LMFDB - Embedded newform 912.2.bn.h.65.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(65,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("912.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bn (of order $6$, degree $2$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.1
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	912.65
Dual form			912.2.bn.h.449.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72474 - 0.158919i) q^{3} +(-1.22474 - 0.707107i) q^{5} +0.449490 q^{7} +(2.94949 + 0.548188i) q^{9} +O(q^{10})$	\(q+(-1.72474 - 0.158919i) q^{3} +(-1.22474 - 0.707107i) q^{5} +0.449490 q^{7} +(2.94949 + 0.548188i) q^{9} -3.14626i q^{11} +(-3.00000 + 1.73205i) q^{13} +(2.00000 + 1.41421i) q^{15} +(-0.550510 - 0.317837i) q^{17} +(-3.17423 + 2.98735i) q^{19} +(-0.775255 - 0.0714323i) q^{21} +(6.12372 - 3.53553i) q^{23} +(-1.50000 - 2.59808i) q^{25} +(-5.00000 - 1.41421i) q^{27} +(1.22474 + 2.12132i) q^{29} +4.24264i q^{31} +(-0.500000 + 5.42650i) q^{33} +(-0.550510 - 0.317837i) q^{35} +7.70674i q^{37} +(5.44949 - 2.51059i) q^{39} +(-1.50000 + 2.59808i) q^{41} +(-4.44949 + 7.70674i) q^{43} +(-3.22474 - 2.75699i) q^{45} +(-11.5732 + 6.68180i) q^{47} -6.79796 q^{49} +(0.898979 + 0.635674i) q^{51} +(-5.44949 - 9.43879i) q^{53} +(-2.22474 + 3.85337i) q^{55} +(5.94949 - 4.64796i) q^{57} +(-5.72474 + 9.91555i) q^{59} +(0.775255 + 1.34278i) q^{61} +(1.32577 + 0.246405i) q^{63} +4.89898 q^{65} +(-2.17423 + 1.25529i) q^{67} +(-11.1237 + 5.12472i) q^{69} +(-3.00000 + 5.19615i) q^{71} +(-4.39898 + 7.61926i) q^{73} +(2.17423 + 4.71940i) q^{75} -1.41421i q^{77} +(7.34847 + 4.24264i) q^{79} +(8.39898 + 3.23375i) q^{81} -17.0027i q^{83} +(0.449490 + 0.778539i) q^{85} +(-1.77526 - 3.85337i) q^{87} +(3.55051 + 6.14966i) q^{89} +(-1.34847 + 0.778539i) q^{91} +(0.674235 - 7.31747i) q^{93} +(6.00000 - 1.41421i) q^{95} +(2.84847 + 1.64456i) q^{97} +(1.72474 - 9.27987i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 8 q^{7} + 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 - 8 * q^7 + 2 * q^9	$ 4 q - 2 q^{3} - 8 q^{7} + 2 q^{9} - 12 q^{13} + 8 q^{15} - 12 q^{17} + 2 q^{19} - 8 q^{21} - 6 q^{25} - 20 q^{27} - 2 q^{33} - 12 q^{35} + 12 q^{39} - 6 q^{41} - 8 q^{43} - 8 q^{45} - 12 q^{47} + 12 q^{49} - 16 q^{51} - 12 q^{53} - 4 q^{55} + 14 q^{57} - 18 q^{59} + 8 q^{61} + 20 q^{63} + 6 q^{67} - 20 q^{69} - 12 q^{71} + 2 q^{73} - 6 q^{75} + 14 q^{81} - 8 q^{85} - 12 q^{87} + 24 q^{89} + 24 q^{91} - 12 q^{93} + 24 q^{95} - 18 q^{97} + 2 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 8 * q^7 + 2 * q^9 - 12 * q^13 + 8 * q^15 - 12 * q^17 + 2 * q^19 - 8 * q^21 - 6 * q^25 - 20 * q^27 - 2 * q^33 - 12 * q^35 + 12 * q^39 - 6 * q^41 - 8 * q^43 - 8 * q^45 - 12 * q^47 + 12 * q^49 - 16 * q^51 - 12 * q^53 - 4 * q^55 + 14 * q^57 - 18 * q^59 + 8 * q^61 + 20 * q^63 + 6 * q^67 - 20 * q^69 - 12 * q^71 + 2 * q^73 - 6 * q^75 + 14 * q^81 - 8 * q^85 - 12 * q^87 + 24 * q^89 + 24 * q^91 - 12 * q^93 + 24 * q^95 - 18 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$1$

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
$3$	−1.72474	−	0.158919i	−0.995782	−	0.0917517i
$3$	−1.72474	−	0.158919i	−0.995782	−	0.0917517i
$4$		0			0
$5$	−1.22474	−	0.707107i	−0.547723	−	0.316228i	0.200480	−	0.979698i	$-0.435750\pi$
$5$	−1.22474	−	0.707107i	−0.547723	−	0.316228i	−0.748203	+	0.663470i	$0.769083\pi$
$6$		0			0
$7$	0.449490			0.169891			0.0849456	−	0.996386i	$-0.472928\pi$
$7$	0.449490			0.169891			0.0849456	+	0.996386i	$0.472928\pi$
$8$		0			0
$9$	2.94949	+	0.548188i	0.983163	+	0.182729i
$10$		0			0
$11$		−	3.14626i		−	0.948634i	−0.880354	−	0.474317i	$-0.842695\pi$
$11$		−	3.14626i		−	0.948634i	0.880354	−	0.474317i	$-0.157305\pi$
$12$		0			0
$13$	−3.00000	+	1.73205i	−0.832050	+	0.480384i	−0.854554	−	0.519362i	$-0.826170\pi$
$13$	−3.00000	+	1.73205i	−0.832050	+	0.480384i	0.0225039	+	0.999747i	$0.492836\pi$
$14$		0			0
$15$	2.00000	+	1.41421i	0.516398	+	0.365148i
$16$		0			0
$17$	−0.550510	−	0.317837i	−0.133518	−	0.0770869i	0.431753	−	0.901992i	$-0.357895\pi$
$17$	−0.550510	−	0.317837i	−0.133518	−	0.0770869i	−0.565271	+	0.824905i	$0.691229\pi$
$18$		0			0
$19$	−3.17423	+	2.98735i	−0.728219	+	0.685344i
$19$	−3.17423	+	2.98735i	−0.728219	+	0.685344i
$20$		0			0
$21$	−0.775255	−	0.0714323i	−0.169175	−	0.0155878i
$22$		0			0
$23$	6.12372	−	3.53553i	1.27688	−	0.737210i	0.300610	−	0.953747i	$-0.402810\pi$
$23$	6.12372	−	3.53553i	1.27688	−	0.737210i	0.976274	+	0.216537i	$0.0694763\pi$
$24$		0			0
$25$	−1.50000	−	2.59808i	−0.300000	−	0.519615i
$26$		0			0
$27$	−5.00000	−	1.41421i	−0.962250	−	0.272166i
$28$		0			0
$29$	1.22474	+	2.12132i	0.227429	+	0.393919i	0.957046	−	0.289938i	$-0.0936346\pi$
$29$	1.22474	+	2.12132i	0.227429	+	0.393919i	−0.729616	+	0.683857i	$0.760301\pi$
$30$		0			0
$31$			4.24264i			0.762001i	0.924575	+	0.381000i	$0.124420\pi$
$31$			4.24264i			0.762001i	−0.924575	+	0.381000i	$0.875580\pi$
$32$		0			0
$33$	−0.500000	+	5.42650i	−0.0870388	+	0.944633i
$34$		0			0
$35$	−0.550510	−	0.317837i	−0.0930532	−	0.0537243i
$36$		0			0
$37$			7.70674i			1.26698i	0.773751	+	0.633490i	$0.218378\pi$
$37$			7.70674i			1.26698i	−0.773751	+	0.633490i	$0.781622\pi$
$38$		0			0
$39$	5.44949	−	2.51059i	0.872617	−	0.402016i
$40$		0			0
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$		0			0
$43$	−4.44949	+	7.70674i	−0.678541	+	1.17527i	0.296880	+	0.954915i	$0.404054\pi$
$43$	−4.44949	+	7.70674i	−0.678541	+	1.17527i	−0.975420	+	0.220352i	$0.929279\pi$
$44$		0			0
$45$	−3.22474	−	2.75699i	−0.480717	−	0.410989i
$46$		0			0
$47$	−11.5732	+	6.68180i	−1.68813	+	0.974640i	−0.732175	+	0.681117i	$0.761495\pi$
$47$	−11.5732	+	6.68180i	−1.68813	+	0.974640i	−0.955952	+	0.293524i	$0.905172\pi$
$48$		0			0
$49$	−6.79796			−0.971137
$50$		0			0
$51$	0.898979	+	0.635674i	0.125882	+	0.0890122i
$52$		0			0
$53$	−5.44949	−	9.43879i	−0.748545	−	1.29652i	−0.948520	−	0.316717i	$-0.897419\pi$
$53$	−5.44949	−	9.43879i	−0.748545	−	1.29652i	0.199975	−	0.979801i	$-0.435914\pi$
$54$		0			0
$55$	−2.22474	+	3.85337i	−0.299985	+	0.519588i
$56$		0			0
$57$	5.94949	−	4.64796i	0.788029	−	0.615638i
$58$		0			0
$59$	−5.72474	+	9.91555i	−0.745298	+	1.29089i	0.204757	+	0.978813i	$0.434360\pi$
$59$	−5.72474	+	9.91555i	−0.745298	+	1.29089i	−0.950055	+	0.312082i	$0.898974\pi$
$60$		0			0
$61$	0.775255	+	1.34278i	0.0992612	+	0.171926i	0.911379	−	0.411568i	$-0.135019\pi$
$61$	0.775255	+	1.34278i	0.0992612	+	0.171926i	−0.812118	+	0.583493i	$0.801685\pi$
$62$		0			0
$63$	1.32577	+	0.246405i	0.167031	+	0.0310441i
$64$		0			0
$65$	4.89898			0.607644
$66$		0			0
$67$	−2.17423	+	1.25529i	−0.265625	+	0.153359i	−0.626898	−	0.779101i	$-0.715676\pi$
