LMFDB - Embedded newform 336.3.be.d.79.2

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)

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")

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);

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			79.2
Root			$-3.78298i$ of defining polynomial
Character	$\chi$	$=$	336.79
Dual form			336.3.be.d.319.2

$q$-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 $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

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

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	−0.958131	−	0.286330i	$-0.907565\pi$
$5$	−1.15548	+	2.00135i	−0.231096	+	0.400270i	0.727035	+	0.686601i	$0.240898\pi$
$6$		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	0.0301093	−	0.999547i	$-0.490414\pi$
$11$	10.0188	−	5.78434i	0.910797	−	0.525849i	0.880687	+	0.473698i	$0.157081\pi$
$12$		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	0.963385	−	0.268122i	$-0.0864032\pi$
$17$	4.24136	+	7.34625i	0.249492	+	0.432132i	−0.713893	+	0.700255i	$0.753070\pi$
$18$		0			0
$19$	2.13819	+	1.23449i	0.112537	+	0.0649730i	0.555212	−	0.831709i	$-0.312637\pi$
$19$	2.13819	+	1.23449i	0.112537	+	0.0649730i	−0.442675	+	0.896682i	$0.645971\pi$
$20$		0			0
$21$	−7.01876	+	9.88620i	−0.334227	+	0.470771i
$22$		0			0
$23$	39.6945	+	22.9176i	1.72585	+	0.996418i	0.905204	+	0.424977i	$0.139718\pi$
$23$	39.6945	+	22.9176i	1.72585	+	0.996418i	0.820643	+	0.571441i	$0.193615\pi$
$24$		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	−0.0176318	−	0.999845i	$-0.505613\pi$
$31$	26.0227	−	15.0242i	0.839443	−	0.484653i	0.857075	+	0.515192i	$0.172279\pi$
$32$		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	0.469010	+	0.883193i	$0.344611\pi$
$37$	−19.6234	+	33.9887i	−0.530362	+	0.918614i	−0.999372	+	0.0354216i	$0.988723\pi$
$38$		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	$-0.994848\pi$
$43$		−	1.39177i		−	0.0323667i	0.999869	−	0.0161834i	$-0.00515155\pi$
$44$		0			0
$45$	3.46644	+	6.00406i	0.0770321	+	0.133423i
$46$		0			0
$47$	−18.4102	−	10.6291i	−0.391705	−	0.226151i	0.291193	−	0.956664i	$-0.405948\pi$
$47$	−18.4102	−	10.6291i	−0.391705	−	0.226151i	−0.682899	+	0.730513i	$0.739281\pi$
$48$		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	0.672401	−	0.740187i	$-0.265263\pi$
$53$	−16.1555	−	27.9821i	−0.304820	−	0.527964i	−0.977221	+	0.212223i	$0.931930\pi$
$54$		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	−0.267389	−	0.963589i	$-0.586161\pi$
$59$	25.5711	−	14.7635i	0.433408	−	0.250228i	0.700798	+	0.713360i	$0.252828\pi$
$60$		0			0
$61$	−51.6970	+	89.5418i	−0.847491	+	1.46790i	0.0359484	+	0.999354i	$0.488555\pi$
$61$	−51.6970	+	89.5418i	−0.847491	+	1.46790i	−0.883440	+	0.468545i	$0.844779\pi$
$62$		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	0.0396861	−	0.999212i	$-0.487364\pi$
$67$	61.9664	−	35.7763i	0.924872	−	0.533975i	0.885186	+	0.465237i	$0.154031\pi$
$68$		0			0
$69$	−79.3890			−1.15056
$70$		0			0
$71$			71.3595i			1.00506i	0.864559	+	0.502532i	$0.167598\pi$
$71$			71.3595i			1.00506i	−0.864559	+	0.502532i	$0.832402\pi$
$72$		0			0
$73$	−14.6234	−	25.3285i	−0.200321	−	0.346965i	0.748311	−	0.663348i	$-0.230865\pi$
$73$	−14.6234	−	25.3285i	−0.200321	−	0.346965i	−0.948632	+	0.316382i	$0.897532\pi$
$74$		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	−0.184790	−	0.982778i	$-0.559160\pi$
