LMFDB - Embedded newform 1386.2.r.c.1277.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(89,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("1386.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1277.4
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1386.1277
Dual form			1386.2.r.c.89.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.25882 + 2.18034i) q^{5} +(1.48356 + 2.19067i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.25882 + 2.18034i) q^{5} +(1.48356 + 2.19067i) q^{7} -1.00000i q^{8} +(2.18034 + 1.25882i) q^{10} +(0.866025 + 0.500000i) q^{11} -2.44949i q^{13} +(2.38014 + 1.15539i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.64626 - 4.58346i) q^{17} +(-4.52761 + 2.61401i) q^{19} +2.51764 q^{20} +1.00000 q^{22} +(4.28376 - 2.47323i) q^{23} +(-0.669251 + 1.15918i) q^{25} +(-1.22474 - 2.12132i) q^{26} +(2.63896 - 0.189469i) q^{28} +8.05986i q^{29} +(7.44414 + 4.29788i) q^{31} +(-0.866025 - 0.500000i) q^{32} -5.29253i q^{34} +(-2.90887 + 5.99233i) q^{35} +(5.91189 + 10.2397i) q^{37} +(-2.61401 + 4.52761i) q^{38} +(2.18034 - 1.25882i) q^{40} -1.92480 q^{41} -11.9841 q^{43} +(0.866025 - 0.500000i) q^{44} +(2.47323 - 4.28376i) q^{46} +(0.637756 + 1.10463i) q^{47} +(-2.59808 + 6.50000i) q^{49} +1.33850i q^{50} +(-2.12132 - 1.22474i) q^{52} +(0.414578 + 0.239357i) q^{53} +2.51764i q^{55} +(2.19067 - 1.48356i) q^{56} +(4.02993 + 6.98004i) q^{58} +(3.02494 - 5.23936i) q^{59} +(10.7536 - 6.20857i) q^{61} +8.59575 q^{62} -1.00000 q^{64} +(5.34072 - 3.08346i) q^{65} +(-6.11571 + 10.5927i) q^{67} +(-2.64626 - 4.58346i) q^{68} +(0.477014 + 6.64394i) q^{70} -14.7055i q^{71} +(-8.52432 - 4.92152i) q^{73} +(10.2397 + 5.91189i) q^{74} +5.22803i q^{76} +(0.189469 + 2.63896i) q^{77} +(3.52677 + 6.10854i) q^{79} +(1.25882 - 2.18034i) q^{80} +(-1.66693 + 0.962402i) q^{82} +9.35827 q^{83} +13.3247 q^{85} +(-10.3786 + 5.99207i) q^{86} +(0.500000 - 0.866025i) q^{88} +(-7.92392 - 13.7246i) q^{89} +(5.36603 - 3.63397i) q^{91} -4.94646i q^{92} +(1.10463 + 0.637756i) q^{94} +(-11.3989 - 6.58114i) q^{95} -13.6556i q^{97} +(1.00000 + 6.92820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 8 q^{5}+O(q^{10}) $ 8 * q + 4 * q^4 + 8 * q^5	$ 8 q + 4 q^{4} + 8 q^{5} - 4 q^{16} - 4 q^{17} + 24 q^{19} + 16 q^{20} + 8 q^{22} + 24 q^{23} - 4 q^{25} + 12 q^{31} + 16 q^{35} + 12 q^{37} - 8 q^{38} + 16 q^{41} - 32 q^{43} + 8 q^{46} + 48 q^{53} - 4 q^{58} + 16 q^{59} + 24 q^{62} - 8 q^{64} - 12 q^{65} - 24 q^{67} + 4 q^{68} - 20 q^{70} - 24 q^{73} - 12 q^{74} + 40 q^{79} + 8 q^{80} + 12 q^{82} + 72 q^{83} - 32 q^{85} - 24 q^{86} + 4 q^{88} - 16 q^{89} + 36 q^{91} + 24 q^{95} + 8 q^{98}+O(q^{100}) $ 8 * q + 4 * q^4 + 8 * q^5 - 4 * q^16 - 4 * q^17 + 24 * q^19 + 16 * q^20 + 8 * q^22 + 24 * q^23 - 4 * q^25 + 12 * q^31 + 16 * q^35 + 12 * q^37 - 8 * q^38 + 16 * q^41 - 32 * q^43 + 8 * q^46 + 48 * q^53 - 4 * q^58 + 16 * q^59 + 24 * q^62 - 8 * q^64 - 12 * q^65 - 24 * q^67 + 4 * q^68 - 20 * q^70 - 24 * q^73 - 12 * q^74 + 40 * q^79 + 8 * q^80 + 12 * q^82 + 72 * q^83 - 32 * q^85 - 24 * q^86 + 4 * q^88 - 16 * q^89 + 36 * q^91 + 24 * q^95 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.25882	+	2.18034i	0.562961	+	0.975077i	0.997236	+	0.0742968i	$0.0236712\pi$
$5$	1.25882	+	2.18034i	0.562961	+	0.975077i	−0.434275	+	0.900780i	$0.642995\pi$
$6$		0			0
$7$	1.48356	+	2.19067i	0.560734	+	0.827996i
$7$	1.48356	+	2.19067i	0.560734	+	0.827996i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	2.18034	+	1.25882i	0.689484	+	0.398074i
$11$	0.866025	+	0.500000i	0.261116	+	0.150756i
$11$	0.866025	+	0.500000i	0.261116	+	0.150756i
$12$		0			0
$13$		−	2.44949i		−	0.679366i	−0.940540	−	0.339683i	$-0.889680\pi$
$13$		−	2.44949i		−	0.679366i	0.940540	−	0.339683i	$-0.110320\pi$
$14$	2.38014	+	1.15539i	0.636119	+	0.308792i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.64626	−	4.58346i	0.641813	−	1.11165i	−0.343214	−	0.939257i	$-0.611516\pi$
$17$	2.64626	−	4.58346i	0.641813	−	1.11165i	0.985028	−	0.172396i	$-0.0551510\pi$
$18$		0			0
$19$	−4.52761	+	2.61401i	−1.03870	+	0.599696i	−0.919466	−	0.393170i	$-0.871379\pi$
$19$	−4.52761	+	2.61401i	−1.03870	+	0.599696i	−0.119238	+	0.992866i	$0.538045\pi$
$20$	2.51764			0.562961
$21$		0			0
$22$	1.00000			0.213201
$23$	4.28376	−	2.47323i	0.893226	−	0.515704i	0.0182299	−	0.999834i	$-0.494197\pi$
$23$	4.28376	−	2.47323i	0.893226	−	0.515704i	0.874996	+	0.484129i	$0.160864\pi$
$24$		0			0
$25$	−0.669251	+	1.15918i	−0.133850	+	0.231835i
$26$	−1.22474	−	2.12132i	−0.240192	−	0.416025i
$27$		0			0
$28$	2.63896	−	0.189469i	0.498716	−	0.0358062i
$29$			8.05986i			1.49668i	0.663317	+	0.748339i	$0.269148\pi$
$29$			8.05986i			1.49668i	−0.663317	+	0.748339i	$0.730852\pi$
$30$		0			0
$31$	7.44414	+	4.29788i	1.33701	+	0.771922i	0.986363	−	0.164587i	$-0.0526291\pi$
$31$	7.44414	+	4.29788i	1.33701	+	0.771922i	0.350645	+	0.936509i	$0.385962\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$		−	5.29253i		−	0.907661i
$35$	−2.90887	+	5.99233i	−0.491688	+	1.01289i
$36$		0			0
$37$	5.91189	+	10.2397i	0.971909	+	1.68340i	0.689780	+	0.724019i	$0.257707\pi$
$37$	5.91189	+	10.2397i	0.971909	+	1.68340i	0.282129	+	0.959376i	$0.408959\pi$
$38$	−2.61401	+	4.52761i	−0.424049	+	0.734475i
$39$		0			0
$40$	2.18034	−	1.25882i	0.344742	−	0.199037i
$41$	−1.92480			−0.300604			−0.150302	−	0.988640i	$-0.548025\pi$
$41$	−1.92480			−0.300604			−0.150302	+	0.988640i	$0.548025\pi$
$42$		0			0
$43$	−11.9841			−1.82756			−0.913782	−	0.406204i	$-0.866852\pi$
$43$	−11.9841			−1.82756			−0.913782	+	0.406204i	$0.866852\pi$
$44$	0.866025	−	0.500000i	0.130558	−	0.0753778i
$45$		0			0
$46$	2.47323	−	4.28376i	0.364658	−	0.631606i
$47$	0.637756	+	1.10463i	0.0930263	+	0.161126i	0.908783	−	0.417269i	$-0.137013\pi$
$47$	0.637756	+	1.10463i	0.0930263	+	0.161126i	−0.815757	+	0.578395i	$0.803679\pi$
$48$		0			0
$49$	−2.59808	+	6.50000i	−0.371154	+	0.928571i
$50$			1.33850i			0.189293i
$51$		0			0
$52$	−2.12132	−	1.22474i	−0.294174	−	0.169842i
$53$	0.414578	+	0.239357i	0.0569467	+	0.0328782i	0.528203	−	0.849118i	$-0.322866\pi$
$53$	0.414578	+	0.239357i	0.0569467	+	0.0328782i	−0.471256	+	0.881996i	$0.656199\pi$
$54$		0			0
$55$			2.51764i			0.339478i
$56$	2.19067	−	1.48356i	0.292741	−	0.198250i
$57$		0			0
$58$	4.02993	+	6.98004i	0.529155	+	0.916524i
$59$	3.02494	−	5.23936i	0.393814	−	0.682106i	−0.599135	−	0.800648i	$-0.704489\pi$
$59$	3.02494	−	5.23936i	0.393814	−	0.682106i	0.992949	+	0.118542i	$0.0378220\pi$
$60$		0			0
$61$	10.7536	−	6.20857i	1.37685	−	0.794925i	0.385072	−	0.922886i	$-0.374177\pi$
$61$	10.7536	−	6.20857i	1.37685	−	0.794925i	0.991779	+	0.127961i	$0.0408432\pi$
$62$	8.59575			1.09166
$63$		0			0
$64$	−1.00000			−0.125000
$65$	5.34072	−	3.08346i	0.662434	−	0.382457i
$66$		0			0
$67$	−6.11571	+	10.5927i	−0.747153	+	1.29411i	0.202028	+	0.979380i	$0.435247\pi$
$67$	−6.11571	+	10.5927i	−0.747153	+	1.29411i	−0.949182	+	0.314728i	$0.898087\pi$
$68$	−2.64626	−	4.58346i	−0.320907	−	0.555827i
$69$		0			0
$70$	0.477014	+	6.64394i	0.0570140	+	0.794103i
$71$		−	14.7055i		−	1.74522i	−0.488416	−	0.872611i	$-0.662425\pi$
$71$		−	14.7055i		−	1.74522i	0.488416	−	0.872611i	$-0.337575\pi$
$72$		0			0
