$		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
$795$	−0.338065	+	1.31355i	−0.0119899	+	0.0465869i
$796$		0			0
$797$	9.50783			0.336785			0.168392	−	0.985720i	$-0.446142\pi$
$797$	9.50783			0.336785			0.168392	+	0.985720i	$0.446142\pi$
$798$		0			0
$799$	−3.16247			−0.111880
$800$		0			0
$801$	−21.5906	+	4.24933i	−0.762865	+	0.150143i
$802$		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
$807$	−11.7906	−	16.4888i	−0.415047	−	0.580434i
$808$		0			0
$809$	31.3018	+	18.0721i	1.10051	+	0.635380i	0.936355	−	0.351054i	$-0.114177\pi$
$809$	31.3018	+	18.0721i	1.10051	+	0.635380i	0.164156	+	0.986434i	$0.447510\pi$
$810$		0			0
$811$	−16.3764	−	19.5167i	−0.575054	−	0.685323i	0.397606	−	0.917556i	$-0.369841\pi$
$811$	−16.3764	−	19.5167i	−0.575054	−	0.685323i	−0.972660	+	0.232233i	$0.925397\pi$
$812$		0			0
$813$	−53.5676	+	5.22135i	−1.87870	+	0.183121i
$814$		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
$819$	19.3373	−	16.8894i	0.675701	−	0.590164i
$820$		0			0
$821$	3.53702	−	9.71788i	0.123443	−	0.339156i	−0.862543	−	0.505983i	$-0.831130\pi$
$821$	3.53702	−	9.71788i	0.123443	−	0.339156i	0.985986	+	0.166827i	$0.0533520\pi$
$822$		0			0
$823$	−11.1336	+	9.34221i	−0.388093	+	0.325649i	−0.815870	−	0.578235i	$-0.803741\pi$
$823$	−11.1336	+	9.34221i	−0.388093	+	0.325649i	0.427776	+	0.903885i	$0.359297\pi$
$824$		0			0
$825$	66.2879	+	5.13880i	2.30785	+	0.178910i
$826$		0			0
$827$	−4.21974	−	23.9313i	−0.146735	−	0.832174i	−0.965958	−	0.258699i	$-0.916706\pi$
$827$	−4.21974	−	23.9313i	−0.146735	−	0.832174i	0.819223	−	0.573475i	$-0.194405\pi$
$828$		0			0
$829$	43.3587	−	25.0331i	1.50591	−	0.869437i	0.505932	−	0.862573i	$-0.331149\pi$
$829$	43.3587	−	25.0331i	1.50591	−	0.869437i	0.999976	−	0.00686327i	$-0.00218466\pi$
$830$		0			0
$831$	−4.65540	+	4.74849i	−0.161494	+	0.164723i
$832$		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	$-0.0848572\pi$
$839$	25.2797	+	21.2122i	0.872752	+	0.732326i	−0.0919238	+	0.995766i	$0.529302\pi$
$840$		0			0
$841$	7.04931	−	2.56574i	0.243080	−	0.0884737i
$842$		0			0
$843$	−35.0661	−	24.0398i	−1.20774	−	0.827974i
$844$		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
$849$	−16.6499	+	36.6485i	−0.571422	+	1.25777i
$850$		0			0
$851$	4.63290	+	1.68624i	0.158814	+	0.0578035i
$852$		0			0
$853$	5.13243	−	29.1074i	0.175731	−	0.996620i	−0.761566	−	0.648088i	$-0.775569\pi$
$853$	5.13243	−	29.1074i	0.175731	−	0.996620i	0.937297	−	0.348532i	$-0.113320\pi$
$854$		0			0
$855$	3.44297	−	43.5012i	0.117747	−	1.48771i
$856$		0			0
$857$	8.49473	−	48.1760i	0.290175	−	1.64566i	−0.396019	−	0.918242i	$-0.629608\pi$
$857$	8.49473	−	48.1760i	0.290175	−	1.64566i	0.686193	−	0.727419i	$-0.259280\pi$
$858$		0			0
$859$	36.8403	+	13.4088i	1.25698	+	0.457502i	0.882753	−	0.469837i	$-0.155687\pi$
$859$	36.8403	+	13.4088i	1.25698	+	0.457502i	0.374222	+	0.927339i	$0.377910\pi$
$860$		0			0