$79$	−89.1353	−	51.4623i	−1.12830	−	0.651421i	−0.943506	+	0.331357i	$0.892494\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			43.1509i			0.519890i	0.965623	+	0.259945i	$0.0837044\pi$
$83$			43.1509i			0.519890i	−0.965623	+	0.259945i	$0.916296\pi$
$84$		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	−0.272269	−	0.962221i	$-0.587774\pi$
$89$	62.0484	−	107.471i	0.697173	−	1.20754i	0.969443	−	0.245318i	$-0.0788925\pi$
$90$		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	0.995262	−	0.0972301i	$-0.0309983\pi$
$101$	41.7561	+	72.3238i	0.413427	+	0.716077i	−0.581835	+	0.813307i	$0.697665\pi$
$102$		0			0
$103$	−107.938	−	62.3179i	−1.04794	−	0.605028i	−0.125868	−	0.992047i	$-0.540172\pi$
$103$	−107.938	−	62.3179i	−1.04794	−	0.605028i	−0.922072	+	0.387019i	$0.873505\pi$
$104$		0			0
$105$	−11.6757	−	25.4703i	−0.111197	−	0.242575i
$106$		0			0
$107$	31.2276	+	18.0293i	0.291847	+	0.168498i	0.638774	−	0.769394i	$-0.279442\pi$
$107$	31.2276	+	18.0293i	0.291847	+	0.168498i	−0.346928	+	0.937892i	$0.612775\pi$
$108$		0			0
$109$	−92.3500	−	159.955i	−0.847247	−	1.46748i	−0.883655	−	0.468139i	$-0.844925\pi$
$109$	−92.3500	−	159.955i	−0.847247	−	1.46748i	0.0364077	−	0.999337i	$-0.488409\pi$
$110$		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	$0.0441360\pi$
$127$			35.1062i			0.276427i	−0.990402	+	0.138213i	$0.955864\pi$
$128$		0			0
$129$	1.20531	+	2.08765i	0.00934346	+	0.0161834i
$130$		0			0
$131$	−136.780	−	78.9699i	−1.04412	−	0.602824i	−0.123124	−	0.992391i	$-0.539291\pi$
$131$	−136.780	−	78.9699i	−1.04412	−	0.602824i	−0.920998	+	0.389568i	$0.872624\pi$
$132$		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	−0.915101	−	0.403225i	$-0.867889\pi$
$137$	−110.525	−	191.435i	−0.806753	−	1.39734i	0.108347	−	0.994113i	$-0.465444\pi$
$138$		0			0
$139$		−	136.854i		−	0.984563i	−0.870436	−	0.492281i	$-0.836163\pi$
$139$		−	136.854i		−	0.984563i	0.870436	−	0.492281i	$-0.163837\pi$
$140$		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	−0.777879	−	0.628414i	$-0.783704\pi$
$149$	23.1372	−	40.0748i	0.155283	−	0.268958i	0.933162	+	0.359456i	$0.117038\pi$
$150$		0			0
$151$	80.3543	−	46.3926i	0.532148	−	0.307236i	−0.209743	−	0.977757i	$-0.567263\pi$
$151$	80.3543	−	46.3926i	0.532148	−	0.307236i	0.741891	+	0.670521i	$0.233929\pi$
$152$		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	0.994741	+	0.102421i	$0.0326588\pi$
$157$	92.0129	+	159.371i	0.586070	+	1.01510i	−0.408672	+	0.912682i	$0.634008\pi$
$158$		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	0.666325	−	0.745661i	$-0.267866\pi$
$163$	57.6574	+	33.2885i	0.353726	+	0.204224i	−0.312599	+	0.949885i	$0.601200\pi$
$164$		0			0
$165$	−23.1530	−	40.1022i	−0.140321	−	0.243043i
$166$		0			0
$167$			118.824i			0.711521i	0.934577	+	0.355761i	$0.115778\pi$
$167$			118.824i			0.711521i	−0.934577	+	0.355761i	$0.884222\pi$
$168$		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	0.416319	+	0.909219i	$0.363320\pi$
$173$	−100.210	+	173.568i	−0.579247	+	1.00329i	−0.995566	+	0.0940666i	$0.970013\pi$
$174$		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	0.0201800	−	0.999796i	$-0.493576\pi$
$179$	160.405	−	92.6100i	0.896119	−	0.517375i	0.875939	+	0.482422i	$0.160243\pi$
$180$		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	0.118682	−	0.992932i	$-0.462133\pi$