$73$	−8.52432	−	4.92152i	−0.997696	−	0.576020i	−0.0901305	−	0.995930i	$-0.528728\pi$
$73$	−8.52432	−	4.92152i	−0.997696	−	0.576020i	−0.907566	+	0.419910i	$0.862062\pi$
$74$	10.2397	+	5.91189i	1.19034	+	0.687243i
$75$		0			0
$76$			5.22803i			0.599696i
$77$	0.189469	+	2.63896i	0.0215920	+	0.300737i
$78$		0			0
$79$	3.52677	+	6.10854i	0.396792	+	0.687265i	0.993328	−	0.115322i	$-0.0367899\pi$
$79$	3.52677	+	6.10854i	0.396792	+	0.687265i	−0.596536	+	0.802587i	$0.703457\pi$
$80$	1.25882	−	2.18034i	0.140740	−	0.243769i
$81$		0			0
$82$	−1.66693	+	0.962402i	−0.184081	+	0.106279i
$83$	9.35827			1.02720			0.513602	−	0.858029i	$-0.328311\pi$
$83$	9.35827			1.02720			0.513602	+	0.858029i	$0.328311\pi$
$84$		0			0
$85$	13.3247			1.44526
$86$	−10.3786	+	5.99207i	−1.11915	+	0.646142i
$87$		0			0
$88$	0.500000	−	0.866025i	0.0533002	−	0.0923186i
$89$	−7.92392	−	13.7246i	−0.839934	−	1.45481i	−0.889949	−	0.456060i	$-0.849260\pi$
$89$	−7.92392	−	13.7246i	−0.839934	−	1.45481i	0.0500147	−	0.998748i	$-0.484073\pi$
$90$		0			0
$91$	5.36603	−	3.63397i	0.562512	−	0.380944i
$92$		−	4.94646i		−	0.515704i
$93$		0			0
$94$	1.10463	+	0.637756i	0.113934	+	0.0657796i
$95$	−11.3989	−	6.58114i	−1.16950	−	0.675211i
$96$		0			0
$97$		−	13.6556i		−	1.38652i	−0.720689	−	0.693259i	$-0.756174\pi$
$97$		−	13.6556i		−	1.38652i	0.720689	−	0.693259i	$-0.243826\pi$
$98$	1.00000	+	6.92820i	0.101015	+	0.699854i
$99$		0			0
$100$	0.669251	+	1.15918i	0.0669251	+	0.115918i
$101$	−0.689211	+	1.19375i	−0.0685791	+	0.118782i	−0.898276	−	0.439432i	$-0.855180\pi$
$101$	−0.689211	+	1.19375i	−0.0685791	+	0.118782i	0.829697	+	0.558214i	$0.188513\pi$
$102$		0			0
$103$	−9.08978	+	5.24799i	−0.895643	+	0.517100i	−0.875784	−	0.482703i	$-0.839655\pi$
$103$	−9.08978	+	5.24799i	−0.895643	+	0.517100i	−0.0198589	+	0.999803i	$0.506322\pi$
$104$	−2.44949			−0.240192
$105$		0			0
$106$	0.478713			0.0464968
$107$	−2.50535	+	1.44646i	−0.242201	+	0.139835i	−0.616188	−	0.787599i	$-0.711324\pi$
$107$	−2.50535	+	1.44646i	−0.242201	+	0.139835i	0.373987	+	0.927434i	$0.377991\pi$
$108$		0			0
$109$	−6.76941	+	11.7250i	−0.648392	+	1.12305i	0.335115	+	0.942177i	$0.391225\pi$
$109$	−6.76941	+	11.7250i	−0.648392	+	1.12305i	−0.983507	+	0.180870i	$0.942109\pi$
$110$	1.25882	+	2.18034i	0.120024	+	0.207887i
$111$		0			0
$112$	1.15539	−	2.38014i	0.109175	−	0.224902i
$113$		−	14.5699i		−	1.37062i	−0.728250	−	0.685312i	$-0.759666\pi$
$113$		−	14.5699i		−	1.37062i	0.728250	−	0.685312i	$-0.240334\pi$
$114$		0			0
$115$	10.7850	+	6.22670i	1.00570	+	0.580643i
$116$	6.98004	+	4.02993i	0.648080	+	0.374169i
$117$		0			0
$118$		−	6.04989i		−	0.556937i
$119$	13.9668	−	1.00277i	1.28033	−	0.0919236i
$120$		0			0
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$	6.20857	−	10.7536i	0.562097	−	0.973581i
$123$		0			0
$124$	7.44414	−	4.29788i	0.668504	−	0.385961i
$125$	9.21833			0.824512
$126$		0			0
$127$	−6.59675			−0.585367			−0.292683	−	0.956209i	$-0.594548\pi$
$127$	−6.59675			−0.585367			−0.292683	+	0.956209i	$0.594548\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	3.08346	−	5.34072i	0.270438	−	0.468412i
$131$	0.757359	+	1.31178i	0.0661708	+	0.114611i	0.897213	−	0.441599i	$-0.145588\pi$
$131$	0.757359	+	1.31178i	0.0661708	+	0.114611i	−0.831042	+	0.556210i	$0.812255\pi$
$132$		0			0
$133$	−12.4434	−	6.04044i	−1.07898	−	0.523772i
$134$			12.2314i			1.05663i
$135$		0			0
$136$	−4.58346	−	2.64626i	−0.393029	−	0.226915i
$137$	−12.0316	−	6.94646i	−1.02793	−	0.593476i	−0.111540	−	0.993760i	$-0.535578\pi$
$137$	−12.0316	−	6.94646i	−1.02793	−	0.593476i	−0.916391	+	0.400284i	$0.868912\pi$
$138$		0			0
$139$		−	13.5911i		−	1.15278i	−0.817174	−	0.576391i	$-0.804460\pi$
$139$		−	13.5911i		−	1.15278i	0.817174	−	0.576391i	$-0.195540\pi$
$140$	3.73508	+	5.51532i	0.315672	+	0.466129i
$141$		0			0
$142$	−7.35275	−	12.7353i	−0.617029	−	1.06873i
$143$	1.22474	−	2.12132i	0.102418	−	0.177394i
$144$		0			0
$145$	−17.5732	+	10.1459i	−1.45938	+	0.842571i
$146$	−9.84304			−0.814616
$147$		0			0
$148$	11.8238			0.971909
$149$	5.76098	−	3.32611i	0.471958	−	0.272485i	−0.245101	−	0.969498i	$-0.578821\pi$
$149$	5.76098	−	3.32611i	0.471958	−	0.272485i	0.717059	+	0.697012i	$0.245488\pi$
$150$		0			0
$151$	−4.00877	+	6.94339i	−0.326229	+	0.565045i	−0.981760	−	0.190123i	$-0.939111\pi$
$151$	−4.00877	+	6.94339i	−0.326229	+	0.565045i	0.655532	+	0.755168i	$0.272445\pi$
$152$	2.61401	+	4.52761i	0.212025	+	0.367237i
$153$		0			0
$154$	1.48356	+	2.19067i	0.119549	+	0.176529i
$155$			21.6410i			1.73825i
$156$		0			0
$157$	−19.0820	−	11.0170i	−1.52291	−	0.879254i	−0.999633	−	0.0270921i	$-0.991375\pi$
$157$	−19.0820	−	11.0170i	−1.52291	−	0.879254i	−0.523279	−	0.852161i	$-0.675291\pi$
$158$	6.10854	+	3.52677i	0.485969	+	0.280575i
$159$		0			0
$160$		−	2.51764i		−	0.199037i
$161$	11.7733	+	5.71512i	0.927864	+	0.450414i
$162$		0			0
$163$	5.03225	+	8.71611i	0.394156	+	0.682699i	0.992993	−	0.118172i	$-0.0377035\pi$
$163$	5.03225	+	8.71611i	0.394156	+	0.682699i	−0.598837	+	0.800871i	$0.704370\pi$
$164$	−0.962402	+	1.66693i	−0.0751509	+	0.130165i
$165$		0			0
$166$	8.10450	−	4.67914i	0.629031	−	0.363171i
$167$	−4.76268			−0.368547			−0.184274	−	0.982875i	$-0.558993\pi$
$167$	−4.76268			−0.368547			−0.184274	+	0.982875i	$0.558993\pi$
$168$		0			0
$169$	7.00000			0.538462
$170$	11.5395	−	6.66234i	0.885040	−	0.510978i
$171$		0			0
$172$	−5.99207	+	10.3786i	−0.456891	+	0.791359i
$173$	−7.36843	−	12.7625i	−0.560211	−	0.970314i	−0.997478	−	0.0709824i	$-0.977387\pi$
$173$	−7.36843	−	12.7625i	−0.560211	−	0.970314i	0.437266	−	0.899332i	$-0.355947\pi$
$174$		0			0
$175$	−3.53225	+	0.253604i	−0.267013	+	0.0191707i
$176$		−	1.00000i		−	0.0753778i
$177$		0			0
$178$	−13.7246	−	7.92392i	−1.02871	−	0.593923i
$179$	2.03491	+	1.17486i	0.152096	+	0.0878129i	0.574117	−	0.818773i	$-0.305346\pi$
$179$	2.03491	+	1.17486i	0.152096	+	0.0878129i	−0.422020	+	0.906586i	$0.638679\pi$
$180$		0			0
$181$		−	11.9236i		−	0.886271i	−0.896455	−	0.443136i	$-0.853866\pi$
$181$		−	11.9236i		−	0.886271i	0.896455	−	0.443136i	$-0.146134\pi$
$182$	2.83013	−	5.83013i	0.209783	−	0.432158i
$183$		0			0
$184$	−2.47323	−	4.28376i	−0.182329	−	0.315803i
$185$	−14.8840	+	25.7798i	−1.09429	+	1.89537i
$186$		0			0
$187$	4.58346	−	2.64626i	0.335176	−	0.193514i
$188$	1.27551			0.0930263
$189$		0			0
$190$	−13.1623			−0.954892
$191$	21.2839	−	12.2882i	1.54005	−	0.889146i	0.541212	−	0.840886i	$-0.317966\pi$
$191$	21.2839	−	12.2882i	1.54005	−	0.889146i	0.998835	−	0.0482604i	$-0.0153677\pi$
$192$		0			0
$193$	7.05657	−	12.2223i	0.507943	−	0.879783i	−0.492015	−	0.870587i	$-0.663739\pi$
$193$	7.05657	−	12.2223i	0.507943	−	0.879783i	0.999958	−	0.00919638i	$-0.00292734\pi$
$194$	−6.82780	−	11.8261i	−0.490208	−	0.849065i
$195$		0			0
$196$	4.33013	+	5.50000i	0.309295	+	0.392857i
$197$			0.579219i			0.0412676i	0.999787	+	0.0206338i	$0.00656841\pi$
$197$			0.579219i			0.0412676i	−0.999787	+	0.0206338i	$0.993432\pi$
$198$		0			0
$199$	2.08228	+	1.20220i	0.147609	+	0.0852220i	0.571985	−	0.820264i	$-0.306173\pi$
$199$	2.08228	+	1.20220i	0.147609	+	0.0852220i	−0.424377	+	0.905486i	$0.639507\pi$
$200$	1.15918	+	0.669251i	0.0819661	+	0.0473232i
$201$		0			0
$202$			1.37842i			0.0969854i