$67$	−2.17423	+	1.25529i	−0.265625	+	0.153359i	0.361273	+	0.932460i	$0.382342\pi$
$68$		0			0
$69$	−11.1237	+	5.12472i	−1.33914	+	0.616944i
$70$		0			0
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$		0			0
$73$	−4.39898	+	7.61926i	−0.514862	+	0.891766i	0.484990	+	0.874520i	$0.338823\pi$
$73$	−4.39898	+	7.61926i	−0.514862	+	0.891766i	−0.999851	+	0.0172466i	$0.994510\pi$
$74$		0			0
$75$	2.17423	+	4.71940i	0.251059	+	0.544949i
$76$		0			0
$77$		−	1.41421i		−	0.161165i
$78$		0			0
$79$	7.34847	+	4.24264i	0.826767	+	0.477334i	0.852745	−	0.522328i	$-0.174936\pi$
$79$	7.34847	+	4.24264i	0.826767	+	0.477334i	−0.0259772	+	0.999663i	$0.508270\pi$
$80$		0			0
$81$	8.39898	+	3.23375i	0.933220	+	0.359306i
$82$		0			0
$83$		−	17.0027i		−	1.86629i	−0.359506	−	0.933143i	$-0.617055\pi$
$83$		−	17.0027i		−	1.86629i	0.359506	−	0.933143i	$-0.382945\pi$
$84$		0			0
$85$	0.449490	+	0.778539i	0.0487540	+	0.0844444i
$86$		0			0
$87$	−1.77526	−	3.85337i	−0.190327	−	0.413125i
$88$		0			0
$89$	3.55051	+	6.14966i	0.376353	+	0.651863i	0.990529	−	0.137307i	$-0.0438445\pi$
$89$	3.55051	+	6.14966i	0.376353	+	0.651863i	−0.614175	+	0.789170i	$0.710511\pi$
$90$		0			0
$91$	−1.34847	+	0.778539i	−0.141358	+	0.0816131i
$92$		0			0
$93$	0.674235	−	7.31747i	0.0699149	−	0.758787i
$94$		0			0
$95$	6.00000	−	1.41421i	0.615587	−	0.145095i
$96$		0			0
$97$	2.84847	+	1.64456i	0.289218	+	0.166980i	0.637589	−	0.770377i	$-0.279932\pi$
$97$	2.84847	+	1.64456i	0.289218	+	0.166980i	−0.348371	+	0.937357i	$0.613265\pi$
$98$		0			0
$99$	1.72474	−	9.27987i	0.173343	−	0.932662i
$100$		0			0
$101$	8.57321	−	4.94975i	0.853067	−	0.492518i	−0.00861771	−	0.999963i	$-0.502743\pi$
$101$	8.57321	−	4.94975i	0.853067	−	0.492518i	0.861684	+	0.507445i	$0.169410\pi$
$102$		0			0
$103$		−	5.02118i		−	0.494752i	−0.968920	−	0.247376i	$-0.920432\pi$
$103$		−	5.02118i		−	0.494752i	0.968920	−	0.247376i	$-0.0795682\pi$
$104$		0			0
$105$	0.898979	+	0.635674i	0.0877314	+	0.0620355i
$106$		0			0
$107$	4.89898			0.473602			0.236801	−	0.971558i	$-0.423901\pi$
$107$	4.89898			0.473602			0.236801	+	0.971558i	$0.423901\pi$
$108$		0			0
$109$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$109$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$110$		0			0
$111$	1.22474	−	13.2922i	0.116248	−	1.26164i
$112$		0			0
$113$	−18.7980			−1.76836			−0.884182	−	0.467143i	$-0.845283\pi$
$113$	−18.7980			−1.76836			−0.884182	+	0.467143i	$0.845283\pi$
$114$		0			0
$115$	−10.0000			−0.932505
$116$		0			0
$117$	−9.79796	+	3.46410i	−0.905822	+	0.320256i
$118$		0			0
$119$	−0.247449	−	0.142865i	−0.0226836	−	0.0130964i
$120$		0			0
$121$	1.10102			0.100093
$122$		0			0
$123$	3.00000	−	4.24264i	0.270501	−	0.382546i
$124$		0			0
$125$			11.3137i			1.01193i
$126$		0			0
$127$	9.00000	−	5.19615i	0.798621	−	0.461084i	−0.0443678	−	0.999015i	$-0.514127\pi$
$127$	9.00000	−	5.19615i	0.798621	−	0.461084i	0.842989	+	0.537931i	$0.180794\pi$
$128$		0			0
$129$	8.89898	−	12.5851i	0.783511	−	1.10805i
$130$		0			0
$131$	−1.92679	−	1.11243i	−0.168344	−	0.0971935i	0.413461	−	0.910522i	$-0.364320\pi$
$131$	−1.92679	−	1.11243i	−0.168344	−	0.0971935i	−0.581805	+	0.813328i	$0.697653\pi$
$132$		0			0
$133$	−1.42679	+	1.34278i	−0.123718	+	0.116434i
$134$		0			0
$135$	5.12372	+	5.26758i	0.440980	+	0.453362i
$136$		0			0
$137$	3.39898	−	1.96240i	0.290394	−	0.167659i	−0.347725	−	0.937596i	$-0.613046\pi$
$137$	3.39898	−	1.96240i	0.290394	−	0.167659i	0.638120	+	0.769937i	$0.279712\pi$
$138$		0			0
$139$	−7.17423	−	12.4261i	−0.608511	−	1.05397i	−0.991486	−	0.130213i	$-0.958434\pi$
$139$	−7.17423	−	12.4261i	−0.608511	−	1.05397i	0.382975	−	0.923759i	$-0.374899\pi$
$140$		0			0
$141$	21.0227	−	9.68520i	1.77043	−	0.815641i
$142$		0			0
$143$	5.44949	+	9.43879i	0.455709	+	0.789312i
$144$		0			0
$145$		−	3.46410i		−	0.287678i
$146$		0			0
$147$	11.7247	+	1.08032i	0.967041	+	0.0891035i
$148$		0			0
$149$	1.77526	+	1.02494i	0.145435	+	0.0839667i	0.570952	−	0.820984i	$-0.306574\pi$
$149$	1.77526	+	1.02494i	0.145435	+	0.0839667i	−0.425517	+	0.904950i	$0.639908\pi$
$150$		0			0
$151$		−	9.61377i		−	0.782357i	−0.920315	−	0.391179i	$-0.872067\pi$
$151$		−	9.61377i		−	0.782357i	0.920315	−	0.391179i	$-0.127933\pi$
$152$		0			0
$153$	−1.44949	−	1.23924i	−0.117184	−	0.100187i
$154$		0			0
$155$	3.00000	−	5.19615i	0.240966	−	0.417365i
$156$		0			0
$157$	−5.34847	+	9.26382i	−0.426854	+	0.739333i	−0.996592	−	0.0824935i	$-0.973712\pi$
$157$	−5.34847	+	9.26382i	−0.426854	+	0.739333i	0.569737	+	0.821827i	$0.307045\pi$
$158$		0			0
$159$	7.89898	+	17.1455i	0.626430	+	1.35973i
$160$		0			0
$161$	2.75255	−	1.58919i	0.216931	−	0.125245i
$162$		0			0
$163$	−18.3485			−1.43716			−0.718582	−	0.695443i	$-0.755208\pi$
$163$	−18.3485			−1.43716			−0.718582	+	0.695443i	$0.755208\pi$
$164$		0			0
$165$	4.44949	−	6.29253i	0.346392	−	0.489873i
$166$		0			0
$167$	2.44949	+	4.24264i	0.189547	+	0.328305i	0.945099	−	0.326783i	$-0.105965\pi$
$167$	2.44949	+	4.24264i	0.189547	+	0.328305i	−0.755552	+	0.655089i	$0.772631\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$		0			0
$171$	−11.0000	+	7.07107i	−0.841191	+	0.540738i
$172$		0			0
$173$	0.550510	−	0.953512i	0.0418545	−	0.0724942i	−0.844339	−	0.535809i	$-0.820007\pi$
$173$	0.550510	−	0.953512i	0.0418545	−	0.0724942i	0.886194	+	0.463315i	$0.153340\pi$
$174$		0			0
$175$	−0.674235	−	1.16781i	−0.0509673	−	0.0882780i
$176$		0			0
$177$	11.4495	−	16.1920i	0.860596	−	1.21707i
$178$		0			0
$179$	7.65153			0.571902			0.285951	−	0.958244i	$-0.407690\pi$
$179$	7.65153			0.571902			0.285951	+	0.958244i	$0.407690\pi$
$180$		0			0
$181$	18.6742	−	10.7816i	1.38804	−	0.801388i	0.394950	−	0.918703i	$-0.370762\pi$
$181$	18.6742	−	10.7816i	1.38804	−	0.801388i	0.993095	+	0.117314i	$0.0374285\pi$
$182$		0			0
$183$	−1.12372	−	2.43916i	−0.0830681	−	0.180308i
$184$		0			0
$185$	5.44949	−	9.43879i	0.400654	−	0.693954i
$186$		0			0
$187$	−1.00000	+	1.73205i	−0.0731272	+	0.126660i
$188$		0			0
$189$	−2.24745	−	0.635674i	−0.163478	−	0.0462385i
$190$		0			0
$191$			8.19955i			0.593299i	0.954986	+	0.296649i	$0.0958693\pi$
$191$			8.19955i			0.593299i	−0.954986	+	0.296649i	$0.904131\pi$
$192$		0			0
$193$	−22.3485	−	12.9029i	−1.60868	−	0.928771i	−0.989666	−	0.143389i	$-0.954200\pi$
$193$	−22.3485	−	12.9029i	−1.60868	−	0.928771i	−0.619012	−	0.785382i	$-0.712467\pi$
$194$		0			0
$195$	−8.44949	−	0.778539i	−0.605081	−	0.0557523i
$196$		0			0
$197$			20.2918i			1.44573i	0.690989	+	0.722865i	$0.257175\pi$
$197$			20.2918i			1.44573i	−0.690989	+	0.722865i	$0.742825\pi$
$198$		0			0
$199$	−1.44949	−	2.51059i	−0.102752	−	0.177971i	0.810066	−	0.586339i	$-0.199431\pi$
