LMFDB - Embedded newform 855.2.n.c.647.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(647,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("855.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.n (of order $4$, 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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			647.3
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	855.647
Dual form			855.2.n.c.818.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41421 - 1.41421i) q^{2} -2.00000i q^{4} +(-1.67303 + 1.48356i) q^{5} +(0.633975 + 0.633975i) q^{7} +O(q^{10})$	\(q+(1.41421 - 1.41421i) q^{2} -2.00000i q^{4} +(-1.67303 + 1.48356i) q^{5} +(0.633975 + 0.633975i) q^{7} +(-0.267949 + 4.46410i) q^{10} +5.79555i q^{11} +(-2.73205 + 2.73205i) q^{13} +1.79315 q^{14} +4.00000 q^{16} +(-0.328169 + 0.328169i) q^{17} -1.00000i q^{19} +(2.96713 + 3.34607i) q^{20} +(8.19615 + 8.19615i) q^{22} +(2.44949 + 2.44949i) q^{23} +(0.598076 - 4.96410i) q^{25} +7.72741i q^{26} +(1.26795 - 1.26795i) q^{28} +5.93426 q^{29} -7.46410 q^{31} +(5.65685 - 5.65685i) q^{32} +0.928203i q^{34} +(-2.00120 - 0.120118i) q^{35} +(-3.46410 - 3.46410i) q^{37} +(-1.41421 - 1.41421i) q^{38} +2.82843i q^{41} +(2.09808 - 2.09808i) q^{43} +11.5911 q^{44} +6.92820 q^{46} +(-0.189469 + 0.189469i) q^{47} -6.19615i q^{49} +(-6.17449 - 7.86611i) q^{50} +(5.46410 + 5.46410i) q^{52} +(4.24264 + 4.24264i) q^{53} +(-8.59808 - 9.69615i) q^{55} +(8.39230 - 8.39230i) q^{58} +3.58630 q^{59} +14.8564 q^{61} +(-10.5558 + 10.5558i) q^{62} -8.00000i q^{64} +(0.517638 - 8.62398i) q^{65} +(2.53590 + 2.53590i) q^{67} +(0.656339 + 0.656339i) q^{68} +(-3.00000 + 2.66025i) q^{70} +10.5558i q^{71} +(-9.09808 + 9.09808i) q^{73} -9.79796 q^{74} -2.00000 q^{76} +(-3.67423 + 3.67423i) q^{77} -6.53590i q^{79} +(-6.69213 + 5.93426i) q^{80} +(4.00000 + 4.00000i) q^{82} +(-10.5558 - 10.5558i) q^{83} +(0.0621778 - 1.03590i) q^{85} -5.93426i q^{86} -5.93426 q^{89} -3.46410 q^{91} +(4.89898 - 4.89898i) q^{92} +0.535898i q^{94} +(1.48356 + 1.67303i) q^{95} +(11.6603 + 11.6603i) q^{97} +(-8.76268 - 8.76268i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{7}+O(q^{10}) $ 8 * q + 12 * q^7	$ 8 q + 12 q^{7} - 16 q^{10} - 8 q^{13} + 32 q^{16} + 24 q^{22} - 16 q^{25} + 24 q^{28} - 32 q^{31} - 4 q^{43} + 16 q^{52} - 48 q^{55} - 16 q^{58} + 8 q^{61} + 48 q^{67} - 24 q^{70} - 52 q^{73} - 16 q^{76} + 32 q^{82} - 48 q^{85} + 24 q^{97}+O(q^{100}) $ 8 * q + 12 * q^7 - 16 * q^10 - 8 * q^13 + 32 * q^16 + 24 * q^22 - 16 * q^25 + 24 * q^28 - 32 * q^31 - 4 * q^43 + 16 * q^52 - 48 * q^55 - 16 * q^58 + 8 * q^61 + 48 * q^67 - 24 * q^70 - 52 * q^73 - 16 * q^76 + 32 * q^82 - 48 * q^85 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.41421	−	1.41421i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$2$	1.41421	−	1.41421i	1.00000	−	1.00000i	1.00000			$0$
$3$		0			0
$3$		0			0
$4$		−	2.00000i		−	1.00000i
$5$	−1.67303	+	1.48356i	−0.748203	+	0.663470i
$5$	−1.67303	+	1.48356i	−0.748203	+	0.663470i
$6$		0			0
$7$	0.633975	+	0.633975i	0.239620	+	0.239620i	0.816693	−	0.577073i	$-0.195805\pi$
$7$	0.633975	+	0.633975i	0.239620	+	0.239620i	−0.577073	+	0.816693i	$0.695805\pi$
$8$		0			0
$9$		0			0
$10$	−0.267949	+	4.46410i	−0.0847330	+	1.41167i
$11$			5.79555i			1.74743i	0.486442	+	0.873713i	$0.338294\pi$
$11$			5.79555i			1.74743i	−0.486442	+	0.873713i	$0.661706\pi$
$12$		0			0
$13$	−2.73205	+	2.73205i	−0.757735	+	0.757735i	−0.975910	−	0.218175i	$-0.929990\pi$
$13$	−2.73205	+	2.73205i	−0.757735	+	0.757735i	0.218175	+	0.975910i	$0.429990\pi$
$14$	1.79315			0.479240
$15$		0			0
$16$	4.00000			1.00000
$17$	−0.328169	+	0.328169i	−0.0795928	+	0.0795928i	−0.745782	−	0.666190i	$-0.767924\pi$
$17$	−0.328169	+	0.328169i	−0.0795928	+	0.0795928i	0.666190	+	0.745782i	$0.267924\pi$
$18$		0			0
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	2.96713	+	3.34607i	0.663470	+	0.748203i
$21$		0			0
$22$	8.19615	+	8.19615i	1.74743	+	1.74743i
$23$	2.44949	+	2.44949i	0.510754	+	0.510754i	0.914757	−	0.404004i	$-0.132382\pi$
$23$	2.44949	+	2.44949i	0.510754	+	0.510754i	−0.404004	+	0.914757i	$0.632382\pi$
$24$		0			0
$25$	0.598076	−	4.96410i	0.119615	−	0.992820i
$26$			7.72741i			1.51547i
$27$		0			0
$28$	1.26795	−	1.26795i	0.239620	−	0.239620i
$29$	5.93426			1.10196			0.550982	−	0.834517i	$-0.314253\pi$
$29$	5.93426			1.10196			0.550982	+	0.834517i	$0.314253\pi$
$30$		0			0
$31$	−7.46410			−1.34059			−0.670296	−	0.742094i	$-0.733833\pi$
$31$	−7.46410			−1.34059			−0.670296	+	0.742094i	$0.733833\pi$
$32$	5.65685	−	5.65685i	1.00000	−	1.00000i
$33$		0			0
$34$			0.928203i			0.159186i
$35$	−2.00120	−	0.120118i	−0.338265	−	0.0203037i
$36$		0			0
$37$	−3.46410	−	3.46410i	−0.569495	−	0.569495i	0.362492	−	0.931987i	$-0.381926\pi$
$37$	−3.46410	−	3.46410i	−0.569495	−	0.569495i	−0.931987	+	0.362492i	$0.881926\pi$
$38$	−1.41421	−	1.41421i	−0.229416	−	0.229416i
$39$		0			0
$40$		0			0
$41$			2.82843i			0.441726i	0.975305	+	0.220863i	$0.0708874\pi$
$41$			2.82843i			0.441726i	−0.975305	+	0.220863i	$0.929113\pi$
$42$		0			0
$43$	2.09808	−	2.09808i	0.319954	−	0.319954i	−0.528796	−	0.848749i	$-0.677356\pi$
$43$	2.09808	−	2.09808i	0.319954	−	0.319954i	0.848749	+	0.528796i	$0.177356\pi$
$44$	11.5911			1.74743
$45$		0			0
$46$	6.92820			1.02151
$47$	−0.189469	+	0.189469i	−0.0276368	+	0.0276368i	−0.720790	−	0.693153i	$-0.756221\pi$
$47$	−0.189469	+	0.189469i	−0.0276368	+	0.0276368i	0.693153	+	0.720790i	$0.256221\pi$
$48$		0			0
$49$		−	6.19615i		−	0.885165i
$50$	−6.17449	−	7.86611i	−0.873205	−	1.11244i
$51$		0			0
$52$	5.46410	+	5.46410i	0.757735	+	0.757735i
$53$	4.24264	+	4.24264i	0.582772	+	0.582772i	0.935664	−	0.352892i	$-0.114802\pi$
$53$	4.24264	+	4.24264i	0.582772	+	0.582772i	−0.352892	+	0.935664i	$0.614802\pi$
$54$		0			0
$55$	−8.59808	−	9.69615i	−1.15936	−	1.30743i
$56$		0			0
$57$		0			0
$58$	8.39230	−	8.39230i	1.10196	−	1.10196i
$59$	3.58630			0.466897			0.233448	−	0.972369i	$-0.424999\pi$
$59$	3.58630			0.466897			0.233448	+	0.972369i	$0.424999\pi$
$60$		0			0
$61$	14.8564			1.90217			0.951084	−	0.308933i	$-0.0999717\pi$
$61$	14.8564			1.90217			0.951084	+	0.308933i	$0.0999717\pi$
$62$	−10.5558	+	10.5558i	−1.34059	+	1.34059i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$	0.517638	−	8.62398i	0.0642051	−	1.06967i
$66$		0			0
$67$	2.53590	+	2.53590i	0.309809	+	0.309809i	0.844835	−	0.535026i	$-0.179698\pi$
$67$	2.53590	+	2.53590i	0.309809	+	0.309809i	−0.535026	+	0.844835i	$0.679698\pi$
$68$	0.656339	+	0.656339i	0.0795928	+	0.0795928i
$69$		0			0
$70$	−3.00000	+	2.66025i	−0.358569	+	0.317961i
$71$			10.5558i			1.25275i	0.779523	+	0.626373i	$0.215461\pi$
$71$			10.5558i			1.25275i	−0.779523	+	0.626373i	$0.784539\pi$
