LMFDB - Embedded newform 336.3.be.d.319.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [336,3,Mod(79,336)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("336.79"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(336, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 0, 2])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	336.be (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,-9,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$9.15533688251$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.1364138928.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 35x^{4} + 364x^{2} + 972 $ x^6 + 35x^4 + 364x^2 + 972
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			319.2
Root			$3.78298i$ of defining polynomial
Character	$\chi$	$=$	336.319
Dual form			336.3.be.d.79.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50000 - 0.866025i) q^{3} +(-1.15548 - 2.00135i) q^{5} +(6.36328 + 2.91696i) q^{7} +(1.50000 + 2.59808i) q^{9} +(10.0188 + 5.78434i) q^{11} -15.7937 q^{13} +4.00270i q^{15} +(4.24136 - 7.34625i) q^{17} +(2.13819 - 1.23449i) q^{19} +(-7.01876 - 9.88620i) q^{21} +(39.6945 - 22.9176i) q^{23} +(9.82973 - 17.0256i) q^{25} -5.19615i q^{27} +35.2814 q^{29} +(26.0227 + 15.0242i) q^{31} +(-10.0188 - 17.3530i) q^{33} +(-1.51479 - 16.1057i) q^{35} +(-19.6234 - 33.9887i) q^{37} +(23.6905 + 13.6777i) q^{39} +27.0405 q^{41} +1.39177i q^{43} +(3.46644 - 6.00406i) q^{45} +(-18.4102 + 10.6291i) q^{47} +(31.9827 + 37.1229i) q^{49} +(-12.7241 + 7.34625i) q^{51} +(-16.1555 + 27.9821i) q^{53} -26.7348i q^{55} -4.27639 q^{57} +(25.5711 + 14.7635i) q^{59} +(-51.6970 - 89.5418i) q^{61} +(1.96644 + 20.9077i) q^{63} +(18.2493 + 31.6087i) q^{65} +(61.9664 + 35.7763i) q^{67} -79.3890 q^{69} -71.3595i q^{71} +(-14.6234 + 25.3285i) q^{73} +(-29.4892 + 17.0256i) q^{75} +(46.8796 + 66.0317i) q^{77} +(-89.1353 + 51.4623i) q^{79} +(-4.50000 + 7.79423i) q^{81} -43.1509i q^{83} -19.6032 q^{85} +(-52.9221 - 30.5546i) q^{87} +(62.0484 + 107.471i) q^{89} +(-100.500 - 46.0695i) q^{91} +(-26.0227 - 45.0727i) q^{93} +(-4.94129 - 2.85285i) q^{95} -14.7186 q^{97} +34.7060i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 9 q^{3} + q^{5} - 11 q^{7} + 9 q^{9} + 3 q^{11} - 44 q^{13} + 8 q^{17} - 30 q^{19} + 15 q^{21} + 24 q^{23} - 14 q^{25} + 34 q^{29} - 39 q^{31} - 3 q^{33} - 90 q^{35} + 6 q^{37} + 66 q^{39} - 136 q^{41}+ \cdots - 266 q^{97}+O(q^{100}) $ 6 * q - 9 * q^3 + q^5 - 11 * q^7 + 9 * q^9 + 3 * q^11 - 44 * q^13 + 8 * q^17 - 30 * q^19 + 15 * q^21 + 24 * q^23 - 14 * q^25 + 34 * q^29 - 39 * q^31 - 3 * q^33 - 90 * q^35 + 6 * q^37 + 66 * q^39 - 136 * q^41 - 3 * q^45 - 258 * q^47 + 157 * q^49 - 24 * q^51 - 89 * q^53 + 60 * q^57 + 63 * q^59 - 50 * q^61 - 12 * q^63 - 184 * q^65 + 348 * q^67 - 48 * q^69 + 36 * q^73 + 42 * q^75 + 221 * q^77 + 3 * q^79 - 27 * q^81 + 536 * q^85 - 51 * q^87 - 202 * q^89 - 62 * q^91 + 39 * q^93 + 432 * q^95 - 266 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$4$		0			0
$5$	−1.15548	−	2.00135i	−0.231096	−	0.400270i	0.727035	−	0.686601i	$-0.240898\pi$
$5$	−1.15548	−	2.00135i	−0.231096	−	0.400270i	−0.958131	+	0.286330i	$0.907565\pi$
$6$		0			0
$7$	6.36328	+	2.91696i	0.909040	+	0.416708i
$7$	6.36328	+	2.91696i	0.909040	+	0.416708i
$8$		0			0
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	10.0188	+	5.78434i	0.910797	+	0.525849i	0.880687	−	0.473698i	$-0.157081\pi$
$11$	10.0188	+	5.78434i	0.910797	+	0.525849i	0.0301093	+	0.999547i	$0.490414\pi$
$12$		0			0
$13$	−15.7937			−1.21490			−0.607449	−	0.794359i	$-0.707807\pi$
$13$	−15.7937			−1.21490			−0.607449	+	0.794359i	$0.707807\pi$
$14$		0			0
$15$			4.00270i			0.266847i
$16$		0			0
$17$	4.24136	−	7.34625i	0.249492	−	0.432132i	−0.713893	−	0.700255i	$-0.753070\pi$
$17$	4.24136	−	7.34625i	0.249492	−	0.432132i	0.963385	+	0.268122i	$0.0864032\pi$
$18$		0			0
$19$	2.13819	−	1.23449i	0.112537	−	0.0649730i	−0.442675	−	0.896682i	$-0.645971\pi$
$19$	2.13819	−	1.23449i	0.112537	−	0.0649730i	0.555212	+	0.831709i	$0.312637\pi$
$20$		0			0
$21$	−7.01876	−	9.88620i	−0.334227	−	0.470771i
$22$		0			0
$23$	39.6945	−	22.9176i	1.72585	−	0.996418i	0.820643	−	0.571441i	$-0.193615\pi$
$23$	39.6945	−	22.9176i	1.72585	−	0.996418i	0.905204	−	0.424977i	$-0.139718\pi$
$24$		0			0
$25$	9.82973	−	17.0256i	0.393189	−	0.681023i
$26$		0			0
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	35.2814			1.21660			0.608300	−	0.793707i	$-0.291852\pi$
$29$	35.2814			1.21660			0.608300	+	0.793707i	$0.291852\pi$
$30$		0			0
$31$	26.0227	+	15.0242i	0.839443	+	0.484653i	0.857075	−	0.515192i	$-0.172279\pi$
$31$	26.0227	+	15.0242i	0.839443	+	0.484653i	−0.0176318	+	0.999845i	$0.505613\pi$
$32$		0			0
$33$	−10.0188	−	17.3530i	−0.303599	−	0.525849i
$34$		0			0
$35$	−1.51479	−	16.1057i	−0.0432798	−	0.460162i
$36$		0			0
$37$	−19.6234	−	33.9887i	−0.530362	−	0.918614i	−0.999372	−	0.0354216i	$-0.988723\pi$
$37$	−19.6234	−	33.9887i	−0.530362	−	0.918614i	0.469010	−	0.883193i	$-0.344611\pi$
$38$		0			0
$39$	23.6905	+	13.6777i	0.607449	+	0.350711i
$40$		0			0
$41$	27.0405			0.659524			0.329762	−	0.944064i	$-0.393032\pi$
$41$	27.0405			0.659524			0.329762	+	0.944064i	$0.393032\pi$
$42$		0			0
$43$			1.39177i			0.0323667i	0.999869	+	0.0161834i	$0.00515155\pi$
$43$			1.39177i			0.0323667i	−0.999869	+	0.0161834i	$0.994848\pi$
$44$		0			0
$45$	3.46644	−	6.00406i	0.0770321	−	0.133423i
$46$		0			0
$47$	−18.4102	+	10.6291i	−0.391705	+	0.226151i	−0.682899	−	0.730513i	$-0.739281\pi$
$47$	−18.4102	+	10.6291i	−0.391705	+	0.226151i	0.291193	+	0.956664i	$0.405948\pi$
$48$		0			0
$49$	31.9827	+	37.1229i	0.652708	+	0.757609i
$50$		0			0
$51$	−12.7241	+	7.34625i	−0.249492	+	0.144044i
$52$		0			0
$53$	−16.1555	+	27.9821i	−0.304820	+	0.527964i	−0.977221	−	0.212223i	$-0.931930\pi$
$53$	−16.1555	+	27.9821i	−0.304820	+	0.527964i	0.672401	+	0.740187i	$0.265263\pi$
$54$		0			0
$55$		−	26.7348i		−	0.486087i
$56$		0			0
$57$	−4.27639			−0.0750244
$58$		0			0
$59$	25.5711	+	14.7635i	0.433408	+	0.250228i	0.700798	−	0.713360i	$-0.252828\pi$
$59$	25.5711	+	14.7635i	0.433408	+	0.250228i	−0.267389	+	0.963589i	$0.586161\pi$
$60$		0			0
$61$	−51.6970	−	89.5418i	−0.847491	−	1.46790i	−0.883440	−	0.468545i	$-0.844779\pi$
$61$	−51.6970	−	89.5418i	−0.847491	−	1.46790i	0.0359484	−	0.999354i	$-0.488555\pi$
$62$		0			0
$63$	1.96644	+	20.9077i	0.0312134	+	0.331869i
$64$		0			0
$65$	18.2493	+	31.6087i	0.280758	+	0.486288i
$66$		0			0
$67$	61.9664	+	35.7763i	0.924872	+	0.533975i	0.885186	−	0.465237i	$-0.154031\pi$
$67$	61.9664	+	35.7763i	0.924872	+	0.533975i	0.0396861	+	0.999212i	$0.487364\pi$