$199$	−1.44949	−	2.51059i	−0.102752	−	0.177971i	−0.912817	+	0.408368i	$0.866098\pi$
$200$		0			0
$201$	3.94949	−	1.81954i	0.278576	−	0.128340i
$202$		0			0
$203$	0.550510	+	0.953512i	0.0386382	+	0.0669234i
$204$		0			0
$205$	3.67423	−	2.12132i	0.256620	−	0.148159i
$206$		0			0
$207$	20.0000	−	7.07107i	1.39010	−	0.491473i
$208$		0			0
$209$	9.39898	+	9.98698i	0.650141	+	0.690814i
$210$		0			0
$211$	1.34847	+	0.778539i	0.0928325	+	0.0535968i	0.545698	−	0.837982i	$-0.316265\pi$
$211$	1.34847	+	0.778539i	0.0928325	+	0.0535968i	−0.452865	+	0.891579i	$0.649598\pi$
$212$		0			0
$213$	6.00000	−	8.48528i	0.411113	−	0.581402i
$214$		0			0
$215$	10.8990	−	6.29253i	0.743304	−	0.429147i
$216$		0			0
$217$			1.90702i			0.129457i
$218$		0			0
$219$	8.79796	−	12.4422i	0.594511	−	0.840765i
$220$		0			0
$221$	2.20204			0.148125
$222$		0			0
$223$	15.6742	+	9.04952i	1.04962	+	0.606001i	0.922544	−	0.385892i	$-0.126106\pi$
$223$	15.6742	+	9.04952i	1.04962	+	0.606001i	0.127080	+	0.991892i	$0.459439\pi$
$224$		0			0
$225$	−3.00000	−	8.48528i	−0.200000	−	0.565685i
$226$		0			0
$227$	−0.550510			−0.0365386			−0.0182693	−	0.999833i	$-0.505816\pi$
$227$	−0.550510			−0.0365386			−0.0182693	+	0.999833i	$0.505816\pi$
$228$		0			0
$229$	0.898979			0.0594062			0.0297031	−	0.999559i	$-0.490544\pi$
$229$	0.898979			0.0594062			0.0297031	+	0.999559i	$0.490544\pi$
$230$		0			0
$231$	−0.224745	+	2.43916i	−0.0147871	+	0.160485i
$232$		0			0
$233$	−15.3990	−	8.89060i	−1.00882	−	0.582443i	−0.0979745	−	0.995189i	$-0.531236\pi$
$233$	−15.3990	−	8.89060i	−1.00882	−	0.582443i	−0.910846	+	0.412746i	$0.864570\pi$
$234$		0			0
$235$	18.8990			1.23283
$236$		0			0
$237$	−12.0000	−	8.48528i	−0.779484	−	0.551178i
$238$		0			0
$239$		−	21.0703i		−	1.36293i	−0.731852	−	0.681463i	$-0.761344\pi$
$239$		−	21.0703i		−	1.36293i	0.731852	−	0.681463i	$-0.238656\pi$
$240$		0			0
$241$	−5.84847	+	3.37662i	−0.376733	+	0.217507i	−0.676396	−	0.736538i	$-0.736459\pi$
$241$	−5.84847	+	3.37662i	−0.376733	+	0.217507i	0.299663	+	0.954045i	$0.403126\pi$
$242$		0			0
$243$	−13.9722	−	6.91215i	−0.896317	−	0.443415i
$244$		0			0
$245$	8.32577	+	4.80688i	0.531914	+	0.307100i
$246$		0			0
$247$	4.34847	−	14.4600i	0.276686	−	0.920066i
$248$		0			0
$249$	−2.70204	+	29.3253i	−0.171235	+	1.85841i
$250$		0			0
$251$	3.27526	−	1.89097i	0.206732	−	0.119357i	−0.393060	−	0.919513i	$-0.628583\pi$
$251$	3.27526	−	1.89097i	0.206732	−	0.119357i	0.599792	+	0.800156i	$0.295250\pi$
$252$		0			0
$253$	−11.1237	−	19.2669i	−0.699343	−	1.21130i
$254$		0			0
$255$	−0.651531	−	1.41421i	−0.0408004	−	0.0885615i
$256$		0			0
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	0.531487	−	0.847066i	$-0.321633\pi$
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	−0.999325	+	0.0367485i	$0.988300\pi$
$258$		0			0
$259$			3.46410i			0.215249i
$260$		0			0
$261$	2.44949	+	6.92820i	0.151620	+	0.428845i
$262$		0			0
$263$	−7.77526	−	4.48905i	−0.479443	−	0.276806i	0.240741	−	0.970589i	$-0.422609\pi$
$263$	−7.77526	−	4.48905i	−0.479443	−	0.276806i	−0.720184	+	0.693783i	$0.755943\pi$
$264$		0			0
$265$			15.4135i			0.946843i
$266$		0			0
$267$	−5.14643	−	11.1708i	−0.314956	−	0.683645i
$268$		0			0
$269$	12.2474	−	21.2132i	0.746740	−	1.29339i	−0.202637	−	0.979254i	$-0.564951\pi$
$269$	12.2474	−	21.2132i	0.746740	−	1.29339i	0.949377	−	0.314138i	$-0.101715\pi$
$270$		0			0
$271$	−10.0227	+	17.3598i	−0.608836	+	1.05453i	0.382597	+	0.923915i	$0.375030\pi$
$271$	−10.0227	+	17.3598i	−0.608836	+	1.05453i	−0.991433	+	0.130619i	$0.958303\pi$
$272$		0			0
$273$	2.44949	−	1.12848i	0.148250	−	0.0682990i
$274$		0			0
$275$	−8.17423	+	4.71940i	−0.492925	+	0.284590i
$276$		0			0
$277$	20.2474			1.21655			0.608276	−	0.793726i	$-0.291862\pi$
$277$	20.2474			1.21655			0.608276	+	0.793726i	$0.291862\pi$
$278$		0			0
$279$	−2.32577	+	12.5136i	−0.139240	+	0.749171i
$280$		0			0
$281$	11.2980	+	19.5686i	0.673980	+	1.16737i	0.976766	+	0.214309i	$0.0687498\pi$
$281$	11.2980	+	19.5686i	0.673980	+	1.16737i	−0.302786	+	0.953058i	$0.597917\pi$
$282$		0			0
$283$	−4.72474	+	8.18350i	−0.280857	+	0.486458i	−0.971596	−	0.236646i	$-0.923952\pi$
$283$	−4.72474	+	8.18350i	−0.280857	+	0.486458i	0.690739	+	0.723104i	$0.257285\pi$
$284$		0			0
$285$	−10.5732	+	1.48565i	−0.626303	+	0.0880021i
$286$		0			0
$287$	−0.674235	+	1.16781i	−0.0397988	+	0.0689336i
$288$		0			0
$289$	−8.29796	−	14.3725i	−0.488115	−	0.845440i
$290$		0			0
$291$	−4.65153	−	3.28913i	−0.272678	−	0.192812i
$292$		0			0
$293$	−19.3485			−1.13035			−0.565175	−	0.824971i	$-0.691191\pi$
$293$	−19.3485			−1.13035			−0.565175	+	0.824971i	$0.691191\pi$
$294$		0			0
$295$	14.0227	−	8.09601i	0.816433	−	0.471368i
$296$		0			0
$297$	−4.44949	+	15.7313i	−0.258186	+	0.912824i
$298$		0			0
$299$	−12.2474	+	21.2132i	−0.708288	+	1.22679i
$300$		0			0
$301$	−2.00000	+	3.46410i	−0.115278	+	0.199667i
$302$		0			0
$303$	−15.5732	+	7.17461i	−0.894658	+	0.412170i
$304$		0			0
$305$		−	2.19275i		−	0.125557i
$306$		0			0
$307$	−18.5227	−	10.6941i	−1.05715	−	0.610344i	−0.132505	−	0.991182i	$-0.542302\pi$
$307$	−18.5227	−	10.6941i	−1.05715	−	0.610344i	−0.924642	+	0.380838i	$0.875635\pi$
$308$		0			0
$309$	−0.797959	+	8.66025i	−0.0453943	+	0.492665i
$310$		0			0
$311$			15.5563i			0.882120i	0.897478	+	0.441060i	$0.145397\pi$
$311$			15.5563i			0.882120i	−0.897478	+	0.441060i	$0.854603\pi$
$312$		0			0
$313$	9.50000	+	16.4545i	0.536972	+	0.930062i	0.999065	+	0.0432311i	$0.0137652\pi$
$313$	9.50000	+	16.4545i	0.536972	+	0.930062i	−0.462093	+	0.886831i	$0.652902\pi$
$314$		0			0
$315$	−1.44949	−	1.23924i	−0.0816695	−	0.0698233i
$316$		0			0
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	0.769395	−	0.638774i	$-0.220558\pi$
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	−0.937892	+	0.346929i	$0.887225\pi$
$318$		0			0
$319$	6.67423	−	3.85337i	0.373685	−	0.215747i
$320$		0			0
$321$	−8.44949	−	0.778539i	−0.471605	−	0.0434538i
$322$		0			0
$323$	2.69694	−	0.635674i	0.150062	−	0.0353699i
$324$		0			0
$325$	9.00000	+	5.19615i	0.499230	+	0.288231i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−5.20204	+	3.00340i	−0.286798	+	0.165583i
$330$		0			0
$331$			23.2952i			1.28042i	0.768200	+	0.640210i	$0.221153\pi$
$331$			23.2952i			1.28042i	−0.768200	+	0.640210i	$0.778847\pi$
$332$		0			0
$333$	−4.22474	+	22.7310i	−0.231515	+	1.24565i
$334$		0			0
$335$	3.55051			0.193985
$336$		0			0
$337$	−17.8485	−	10.3048i	−0.972268	−	0.561339i	−0.0723411	−	0.997380i	$-0.523047\pi$
$337$	−17.8485	−	10.3048i	−0.972268	−	0.561339i	−0.899927	+	0.436041i	$0.856380\pi$
$338$		0			0
$339$	32.4217	+	2.98735i	1.76090	+	0.162250i
$340$		0			0
$341$	13.3485			0.722860
$342$		0			0
$343$	−6.20204			−0.334879