$72$		0			0
$73$	−9.09808	+	9.09808i	−1.06485	+	1.06485i	−0.0671032	+	0.997746i	$0.521376\pi$
$73$	−9.09808	+	9.09808i	−1.06485	+	1.06485i	−0.997746	+	0.0671032i	$0.978624\pi$
$74$	−9.79796			−1.13899
$75$		0			0
$76$	−2.00000			−0.229416
$77$	−3.67423	+	3.67423i	−0.418718	+	0.418718i
$78$		0			0
$79$		−	6.53590i		−	0.735346i	−0.929955	−	0.367673i	$-0.880155\pi$
$79$		−	6.53590i		−	0.735346i	0.929955	−	0.367673i	$-0.119845\pi$
$80$	−6.69213	+	5.93426i	−0.748203	+	0.663470i
$81$		0			0
$82$	4.00000	+	4.00000i	0.441726	+	0.441726i
$83$	−10.5558	−	10.5558i	−1.15865	−	1.15865i	−0.984765	−	0.173888i	$-0.944367\pi$
$83$	−10.5558	−	10.5558i	−1.15865	−	1.15865i	−0.173888	−	0.984765i	$-0.555633\pi$
$84$		0			0
$85$	0.0621778	−	1.03590i	0.00674413	−	0.112359i
$86$		−	5.93426i		−	0.639907i
$87$		0			0
$88$		0			0
$89$	−5.93426			−0.629030			−0.314515	−	0.949253i	$-0.601842\pi$
$89$	−5.93426			−0.629030			−0.314515	+	0.949253i	$0.601842\pi$
$90$		0			0
$91$	−3.46410			−0.363137
$92$	4.89898	−	4.89898i	0.510754	−	0.510754i
$93$		0			0
$94$			0.535898i			0.0552737i
$95$	1.48356	+	1.67303i	0.152210	+	0.171650i
$96$		0			0
$97$	11.6603	+	11.6603i	1.18392	+	1.18392i	0.978720	+	0.205199i	$0.0657842\pi$
$97$	11.6603	+	11.6603i	1.18392	+	1.18392i	0.205199	+	0.978720i	$0.434216\pi$
$98$	−8.76268	−	8.76268i	−0.885165	−	0.885165i
$99$		0			0
$100$	−9.92820	−	1.19615i	−0.992820	−	0.119615i
$101$		−	10.4543i		−	1.04024i	−0.854093	−	0.520121i	$-0.825887\pi$
$101$		−	10.4543i		−	1.04024i	0.854093	−	0.520121i	$-0.174113\pi$
$102$		0			0
$103$	12.1962	−	12.1962i	1.20172	−	1.20172i	0.228080	−	0.973642i	$-0.426755\pi$
$103$	12.1962	−	12.1962i	1.20172	−	1.20172i	0.973642	−	0.228080i	$-0.0732449\pi$
$104$		0			0
$105$		0			0
$106$	12.0000			1.16554
$107$	−5.27792	+	5.27792i	−0.510235	+	0.510235i	−0.914599	−	0.404363i	$-0.867493\pi$
$107$	−5.27792	+	5.27792i	−0.510235	+	0.510235i	0.404363	+	0.914599i	$0.367493\pi$
$108$		0			0
$109$		−	12.3923i		−	1.18697i	−0.804846	−	0.593484i	$-0.797752\pi$
$109$		−	12.3923i		−	1.18697i	0.804846	−	0.593484i	$-0.202248\pi$
$110$	−25.8719	−	1.55291i	−2.46679	−	0.148065i
$111$		0			0
$112$	2.53590	+	2.53590i	0.239620	+	0.239620i
$113$	−6.03579	−	6.03579i	−0.567800	−	0.567800i	0.363712	−	0.931511i	$-0.381509\pi$
$113$	−6.03579	−	6.03579i	−0.567800	−	0.567800i	−0.931511	+	0.363712i	$0.881509\pi$
$114$		0			0
$115$	−7.73205	−	0.464102i	−0.721017	−	0.0432777i
$116$		−	11.8685i		−	1.10196i
$117$		0			0
$118$	5.07180	−	5.07180i	0.466897	−	0.466897i
$119$	−0.416102			−0.0381440
$120$		0			0
$121$	−22.5885			−2.05350
$122$	21.0101	−	21.0101i	1.90217	−	1.90217i
$123$		0			0
$124$			14.9282i			1.34059i
$125$	6.36396	+	9.19239i	0.569210	+	0.822192i
$126$		0			0
$127$	−4.73205	−	4.73205i	−0.419902	−	0.419902i	0.465268	−	0.885170i	$-0.345958\pi$
$127$	−4.73205	−	4.73205i	−0.419902	−	0.419902i	−0.885170	+	0.465268i	$0.845958\pi$
$128$		0			0
$129$		0			0
$130$	−11.4641	−	12.9282i	−1.00547	−	1.13388i
$131$			5.51815i			0.482123i	0.970510	+	0.241062i	$0.0774956\pi$
$131$			5.51815i			0.482123i	−0.970510	+	0.241062i	$0.922504\pi$
$132$		0			0
$133$	0.633975	−	0.633975i	0.0549726	−	0.0549726i
$134$	7.17260			0.619619
$135$		0			0
$136$		0			0
$137$	−5.98502	+	5.98502i	−0.511335	+	0.511335i	−0.914935	−	0.403600i	$-0.867759\pi$
$137$	−5.98502	+	5.98502i	−0.511335	+	0.511335i	0.403600	+	0.914935i	$0.367759\pi$
$138$		0			0
$139$			6.26795i			0.531641i	0.964023	+	0.265820i	$0.0856428\pi$
$139$			6.26795i			0.531641i	−0.964023	+	0.265820i	$0.914357\pi$
$140$	−0.240237	+	4.00240i	−0.0203037	+	0.338265i
$141$		0			0
$142$	14.9282	+	14.9282i	1.25275	+	1.25275i
$143$	−15.8338	−	15.8338i	−1.32408	−	1.32408i
$144$		0			0
$145$	−9.92820	+	8.80385i	−0.824492	+	0.731120i
$146$			25.7332i			2.12970i
$147$		0			0
$148$	−6.92820	+	6.92820i	−0.569495	+	0.569495i
$149$	17.2851			1.41605			0.708026	−	0.706186i	$-0.249586\pi$
$149$	17.2851			1.41605			0.708026	+	0.706186i	$0.249586\pi$
$150$		0			0
$151$	14.9282			1.21484			0.607420	−	0.794381i	$-0.292205\pi$
$151$	14.9282			1.21484			0.607420	+	0.794381i	$0.292205\pi$
$152$		0			0
$153$		0			0
$154$			10.3923i			0.837436i
$155$	12.4877	−	11.0735i	1.00304	−	0.889443i
$156$		0			0
$157$	−13.9282	−	13.9282i	−1.11159	−	1.11159i	−0.992935	−	0.118656i	$-0.962141\pi$
$157$	−13.9282	−	13.9282i	−1.11159	−	1.11159i	−0.118656	−	0.992935i	$-0.537859\pi$
$158$	−9.24316	−	9.24316i	−0.735346	−	0.735346i
$159$		0			0
$160$	−1.07180	+	17.8564i	−0.0847330	+	1.41167i
$161$			3.10583i			0.244774i
$162$		0			0
$163$	1.19615	−	1.19615i	0.0936899	−	0.0936899i	−0.658708	−	0.752398i	$-0.728897\pi$
$163$	1.19615	−	1.19615i	0.0936899	−	0.0936899i	0.752398	+	0.658708i	$0.228897\pi$
$164$	5.65685			0.441726
$165$		0			0
$166$	−29.8564			−2.31731
$167$	−5.55532	+	5.55532i	−0.429883	+	0.429883i	−0.888589	−	0.458705i	$-0.848313\pi$
$167$	−5.55532	+	5.55532i	−0.429883	+	0.429883i	0.458705	+	0.888589i	$0.348313\pi$
$168$		0			0
$169$		−	1.92820i		−	0.148323i
$170$	−1.37705	−	1.55291i	−0.105615	−	0.119103i
$171$		0			0
$172$	−4.19615	−	4.19615i	−0.319954	−	0.319954i
$173$	−3.20736	−	3.20736i	−0.243851	−	0.243851i	0.574590	−	0.818441i	$-0.305162\pi$
$173$	−3.20736	−	3.20736i	−0.243851	−	0.243851i	−0.818441	+	0.574590i	$0.805162\pi$
$174$		0			0
$175$	3.52628	−	2.76795i	0.266562	−	0.209237i
$176$			23.1822i			1.74743i
$177$		0			0
$178$	−8.39230	+	8.39230i	−0.629030	+	0.629030i
$179$	19.3185			1.44393			0.721967	−	0.691928i	$-0.243238\pi$
$179$	19.3185			1.44393			0.721967	+	0.691928i	$0.243238\pi$
$180$		0			0
$181$	−2.39230			−0.177819			−0.0889093	−	0.996040i	$-0.528338\pi$
$181$	−2.39230			−0.177819			−0.0889093	+	0.996040i	$0.528338\pi$
$182$	−4.89898	+	4.89898i	−0.363137	+	0.363137i
$183$		0			0
$184$		0			0
$185$	10.9348	+	0.656339i	0.803940	+	0.0482550i
$186$		0			0
$187$	−1.90192	−	1.90192i	−0.139082	−	0.139082i
$188$	0.378937	+	0.378937i	0.0276368	+	0.0276368i
$189$		0			0
$190$	4.46410	+	0.267949i	0.323860	+	0.0194391i
$191$			9.65926i			0.698919i	0.936951	+	0.349460i	$0.113635\pi$
$191$			9.65926i			0.698919i	−0.936951	+	0.349460i	$0.886365\pi$
$192$		0			0
$193$	−4.53590	+	4.53590i	−0.326501	+	0.326501i	−0.851254	−	0.524753i	$-0.824158\pi$
$193$	−4.53590	+	4.53590i	−0.326501	+	0.326501i	0.524753	+	0.851254i	$0.324158\pi$
$194$	32.9802			2.36784
$195$		0			0
$196$	−12.3923			−0.885165
$197$	9.79796	−	9.79796i	0.698076	−	0.698076i	−0.265920	−	0.963995i	$-0.585676\pi$
$197$	9.79796	−	9.79796i	0.698076	−	0.698076i	0.963995	+	0.265920i	$0.0856756\pi$
$198$		0			0
$199$			6.26795i			0.444323i	0.975010	+	0.222162i	$0.0713112\pi$
$199$			6.26795i			0.444323i	−0.975010	+	0.222162i	$0.928689\pi$
$200$		0			0