$861$	1.86068	−	4.09562i	0.0634120	−	0.139578i
$862$		0			0
$863$	−17.6337	+	30.5424i	−0.600257	+	1.03967i	0.392525	+	0.919741i	$0.371602\pi$
$863$	−17.6337	+	30.5424i	−0.600257	+	1.03967i	−0.992782	+	0.119934i	$0.961732\pi$
$864$		0			0
$865$	72.0215	−	12.6993i	2.44880	−	0.431790i
$866$		0			0
$867$	24.0459	+	16.4848i	0.816640	+	0.559853i
$868$		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	−0.464050	−	0.885809i	$-0.653604\pi$
$877$	14.4779	−	17.2541i	0.488883	−	0.582628i	0.952933	+	0.303181i	$0.0980486\pi$
$878$		0			0
$879$	−13.3057	+	13.5718i	−0.448791	+	0.457765i
$880$		0			0
$881$	−47.0165	+	27.1450i	−1.58403	+	0.914539i	−0.589765	+	0.807575i	$0.700780\pi$
$881$	−47.0165	+	27.1450i	−1.58403	+	0.914539i	−0.994263	+	0.106964i	$0.965887\pi$
$882$		0			0
$883$	−4.51473	−	25.6043i	−0.151933	−	0.861653i	−0.961537	−	0.274677i	$-0.911429\pi$
$883$	−4.51473	−	25.6043i	−0.151933	−	0.861653i	0.809604	−	0.586977i	$-0.199682\pi$
$884$		0			0
$885$	30.8750	+	2.39350i	1.03785	+	0.0804568i
$886$		0			0
$887$	4.19836	−	3.52284i	0.140967	−	0.118286i	−0.569577	−	0.821938i	$-0.692893\pi$
$887$	4.19836	−	3.52284i	0.140967	−	0.118286i	0.710545	+	0.703652i	$0.248449\pi$
$888$		0			0
$889$	0.905006	−	2.48648i	0.0303529	−	0.0833939i
$890$		0			0
$891$	2.22883	+	56.2613i	0.0746687	+	1.88482i
$892$		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
$897$	5.63345	−	0.549105i	0.188096	−	0.0183341i
$898$		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
$903$	13.5212	+	18.9091i	0.449958	+	0.629257i
$904$		0			0
$905$	−30.5062	−	52.8383i	−1.01406	−	1.75640i
$906$		0			0
$907$	−20.0545	−	55.0993i	−0.665899	−	1.82954i	−0.547928	−	0.836526i	$-0.684583\pi$
$907$	−20.0545	−	55.0993i	−0.665899	−	1.82954i	−0.117971	−	0.993017i	$-0.537639\pi$
$908$		0			0
$909$	−3.32758	−	16.9072i	−0.110369	−	0.560776i
$910$		0			0
$911$	2.91388			0.0965412			0.0482706	−	0.998834i	$-0.484629\pi$
$911$	2.91388			0.0965412			0.0482706	+	0.998834i	$0.484629\pi$
$912$		0			0
$913$	−57.9060			−1.91641
$914$		0			0
$915$	11.2022	−	43.5261i	0.370333	−	1.43893i
$916$		0			0
$917$	−4.73006	−	12.9957i	−0.156200	−	0.429157i
$918$		0			0
$919$	−2.94881	−	5.10749i	−0.0972722	−	0.168480i	0.813282	−	0.581869i	$-0.197678\pi$
$919$	−2.94881	−	5.10749i	−0.0972722	−	0.168480i	−0.910555	+	0.413389i	$0.864345\pi$
$920$		0			0
$921$	−0.770536	+	0.550982i	−0.0253900	+	0.0181555i
$922$		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
$927$	1.71431	+	2.83800i	0.0563053	+	0.0932121i
$928$		0			0
$929$	−22.4137	−	3.95214i	−0.735369	−	0.129665i	−0.206593	−	0.978427i	$-0.566238\pi$
$929$	−22.4137	−	3.95214i	−0.735369	−	0.129665i	−0.528776	+	0.848762i	$0.677349\pi$
$930$		0			0
$931$	−4.51085	+	9.38978i	−0.147837	+	0.307738i
$932$		0			0
$933$	23.4872	−	6.54323i	0.768936	−	0.214216i
$934$		0			0
$935$	2.92637	−	8.04015i	0.0957027	−	0.262941i
$936$		0			0