$344$		0			0
$345$	17.2474	+	1.58919i	0.928571	+	0.0855589i
$346$		0			0
$347$	−3.27526	−	1.89097i	−0.175825	−	0.101513i	0.409505	−	0.912308i	$-0.365702\pi$
$347$	−3.27526	−	1.89097i	−0.175825	−	0.101513i	−0.585330	+	0.810795i	$0.699035\pi$
$348$		0			0
$349$	32.4949			1.73941			0.869706	−	0.493570i	$-0.164308\pi$
$349$	32.4949			1.73941			0.869706	+	0.493570i	$0.164308\pi$
$350$		0			0
$351$	17.4495	−	4.41761i	0.931385	−	0.235795i
$352$		0			0
$353$		−	24.9951i		−	1.33036i	−0.746684	−	0.665179i	$-0.768355\pi$
$353$		−	24.9951i		−	1.33036i	0.746684	−	0.665179i	$-0.231645\pi$
$354$		0			0
$355$	7.34847	−	4.24264i	0.390016	−	0.225176i
$356$		0			0
$357$	0.404082	+	0.285729i	0.0213863	+	0.0151224i
$358$		0			0
$359$	−20.8207	−	12.0208i	−1.09887	−	0.634434i	−0.162948	−	0.986635i	$-0.552100\pi$
$359$	−20.8207	−	12.0208i	−1.09887	−	0.634434i	−0.935925	+	0.352200i	$0.885434\pi$
$360$		0			0
$361$	1.15153	−	18.9651i	0.0606069	−	0.998162i
$362$		0			0
$363$	−1.89898	−	0.174973i	−0.0996706	−	0.00918368i
$364$		0			0
$365$	10.7753	−	6.22110i	0.564003	−	0.325627i
$366$		0			0
$367$	−4.32577	−	7.49245i	−0.225803	−	0.391102i	0.730757	−	0.682638i	$-0.239167\pi$
$367$	−4.32577	−	7.49245i	−0.225803	−	0.391102i	−0.956560	+	0.291535i	$0.905834\pi$
$368$		0			0
$369$	−5.84847	+	6.84072i	−0.304459	+	0.356113i
$370$		0			0
$371$	−2.44949	−	4.24264i	−0.127171	−	0.220267i
$372$		0			0
$373$			25.4558i			1.31805i	0.752119	+	0.659027i	$0.229032\pi$
$373$			25.4558i			1.31805i	−0.752119	+	0.659027i	$0.770968\pi$
$374$		0			0
$375$	1.79796	−	19.5133i	0.0928462	−	1.00766i
$376$		0			0
$377$	−7.34847	−	4.24264i	−0.378465	−	0.218507i
$378$		0			0
$379$			1.55708i			0.0799817i	0.999200	+	0.0399909i	$0.0127329\pi$
$379$			1.55708i			0.0799817i	−0.999200	+	0.0399909i	$0.987267\pi$
$380$		0			0
$381$	−16.3485	+	7.53177i	−0.837557	+	0.385864i
$382$		0			0
$383$	−10.2247	+	17.7098i	−0.522460	+	0.904927i	0.477198	+	0.878796i	$0.341652\pi$
$383$	−10.2247	+	17.7098i	−0.522460	+	0.904927i	−0.999659	+	0.0261318i	$0.991681\pi$
$384$		0			0
$385$	−1.00000	+	1.73205i	−0.0509647	+	0.0882735i
$386$		0			0
$387$	−17.3485	+	20.2918i	−0.881872	+	1.03149i
$388$		0			0
$389$	−13.1010	+	7.56388i	−0.664248	+	0.383504i	−0.793894	−	0.608057i	$-0.791949\pi$
$389$	−13.1010	+	7.56388i	−0.664248	+	0.383504i	0.129646	+	0.991560i	$0.458616\pi$
$390$		0			0
$391$	−4.49490			−0.227317
$392$		0			0
$393$	3.14643	+	2.22486i	0.158716	+	0.112229i
$394$		0			0
$395$	−6.00000	−	10.3923i	−0.301893	−	0.522894i
$396$		0			0
$397$	2.67423	−	4.63191i	0.134216	−	0.232469i	−0.791082	−	0.611711i	$-0.790482\pi$
$397$	2.67423	−	4.63191i	0.134216	−	0.232469i	0.925298	+	0.379242i	$0.123815\pi$
$398$		0			0
$399$	2.67423	−	2.08921i	0.133879	−	0.104591i
$400$		0			0
$401$	−3.39898	+	5.88721i	−0.169737	+	0.293993i	−0.938327	−	0.345748i	$-0.887625\pi$
$401$	−3.39898	+	5.88721i	−0.169737	+	0.293993i	0.768590	+	0.639741i	$0.220958\pi$
$402$		0			0
$403$	−7.34847	−	12.7279i	−0.366053	−	0.634023i
$404$		0			0
$405$	−8.00000	−	9.89949i	−0.397523	−	0.491910i
$406$		0			0
$407$	24.2474			1.20190
$408$		0			0
$409$	3.15153	−	1.81954i	0.155833	−	0.0899703i	−0.420056	−	0.907498i	$-0.637989\pi$
$409$	3.15153	−	1.81954i	0.155833	−	0.0899703i	0.575889	+	0.817528i	$0.304656\pi$
$410$		0			0
$411$	−6.17423	+	2.84448i	−0.304553	+	0.140308i
$412$		0			0
$413$	−2.57321	+	4.45694i	−0.126620	+	0.219312i
$414$		0			0
$415$	−12.0227	+	20.8239i	−0.590171	+	1.02221i
$416$		0			0
$417$	10.3990	+	22.5720i	0.509240	+	1.10536i
$418$		0			0
$419$		−	24.5344i		−	1.19859i	−0.800530	−	0.599293i	$-0.795448\pi$
$419$		−	24.5344i		−	1.19859i	0.800530	−	0.599293i	$-0.204552\pi$
$420$		0			0
$421$	−3.97730	−	2.29629i	−0.193842	−	0.111914i	0.399938	−	0.916542i	$-0.369032\pi$
$421$	−3.97730	−	2.29629i	−0.193842	−	0.111914i	−0.593780	+	0.804628i	$0.702365\pi$
$422$		0			0
$423$	−37.7980	+	13.3636i	−1.83780	+	0.649760i
$424$		0			0
$425$			1.90702i			0.0925042i
$426$		0			0
$427$	0.348469	+	0.603566i	0.0168636	+	0.0292086i
$428$		0			0
$429$	−7.89898	−	17.1455i	−0.381366	−	0.827794i
$430$		0			0
$431$	−1.65153	−	2.86054i	−0.0795514	−	0.137787i	0.823505	−	0.567309i	$-0.192015\pi$
$431$	−1.65153	−	2.86054i	−0.0795514	−	0.137787i	−0.903056	+	0.429522i	$0.858682\pi$
$432$		0			0
$433$	−17.6969	+	10.2173i	−0.850461	+	0.491014i	−0.860806	−	0.508933i	$-0.830040\pi$
$433$	−17.6969	+	10.2173i	−0.850461	+	0.491014i	0.0103456	+	0.999946i	$0.496707\pi$
$434$		0			0
$435$	−0.550510	+	5.97469i	−0.0263949	+	0.286465i
$436$		0			0
$437$	−8.87628	+	29.5163i	−0.424610	+	1.41196i
$438$		0			0
$439$	9.67423	+	5.58542i	0.461726	+	0.266578i	0.712770	−	0.701398i	$-0.247440\pi$
$439$	9.67423	+	5.58542i	0.461726	+	0.266578i	−0.251044	+	0.967976i	$0.580774\pi$
$440$		0			0
$441$	−20.0505	−	3.72656i	−0.954786	−	0.177455i
$442$		0			0
$443$	16.3207	−	9.42274i	0.775418	−	0.447688i	−0.0593859	−	0.998235i	$-0.518914\pi$
$443$	16.3207	−	9.42274i	0.775418	−	0.447688i	0.834804	+	0.550547i	$0.185581\pi$
$444$		0			0
$445$		−	10.0424i		−	0.476053i
$446$		0			0
$447$	−2.89898	−	2.04989i	−0.137117	−	0.0969564i
$448$		0			0
$449$	30.7980			1.45345			0.726723	−	0.686931i	$-0.241042\pi$
$449$	30.7980			1.45345			0.726723	+	0.686931i	$0.241042\pi$
$450$		0			0
$451$	8.17423	+	4.71940i	0.384910	+	0.222228i
$452$		0			0
$453$	−1.52781	+	16.5813i	−0.0717826	+	0.779057i
$454$		0			0
$455$	2.20204			0.103233
$456$		0			0
$457$	−13.0000			−0.608114			−0.304057	−	0.952654i	$-0.598341\pi$
$457$	−13.0000			−0.608114			−0.304057	+	0.952654i	$0.598341\pi$
$458$		0			0
$459$	2.30306	+	2.36773i	0.107498	+	0.110516i
$460$		0			0
$461$	−33.2474	−	19.1954i	−1.54849	−	0.894020i	−0.998258	−	0.0590072i	$-0.981207\pi$
$461$	−33.2474	−	19.1954i	−1.54849	−	0.894020i	−0.550231	−	0.835013i	$-0.685460\pi$
$462$		0			0
$463$	19.7980			0.920089			0.460045	−	0.887896i	$-0.347833\pi$
$463$	19.7980			0.920089			0.460045	+	0.887896i	$0.347833\pi$
$464$		0			0
$465$	−6.00000	+	8.48528i	−0.278243	+	0.393496i
$466$		0			0
$467$			12.6172i			0.583853i	0.956441	+	0.291926i	$0.0942962\pi$
$467$			12.6172i			0.583853i	−0.956441	+	0.291926i	$0.905704\pi$
$468$		0			0
$469$	−0.977296	+	0.564242i	−0.0451273	+	0.0260543i
$470$		0			0
$471$	10.6969	−	15.1278i	0.492889	−	0.697050i
$472$		0			0
$473$	24.2474	+	13.9993i	1.11490	+	0.643687i
$474$		0			0
$475$	12.5227	+	3.76588i	0.574581	+	0.172791i
$476$		0			0
$477$	−10.8990	−	30.8270i	−0.499030	−	1.41147i
$478$		0			0
$479$	−0.853572	+	0.492810i	−0.0390007	+	0.0225171i	−0.519374	−	0.854547i	$-0.673835\pi$
$479$	−0.853572	+	0.492810i	−0.0390007	+	0.0225171i	0.480373	+	0.877064i	$0.340501\pi$
$480$		0			0