$203$	−17.6565	+	11.9573i	−1.23924	+	0.839239i
$204$		0			0
$205$	−2.42298	−	4.19672i	−0.169228	−	0.293112i
$206$	−5.24799	+	9.08978i	−0.365645	+	0.633315i
$207$		0			0
$208$	−2.12132	+	1.22474i	−0.147087	+	0.0849208i
$209$	−5.22803			−0.361630
$210$		0			0
$211$	−5.99343			−0.412605			−0.206302	−	0.978488i	$-0.566143\pi$
$211$	−5.99343			−0.412605			−0.206302	+	0.978488i	$0.566143\pi$
$212$	0.414578	−	0.239357i	0.0284733	−	0.0164391i
$213$		0			0
$214$	−1.44646	+	2.50535i	−0.0988782	+	0.171262i
$215$	−15.0859	−	26.1295i	−1.02885	−	1.78202i
$216$		0			0
$217$	1.62863	+	22.6838i	0.110558	+	1.53988i
$218$			13.5388i			0.916964i
$219$		0			0
$220$	2.18034	+	1.25882i	0.146998	+	0.0848696i
$221$	−11.2271	−	6.48200i	−0.755220	−	0.436026i
$222$		0			0
$223$			7.48993i			0.501563i	0.968044	+	0.250781i	$0.0806875\pi$
$223$			7.48993i			0.501563i	−0.968044	+	0.250781i	$0.919313\pi$
$224$	−0.189469	−	2.63896i	−0.0126594	−	0.176323i
$225$		0			0
$226$	−7.28497	−	12.6179i	−0.484589	−	0.839332i
$227$	−4.88304	+	8.45768i	−0.324099	+	0.561356i	−0.981330	−	0.192334i	$-0.938394\pi$
$227$	−4.88304	+	8.45768i	−0.324099	+	0.561356i	0.657231	+	0.753689i	$0.271728\pi$
$228$		0			0
$229$	0.195181	−	0.112688i	0.0128980	−	0.00744664i	−0.493537	−	0.869725i	$-0.664296\pi$
$229$	0.195181	−	0.112688i	0.0128980	−	0.00744664i	0.506435	+	0.862278i	$0.330963\pi$
$230$	12.4534			0.821153
$231$		0			0
$232$	8.05986			0.529155
$233$	−0.445759	+	0.257359i	−0.0292027	+	0.0168602i	−0.514530	−	0.857472i	$-0.672034\pi$
$233$	−0.445759	+	0.257359i	−0.0292027	+	0.0168602i	0.485328	+	0.874332i	$0.338700\pi$
$234$		0			0
$235$	−1.60564	+	2.78105i	−0.104740	+	0.181416i
$236$	−3.02494	−	5.23936i	−0.196907	−	0.341053i
$237$		0			0
$238$	11.5942	−	7.85180i	0.751540	−	0.508957i
$239$			15.4899i			1.00196i	0.865459	+	0.500980i	$0.167027\pi$
$239$			15.4899i			1.00196i	−0.865459	+	0.500980i	$0.832973\pi$
$240$		0			0
$241$	−14.2882	−	8.24932i	−0.920387	−	0.531386i	−0.0366285	−	0.999329i	$-0.511662\pi$
$241$	−14.2882	−	8.24932i	−0.920387	−	0.531386i	−0.883759	+	0.467943i	$0.844995\pi$
$242$	0.866025	+	0.500000i	0.0556702	+	0.0321412i
$243$		0			0
$244$		−	12.4171i		−	0.794925i
$245$	−17.4427	+	2.51764i	−1.11437	+	0.160846i
$246$		0			0
$247$	6.40300	+	11.0903i	0.407413	+	0.705660i
$248$	4.29788	−	7.44414i	0.272915	−	0.472703i
$249$		0			0
$250$	7.98331	−	4.60916i	0.504909	−	0.291509i
$251$	−18.6367			−1.17634			−0.588169	−	0.808738i	$-0.700151\pi$
$251$	−18.6367			−1.17634			−0.588169	+	0.808738i	$0.700151\pi$
$252$		0			0
$253$	4.94646			0.310981
$254$	−5.71295	+	3.29837i	−0.358463	+	0.206958i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.575454	+	0.996716i	0.0358959	+	0.0621734i	0.883415	−	0.468591i	$-0.155238\pi$
$257$	0.575454	+	0.996716i	0.0358959	+	0.0621734i	−0.847519	+	0.530764i	$0.821905\pi$
$258$		0			0
$259$	−13.6611	+	28.1423i	−0.848862	+	1.74867i
$260$		−	6.16693i		−	0.382457i
$261$		0			0
$262$	1.31178	+	0.757359i	0.0810423	+	0.0467898i
$263$	−6.18929	−	3.57339i	−0.381648	−	0.220345i	0.296887	−	0.954913i	$-0.404052\pi$
$263$	−6.18929	−	3.57339i	−0.381648	−	0.220345i	−0.678535	+	0.734568i	$0.737385\pi$
$264$		0			0
$265$			1.20523i			0.0740365i
$266$	−13.7966	+	0.990548i	−0.845921	+	0.0607344i
$267$		0			0
$268$	6.11571	+	10.5927i	0.373577	+	0.647054i
$269$	−6.68968	+	11.5869i	−0.407877	+	0.706464i	−0.994652	−	0.103286i	$-0.967064\pi$
$269$	−6.68968	+	11.5869i	−0.407877	+	0.706464i	0.586774	+	0.809750i	$0.300398\pi$
$270$		0			0
$271$	5.92100	−	3.41849i	0.359675	−	0.207659i	−0.309263	−	0.950977i	$-0.600082\pi$
$271$	5.92100	−	3.41849i	0.359675	−	0.207659i	0.668938	+	0.743318i	$0.266749\pi$
$272$	−5.29253			−0.320907
$273$		0			0
$274$	−13.8929			−0.839302
$275$	−1.15918	+	0.669251i	−0.0699010	+	0.0403573i
$276$		0			0
$277$	2.87404	−	4.97798i	0.172684	−	0.299098i	−0.766673	−	0.642037i	$-0.778089\pi$
$277$	2.87404	−	4.97798i	0.172684	−	0.299098i	0.939357	+	0.342940i	$0.111423\pi$
$278$	−6.79555	−	11.7702i	−0.407570	−	0.705932i
$279$		0			0
$280$	5.99233	+	2.90887i	0.358110	+	0.173838i
$281$		−	6.45821i		−	0.385265i	−0.981271	−	0.192632i	$-0.938298\pi$
$281$		−	6.45821i		−	0.385265i	0.981271	−	0.192632i	$-0.0617025\pi$
$282$		0			0
$283$	5.87843	+	3.39391i	0.349436	+	0.201747i	0.664437	−	0.747344i	$-0.268671\pi$
$283$	5.87843	+	3.39391i	0.349436	+	0.201747i	−0.315001	+	0.949091i	$0.602005\pi$
$284$	−12.7353	−	7.35275i	−0.755703	−	0.436305i
$285$		0			0
$286$		−	2.44949i		−	0.144841i
$287$	−2.85557	−	4.21661i	−0.168559	−	0.248899i
$288$		0			0
$289$	−5.50543	−	9.53568i	−0.323849	−	0.560923i
$290$	−10.1459	+	17.5732i	−0.595788	+	1.03193i
$291$		0			0
$292$	−8.52432	+	4.92152i	−0.498848	+	0.288010i
$293$	3.15159			0.184118			0.0920589	−	0.995754i	$-0.470655\pi$
$293$	3.15159			0.184118			0.0920589	+	0.995754i	$0.470655\pi$
$294$		0			0
$295$	15.2314			0.886808
$296$	10.2397	−	5.91189i	0.595170	−	0.343622i
$297$		0			0
$298$	3.32611	−	5.76098i	0.192676	−	0.333725i
$299$	−6.05816	−	10.4930i	−0.350352	−	0.606828i
$300$		0			0
$301$	−17.7792	−	26.2533i	−1.02478	−	1.51322i
$302$			8.01753i			0.461357i
$303$		0			0
$304$	4.52761	+	2.61401i	0.259676	+	0.149924i
$305$	27.0736	+	15.6309i	1.55023	+	0.895024i
$306$		0			0
$307$		−	15.0711i		−	0.860151i	−0.902793	−	0.430076i	$-0.858487\pi$
$307$		−	15.0711i		−	0.860151i	0.902793	−	0.430076i	$-0.141513\pi$
$308$	2.38014	+	1.15539i	0.135621	+	0.0658347i
$309$		0			0
$310$	10.8205	+	18.7417i	0.614563	+	1.06445i
$311$	−15.9573	+	27.6388i	−0.904854	+	1.56725i	−0.0837402	+	0.996488i	$0.526687\pi$
$311$	−15.9573	+	27.6388i	−0.904854	+	1.56725i	−0.821113	+	0.570765i	$0.806647\pi$
$312$		0			0
$313$	13.8126	−	7.97469i	0.780733	−	0.450756i	−0.0559572	−	0.998433i	$-0.517821\pi$
$313$	13.8126	−	7.97469i	0.780733	−	0.450756i	0.836690	+	0.547677i	$0.184488\pi$
$314$	−22.0340			−1.24345
$315$		0			0
$316$	7.05354			0.396792
$317$	21.9318	−	12.6623i	1.23181	−	0.711188i	0.264405	−	0.964412i	$-0.414824\pi$
$317$	21.9318	−	12.6623i	1.23181	−	0.711188i	0.967408	+	0.253224i	$0.0814910\pi$
$318$		0			0
$319$	−4.02993	+	6.98004i	−0.225633	+	0.390807i
$320$	−1.25882	−	2.18034i	−0.0703701	−	0.121885i
$321$		0			0
$322$	13.0535	−	0.937200i	0.727444	−	0.0522281i
$323$			27.6695i			1.53957i
$324$		0			0
$325$	2.83939	+	1.63932i	0.157501	+	0.0909333i
$326$	8.71611	+	5.03225i	0.482741	+	0.278711i
$327$		0			0
$328$			1.92480i			0.106279i
$329$	−1.47372	+	3.03590i	−0.0812488	+	0.167374i
$330$		0			0
$331$	−7.03882	−	12.1916i	−0.386888	−	0.670110i	0.605141	−	0.796118i	$-0.293117\pi$
$331$	−7.03882	−	12.1916i	−0.386888	−	0.670110i	−0.992029	+	0.126008i	$0.959783\pi$
$332$	4.67914	−	8.10450i	0.256801	−	0.444792i
$333$		0			0
$334$	−4.12460	+	2.38134i	−0.225688	+	0.130301i
$335$	−30.7943			−1.68247
$336$		0			0
$337$	−8.15142			−0.444036			−0.222018	−	0.975043i	$-0.571264\pi$
$337$	−8.15142			−0.444036			−0.222018	+	0.975043i	$0.571264\pi$
$338$	6.06218	−	3.50000i	0.329739	−	0.190375i
$339$		0			0
$340$	6.66234	−	11.5395i	0.361316	−	0.625817i
$341$	4.29788	+	7.44414i	0.232743	+	0.403123i
$342$		0			0
$343$	−18.0938	+	3.95164i	−0.976972	+	0.213368i
$344$			11.9841i			0.646142i
$345$		0			0