$937$	−33.5028	+	28.1122i	−1.09449	+	0.918384i	−0.997042	−	0.0768570i	$-0.975512\pi$
$937$	−33.5028	+	28.1122i	−1.09449	+	0.918384i	−0.0974452	+	0.995241i	$0.531067\pi$
$938$		0			0
$939$	−2.49025	+	32.1230i	−0.0812663	+	1.04829i
$940$		0			0
$941$	1.06108	+	6.01769i	0.0345903	+	0.196171i	0.997206	−	0.0746992i	$-0.0237997\pi$
$941$	1.06108	+	6.01769i	0.0345903	+	0.196171i	−0.962616	+	0.270870i	$0.912689\pi$
$942$		0			0
$943$	0.858855	−	0.495860i	0.0279682	−	0.0161474i
$944$		0			0
$945$	36.9762	−	4.34467i	1.20283	−	0.141332i
$946$		0			0
$947$	19.9420	−	23.7660i	0.648029	−	0.772291i	−0.337586	−	0.941295i	$-0.609611\pi$
$947$	19.9420	−	23.7660i	0.648029	−	0.772291i	0.985615	+	0.169004i	$0.0540550\pi$
$948$		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	−0.997797	−	0.0663415i	$-0.978867\pi$
$953$	−38.1684	−	32.0271i	−1.23640	−	1.03746i	−0.238599	−	0.971118i	$-0.576688\pi$
$954$		0			0
$955$	10.8534	−	3.95033i	0.351209	−	0.127830i
$956$		0			0
$957$	28.4090	−	41.4394i	0.918334	−	1.33954i
$958$		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
$963$	0.412901	+	20.8535i	0.0133055	+	0.671993i
$964$		0			0
$965$	32.4128	+	11.7973i	1.04341	+	0.379769i
$966$		0			0
$967$	1.94625	−	11.0377i	0.0625873	−	0.354950i	−0.937390	−	0.348280i	$-0.886766\pi$
$967$	1.94625	−	11.0377i	0.0625873	−	0.354950i	0.999978	−	0.00666987i	$-0.00212310\pi$
$968$		0			0
$969$	−2.90589	−	1.06297i	−0.0933505	−	0.0341475i
$970$		0			0
$971$	8.32593	−	47.2187i	0.267192	−	1.51532i	−0.495528	−	0.868592i	$-0.665026\pi$
$971$	8.32593	−	47.2187i	0.267192	−	1.51532i	0.762720	−	0.646729i	$-0.223863\pi$
$972$		0			0
$973$	−17.0139	−	6.19254i	−0.545440	−	0.198524i
$974$		0			0
$975$	−38.5662	−	17.5211i	−1.23511	−	0.561123i
$976$		0			0
$977$	−5.39563	+	9.34550i	−0.172621	+	0.298989i	−0.939336	−	0.343000i	$-0.888557\pi$
$977$	−5.39563	+	9.34550i	−0.172621	+	0.298989i	0.766714	+	0.641989i	$0.221890\pi$
$978$		0			0
$979$	−45.1913	+	7.96844i	−1.44432	+	0.254672i
$980$		0			0
$981$	−3.28344	+	21.0501i	−0.104832	+	0.672078i
$982$		0			0
$983$	−34.3549	+	12.5042i	−1.09575	+	0.398821i	−0.825748	−	0.564039i	$-0.809247\pi$
$983$	−34.3549	+	12.5042i	−1.09575	+	0.398821i	−0.270003	+	0.962860i	$0.587025\pi$
$984$		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	−0.699332	−	0.714797i	$-0.746519\pi$
$991$	3.96786	−	4.72871i	0.126043	−	0.150213i	0.825375	+	0.564584i	$0.190964\pi$
$992$		0			0
$993$	36.3064	+	35.5947i	1.15215	+	1.12956i
$994$		0			0
$995$	70.6194	−	40.7721i	2.23879	−	1.29256i
$996$		0			0
$997$	3.18227	+	18.0475i	0.100783	+	0.571571i	0.992821	+	0.119610i	$0.0381643\pi$
$997$	3.18227	+	18.0475i	0.100783	+	0.571571i	−0.892038	+	0.451961i	$0.850725\pi$
$998$		0			0
$999$	21.4291	−	22.7412i	0.677986	−	0.719498i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.29.1	✓	18	76.67	even	18
114.2.l.a.59.1	yes	18	12.11	even	2
114.2.l.b.29.3	yes	18	228.143	odd	18