$68$		0			0
$69$	−79.3890			−1.15056
$70$		0			0
$71$		−	71.3595i		−	1.00506i	−0.864559	−	0.502532i	$-0.832402\pi$
$71$		−	71.3595i		−	1.00506i	0.864559	−	0.502532i	$-0.167598\pi$
$72$		0			0
$73$	−14.6234	+	25.3285i	−0.200321	+	0.346965i	−0.948632	−	0.316382i	$-0.897532\pi$
$73$	−14.6234	+	25.3285i	−0.200321	+	0.346965i	0.748311	+	0.663348i	$0.230865\pi$
$74$		0			0
$75$	−29.4892	+	17.0256i	−0.393189	+	0.227008i
$76$		0			0
$77$	46.8796	+	66.0317i	0.608825	+	0.857554i
$78$		0			0
$79$	−89.1353	+	51.4623i	−1.12830	+	0.651421i	−0.943506	−	0.331357i	$-0.892494\pi$
$79$	−89.1353	+	51.4623i	−1.12830	+	0.651421i	−0.184790	+	0.982778i	$0.559160\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	43.1509i		−	0.519890i	−0.965623	−	0.259945i	$-0.916296\pi$
$83$		−	43.1509i		−	0.519890i	0.965623	−	0.259945i	$-0.0837044\pi$
$84$		0			0
$85$	−19.6032			−0.230626
$86$		0			0
$87$	−52.9221	−	30.5546i	−0.608300	−	0.351202i
$88$		0			0
$89$	62.0484	+	107.471i	0.697173	+	1.20754i	0.969443	+	0.245318i	$0.0788925\pi$
$89$	62.0484	+	107.471i	0.697173	+	1.20754i	−0.272269	+	0.962221i	$0.587774\pi$
$90$		0			0
$91$	−100.500	−	46.0695i	−1.10439	−	0.506258i
$92$		0			0
$93$	−26.0227	−	45.0727i	−0.279814	−	0.484653i
$94$		0			0
$95$	−4.94129	−	2.85285i	−0.0520136	−	0.0300300i
$96$		0			0
$97$	−14.7186			−0.151738			−0.0758692	−	0.997118i	$-0.524173\pi$
$97$	−14.7186			−0.151738			−0.0758692	+	0.997118i	$0.524173\pi$
$98$		0			0
$99$			34.7060i			0.350566i
$100$		0			0
$101$	41.7561	−	72.3238i	0.413427	−	0.716077i	−0.581835	−	0.813307i	$-0.697665\pi$
$101$	41.7561	−	72.3238i	0.413427	−	0.716077i	0.995262	+	0.0972301i	$0.0309983\pi$
$102$		0			0
$103$	−107.938	+	62.3179i	−1.04794	+	0.605028i	−0.922072	−	0.387019i	$-0.873505\pi$
$103$	−107.938	+	62.3179i	−1.04794	+	0.605028i	−0.125868	+	0.992047i	$0.540172\pi$
$104$		0			0
$105$	−11.6757	+	25.4703i	−0.111197	+	0.242575i
$106$		0			0
$107$	31.2276	−	18.0293i	0.291847	−	0.168498i	−0.346928	−	0.937892i	$-0.612775\pi$
$107$	31.2276	−	18.0293i	0.291847	−	0.168498i	0.638774	+	0.769394i	$0.279442\pi$
$108$		0			0
$109$	−92.3500	+	159.955i	−0.847247	+	1.46748i	0.0364077	+	0.999337i	$0.488409\pi$
$109$	−92.3500	+	159.955i	−0.847247	+	1.46748i	−0.883655	+	0.468139i	$0.844925\pi$
$110$		0			0
$111$			67.9775i			0.612410i
$112$		0			0
$113$	211.813			1.87446			0.937228	−	0.348718i	$-0.113383\pi$
$113$	211.813			1.87446			0.937228	+	0.348718i	$0.113383\pi$
$114$		0			0
$115$	−91.7325	−	52.9618i	−0.797674	−	0.460537i
$116$		0			0
$117$	−23.6905	−	41.0332i	−0.202483	−	0.350711i
$118$		0			0
$119$	48.4176	−	34.3744i	0.406871	−	0.288860i
$120$		0			0
$121$	6.41708	+	11.1147i	0.0530337	+	0.0918571i
$122$		0			0
$123$	−40.5607	−	23.4177i	−0.329762	−	0.190388i
$124$		0			0
$125$	−103.206			−0.825651
$126$		0			0
$127$		−	35.1062i		−	0.276427i	−0.990402	−	0.138213i	$-0.955864\pi$
$127$		−	35.1062i		−	0.276427i	0.990402	−	0.138213i	$-0.0441360\pi$
$128$		0			0
$129$	1.20531	−	2.08765i	0.00934346	−	0.0161834i
$130$		0			0
$131$	−136.780	+	78.9699i	−1.04412	+	0.602824i	−0.920998	−	0.389568i	$-0.872624\pi$
$131$	−136.780	+	78.9699i	−1.04412	+	0.602824i	−0.123124	+	0.992391i	$0.539291\pi$
$132$		0			0
$133$	17.2069	−	1.61837i	0.129375	−	0.0121682i
$134$		0			0
$135$	−10.3993	+	6.00406i	−0.0770321	+	0.0444745i
$136$		0			0
$137$	−110.525	+	191.435i	−0.806753	+	1.39734i	0.108347	+	0.994113i	$0.465444\pi$
$137$	−110.525	+	191.435i	−0.806753	+	1.39734i	−0.915101	+	0.403225i	$0.867889\pi$
$138$		0			0
$139$			136.854i			0.984563i	0.870436	+	0.492281i	$0.163837\pi$
$139$			136.854i			0.984563i	−0.870436	+	0.492281i	$0.836163\pi$
$140$		0			0
$141$	36.8203			0.261137
$142$		0			0
$143$	−158.233	−	91.3559i	−1.10653	−	0.638853i
$144$		0			0
$145$	−40.7670	−	70.6105i	−0.281152	−	0.486969i
$146$		0			0
$147$	−15.8247	−	83.3821i	−0.107651	−	0.567225i
$148$		0			0
$149$	23.1372	+	40.0748i	0.155283	+	0.268958i	0.933162	−	0.359456i	$-0.117038\pi$
$149$	23.1372	+	40.0748i	0.155283	+	0.268958i	−0.777879	+	0.628414i	$0.783704\pi$
$150$		0			0
$151$	80.3543	+	46.3926i	0.532148	+	0.307236i	0.741891	−	0.670521i	$-0.233929\pi$
$151$	80.3543	+	46.3926i	0.532148	+	0.307236i	−0.209743	+	0.977757i	$0.567263\pi$
$152$		0			0
$153$	25.4481			0.166328
$154$		0			0
$155$		−	69.4409i		−	0.448006i
$156$		0			0
$157$	92.0129	−	159.371i	0.586070	−	1.01510i	−0.408672	−	0.912682i	$-0.634008\pi$
$157$	92.0129	−	159.371i	0.586070	−	1.01510i	0.994741	−	0.102421i	$-0.0326588\pi$
$158$		0			0
$159$	48.4664	−	27.9821i	0.304820	−	0.175988i
$160$		0			0
$161$	319.437	−	30.0441i	1.98408	−	0.186610i
$162$		0			0
$163$	57.6574	−	33.2885i	0.353726	−	0.204224i	−0.312599	−	0.949885i	$-0.601200\pi$
$163$	57.6574	−	33.2885i	0.353726	−	0.204224i	0.666325	+	0.745661i	$0.267866\pi$
$164$		0			0
$165$	−23.1530	+	40.1022i	−0.140321	+	0.243043i
$166$		0			0
$167$		−	118.824i		−	0.711521i	−0.934577	−	0.355761i	$-0.884222\pi$
$167$		−	118.824i		−	0.711521i	0.934577	−	0.355761i	$-0.115778\pi$
$168$		0			0
$169$	80.4402			0.475978
$170$		0			0
$171$	6.41458	+	3.70346i	0.0375122	+	0.0216577i
$172$		0			0
$173$	−100.210	−	173.568i	−0.579247	−	1.00329i	−0.995566	−	0.0940666i	$-0.970013\pi$
$173$	−100.210	−	173.568i	−0.579247	−	1.00329i	0.416319	−	0.909219i	$-0.363320\pi$
$174$		0			0
$175$	112.212	−	79.6657i	0.641213	−	0.455233i
$176$		0			0
$177$	−25.5711	−	44.2904i	−0.144469	−	0.250228i
$178$		0			0
$179$	160.405	+	92.6100i	0.896119	+	0.517375i	0.875939	−	0.482422i	$-0.160243\pi$
$179$	160.405	+	92.6100i	0.896119	+	0.517375i	0.0201800	+	0.999796i	$0.493576\pi$
$180$		0			0
$181$	−228.372			−1.26173			−0.630863	−	0.775894i	$-0.717299\pi$
$181$	−228.372			−1.26173			−0.630863	+	0.775894i	$0.717299\pi$
$182$		0			0
$183$			179.084i			0.978599i
$184$		0			0
$185$	−45.3489	+	78.5467i	−0.245129	+	0.424577i
$186$		0			0
$187$	84.9863	−	49.0669i	0.454472	−	0.262390i
$188$		0			0
$189$	15.1570	−	33.0646i	0.0801955	−	0.174945i
$190$		0			0
$191$	−130.239	+	75.1937i	−0.681881	+	0.393684i	−0.800563	−	0.599248i	$-0.795466\pi$
$191$	−130.239	+	75.1937i	−0.681881	+	0.393684i	0.118682	+	0.992932i	$0.462133\pi$
$192$		0			0
$193$	−40.7705	+	70.6165i	−0.211246	+	0.365889i	−0.952105	−	0.305772i	$-0.901085\pi$
$193$	−40.7705	+	70.6165i	−0.211246	+	0.365889i	0.740859	+	0.671661i	$0.234419\pi$
$194$		0			0
$195$		−	63.2174i		−	0.324192i
$196$		0			0
$197$	−192.720			−0.978273			−0.489136	−	0.872207i	$-0.662688\pi$
$197$	−192.720			−0.978273			−0.489136	+	0.872207i	$0.662688\pi$
$198$		0			0
$199$	75.8234	+	43.7767i	0.381022	+	0.219983i	0.678263	−	0.734819i	$-0.262733\pi$