$346$	−12.7625	−	7.36843i	−0.686116	−	0.396129i
$347$	−19.5502	−	11.2873i	−1.04951	−	0.605933i	−0.126996	−	0.991903i	$-0.540534\pi$
$347$	−19.5502	−	11.2873i	−1.04951	−	0.605933i	−0.922511	+	0.385970i	$0.873867\pi$
$348$		0			0
$349$		−	22.9498i		−	1.22848i	−0.789121	−	0.614238i	$-0.789464\pi$
$349$		−	22.9498i		−	1.22848i	0.789121	−	0.614238i	$-0.210536\pi$
$350$	−2.93222	+	1.98575i	−0.156734	+	0.106143i
$351$		0			0
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	12.5990	−	21.8222i	0.670579	−	1.16148i	−0.307161	−	0.951658i	$-0.599379\pi$
$353$	12.5990	−	21.8222i	0.670579	−	1.16148i	0.977740	−	0.209820i	$-0.0672877\pi$
$354$		0			0
$355$	32.0630	−	18.5116i	1.70173	−	0.982492i
$356$	−15.8478			−0.839934
$357$		0			0
$358$	2.34971			0.124186
$359$	−17.0558	+	9.84714i	−0.900168	+	0.519712i	−0.877255	−	0.480025i	$-0.840628\pi$
$359$	−17.0558	+	9.84714i	−0.900168	+	0.519712i	−0.0229134	+	0.999737i	$0.507294\pi$
$360$		0			0
$361$	4.16614	−	7.21597i	0.219271	−	0.379788i
$362$	−5.96178	−	10.3261i	−0.313344	−	0.542728i
$363$		0			0
$364$	−0.464102	−	6.46410i	−0.0243255	−	0.338811i
$365$		−	24.7812i		−	1.29711i
$366$		0			0
$367$	2.81282	+	1.62398i	0.146828	+	0.0847712i	0.571614	−	0.820523i	$-0.306317\pi$
$367$	2.81282	+	1.62398i	0.146828	+	0.0847712i	−0.424786	+	0.905294i	$0.639651\pi$
$368$	−4.28376	−	2.47323i	−0.223307	−	0.128926i
$369$		0			0
$370$			29.7680i			1.54756i
$371$	0.0907012	+	1.26330i	0.00470897	+	0.0655875i
$372$		0			0
$373$	−3.41177	−	5.90935i	−0.176655	−	0.305975i	0.764078	−	0.645124i	$-0.223194\pi$
$373$	−3.41177	−	5.90935i	−0.176655	−	0.305975i	−0.940733	+	0.339149i	$0.889861\pi$
$374$	2.64626	−	4.58346i	0.136835	−	0.237005i
$375$		0			0
$376$	1.10463	−	0.637756i	0.0569668	−	0.0328898i
$377$	19.7425			1.01679
$378$		0			0
$379$	18.8929			0.970464			0.485232	−	0.874385i	$-0.338735\pi$
$379$	18.8929			0.970464			0.485232	+	0.874385i	$0.338735\pi$
$380$	−11.3989	+	6.58114i	−0.584750	+	0.337605i
$381$		0			0
$382$	12.2882	−	21.2839i	0.628722	−	1.08898i
$383$	13.2165	+	22.8916i	0.675329	+	1.16970i	0.976373	+	0.216094i	$0.0693318\pi$
$383$	13.2165	+	22.8916i	0.675329	+	1.16970i	−0.301043	+	0.953610i	$0.597335\pi$
$384$		0			0
$385$	−5.51532	+	3.73508i	−0.281087	+	0.190357i
$386$		−	14.1131i		−	0.718340i
$387$		0			0
$388$	−11.8261	−	6.82780i	−0.600380	−	0.346629i
$389$	10.1046	+	5.83391i	0.512325	+	0.295791i	0.733789	−	0.679378i	$-0.237750\pi$
$389$	10.1046	+	5.83391i	0.512325	+	0.295791i	−0.221464	+	0.975169i	$0.571083\pi$
$390$		0			0
$391$		−	26.1793i		−	1.32394i
$392$	6.50000	+	2.59808i	0.328300	+	0.131223i
$393$		0			0
$394$	0.289609	+	0.501618i	0.0145903	+	0.0252711i
$395$	−8.87913	+	15.3791i	−0.446757	+	0.773806i
$396$		0			0
$397$	−8.68678	+	5.01532i	−0.435977	+	0.251711i	−0.701890	−	0.712286i	$-0.747660\pi$
$397$	−8.68678	+	5.01532i	−0.435977	+	0.251711i	0.265913	+	0.963997i	$0.414327\pi$
$398$	2.40441			0.120522
$399$		0			0
$400$	1.33850			0.0669251
$401$	4.52281	−	2.61125i	0.225858	−	0.130399i	−0.382802	−	0.923831i	$-0.625041\pi$
$401$	4.52281	−	2.61125i	0.225858	−	0.130399i	0.608660	+	0.793431i	$0.291707\pi$
$402$		0			0
$403$	10.5276	−	18.2343i	0.524417	−	0.908318i
$404$	0.689211	+	1.19375i	0.0342895	+	0.0593912i
$405$		0			0
$406$	−9.31231	+	19.1836i	−0.462162	+	0.952065i
$407$			11.8238i			0.586083i
$408$		0			0
$409$	−16.6456	−	9.61037i	−0.823074	−	0.475202i	0.0284013	−	0.999597i	$-0.490958\pi$
$409$	−16.6456	−	9.61037i	−0.823074	−	0.475202i	−0.851475	+	0.524395i	$0.824292\pi$
$410$	−4.19672	−	2.42298i	−0.207261	−	0.119662i
$411$		0			0
$412$			10.4960i			0.517100i
$413$	15.9654	−	1.14626i	0.785606	−	0.0564040i
$414$		0			0
$415$	11.7804	+	20.4042i	0.578276	+	1.00160i
$416$	−1.22474	+	2.12132i	−0.0600481	+	0.104006i
$417$		0			0
$418$	−4.52761	+	2.61401i	−0.221452	+	0.127856i
$419$	−17.4755			−0.853733			−0.426866	−	0.904315i	$-0.640383\pi$
$419$	−17.4755			−0.853733			−0.426866	+	0.904315i	$0.640383\pi$
$420$		0			0
$421$	27.8519			1.35742			0.678710	−	0.734406i	$-0.262539\pi$
$421$	27.8519			1.35742			0.678710	+	0.734406i	$0.262539\pi$
$422$	−5.19046	+	2.99672i	−0.252668	+	0.145878i
$423$		0			0
$424$	0.239357	−	0.414578i	0.0116242	−	0.0201337i
$425$	3.54203	+	6.13497i	0.171814	+	0.297590i
$426$		0			0
$427$	29.5545	+	14.3467i	1.43024	+	0.694285i
$428$			2.89293i			0.139835i
$429$		0			0
$430$	−26.1295	−	15.0859i	−1.26008	−	0.727505i
$431$	−30.1846	−	17.4271i	−1.45394	−	0.839434i	−0.455240	−	0.890369i	$-0.650447\pi$
$431$	−30.1846	−	17.4271i	−1.45394	−	0.839434i	−0.998702	+	0.0509348i	$0.983780\pi$
$432$		0			0
$433$			27.2068i			1.30748i	0.756721	+	0.653738i	$0.226800\pi$
$433$			27.2068i			1.30748i	−0.756721	+	0.653738i	$0.773200\pi$
$434$	12.7524	+	18.8305i	0.612132	+	0.903891i
$435$		0			0
$436$	6.76941	+	11.7250i	0.324196	+	0.561524i
$437$	−12.9301	+	22.3956i	−0.618532	+	1.07133i
$438$		0			0
$439$	−20.0987	+	11.6040i	−0.959260	+	0.553829i	−0.895945	−	0.444165i	$-0.853501\pi$
$439$	−20.0987	+	11.6040i	−0.959260	+	0.553829i	−0.0633147	+	0.997994i	$0.520167\pi$
$440$	2.51764			0.120024
$441$		0			0
$442$	−12.9640			−0.616634
$443$	15.7172	−	9.07435i	0.746749	−	0.431135i	−0.0777693	−	0.996971i	$-0.524780\pi$
$443$	15.7172	−	9.07435i	0.746749	−	0.431135i	0.824518	+	0.565836i	$0.191446\pi$
$444$		0			0
$445$	19.9496	−	34.5537i	0.945700	−	1.63800i
$446$	3.74496	+	6.48647i	0.177329	+	0.307143i
$447$		0			0
$448$	−1.48356	−	2.19067i	−0.0700918	−	0.103499i
$449$			31.9656i			1.50855i	0.656560	+	0.754274i	$0.272011\pi$
$449$			31.9656i			1.50855i	−0.656560	+	0.754274i	$0.727989\pi$
$450$		0			0
$451$	−1.66693	−	0.962402i	−0.0784926	−	0.0453177i
$452$	−12.6179	−	7.28497i	−0.593497	−	0.342656i
$453$		0			0
$454$			9.76608i			0.458345i
$455$	14.6781	+	7.12524i	0.688122	+	0.334036i
$456$		0			0
$457$	−12.9607	−	22.4486i	−0.606276	−	1.05010i	−0.991848	−	0.127424i	$-0.959329\pi$
$457$	−12.9607	−	22.4486i	−0.606276	−	1.05010i	0.385572	−	0.922678i	$-0.374004\pi$
$458$	0.112688	−	0.195181i	0.00526557	−	0.00912023i
$459$		0			0
$460$	10.7850	−	6.22670i	0.502852	−	0.290322i
$461$	21.8282			1.01664			0.508321	−	0.861168i	$-0.330266\pi$
$461$	21.8282			1.01664			0.508321	+	0.861168i	$0.330266\pi$
$462$		0			0
$463$	4.92621			0.228940			0.114470	−	0.993427i	$-0.463483\pi$
$463$	4.92621			0.228940			0.114470	+	0.993427i	$0.463483\pi$
$464$	6.98004	−	4.02993i	0.324040	−	0.187085i
$465$		0			0
$466$	−0.257359	+	0.445759i	−0.0119219	+	0.0206494i
$467$	1.87404	+	3.24592i	0.0867200	+	0.150203i	0.906123	−	0.423015i	$-0.139028\pi$
$467$	1.87404	+	3.24592i	0.0867200	+	0.150203i	−0.819403	+	0.573218i	$0.805695\pi$
$468$		0			0
$469$	−32.2782	+	2.31747i	−1.49047	+	0.107011i
$470$			3.21128i			0.148125i
$471$		0			0
$472$	−5.23936	−	3.02494i	−0.241161	−	0.139234i
$473$	−10.3786	−	5.99207i	−0.477207	−	0.275516i
$474$		0			0
$475$		−	6.99772i		−	0.321078i
$476$	6.11496	−	12.5970i	0.280279	−	0.577381i
$477$		0			0
$478$	7.74496	+	13.4147i	0.354246	+	0.613573i
$479$	−1.93134	+	3.34517i	−0.0882450	+	0.152845i	−0.906769	−	0.421627i	$-0.861459\pi$
$479$	−1.93134	+	3.34517i	−0.0882450	+	0.152845i	0.818524	+	0.574472i	$0.194793\pi$
$480$		0			0
$481$	25.0820	−	14.4811i	1.14364	−	0.660282i