$201$		0			0
$202$	−14.7846	−	14.7846i	−1.04024	−	1.04024i
$203$	3.76217	+	3.76217i	0.264052	+	0.264052i
$204$		0			0
$205$	−4.19615	−	4.73205i	−0.293072	−	0.330501i
$206$		−	34.4959i		−	2.40345i
$207$		0			0
$208$	−10.9282	+	10.9282i	−0.757735	+	0.757735i
$209$	5.79555			0.400887
$210$		0			0
$211$	21.8564			1.50466			0.752329	−	0.658788i	$-0.228931\pi$
$211$	21.8564			1.50466			0.752329	+	0.658788i	$0.228931\pi$
$212$	8.48528	−	8.48528i	0.582772	−	0.582772i
$213$		0			0
$214$			14.9282i			1.02047i
$215$	−0.397520	+	6.62278i	−0.0271106	+	0.451670i
$216$		0			0
$217$	−4.73205	−	4.73205i	−0.321233	−	0.321233i
$218$	−17.5254	−	17.5254i	−1.18697	−	1.18697i
$219$		0			0
$220$	−19.3923	+	17.1962i	−1.30743	+	1.15936i
$221$		−	1.79315i		−	0.120620i
$222$		0			0
$223$	8.92820	−	8.92820i	0.597877	−	0.597877i	−0.341870	−	0.939747i	$-0.611060\pi$
$223$	8.92820	−	8.92820i	0.597877	−	0.597877i	0.939747	+	0.341870i	$0.111060\pi$
$224$	7.17260			0.479240
$225$		0			0
$226$	−17.0718			−1.13560
$227$	17.1464	−	17.1464i	1.13805	−	1.13805i	0.149249	−	0.988800i	$-0.452314\pi$
$227$	17.1464	−	17.1464i	1.13805	−	1.13805i	0.988800	−	0.149249i	$-0.0476855\pi$
$228$		0			0
$229$		−	4.66025i		−	0.307958i	−0.988074	−	0.153979i	$-0.950791\pi$
$229$		−	4.66025i		−	0.307958i	0.988074	−	0.153979i	$-0.0492089\pi$
$230$	−11.5911	+	10.2784i	−0.764295	+	0.677740i
$231$		0			0
$232$		0			0
$233$	−3.01790	−	3.01790i	−0.197709	−	0.197709i	0.601308	−	0.799017i	$-0.294646\pi$
$233$	−3.01790	−	3.01790i	−0.197709	−	0.197709i	−0.799017	+	0.601308i	$0.794646\pi$
$234$		0			0
$235$	0.0358984	−	0.598076i	0.00234175	−	0.0390142i
$236$		−	7.17260i		−	0.466897i
$237$		0			0
$238$	−0.588457	+	0.588457i	−0.0381440	+	0.0381440i
$239$	−23.6999			−1.53302			−0.766508	−	0.642235i	$-0.778008\pi$
$239$	−23.6999			−1.53302			−0.766508	+	0.642235i	$0.778008\pi$
$240$		0			0
$241$	7.60770			0.490055			0.245027	−	0.969516i	$-0.421203\pi$
$241$	7.60770			0.490055			0.245027	+	0.969516i	$0.421203\pi$
$242$	−31.9449	+	31.9449i	−2.05350	+	2.05350i
$243$		0			0
$244$		−	29.7128i		−	1.90217i
$245$	9.19239	+	10.3664i	0.587280	+	0.662283i
$246$		0			0
$247$	2.73205	+	2.73205i	0.173836	+	0.173836i
$248$		0			0
$249$		0			0
$250$	22.0000	+	4.00000i	1.39140	+	0.252982i
$251$		−	17.4882i		−	1.10385i	−0.833895	−	0.551923i	$-0.813894\pi$
$251$		−	17.4882i		−	1.10385i	0.833895	−	0.551923i	$-0.186106\pi$
$252$		0			0
$253$	−14.1962	+	14.1962i	−0.892504	+	0.892504i
$254$	−13.3843			−0.839803
$255$		0			0
$256$	16.0000			1.00000
$257$	15.7322	−	15.7322i	0.981349	−	0.981349i	−0.0184806	−	0.999829i	$-0.505883\pi$
$257$	15.7322	−	15.7322i	0.981349	−	0.981349i	0.999829	+	0.0184806i	$0.00588290\pi$
$258$		0			0
$259$		−	4.39230i		−	0.272925i
$260$	−17.2480	−	1.03528i	−1.06967	−	0.0642051i
$261$		0			0
$262$	7.80385	+	7.80385i	0.482123	+	0.482123i
$263$	11.5403	+	11.5403i	0.711608	+	0.711608i	0.966872	−	0.255264i	$-0.0821622\pi$
$263$	11.5403	+	11.5403i	0.711608	+	0.711608i	−0.255264	+	0.966872i	$0.582162\pi$
$264$		0			0
$265$	−13.3923	−	0.803848i	−0.822683	−	0.0493800i
$266$		−	1.79315i		−	0.109945i
$267$		0			0
$268$	5.07180	−	5.07180i	0.309809	−	0.309809i
$269$	8.00481			0.488062			0.244031	−	0.969767i	$-0.421530\pi$
$269$	8.00481			0.488062			0.244031	+	0.969767i	$0.421530\pi$
$270$		0			0
$271$	12.5359			0.761502			0.380751	−	0.924678i	$-0.375666\pi$
$271$	12.5359			0.761502			0.380751	+	0.924678i	$0.375666\pi$
$272$	−1.31268	+	1.31268i	−0.0795928	+	0.0795928i
$273$		0			0
$274$			16.9282i			1.02267i
$275$	28.7697	+	3.46618i	1.73488	+	0.209019i
$276$		0			0
$277$	−17.8301	−	17.8301i	−1.07131	−	1.07131i	−0.997254	−	0.0740543i	$-0.976406\pi$
$277$	−17.8301	−	17.8301i	−1.07131	−	1.07131i	−0.0740543	−	0.997254i	$-0.523594\pi$
$278$	8.86422	+	8.86422i	0.531641	+	0.531641i
$279$		0			0
$280$		0			0
$281$			11.5911i			0.691468i	0.938333	+	0.345734i	$0.112370\pi$
$281$			11.5911i			0.691468i	−0.938333	+	0.345734i	$0.887630\pi$
$282$		0			0
$283$	2.36603	−	2.36603i	0.140646	−	0.140646i	−0.633278	−	0.773924i	$-0.718291\pi$
$283$	2.36603	−	2.36603i	0.140646	−	0.140646i	0.773924	+	0.633278i	$0.218291\pi$
$284$	21.1117			1.25275
$285$		0			0
$286$	−44.7846			−2.64817
$287$	−1.79315	+	1.79315i	−0.105846	+	0.105846i
$288$		0			0
$289$			16.7846i			0.987330i
$290$	−1.59008	+	26.4911i	−0.0933727	+	1.55561i
$291$		0			0
$292$	18.1962	+	18.1962i	1.06485	+	1.06485i
$293$	−15.1774	−	15.1774i	−0.886674	−	0.886674i	0.107528	−	0.994202i	$-0.465706\pi$
$293$	−15.1774	−	15.1774i	−0.886674	−	0.886674i	−0.994202	+	0.107528i	$0.965706\pi$
$294$		0			0
$295$	−6.00000	+	5.32051i	−0.349334	+	0.309772i
$296$		0			0
$297$		0			0
$298$	24.4449	−	24.4449i	1.41605	−	1.41605i
$299$	−13.3843			−0.774032
$300$		0			0
$301$	2.66025			0.153334
$302$	21.1117	−	21.1117i	1.21484	−	1.21484i
$303$		0			0
$304$		−	4.00000i		−	0.229416i
$305$	−24.8553	+	22.0404i	−1.42321	+	1.26203i
$306$		0			0
$307$	2.39230	+	2.39230i	0.136536	+	0.136536i	0.772072	−	0.635536i	$-0.219221\pi$
$307$	2.39230	+	2.39230i	0.136536	+	0.136536i	−0.635536	+	0.772072i	$0.719221\pi$
$308$	7.34847	+	7.34847i	0.418718	+	0.418718i
$309$		0			0
$310$	2.00000	−	33.3205i	0.113592	−	1.89248i
$311$		−	2.58819i		−	0.146763i	−0.997304	−	0.0733814i	$-0.976621\pi$
$311$		−	2.58819i		−	0.146763i	0.997304	−	0.0733814i	$-0.0233790\pi$
$312$		0			0
$313$	−12.3205	+	12.3205i	−0.696396	+	0.696396i	−0.963631	−	0.267235i	$-0.913890\pi$
$313$	−12.3205	+	12.3205i	−0.696396	+	0.696396i	0.267235	+	0.963631i	$0.413890\pi$
$314$	−39.3949			−2.22318
$315$		0			0
$316$	−13.0718			−0.735346
$317$	12.3490	−	12.3490i	0.693588	−	0.693588i	−0.269431	−	0.963020i	$-0.586836\pi$
$317$	12.3490	−	12.3490i	0.693588	−	0.693588i	0.963020	+	0.269431i	$0.0868358\pi$
$318$		0			0
$319$			34.3923i			1.92560i
$320$	11.8685	+	13.3843i	0.663470	+	0.748203i
$321$		0			0
$322$	4.39230	+	4.39230i	0.244774	+	0.244774i
$323$	0.328169	+	0.328169i	0.0182598	+	0.0182598i
$324$		0			0
$325$	11.9282	+	15.1962i	0.661658	+	0.842931i
$326$		−	3.38323i		−	0.187380i
$327$		0			0
$328$		0			0
$329$	−0.240237			−0.0132447
$330$		0			0
$331$	29.8564			1.64106			0.820528	−	0.571606i	$-0.193679\pi$
$331$	29.8564			1.64106			0.820528	+	0.571606i	$0.193679\pi$
$332$	−21.1117	+	21.1117i	−1.15865	+	1.15865i
$333$		0			0
$334$			15.7128i			0.859767i
$335$	−8.00481	−	0.480473i	−0.437349	−	0.0262511i
$336$		0			0
$337$	−13.6603	−	13.6603i	−0.744121	−	0.744121i	0.229247	−	0.973368i	$-0.426374\pi$
$337$	−13.6603	−	13.6603i	−0.744121	−	0.744121i	−0.973368	+	0.229247i	$0.926374\pi$
$338$	−2.72689	−	2.72689i	−0.148323	−	0.148323i
$339$		0			0
$340$	−2.07180	−	0.124356i	−0.112359	−	0.00674413i
$341$		−	43.2586i		−	2.34259i
$342$		0			0