$199$	75.8234	+	43.7767i	0.381022	+	0.219983i	−0.297241	+	0.954803i	$0.596066\pi$
$200$		0			0
$201$	−61.9664	−	107.329i	−0.308291	−	0.533975i
$202$		0			0
$203$	224.505	+	102.914i	1.10594	+	0.506967i
$204$		0			0
$205$	−31.2448	−	54.1175i	−0.152414	−	0.263988i
$206$		0			0
$207$	119.083	+	68.7529i	0.575282	+	0.332139i
$208$		0			0
$209$	28.5628			0.136664
$210$		0			0
$211$		−	127.785i		−	0.605618i	−0.953051	−	0.302809i	$-0.902076\pi$
$211$		−	127.785i		−	0.605618i	0.953051	−	0.302809i	$-0.0979244\pi$
$212$		0			0
$213$	−61.7991	+	107.039i	−0.290137	+	0.502532i
$214$		0			0
$215$	2.78542	−	1.60816i	0.0129554	−	0.00747982i
$216$		0			0
$217$	121.765	+	171.511i	0.561129	+	0.790372i
$218$		0			0
$219$	43.8702	−	25.3285i	0.200321	−	0.115655i
$220$		0			0
$221$	−66.9866	+	116.024i	−0.303107	+	0.524996i
$222$		0			0
$223$			283.951i			1.27332i	0.771144	+	0.636660i	$0.219685\pi$
$223$			283.951i			1.27332i	−0.771144	+	0.636660i	$0.780315\pi$
$224$		0			0
$225$	58.9784			0.262126
$226$		0			0
$227$	358.164	+	206.786i	1.57782	+	0.910952i	0.995164	+	0.0982297i	$0.0313180\pi$
$227$	358.164	+	206.786i	1.57782	+	0.910952i	0.582651	+	0.812722i	$0.302015\pi$
$228$		0			0
$229$	−80.6550	−	139.699i	−0.352205	−	0.610038i	0.634430	−	0.772980i	$-0.281235\pi$
$229$	−80.6550	−	139.699i	−0.352205	−	0.610038i	−0.986636	+	0.162943i	$0.947901\pi$
$230$		0			0
$231$	−13.1342	−	139.646i	−0.0568581	−	0.604530i
$232$		0			0
$233$	−181.365	−	314.133i	−0.778390	−	1.34821i	−0.932869	−	0.360215i	$-0.882703\pi$
$233$	−181.365	−	314.133i	−0.778390	−	1.34821i	0.154480	−	0.987996i	$-0.450630\pi$
$234$		0			0
$235$	42.5452	+	24.5635i	0.181043	+	0.104525i
$236$		0			0
$237$	178.271			0.752197
$238$		0			0
$239$		−	342.283i		−	1.43215i	−0.698026	−	0.716073i	$-0.745938\pi$
$239$		−	342.283i		−	1.43215i	0.698026	−	0.716073i	$-0.254062\pi$
$240$		0			0
$241$	117.864	−	204.146i	0.489061	−	0.847079i	−0.510859	−	0.859664i	$-0.670673\pi$
$241$	117.864	−	204.146i	0.489061	−	0.847079i	0.999921	+	0.0125850i	$0.00400604\pi$
$242$		0			0
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$		0			0
$245$	37.3405	−	106.903i	0.152410	−	0.436341i
$246$		0			0
$247$	−33.7700	+	19.4971i	−0.136720	+	0.0789356i
$248$		0			0
$249$	−37.3697	+	64.7263i	−0.150079	+	0.259945i
$250$		0			0
$251$			409.935i			1.63321i	0.577198	+	0.816604i	$0.304146\pi$
$251$			409.935i			1.63321i	−0.577198	+	0.816604i	$0.695854\pi$
$252$		0			0
$253$	530.253			2.09586
$254$		0			0
$255$	29.4049	+	16.9769i	0.115313	+	0.0665761i
$256$		0			0
$257$	−193.134	−	334.518i	−0.751494	−	1.30163i	−0.947099	−	0.320943i	$-0.896000\pi$
$257$	−193.134	−	334.518i	−0.751494	−	1.30163i	0.195605	−	0.980683i	$-0.437333\pi$
$258$		0			0
$259$	−25.7255	−	273.521i	−0.0993264	−	1.05606i
$260$		0			0
$261$	52.9221	+	91.6637i	0.202767	+	0.351202i
$262$		0			0
$263$	−38.7395	−	22.3663i	−0.147298	−	0.0850428i	0.424539	−	0.905409i	$-0.360436\pi$
$263$	−38.7395	−	22.3663i	−0.147298	−	0.0850428i	−0.571838	+	0.820367i	$0.693769\pi$
$264$		0			0
$265$	74.6694			0.281771
$266$		0			0
$267$		−	214.942i		−	0.805026i
$268$		0			0
$269$	194.507	−	336.897i	0.723076	−	1.25240i	−0.236685	−	0.971586i	$-0.576061\pi$
$269$	194.507	−	336.897i	0.723076	−	1.25240i	0.959761	−	0.280818i	$-0.0906056\pi$
$270$		0			0
$271$	354.619	−	204.739i	1.30856	−	0.755496i	0.326701	−	0.945128i	$-0.394063\pi$
$271$	354.619	−	204.739i	1.30856	−	0.755496i	0.981855	+	0.189632i	$0.0607295\pi$
$272$		0			0
$273$	110.852	+	156.139i	0.406052	+	0.571939i
$274$		0			0
$275$	196.963	−	113.717i	0.716231	−	0.413516i
$276$		0			0
$277$	−90.0281	+	155.933i	−0.325011	+	0.562936i	−0.981515	−	0.191387i	$-0.938701\pi$
$277$	−90.0281	+	155.933i	−0.325011	+	0.562936i	0.656503	+	0.754323i	$0.272035\pi$
$278$		0			0
$279$			90.1454i			0.323102i
$280$		0			0
$281$	−210.919			−0.750601			−0.375301	−	0.926903i	$-0.622461\pi$
$281$	−210.919			−0.750601			−0.375301	+	0.926903i	$0.622461\pi$
$282$		0			0
$283$	−212.192	−	122.509i	−0.749794	−	0.432894i	0.0758257	−	0.997121i	$-0.475841\pi$
$283$	−212.192	−	122.509i	−0.749794	−	0.432894i	−0.825619	+	0.564228i	$0.809174\pi$
$284$		0			0
$285$	4.94129	+	8.55856i	0.0173379	+	0.0300300i
$286$		0			0
$287$	172.066	+	78.8759i	0.599534	+	0.274829i
$288$		0			0
$289$	108.522	+	187.965i	0.375508	+	0.650399i
$290$		0			0
$291$	22.0779	+	12.7467i	0.0758692	+	0.0438031i
$292$		0			0
$293$	−262.124			−0.894622			−0.447311	−	0.894378i	$-0.647618\pi$
$293$	−262.124			−0.894622			−0.447311	+	0.894378i	$0.647618\pi$
$294$		0			0
$295$		−	68.2357i		−	0.231307i
$296$		0			0
$297$	30.0563	−	52.0590i	0.101200	−	0.175283i
$298$		0			0
$299$	−626.922	+	361.953i	−2.09673	+	1.21055i
$300$		0			0
$301$	−4.05973	+	8.85621i	−0.0134875	+	0.0294226i
$302$		0			0
$303$	−125.268	+	72.3238i	−0.413427	+	0.238692i
$304$		0			0
$305$	−119.470	+	206.928i	−0.391704	+	0.678452i
$306$		0			0
$307$		−	146.501i		−	0.477203i	−0.971118	−	0.238601i	$-0.923311\pi$
$307$		−	146.501i		−	0.477203i	0.971118	−	0.238601i	$-0.0766889\pi$
$308$		0			0
$309$	215.876			0.698626
$310$		0			0
$311$	−13.0394	−	7.52828i	−0.0419272	−	0.0242067i	0.478890	−	0.877875i	$-0.341039\pi$
$311$	−13.0394	−	7.52828i	−0.0419272	−	0.0242067i	−0.520817	+	0.853668i	$0.674373\pi$
$312$		0			0
$313$	−222.787	−	385.879i	−0.711780	−	1.23284i	−0.964188	−	0.265219i	$-0.914556\pi$
$313$	−222.787	−	385.879i	−0.711780	−	1.23284i	0.252408	−	0.967621i	$-0.418778\pi$
$314$		0			0
$315$	39.5715	−	28.0940i	0.125624	−	0.0891874i
$316$		0			0
$317$	−47.4373	−	82.1638i	−0.149645	−	0.259192i	0.781452	−	0.623966i	$-0.214480\pi$
$317$	−47.4373	−	82.1638i	−0.149645	−	0.259192i	−0.931096	+	0.364774i	$0.881146\pi$
$318$		0			0
$319$	353.476	+	204.079i	1.10807	+	0.639747i
$320$		0			0
$321$	−62.4552			−0.194564
$322$		0			0
$323$		−	20.9436i		−	0.0648409i
$324$		0			0
$325$	−155.248	+	268.897i	−0.477685	+	0.827374i
$326$		0			0
$327$	277.050	−	159.955i	0.847247	−	0.489159i
$328$		0			0
$329$	−148.154	+	13.9344i	−0.450315	+	0.0423537i
$330$		0			0
$331$	−60.6928	+	35.0410i	−0.183362	+	0.105864i	−0.588871	−	0.808227i	$-0.700428\pi$
$331$	−60.6928	+	35.0410i	−0.183362	+	0.105864i	0.405509	+	0.914091i	$0.367094\pi$
$332$		0			0
$333$	58.8702	−	101.966i	0.176787	−	0.306205i
$334$		0			0
$335$		−	165.356i		−	0.493599i
$336$		0			0
$337$	25.8353			0.0766625			0.0383313	−	0.999265i	$-0.487796\pi$
$337$	25.8353			0.0766625			0.0383313	+	0.999265i	$0.487796\pi$
$338$		0			0
$339$	−317.720	−	183.436i	−0.937228	−	0.541109i
$340$		0			0
$341$	173.810	+	301.048i	0.509708	+	0.882840i