$482$	−16.4986			−0.751493
$483$		0			0
$484$	1.00000			0.0454545
$485$	29.7739	−	17.1899i	1.35196	−	0.780555i
$486$		0			0
$487$	−5.80946	+	10.0623i	−0.263252	+	0.455966i	−0.967104	−	0.254381i	$-0.918128\pi$
$487$	−5.80946	+	10.0623i	−0.263252	+	0.455966i	0.703852	+	0.710346i	$0.251462\pi$
$488$	−6.20857	−	10.7536i	−0.281049	−	0.486790i
$489$		0			0
$490$	−13.8470	+	10.9017i	−0.625544	+	0.492488i
$491$			25.7345i			1.16138i	0.814124	+	0.580691i	$0.197217\pi$
$491$			25.7345i			1.16138i	−0.814124	+	0.580691i	$0.802783\pi$
$492$		0			0
$493$	36.9421	+	21.3285i	1.66379	+	0.960588i
$494$	11.0903	+	6.40300i	0.498977	+	0.288085i
$495$		0			0
$496$		−	8.59575i		−	0.385961i
$497$	32.2149	−	21.8165i	1.44504	−	0.978606i
$498$		0			0
$499$	−11.3984	−	19.7425i	−0.510261	−	0.883797i	−0.999929	−	0.0118887i	$-0.996216\pi$
$499$	−11.3984	−	19.7425i	−0.510261	−	0.883797i	0.489669	−	0.871909i	$-0.337118\pi$
$500$	4.60916	−	7.98331i	0.206128	−	0.357024i
$501$		0			0
$502$	−16.1399	+	9.31835i	−0.720357	+	0.415898i
$503$	20.4955			0.913848			0.456924	−	0.889506i	$-0.348951\pi$
$503$	20.4955			0.913848			0.456924	+	0.889506i	$0.348951\pi$
$504$		0			0
$505$	−3.47037			−0.154429
$506$	4.28376	−	2.47323i	0.190436	−	0.109949i
$507$		0			0
$508$	−3.29837	+	5.71295i	−0.146342	+	0.253471i
$509$	−5.99259	−	10.3795i	−0.265617	−	0.460062i	0.702108	−	0.712070i	$-0.252242\pi$
$509$	−5.99259	−	10.3795i	−0.265617	−	0.460062i	−0.967725	+	0.252008i	$0.918909\pi$
$510$		0			0
$511$	−1.86495	−	25.9754i	−0.0825004	−	1.14908i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	0.996716	+	0.575454i	0.0439633	+	0.0253822i
$515$	−22.8848	−	13.2125i	−1.00842	−	0.582214i
$516$		0			0
$517$			1.27551i			0.0560970i
$518$	2.24024	+	31.2025i	0.0984303	+	1.37096i
$519$		0			0
$520$	−3.08346	−	5.34072i	−0.135219	−	0.234206i
$521$	−2.33369	+	4.04208i	−0.102241	+	0.177087i	−0.912608	−	0.408837i	$-0.865935\pi$
$521$	−2.33369	+	4.04208i	−0.102241	+	0.177087i	0.810367	+	0.585923i	$0.199268\pi$
$522$		0			0
$523$	−17.5494	+	10.1322i	−0.767383	+	0.443049i	−0.831940	−	0.554865i	$-0.812770\pi$
$523$	−17.5494	+	10.1322i	−0.767383	+	0.443049i	0.0645573	+	0.997914i	$0.479436\pi$
$524$	1.51472			0.0661708
$525$		0			0
$526$	−7.14678			−0.311614
$527$	39.3983	−	22.7466i	1.71622	−	0.990859i
$528$		0			0
$529$	0.733751	−	1.27089i	0.0319022	−	0.0552562i
$530$	0.602614	+	1.04376i	0.0261759	+	0.0453379i
$531$		0			0
$532$	−11.4529	+	7.75611i	−0.496546	+	0.336270i
$533$			4.71479i			0.204220i
$534$		0			0
$535$	−6.30756	−	3.64167i	−0.272700	−	0.157443i
$536$	10.5927	+	6.11571i	0.457536	+	0.264159i
$537$		0			0
$538$			13.3794i			0.576826i
$539$	−5.50000	+	4.33013i	−0.236902	+	0.186512i
$540$		0			0
$541$	6.53334	+	11.3161i	0.280890	+	0.486516i	0.971604	−	0.236612i	$-0.0760370\pi$
$541$	6.53334	+	11.3161i	0.280890	+	0.486516i	−0.690714	+	0.723128i	$0.742704\pi$
$542$	3.41849	−	5.92100i	0.146837	−	0.254329i
$543$		0			0
$544$	−4.58346	+	2.64626i	−0.196514	+	0.113458i
$545$	−34.0858			−1.46008
$546$		0			0
$547$	24.2492			1.03682			0.518411	−	0.855132i	$-0.326524\pi$
$547$	24.2492			1.03682			0.518411	+	0.855132i	$0.326524\pi$
$548$	−12.0316	+	6.94646i	−0.513966	+	0.296738i
$549$		0			0
$550$	−0.669251	+	1.15918i	−0.0285369	+	0.0494274i
$551$	−21.0686	−	36.4918i	−0.897552	−	1.55461i
$552$		0			0
$553$	−8.14962	+	16.7884i	−0.346557	+	0.713915i
$554$		−	5.74807i		−	0.244212i
$555$		0			0
$556$	−11.7702	−	6.79555i	−0.499170	−	0.288196i
$557$	−20.6838	−	11.9418i	−0.876402	−	0.505991i	−0.00693183	−	0.999976i	$-0.502206\pi$
$557$	−20.6838	−	11.9418i	−0.876402	−	0.505991i	−0.869471	+	0.493985i	$0.835540\pi$
$558$		0			0
$559$			29.3550i			1.24159i
$560$	6.64394	−	0.477014i	0.280758	−	0.0201575i
$561$		0			0
$562$	−3.22911	−	5.59298i	−0.136212	−	0.235925i
$563$	1.15091	−	1.99343i	0.0485050	−	0.0840131i	−0.840754	−	0.541418i	$-0.817888\pi$
$563$	1.15091	−	1.99343i	0.0485050	−	0.0840131i	0.889259	+	0.457405i	$0.151221\pi$
$564$		0			0
$565$	31.7674	−	18.3409i	1.33646	−	0.771608i
$566$	6.78783			0.285314
$567$		0			0
$568$	−14.7055			−0.617029
$569$	−21.7718	+	12.5699i	−0.912720	+	0.526959i	−0.881305	−	0.472548i	$-0.843334\pi$
$569$	−21.7718	+	12.5699i	−0.912720	+	0.526959i	−0.0314144	+	0.999506i	$0.510001\pi$
$570$		0			0
$571$	−17.9626	+	31.1122i	−0.751713	+	1.30200i	0.195279	+	0.980748i	$0.437439\pi$
$571$	−17.9626	+	31.1122i	−0.751713	+	1.30200i	−0.946992	+	0.321257i	$0.895895\pi$
$572$	−1.22474	−	2.12132i	−0.0512092	−	0.0886969i
$573$		0			0
$574$	−4.58130	−	2.22391i	−0.191220	−	0.0928241i
$575$			6.62085i			0.276108i
$576$		0			0
$577$	−2.60396	−	1.50340i	−0.108404	−	0.0625874i	0.444818	−	0.895621i	$-0.353269\pi$
$577$	−2.60396	−	1.50340i	−0.108404	−	0.0625874i	−0.553222	+	0.833034i	$0.686602\pi$
$578$	−9.53568	−	5.50543i	−0.396632	−	0.228996i
$579$		0			0
$580$			20.2918i			0.842571i
$581$	13.8836	+	20.5009i	0.575989	+	0.850520i
$582$		0			0
$583$	0.239357	+	0.414578i	0.00991314	+	0.0171701i
$584$	−4.92152	+	8.52432i	−0.203654	+	0.352739i
$585$		0			0
$586$	2.72936	−	1.57579i	0.112749	−	0.0650954i
$587$	−30.2752			−1.24959			−0.624796	−	0.780788i	$-0.714818\pi$
$587$	−30.2752			−1.24959			−0.624796	+	0.780788i	$0.714818\pi$
$588$		0			0
$589$	−44.9389			−1.85167
$590$	13.1908	−	7.61571i	0.543057	−	0.313534i
$591$		0			0
$592$	5.91189	−	10.2397i	0.242977	−	0.420849i
$593$	−2.54071	−	4.40063i	−0.104334	−	0.180712i	0.809132	−	0.587627i	$-0.199938\pi$
$593$	−2.54071	−	4.40063i	−0.104334	−	0.180712i	−0.913466	+	0.406915i	$0.866605\pi$
$594$		0			0
$595$	19.7680	+	29.1900i	0.810409	+	1.19667i
$596$		−	6.65221i		−	0.272485i
$597$		0			0
$598$	−10.4930	−	6.05816i	−0.429092	−	0.247736i
$599$	34.0097	+	19.6355i	1.38960	+	0.802285i	0.993270	−	0.115823i	$-0.0369505\pi$
$599$	34.0097	+	19.6355i	1.38960	+	0.802285i	0.396329	+	0.918108i	$0.370284\pi$
$600$		0			0
$601$			8.04133i			0.328013i	0.986459	+	0.164006i	$0.0524417\pi$
$601$			8.04133i			0.328013i	−0.986459	+	0.164006i	$0.947558\pi$
$602$	−28.5239	−	13.8464i	−1.16255	−	0.564338i
$603$		0			0
$604$	4.00877	+	6.94339i	0.163114	+	0.282522i
$605$	−1.25882	+	2.18034i	−0.0511783	+	0.0886434i
$606$		0			0
$607$	29.6848	−	17.1385i	1.20487	−	0.695632i	0.243236	−	0.969967i	$-0.421791\pi$
$607$	29.6848	−	17.1385i	1.20487	−	0.695632i	0.961634	+	0.274335i	$0.0884578\pi$
$608$	5.22803			0.212025
$609$		0			0
$610$	31.2618			1.26576
$611$	2.70577	−	1.56218i	0.109464	−	0.0631990i
$612$		0			0
$613$	−18.8924	+	32.7226i	−0.763057	+	1.32165i	0.178211	+	0.983992i	$0.442969\pi$
$613$	−18.8924	+	32.7226i	−0.763057	+	1.32165i	−0.941268	+	0.337661i	$0.890364\pi$
$614$	−7.53553	−	13.0519i	−0.304109	−	0.526733i
$615$		0			0
$616$	2.63896	−	0.189469i	0.106327	−	0.00763391i
$617$			0.0377832i			0.00152109i	1.00000		0.000760547i	$0.000242090\pi$
$617$			0.0377832i			0.00152109i	−1.00000		0.000760547i	$0.999758\pi$
$618$		0			0
$619$	5.61028	+	3.23910i	0.225496	+	0.130190i	0.608493	−	0.793559i	$-0.291774\pi$
$619$	5.61028	+	3.23910i	0.225496	+	0.130190i	−0.382996	+	0.923750i	$0.625108\pi$
$620$	18.7417	+	10.8205i	0.752683	+	0.434562i
$621$		0			0
$622$			31.9145i			1.27966i
$623$	18.3105	−	37.7201i	0.733595	−	1.51122i
$624$		0			0