$343$	8.36603	−	8.36603i	0.451723	−	0.451723i
$344$		0			0
$345$		0			0
$346$	−9.07180			−0.487703
$347$	−19.9241	+	19.9241i	−1.06958	+	1.06958i	−0.0721902	+	0.997391i	$0.522999\pi$
$347$	−19.9241	+	19.9241i	−1.06958	+	1.06958i	−0.997391	+	0.0721902i	$0.977001\pi$
$348$		0			0
$349$			28.6603i			1.53415i	0.641558	+	0.767074i	$0.278288\pi$
$349$			28.6603i			1.53415i	−0.641558	+	0.767074i	$0.721712\pi$
$350$	1.07244	−	8.90138i	0.0573244	−	0.475799i
$351$		0			0
$352$	32.7846	+	32.7846i	1.74743	+	1.74743i
$353$	−6.96953	−	6.96953i	−0.370951	−	0.370951i	0.496873	−	0.867823i	$-0.334482\pi$
$353$	−6.96953	−	6.96953i	−0.370951	−	0.370951i	−0.867823	+	0.496873i	$0.834482\pi$
$354$		0			0
$355$	−15.6603	−	17.6603i	−0.831160	−	0.937309i
$356$			11.8685i			0.629030i
$357$		0			0
$358$	27.3205	−	27.3205i	1.44393	−	1.44393i
$359$	−1.93185			−0.101959			−0.0509796	−	0.998700i	$-0.516234\pi$
$359$	−1.93185			−0.101959			−0.0509796	+	0.998700i	$0.516234\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	−3.38323	+	3.38323i	−0.177819	+	0.177819i
$363$		0			0
$364$			6.92820i			0.363137i
$365$	1.72380	−	28.7190i	0.0902278	−	1.50322i
$366$		0			0
$367$	−10.2679	−	10.2679i	−0.535983	−	0.535983i	0.386364	−	0.922346i	$-0.373731\pi$
$367$	−10.2679	−	10.2679i	−0.535983	−	0.535983i	−0.922346	+	0.386364i	$0.873731\pi$
$368$	9.79796	+	9.79796i	0.510754	+	0.510754i
$369$		0			0
$370$	16.3923	−	14.5359i	0.852195	−	0.755685i
$371$			5.37945i			0.279287i
$372$		0			0
$373$	3.46410	−	3.46410i	0.179364	−	0.179364i	−0.611714	−	0.791079i	$-0.709520\pi$
$373$	3.46410	−	3.46410i	0.179364	−	0.179364i	0.791079	+	0.611714i	$0.209520\pi$
$374$	−5.37945			−0.278165
$375$		0			0
$376$		0			0
$377$	−16.2127	+	16.2127i	−0.834996	+	0.834996i
$378$		0			0
$379$		−	7.07180i		−	0.363254i	−0.983368	−	0.181627i	$-0.941864\pi$
$379$		−	7.07180i		−	0.363254i	0.983368	−	0.181627i	$-0.0581363\pi$
$380$	3.34607	−	2.96713i	0.171650	−	0.152210i
$381$		0			0
$382$	13.6603	+	13.6603i	0.698919	+	0.698919i
$383$	5.55532	+	5.55532i	0.283864	+	0.283864i	0.834648	−	0.550784i	$-0.185671\pi$
$383$	5.55532	+	5.55532i	0.283864	+	0.283864i	−0.550784	+	0.834648i	$0.685671\pi$
$384$		0			0
$385$	0.696152	−	11.5981i	0.0354792	−	0.591093i
$386$			12.8295i			0.653002i
$387$		0			0
$388$	23.3205	−	23.3205i	1.18392	−	1.18392i
$389$	1.17398			0.0595230			0.0297615	−	0.999557i	$-0.490525\pi$
$389$	1.17398			0.0595230			0.0297615	+	0.999557i	$0.490525\pi$
$390$		0			0
$391$	−1.60770			−0.0813046
$392$		0			0
$393$		0			0
$394$		−	27.7128i		−	1.39615i
$395$	9.69642	+	10.9348i	0.487880	+	0.550188i
$396$		0			0
$397$	−6.22243	−	6.22243i	−0.312295	−	0.312295i	0.533503	−	0.845798i	$-0.320875\pi$
$397$	−6.22243	−	6.22243i	−0.312295	−	0.312295i	−0.845798	+	0.533503i	$0.820875\pi$
$398$	8.86422	+	8.86422i	0.444323	+	0.444323i
$399$		0			0
$400$	2.39230	−	19.8564i	0.119615	−	0.992820i
$401$		−	9.24316i		−	0.461581i	−0.973003	−	0.230791i	$-0.925869\pi$
$401$		−	9.24316i		−	0.461581i	0.973003	−	0.230791i	$-0.0741312\pi$
$402$		0			0
$403$	20.3923	−	20.3923i	1.01581	−	1.01581i
$404$	−20.9086			−1.04024
$405$		0			0
$406$	10.6410			0.528105
$407$	20.0764	−	20.0764i	0.995150	−	0.995150i
$408$		0			0
$409$			15.8564i			0.784049i	0.919955	+	0.392024i	$0.128225\pi$
$409$			15.8564i			0.784049i	−0.919955	+	0.392024i	$0.871775\pi$
$410$	−12.6264	−	0.757875i	−0.623573	−	0.0374288i
$411$		0			0
$412$	−24.3923	−	24.3923i	−1.20172	−	1.20172i
$413$	2.27362	+	2.27362i	0.111878	+	0.111878i
$414$		0			0
$415$	33.3205	+	2.00000i	1.63564	+	0.0981761i
$416$			30.9096i			1.51547i
$417$		0			0
$418$	8.19615	−	8.19615i	0.400887	−	0.400887i
$419$	15.2789			0.746425			0.373213	−	0.927746i	$-0.378256\pi$
$419$	15.2789			0.746425			0.373213	+	0.927746i	$0.378256\pi$
$420$		0			0
$421$	30.3923			1.48123			0.740615	−	0.671929i	$-0.234534\pi$
$421$	30.3923			1.48123			0.740615	+	0.671929i	$0.234534\pi$
$422$	30.9096	−	30.9096i	1.50466	−	1.50466i
$423$		0			0
$424$		0			0
$425$	1.43280	+	1.82534i	0.0695008	+	0.0885418i
$426$		0			0
$427$	9.41858	+	9.41858i	0.455797	+	0.455797i
$428$	10.5558	+	10.5558i	0.510235	+	0.510235i
$429$		0			0
$430$	8.80385	+	9.92820i	0.424559	+	0.478780i
$431$			5.93426i			0.285843i	0.989734	+	0.142922i	$0.0456497\pi$
$431$			5.93426i			0.285843i	−0.989734	+	0.142922i	$0.954350\pi$
$432$		0			0
$433$	−1.26795	+	1.26795i	−0.0609337	+	0.0609337i	−0.736917	−	0.675983i	$-0.763719\pi$
$433$	−1.26795	+	1.26795i	−0.0609337	+	0.0609337i	0.675983	+	0.736917i	$0.263719\pi$
$434$	−13.3843			−0.642465
$435$		0			0
$436$	−24.7846			−1.18697
$437$	2.44949	−	2.44949i	0.117175	−	0.117175i
$438$		0			0
$439$		−	4.14359i		−	0.197763i	−0.995099	−	0.0988815i	$-0.968474\pi$
$439$		−	4.14359i		−	0.197763i	0.995099	−	0.0988815i	$-0.0315265\pi$
$440$		0			0
$441$		0			0
$442$	−2.53590	−	2.53590i	−0.120620	−	0.120620i
$443$	−19.9885	−	19.9885i	−0.949680	−	0.949680i	0.0491129	−	0.998793i	$-0.484361\pi$
$443$	−19.9885	−	19.9885i	−0.949680	−	0.949680i	−0.998793	+	0.0491129i	$0.984361\pi$
$444$		0			0
$445$	9.92820	−	8.80385i	0.470642	−	0.417342i
$446$		−	25.2528i		−	1.19575i
$447$		0			0
$448$	5.07180	−	5.07180i	0.239620	−	0.239620i
$449$	−16.2127			−0.765124			−0.382562	−	0.923930i	$-0.624958\pi$
$449$	−16.2127			−0.765124			−0.382562	+	0.923930i	$0.624958\pi$
$450$		0			0
$451$	−16.3923			−0.771883
$452$	−12.0716	+	12.0716i	−0.567800	+	0.567800i
$453$		0			0
$454$		−	48.4974i		−	2.27610i
$455$	5.79555	−	5.13922i	0.271700	−	0.240930i
$456$		0			0
$457$	−19.0263	−	19.0263i	−0.890012	−	0.890012i	0.104512	−	0.994524i	$-0.466672\pi$
$457$	−19.0263	−	19.0263i	−0.890012	−	0.890012i	−0.994524	+	0.104512i	$0.966672\pi$
$458$	−6.59059	−	6.59059i	−0.307958	−	0.307958i
$459$		0			0
$460$	−0.928203	+	15.4641i	−0.0432777	+	0.721017i
$461$			34.7362i			1.61782i	0.587929	+	0.808912i	$0.299943\pi$
$461$			34.7362i			1.61782i	−0.587929	+	0.808912i	$0.700057\pi$
$462$		0			0
$463$	29.0263	−	29.0263i	1.34897	−	1.34897i	0.462179	−	0.886787i	$-0.347068\pi$
$463$	29.0263	−	29.0263i	1.34897	−	1.34897i	0.886787	−	0.462179i	$-0.152932\pi$
$464$	23.7370			1.10196
$465$		0			0
$466$	−8.53590			−0.395418
$467$	−0.568406	+	0.568406i	−0.0263027	+	0.0263027i	−0.720136	−	0.693833i	$-0.755921\pi$
$467$	−0.568406	+	0.568406i	−0.0263027	+	0.0263027i	0.693833	+	0.720136i	$0.255921\pi$
$468$		0			0
$469$			3.21539i			0.148473i
$470$	−0.795040	−	0.896575i	−0.0366724	−	0.0413559i
$471$		0			0
$472$		0			0
$473$	12.1595	+	12.1595i	0.559095	+	0.559095i
$474$		0			0
$475$	−4.96410	−	0.598076i	−0.227769	−	0.0274416i
$476$			0.832204i			0.0381440i
$477$		0			0
$478$	−33.5167	+	33.5167i	−1.53302	+	1.53302i
$479$	−38.4612			−1.75734			−0.878668	−	0.477434i	$-0.841567\pi$