$191$	−130.239	−	75.1937i	−0.681881	−	0.393684i	−0.800563	+	0.599248i	$0.795466\pi$
$192$		0			0
$193$	−40.7705	−	70.6165i	−0.211246	−	0.365889i	0.740859	−	0.671661i	$-0.234419\pi$
$193$	−40.7705	−	70.6165i	−0.211246	−	0.365889i	−0.952105	+	0.305772i	$0.901085\pi$
$194$		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	−0.297241	−	0.954803i	$-0.596066\pi$
$199$	75.8234	−	43.7767i	0.381022	−	0.219983i	0.678263	+	0.734819i	$0.262733\pi$
$200$		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	$0.0979244\pi$
$211$			127.785i			0.605618i	−0.953051	+	0.302809i	$0.902076\pi$
$212$		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	$-0.780315\pi$
$223$		−	283.951i		−	1.27332i	0.771144	−	0.636660i	$-0.219685\pi$
$224$		0			0
$225$	58.9784			0.262126
$226$		0			0
$227$	358.164	−	206.786i	1.57782	−	0.910952i	0.582651	−	0.812722i	$-0.302015\pi$
$227$	358.164	−	206.786i	1.57782	−	0.910952i	0.995164	−	0.0982297i	$-0.0313180\pi$
$228$		0			0
$229$	−80.6550	+	139.699i	−0.352205	+	0.610038i	−0.986636	−	0.162943i	$-0.947901\pi$
$229$	−80.6550	+	139.699i	−0.352205	+	0.610038i	0.634430	+	0.772980i	$0.281235\pi$
$230$		0			0
$231$	−13.1342	+	139.646i	−0.0568581	+	0.604530i
$232$		0			0
$233$	−181.365	+	314.133i	−0.778390	+	1.34821i	0.154480	+	0.987996i	$0.450630\pi$
$233$	−181.365	+	314.133i	−0.778390	+	1.34821i	−0.932869	+	0.360215i	$0.882703\pi$
$234$		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	$0.254062\pi$
$239$			342.283i			1.43215i	−0.698026	+	0.716073i	$0.745938\pi$
$240$		0			0
$241$	117.864	+	204.146i	0.489061	+	0.847079i	0.999921	−	0.0125850i	$-0.00400604\pi$
$241$	117.864	+	204.146i	0.489061	+	0.847079i	−0.510859	+	0.859664i	$0.670673\pi$
$242$		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	$-0.695854\pi$
$251$		−	409.935i		−	1.63321i	0.577198	−	0.816604i	$-0.304146\pi$
$252$		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	0.195605	+	0.980683i	$0.437333\pi$
$257$	−193.134	+	334.518i	−0.751494	+	1.30163i	−0.947099	+	0.320943i	$0.896000\pi$
$258$		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	−0.571838	−	0.820367i	$-0.693769\pi$
$263$	−38.7395	+	22.3663i	−0.147298	+	0.0850428i	0.424539	+	0.905409i	$0.360436\pi$
$264$		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	0.959761	+	0.280818i	$0.0906056\pi$
$269$	194.507	+	336.897i	0.723076	+	1.25240i	−0.236685	+	0.971586i	$0.576061\pi$
$270$		0			0
$271$	354.619	+	204.739i	1.30856	+	0.755496i	0.981855	−	0.189632i	$-0.0607295\pi$
$271$	354.619	+	204.739i	1.30856	+	0.755496i	0.326701	+	0.945128i	$0.394063\pi$
$272$		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	0.656503	−	0.754323i	$-0.272035\pi$
$277$	−90.0281	−	155.933i	−0.325011	−	0.562936i	−0.981515	+	0.191387i	$0.938701\pi$
$278$		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	−0.825619	−	0.564228i	$-0.809174\pi$
$283$	−212.192	+	122.509i	−0.749794	+	0.432894i	0.0758257	+	0.997121i	$0.475841\pi$
$284$		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	$0.0766889\pi$
$307$			146.501i			0.477203i	−0.971118	+	0.238601i	$0.923311\pi$
$308$		0			0
$309$	215.876			0.698626
$310$		0			0
$311$	−13.0394	+	7.52828i	−0.0419272	+	0.0242067i	−0.520817	−	0.853668i	$-0.674373\pi$
$311$	−13.0394	+	7.52828i	−0.0419272	+	0.0242067i	0.478890	+	0.877875i	$0.341039\pi$
$312$		0			0
$313$	−222.787	+	385.879i	−0.711780	+	1.23284i	0.252408	+	0.967621i	$0.418778\pi$