$625$	14.9505	+	25.8950i	0.598018	+	1.03580i
$626$	7.97469	−	13.8126i	0.318733	−	0.552061i
$627$		0			0
$628$	−19.0820	+	11.0170i	−0.761456	+	0.439627i
$629$	62.5777			2.49514
$630$		0			0
$631$	−17.8145			−0.709184			−0.354592	−	0.935021i	$-0.615380\pi$
$631$	−17.8145			−0.709184			−0.354592	+	0.935021i	$0.615380\pi$
$632$	6.10854	−	3.52677i	0.242985	−	0.140287i
$633$		0			0
$634$	12.6623	−	21.9318i	0.502886	−	0.871023i
$635$	−8.30411	−	14.3831i	−0.329539	−	0.570778i
$636$		0			0
$637$	15.9217	+	6.36396i	0.630840	+	0.252149i
$638$			8.05986i			0.319093i
$639$		0			0
$640$	−2.18034	−	1.25882i	−0.0861854	−	0.0497592i
$641$	16.1473	+	9.32265i	0.637780	+	0.368222i	0.783759	−	0.621065i	$-0.213300\pi$
$641$	16.1473	+	9.32265i	0.637780	+	0.368222i	−0.145979	+	0.989288i	$0.546633\pi$
$642$		0			0
$643$		−	7.04112i		−	0.277674i	−0.990315	−	0.138837i	$-0.955664\pi$
$643$		−	7.04112i		−	0.277674i	0.990315	−	0.138837i	$-0.0443365\pi$
$644$	10.8361	−	7.33839i	0.427001	−	0.289173i
$645$		0			0
$646$	13.8347	+	23.9625i	0.544321	+	0.942791i
$647$	25.0127	−	43.3232i	0.983350	−	1.70321i	0.334299	−	0.942467i	$-0.391500\pi$
$647$	25.0127	−	43.3232i	0.983350	−	1.70321i	0.649051	−	0.760745i	$-0.275166\pi$
$648$		0			0
$649$	5.23936	−	3.02494i	0.205663	−	0.118739i
$650$	3.27865			0.128599
$651$		0			0
$652$	10.0645			0.394156
$653$	2.68285	−	1.54894i	0.104988	−	0.0606149i	−0.446587	−	0.894740i	$-0.647361\pi$
$653$	2.68285	−	1.54894i	0.104988	−	0.0606149i	0.551575	+	0.834126i	$0.314027\pi$
$654$		0			0
$655$	−1.90676	+	3.30260i	−0.0745031	+	0.129043i
$656$	0.962402	+	1.66693i	0.0375755	+	0.0650826i
$657$		0			0
$658$	0.241670	+	3.36603i	0.00942127	+	0.131221i
$659$		−	41.9739i		−	1.63507i	−0.575878	−	0.817536i	$-0.695340\pi$
$659$		−	41.9739i		−	1.63507i	0.575878	−	0.817536i	$-0.304660\pi$
$660$		0			0
$661$	−22.8408	−	13.1872i	−0.888405	−	0.512921i	−0.0149846	−	0.999888i	$-0.504770\pi$
$661$	−22.8408	−	13.1872i	−0.888405	−	0.512921i	−0.873420	+	0.486967i	$0.838103\pi$
$662$	−12.1916	−	7.03882i	−0.473840	−	0.273571i
$663$		0			0
$664$		−	9.35827i		−	0.363171i
$665$	−2.49384	−	34.7347i	−0.0967070	−	1.34695i
$666$		0			0
$667$	19.9339	+	34.5265i	0.771843	+	1.33687i
$668$	−2.38134	+	4.12460i	−0.0921369	+	0.159586i
$669$		0			0
$670$	−26.6687	+	15.3972i	−1.03030	+	0.594844i
$671$	12.4171			0.479358
$672$		0			0
$673$	−6.60164			−0.254475			−0.127237	−	0.991872i	$-0.540611\pi$
$673$	−6.60164			−0.254475			−0.127237	+	0.991872i	$0.540611\pi$
$674$	−7.05934	+	4.07571i	−0.271916	+	0.156991i
$675$		0			0
$676$	3.50000	−	6.06218i	0.134615	−	0.233161i
$677$	4.52228	+	7.83282i	0.173805	+	0.301040i	0.939747	−	0.341870i	$-0.111060\pi$
$677$	4.52228	+	7.83282i	0.173805	+	0.301040i	−0.765942	+	0.642910i	$0.777727\pi$
$678$		0			0
$679$	29.9149	−	20.2590i	1.14803	−	0.777468i
$680$		−	13.3247i		−	0.510978i
$681$		0			0
$682$	7.44414	+	4.29788i	0.285051	+	0.164574i
$683$	27.2954	+	15.7590i	1.04443	+	0.603003i	0.921085	−	0.389361i	$-0.127304\pi$
$683$	27.2954	+	15.7590i	1.04443	+	0.603003i	0.123346	+	0.992364i	$0.460637\pi$
$684$		0			0
$685$		−	34.9774i		−	1.33642i
$686$	−13.6938	+	12.4691i	−0.522834	+	0.476073i
$687$		0			0
$688$	5.99207	+	10.3786i	0.228446	+	0.395679i
$689$	0.586302	−	1.01550i	0.0223363	−	0.0386876i
$690$		0			0
$691$	26.3742	−	15.2272i	1.00332	−	0.579268i	0.0940927	−	0.995563i	$-0.470005\pi$
$691$	26.3742	−	15.2272i	1.00332	−	0.579268i	0.909230	+	0.416295i	$0.136672\pi$
$692$	−14.7369			−0.560211
$693$		0			0
$694$	−22.5746			−0.856919
$695$	29.6332	−	17.1087i	1.12405	−	0.648972i
$696$		0			0
$697$	−5.09354	+	8.82227i	−0.192932	+	0.334167i
$698$	−11.4749	−	19.8751i	−0.434332	−	0.752284i
$699$		0			0
$700$	−1.54650	+	3.18582i	−0.0584521	+	0.120413i
$701$			26.3465i			0.995093i	0.867437	+	0.497547i	$0.165766\pi$
$701$			26.3465i			0.995093i	−0.867437	+	0.497547i	$0.834234\pi$
$702$		0			0
$703$	−53.5334	−	30.9075i	−2.01905	−	1.16570i
$704$	−0.866025	−	0.500000i	−0.0326396	−	0.0188445i
$705$		0			0
$706$		−	25.1981i		−	0.948342i
$707$	−3.63760	+	0.261168i	−0.136806	+	0.00982223i
$708$		0			0
$709$	−5.35292	−	9.27154i	−0.201033	−	0.348200i	0.747828	−	0.663892i	$-0.231097\pi$
$709$	−5.35292	−	9.27154i	−0.201033	−	0.348200i	−0.948862	+	0.315692i	$0.897763\pi$
$710$	18.5116	−	32.0630i	0.694726	−	1.20330i
$711$		0			0
$712$	−13.7246	+	7.92392i	−0.514353	+	0.296962i
$713$	42.5186			1.59233
$714$		0			0
$715$	6.16693			0.230630
$716$	2.03491	−	1.17486i	0.0760482	−	0.0439065i
$717$		0			0
$718$	−9.84714	+	17.0558i	−0.367492	+	0.636515i
$719$	15.3059	+	26.5107i	0.570815	+	0.988681i	0.996482	+	0.0838012i	$0.0267061\pi$
$719$	15.3059	+	26.5107i	0.570815	+	0.988681i	−0.425667	+	0.904880i	$0.639961\pi$
$720$		0			0
$721$	−24.9819	−	12.1270i	−0.930374	−	0.451633i
$722$		−	8.33229i		−	0.310096i
$723$		0			0
$724$	−10.3261	−	5.96178i	−0.383767	−	0.221568i
$725$	−9.34279	−	5.39406i	−0.346983	−	0.200331i
$726$		0			0
$727$		−	7.03188i		−	0.260798i	−0.991462	−	0.130399i	$-0.958374\pi$
$727$		−	7.03188i		−	0.260798i	0.991462	−	0.130399i	$-0.0416258\pi$
$728$	−3.63397	−	5.36603i	−0.134684	−	0.198878i
$729$		0			0
$730$	−12.3906	−	21.4612i	−0.458597	−	0.794313i
$731$	−31.7132	+	54.9289i	−1.17296	+	2.03162i
$732$		0			0
$733$	19.5539	−	11.2895i	0.722240	−	0.416985i	−0.0933367	−	0.995635i	$-0.529753\pi$
$733$	19.5539	−	11.2895i	0.722240	−	0.416985i	0.815577	+	0.578649i	$0.196420\pi$
$734$	3.24796			0.119885
$735$		0			0
$736$	−4.94646			−0.182329
$737$	−10.5927	+	6.11571i	−0.390188	+	0.225275i
$738$		0			0
$739$	−9.24921	+	16.0201i	−0.340238	+	0.589309i	−0.984477	−	0.175515i	$-0.943841\pi$
$739$	−9.24921	+	16.0201i	−0.340238	+	0.589309i	0.644239	+	0.764824i	$0.277174\pi$
$740$	14.8840	+	25.7798i	0.547147	+	0.947686i
$741$		0			0
$742$	0.710202	+	1.04870i	0.0260723	+	0.0384991i
$743$			22.8029i			0.836558i	0.908319	+	0.418279i	$0.137367\pi$
$743$			22.8029i			0.836558i	−0.908319	+	0.418279i	$0.862633\pi$
$744$		0			0
$745$	14.5041	+	8.37393i	0.531388	+	0.306797i
$746$	−5.90935	−	3.41177i	−0.216357	−	0.124914i
$747$		0			0
$748$		−	5.29253i		−	0.193514i
$749$	−6.88557	−	3.34247i	−0.251593	−	0.122131i
$750$		0			0
$751$	15.6992	+	27.1918i	0.572871	+	0.992242i	0.996269	+	0.0862983i	$0.0275038\pi$
$751$	15.6992	+	27.1918i	0.572871	+	0.992242i	−0.423398	+	0.905944i	$0.639163\pi$
$752$	0.637756	−	1.10463i	0.0232566	−	0.0402816i
$753$		0			0
$754$	17.0975	−	9.87127i	0.622656	−	0.359490i
$755$	−20.1852			−0.734616
$756$		0			0
$757$	−15.6251			−0.567905			−0.283953	−	0.958838i	$-0.591646\pi$
$757$	−15.6251			−0.567905			−0.283953	+	0.958838i	$0.591646\pi$
$758$	16.3618	−	9.44646i	0.594286	−	0.343111i
$759$		0			0
$760$	−6.58114	+	11.3989i	−0.238723	+	0.413481i
$761$	20.4241	+	35.3755i	0.740372	+	1.28236i	0.952326	+	0.305082i	$0.0986840\pi$
$761$	20.4241	+	35.3755i	0.740372	+	1.28236i	−0.211954	+	0.977280i	$0.567983\pi$
$762$		0			0
$763$	−35.7284	+	2.56518i	−1.29345	+	0.0928658i
$764$		−	24.5765i		−	0.889146i
$765$		0			0
$766$	22.8916	+	13.2165i	0.827106	+	0.477530i
$767$	−12.8338	−	7.40957i	−0.463400	−	0.267544i
$768$		0			0
$769$		−	1.71477i		−	0.0618361i	−0.999522	−	0.0309181i	$-0.990157\pi$
$769$		−	1.71477i		−	0.0618361i	0.999522	−	0.0309181i	$-0.00984309\pi$