$479$	−38.4612			−1.75734			−0.878668	+	0.477434i	$0.841567\pi$
$480$		0			0
$481$	18.9282			0.863052
$482$	10.7589	−	10.7589i	0.490055	−	0.490055i
$483$		0			0
$484$			45.1769i			2.05350i
$485$	−36.8067	−	2.20925i	−1.67131	−	0.100317i
$486$		0			0
$487$	−13.0718	−	13.0718i	−0.592340	−	0.592340i	0.345923	−	0.938263i	$-0.387566\pi$
$487$	−13.0718	−	13.0718i	−0.592340	−	0.592340i	−0.938263	+	0.345923i	$0.887566\pi$
$488$		0			0
$489$		0			0
$490$	27.6603	+	1.66025i	1.24956	+	0.0750026i
$491$		−	13.2084i		−	0.596087i	−0.954552	−	0.298043i	$-0.903666\pi$
$491$		−	13.2084i		−	0.596087i	0.954552	−	0.298043i	$-0.0963340\pi$
$492$		0			0
$493$	−1.94744	+	1.94744i	−0.0877083	+	0.0877083i
$494$	7.72741			0.347672
$495$		0			0
$496$	−29.8564			−1.34059
$497$	−6.69213	+	6.69213i	−0.300183	+	0.300183i
$498$		0			0
$499$			38.2679i			1.71311i	0.516057	+	0.856554i	$0.327399\pi$
$499$			38.2679i			1.71311i	−0.516057	+	0.856554i	$0.672601\pi$
$500$	18.3848	−	12.7279i	0.822192	−	0.569210i
$501$		0			0
$502$	−24.7321	−	24.7321i	−1.10385	−	1.10385i
$503$	7.72741	+	7.72741i	0.344548	+	0.344548i	0.858074	−	0.513526i	$-0.171661\pi$
$503$	7.72741	+	7.72741i	0.344548	+	0.344548i	−0.513526	+	0.858074i	$0.671661\pi$
$504$		0			0
$505$	15.5096	+	17.4904i	0.690169	+	0.778312i
$506$			40.1528i			1.78501i
$507$		0			0
$508$	−9.46410	+	9.46410i	−0.419902	+	0.419902i
$509$	−25.7332			−1.14061			−0.570303	−	0.821434i	$-0.693174\pi$
$509$	−25.7332			−1.14061			−0.570303	+	0.821434i	$0.693174\pi$
$510$		0			0
$511$	−11.5359			−0.510318
$512$	22.6274	−	22.6274i	1.00000	−	1.00000i
$513$		0			0
$514$		−	44.4974i		−	1.96270i
$515$	−2.31079	+	38.4983i	−0.101826	+	1.69644i
$516$		0			0
$517$	−1.09808	−	1.09808i	−0.0482933	−	0.0482933i
$518$	−6.21166	−	6.21166i	−0.272925	−	0.272925i
$519$		0			0
$520$		0			0
$521$		−	5.65685i		−	0.247831i	−0.992293	−	0.123916i	$-0.960455\pi$
$521$		−	5.65685i		−	0.247831i	0.992293	−	0.123916i	$-0.0395452\pi$
$522$		0			0
$523$	8.33975	−	8.33975i	0.364672	−	0.364672i	−0.500858	−	0.865530i	$-0.666982\pi$
$523$	8.33975	−	8.33975i	0.364672	−	0.364672i	0.865530	+	0.500858i	$0.166982\pi$
$524$	11.0363			0.482123
$525$		0			0
$526$	32.6410			1.42322
$527$	2.44949	−	2.44949i	0.106701	−	0.106701i
$528$		0			0
$529$		−	11.0000i		−	0.478261i
$530$	−20.0764	+	17.8028i	−0.872063	+	0.773303i
$531$		0			0
$532$	−1.26795	−	1.26795i	−0.0549726	−	0.0549726i
$533$	−7.72741	−	7.72741i	−0.334711	−	0.334711i
$534$		0			0
$535$	1.00000	−	16.6603i	0.0432338	−	0.720286i
$536$		0			0
$537$		0			0
$538$	11.3205	−	11.3205i	0.488062	−	0.488062i
$539$	35.9101			1.54676
$540$		0			0
$541$	18.8038			0.808441			0.404220	−	0.914662i	$-0.367543\pi$
$541$	18.8038			0.808441			0.404220	+	0.914662i	$0.367543\pi$
$542$	17.7284	−	17.7284i	0.761502	−	0.761502i
$543$		0			0
$544$			3.71281i			0.159186i
$545$	18.3848	+	20.7327i	0.787517	+	0.888093i
$546$		0			0
$547$	16.0526	+	16.0526i	0.686358	+	0.686358i	0.961425	−	0.275067i	$-0.0887001\pi$
$547$	16.0526	+	16.0526i	0.686358	+	0.686358i	−0.275067	+	0.961425i	$0.588700\pi$
$548$	11.9700	+	11.9700i	0.511335	+	0.511335i
$549$		0			0
$550$	45.5885	−	35.7846i	1.94390	−	1.52586i
$551$		−	5.93426i		−	0.252808i
$552$		0			0
$553$	4.14359	−	4.14359i	0.176204	−	0.176204i
$554$	−50.4312			−2.14262
$555$		0			0
$556$	12.5359			0.531641
$557$	27.3369	−	27.3369i	1.15830	−	1.15830i	0.173462	−	0.984841i	$-0.444505\pi$
$557$	27.3369	−	27.3369i	1.15830	−	1.15830i	0.984841	−	0.173462i	$-0.0554955\pi$
$558$		0			0
$559$			11.4641i			0.484880i
$560$	−8.00481	−	0.480473i	−0.338265	−	0.0203037i
$561$		0			0
$562$	16.3923	+	16.3923i	0.691468	+	0.691468i
$563$	28.2843	+	28.2843i	1.19204	+	1.19204i	0.976494	+	0.215546i	$0.0691532\pi$
$563$	28.2843	+	28.2843i	1.19204	+	1.19204i	0.215546	+	0.976494i	$0.430847\pi$
$564$		0			0
$565$	19.0526	+	1.14359i	0.801547	+	0.0481113i
$566$		−	6.69213i		−	0.281291i
$567$		0			0
$568$		0			0
$569$	−41.9459			−1.75847			−0.879233	−	0.476393i	$-0.841944\pi$
$569$	−41.9459			−1.75847			−0.879233	+	0.476393i	$0.841944\pi$
$570$		0			0
$571$	−21.6077			−0.904254			−0.452127	−	0.891954i	$-0.649335\pi$
$571$	−21.6077			−0.904254			−0.452127	+	0.891954i	$0.649335\pi$
$572$	−31.6675	+	31.6675i	−1.32408	+	1.32408i
$573$		0			0
$574$			5.07180i			0.211693i
$575$	13.6245	−	10.6945i	0.568181	−	0.445993i
$576$		0			0
$577$	6.16987	+	6.16987i	0.256855	+	0.256855i	0.823774	−	0.566919i	$-0.191865\pi$
$577$	6.16987	+	6.16987i	0.256855	+	0.256855i	−0.566919	+	0.823774i	$0.691865\pi$
$578$	23.7370	+	23.7370i	0.987330	+	0.987330i
$579$		0			0
$580$	17.6077	+	19.8564i	0.731120	+	0.824492i
$581$		−	13.3843i		−	0.555273i
$582$		0			0
$583$	−24.5885	+	24.5885i	−1.01835	+	1.01835i
$584$		0			0
$585$		0			0
$586$	−42.9282			−1.77335
$587$	−21.8559	+	21.8559i	−0.902091	+	0.902091i	−0.995617	−	0.0935257i	$-0.970186\pi$
$587$	−21.8559	+	21.8559i	−0.902091	+	0.902091i	0.0935257	+	0.995617i	$0.470186\pi$
$588$		0			0
$589$			7.46410i			0.307553i
$590$	−0.960947	+	16.0096i	−0.0395615	+	0.659105i
$591$		0			0
$592$	−13.8564	−	13.8564i	−0.569495	−	0.569495i
$593$	−14.7985	−	14.7985i	−0.607701	−	0.607701i	0.334644	−	0.942345i	$-0.391384\pi$
$593$	−14.7985	−	14.7985i	−0.607701	−	0.607701i	−0.942345	+	0.334644i	$0.891384\pi$
$594$		0			0
$595$	0.696152	−	0.617314i	0.0285395	−	0.0253074i
$596$		−	34.5703i		−	1.41605i
$597$		0			0
$598$	−18.9282	+	18.9282i	−0.774032	+	0.774032i
$599$	33.1833			1.35583			0.677915	−	0.735140i	$-0.262884\pi$
$599$	33.1833			1.35583			0.677915	+	0.735140i	$0.262884\pi$
$600$		0			0
$601$	16.0000			0.652654			0.326327	−	0.945257i	$-0.394189\pi$
$601$	16.0000			0.652654			0.326327	+	0.945257i	$0.394189\pi$
$602$	3.76217	−	3.76217i	0.153334	−	0.153334i
$603$		0			0
$604$		−	29.8564i		−	1.21484i
$605$	37.7912	−	33.5114i	1.53643	−	1.36243i
$606$		0			0
$607$	33.5167	+	33.5167i	1.36040	+	1.36040i	0.873405	+	0.486994i	$0.161907\pi$
$607$	33.5167	+	33.5167i	1.36040	+	1.36040i	0.486994	+	0.873405i	$0.338093\pi$
$608$	−5.65685	−	5.65685i	−0.229416	−	0.229416i
$609$		0			0
$610$	−3.98076	+	66.3205i	−0.161176	+	2.68524i
$611$		−	1.03528i		−	0.0418828i
$612$		0			0
$613$	−30.1506	+	30.1506i	−1.21777	+	1.21777i	−0.249362	+	0.968410i	$0.580221\pi$
$613$	−30.1506	+	30.1506i	−1.21777	+	1.21777i	−0.968410	+	0.249362i	$0.919779\pi$
$614$	6.76646			0.273072
$615$		0			0
$616$		0			0
$617$	−4.01601	+	4.01601i	−0.161678	+	0.161678i	−0.783310	−	0.621631i	$-0.786470\pi$
$617$	−4.01601	+	4.01601i	−0.161678	+	0.161678i	0.621631	+	0.783310i	$0.286470\pi$
$618$		0			0
$619$		−	12.2487i		−	0.492317i	−0.969230	−	0.246159i	$-0.920832\pi$
$619$		−	12.2487i		−	0.492317i	0.969230	−	0.246159i	$-0.0791684\pi$