$313$	−222.787	+	385.879i	−0.711780	+	1.23284i	−0.964188	+	0.265219i	$0.914556\pi$
$314$		0			0
$315$	39.5715	+	28.0940i	0.125624	+	0.0891874i
$316$		0			0
$317$	−47.4373	+	82.1638i	−0.149645	+	0.259192i	−0.931096	−	0.364774i	$-0.881146\pi$
$317$	−47.4373	+	82.1638i	−0.149645	+	0.259192i	0.781452	+	0.623966i	$0.214480\pi$
$318$		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	0.405509	−	0.914091i	$-0.367094\pi$
$331$	−60.6928	−	35.0410i	−0.183362	−	0.105864i	−0.588871	+	0.808227i	$0.700428\pi$
$332$		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	−0.929811	−	0.368038i	$-0.880029\pi$
$347$	−373.367	+	215.563i	−1.07599	+	0.621220i	−0.146175	+	0.989259i	$0.546696\pi$
$348$		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	0.922628	−	0.385691i	$-0.126037\pi$
$353$	44.9354	+	77.8304i	0.127296	+	0.220483i	−0.795332	+	0.606174i	$0.792704\pi$
$354$		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	−0.000173257	−	1.00000i	$-0.500055\pi$
$359$	−310.996	−	179.554i	−0.866285	−	0.500150i	−0.866112	+	0.499850i	$0.833388\pi$
$360$		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	−0.953800	−	0.300441i	$-0.902866\pi$
$367$	−429.578	+	248.017i	−1.17051	+	0.675795i	−0.216711	+	0.976236i	$0.569533\pi$
$368$		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	−0.449840	−	0.893109i	$-0.648519\pi$
$373$	204.604	−	354.384i	0.548535	−	0.950091i	0.998375	−	0.0569816i	$-0.0181476\pi$
$374$		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	$-0.752600\pi$
$379$		−	531.591i		−	1.40261i	0.712859	−	0.701307i	$-0.247400\pi$
$380$		0			0
$381$	−30.4028	−	52.6593i	−0.0797975	−	0.138213i
$382$		0			0
$383$	−646.737	−	373.394i	−1.68861	−	0.974918i	−0.955585	−	0.294714i	$-0.904776\pi$
$383$	−646.737	−	373.394i	−1.68861	−	0.974918i	−0.733023	−	0.680204i	$-0.761891\pi$
$384$		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	0.570439	−	0.821340i	$-0.306773\pi$
$389$	−165.746	−	287.080i	−0.426082	−	0.737995i	−0.996521	+	0.0833446i	$0.973440\pi$
$390$		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	−0.767142	−	0.641478i	$-0.778322\pi$
$397$	68.2701	−	118.247i	0.171965	−	0.297852i	0.939107	+	0.343626i	$0.111655\pi$
$398$		0			0
$399$	−27.2119	+	12.4740i	−0.0682002	+	0.0312633i
$400$		0			0
$401$	−195.014	+	337.775i	−0.486320	+	0.842331i	−0.999876	−	0.0157250i	$-0.994994\pi$
$401$	−195.014	+	337.775i	−0.486320	+	0.842331i	0.513556	+	0.858056i	$0.328328\pi$
$402$		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	−0.765207	−	0.643784i	$-0.777363\pi$
$409$	−384.516	−	666.001i	−0.940137	−	1.62837i	−0.174930	−	0.984581i	$-0.555970\pi$
$410$		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	$-0.708591\pi$
$419$		−	664.417i		−	1.58572i	0.609403	−	0.792861i	$-0.291409\pi$
$420$		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	−0.845619	−	0.533786i	$-0.820769\pi$
$431$	−347.454	+	200.602i	−0.806157	+	0.465435i	0.0394627	+	0.999221i	$0.487435\pi$
$432$		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	0.00231345	−	0.999997i	$-0.499264\pi$
$439$	−378.661	−	218.620i	−0.862553	−	0.497995i	−0.864866	+	0.502002i	$0.832597\pi$
$440$		0			0
$441$	−48.4739	−	138.778i	−0.109918	−	0.314689i
$442$		0			0
$443$	507.040	+	292.740i	1.14456	+	0.660812i	0.947556	−	0.319591i	$-0.103545\pi$
$443$	507.040	+	292.740i	1.14456	+	0.660812i	0.197004	+	0.980403i	$0.436879\pi$