$770$	−2.90887	+	5.99233i	−0.104828	+	0.215949i
$771$		0			0
$772$	−7.05657	−	12.2223i	−0.253972	−	0.439892i
$773$	−8.25433	+	14.2969i	−0.296887	+	0.514224i	−0.975422	−	0.220344i	$-0.929282\pi$
$773$	−8.25433	+	14.2969i	−0.296887	+	0.514224i	0.678535	+	0.734568i	$0.262615\pi$
$774$		0			0
$775$	−9.96399	+	5.75272i	−0.357917	+	0.206644i
$776$	−13.6556			−0.490208
$777$		0			0
$778$	11.6678			0.418312
$779$	8.71475	−	5.03146i	0.312238	−	0.180271i
$780$		0			0
$781$	7.35275	−	12.7353i	0.263102	−	0.455706i
$782$	−13.0897	−	22.6719i	−0.468085	−	0.810747i
$783$		0			0
$784$	6.92820	−	1.00000i	0.247436	−	0.0357143i
$785$		−	55.4737i		−	1.97994i
$786$		0			0
$787$	37.9077	+	21.8860i	1.35126	+	0.780153i	0.988427	−	0.151699i	$-0.0484744\pi$
$787$	37.9077	+	21.8860i	1.35126	+	0.780153i	0.362838	+	0.931852i	$0.381808\pi$
$788$	0.501618	+	0.289609i	0.0178694	+	0.0103169i
$789$		0			0
$790$			17.7583i			0.631810i
$791$	31.9179	−	21.6154i	1.13487	−	0.768556i
$792$		0			0
$793$	−15.2078	−	26.3407i	−0.540046	−	0.935386i
$794$	−5.01532	+	8.68678i	−0.177987	+	0.308282i
$795$		0			0
$796$	2.08228	−	1.20220i	0.0738045	−	0.0426110i
$797$	27.8981			0.988203			0.494102	−	0.869404i	$-0.335497\pi$
$797$	27.8981			0.988203			0.494102	+	0.869404i	$0.335497\pi$
$798$		0			0
$799$	6.75069			0.238822
$800$	1.15918	−	0.669251i	0.0409831	−	0.0236616i
$801$		0			0
$802$	2.61125	−	4.52281i	0.0922063	−	0.159706i
$803$	−4.92152	−	8.52432i	−0.173677	−	0.300817i
$804$		0			0
$805$	2.35953	+	32.8640i	0.0831625	+	1.15830i
$806$		−	21.0552i		−	0.741638i
$807$		0			0
$808$	1.19375	+	0.689211i	0.0419959	+	0.0242464i
$809$	−9.97340	−	5.75815i	−0.350646	−	0.202446i	0.314324	−	0.949316i	$-0.398222\pi$
$809$	−9.97340	−	5.75815i	−0.350646	−	0.202446i	−0.664970	+	0.746870i	$0.731556\pi$
$810$		0			0
$811$			7.86619i			0.276219i	0.990417	+	0.138110i	$0.0441026\pi$
$811$			7.86619i			0.276219i	−0.990417	+	0.138110i	$0.955897\pi$
$812$	1.52709	+	21.2696i	0.0535904	+	0.746417i
$813$		0			0
$814$	5.91189	+	10.2397i	0.207212	+	0.358901i
$815$	−12.6694	+	21.9440i	−0.443789	+	0.768665i
$816$		0			0
$817$	54.2595	−	31.3267i	1.89830	−	1.09598i
$818$	−19.2207			−0.672037
$819$		0			0
$820$	−4.84596			−0.169228
$821$	7.40031	−	4.27257i	0.258272	−	0.149114i	−0.365274	−	0.930900i	$-0.619025\pi$
$821$	7.40031	−	4.27257i	0.258272	−	0.149114i	0.623546	+	0.781786i	$0.285691\pi$
$822$		0			0
$823$	4.71503	−	8.16668i	0.164356	−	0.284673i	−0.772071	−	0.635537i	$-0.780779\pi$
$823$	4.71503	−	8.16668i	0.164356	−	0.284673i	0.936426	+	0.350864i	$0.114112\pi$
$824$	5.24799	+	9.08978i	0.182822	+	0.316658i
$825$		0			0
$826$	13.2533	−	8.97540i	0.461142	−	0.312294i
$827$		−	10.9084i		−	0.379323i	−0.981850	−	0.189662i	$-0.939261\pi$
$827$		−	10.9084i		−	0.379323i	0.981850	−	0.189662i	$-0.0607391\pi$
$828$		0			0
$829$	−9.54168	−	5.50889i	−0.331396	−	0.191332i	0.325065	−	0.945692i	$-0.394614\pi$
$829$	−9.54168	−	5.50889i	−0.331396	−	0.191332i	−0.656461	+	0.754360i	$0.727947\pi$
$830$	20.4042	+	11.7804i	0.708240	+	0.408903i
$831$		0			0
$832$			2.44949i			0.0849208i
$833$	22.9173	+	29.1089i	0.794038	+	1.00856i
$834$		0			0
$835$	−5.99536	−	10.3843i	−0.207478	−	0.359362i
$836$	−2.61401	+	4.52761i	−0.0904076	+	0.156591i
$837$		0			0
$838$	−15.1342	+	8.73774i	−0.522803	+	0.301840i
$839$	−19.2163			−0.663422			−0.331711	−	0.943381i	$-0.607626\pi$
$839$	−19.2163			−0.663422			−0.331711	+	0.943381i	$0.607626\pi$
$840$		0			0
$841$	−35.9613			−1.24004
$842$	24.1205	−	13.9260i	0.831246	−	0.479920i
$843$		0			0
$844$	−2.99672	+	5.19046i	−0.103151	+	0.178663i
$845$	8.81173	+	15.2624i	0.303133	+	0.525041i
$846$		0			0
$847$	−1.15539	+	2.38014i	−0.0396998	+	0.0817826i
$848$		−	0.478713i		−	0.0164391i
$849$		0			0
$850$	6.13497	+	3.54203i	0.210428	+	0.121491i
$851$	50.6503	+	29.2430i	1.73627	+	1.00244i
$852$		0			0
$853$		−	50.2570i		−	1.72077i	−0.509649	−	0.860383i	$-0.670225\pi$
$853$		−	50.2570i		−	1.72077i	0.509649	−	0.860383i	$-0.329775\pi$
$854$	32.7683	−	2.35266i	1.12131	−	0.0805063i
$855$		0			0
$856$	1.44646	+	2.50535i	0.0494391	+	0.0856310i
$857$	6.92321	−	11.9914i	0.236492	−	0.409617i	−0.723213	−	0.690625i	$-0.757336\pi$
$857$	6.92321	−	11.9914i	0.236492	−	0.409617i	0.959705	+	0.281008i	$0.0906688\pi$
$858$		0			0
$859$	−11.3460	+	6.55059i	−0.387119	+	0.223503i	−0.680911	−	0.732366i	$-0.738416\pi$
$859$	−11.3460	+	6.55059i	−0.387119	+	0.223503i	0.293792	+	0.955869i	$0.405083\pi$
$860$	−30.1717			−1.02885
$861$		0			0
$862$	−34.8542			−1.18714
$863$	−29.1086	+	16.8058i	−0.990867	+	0.572077i	−0.905533	−	0.424275i	$-0.860529\pi$
$863$	−29.1086	+	16.8058i	−0.990867	+	0.572077i	−0.0853335	+	0.996352i	$0.527196\pi$
$864$		0			0
$865$	18.5510	−	32.1313i	0.630754	−	1.09250i
$866$	13.6034	+	23.5618i	0.462262	+	0.800662i
$867$		0			0
$868$	20.4591	+	9.93149i	0.694427	+	0.337097i
$869$			7.05354i			0.239275i
$870$		0			0
$871$	25.9468	+	14.9804i	0.879173	+	0.507591i
$872$	11.7250	+	6.76941i	0.397057	+	0.229241i
$873$		0			0
$874$			25.8603i			0.874736i
$875$	13.6760	+	20.1943i	0.462332	+	0.682693i
$876$		0			0
$877$	14.0399	+	24.3178i	0.474093	+	0.821153i	0.999560	−	0.0296608i	$-0.00944271\pi$
$877$	14.0399	+	24.3178i	0.474093	+	0.821153i	−0.525467	+	0.850814i	$0.676109\pi$
$878$	−11.6040	+	20.0987i	−0.391616	+	0.678299i
$879$		0			0
$880$	2.18034	−	1.25882i	0.0734992	−	0.0424348i
$881$	20.4395			0.688623			0.344312	−	0.938855i	$-0.388112\pi$
$881$	20.4395			0.688623			0.344312	+	0.938855i	$0.388112\pi$
$882$		0			0
$883$	−28.7609			−0.967880			−0.483940	−	0.875101i	$-0.660795\pi$
$883$	−28.7609			−0.967880			−0.483940	+	0.875101i	$0.660795\pi$
$884$	−11.2271	+	6.48200i	−0.377610	+	0.218013i
$885$		0			0
$886$	9.07435	−	15.7172i	0.304859	−	0.528031i
$887$	−24.6498	−	42.6947i	−0.827659	−	1.43355i	−0.899870	−	0.436158i	$-0.856339\pi$
$887$	−24.6498	−	42.6947i	−0.827659	−	1.43355i	0.0722117	−	0.997389i	$-0.476994\pi$
$888$		0			0
$889$	−9.78670	−	14.4513i	−0.328235	−	0.484681i
$890$		−	39.8991i		−	1.33742i
$891$		0			0
$892$	6.48647	+	3.74496i	0.217183	+	0.125391i
$893$	−5.77502	−	3.33421i	−0.193254	−	0.111575i
$894$		0			0
$895$			5.91573i			0.197741i
$896$	−2.38014	−	1.15539i	−0.0795149	−	0.0385990i
$897$		0			0
$898$	15.9828	+	27.6830i	0.533352	+	0.923793i
$899$	−34.6403	+	59.9987i	−1.15532	+	2.00107i
$900$		0			0
$901$	2.19417	−	1.26680i	0.0730983	−	0.0422033i
$902$	−1.92480			−0.0640889
$903$		0			0
$904$	−14.5699			−0.484589
$905$	25.9974	−	15.0096i	0.864183	−	0.498936i
$906$		0			0
$907$	−18.2780	+	31.6584i	−0.606911	+	1.05120i	0.384835	+	0.922985i	$0.374258\pi$
$907$	−18.2780	+	31.6584i	−0.606911	+	1.05120i	−0.991746	+	0.128215i	$0.959075\pi$
$908$	4.88304	+	8.45768i	0.162049	+	0.280678i
$909$		0			0
$910$	16.2743	−	1.16844i	0.539487	−	0.0387334i
$911$			33.3749i			1.10576i	0.833261	+	0.552880i	$0.186471\pi$
$911$			33.3749i			1.10576i	−0.833261	+	0.552880i	$0.813529\pi$
$912$		0			0
$913$	8.10450	+	4.67914i	0.268220	+	0.154857i
$914$	−22.4486	−	12.9607i	−0.742534	−	0.428702i
$915$		0			0
$916$		−	0.225376i		−	0.00744664i
$917$	−1.75010	+	3.60524i	−0.0577933	+	0.119056i
$918$		0			0
$919$	4.34095	+	7.51874i	0.143195	+	0.248020i	0.928698	−	0.370837i	$-0.120929\pi$