$481$	−13.3485	−	23.1202i	−0.608638	−	1.05419i
$482$		0			0
$483$	−5.00000	+	2.30351i	−0.227508	+	0.104813i
$484$		0			0
$485$	−2.32577	−	4.02834i	−0.105608	−	0.182918i
$486$		0			0
$487$			25.0273i			1.13409i	0.823686	+	0.567046i	$0.191914\pi$
$487$			25.0273i			1.13409i	−0.823686	+	0.567046i	$0.808086\pi$
$488$		0			0
$489$	31.6464	+	2.91591i	1.43110	+	0.131862i
$490$		0			0
$491$	13.8990	+	8.02458i	0.627252	+	0.362144i	0.779687	−	0.626169i	$-0.215378\pi$
$491$	13.8990	+	8.02458i	0.627252	+	0.362144i	−0.152435	+	0.988314i	$0.548711\pi$
$492$		0			0
$493$		−	1.55708i		−	0.0701273i
$494$		0			0
$495$	−8.67423	+	10.1459i	−0.389878	+	0.456024i
$496$		0			0
$497$	−1.34847	+	2.33562i	−0.0604871	+	0.104767i
$498$		0			0
$499$	3.72474	−	6.45145i	0.166742	−	0.288806i	−0.770530	−	0.637403i	$-0.780008\pi$
$499$	3.72474	−	6.45145i	0.166742	−	0.288806i	0.937273	+	0.348597i	$0.113342\pi$
$500$		0			0
$501$	−3.55051	−	7.70674i	−0.158625	−	0.344312i
$502$		0			0
$503$	13.4722	−	7.77817i	0.600695	−	0.346812i	−0.168620	−	0.985681i	$-0.553931\pi$
$503$	13.4722	−	7.77817i	0.600695	−	0.346812i	0.769315	+	0.638870i	$0.220598\pi$
$504$		0			0
$505$	−14.0000			−0.622992
$506$		0			0
$507$	1.00000	−	1.41421i	0.0444116	−	0.0628074i
$508$		0			0
$509$	8.69694	+	15.0635i	0.385485	+	0.667680i	0.991836	−	0.127517i	$-0.0407008\pi$
$509$	8.69694	+	15.0635i	0.385485	+	0.667680i	−0.606351	+	0.795197i	$0.707367\pi$
$510$		0			0
$511$	−1.97730	+	3.42478i	−0.0874704	+	0.151503i
$512$		0			0
$513$	20.0959	−	10.4477i	0.887256	−	0.461276i
$514$		0			0
$515$	−3.55051	+	6.14966i	−0.156454	+	0.270987i
$516$		0			0
$517$	21.0227	+	36.4124i	0.924577	+	1.60142i
$518$		0			0
$519$	−1.10102	+	1.55708i	−0.0483294	+	0.0683481i
$520$		0			0
$521$	−25.8990			−1.13465			−0.567327	−	0.823492i	$-0.692023\pi$
$521$	−25.8990			−1.13465			−0.567327	+	0.823492i	$0.692023\pi$
$522$		0			0
$523$	5.69694	−	3.28913i	0.249110	−	0.143824i	−0.370247	−	0.928933i	$-0.620727\pi$
$523$	5.69694	−	3.28913i	0.249110	−	0.143824i	0.619357	+	0.785110i	$0.287394\pi$
$524$		0			0
$525$	0.977296	+	2.12132i	0.0426527	+	0.0925820i
$526$		0			0
$527$	1.34847	−	2.33562i	0.0587402	−	0.101741i
$528$		0			0
$529$	13.5000	−	23.3827i	0.586957	−	1.01664i
$530$		0			0
$531$	−22.3207	+	26.1076i	−0.968634	+	1.13297i
$532$		0			0
$533$		−	10.3923i		−	0.450141i
$534$		0			0
$535$	−6.00000	−	3.46410i	−0.259403	−	0.149766i
$536$		0			0
$537$	−13.1969	−	1.21597i	−0.569490	−	0.0524730i
$538$		0			0
$539$			21.3882i			0.921254i
$540$		0			0
$541$	−5.34847	−	9.26382i	−0.229949	−	0.398283i	0.727844	−	0.685743i	$-0.240522\pi$
$541$	−5.34847	−	9.26382i	−0.229949	−	0.398283i	−0.957793	+	0.287460i	$0.907189\pi$
$542$		0			0
$543$	−33.9217	+	15.6278i	−1.45572	+	0.670652i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	32.3939	−	18.7026i	1.38506	−	0.799666i	0.392309	−	0.919834i	$-0.371677\pi$
$547$	32.3939	−	18.7026i	1.38506	−	0.799666i	0.992754	+	0.120168i	$0.0383432\pi$
$548$		0			0
$549$	1.55051	+	4.38551i	0.0661742	+	0.187169i
$550$		0			0
$551$	−10.2247	−	3.07483i	−0.435589	−	0.130992i
$552$		0			0
$553$	3.30306	+	1.90702i	0.140460	+	0.0810949i
$554$		0			0
$555$	−10.8990	+	15.4135i	−0.462636	+	0.654266i
$556$		0			0
$557$	0.247449	−	0.142865i	0.0104847	−	0.00605337i	−0.494748	−	0.869036i	$-0.664740\pi$
$557$	0.247449	−	0.142865i	0.0104847	−	0.00605337i	0.505233	+	0.862983i	$0.331406\pi$
$558$		0			0
$559$		−	30.8270i		−	1.30384i
$560$		0			0
$561$	2.00000	−	2.82843i	0.0844401	−	0.119416i
$562$		0			0
$563$	−40.8434			−1.72134			−0.860671	−	0.509161i	$-0.829956\pi$
$563$	−40.8434			−1.72134			−0.860671	+	0.509161i	$0.829956\pi$
$564$		0			0
$565$	23.0227	+	13.2922i	0.968572	+	0.559206i
$566$		0			0
$567$	3.77526	+	1.45354i	0.158546	+	0.0610428i
$568$		0			0
$569$	−34.2929			−1.43763			−0.718816	−	0.695201i	$-0.755315\pi$
$569$	−34.2929			−1.43763			−0.718816	+	0.695201i	$0.755315\pi$
$570$		0			0
$571$	−33.0454			−1.38291			−0.691454	−	0.722421i	$-0.743029\pi$
$571$	−33.0454			−1.38291			−0.691454	+	0.722421i	$0.743029\pi$
$572$		0			0
$573$	1.30306	−	14.1421i	0.0544362	−	0.590796i
$574$		0			0
$575$	−18.3712	−	10.6066i	−0.766131	−	0.442326i
$576$		0			0
$577$	18.5959			0.774158			0.387079	−	0.922047i	$-0.373484\pi$
$577$	18.5959			0.774158			0.387079	+	0.922047i	$0.373484\pi$
$578$		0			0
$579$	36.4949	+	25.8058i	1.51668	+	1.07245i
$580$		0			0
$581$		−	7.64253i		−	0.317065i
$582$		0			0
$583$	−29.6969	+	17.1455i	−1.22992	+	0.710096i
$584$		0			0
$585$	14.4495	+	2.68556i	0.597413	+	0.111034i
$586$		0			0
$587$	13.8990	+	8.02458i	0.573672	+	0.331210i	0.758615	−	0.651540i	$-0.225877\pi$
$587$	13.8990	+	8.02458i	0.573672	+	0.331210i	−0.184942	+	0.982749i	$0.559210\pi$
$588$		0			0
$589$	−12.6742	−	13.4671i	−0.522233	−	0.554904i
$590$		0			0
$591$	3.22474	−	34.9982i	0.132648	−	1.43963i
$592$		0			0
$593$	15.0959	−	8.71563i	0.619915	−	0.357908i	−0.156921	−	0.987611i	$-0.550157\pi$
$593$	15.0959	−	8.71563i	0.619915	−	0.357908i	0.776836	+	0.629703i	$0.216823\pi$
$594$		0			0
$595$	0.202041	+	0.349945i	0.00828287	+	0.0143464i
$596$		0			0
$597$	2.10102	+	4.56048i	0.0859890	+	0.186648i
$598$		0			0
$599$	2.57321	+	4.45694i	0.105139	+	0.182106i	0.913795	−	0.406176i	$-0.133138\pi$
$599$	2.57321	+	4.45694i	0.105139	+	0.182106i	−0.808656	+	0.588282i	$0.799805\pi$
$600$		0			0
$601$			14.0314i			0.572352i	0.958177	+	0.286176i	$0.0923842\pi$
$601$			14.0314i			0.572352i	−0.958177	+	0.286176i	$0.907616\pi$
$602$		0			0
$603$	−7.10102	+	2.51059i	−0.289176	+	0.102239i
$604$		0			0
$605$	−1.34847	−	0.778539i	−0.0548231	−	0.0316521i
$606$		0			0
$607$			11.5208i			0.467614i	0.972283	+	0.233807i	$0.0751185\pi$
$607$			11.5208i			0.467614i	−0.972283	+	0.233807i	$0.924882\pi$
$608$		0			0
$609$	−0.797959	−	1.73205i	−0.0323349	−	0.0701862i
$610$		0			0
$611$	23.1464	−	40.0908i	0.936404	−	1.62190i
$612$		0			0
$613$	−23.8990	+	41.3942i	−0.965271	+	1.67190i	−0.256385	+	0.966575i	$0.582531\pi$
$613$	−23.8990	+	41.3942i	−0.965271	+	1.67190i	−0.708886	+	0.705323i	$0.750802\pi$
$614$		0			0
$615$	−6.67423	+	3.07483i	−0.269131	+	0.123989i
$616$		0			0
$617$	8.05051	−	4.64796i	0.324101	−	0.187120i	−0.329118	−	0.944289i	$-0.606751\pi$
$617$	8.05051	−	4.64796i	0.324101	−	0.187120i	0.653219	+	0.757169i	$0.273418\pi$
$618$		0			0
$619$	30.6969			1.23381			0.616907	−	0.787036i	$-0.288385\pi$
$619$	30.6969			1.23381			0.616907	+	0.787036i	$0.288385\pi$
$620$		0			0
$621$	−35.6186	+	9.01742i	−1.42933	+	0.361856i
$622$		0			0
$623$	1.59592	+	2.76421i	0.0639391	+	0.110746i
$624$		0			0
$625$	0.500000	−	0.866025i	0.0200000	−	0.0346410i
$626$		0			0
$627$	−14.6237	−	18.7187i	−0.584015	−	0.747552i
$628$		0			0