$342$		0			0
$343$	95.2292	+	329.515i	0.277636	+	0.960686i
$344$		0			0
$345$	91.7325	+	158.885i	0.265891	+	0.460537i
$346$		0			0
$347$	−373.367	−	215.563i	−1.07599	−	0.621220i	−0.146175	−	0.989259i	$-0.546696\pi$
$347$	−373.367	−	215.563i	−1.07599	−	0.621220i	−0.929811	+	0.368038i	$0.880029\pi$
$348$		0			0
$349$	340.822			0.976566			0.488283	−	0.872685i	$-0.337623\pi$
$349$	340.822			0.976566			0.488283	+	0.872685i	$0.337623\pi$
$350$		0			0
$351$			82.0663i			0.233807i
$352$		0			0
$353$	44.9354	−	77.8304i	0.127296	−	0.220483i	−0.795332	−	0.606174i	$-0.792704\pi$
$353$	44.9354	−	77.8304i	0.127296	−	0.220483i	0.922628	+	0.385691i	$0.126037\pi$
$354$		0			0
$355$	−142.815	+	82.4545i	−0.402297	+	0.232266i
$356$		0			0
$357$	−102.396	+	9.63065i	−0.286822	+	0.0269766i
$358$		0			0
$359$	−310.996	+	179.554i	−0.866285	+	0.500150i	−0.866112	−	0.499850i	$-0.833388\pi$
$359$	−310.996	+	179.554i	−0.866285	+	0.500150i	−0.000173257		1.00000i	$0.500055\pi$
$360$		0			0
$361$	−177.452	+	307.356i	−0.491557	+	0.851402i
$362$		0			0
$363$		−	22.2294i		−	0.0612380i
$364$		0			0
$365$	67.5883			0.185173
$366$		0			0
$367$	−429.578	−	248.017i	−1.17051	−	0.675795i	−0.216711	−	0.976236i	$-0.569533\pi$
$367$	−429.578	−	248.017i	−1.17051	−	0.675795i	−0.953800	+	0.300441i	$0.902866\pi$
$368$		0			0
$369$	40.5607	+	70.2532i	0.109921	+	0.190388i
$370$		0			0
$371$	−184.425	+	130.933i	−0.497101	+	0.352920i
$372$		0			0
$373$	204.604	+	354.384i	0.548535	+	0.950091i	0.998375	+	0.0569816i	$0.0181476\pi$
$373$	204.604	+	354.384i	0.548535	+	0.950091i	−0.449840	+	0.893109i	$0.648519\pi$
$374$		0			0
$375$	154.809	+	89.3793i	0.412825	+	0.238345i
$376$		0			0
$377$	−557.223			−1.47804
$378$		0			0
$379$			531.591i			1.40261i	0.712859	+	0.701307i	$0.247400\pi$
$379$			531.591i			1.40261i	−0.712859	+	0.701307i	$0.752600\pi$
$380$		0			0
$381$	−30.4028	+	52.6593i	−0.0797975	+	0.138213i
$382$		0			0
$383$	−646.737	+	373.394i	−1.68861	+	0.974918i	−0.733023	+	0.680204i	$0.761891\pi$
$383$	−646.737	+	373.394i	−1.68861	+	0.974918i	−0.955585	+	0.294714i	$0.904776\pi$
$384$		0			0
$385$	77.9842	−	170.121i	0.202556	−	0.441872i
$386$		0			0
$387$	−3.61592	+	2.08765i	−0.00934346	+	0.00539445i
$388$		0			0
$389$	−165.746	+	287.080i	−0.426082	+	0.737995i	−0.996521	−	0.0833446i	$-0.973440\pi$
$389$	−165.746	+	287.080i	−0.426082	+	0.737995i	0.570439	+	0.821340i	$0.306773\pi$
$390$		0			0
$391$		−	388.807i		−	0.994392i
$392$		0			0
$393$	273.560			0.696081
$394$		0			0
$395$	205.988	+	118.927i	0.521490	+	0.301082i
$396$		0			0
$397$	68.2701	+	118.247i	0.171965	+	0.297852i	0.939107	−	0.343626i	$-0.111655\pi$
$397$	68.2701	+	118.247i	0.171965	+	0.297852i	−0.767142	+	0.641478i	$0.778322\pi$
$398$		0			0
$399$	−27.2119	−	12.4740i	−0.0682002	−	0.0312633i
$400$		0			0
$401$	−195.014	−	337.775i	−0.486320	−	0.842331i	0.513556	−	0.858056i	$-0.328328\pi$
$401$	−195.014	−	337.775i	−0.486320	−	0.842331i	−0.999876	+	0.0157250i	$0.994994\pi$
$402$		0			0
$403$	−410.995	−	237.288i	−1.01984	−	0.588804i
$404$		0			0
$405$	20.7987			0.0513547
$406$		0			0
$407$		−	454.033i		−	1.11556i
$408$		0			0
$409$	−384.516	+	666.001i	−0.940137	+	1.62837i	−0.174930	+	0.984581i	$0.555970\pi$
$409$	−384.516	+	666.001i	−0.940137	+	1.62837i	−0.765207	+	0.643784i	$0.777363\pi$
$410$		0			0
$411$	331.576	−	191.435i	0.806753	−	0.465779i
$412$		0			0
$413$	119.652	+	168.534i	0.289713	+	0.408072i
$414$		0			0
$415$	−86.3601	+	49.8600i	−0.208097	+	0.120145i
$416$		0			0
$417$	118.519	−	205.281i	0.284219	−	0.492281i
$418$		0			0
$419$			664.417i			1.58572i	0.609403	+	0.792861i	$0.291409\pi$
$419$			664.417i			1.58572i	−0.609403	+	0.792861i	$0.708591\pi$
$420$		0			0
$421$	83.6243			0.198633			0.0993163	−	0.995056i	$-0.468334\pi$
$421$	83.6243			0.198633			0.0993163	+	0.995056i	$0.468334\pi$
$422$		0			0
$423$	−55.2305	−	31.8873i	−0.130568	−	0.0753837i
$424$		0			0
$425$	−83.3827	−	144.423i	−0.196195	−	0.339819i
$426$		0			0
$427$	−67.7728	−	720.578i	−0.158719	−	1.68754i
$428$		0			0
$429$	158.233	+	274.068i	0.368842	+	0.638853i
$430$		0			0
$431$	−347.454	−	200.602i	−0.806157	−	0.465435i	0.0394627	−	0.999221i	$-0.487435\pi$
$431$	−347.454	−	200.602i	−0.806157	−	0.465435i	−0.845619	+	0.533786i	$0.820769\pi$
$432$		0			0
$433$	96.9743			0.223959			0.111980	−	0.993711i	$-0.464281\pi$
$433$	96.9743			0.223959			0.111980	+	0.993711i	$0.464281\pi$
$434$		0			0
$435$			141.221i			0.324646i
$436$		0			0
$437$	56.5830	−	98.0047i	0.129481	−	0.224267i
$438$		0			0
$439$	−378.661	+	218.620i	−0.862553	+	0.497995i	−0.864866	−	0.502002i	$-0.832597\pi$
$439$	−378.661	+	218.620i	−0.862553	+	0.497995i	0.00231345	+	0.999997i	$0.499264\pi$
$440$		0			0
$441$	−48.4739	+	138.778i	−0.109918	+	0.314689i
$442$		0			0
$443$	507.040	−	292.740i	1.14456	−	0.660812i	0.197004	−	0.980403i	$-0.436879\pi$
$443$	507.040	−	292.740i	1.14456	−	0.660812i	0.947556	+	0.319591i	$0.103545\pi$
$444$		0			0
$445$	143.392	−	248.362i	0.322228	−	0.558116i
$446$		0			0
$447$		−	80.1495i		−	0.179305i
$448$		0			0
$449$	−430.149			−0.958016			−0.479008	−	0.877811i	$-0.659004\pi$
$449$	−430.149			−0.958016			−0.479008	+	0.877811i	$0.659004\pi$
$450$		0			0
$451$	270.912	+	156.411i	0.600692	+	0.346810i
$452$		0			0
$453$	−80.3543	−	139.178i	−0.177383	−	0.307236i
$454$		0			0
$455$	23.9241	+	254.368i	0.0525805	+	0.559050i
$456$		0			0
$457$	−408.249	−	707.109i	−0.893325	−	1.54728i	−0.835864	−	0.548936i	$-0.815033\pi$
$457$	−408.249	−	707.109i	−0.893325	−	1.54728i	−0.0574604	−	0.998348i	$-0.518300\pi$
$458$		0			0
$459$	−38.1722	−	22.0387i	−0.0831639	−	0.0480147i
$460$		0			0
$461$	280.569			0.608609			0.304305	−	0.952575i	$-0.401576\pi$
$461$	280.569			0.608609			0.304305	+	0.952575i	$0.401576\pi$
$462$		0			0
$463$			181.939i			0.392958i	0.980508	+	0.196479i	$0.0629507\pi$
$463$			181.939i			0.392958i	−0.980508	+	0.196479i	$0.937049\pi$
$464$		0			0
$465$	−60.1376	+	104.161i	−0.129328	+	0.224003i
$466$		0			0
$467$	−76.9351	+	44.4185i	−0.164743	+	0.0951146i	−0.580105	−	0.814542i	$-0.696988\pi$
$467$	−76.9351	+	44.4185i	−0.164743	+	0.0951146i	0.415362	+	0.909656i	$0.363655\pi$
$468$		0			0
$469$	289.952	+	408.408i	0.618234	+	0.870807i
$470$		0			0
$471$	−276.039	+	159.371i	−0.586070	+	0.338367i
$472$		0			0
$473$	−8.05046	+	13.9438i	−0.0170200	+	0.0294795i
$474$		0			0
$475$		−	48.5387i		−	0.102187i
$476$		0			0
$477$	−96.9329			−0.203214
$478$		0			0
$479$	109.953	+	63.4813i	0.229547	+	0.132529i	0.610363	−	0.792122i	$-0.291024\pi$
$479$	109.953	+	63.4813i	0.229547	+	0.132529i	−0.380816	+	0.924651i	$0.624357\pi$
$480$		0			0