$620$	−22.1469	−	24.9754i	−0.889443	−	1.00304i
$621$		0			0
$622$	−3.66025	−	3.66025i	−0.146763	−	0.146763i
$623$	−3.76217	−	3.76217i	−0.150728	−	0.150728i
$624$		0			0
$625$	−24.2846	−	5.93782i	−0.971384	−	0.237513i
$626$			34.8477i			1.39279i
$627$		0			0
$628$	−27.8564	+	27.8564i	−1.11159	+	1.11159i
$629$	2.27362			0.0906553
$630$		0			0
$631$	7.00000			0.278666			0.139333	−	0.990246i	$-0.455504\pi$
$631$	7.00000			0.278666			0.139333	+	0.990246i	$0.455504\pi$
$632$		0			0
$633$		0			0
$634$		−	34.9282i		−	1.38718i
$635$	14.9372	+	0.896575i	0.592764	+	0.0355795i
$636$		0			0
$637$	16.9282	+	16.9282i	0.670720	+	0.670720i
$638$	48.6381	+	48.6381i	1.92560	+	1.92560i
$639$		0			0
$640$		0			0
$641$		−	46.8449i		−	1.85026i	−0.379647	−	0.925131i	$-0.623955\pi$
$641$		−	46.8449i		−	1.85026i	0.379647	−	0.925131i	$-0.376045\pi$
$642$		0			0
$643$	−30.7583	+	30.7583i	−1.21299	+	1.21299i	−0.242952	+	0.970038i	$0.578116\pi$
$643$	−30.7583	+	30.7583i	−1.21299	+	1.21299i	−0.970038	+	0.242952i	$0.921884\pi$
$644$	6.21166			0.244774
$645$		0			0
$646$	0.928203			0.0365197
$647$	−7.50077	+	7.50077i	−0.294886	+	0.294886i	−0.839007	−	0.544121i	$-0.816863\pi$
$647$	−7.50077	+	7.50077i	−0.294886	+	0.294886i	0.544121	+	0.839007i	$0.316863\pi$
$648$		0			0
$649$			20.7846i			0.815867i
$650$	38.3596	+	4.62158i	1.50459	+	0.181273i
$651$		0			0
$652$	−2.39230	−	2.39230i	−0.0936899	−	0.0936899i
$653$	0.984508	+	0.984508i	0.0385268	+	0.0385268i	0.726108	−	0.687581i	$-0.241327\pi$
$653$	0.984508	+	0.984508i	0.0385268	+	0.0385268i	−0.687581	+	0.726108i	$0.741327\pi$
$654$		0			0
$655$	−8.18653	−	9.23205i	−0.319874	−	0.360726i
$656$			11.3137i			0.441726i
$657$		0			0
$658$	−0.339746	+	0.339746i	−0.0132447	+	0.0132447i
$659$	21.3891			0.833200			0.416600	−	0.909090i	$-0.363222\pi$
$659$	21.3891			0.833200			0.416600	+	0.909090i	$0.363222\pi$
$660$		0			0
$661$	−45.5692			−1.77244			−0.886219	−	0.463267i	$-0.846677\pi$
$661$	−45.5692			−1.77244			−0.886219	+	0.463267i	$0.846677\pi$
$662$	42.2233	−	42.2233i	1.64106	−	1.64106i
$663$		0			0
$664$		0			0
$665$	−0.120118	+	2.00120i	−0.00465799	+	0.0776033i
$666$		0			0
$667$	14.5359	+	14.5359i	0.562832	+	0.562832i
$668$	11.1106	+	11.1106i	0.429883	+	0.429883i
$669$		0			0
$670$	−12.0000	+	10.6410i	−0.463600	+	0.411098i
$671$			86.1011i			3.32390i
$672$		0			0
$673$	−6.92820	+	6.92820i	−0.267063	+	0.267063i	−0.827915	−	0.560853i	$-0.810473\pi$
$673$	−6.92820	+	6.92820i	−0.267063	+	0.267063i	0.560853	+	0.827915i	$0.310473\pi$
$674$	−38.6370			−1.48824
$675$		0			0
$676$	−3.85641			−0.148323
$677$	−12.2474	+	12.2474i	−0.470708	+	0.470708i	−0.902144	−	0.431436i	$-0.858007\pi$
$677$	−12.2474	+	12.2474i	−0.470708	+	0.470708i	0.431436	+	0.902144i	$0.358007\pi$
$678$		0			0
$679$			14.7846i			0.567381i
$680$		0			0
$681$		0			0
$682$	−61.1769	−	61.1769i	−2.34259	−	2.34259i
$683$	21.2132	+	21.2132i	0.811701	+	0.811701i	0.984889	−	0.173188i	$-0.0554069\pi$
$683$	21.2132	+	21.2132i	0.811701	+	0.811701i	−0.173188	+	0.984889i	$0.555407\pi$
$684$		0			0
$685$	1.13397	−	18.8923i	0.0433269	−	0.721838i
$686$		−	23.6627i		−	0.903446i
$687$		0			0
$688$	8.39230	−	8.39230i	0.319954	−	0.319954i
$689$	−23.1822			−0.883172
$690$		0			0
$691$	−14.5167			−0.552240			−0.276120	−	0.961123i	$-0.589049\pi$
$691$	−14.5167			−0.552240			−0.276120	+	0.961123i	$0.589049\pi$
$692$	−6.41473	+	6.41473i	−0.243851	+	0.243851i
$693$		0			0
$694$			56.3538i			2.13916i
$695$	−9.29890	−	10.4865i	−0.352728	−	0.397775i
$696$		0			0
$697$	−0.928203	−	0.928203i	−0.0351582	−	0.0351582i
$698$	40.5317	+	40.5317i	1.53415	+	1.53415i
$699$		0			0
$700$	−5.53590	−	7.05256i	−0.209237	−	0.266562i
$701$			6.11012i			0.230776i	0.993320	+	0.115388i	$0.0368112\pi$
$701$			6.11012i			0.230776i	−0.993320	+	0.115388i	$0.963189\pi$
$702$		0			0
$703$	−3.46410	+	3.46410i	−0.130651	+	0.130651i
$704$	46.3644			1.74743
$705$		0			0
$706$	−19.7128			−0.741902
$707$	6.62776	−	6.62776i	0.249263	−	0.249263i
$708$		0			0
$709$			2.14359i			0.0805043i	0.999190	+	0.0402522i	$0.0128161\pi$
$709$			2.14359i			0.0805043i	−0.999190	+	0.0402522i	$0.987184\pi$
$710$	−47.1223	−	2.82843i	−1.76847	−	0.106149i
$711$		0			0
$712$		0			0
$713$	−18.2832	−	18.2832i	−0.684713	−	0.684713i
$714$		0			0
$715$	49.9808	+	3.00000i	1.86917	+	0.112194i
$716$		−	38.6370i		−	1.44393i
$717$		0			0
$718$	−2.73205	+	2.73205i	−0.101959	+	0.101959i
$719$	37.5646			1.40092			0.700461	−	0.713690i	$-0.252978\pi$
$719$	37.5646			1.40092			0.700461	+	0.713690i	$0.252978\pi$
$720$		0			0
$721$	15.4641			0.575913
$722$	−1.41421	+	1.41421i	−0.0526316	+	0.0526316i
$723$		0			0
$724$			4.78461i			0.177819i
$725$	3.54914	−	29.4582i	0.131812	−	1.09405i
$726$		0			0
$727$	−23.9545	−	23.9545i	−0.888423	−	0.888423i	0.105949	−	0.994372i	$-0.466212\pi$
$727$	−23.9545	−	23.9545i	−0.888423	−	0.888423i	−0.994372	+	0.105949i	$0.966212\pi$
$728$		0			0
$729$		0			0
$730$	−38.1769	−	43.0526i	−1.41299	−	1.59345i
$731$			1.37705i			0.0509320i
$732$		0			0
$733$	−3.00000	+	3.00000i	−0.110808	+	0.110808i	−0.760337	−	0.649529i	$-0.774966\pi$
$733$	−3.00000	+	3.00000i	−0.110808	+	0.110808i	0.649529	+	0.760337i	$0.274966\pi$
$734$	−29.0421			−1.07197
$735$		0			0
$736$	27.7128			1.02151
$737$	−14.6969	+	14.6969i	−0.541369	+	0.541369i
$738$		0			0
$739$			37.7846i			1.38993i	0.719044	+	0.694965i	$0.244580\pi$
$739$			37.7846i			1.38993i	−0.719044	+	0.694965i	$0.755420\pi$
$740$	1.31268	−	21.8695i	0.0482550	−	0.803940i
$741$		0			0
$742$	7.60770	+	7.60770i	0.279287	+	0.279287i
$743$	5.93426	+	5.93426i	0.217707	+	0.217707i	0.807531	−	0.589825i	$-0.200803\pi$
$743$	5.93426	+	5.93426i	0.217707	+	0.217707i	−0.589825	+	0.807531i	$0.700803\pi$
$744$		0			0
$745$	−28.9186	+	25.6436i	−1.05949	+	0.939509i
$746$		−	9.79796i		−	0.358729i
$747$		0			0
$748$	−3.80385	+	3.80385i	−0.139082	+	0.139082i
$749$	−6.69213			−0.244525
$750$		0			0
$751$	36.1051			1.31749			0.658747	−	0.752364i	$-0.271087\pi$
$751$	36.1051			1.31749			0.658747	+	0.752364i	$0.271087\pi$
$752$	−0.757875	+	0.757875i	−0.0276368	+	0.0276368i
$753$		0			0
$754$			45.8564i			1.66999i
$755$	−24.9754	+	22.1469i	−0.908947	+	0.806010i
$756$		0			0
$757$	−17.5622	−	17.5622i	−0.638308	−	0.638308i	0.311830	−	0.950138i	$-0.399058\pi$
$757$	−17.5622	−	17.5622i	−0.638308	−	0.638308i	−0.950138	+	0.311830i	$0.899058\pi$
$758$	−10.0010	−	10.0010i	−0.363254	−	0.363254i
$759$		0			0
$760$		0			0
$761$			0.619174i			0.0224450i	0.999937	+	0.0112225i	$0.00357231\pi$
$761$			0.619174i			0.0224450i	−0.999937	+	0.0112225i	$0.996428\pi$
$762$		0			0
$763$	7.85641	−	7.85641i	0.284421	−	0.284421i
$764$	19.3185			0.698919
$765$		0			0
$766$	15.7128			0.567727
$767$	−9.79796	+	9.79796i	−0.353784	+	0.353784i