$919$	4.34095	+	7.51874i	0.143195	+	0.248020i	−0.785503	+	0.618857i	$0.787596\pi$
$920$	6.22670	−	10.7850i	0.205288	−	0.355570i
$921$		0			0
$922$	18.9038	−	10.9141i	0.622563	−	0.359437i
$923$	−36.0210			−1.18564
$924$		0			0
$925$	−15.8262			−0.520361
$926$	4.26622	−	2.46311i	0.140197	−	0.0809427i
$927$		0			0
$928$	4.02993	−	6.98004i	0.132289	−	0.229131i
$929$	−18.8642	−	32.6738i	−0.618915	−	1.07199i	−0.989684	−	0.143267i	$-0.954239\pi$
$929$	−18.8642	−	32.6738i	−0.618915	−	1.07199i	0.370769	−	0.928725i	$-0.379094\pi$
$930$		0			0
$931$	−5.22803	−	36.2208i	−0.171342	−	1.18709i
$932$			0.514719i			0.0168602i
$933$		0			0
$934$	3.24592	+	1.87404i	0.106210	+	0.0613203i
$935$	11.5395	+	6.66234i	0.377382	+	0.217882i
$936$		0			0
$937$		−	2.55832i		−	0.0835768i	−0.999126	−	0.0417884i	$-0.986694\pi$
$937$		−	2.55832i		−	0.0835768i	0.999126	−	0.0417884i	$-0.0133055\pi$
$938$	−26.7950	+	18.1461i	−0.874889	+	0.592491i
$939$		0			0
$940$	1.60564	+	2.78105i	0.0523702	+	0.0907078i
$941$	24.3638	−	42.1993i	0.794236	−	1.37566i	−0.129087	−	0.991633i	$-0.541205\pi$
$941$	24.3638	−	42.1993i	0.794236	−	1.37566i	0.923323	−	0.384024i	$-0.125462\pi$
$942$		0			0
$943$	−8.24540	+	4.76049i	−0.268507	+	0.155023i
$944$	−6.04989			−0.196907
$945$		0			0
$946$	−11.9841			−0.389638
$947$	30.4320	−	17.5699i	0.988908	−	0.570946i	0.0839599	−	0.996469i	$-0.473243\pi$
$947$	30.4320	−	17.5699i	0.988908	−	0.570946i	0.904948	+	0.425523i	$0.139910\pi$
$948$		0			0
$949$	−12.0552	+	20.8802i	−0.391329	+	0.677801i
$950$	−3.49886	−	6.06021i	−0.113518	−	0.196619i
$951$		0			0
$952$	−1.00277	−	13.9668i	−0.0324999	−	0.452665i
$953$			1.34315i			0.0435088i	0.999763	+	0.0217544i	$0.00692518\pi$
$953$			1.34315i			0.0435088i	−0.999763	+	0.0217544i	$0.993075\pi$
$954$		0			0
$955$	53.5851	+	30.9374i	1.73397	+	1.00111i
$956$	13.4147	+	7.74496i	0.433861	+	0.250490i
$957$		0			0
$958$			3.86267i			0.124797i
$959$	−2.63227	−	36.6629i	−0.0850006	−	1.18391i
$960$		0			0
$961$	21.4435	+	37.1412i	0.691726	+	1.19810i
$962$	14.4811	−	25.0820i	0.466890	−	0.808677i
$963$		0			0
$964$	−14.2882	+	8.24932i	−0.460194	+	0.265693i
$965$	35.5318			1.14381
$966$		0			0
$967$	−34.3045			−1.10316			−0.551580	−	0.834122i	$-0.685975\pi$
$967$	−34.3045			−1.10316			−0.551580	+	0.834122i	$0.685975\pi$
$968$	0.866025	−	0.500000i	0.0278351	−	0.0160706i
$969$		0			0
$970$	17.1899	−	29.7739i	0.551936	−	0.955981i
$971$	2.71114	+	4.69583i	0.0870046	+	0.150696i	0.906244	−	0.422756i	$-0.138937\pi$
$971$	2.71114	+	4.69583i	0.0870046	+	0.150696i	−0.819239	+	0.573452i	$0.805604\pi$
$972$		0			0
$973$	29.7736	−	20.1633i	0.954499	−	0.646405i
$974$			11.6189i			0.372294i
$975$		0			0
$976$	−10.7536	−	6.20857i	−0.344213	−	0.198731i
$977$	−3.04148	−	1.75600i	−0.0973056	−	0.0561794i	0.450558	−	0.892747i	$-0.351225\pi$
$977$	−3.04148	−	1.75600i	−0.0973056	−	0.0561794i	−0.547863	+	0.836568i	$0.684559\pi$
$978$		0			0
$979$		−	15.8478i		−	0.506499i
$980$	−6.54102	+	16.3646i	−0.208945	+	0.522749i
$981$		0			0
$982$	12.8672	+	22.2867i	0.410610	+	0.711198i
$983$	0.0659506	−	0.114230i	0.00210350	−	0.00364336i	−0.864972	−	0.501821i	$-0.832664\pi$
$983$	0.0659506	−	0.114230i	0.00210350	−	0.00364336i	0.867075	+	0.498177i	$0.165997\pi$
$984$		0			0
$985$	−1.26289	+	0.729131i	−0.0402391	+	0.0232321i
$986$	42.6570			1.35848
$987$		0			0
$988$	12.8060			0.407413
$989$	−51.3372	+	29.6396i	−1.63243	+	0.942483i
$990$		0			0
$991$	−13.6398	+	23.6249i	−0.433283	+	0.750468i	−0.997154	−	0.0753949i	$-0.975978\pi$
$991$	−13.6398	+	23.6249i	−0.433283	+	0.750468i	0.563871	+	0.825863i	$0.309312\pi$
$992$	−4.29788	−	7.44414i	−0.136458	−	0.236352i
$993$		0			0
$994$	16.9907	−	35.0011i	0.538911	−	1.11017i
$995$			6.05343i			0.191907i
$996$		0			0
$997$	39.6642	+	22.9001i	1.25618	+	0.725254i	0.972329	−	0.233615i	$-0.0750555\pi$
$997$	39.6642	+	22.9001i	1.25618	+	0.725254i	0.283848	+	0.958869i	$0.408389\pi$
$998$	−19.7425	−	11.3984i	−0.624939	−	0.360809i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.r.c.1277.4	yes	8
3.2	odd	2		1386.2.r.a.1277.1	yes	8
7.5	odd	6		1386.2.r.a.89.1	✓	8
21.5	even	6	inner	1386.2.r.c.89.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.r.a.89.1	✓	8	7.5	odd	6
1386.2.r.a.1277.1	yes	8	3.2	odd	2
1386.2.r.c.89.4	yes	8	21.5	even	6	inner
1386.2.r.c.1277.4	yes	8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.25882 + 2.18034i) q^{5} +(1.48356 + 2.19067i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.25882 + 2.18034i) q^{5} +(1.48356 + 2.19067i) q^{7} -1.00000i q^{8} +(2.18034 + 1.25882i) q^{10} +(0.866025 + 0.500000i) q^{11} -2.44949i q^{13} +(2.38014 + 1.15539i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.64626 - 4.58346i) q^{17} +(-4.52761 + 2.61401i) q^{19} +2.51764 q^{20} +1.00000 q^{22} +(4.28376 - 2.47323i) q^{23} +(-0.669251 + 1.15918i) q^{25} +(-1.22474 - 2.12132i) q^{26} +(2.63896 - 0.189469i) q^{28} +8.05986i q^{29} +(7.44414 + 4.29788i) q^{31} +(-0.866025 - 0.500000i) q^{32} -5.29253i q^{34} +(-2.90887 + 5.99233i) q^{35} +(5.91189 + 10.2397i) q^{37} +(-2.61401 + 4.52761i) q^{38} +(2.18034 - 1.25882i) q^{40} -1.92480 q^{41} -11.9841 q^{43} +(0.866025 - 0.500000i) q^{44} +(2.47323 - 4.28376i) q^{46} +(0.637756 + 1.10463i) q^{47} +(-2.59808 + 6.50000i) q^{49} +1.33850i q^{50} +(-2.12132 - 1.22474i) q^{52} +(0.414578 + 0.239357i) q^{53} +2.51764i q^{55} +(2.19067 - 1.48356i) q^{56} +(4.02993 + 6.98004i) q^{58} +(3.02494 - 5.23936i) q^{59} +(10.7536 - 6.20857i) q^{61} +8.59575 q^{62} -1.00000 q^{64} +(5.34072 - 3.08346i) q^{65} +(-6.11571 + 10.5927i) q^{67} +(-2.64626 - 4.58346i) q^{68} +(0.477014 + 6.64394i) q^{70} -14.7055i q^{71} +(-8.52432 - 4.92152i) q^{73} +(10.2397 + 5.91189i) q^{74} +5.22803i q^{76} +(0.189469 + 2.63896i) q^{77} +(3.52677 + 6.10854i) q^{79} +(1.25882 - 2.18034i) q^{80} +(-1.66693 + 0.962402i) q^{82} +9.35827 q^{83} +13.3247 q^{85} +(-10.3786 + 5.99207i) q^{86} +(0.500000 - 0.866025i) q^{88} +(-7.92392 - 13.7246i) q^{89} +(5.36603 - 3.63397i) q^{91} -4.94646i q^{92} +(1.10463 + 0.637756i) q^{94} +(-11.3989 - 6.58114i) q^{95} -13.6556i q^{97} +(1.00000 + 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 8 q^{5}+O(q^{10}) \) 8 * q + 4 * q^4 + 8 * q^5	\( 8 q + 4 q^{4} + 8 q^{5} - 4 q^{16} - 4 q^{17} + 24 q^{19} + 16 q^{20} + 8 q^{22} + 24 q^{23} - 4 q^{25} + 12 q^{31} + 16 q^{35} + 12 q^{37} - 8 q^{38} + 16 q^{41} - 32 q^{43} + 8 q^{46} + 48 q^{53} - 4 q^{58} + 16 q^{59} + 24 q^{62} - 8 q^{64} - 12 q^{65} - 24 q^{67} + 4 q^{68} - 20 q^{70} - 24 q^{73} - 12 q^{74} + 40 q^{79} + 8 q^{80} + 12 q^{82} + 72 q^{83} - 32 q^{85} - 24 q^{86} + 4 q^{88} - 16 q^{89} + 36 q^{91} + 24 q^{95} + 8 q^{98}+O(q^{100}) \) 8 * q + 4 * q^4 + 8 * q^5 - 4 * q^16 - 4 * q^17 + 24 * q^19 + 16 * q^20 + 8 * q^22 + 24 * q^23 - 4 * q^25 + 12 * q^31 + 16 * q^35 + 12 * q^37 - 8 * q^38 + 16 * q^41 - 32 * q^43 + 8 * q^46 + 48 * q^53 - 4 * q^58 + 16 * q^59 + 24 * q^62 - 8 * q^64 - 12 * q^65 - 24 * q^67 + 4 * q^68 - 20 * q^70 - 24 * q^73 - 12 * q^74 + 40 * q^79 + 8 * q^80 + 12 * q^82 + 72 * q^83 - 32 * q^85 - 24 * q^86 + 4 * q^88 - 16 * q^89 + 36 * q^91 + 24 * q^95 + 8 * q^98

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