$481$	309.926	+	536.807i	0.644336	+	1.11602i
$482$		0			0
$483$	−505.174	−	231.574i	−1.04591	−	0.479450i
$484$		0			0
$485$	17.0071	+	29.4572i	0.0350662	+	0.0607364i
$486$		0			0
$487$	249.054	+	143.791i	0.511404	+	0.295259i	0.733410	−	0.679786i	$-0.237927\pi$
$487$	249.054	+	143.791i	0.511404	+	0.295259i	−0.222007	+	0.975045i	$0.571261\pi$
$488$		0			0
$489$	−115.315			−0.235818
$490$		0			0
$491$		−	23.7600i		−	0.0483910i	−0.999707	−	0.0241955i	$-0.992298\pi$
$491$		−	23.7600i		−	0.0483910i	0.999707	−	0.0241955i	$-0.00770241\pi$
$492$		0			0
$493$	149.641	−	259.186i	0.303531	−	0.525732i
$494$		0			0
$495$	69.4590	−	40.1022i	0.140321	−	0.0810144i
$496$		0			0
$497$	208.153	−	454.080i	0.418818	−	0.913643i
$498$		0			0
$499$	−48.6932	+	28.1130i	−0.0975815	+	0.0563387i	−0.547997	−	0.836481i	$-0.684609\pi$
$499$	−48.6932	+	28.1130i	−0.0975815	+	0.0563387i	0.450415	+	0.892819i	$0.351276\pi$
$500$		0			0
$501$	−102.905	+	178.236i	−0.205399	+	0.355761i
$502$		0			0
$503$		−	913.863i		−	1.81683i	−0.418075	−	0.908413i	$-0.637295\pi$
$503$		−	913.863i		−	1.81683i	0.418075	−	0.908413i	$-0.362705\pi$
$504$		0			0
$505$	−192.994			−0.382166
$506$		0			0
$507$	−120.660	−	69.6633i	−0.237989	−	0.137403i
$508$		0			0
$509$	449.411	+	778.404i	0.882930	+	1.52928i	0.848068	+	0.529888i	$0.177766\pi$
$509$	449.411	+	778.404i	0.882930	+	1.52928i	0.0348625	+	0.999392i	$0.488901\pi$
$510$		0			0
$511$	−166.935	+	118.516i	−0.326683	+	0.231930i
$512$		0			0
$513$	−6.41458	−	11.1104i	−0.0125041	−	0.0216577i
$514$		0			0
$515$	249.440	+	144.014i	0.484350	+	0.279640i
$516$		0			0
$517$	−245.929			−0.475685
$518$		0			0
$519$			347.137i			0.668857i
$520$		0			0
$521$	155.780	−	269.819i	0.299002	−	0.517886i	−0.676906	−	0.736069i	$-0.736680\pi$
$521$	155.780	−	269.819i	0.299002	−	0.517886i	0.975908	+	0.218183i	$0.0700130\pi$
$522$		0			0
$523$	681.450	−	393.436i	1.30296	−	0.752267i	0.322053	−	0.946722i	$-0.395627\pi$
$523$	681.450	−	393.436i	1.30296	−	0.752267i	0.980911	+	0.194455i	$0.0622938\pi$
$524$		0			0
$525$	−237.311	+	22.3199i	−0.452021	+	0.0425141i
$526$		0			0
$527$	220.743	−	127.446i	0.418868	−	0.241834i
$528$		0			0
$529$	785.935	−	1361.28i	1.48570	−	2.57331i
$530$		0			0
$531$			88.5808i			0.166819i
$532$		0			0
$533$	−427.069			−0.801254
$534$		0			0
$535$	−72.1658	−	41.6649i	−0.134889	−	0.0778784i
$536$		0			0
$537$	−160.405	−	277.830i	−0.298706	−	0.517375i
$538$		0			0
$539$	105.696	+	556.924i	0.196097	+	1.03325i
$540$		0			0
$541$	140.349	+	243.091i	0.259425	+	0.449337i	0.966088	−	0.258213i	$-0.0831337\pi$
$541$	140.349	+	243.091i	0.259425	+	0.449337i	−0.706663	+	0.707550i	$0.749800\pi$
$542$		0			0
$543$	342.558	+	197.776i	0.630863	+	0.364229i
$544$		0			0
$545$	426.835			0.783183
$546$		0			0
$547$			153.761i			0.281099i	0.990074	+	0.140549i	$0.0448869\pi$
$547$			153.761i			0.281099i	−0.990074	+	0.140549i	$0.955113\pi$
$548$		0			0
$549$	155.091	−	268.625i	0.282497	−	0.489299i
$550$		0			0
$551$	75.4384	−	43.5544i	0.136912	−	0.0790461i
$552$		0			0
$553$	−717.306	+	67.4651i	−1.29712	+	0.121998i
$554$		0			0
$555$	136.047	−	78.5467i	0.245129	−	0.141526i
$556$		0			0
$557$	390.366	−	676.135i	0.700837	−	1.21389i	−0.267335	−	0.963604i	$-0.586143\pi$
$557$	390.366	−	676.135i	0.700837	−	1.21389i	0.968173	−	0.250283i	$-0.0805235\pi$
$558$		0			0
$559$		−	21.9811i		−	0.0393222i
$560$		0			0
$561$	−169.973			−0.302981
$562$		0			0
$563$	811.598	+	468.577i	1.44156	+	0.832285i	0.997954	−	0.0639367i	$-0.0203656\pi$
$563$	811.598	+	468.577i	1.44156	+	0.832285i	0.443606	+	0.896222i	$0.353699\pi$
$564$		0			0
$565$	−244.746	−	423.913i	−0.433180	−	0.750289i
$566$		0			0
$567$	−51.3702	+	36.4706i	−0.0906000	+	0.0643220i
$568$		0			0
$569$	393.400	+	681.388i	0.691388	+	1.19752i	0.971383	+	0.237517i	$0.0763337\pi$
$569$	393.400	+	681.388i	0.691388	+	1.19752i	−0.279995	+	0.960001i	$0.590333\pi$
$570$		0			0
$571$	227.876	+	131.564i	0.399082	+	0.230410i	0.686088	−	0.727519i	$-0.259327\pi$
$571$	227.876	+	131.564i	0.399082	+	0.230410i	−0.287006	+	0.957929i	$0.592660\pi$
$572$		0			0
$573$	260.479			0.454588
$574$		0			0
$575$		−	901.096i		−	1.56712i
$576$		0			0
$577$	−5.50000	+	9.52628i	−0.00953206	+	0.0165100i	−0.870752	−	0.491722i	$-0.836368\pi$
$577$	−5.50000	+	9.52628i	−0.00953206	+	0.0165100i	0.861220	+	0.508232i	$0.169701\pi$
$578$		0			0
$579$	122.311	−	70.6165i	0.211246	−	0.121963i
$580$		0			0
$581$	125.869	−	274.581i	0.216642	−	0.472601i
$582$		0			0
$583$	−323.716	+	186.897i	−0.555259	+	0.320579i
$584$		0			0
$585$	−54.7479	+	94.8261i	−0.0935861	+	0.162096i
$586$		0			0
$587$		−	461.546i		−	0.786279i	−0.919479	−	0.393139i	$-0.871389\pi$
$587$		−	461.546i		−	0.786279i	0.919479	−	0.393139i	$-0.128611\pi$
$588$		0			0
$589$	74.1889			0.125957
$590$		0			0
$591$	289.080	+	166.900i	0.489136	+	0.282403i
$592$		0			0
$593$	388.103	+	672.214i	0.654474	+	1.13358i	0.982025	+	0.188749i	$0.0604431\pi$
$593$	388.103	+	672.214i	0.654474	+	1.13358i	−0.327552	+	0.944833i	$0.606224\pi$
$594$		0			0
$595$	−124.741	−	57.1818i	−0.209649	−	0.0961039i
$596$		0			0
$597$	−75.8234	−	131.330i	−0.127007	−	0.219983i
$598$		0			0
$599$	209.520	+	120.967i	0.349783	+	0.201947i	0.664590	−	0.747208i	$-0.268606\pi$
$599$	209.520	+	120.967i	0.349783	+	0.201947i	−0.314807	+	0.949156i	$0.601940\pi$
$600$		0			0
$601$	−521.217			−0.867250			−0.433625	−	0.901093i	$-0.642766\pi$
$601$	−521.217			−0.867250			−0.433625	+	0.901093i	$0.642766\pi$
$602$		0			0
$603$			214.658i			0.355984i
$604$		0			0
$605$	14.8296	−	25.6857i	0.0245118	−	0.0424556i
$606$		0			0
$607$	986.613	−	569.621i	1.62539	−	0.938420i	0.639948	−	0.768419i	$-0.278956\pi$
$607$	986.613	−	569.621i	1.62539	−	0.938420i	0.985444	−	0.170002i	$-0.0543773\pi$
$608$		0			0
$609$	−247.632	−	348.799i	−0.406620	−	0.572740i
$610$		0			0
$611$	290.764	−	167.873i	0.475882	−	0.274751i
$612$		0			0
$613$	−267.033	+	462.514i	−0.435616	+	0.754510i	−0.997346	−	0.0728114i	$-0.976803\pi$
$613$	−267.033	+	462.514i	−0.435616	+	0.754510i	0.561729	+	0.827321i	$0.310136\pi$
$614$		0			0
$615$			108.235i			0.175992i
$616$		0			0
$617$	−802.979			−1.30142			−0.650712	−	0.759324i	$-0.725530\pi$
$617$	−802.979			−1.30142			−0.650712	+	0.759324i	$0.725530\pi$
$618$		0			0
$619$	−274.573	−	158.525i	−0.443575	−	0.256098i	0.261538	−	0.965193i	$-0.415770\pi$
$619$	−274.573	−	158.525i	−0.443575	−	0.256098i	−0.705113	+	0.709095i	$0.749104\pi$
$620$		0			0
$621$	−119.083	−	206.259i	−0.191761	−	0.332139i
$622$		0			0
$623$	81.3432	+	864.861i	0.130567	+	1.38822i
$624$		0			0
$625$	−126.490	−	219.087i	−0.202384	−	0.350540i