$444$		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	−0.0574604	+	0.998348i	$0.518300\pi$
$457$	−408.249	+	707.109i	−0.893325	+	1.54728i	−0.835864	+	0.548936i	$0.815033\pi$
$458$		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	$-0.937049\pi$
$463$		−	181.939i		−	0.392958i	0.980508	−	0.196479i	$-0.0629507\pi$
$464$		0			0
$465$	−60.1376	−	104.161i	−0.129328	−	0.224003i
$466$		0			0
$467$	−76.9351	−	44.4185i	−0.164743	−	0.0951146i	0.415362	−	0.909656i	$-0.363655\pi$
$467$	−76.9351	−	44.4185i	−0.164743	−	0.0951146i	−0.580105	+	0.814542i	$0.696988\pi$
$468$		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	−0.380816	−	0.924651i	$-0.624357\pi$
$479$	109.953	−	63.4813i	0.229547	−	0.132529i	0.610363	+	0.792122i	$0.291024\pi$
$480$		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	−0.222007	−	0.975045i	$-0.571261\pi$
$487$	249.054	−	143.791i	0.511404	−	0.295259i	0.733410	+	0.679786i	$0.237927\pi$
$488$		0			0
$489$	−115.315			−0.235818
$490$		0			0
$491$			23.7600i			0.0483910i	0.999707	+	0.0241955i	$0.00770241\pi$
$491$			23.7600i			0.0483910i	−0.999707	+	0.0241955i	$0.992298\pi$
$492$		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	0.450415	−	0.892819i	$-0.351276\pi$
$499$	−48.6932	−	28.1130i	−0.0975815	−	0.0563387i	−0.547997	+	0.836481i	$0.684609\pi$
$500$		0			0
$501$	−102.905	−	178.236i	−0.205399	−	0.355761i
$502$		0			0
$503$			913.863i			1.81683i	0.418075	+	0.908413i	$0.362705\pi$
$503$			913.863i			1.81683i	−0.418075	+	0.908413i	$0.637295\pi$
$504$		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	0.0348625	−	0.999392i	$-0.488901\pi$
$509$	449.411	−	778.404i	0.882930	−	1.52928i	0.848068	−	0.529888i	$-0.177766\pi$
$510$		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	0.975908	−	0.218183i	$-0.0700130\pi$
$521$	155.780	+	269.819i	0.299002	+	0.517886i	−0.676906	+	0.736069i	$0.736680\pi$
$522$		0			0
$523$	681.450	+	393.436i	1.30296	+	0.752267i	0.980911	−	0.194455i	$-0.0622938\pi$
$523$	681.450	+	393.436i	1.30296	+	0.752267i	0.322053	+	0.946722i	$0.395627\pi$
$524$		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	−0.706663	−	0.707550i	$-0.749800\pi$
$541$	140.349	−	243.091i	0.259425	−	0.449337i	0.966088	+	0.258213i	$0.0831337\pi$
$542$		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	$-0.955113\pi$
$547$		−	153.761i		−	0.281099i	0.990074	−	0.140549i	$-0.0448869\pi$
$548$		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	0.968173	+	0.250283i	$0.0805235\pi$
$557$	390.366	+	676.135i	0.700837	+	1.21389i	−0.267335	+	0.963604i	$0.586143\pi$
$558$		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	0.443606	−	0.896222i	$-0.353699\pi$
$563$	811.598	−	468.577i	1.44156	−	0.832285i	0.997954	+	0.0639367i	$0.0203656\pi$
$564$		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	−0.279995	−	0.960001i	$-0.590333\pi$
$569$	393.400	−	681.388i	0.691388	−	1.19752i	0.971383	−	0.237517i	$-0.0763337\pi$
$570$		0			0
$571$	227.876	−	131.564i	0.399082	−	0.230410i	−0.287006	−	0.957929i	$-0.592660\pi$
$571$	227.876	−	131.564i	0.399082	−	0.230410i	0.686088	+	0.727519i	$0.259327\pi$
$572$		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	0.861220	−	0.508232i	$-0.169701\pi$
$577$	−5.50000	−	9.52628i	−0.00953206	−	0.0165100i	−0.870752	+	0.491722i	$0.836368\pi$
$578$		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	$0.128611\pi$