$768$		0			0
$769$			21.1962i			0.764353i	0.924089	+	0.382176i	$0.124825\pi$
$769$			21.1962i			0.764353i	−0.924089	+	0.382176i	$0.875175\pi$
$770$	−15.4176	−	17.3867i	−0.555613	−	0.626572i
$771$		0			0
$772$	9.07180	+	9.07180i	0.326501	+	0.326501i
$773$	−27.3233	−	27.3233i	−0.982752	−	0.982752i	0.0171021	−	0.999854i	$-0.494556\pi$
$773$	−27.3233	−	27.3233i	−0.982752	−	0.982752i	−0.999854	+	0.0171021i	$0.994556\pi$
$774$		0			0
$775$	−4.46410	+	37.0526i	−0.160355	+	1.33097i
$776$		0			0
$777$		0			0
$778$	1.66025	−	1.66025i	0.0595230	−	0.0595230i
$779$	2.82843			0.101339
$780$		0			0
$781$	−61.1769			−2.18908
$782$	−2.27362	+	2.27362i	−0.0813046	+	0.0813046i
$783$		0			0
$784$		−	24.7846i		−	0.885165i
$785$	43.9657	+	2.63896i	1.56920	+	0.0941885i
$786$		0			0
$787$	−2.53590	−	2.53590i	−0.0903950	−	0.0903950i	0.660463	−	0.750858i	$-0.270360\pi$
$787$	−2.53590	−	2.53590i	−0.0903950	−	0.0903950i	−0.750858	+	0.660463i	$0.770360\pi$
$788$	−19.5959	−	19.5959i	−0.698076	−	0.698076i
$789$		0			0
$790$	29.1769	+	1.75129i	1.03807	+	0.0623081i
$791$		−	7.65308i		−	0.272112i
$792$		0			0
$793$	−40.5885	+	40.5885i	−1.44134	+	1.44134i
$794$	−17.5997			−0.624590
$795$		0			0
$796$	12.5359			0.444323
$797$	−35.2538	+	35.2538i	−1.24875	+	1.24875i	−0.292483	+	0.956271i	$0.594482\pi$
$797$	−35.2538	+	35.2538i	−1.24875	+	1.24875i	−0.956271	+	0.292483i	$0.905518\pi$
$798$		0			0
$799$		−	0.124356i		−	0.00439939i
$800$	−24.6980	−	31.4644i	−0.873205	−	1.11244i
$801$		0			0
$802$	−13.0718	−	13.0718i	−0.461581	−	0.461581i
$803$	−52.7284	−	52.7284i	−1.86074	−	1.86074i
$804$		0			0
$805$	−4.60770	−	5.19615i	−0.162400	−	0.183140i
$806$		−	57.6781i		−	2.03163i
$807$		0			0
$808$		0			0
$809$	−41.3268			−1.45297			−0.726486	−	0.687182i	$-0.758848\pi$
$809$	−41.3268			−1.45297			−0.726486	+	0.687182i	$0.758848\pi$
$810$		0			0
$811$	12.1436			0.426419			0.213210	−	0.977006i	$-0.431608\pi$
$811$	12.1436			0.426419			0.213210	+	0.977006i	$0.431608\pi$
$812$	7.52433	−	7.52433i	0.264052	−	0.264052i
$813$		0			0
$814$		−	56.7846i		−	1.99030i
$815$	−0.226633	+	3.77577i	−0.00793862	+	0.132259i
$816$		0			0
$817$	−2.09808	−	2.09808i	−0.0734024	−	0.0734024i
$818$	22.4243	+	22.4243i	0.784049	+	0.784049i
$819$		0			0
$820$	−9.46410	+	8.39230i	−0.330501	+	0.293072i
$821$		−	32.3610i		−	1.12941i	−0.825294	−	0.564703i	$-0.808991\pi$
$821$		−	32.3610i		−	1.12941i	0.825294	−	0.564703i	$-0.191009\pi$
$822$		0			0
$823$	14.3660	−	14.3660i	0.500768	−	0.500768i	−0.410908	−	0.911677i	$-0.634788\pi$
$823$	14.3660	−	14.3660i	0.500768	−	0.500768i	0.911677	+	0.410908i	$0.134788\pi$
$824$		0			0
$825$		0			0
$826$	6.43078			0.223755
$827$	−39.1918	+	39.1918i	−1.36283	+	1.36283i	−0.492549	+	0.870285i	$0.663935\pi$
$827$	−39.1918	+	39.1918i	−1.36283	+	1.36283i	−0.870285	+	0.492549i	$0.836065\pi$
$828$		0			0
$829$		−	51.3205i		−	1.78243i	−0.453576	−	0.891217i	$-0.649852\pi$
$829$		−	51.3205i		−	1.78243i	0.453576	−	0.891217i	$-0.350148\pi$
$830$	49.9507	−	44.2939i	1.73382	−	1.53746i
$831$		0			0
$832$	21.8564	+	21.8564i	0.757735	+	0.757735i
$833$	2.03339	+	2.03339i	0.0704527	+	0.0704527i
$834$		0			0
$835$	1.05256	−	17.5359i	0.0364253	−	0.606855i
$836$		−	11.5911i		−	0.400887i
$837$		0			0
$838$	21.6077	−	21.6077i	0.746425	−	0.746425i
$839$	−26.4911			−0.914575			−0.457288	−	0.889319i	$-0.651179\pi$
$839$	−26.4911			−0.914575			−0.457288	+	0.889319i	$0.651179\pi$
$840$		0			0
$841$	6.21539			0.214324
$842$	42.9812	−	42.9812i	1.48123	−	1.48123i
$843$		0			0
$844$		−	43.7128i		−	1.50466i
$845$	2.86061	+	3.22595i	0.0984081	+	0.110976i
$846$		0			0
$847$	−14.3205	−	14.3205i	−0.492058	−	0.492058i
$848$	16.9706	+	16.9706i	0.582772	+	0.582772i
$849$		0			0
$850$	4.60770	+	0.555136i	0.158043	+	0.0190410i
$851$		−	16.9706i		−	0.581743i
$852$		0			0
$853$	30.7128	−	30.7128i	1.05159	−	1.05159i	0.0529917	−	0.998595i	$-0.483124\pi$
$853$	30.7128	−	30.7128i	1.05159	−	1.05159i	0.998595	−	0.0529917i	$-0.0168757\pi$
$854$	26.6398			0.911594
$855$		0			0
$856$		0			0
$857$	−9.52056	+	9.52056i	−0.325216	+	0.325216i	−0.850764	−	0.525548i	$-0.823860\pi$
$857$	−9.52056	+	9.52056i	−0.325216	+	0.325216i	0.525548	+	0.850764i	$0.323860\pi$
$858$		0			0
$859$		−	54.5692i		−	1.86188i	−0.365175	−	0.930939i	$-0.618991\pi$
$859$		−	54.5692i		−	1.86188i	0.365175	−	0.930939i	$-0.381009\pi$
$860$	13.2456	+	0.795040i	0.451670	+	0.0271106i
$861$		0			0
$862$	8.39230	+	8.39230i	0.285843	+	0.285843i
$863$	3.10583	+	3.10583i	0.105724	+	0.105724i	0.757990	−	0.652266i	$-0.226182\pi$
$863$	3.10583	+	3.10583i	0.105724	+	0.105724i	−0.652266	+	0.757990i	$0.726182\pi$
$864$		0			0
$865$	10.1244	+	0.607695i	0.344238	+	0.0206623i
$866$			3.58630i			0.121867i
$867$		0			0
$868$	−9.46410	+	9.46410i	−0.321233	+	0.321233i
$869$	37.8792			1.28496
$870$		0			0
$871$	−13.8564			−0.469506
$872$		0			0
$873$		0			0
$874$		−	6.92820i		−	0.234350i
$875$	−1.79315	+	9.86233i	−0.0606196	+	0.333408i
$876$		0			0
$877$	−20.7321	−	20.7321i	−0.700072	−	0.700072i	0.264354	−	0.964426i	$-0.414841\pi$
$877$	−20.7321	−	20.7321i	−0.700072	−	0.700072i	−0.964426	+	0.264354i	$0.914841\pi$
$878$	−5.85993	−	5.85993i	−0.197763	−	0.197763i
$879$		0			0
$880$	−34.3923	−	38.7846i	−1.15936	−	1.30743i
$881$			11.6283i			0.391767i	0.980627	+	0.195883i	$0.0627574\pi$
$881$			11.6283i			0.391767i	−0.980627	+	0.195883i	$0.937243\pi$
$882$		0			0
$883$	−26.3660	+	26.3660i	−0.887287	+	0.887287i	−0.994262	−	0.106974i	$-0.965884\pi$
$883$	−26.3660	+	26.3660i	−0.887287	+	0.887287i	0.106974	+	0.994262i	$0.465884\pi$
$884$	−3.58630			−0.120620
$885$		0			0
$886$	−56.5359			−1.89936
$887$	6.41473	−	6.41473i	0.215386	−	0.215386i	−0.591165	−	0.806551i	$-0.701332\pi$
$887$	6.41473	−	6.41473i	0.215386	−	0.215386i	0.806551	+	0.591165i	$0.201332\pi$
$888$		0			0
$889$		−	6.00000i		−	0.201234i
$890$	1.59008	−	26.4911i	0.0532996	−	0.887984i
$891$		0			0
$892$	−17.8564	−	17.8564i	−0.597877	−	0.597877i
$893$	0.189469	+	0.189469i	0.00634033	+	0.00634033i
$894$		0			0
$895$	−32.3205	+	28.6603i	−1.08036	+	0.958007i
$896$		0			0
$897$		0			0
$898$	−22.9282	+	22.9282i	−0.765124	+	0.765124i
$899$	−44.2939			−1.47728
$900$		0			0
$901$	−2.78461			−0.0927688
$902$	−23.1822	+	23.1822i	−0.771883	+	0.771883i
$903$		0			0
$904$		0			0
$905$	4.00240	−	3.54914i	0.133044	−	0.117977i
$906$		0			0
$907$	−23.6603	−	23.6603i	−0.785626	−	0.785626i	0.195148	−	0.980774i	$-0.437481\pi$
$907$	−23.6603	−	23.6603i	−0.785626	−	0.785626i	−0.980774	+	0.195148i	$0.937481\pi$
$908$	−34.2929	−	34.2929i	−1.13805	−	1.13805i
$909$		0			0
$910$	0.928203	−	15.4641i	0.0307696	−	0.512630i
$911$			13.3099i			0.440978i	0.975389	+	0.220489i	$0.0707653\pi$
$911$			13.3099i			0.440978i	−0.975389	+	0.220489i	$0.929235\pi$