$626$		0			0
$627$	−42.8441	−	24.7361i	−0.0683319	−	0.0394515i
$628$		0			0
$629$	−332.919			−0.529284
$630$		0			0
$631$			1168.77i			1.85225i	0.377222	+	0.926123i	$0.376879\pi$
$631$			1168.77i			1.85225i	−0.377222	+	0.926123i	$0.623121\pi$
$632$		0			0
$633$	−110.665	+	191.678i	−0.174827	+	0.302809i
$634$		0			0
$635$	−70.2598	+	40.5645i	−0.110645	+	0.0638812i
$636$		0			0
$637$	−505.125	−	586.306i	−0.792974	−	0.920418i
$638$		0			0
$639$	185.397	−	107.039i	0.290137	−	0.167511i
$640$		0			0
$641$	8.12563	−	14.0740i	0.0126765	−	0.0219563i	−0.859618	−	0.510938i	$-0.829298\pi$
$641$	8.12563	−	14.0740i	0.0126765	−	0.0219563i	0.872294	+	0.488982i	$0.162632\pi$
$642$		0			0
$643$			956.475i			1.48752i	0.668447	+	0.743760i	$0.266959\pi$
$643$			956.475i			1.48752i	−0.668447	+	0.743760i	$0.733041\pi$
$644$		0			0
$645$	−5.57084			−0.00863696
$646$		0			0
$647$	456.676	+	263.662i	0.705836	+	0.407515i	0.809517	−	0.587096i	$-0.199729\pi$
$647$	456.676	+	263.662i	0.705836	+	0.407515i	−0.103681	+	0.994611i	$0.533062\pi$
$648$		0			0
$649$	170.794	+	295.823i	0.263164	+	0.455814i
$650$		0			0
$651$	−34.1148	−	362.717i	−0.0524037	−	0.557170i
$652$		0			0
$653$	−159.664	−	276.547i	−0.244509	−	0.423502i	0.717484	−	0.696575i	$-0.245293\pi$
$653$	−159.664	−	276.547i	−0.244509	−	0.423502i	−0.961993	+	0.273073i	$0.911960\pi$
$654$		0			0
$655$	316.093	+	182.497i	0.482585	+	0.278621i
$656$		0			0
$657$	−87.7404			−0.133547
$658$		0			0
$659$		−	289.303i		−	0.439004i	−0.975612	−	0.219502i	$-0.929557\pi$
$659$		−	289.303i		−	0.439004i	0.975612	−	0.219502i	$-0.0704432\pi$
$660$		0			0
$661$	8.20984	−	14.2199i	0.0124203	−	0.0215126i	−0.859748	−	0.510718i	$-0.829380\pi$
$661$	8.20984	−	14.2199i	0.0124203	−	0.0215126i	0.872169	+	0.489205i	$0.162713\pi$
$662$		0			0
$663$	200.960	−	116.024i	0.303107	−	0.174999i
$664$		0			0
$665$	−23.1212	−	32.5670i	−0.0347687	−	0.0489730i
$666$		0			0
$667$	1400.48	−	808.565i	2.09966	−	1.21224i
$668$		0			0
$669$	245.908	−	425.926i	0.367576	−	0.636660i
$670$		0			0
$671$		−	1196.13i		−	1.78261i
$672$		0			0
$673$	−65.5702			−0.0974297			−0.0487149	−	0.998813i	$-0.515513\pi$
$673$	−65.5702			−0.0974297			−0.0487149	+	0.998813i	$0.515513\pi$
$674$		0			0
$675$	−88.4675	−	51.0768i	−0.131063	−	0.0756693i
$676$		0			0
$677$	595.229	+	1030.97i	0.879216	+	1.52285i	0.852203	+	0.523211i	$0.175266\pi$
$677$	595.229	+	1030.97i	0.879216	+	1.52285i	0.0270124	+	0.999635i	$0.491401\pi$
$678$		0			0
$679$	−93.6587	−	42.9336i	−0.137936	−	0.0632306i
$680$		0			0
$681$	−358.164	−	620.358i	−0.525938	−	0.910952i
$682$		0			0
$683$	−770.901	−	445.080i	−1.12870	−	0.651654i	−0.185091	−	0.982721i	$-0.559258\pi$
$683$	−770.901	−	445.080i	−1.12870	−	0.651654i	−0.943607	+	0.331067i	$0.892591\pi$
$684$		0			0
$685$	510.839			0.745751
$686$		0			0
$687$			279.397i			0.406692i
$688$		0			0
$689$	255.154	−	441.940i	0.370326	−	0.641423i
$690$		0			0
$691$	−303.625	+	175.298i	−0.439400	+	0.253688i	−0.703343	−	0.710851i	$-0.748310\pi$
$691$	−303.625	+	175.298i	−0.439400	+	0.253688i	0.263943	+	0.964538i	$0.414977\pi$
$692$		0			0
$693$	−101.236	+	220.844i	−0.146084	+	0.318678i
$694$		0			0
$695$	273.893	−	158.132i	0.394091	−	0.227529i
$696$		0			0
$697$	114.688	−	198.646i	0.164546	−	0.285001i
$698$		0			0
$699$			628.266i			0.898807i
$700$		0			0
$701$	998.973			1.42507			0.712534	−	0.701637i	$-0.247547\pi$
$701$	998.973			1.42507			0.712534	+	0.701637i	$0.247547\pi$
$702$		0			0
$703$	−83.9173	−	48.4497i	−0.119370	−	0.0689185i
$704$		0			0
$705$	−42.5452	−	73.6904i	−0.0603478	−	0.104525i
$706$		0			0
$707$	476.672	−	338.416i	0.674217	−	0.478664i
$708$		0			0
$709$	−233.324	−	404.129i	−0.329089	−	0.569998i	0.653243	−	0.757149i	$-0.273408\pi$
$709$	−233.324	−	404.129i	−0.329089	−	0.569998i	−0.982331	+	0.187150i	$0.940075\pi$
$710$		0			0
$711$	−267.406	−	154.387i	−0.376098	−	0.217140i
$712$		0			0
$713$	1377.28			1.93167
$714$		0			0
$715$			422.240i			0.590546i
$716$		0			0
$717$	−296.426	+	513.424i	−0.413425	+	0.716073i
$718$		0			0
$719$	−329.811	+	190.416i	−0.458707	+	0.264835i	−0.711501	−	0.702685i	$-0.751984\pi$
$719$	−329.811	+	190.416i	−0.458707	+	0.264835i	0.252793	+	0.967520i	$0.418651\pi$
$720$		0			0
$721$	−868.617	+	81.6964i	−1.20474	+	0.113310i
$722$		0			0
$723$	−353.591	+	204.146i	−0.489061	+	0.282360i
$724$		0			0
$725$	346.806	−	600.686i	0.478353	−	0.828533i
$726$		0			0
$727$		−	868.875i		−	1.19515i	−0.801813	−	0.597575i	$-0.796131\pi$
$727$		−	868.875i		−	1.19515i	0.801813	−	0.597575i	$-0.203869\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	10.2243	+	5.90299i	0.0139867	+	0.00807522i
$732$		0			0
$733$	−135.684	−	235.011i	−0.185108	−	0.320616i	0.758505	−	0.651667i	$-0.225930\pi$
$733$	−135.684	−	235.011i	−0.185108	−	0.320616i	−0.943613	+	0.331051i	$0.892597\pi$
$734$		0			0
$735$	−148.592	+	128.017i	−0.202166	+	0.174173i
$736$		0			0
$737$	413.885	+	716.869i	0.561580	+	0.972686i
$738$		0			0
$739$	−1121.40	−	647.443i	−1.51746	−	0.876107i	−0.999789	−	0.0205291i	$-0.993465\pi$
$739$	−1121.40	−	647.443i	−1.51746	−	0.876107i	−0.517673	−	0.855578i	$-0.673202\pi$
$740$		0			0
$741$	67.5399			0.0911470
$742$		0			0
$743$			69.5251i			0.0935735i	0.998905	+	0.0467868i	$0.0148981\pi$
$743$			69.5251i			0.0935735i	−0.998905	+	0.0467868i	$0.985102\pi$
$744$		0			0
$745$	53.4692	−	92.6113i	0.0717707	−	0.124310i
$746$		0			0
$747$	112.109	−	64.7263i	0.150079	−	0.0866483i
$748$		0			0
$749$	251.300	−	23.6357i	0.335515	−	0.0315563i
$750$		0			0
$751$	−935.360	+	540.030i	−1.24549	+	0.719082i	−0.970206	−	0.242282i	$-0.922104\pi$
$751$	−935.360	+	540.030i	−1.24549	+	0.719082i	−0.275280	+	0.961364i	$0.588771\pi$
$752$		0			0
$753$	355.014	−	614.903i	0.471467	−	0.816604i
$754$		0			0
$755$		−	214.423i		−	0.284004i
$756$		0			0
$757$	−1073.01			−1.41745			−0.708727	−	0.705482i	$-0.750730\pi$
$757$	−1073.01			−1.41745			−0.708727	+	0.705482i	$0.750730\pi$
$758$		0			0
$759$	−795.379	−	459.212i	−1.04793	−	0.605023i
$760$		0			0
$761$	594.859	+	1030.33i	0.781681	+	1.35391i	0.930962	+	0.365117i	$0.118971\pi$
$761$	594.859	+	1030.33i	0.781681	+	1.35391i	−0.149280	+	0.988795i	$0.547696\pi$
$762$		0			0
$763$	−1054.23	+	748.457i	−1.38169	+	0.980939i
$764$		0			0
$765$	−29.4049	−	50.9307i	−0.0384377	−	0.0665761i
$766$		0			0
$767$	−403.861	−	233.169i	−0.526547	−	0.304002i
$768$		0			0
$769$	497.083			0.646402			0.323201	−	0.946330i	$-0.395241\pi$
$769$	497.083			0.646402			0.323201	+	0.946330i	$0.395241\pi$
$770$		0			0
$771$			669.035i			0.867750i
$772$		0			0