$587$			461.546i			0.786279i	−0.919479	+	0.393139i	$0.871389\pi$
$588$		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	−0.327552	−	0.944833i	$-0.606224\pi$
$593$	388.103	−	672.214i	0.654474	−	1.13358i	0.982025	−	0.188749i	$-0.0604431\pi$
$594$		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	−0.314807	−	0.949156i	$-0.601940\pi$
$599$	209.520	−	120.967i	0.349783	−	0.201947i	0.664590	+	0.747208i	$0.268606\pi$
$600$		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	0.985444	+	0.170002i	$0.0543773\pi$
$607$	986.613	+	569.621i	1.62539	+	0.938420i	0.639948	+	0.768419i	$0.278956\pi$
$608$		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	0.561729	−	0.827321i	$-0.310136\pi$
$613$	−267.033	−	462.514i	−0.435616	−	0.754510i	−0.997346	+	0.0728114i	$0.976803\pi$
$614$		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	−0.705113	−	0.709095i	$-0.749104\pi$
$619$	−274.573	+	158.525i	−0.443575	+	0.256098i	0.261538	+	0.965193i	$0.415770\pi$
$620$		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	$-0.623121\pi$
$631$		−	1168.77i		−	1.85225i	0.377222	−	0.926123i	$-0.376879\pi$
$632$		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	0.872294	−	0.488982i	$-0.162632\pi$
$641$	8.12563	+	14.0740i	0.0126765	+	0.0219563i	−0.859618	+	0.510938i	$0.829298\pi$
$642$		0			0
$643$		−	956.475i		−	1.48752i	−0.668447	−	0.743760i	$-0.733041\pi$
$643$		−	956.475i		−	1.48752i	0.668447	−	0.743760i	$-0.266959\pi$
$644$		0			0
$645$	−5.57084			−0.00863696
$646$		0			0
$647$	456.676	−	263.662i	0.705836	−	0.407515i	−0.103681	−	0.994611i	$-0.533062\pi$
$647$	456.676	−	263.662i	0.705836	−	0.407515i	0.809517	+	0.587096i	$0.199729\pi$
$648$		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	−0.961993	−	0.273073i	$-0.911960\pi$
$653$	−159.664	+	276.547i	−0.244509	+	0.423502i	0.717484	+	0.696575i	$0.245293\pi$
$654$		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	$0.0704432\pi$
$659$			289.303i			0.439004i	−0.975612	+	0.219502i	$0.929557\pi$
$660$		0			0
$661$	8.20984	+	14.2199i	0.0124203	+	0.0215126i	0.872169	−	0.489205i	$-0.162713\pi$
$661$	8.20984	+	14.2199i	0.0124203	+	0.0215126i	−0.859748	+	0.510718i	$0.829380\pi$
$662$		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	0.0270124	−	0.999635i	$-0.491401\pi$
$677$	595.229	−	1030.97i	0.879216	−	1.52285i	0.852203	−	0.523211i	$-0.175266\pi$
$678$		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	−0.943607	−	0.331067i	$-0.892591\pi$
$683$	−770.901	+	445.080i	−1.12870	+	0.651654i	−0.185091	+	0.982721i	$0.559258\pi$
$684$		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	0.263943	−	0.964538i	$-0.414977\pi$
$691$	−303.625	−	175.298i	−0.439400	−	0.253688i	−0.703343	+	0.710851i	$0.748310\pi$
$692$		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	−0.982331	−	0.187150i	$-0.940075\pi$
$709$	−233.324	+	404.129i	−0.329089	+	0.569998i	0.653243	+	0.757149i	$0.273408\pi$
$710$		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	0.252793	−	0.967520i	$-0.418651\pi$
$719$	−329.811	−	190.416i	−0.458707	−	0.264835i	−0.711501	+	0.702685i	$0.751984\pi$
$720$		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	$0.203869\pi$
$727$			868.875i			1.19515i	−0.801813	+	0.597575i	$0.796131\pi$
$728$		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	−0.943613	−	0.331051i	$-0.892597\pi$
$733$	−135.684	+	235.011i	−0.185108	+	0.320616i	0.758505	+	0.651667i	$0.225930\pi$