$629$	2.44949	−	4.24264i	0.0976676	−	0.169165i
$630$		0			0
$631$	−17.1237	−	29.6592i	−0.681685	−	1.18071i	−0.974466	−	0.224533i	$-0.927914\pi$
$631$	−17.1237	−	29.6592i	−0.681685	−	1.18071i	0.292782	−	0.956179i	$-0.405419\pi$
$632$		0			0
$633$	−2.20204	−	1.55708i	−0.0875233	−	0.0618883i
$634$		0			0
$635$	−14.6969			−0.583230
$636$		0			0
$637$	20.3939	−	11.7744i	0.808035	−	0.466519i
$638$		0			0
$639$	−11.6969	+	13.6814i	−0.462724	+	0.541229i
$640$		0			0
$641$	−13.1969	+	22.8578i	−0.521248	+	0.902828i	0.478447	+	0.878116i	$0.341200\pi$
$641$	−13.1969	+	22.8578i	−0.521248	+	0.902828i	−0.999695	+	0.0247111i	$0.992133\pi$
$642$		0			0
$643$	5.07321	−	8.78706i	0.200068	−	0.346528i	−0.748482	−	0.663155i	$-0.769217\pi$
$643$	5.07321	−	8.78706i	0.200068	−	0.346528i	0.948550	+	0.316627i	$0.102550\pi$
$644$		0			0
$645$	−19.7980	+	9.12096i	−0.779544	+	0.359137i
$646$		0			0
$647$			14.7778i			0.580976i	0.956879	+	0.290488i	$0.0938176\pi$
$647$			14.7778i			0.580976i	−0.956879	+	0.290488i	$0.906182\pi$
$648$		0			0
$649$	31.1969	+	18.0116i	1.22459	+	0.707016i
$650$		0			0
$651$	0.303062	−	3.28913i	0.0118779	−	0.128911i
$652$		0			0
$653$		−	8.19955i		−	0.320873i	−0.987046	−	0.160437i	$-0.948710\pi$
$653$		−	8.19955i		−	0.320873i	0.987046	−	0.160437i	$-0.0512902\pi$
$654$		0			0
$655$	1.57321	+	2.72489i	0.0614706	+	0.106470i
$656$		0			0
$657$	−17.1515	+	20.0614i	−0.669145	+	0.782672i
$658$		0			0
$659$	12.0000	+	20.7846i	0.467454	+	0.809653i	0.999309	−	0.0371821i	$-0.0118382\pi$
$659$	12.0000	+	20.7846i	0.467454	+	0.809653i	−0.531855	+	0.846836i	$0.678505\pi$
$660$		0			0
$661$	25.7196	−	14.8492i	1.00038	−	0.577569i	0.0920180	−	0.995757i	$-0.470668\pi$
$661$	25.7196	−	14.8492i	1.00038	−	0.577569i	0.908360	+	0.418189i	$0.137335\pi$
$662$		0			0
$663$	−3.79796	−	0.349945i	−0.147501	−	0.0135908i
$664$		0			0
$665$	2.69694	−	0.635674i	0.104583	−	0.0246504i
$666$		0			0
$667$	15.0000	+	8.66025i	0.580802	+	0.335326i
$668$		0			0
$669$	−25.5959	−	18.0990i	−0.989595	−	0.699750i
$670$		0			0
$671$	4.22474	−	2.43916i	0.163094	−	0.0941626i
$672$		0			0
$673$		−	3.46410i		−	0.133531i	−0.997769	−	0.0667657i	$-0.978732\pi$
$673$		−	3.46410i		−	0.133531i	0.997769	−	0.0667657i	$-0.0212680\pi$
$674$		0			0
$675$	3.82577	+	15.1117i	0.147254	+	0.581650i
$676$		0			0
$677$	−32.6969			−1.25665			−0.628323	−	0.777953i	$-0.716258\pi$
$677$	−32.6969			−1.25665			−0.628323	+	0.777953i	$0.716258\pi$
$678$		0			0
$679$	1.28036	+	0.739215i	0.0491356	+	0.0283685i
$680$		0			0
$681$	0.949490	+	0.0874863i	0.0363845	+	0.00335248i
$682$		0			0
$683$	−17.3939			−0.665558			−0.332779	−	0.943005i	$-0.607986\pi$
$683$	−17.3939			−0.665558			−0.332779	+	0.943005i	$0.607986\pi$
$684$		0			0
$685$	−5.55051			−0.212074
$686$		0			0
$687$	−1.55051	−	0.142865i	−0.0591557	−	0.00545062i
$688$		0			0
$689$	32.6969	+	18.8776i	1.24565	+	0.719179i
$690$		0			0
$691$	40.0000			1.52167			0.760836	−	0.648944i	$-0.224789\pi$
$691$	40.0000			1.52167			0.760836	+	0.648944i	$0.224789\pi$
$692$		0			0
$693$	0.775255	−	4.17121i	0.0294495	−	0.158451i
$694$		0			0
$695$			20.2918i			0.769712i
$696$		0			0
$697$	1.65153	−	0.953512i	0.0625562	−	0.0361168i
$698$		0			0
$699$	25.1464	+	17.7812i	0.951125	+	0.672547i
$700$		0			0
$701$	−8.57321	−	4.94975i	−0.323806	−	0.186949i	0.329282	−	0.944232i	$-0.393193\pi$
$701$	−8.57321	−	4.94975i	−0.323806	−	0.186949i	−0.653088	+	0.757282i	$0.726527\pi$
$702$		0			0
$703$	−23.0227	−	24.4630i	−0.868318	−	0.922640i
$704$		0			0
$705$	−32.5959	−	3.00340i	−1.22763	−	0.113115i
$706$		0			0
$707$	3.85357	−	2.22486i	0.144928	−	0.0836745i
$708$		0			0
$709$	8.67423	+	15.0242i	0.325768	+	0.564246i	0.981667	−	0.190602i	$-0.0610439\pi$
$709$	8.67423	+	15.0242i	0.325768	+	0.564246i	−0.655900	+	0.754848i	$0.727711\pi$
$710$		0			0
$711$	19.3485	+	16.5420i	0.725624	+	0.620372i
$712$		0			0
$713$	15.0000	+	25.9808i	0.561754	+	0.972987i
$714$		0			0
$715$		−	15.4135i		−	0.576432i
$716$		0			0
$717$	−3.34847	+	36.3410i	−0.125051	+	1.35718i
$718$		0			0
$719$	−26.1464	−	15.0956i	−0.975097	−	0.562973i	−0.0743109	−	0.997235i	$-0.523676\pi$
$719$	−26.1464	−	15.0956i	−0.975097	−	0.562973i	−0.900786	+	0.434262i	$0.857009\pi$
$720$		0			0
$721$		−	2.25697i		−	0.0840539i
$722$		0			0
$723$	10.6237	−	4.89437i	0.395101	−	0.182024i
$724$		0			0
$725$	3.67423	−	6.36396i	0.136458	−	0.236352i
$726$		0			0
$727$	4.00000	−	6.92820i	0.148352	−	0.256953i	−0.782267	−	0.622944i	$-0.785937\pi$
$727$	4.00000	−	6.92820i	0.148352	−	0.256953i	0.930618	+	0.365991i	$0.119270\pi$
$728$		0			0
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$		0			0
$731$	4.89898	−	2.82843i	0.181195	−	0.104613i
$732$		0			0
$733$	−20.0454			−0.740394			−0.370197	−	0.928953i	$-0.620710\pi$
$733$	−20.0454			−0.740394			−0.370197	+	0.928953i	$0.620710\pi$
$734$		0			0
$735$	−13.5959	−	9.61377i	−0.501493	−	0.354609i
$736$		0			0
$737$	3.94949	+	6.84072i	0.145481	+	0.251981i
$738$		0			0
$739$	12.1742	−	21.0864i	0.447836	−	0.775676i	−0.550408	−	0.834895i	$-0.685528\pi$
$739$	12.1742	−	21.0864i	0.447836	−	0.775676i	0.998245	+	0.0592200i	$0.0188613\pi$
$740$		0			0
$741$	−9.79796	+	24.2487i	−0.359937	+	0.890799i
$742$		0			0
$743$	2.32577	−	4.02834i	0.0853241	−	0.147786i	−0.820205	−	0.572069i	$-0.806141\pi$
$743$	2.32577	−	4.02834i	0.0853241	−	0.147786i	0.905529	+	0.424284i	$0.139474\pi$
$744$		0			0
$745$	−1.44949	−	2.51059i	−0.0531052	−	0.0919809i
$746$		0			0
$747$	9.32066	−	50.1492i	0.341025	−	1.83486i
$748$		0			0
$749$	2.20204			0.0804608
$750$		0			0
$751$	−17.6969	+	10.2173i	−0.645770	+	0.372836i	−0.786834	−	0.617165i	$-0.788281\pi$
$751$	−17.6969	+	10.2173i	−0.645770	+	0.372836i	0.141063	+	0.990001i	$0.454948\pi$
$752$		0			0
$753$	−5.94949	+	2.74094i	−0.216811	+	0.0998854i
$754$		0			0
$755$	−6.79796	+	11.7744i	−0.247403	+	0.428515i
$756$		0			0
$757$	19.6969	−	34.1161i	0.715897	−	1.23997i	−0.246715	−	0.969088i	$-0.579351\pi$
$757$	19.6969	−	34.1161i	0.715897	−	1.23997i	0.962612	−	0.270883i	$-0.0873155\pi$
$758$		0			0
$759$	16.1237	+	34.9982i	0.585254	+	1.27035i
$760$		0			0
$761$		−	31.5734i		−	1.14453i	−0.820067	−	0.572267i	$-0.806064\pi$
$761$		−	31.5734i		−	1.14453i	0.820067	−	0.572267i	$-0.193936\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	0.898979	+	2.54270i	0.0325027	+	0.0919314i
$766$		0			0
$767$		−	39.6622i		−	1.43212i
$768$		0			0
$769$	−1.79796	−	3.11416i	−0.0648361	−	0.112299i	0.831785	−	0.555098i	$-0.187319\pi$
$769$	−1.79796	−	3.11416i	−0.0648361	−	0.112299i	−0.896621	+	0.442798i	$0.853986\pi$
$770$		0			0
$771$	10.8712	+	23.5970i	0.391516	+	0.849825i
$772$		0			0
$773$	−1.22474	−	2.12132i	−0.0440510	−	0.0762986i	0.843159	−	0.537664i	$-0.180693\pi$