$773$	−610.658	+	1057.69i	−0.789984	+	1.36829i	0.135992	+	0.990710i	$0.456578\pi$
$773$	−610.658	+	1057.69i	−0.789984	+	1.36829i	−0.925976	+	0.377583i	$0.876755\pi$
$774$		0			0
$775$	511.593	−	295.368i	0.660120	−	0.381120i
$776$		0			0
$777$	−198.287	+	432.560i	−0.255196	+	0.556705i
$778$		0			0
$779$	57.8178	−	33.3811i	0.0742205	−	0.0428513i
$780$		0			0
$781$	412.767	−	714.934i	0.528511	−	0.915408i
$782$		0			0
$783$		−	183.327i		−	0.234135i
$784$		0			0
$785$	−425.277			−0.541754
$786$		0			0
$787$	364.854	+	210.649i	0.463601	+	0.267660i	0.713557	−	0.700597i	$-0.247083\pi$
$787$	364.854	+	210.649i	0.463601	+	0.267660i	−0.249956	+	0.968257i	$0.580416\pi$
$788$		0			0
$789$	38.7395	+	67.0988i	0.0490995	+	0.0850428i
$790$		0			0
$791$	1347.83	+	617.851i	1.70396	+	0.781101i
$792$		0			0
$793$	816.485	+	1414.19i	1.02962	+	1.78335i
$794$		0			0
$795$	−112.004	−	64.6656i	−0.140886	−	0.0813404i
$796$		0			0
$797$	−395.391			−0.496099			−0.248050	−	0.968747i	$-0.579790\pi$
$797$	−395.391			−0.496099			−0.248050	+	0.968747i	$0.579790\pi$
$798$		0			0
$799$			180.327i			0.225691i
$800$		0			0
$801$	−186.145	+	322.413i	−0.232391	+	0.402513i
$802$		0			0
$803$	−293.017	+	169.173i	−0.364903	+	0.210677i
$804$		0			0
$805$	−429.232	−	604.590i	−0.533208	−	0.751044i
$806$		0			0
$807$	−583.522	+	336.897i	−0.723076	+	0.417468i
$808$		0			0
$809$	238.454	−	413.014i	0.294751	−	0.510524i	−0.680176	−	0.733049i	$-0.738097\pi$
$809$	238.454	−	413.014i	0.294751	−	0.510524i	0.974927	+	0.222525i	$0.0714300\pi$
$810$		0			0
$811$			268.467i			0.331032i	0.986207	+	0.165516i	$0.0529289\pi$
$811$			268.467i			0.331032i	−0.986207	+	0.165516i	$0.947071\pi$
$812$		0			0
$813$	−709.238			−0.872371
$814$		0			0
$815$	−133.244	−	76.9285i	−0.163490	−	0.0943908i
$816$		0			0
$817$	1.71812	+	2.97587i	0.00210296	+	0.00364244i
$818$		0			0
$819$	−31.0574	−	330.210i	−0.0379211	−	0.403187i
$820$		0			0
$821$	−323.328	−	560.021i	−0.393822	−	0.682120i	0.599128	−	0.800653i	$-0.295514\pi$
$821$	−323.328	−	560.021i	−0.393822	−	0.682120i	−0.992950	+	0.118533i	$0.962181\pi$
$822$		0			0
$823$	−181.913	−	105.028i	−0.221037	−	0.127616i	0.385393	−	0.922752i	$-0.374066\pi$
$823$	−181.913	−	105.028i	−0.221037	−	0.127616i	−0.606430	+	0.795137i	$0.707399\pi$
$824$		0			0
$825$	−393.927			−0.477487
$826$		0			0
$827$		−	590.763i		−	0.714345i	−0.934038	−	0.357173i	$-0.883741\pi$
$827$		−	590.763i		−	0.714345i	0.934038	−	0.357173i	$-0.116259\pi$
$828$		0			0
$829$	−746.646	+	1293.23i	−0.900659	+	1.55999i	−0.0740183	+	0.997257i	$0.523582\pi$
$829$	−746.646	+	1293.23i	−0.900659	+	1.55999i	−0.826641	+	0.562730i	$0.809751\pi$
$830$		0			0
$831$	270.084	−	155.933i	0.325011	−	0.187645i
$832$		0			0
$833$	408.364	−	77.5016i	0.490232	−	0.0930391i
$834$		0			0
$835$	−237.809	+	137.299i	−0.284801	+	0.164430i
$836$		0			0
$837$	78.0682	−	135.218i	0.0932714	−	0.161551i
$838$		0			0
$839$			529.587i			0.631212i	0.948890	+	0.315606i	$0.102208\pi$
$839$			529.587i			0.631212i	−0.948890	+	0.315606i	$0.897792\pi$
$840$		0			0
$841$	403.776			0.480114
$842$		0			0
$843$	316.378	+	182.661i	0.375301	+	0.216680i
$844$		0			0
$845$	−92.9471	−	160.989i	−0.109997	−	0.190520i
$846$		0			0
$847$	8.41255	+	89.4443i	0.00993217	+	0.105601i
$848$		0			0
$849$	212.192	+	367.527i	0.249931	+	0.432894i
$850$		0			0
$851$	−1557.88	−	899.443i	−1.83065	−	1.05693i
$852$		0			0
$853$	544.072			0.637833			0.318917	−	0.947783i	$-0.396681\pi$
$853$	544.072			0.637833			0.318917	+	0.947783i	$0.396681\pi$
$854$		0			0
$855$		−	17.1171i		−	0.0200200i
$856$		0			0
$857$	−312.526	+	541.310i	−0.364674	+	0.631634i	−0.988724	−	0.149751i	$-0.952153\pi$
$857$	−312.526	+	541.310i	−0.364674	+	0.631634i	0.624050	+	0.781384i	$0.285486\pi$
$858$		0			0
$859$	−648.151	+	374.210i	−0.754542	+	0.435635i	−0.827333	−	0.561712i	$-0.810143\pi$
$859$	−648.151	+	374.210i	−0.754542	+	0.435635i	0.0727908	+	0.997347i	$0.476809\pi$
$860$		0			0
$861$	−189.791	−	267.328i	−0.220431	−	0.310485i
$862$		0			0
$863$	−750.798	+	433.473i	−0.869986	+	0.502286i	−0.867343	−	0.497710i	$-0.834174\pi$
$863$	−750.798	+	433.473i	−0.869986	+	0.502286i	−0.00264216	+	0.999997i	$0.500841\pi$
$864$		0			0
$865$	−231.581	+	401.110i	−0.267724	+	0.463711i
$866$		0			0
$867$		−	375.930i		−	0.433599i
$868$		0			0
$869$	−1190.70			−1.37020
$870$		0			0
$871$	−978.678	−	565.040i	−1.12363	−	0.648726i
$872$		0			0
$873$	−22.0779	−	38.2401i	−0.0252897	−	0.0438031i
$874$		0			0
$875$	−656.731	−	301.049i	−0.750550	−	0.344055i
$876$		0			0
$877$	284.689	+	493.096i	0.324617	+	0.562253i	0.981435	−	0.191796i	$-0.0614313\pi$
$877$	284.689	+	493.096i	0.324617	+	0.562253i	−0.656818	+	0.754049i	$0.728098\pi$
$878$		0			0
$879$	393.187	+	227.006i	0.447311	+	0.258255i
$880$		0			0
$881$	781.679			0.887263			0.443632	−	0.896209i	$-0.353690\pi$
$881$	781.679			0.887263			0.443632	+	0.896209i	$0.353690\pi$
$882$		0			0
$883$		−	1139.96i		−	1.29101i	−0.763757	−	0.645504i	$-0.776647\pi$
$883$		−	1139.96i		−	1.29101i	0.763757	−	0.645504i	$-0.223353\pi$
$884$		0			0
$885$	−59.0938	+	102.353i	−0.0667727	+	0.115654i
$886$		0			0
$887$	131.848	−	76.1227i	0.148645	−	0.0858204i	−0.423833	−	0.905741i	$-0.639316\pi$
$887$	131.848	−	76.1227i	0.148645	−	0.0858204i	0.572478	+	0.819920i	$0.305982\pi$
$888$		0			0
$889$	102.403	−	223.391i	0.115189	−	0.251283i
$890$		0			0
$891$	−90.1689	+	52.0590i	−0.101200	+	0.0584276i
$892$		0			0
$893$	−26.2430	+	45.4542i	−0.0293875	+	0.0509006i
$894$		0			0
$895$		−	428.037i		−	0.478253i
$896$		0			0
$897$	1253.84			1.39782
$898$		0			0
$899$	918.118	+	530.076i	1.02127	+	0.589628i
$900$		0			0
$901$	137.042	+	237.364i	0.152100	+	0.263445i
$902$		0			0
$903$	13.7593	−	9.76849i	0.0152373	−	0.0108178i
$904$		0			0
$905$	263.880	+	457.053i	0.291580	+	0.505031i
$906$		0			0
$907$	−406.700	−	234.808i	−0.448401	−	0.258885i	0.258754	−	0.965943i	$-0.416688\pi$
$907$	−406.700	−	234.808i	−0.448401	−	0.258885i	−0.707155	+	0.707059i	$0.750022\pi$
$908$		0			0
$909$	250.537			0.275618
$910$		0			0
$911$		−	309.559i		−	0.339801i	−0.985461	−	0.169901i	$-0.945655\pi$
$911$		−	309.559i		−	0.339801i	0.985461	−	0.169901i	$-0.0543447\pi$
$912$		0			0
$913$	249.599	−	432.318i	0.273383	−	0.473514i
$914$		0			0
$915$	358.409	−	206.928i	0.391704	−	0.226151i
$916$		0			0
$917$	−1100.72	+	103.527i	−1.20035	+	0.112897i
$918$		0			0
$919$	−1020.42	+	589.137i	−1.11035	+	0.641063i	−0.938921	−	0.344133i	$-0.888173\pi$
$919$	−1020.42	+	589.137i	−1.11035	+	0.641063i	−0.171433	+	0.985196i	$0.554840\pi$
$920$		0			0
$921$	−126.874	+	219.752i	−0.137757	+	0.238601i
$922$		0			0