$734$		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	−0.517673	+	0.855578i	$0.673202\pi$
$739$	−1121.40	+	647.443i	−1.51746	+	0.876107i	−0.999789	+	0.0205291i	$0.993465\pi$
$740$		0			0
$741$	67.5399			0.0911470
$742$		0			0
$743$		−	69.5251i		−	0.0935735i	−0.998905	−	0.0467868i	$-0.985102\pi$
$743$		−	69.5251i		−	0.0935735i	0.998905	−	0.0467868i	$-0.0148981\pi$
$744$		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	−0.275280	−	0.961364i	$-0.588771\pi$
$751$	−935.360	−	540.030i	−1.24549	−	0.719082i	−0.970206	+	0.242282i	$0.922104\pi$
$752$		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	−0.149280	−	0.988795i	$-0.547696\pi$
$761$	594.859	−	1030.33i	0.781681	−	1.35391i	0.930962	−	0.365117i	$-0.118971\pi$
$762$		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	−0.925976	−	0.377583i	$-0.876755\pi$
$773$	−610.658	−	1057.69i	−0.789984	−	1.36829i	0.135992	−	0.990710i	$-0.456578\pi$
$774$		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	−0.249956	−	0.968257i	$-0.580416\pi$
$787$	364.854	−	210.649i	0.463601	−	0.267660i	0.713557	+	0.700597i	$0.247083\pi$
$788$		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	0.974927	−	0.222525i	$-0.0714300\pi$
$809$	238.454	+	413.014i	0.294751	+	0.510524i	−0.680176	+	0.733049i	$0.738097\pi$
$810$		0			0
$811$		−	268.467i		−	0.331032i	−0.986207	−	0.165516i	$-0.947071\pi$
$811$		−	268.467i		−	0.331032i	0.986207	−	0.165516i	$-0.0529289\pi$
$812$		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	−0.992950	−	0.118533i	$-0.962181\pi$
$821$	−323.328	+	560.021i	−0.393822	+	0.682120i	0.599128	+	0.800653i	$0.295514\pi$
$822$		0			0
$823$	−181.913	+	105.028i	−0.221037	+	0.127616i	−0.606430	−	0.795137i	$-0.707399\pi$
$823$	−181.913	+	105.028i	−0.221037	+	0.127616i	0.385393	+	0.922752i	$0.374066\pi$
$824$		0			0
$825$	−393.927			−0.477487
$826$		0			0
$827$			590.763i			0.714345i	0.934038	+	0.357173i	$0.116259\pi$
$827$			590.763i			0.714345i	−0.934038	+	0.357173i	$0.883741\pi$
$828$		0			0
$829$	−746.646	−	1293.23i	−0.900659	−	1.55999i	−0.826641	−	0.562730i	$-0.809751\pi$
$829$	−746.646	−	1293.23i	−0.900659	−	1.55999i	−0.0740183	−	0.997257i	$-0.523582\pi$
$830$		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	$-0.897792\pi$
$839$		−	529.587i		−	0.631212i	0.948890	−	0.315606i	$-0.102208\pi$
$840$		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	0.624050	−	0.781384i	$-0.285486\pi$
$857$	−312.526	−	541.310i	−0.364674	−	0.631634i	−0.988724	+	0.149751i	$0.952153\pi$
$858$		0			0
$859$	−648.151	−	374.210i	−0.754542	−	0.435635i	0.0727908	−	0.997347i	$-0.476809\pi$
$859$	−648.151	−	374.210i	−0.754542	−	0.435635i	−0.827333	+	0.561712i	$0.810143\pi$
$860$		0			0
$861$	−189.791	+	267.328i	−0.220431	+	0.310485i
$862$		0			0
$863$	−750.798	−	433.473i	−0.869986	−	0.502286i	−0.00264216	−	0.999997i	$-0.500841\pi$
$863$	−750.798	−	433.473i	−0.869986	−	0.502286i	−0.867343	+	0.497710i	$0.834174\pi$
$864$		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	−0.656818	−	0.754049i	$-0.728098\pi$
$877$	284.689	−	493.096i	0.324617	−	0.562253i	0.981435	+	0.191796i	$0.0614313\pi$
$878$		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	$0.223353\pi$
$883$			1139.96i			1.29101i	−0.763757	+	0.645504i	$0.776647\pi$
$884$		0			0
$885$	−59.0938	−	102.353i	−0.0667727	−	0.115654i
$886$		0			0