$773$	−1.22474	−	2.12132i	−0.0440510	−	0.0762986i	−0.887210	+	0.461365i	$0.847360\pi$
$774$		0			0
$775$	11.0227	−	6.36396i	0.395947	−	0.228600i
$776$		0			0
$777$	0.550510	−	5.97469i	0.0197494	−	0.214341i
$778$		0			0
$779$	−3.00000	−	12.7279i	−0.107486	−	0.456025i
$780$		0			0
$781$	16.3485	+	9.43879i	0.584994	+	0.337747i
$782$		0			0
$783$	−3.12372	−	12.3387i	−0.111633	−	0.440947i
$784$		0			0
$785$	13.1010	−	7.56388i	0.467595	−	0.269966i
$786$		0			0
$787$			7.53177i			0.268479i	0.990949	+	0.134239i	$0.0428591\pi$
$787$			7.53177i			0.268479i	−0.990949	+	0.134239i	$0.957141\pi$
$788$		0			0
$789$	12.6969	+	8.97809i	0.452023	+	0.319629i
$790$		0			0
$791$	−8.44949			−0.300429
$792$		0			0
$793$	−4.65153	−	2.68556i	−0.165181	−	0.0953671i
$794$		0			0
$795$	2.44949	−	26.5843i	0.0868744	−	0.942849i
$796$		0			0
$797$	37.3485			1.32295			0.661475	−	0.749967i	$-0.269931\pi$
$797$	37.3485			1.32295			0.661475	+	0.749967i	$0.269931\pi$
$798$		0			0
$799$	8.49490			0.300528
$800$		0			0
$801$	7.10102	+	20.0847i	0.250902	+	0.709659i
$802$		0			0
$803$	23.9722	+	13.8404i	0.845960	+	0.488415i
$804$		0			0
$805$	−4.49490			−0.158424
$806$		0			0
$807$	−24.4949	+	34.6410i	−0.862261	+	1.21942i
$808$		0			0
$809$		−	8.02458i		−	0.282129i	−0.990000	−	0.141065i	$-0.954947\pi$
$809$		−	8.02458i		−	0.282129i	0.990000	−	0.141065i	$-0.0450525\pi$
$810$		0			0
$811$	−3.00000	+	1.73205i	−0.105344	+	0.0608205i	−0.551746	−	0.834012i	$-0.686038\pi$
$811$	−3.00000	+	1.73205i	−0.105344	+	0.0608205i	0.446402	+	0.894832i	$0.352705\pi$
$812$		0			0
$813$	20.0454	−	28.3485i	0.703023	−	0.994225i
$814$		0			0
$815$	22.4722	+	12.9743i	0.787167	+	0.454471i
$816$		0			0
$817$	−8.89898	−	37.7552i	−0.311336	−	1.32089i
$818$		0			0
$819$	−4.40408	+	1.55708i	−0.153891	+	0.0544087i
$820$		0			0
$821$	−5.44949	+	3.14626i	−0.190189	+	0.109805i	−0.592071	−	0.805886i	$-0.701689\pi$
$821$	−5.44949	+	3.14626i	−0.190189	+	0.109805i	0.401882	+	0.915691i	$0.368356\pi$
$822$		0			0
$823$	−24.3485	−	42.1728i	−0.848734	−	1.47005i	−0.882338	−	0.470616i	$-0.844032\pi$
$823$	−24.3485	−	42.1728i	−0.848734	−	1.47005i	0.0336040	−	0.999435i	$-0.489301\pi$
$824$		0			0
$825$	14.8485	−	6.84072i	0.516957	−	0.238163i
$826$		0			0
$827$	10.6237	+	18.4008i	0.369423	+	0.639860i	0.989475	−	0.144701i	$-0.0462220\pi$
$827$	10.6237	+	18.4008i	0.369423	+	0.639860i	−0.620052	+	0.784560i	$0.712889\pi$
$828$		0			0
$829$		−	19.2275i		−	0.667800i	−0.942609	−	0.333900i	$-0.891635\pi$
$829$		−	19.2275i		−	0.667800i	0.942609	−	0.333900i	$-0.108365\pi$
$830$		0			0
$831$	−34.9217	−	3.21770i	−1.21142	−	0.111621i
$832$		0			0
$833$	3.74235	+	2.16064i	0.129665	+	0.0748619i
$834$		0			0
$835$		−	6.92820i		−	0.239760i
$836$		0			0
$837$	6.00000	−	21.2132i	0.207390	−	0.733236i
$838$		0			0
$839$	−6.67423	+	11.5601i	−0.230420	+	0.399099i	−0.957932	−	0.286996i	$-0.907343\pi$
$839$	−6.67423	+	11.5601i	−0.230420	+	0.399099i	0.727512	+	0.686095i	$0.240677\pi$
$840$		0			0
$841$	11.5000	−	19.9186i	0.396552	−	0.686848i
$842$		0			0
$843$	−16.3763	−	35.5464i	−0.564029	−	1.22428i
$844$		0			0
$845$	1.22474	−	0.707107i	0.0421325	−	0.0243252i
$846$		0			0
$847$	0.494897			0.0170049
$848$		0			0
$849$	9.44949	−	13.3636i	0.324306	−	0.458637i
$850$		0			0
$851$	27.2474	+	47.1940i	0.934031	+	1.61779i
$852$		0			0
$853$	5.00000	−	8.66025i	0.171197	−	0.296521i	−0.767642	−	0.640879i	$-0.778570\pi$
$853$	5.00000	−	8.66025i	0.171197	−	0.296521i	0.938839	+	0.344358i	$0.111903\pi$
$854$		0			0
$855$	18.4722	−	0.882079i	0.631736	−	0.0301665i
$856$		0			0
$857$	8.29796	−	14.3725i	0.283453	−	0.490955i	−0.688780	−	0.724970i	$-0.741853\pi$
$857$	8.29796	−	14.3725i	0.283453	−	0.490955i	0.972233	+	0.234016i	$0.0751867\pi$
$858$		0			0
$859$	9.42168	+	16.3188i	0.321464	+	0.556791i	0.980790	−	0.195065i	$-0.0624919\pi$
$859$	9.42168	+	16.3188i	0.321464	+	0.556791i	−0.659327	+	0.751857i	$0.729159\pi$
$860$		0			0
$861$	1.34847	−	1.90702i	0.0459557	−	0.0649912i
$862$		0			0
$863$	−16.6515			−0.566825			−0.283412	−	0.958998i	$-0.591467\pi$
$863$	−16.6515			−0.566825			−0.283412	+	0.958998i	$0.591467\pi$
$864$		0			0
$865$	−1.34847	+	0.778539i	−0.0458493	+	0.0264711i
$866$		0			0
$867$	12.0278	+	26.1076i	0.408486	+	0.886660i
$868$		0			0
$869$	13.3485	−	23.1202i	0.452816	−	0.784300i
$870$		0			0
$871$	4.34847	−	7.53177i	0.147342	−	0.255204i
$872$		0			0
$873$	7.50000	+	6.41212i	0.253837	+	0.217017i
$874$		0			0
$875$			5.08540i			0.171918i
$876$		0			0
$877$	−36.3712	−	20.9989i	−1.22817	−	0.709083i	−0.261521	−	0.965198i	$-0.584224\pi$
$877$	−36.3712	−	20.9989i	−1.22817	−	0.709083i	−0.966646	+	0.256115i	$0.917557\pi$
$878$		0			0
$879$	33.3712	+	3.07483i	1.12558	+	0.103712i
$880$		0			0
$881$		−	10.2815i		−	0.346394i	−0.984887	−	0.173197i	$-0.944590\pi$
$881$		−	10.2815i		−	0.346394i	0.984887	−	0.173197i	$-0.0554098\pi$
$882$		0			0
$883$	−10.4217	−	18.0509i	−0.350718	−	0.607461i	0.635658	−	0.771971i	$-0.280729\pi$
$883$	−10.4217	−	18.0509i	−0.350718	−	0.607461i	−0.986375	+	0.164510i	$0.947396\pi$
$884$		0			0
$885$	−25.4722	+	11.7351i	−0.856238	+	0.394471i
$886$		0			0
$887$	−28.0454	−	48.5761i	−0.941673	−	1.63102i	−0.762280	−	0.647247i	$-0.775920\pi$
$887$	−28.0454	−	48.5761i	−0.941673	−	1.63102i	−0.179393	−	0.983778i	$-0.557413\pi$
$888$		0			0
$889$	4.04541	−	2.33562i	0.135679	−	0.0783341i
$890$		0			0
$891$	10.1742	−	26.4254i	0.340850	−	0.885285i
$892$		0			0
$893$	16.7753	−	55.7828i	0.561363	−	1.86670i
$894$		0			0
$895$	−9.37117	−	5.41045i	−0.313244	−	0.180851i
$896$		0			0
$897$	24.4949	−	34.6410i	0.817861	−	1.15663i
$898$		0			0
$899$	−9.00000	+	5.19615i	−0.300167	+	0.173301i
$900$		0			0
$901$			6.92820i			0.230812i
$902$		0			0
$903$	4.00000	−	5.65685i	0.133112	−	0.188248i
$904$		0			0
$905$	−30.4949			−1.01368
$906$		0			0
$907$	32.9166	+	19.0044i	1.09298	+	0.631031i	0.934368	−	0.356311i	$-0.115966\pi$
$907$	32.9166	+	19.0044i	1.09298	+	0.631031i	0.158610	+	0.987341i	$0.449299\pi$
$908$		0			0
$909$	28.0000	−	9.89949i	0.928701	−	0.328346i
$910$		0			0
$911$	28.6515			0.949268			0.474634	−	0.880183i	$-0.342581\pi$
$911$	28.6515			0.949268			0.474634	+	0.880183i	$0.342581\pi$
$912$		0			0
$913$	−53.4949			−1.77042
$914$		0			0
$915$	−0.348469	+	3.78194i	−0.0115200	+	0.125027i
$916$		0			0
$917$	−0.866070	−	0.500026i	−0.0286002	−	0.0165123i
$918$		0			0
$919$	36.6969			1.21052			0.605260	−	0.796028i	$-0.293069\pi$
$919$	36.6969			1.21052			0.605260	+	0.796028i	$0.293069\pi$
$920$		0			0
$921$	30.2474	+	21.3882i	0.996687	+	0.704764i
$922$		0			0
$923$		−	20.7846i		−	0.684134i
$924$		0			0
$925$	20.0227	−	11.5601i	0.658342	−	0.380094i
$926$		0			0