$923$			1127.03i			1.22105i
$924$		0			0
$925$	−771.571			−0.834130
$926$		0			0
$927$	−323.813	−	186.954i	−0.349313	−	0.201676i
$928$		0			0
$929$	141.746	+	245.511i	0.152579	+	0.264275i	0.932175	−	0.362008i	$-0.117909\pi$
$929$	141.746	+	245.511i	0.152579	+	0.264275i	−0.779596	+	0.626283i	$0.784575\pi$
$930$		0			0
$931$	114.213	+	39.8936i	0.122678	+	0.0428503i
$932$		0			0
$933$	13.0394	+	22.5848i	0.0139757	+	0.0242067i
$934$		0			0
$935$	−196.400	−	113.392i	−0.210054	−	0.121275i
$936$		0			0
$937$	−343.658			−0.366764			−0.183382	−	0.983042i	$-0.558705\pi$
$937$	−343.658			−0.366764			−0.183382	+	0.983042i	$0.558705\pi$
$938$		0			0
$939$			771.758i			0.821893i
$940$		0			0
$941$	307.299	−	532.257i	0.326566	−	0.565629i	−0.655262	−	0.755402i	$-0.727442\pi$
$941$	307.299	−	532.257i	0.326566	−	0.565629i	0.981828	+	0.189773i	$0.0607751\pi$
$942$		0			0
$943$	1073.36	−	619.703i	1.13824	−	0.657162i
$944$		0			0
$945$	−83.6875	+	7.87109i	−0.0885582	+	0.00832920i
$946$		0			0
$947$	1353.87	−	781.658i	1.42964	−	0.825404i	0.432550	−	0.901610i	$-0.357614\pi$
$947$	1353.87	−	781.658i	1.42964	−	0.825404i	0.997092	+	0.0762056i	$0.0242805\pi$
$948$		0			0
$949$	230.957	−	400.030i	0.243369	−	0.421528i
$950$		0			0
$951$			164.328i			0.172795i
$952$		0			0
$953$	−65.3694			−0.0685933			−0.0342966	−	0.999412i	$-0.510919\pi$
$953$	−65.3694			−0.0685933			−0.0342966	+	0.999412i	$0.510919\pi$
$954$		0			0
$955$	300.978	+	173.770i	0.315160	+	0.181958i
$956$		0			0
$957$	−353.476	−	612.238i	−0.369358	−	0.639747i
$958$		0			0
$959$	−1261.71	+	895.759i	−1.31565	+	0.934056i
$960$		0			0
$961$	−29.0449	−	50.3072i	−0.0302236	−	0.0523488i
$962$		0			0
$963$	93.6827	+	54.0878i	0.0972822	+	0.0561659i
$964$		0			0
$965$	188.438			0.195273
$966$		0			0
$967$			54.5021i			0.0563620i	0.999603	+	0.0281810i	$0.00897148\pi$
$967$			54.5021i			0.0563620i	−0.999603	+	0.0281810i	$0.991029\pi$
$968$		0			0
$969$	−18.1377	+	31.4154i	−0.0187179	+	0.0324204i
$970$		0			0
$971$	−1112.98	+	642.578i	−1.14622	+	0.661769i	−0.947963	−	0.318381i	$-0.896861\pi$
$971$	−1112.98	+	642.578i	−1.14622	+	0.661769i	−0.198255	+	0.980150i	$0.563527\pi$
$972$		0			0
$973$	−399.198	+	870.842i	−0.410275	+	0.895007i
$974$		0			0
$975$	465.743	−	268.897i	0.477685	−	0.275791i
$976$		0			0
$977$	−776.204	+	1344.43i	−0.794477	+	1.37607i	0.128693	+	0.991684i	$0.458922\pi$
$977$	−776.204	+	1344.43i	−0.794477	+	1.37607i	−0.923171	+	0.384390i	$0.874412\pi$
$978$		0			0
$979$			1435.64i			1.46643i
$980$		0			0
$981$	−554.100			−0.564832
$982$		0			0
$983$	−59.1187	−	34.1322i	−0.0601411	−	0.0347225i	0.469628	−	0.882864i	$-0.344388\pi$
$983$	−59.1187	−	34.1322i	−0.0601411	−	0.0347225i	−0.529769	+	0.848142i	$0.677721\pi$
$984$		0			0
$985$	222.684	+	385.700i	0.226075	+	0.391574i
$986$		0			0
$987$	234.298	+	107.403i	0.237384	+	0.108818i
$988$		0			0
$989$	31.8960	+	55.2455i	0.0322508	+	0.0558600i
$990$		0			0
$991$	688.196	+	397.330i	0.694446	+	0.400939i	0.805275	−	0.592901i	$-0.202017\pi$
$991$	688.196	+	397.330i	0.694446	+	0.400939i	−0.110829	+	0.993839i	$0.535351\pi$
$992$		0			0
$993$	121.386			0.122241
$994$		0			0
$995$		−	202.332i		−	0.203349i
$996$		0			0
$997$	513.493	−	889.397i	0.515039	−	0.892073i	−0.484809	−	0.874620i	$-0.661111\pi$
$997$	513.493	−	889.397i	0.515039	−	0.892073i	0.999848	−	0.0174530i	$-0.00555575\pi$
$998$		0			0
$999$	−176.611	+	101.966i	−0.176787	+	0.102068i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.3.be.d.319.2	yes	6
3.2	odd	2		1008.3.cd.h.991.2		6
4.3	odd	2		336.3.be.f.319.2	yes	6
7.2	even	3		336.3.be.f.79.2	yes	6
7.3	odd	6		2352.3.m.o.1471.2		6
7.4	even	3		2352.3.m.n.1471.5		6
12.11	even	2		1008.3.cd.i.991.2		6
21.2	odd	6		1008.3.cd.i.415.2		6
28.3	even	6		2352.3.m.o.1471.5		6
28.11	odd	6		2352.3.m.n.1471.2		6
28.23	odd	6	inner	336.3.be.d.79.2	✓	6
84.23	even	6		1008.3.cd.h.415.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.3.be.d.79.2	✓	6	28.23	odd	6	inner
336.3.be.d.319.2	yes	6	1.1	even	1	trivial
336.3.be.f.79.2	yes	6	7.2	even	3
336.3.be.f.319.2	yes	6	4.3	odd	2
1008.3.cd.h.415.2		6	84.23	even	6
1008.3.cd.h.991.2		6	3.2	odd	2
1008.3.cd.i.415.2		6	21.2	odd	6
1008.3.cd.i.991.2		6	12.11	even	2
2352.3.m.n.1471.2		6	28.11	odd	6
2352.3.m.n.1471.5		6	7.4	even	3
2352.3.m.o.1471.2		6	7.3	odd	6
2352.3.m.o.1471.5		6	28.3	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	336.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 0.866025i) q^{3} +(-1.15548 - 2.00135i) q^{5} +(6.36328 + 2.91696i) q^{7} +(1.50000 + 2.59808i) q^{9} +(10.0188 + 5.78434i) q^{11} -15.7937 q^{13} +4.00270i q^{15} +(4.24136 - 7.34625i) q^{17} +(2.13819 - 1.23449i) q^{19} +(-7.01876 - 9.88620i) q^{21} +(39.6945 - 22.9176i) q^{23} +(9.82973 - 17.0256i) q^{25} -5.19615i q^{27} +35.2814 q^{29} +(26.0227 + 15.0242i) q^{31} +(-10.0188 - 17.3530i) q^{33} +(-1.51479 - 16.1057i) q^{35} +(-19.6234 - 33.9887i) q^{37} +(23.6905 + 13.6777i) q^{39} +27.0405 q^{41} +1.39177i q^{43} +(3.46644 - 6.00406i) q^{45} +(-18.4102 + 10.6291i) q^{47} +(31.9827 + 37.1229i) q^{49} +(-12.7241 + 7.34625i) q^{51} +(-16.1555 + 27.9821i) q^{53} -26.7348i q^{55} -4.27639 q^{57} +(25.5711 + 14.7635i) q^{59} +(-51.6970 - 89.5418i) q^{61} +(1.96644 + 20.9077i) q^{63} +(18.2493 + 31.6087i) q^{65} +(61.9664 + 35.7763i) q^{67} -79.3890 q^{69} -71.3595i q^{71} +(-14.6234 + 25.3285i) q^{73} +(-29.4892 + 17.0256i) q^{75} +(46.8796 + 66.0317i) q^{77} +(-89.1353 + 51.4623i) q^{79} +(-4.50000 + 7.79423i) q^{81} -43.1509i q^{83} -19.6032 q^{85} +(-52.9221 - 30.5546i) q^{87} +(62.0484 + 107.471i) q^{89} +(-100.500 - 46.0695i) q^{91} +(-26.0227 - 45.0727i) q^{93} +(-4.94129 - 2.85285i) q^{95} -14.7186 q^{97} +34.7060i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{3} + q^{5} - 11 q^{7} + 9 q^{9} + 3 q^{11} - 44 q^{13} + 8 q^{17} - 30 q^{19} + 15 q^{21} + 24 q^{23} - 14 q^{25} + 34 q^{29} - 39 q^{31} - 3 q^{33} - 90 q^{35} + 6 q^{37} + 66 q^{39} - 136 q^{41}+ \cdots - 266 q^{97}+O(q^{100}) \) 6 * q - 9 * q^3 + q^5 - 11 * q^7 + 9 * q^9 + 3 * q^11 - 44 * q^13 + 8 * q^17 - 30 * q^19 + 15 * q^21 + 24 * q^23 - 14 * q^25 + 34 * q^29 - 39 * q^31 - 3 * q^33 - 90 * q^35 + 6 * q^37 + 66 * q^39 - 136 * q^41 - 3 * q^45 - 258 * q^47 + 157 * q^49 - 24 * q^51 - 89 * q^53 + 60 * q^57 + 63 * q^59 - 50 * q^61 - 12 * q^63 - 184 * q^65 + 348 * q^67 - 48 * q^69 + 36 * q^73 + 42 * q^75 + 221 * q^77 + 3 * q^79 - 27 * q^81 + 536 * q^85 - 51 * q^87 - 202 * q^89 - 62 * q^91 + 39 * q^93 + 432 * q^95 - 266 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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