114.2.l.b.59.3	yes	18	4.3	odd	2
912.2.cc.c.257.1		18	57.29	even	18	inner
912.2.cc.c.401.1		18	1.1	even	1	trivial
912.2.cc.d.257.3		18	19.10	odd	18
912.2.cc.d.401.3		18	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.67739 - 0.431705i) q^{3} +(1.14133 + 3.13578i) q^{5} +(1.07356 + 1.85947i) q^{7} +(2.62726 + 1.44827i) q^{9} +O(q^{10})\)	\(q+(-1.67739 - 0.431705i) q^{3} +(1.14133 + 3.13578i) q^{5} +(1.07356 + 1.85947i) q^{7} +(2.62726 + 1.44827i) q^{9} +(5.41799 + 3.12808i) q^{11} +(-2.56208 - 3.05336i) q^{13} +(-0.560722 - 5.75264i) q^{15} +(-0.403611 - 0.0711674i) q^{17} +(-4.34640 + 0.329887i) q^{19} +(-0.998042 - 3.58251i) q^{21} +(0.280411 - 0.770422i) q^{23} +(-4.70025 + 3.94398i) q^{25} +(-3.78171 - 3.56352i) q^{27} +(0.805141 + 4.56618i) q^{29} +(2.02597 - 1.16970i) q^{31} +(-7.73767 - 7.58597i) q^{33} +(-4.60559 + 5.48872i) q^{35} +6.01346i q^{37} +(2.97944 + 6.22774i) q^{39} +(0.926617 + 0.777524i) q^{41} +(-5.87377 + 2.13788i) q^{43} +(-1.54289 + 9.89147i) q^{45} +(7.59919 - 1.33994i) q^{47} +(1.19492 - 2.06967i) q^{49} +(0.646288 + 0.293616i) q^{51} +(-0.220516 - 0.0802612i) q^{53} +(-3.62525 + 20.5598i) q^{55} +(7.43301 + 1.32301i) q^{57} +(-0.930375 + 5.27642i) q^{59} +(7.30705 + 2.65955i) q^{61} +(0.127515 + 6.44012i) q^{63} +(6.65050 - 11.5190i) q^{65} +(-3.48689 + 0.614832i) q^{67} +(-0.802953 + 1.17124i) q^{69} +(-4.19799 + 1.52794i) q^{71} +(-4.33185 - 3.63485i) q^{73} +(9.58679 - 4.58646i) q^{75} +13.4328i q^{77} +(8.05412 - 9.59853i) q^{79} +(4.80501 + 7.60999i) q^{81} +(-8.01579 + 4.62792i) q^{83} +(-0.237488 - 1.34686i) q^{85} +(0.620710 - 8.00685i) q^{87} +(-5.61888 + 4.71480i) q^{89} +(2.92708 - 8.04207i) q^{91} +(-3.90331 + 1.08741i) q^{93} +(-5.99513 - 13.2528i) q^{95} +(-16.0734 - 2.83418i) q^{97} +(9.70416 + 16.0650i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{3} - 3 q^{9}+O(q^{10}) \) 18 * q - 3 * q^3 - 3 * q^9	\( 18 q - 3 q^{3} - 3 q^{9} - 12 q^{13} - 18 q^{15} + 6 q^{17} + 6 q^{19} - 18 q^{25} + 6 q^{27} - 6 q^{29} - 24 q^{33} + 24 q^{35} - 6 q^{39} + 3 q^{41} + 6 q^{43} - 54 q^{45} - 30 q^{47} + 21 q^{49} - 42 q^{51} - 60 q^{53} - 30 q^{55} + 12 q^{57} - 3 q^{59} + 54 q^{61} + 18 q^{63} + 24 q^{65} + 15 q^{67} + 30 q^{69} - 36 q^{71} - 42 q^{73} + 6 q^{79} - 3 q^{81} - 36 q^{83} - 60 q^{89} + 18 q^{91} - 66 q^{93} - 6 q^{95} + 9 q^{97} + 102 q^{99}+O(q^{100}) \) 18 * q - 3 * q^3 - 3 * q^9 - 12 * q^13 - 18 * q^15 + 6 * q^17 + 6 * q^19 - 18 * q^25 + 6 * q^27 - 6 * q^29 - 24 * q^33 + 24 * q^35 - 6 * q^39 + 3 * q^41 + 6 * q^43 - 54 * q^45 - 30 * q^47 + 21 * q^49 - 42 * q^51 - 60 * q^53 - 30 * q^55 + 12 * q^57 - 3 * q^59 + 54 * q^61 + 18 * q^63 + 24 * q^65 + 15 * q^67 + 30 * q^69 - 36 * q^71 - 42 * q^73 + 6 * q^79 - 3 * q^81 - 36 * q^83 - 60 * q^89 + 18 * q^91 - 66 * q^93 - 6 * q^95 + 9 * q^97 + 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more