$927$	2.75255	−	14.8099i	0.0904056	−	0.486422i
$928$		0			0
$929$	−24.0959	−	13.9118i	−0.790561	−	0.456431i	0.0495987	−	0.998769i	$-0.484206\pi$
$929$	−24.0959	−	13.9118i	−0.790561	−	0.456431i	−0.840160	+	0.542338i	$0.817539\pi$
$930$		0			0
$931$	21.5783	−	20.3079i	0.707201	−	0.665563i
$932$		0			0
$933$	2.47219	−	26.8307i	0.0809360	−	0.878399i
$934$		0			0
$935$	2.44949	−	1.41421i	0.0801069	−	0.0462497i
$936$		0			0
$937$	−11.5000	−	19.9186i	−0.375689	−	0.650712i	0.614741	−	0.788729i	$-0.289260\pi$
$937$	−11.5000	−	19.9186i	−0.375689	−	0.650712i	−0.990430	+	0.138017i	$0.955927\pi$
$938$		0			0
$939$	−13.7702	−	29.8895i	−0.449372	−	0.975407i
$940$		0			0
$941$	21.4949	+	37.2303i	0.700714	+	1.21367i	0.968216	+	0.250114i	$0.0804683\pi$
$941$	21.4949	+	37.2303i	0.700714	+	1.21367i	−0.267503	+	0.963557i	$0.586198\pi$
$942$		0			0
$943$			21.2132i			0.690797i
$944$		0			0
$945$	2.30306	+	2.36773i	0.0749186	+	0.0770221i
$946$		0			0
$947$	6.55051	+	3.78194i	0.212863	+	0.122896i	0.602641	−	0.798012i	$-0.294115\pi$
$947$	6.55051	+	3.78194i	0.212863	+	0.122896i	−0.389778	+	0.920909i	$0.627448\pi$
$948$		0			0
$949$		−	30.4770i		−	0.989326i
$950$		0			0
$951$	4.34847	+	9.43879i	0.141009	+	0.306074i
$952$		0			0
$953$	−12.3990	+	21.4757i	−0.401642	+	0.695665i	−0.993924	−	0.110066i	$-0.964894\pi$
$953$	−12.3990	+	21.4757i	−0.401642	+	0.695665i	0.592282	+	0.805731i	$0.298227\pi$
$954$		0			0
$955$	5.79796	−	10.0424i	0.187618	−	0.324963i
$956$		0			0
$957$	−12.1237	+	5.58542i	−0.391904	+	0.180551i
$958$		0			0
$959$	1.52781	−	0.882079i	0.0493354	−	0.0284838i
$960$		0			0
$961$	13.0000			0.419355
$962$		0			0
$963$	14.4495	+	2.68556i	0.465628	+	0.0865410i
$964$		0			0
$965$	18.2474	+	31.6055i	0.587406	+	1.01742i
$966$		0			0
$967$	−25.6969	+	44.5084i	−0.826358	+	1.43129i	0.0745193	+	0.997220i	$0.476258\pi$
$967$	−25.6969	+	44.5084i	−0.826358	+	1.43129i	−0.900877	+	0.434074i	$0.857076\pi$
$968$		0			0
$969$	−4.75255	+	0.667783i	−0.152674	+	0.0214523i
$970$		0			0
$971$	4.07321	−	7.05501i	0.130716	−	0.226406i	−0.793237	−	0.608913i	$-0.791606\pi$
$971$	4.07321	−	7.05501i	0.130716	−	0.226406i	0.923953	+	0.382507i	$0.124939\pi$
$972$		0			0
$973$	−3.22474	−	5.58542i	−0.103381	−	0.179060i
$974$		0			0
$975$	−14.6969	−	10.3923i	−0.470679	−	0.332820i
$976$		0			0
$977$	40.1010			1.28295			0.641473	−	0.767146i	$-0.278324\pi$
$977$	40.1010			1.28295			0.641473	+	0.767146i	$0.278324\pi$
$978$		0			0
$979$	19.3485	−	11.1708i	0.618380	−	0.357022i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	28.8990	−	50.0545i	0.921734	−	1.59649i	0.125003	−	0.992156i	$-0.460106\pi$
$983$	28.8990	−	50.0545i	0.921734	−	1.59649i	0.796731	−	0.604334i	$-0.206561\pi$
$984$		0			0
$985$	14.3485	−	24.8523i	0.457180	−	0.791859i
$986$		0			0
$987$	9.44949	−	4.35340i	0.300781	−	0.138570i
$988$		0			0
$989$			62.9253i			2.00091i
$990$		0			0
$991$	−15.3031	−	8.83523i	−0.486118	−	0.280660i	0.236845	−	0.971548i	$-0.423887\pi$
$991$	−15.3031	−	8.83523i	−0.486118	−	0.280660i	−0.722962	+	0.690887i	$0.757220\pi$
$992$		0			0
$993$	3.70204	−	40.1783i	0.117481	−	1.27502i
$994$		0			0
$995$			4.09978i			0.129972i
$996$		0			0
$997$	21.7196	+	37.6195i	0.687868	+	1.19142i	0.972526	+	0.232793i	$0.0747865\pi$
$997$	21.7196	+	37.6195i	0.687868	+	1.19142i	−0.284658	+	0.958629i	$0.591880\pi$
$998$		0			0
$999$	10.8990	−	38.5337i	0.344828	−	1.21915i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bn.h.65.1		4
3.2	odd	2		912.2.bn.g.65.1		4
4.3	odd	2		114.2.h.f.65.2	yes	4
12.11	even	2		114.2.h.e.65.2	✓	4
19.12	odd	6		912.2.bn.g.449.2		4
57.50	even	6	inner	912.2.bn.h.449.1		4
76.31	even	6		114.2.h.e.107.1	yes	4
228.107	odd	6		114.2.h.f.107.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.h.e.65.2	✓	4	12.11	even	2
114.2.h.e.107.1	yes	4	76.31	even	6
114.2.h.f.65.2	yes	4	4.3	odd	2
114.2.h.f.107.2	yes	4	228.107	odd	6
912.2.bn.g.65.1		4	3.2	odd	2
912.2.bn.g.449.2		4	19.12	odd	6
912.2.bn.h.65.1		4	1.1	even	1	trivial
912.2.bn.h.449.1		4	57.50	even	6	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.72474 - 0.158919i) q^{3} +(-1.22474 - 0.707107i) q^{5} +0.449490 q^{7} +(2.94949 + 0.548188i) q^{9} +O(q^{10})\)	\(q+(-1.72474 - 0.158919i) q^{3} +(-1.22474 - 0.707107i) q^{5} +0.449490 q^{7} +(2.94949 + 0.548188i) q^{9} -3.14626i q^{11} +(-3.00000 + 1.73205i) q^{13} +(2.00000 + 1.41421i) q^{15} +(-0.550510 - 0.317837i) q^{17} +(-3.17423 + 2.98735i) q^{19} +(-0.775255 - 0.0714323i) q^{21} +(6.12372 - 3.53553i) q^{23} +(-1.50000 - 2.59808i) q^{25} +(-5.00000 - 1.41421i) q^{27} +(1.22474 + 2.12132i) q^{29} +4.24264i q^{31} +(-0.500000 + 5.42650i) q^{33} +(-0.550510 - 0.317837i) q^{35} +7.70674i q^{37} +(5.44949 - 2.51059i) q^{39} +(-1.50000 + 2.59808i) q^{41} +(-4.44949 + 7.70674i) q^{43} +(-3.22474 - 2.75699i) q^{45} +(-11.5732 + 6.68180i) q^{47} -6.79796 q^{49} +(0.898979 + 0.635674i) q^{51} +(-5.44949 - 9.43879i) q^{53} +(-2.22474 + 3.85337i) q^{55} +(5.94949 - 4.64796i) q^{57} +(-5.72474 + 9.91555i) q^{59} +(0.775255 + 1.34278i) q^{61} +(1.32577 + 0.246405i) q^{63} +4.89898 q^{65} +(-2.17423 + 1.25529i) q^{67} +(-11.1237 + 5.12472i) q^{69} +(-3.00000 + 5.19615i) q^{71} +(-4.39898 + 7.61926i) q^{73} +(2.17423 + 4.71940i) q^{75} -1.41421i q^{77} +(7.34847 + 4.24264i) q^{79} +(8.39898 + 3.23375i) q^{81} -17.0027i q^{83} +(0.449490 + 0.778539i) q^{85} +(-1.77526 - 3.85337i) q^{87} +(3.55051 + 6.14966i) q^{89} +(-1.34847 + 0.778539i) q^{91} +(0.674235 - 7.31747i) q^{93} +(6.00000 - 1.41421i) q^{95} +(2.84847 + 1.64456i) q^{97} +(1.72474 - 9.27987i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 8 q^{7} + 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 - 8 * q^7 + 2 * q^9	\( 4 q - 2 q^{3} - 8 q^{7} + 2 q^{9} - 12 q^{13} + 8 q^{15} - 12 q^{17} + 2 q^{19} - 8 q^{21} - 6 q^{25} - 20 q^{27} - 2 q^{33} - 12 q^{35} + 12 q^{39} - 6 q^{41} - 8 q^{43} - 8 q^{45} - 12 q^{47} + 12 q^{49} - 16 q^{51} - 12 q^{53} - 4 q^{55} + 14 q^{57} - 18 q^{59} + 8 q^{61} + 20 q^{63} + 6 q^{67} - 20 q^{69} - 12 q^{71} + 2 q^{73} - 6 q^{75} + 14 q^{81} - 8 q^{85} - 12 q^{87} + 24 q^{89} + 24 q^{91} - 12 q^{93} + 24 q^{95} - 18 q^{97} + 2 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 8 * q^7 + 2 * q^9 - 12 * q^13 + 8 * q^15 - 12 * q^17 + 2 * q^19 - 8 * q^21 - 6 * q^25 - 20 * q^27 - 2 * q^33 - 12 * q^35 + 12 * q^39 - 6 * q^41 - 8 * q^43 - 8 * q^45 - 12 * q^47 + 12 * q^49 - 16 * q^51 - 12 * q^53 - 4 * q^55 + 14 * q^57 - 18 * q^59 + 8 * q^61 + 20 * q^63 + 6 * q^67 - 20 * q^69 - 12 * q^71 + 2 * q^73 - 6 * q^75 + 14 * q^81 - 8 * q^85 - 12 * q^87 + 24 * q^89 + 24 * q^91 - 12 * q^93 + 24 * q^95 - 18 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more