$887$	131.848	+	76.1227i	0.148645	+	0.0858204i	0.572478	−	0.819920i	$-0.305982\pi$
$887$	131.848	+	76.1227i	0.148645	+	0.0858204i	−0.423833	+	0.905741i	$0.639316\pi$
$888$		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	−0.707155	−	0.707059i	$-0.750022\pi$
$907$	−406.700	+	234.808i	−0.448401	+	0.258885i	0.258754	+	0.965943i	$0.416688\pi$
$908$		0			0
$909$	250.537			0.275618
$910$		0			0
$911$			309.559i			0.339801i	0.985461	+	0.169901i	$0.0543447\pi$
$911$			309.559i			0.339801i	−0.985461	+	0.169901i	$0.945655\pi$
$912$		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	−0.171433	−	0.985196i	$-0.554840\pi$
$919$	−1020.42	−	589.137i	−1.11035	−	0.641063i	−0.938921	+	0.344133i	$0.888173\pi$
$920$		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	−0.779596	−	0.626283i	$-0.784575\pi$
$929$	141.746	−	245.511i	0.152579	−	0.264275i	0.932175	+	0.362008i	$0.117909\pi$
$930$		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	0.981828	−	0.189773i	$-0.0607751\pi$
$941$	307.299	+	532.257i	0.326566	+	0.565629i	−0.655262	+	0.755402i	$0.727442\pi$
$942$		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	0.997092	−	0.0762056i	$-0.0242805\pi$
$947$	1353.87	+	781.658i	1.42964	+	0.825404i	0.432550	+	0.901610i	$0.357614\pi$
$948$		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	$-0.991029\pi$
$967$		−	54.5021i		−	0.0563620i	0.999603	−	0.0281810i	$-0.00897148\pi$
$968$		0			0
$969$	−18.1377	−	31.4154i	−0.0187179	−	0.0324204i
$970$		0			0
$971$	−1112.98	−	642.578i	−1.14622	−	0.661769i	−0.198255	−	0.980150i	$-0.563527\pi$
$971$	−1112.98	−	642.578i	−1.14622	−	0.661769i	−0.947963	+	0.318381i	$0.896861\pi$
$972$		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	−0.923171	−	0.384390i	$-0.874412\pi$
$977$	−776.204	−	1344.43i	−0.794477	−	1.37607i	0.128693	−	0.991684i	$-0.458922\pi$
$978$		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	−0.529769	−	0.848142i	$-0.677721\pi$
$983$	−59.1187	+	34.1322i	−0.0601411	+	0.0347225i	0.469628	+	0.882864i	$0.344388\pi$
$984$		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	−0.110829	−	0.993839i	$-0.535351\pi$
$991$	688.196	−	397.330i	0.694446	−	0.400939i	0.805275	+	0.592901i	$0.202017\pi$
$992$		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	0.999848	+	0.0174530i	$0.00555575\pi$
$997$	513.493	+	889.397i	0.515039	+	0.892073i	−0.484809	+	0.874620i	$0.661111\pi$
$998$		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.79.2	✓	6
3.2	odd	2		1008.3.cd.h.415.2		6
4.3	odd	2		336.3.be.f.79.2	yes	6
7.2	even	3		2352.3.m.n.1471.2		6
7.4	even	3		336.3.be.f.319.2	yes	6
7.5	odd	6		2352.3.m.o.1471.5		6
12.11	even	2		1008.3.cd.i.415.2		6
21.11	odd	6		1008.3.cd.i.991.2		6
28.11	odd	6	inner	336.3.be.d.319.2	yes	6
28.19	even	6		2352.3.m.o.1471.2		6
28.23	odd	6		2352.3.m.n.1471.5		6
84.11	even	6		1008.3.cd.h.991.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.3.be.d.79.2	✓	6	1.1	even	1	trivial
336.3.be.d.319.2	yes	6	28.11	odd	6	inner
336.3.be.f.79.2	yes	6	4.3	odd	2
336.3.be.f.319.2	yes	6	7.4	even	3
1008.3.cd.h.415.2		6	3.2	odd	2
1008.3.cd.h.991.2		6	84.11	even	6
1008.3.cd.i.415.2		6	12.11	even	2
1008.3.cd.i.991.2		6	21.11	odd	6
2352.3.m.n.1471.2		6	7.2	even	3
2352.3.m.n.1471.5		6	28.23	odd	6
2352.3.m.o.1471.2		6	28.19	even	6
2352.3.m.o.1471.5		6	7.5	odd	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

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