$912$		0			0
$913$	61.1769	−	61.1769i	2.02466	−	2.02466i
$914$	−53.8144			−1.78002
$915$		0			0
$916$	−9.32051			−0.307958
$917$	−3.49837	+	3.49837i	−0.115526	+	0.115526i
$918$		0			0
$919$			11.7128i			0.386370i	0.981162	+	0.193185i	$0.0618818\pi$
$919$			11.7128i			0.386370i	−0.981162	+	0.193185i	$0.938118\pi$
$920$		0			0
$921$		0			0
$922$	49.1244	+	49.1244i	1.61782	+	1.61782i
$923$	−28.8391	−	28.8391i	−0.949250	−	0.949250i
$924$		0			0
$925$	−19.2679	+	15.1244i	−0.633526	+	0.497286i
$926$		−	82.0987i		−	2.69793i
$927$		0			0
$928$	33.5692	−	33.5692i	1.10196	−	1.10196i
$929$	−14.7985			−0.485522			−0.242761	−	0.970086i	$-0.578053\pi$
$929$	−14.7985			−0.485522			−0.242761	+	0.970086i	$0.578053\pi$
$930$		0			0
$931$	−6.19615			−0.203071
$932$	−6.03579	+	6.03579i	−0.197709	+	0.197709i
$933$		0			0
$934$			1.60770i			0.0526054i
$935$	6.00361	+	0.360355i	0.196339	+	0.0117849i
$936$		0			0
$937$	8.75833	+	8.75833i	0.286122	+	0.286122i	0.835545	−	0.549423i	$-0.185152\pi$
$937$	8.75833	+	8.75833i	0.286122	+	0.286122i	−0.549423	+	0.835545i	$0.685152\pi$
$938$	4.54725	+	4.54725i	0.148473	+	0.148473i
$939$		0			0
$940$	−1.19615	−	0.0717968i	−0.0390142	−	0.00234175i
$941$		−	6.48906i		−	0.211537i	−0.994391	−	0.105769i	$-0.966270\pi$
$941$		−	6.48906i		−	0.211537i	0.994391	−	0.105769i	$-0.0337303\pi$
$942$		0			0
$943$	−6.92820	+	6.92820i	−0.225613	+	0.225613i
$944$	14.3452			0.466897
$945$		0			0
$946$	34.3923			1.11819
$947$	−2.27362	+	2.27362i	−0.0738829	+	0.0738829i	−0.743083	−	0.669200i	$-0.766637\pi$
$947$	−2.27362	+	2.27362i	−0.0738829	+	0.0738829i	0.669200	+	0.743083i	$0.266637\pi$
$948$		0			0
$949$		−	49.7128i		−	1.61375i
$950$	−7.86611	+	6.17449i	−0.255210	+	0.200327i
$951$		0			0
$952$		0			0
$953$	30.0774	+	30.0774i	0.974303	+	0.974303i	0.999678	−	0.0253747i	$-0.00807790\pi$
$953$	30.0774	+	30.0774i	0.974303	+	0.974303i	−0.0253747	+	0.999678i	$0.508078\pi$
$954$		0			0
$955$	−14.3301	−	16.1603i	−0.463712	−	0.522934i
$956$			47.3997i			1.53302i
$957$		0			0
$958$	−54.3923	+	54.3923i	−1.75734	+	1.75734i
$959$	−7.58871			−0.245052
$960$		0			0
$961$	24.7128			0.797188
$962$	26.7685	−	26.7685i	0.863052	−	0.863052i
$963$		0			0
$964$		−	15.2154i		−	0.490055i
$965$	0.859411	−	14.3180i	0.0276654	−	0.460913i
$966$		0			0
$967$	25.9808	+	25.9808i	0.835485	+	0.835485i	0.988261	−	0.152776i	$-0.0488213\pi$
$967$	25.9808	+	25.9808i	0.835485	+	0.835485i	−0.152776	+	0.988261i	$0.548821\pi$
$968$		0			0
$969$		0			0
$970$	−55.1769	+	48.9282i	−1.77162	+	1.57099i
$971$			3.38323i			0.108573i	0.998525	+	0.0542865i	$0.0172884\pi$
$971$			3.38323i			0.108573i	−0.998525	+	0.0542865i	$0.982712\pi$
$972$		0			0
$973$	−3.97372	+	3.97372i	−0.127392	+	0.127392i
$974$	−36.9726			−1.18468
$975$		0			0
$976$	59.4256			1.90217
$977$	−41.8444	+	41.8444i	−1.33872	+	1.33872i	−0.441421	+	0.897300i	$0.645525\pi$
$977$	−41.8444	+	41.8444i	−1.33872	+	1.33872i	−0.897300	+	0.441421i	$0.854475\pi$
$978$		0			0
$979$		−	34.3923i		−	1.09918i
$980$	20.7327	−	18.3848i	0.662283	−	0.587280i
$981$		0			0
$982$	−18.6795	−	18.6795i	−0.596087	−	0.596087i
$983$	25.2528	+	25.2528i	0.805438	+	0.805438i	0.983940	−	0.178501i	$-0.0571249\pi$
$983$	25.2528	+	25.2528i	0.805438	+	0.805438i	−0.178501	+	0.983940i	$0.557125\pi$
$984$		0			0
$985$	−1.85641	+	30.9282i	−0.0591500	+	0.985454i
$986$			5.50820i			0.175417i
$987$		0			0
$988$	5.46410	−	5.46410i	0.173836	−	0.173836i
$989$	10.2784			0.326835
$990$		0			0
$991$	53.8564			1.71081			0.855403	−	0.517964i	$-0.173310\pi$
$991$	53.8564			1.71081			0.855403	+	0.517964i	$0.173310\pi$
$992$	−42.2233	+	42.2233i	−1.34059	+	1.34059i
$993$		0			0
$994$			18.9282i			0.600366i
$995$	−9.29890	−	10.4865i	−0.294795	−	0.332444i
$996$		0			0
$997$	−14.6340	−	14.6340i	−0.463463	−	0.463463i	0.436326	−	0.899789i	$-0.356279\pi$
$997$	−14.6340	−	14.6340i	−0.463463	−	0.463463i	−0.899789	+	0.436326i	$0.856279\pi$
$998$	54.1191	+	54.1191i	1.71311	+	1.71311i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.n.c.647.3	yes	8
3.2	odd	2	inner	855.2.n.c.647.2	✓	8
5.3	odd	4	inner	855.2.n.c.818.2	yes	8
15.8	even	4	inner	855.2.n.c.818.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
855.2.n.c.647.2	✓	8	3.2	odd	2	inner
855.2.n.c.647.3	yes	8	1.1	even	1	trivial
855.2.n.c.818.2	yes	8	5.3	odd	4	inner
855.2.n.c.818.3	yes	8	15.8	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41421 - 1.41421i) q^{2} -2.00000i q^{4} +(-1.67303 + 1.48356i) q^{5} +(0.633975 + 0.633975i) q^{7} +O(q^{10})\)	\(q+(1.41421 - 1.41421i) q^{2} -2.00000i q^{4} +(-1.67303 + 1.48356i) q^{5} +(0.633975 + 0.633975i) q^{7} +(-0.267949 + 4.46410i) q^{10} +5.79555i q^{11} +(-2.73205 + 2.73205i) q^{13} +1.79315 q^{14} +4.00000 q^{16} +(-0.328169 + 0.328169i) q^{17} -1.00000i q^{19} +(2.96713 + 3.34607i) q^{20} +(8.19615 + 8.19615i) q^{22} +(2.44949 + 2.44949i) q^{23} +(0.598076 - 4.96410i) q^{25} +7.72741i q^{26} +(1.26795 - 1.26795i) q^{28} +5.93426 q^{29} -7.46410 q^{31} +(5.65685 - 5.65685i) q^{32} +0.928203i q^{34} +(-2.00120 - 0.120118i) q^{35} +(-3.46410 - 3.46410i) q^{37} +(-1.41421 - 1.41421i) q^{38} +2.82843i q^{41} +(2.09808 - 2.09808i) q^{43} +11.5911 q^{44} +6.92820 q^{46} +(-0.189469 + 0.189469i) q^{47} -6.19615i q^{49} +(-6.17449 - 7.86611i) q^{50} +(5.46410 + 5.46410i) q^{52} +(4.24264 + 4.24264i) q^{53} +(-8.59808 - 9.69615i) q^{55} +(8.39230 - 8.39230i) q^{58} +3.58630 q^{59} +14.8564 q^{61} +(-10.5558 + 10.5558i) q^{62} -8.00000i q^{64} +(0.517638 - 8.62398i) q^{65} +(2.53590 + 2.53590i) q^{67} +(0.656339 + 0.656339i) q^{68} +(-3.00000 + 2.66025i) q^{70} +10.5558i q^{71} +(-9.09808 + 9.09808i) q^{73} -9.79796 q^{74} -2.00000 q^{76} +(-3.67423 + 3.67423i) q^{77} -6.53590i q^{79} +(-6.69213 + 5.93426i) q^{80} +(4.00000 + 4.00000i) q^{82} +(-10.5558 - 10.5558i) q^{83} +(0.0621778 - 1.03590i) q^{85} -5.93426i q^{86} -5.93426 q^{89} -3.46410 q^{91} +(4.89898 - 4.89898i) q^{92} +0.535898i q^{94} +(1.48356 + 1.67303i) q^{95} +(11.6603 + 11.6603i) q^{97} +(-8.76268 - 8.76268i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{7}+O(q^{10}) \) 8 * q + 12 * q^7	\( 8 q + 12 q^{7} - 16 q^{10} - 8 q^{13} + 32 q^{16} + 24 q^{22} - 16 q^{25} + 24 q^{28} - 32 q^{31} - 4 q^{43} + 16 q^{52} - 48 q^{55} - 16 q^{58} + 8 q^{61} + 48 q^{67} - 24 q^{70} - 52 q^{73} - 16 q^{76} + 32 q^{82} - 48 q^{85} + 24 q^{97}+O(q^{100}) \) 8 * q + 12 * q^7 - 16 * q^10 - 8 * q^13 + 32 * q^16 + 24 * q^22 - 16 * q^25 + 24 * q^28 - 32 * q^31 - 4 * q^43 + 16 * q^52 - 48 * q^55 - 16 * q^58 + 8 * q^61 + 48 * q^67 - 24 * q^70 - 52 * q^73 - 16 * q^76 + 32 * q^82 - 48 * q^85 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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