LMFDB - Embedded newform 1680.2.dx.f.271.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1680,2,Mod(31,1680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1680.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1680, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 0, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.dx (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,-6,0,0,0,2,0,-6,0,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 35 x^{10} - 120 x^{9} + 328 x^{8} - 658 x^{7} + 1045 x^{6} - 1270 x^{5} + 1183 x^{4} + \cdots + 13 $ x^12 - 6x^11 + 35x^10 - 120x^9 + 328x^8 - 658x^7 + 1045x^6 - 1270x^5 + 1183x^4 - 810x^3 + 376x^2 - 104*x + 13
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.5
Root			$0.500000 + 1.60175i$ of defining polynomial
Character	$\chi$	$=$	1680.271
Dual form			1680.2.dx.f.31.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{3} +(0.866025 + 0.500000i) q^{5} +(0.407721 - 2.61415i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-5.57010 + 3.21590i) q^{11} +1.38806i q^{13} -1.00000i q^{15} +(3.91777 - 2.26192i) q^{17} +(-3.88789 + 6.73403i) q^{19} +(-2.46778 + 0.953976i) q^{21} +(3.02783 + 1.74812i) q^{23} +(0.500000 + 0.866025i) q^{25} +1.00000 q^{27} +9.76080 q^{29} +(1.90023 + 3.29129i) q^{31} +(5.57010 + 3.21590i) q^{33} +(1.66017 - 2.06006i) q^{35} +(-4.66988 + 8.08846i) q^{37} +(1.20210 - 0.694031i) q^{39} +7.82852i q^{41} +0.143761i q^{43} +(-0.866025 + 0.500000i) q^{45} +(4.69975 - 8.14020i) q^{47} +(-6.66753 - 2.13169i) q^{49} +(-3.91777 - 2.26192i) q^{51} +(-2.93556 - 5.08453i) q^{53} -6.43180 q^{55} +7.77579 q^{57} +(-0.870353 - 1.50750i) q^{59} +(8.62835 + 4.98158i) q^{61} +(2.06006 + 1.66017i) q^{63} +(-0.694031 + 1.20210i) q^{65} +(4.20817 - 2.42959i) q^{67} -3.49624i q^{69} -1.97521i q^{71} +(5.53477 - 3.19550i) q^{73} +(0.500000 - 0.866025i) q^{75} +(6.13578 + 15.8723i) q^{77} +(-2.49151 - 1.43848i) q^{79} +(-0.500000 - 0.866025i) q^{81} +5.81544 q^{83} +4.52385 q^{85} +(-4.88040 - 8.45310i) q^{87} +(1.02870 + 0.593918i) q^{89} +(3.62860 + 0.565943i) q^{91} +(1.90023 - 3.29129i) q^{93} +(-6.73403 + 3.88789i) q^{95} +12.3645i q^{97} -6.43180i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} + 2 q^{7} - 6 q^{9} - 10 q^{19} - 4 q^{21} - 12 q^{23} + 6 q^{25} + 12 q^{27} + 8 q^{29} + 2 q^{31} + 4 q^{35} - 10 q^{37} - 6 q^{39} + 2 q^{49} + 16 q^{53} + 20 q^{57} + 24 q^{61} + 2 q^{63}+ \cdots - 24 q^{95}+O(q^{100}) $ 12 * q - 6 * q^3 + 2 * q^7 - 6 * q^9 - 10 * q^19 - 4 * q^21 - 12 * q^23 + 6 * q^25 + 12 * q^27 + 8 * q^29 + 2 * q^31 + 4 * q^35 - 10 * q^37 - 6 * q^39 + 2 * q^49 + 16 * q^53 + 20 * q^57 + 24 * q^61 + 2 * q^63 + 4 * q^65 + 6 * q^67 + 30 * q^73 + 6 * q^75 + 36 * q^77 - 42 * q^79 - 6 * q^81 + 64 * q^83 - 8 * q^85 - 4 * q^87 - 14 * q^91 + 2 * q^93 - 24 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$		0			0
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$		0			0
$7$	0.407721	−	2.61415i	0.154104	−	0.988055i
$7$	0.407721	−	2.61415i	0.154104	−	0.988055i
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−5.57010	+	3.21590i	−1.67945	+	0.969630i	−0.717437	+	0.696624i	$0.754685\pi$
$11$	−5.57010	+	3.21590i	−1.67945	+	0.969630i	−0.962012	+	0.273006i	$0.911982\pi$
$12$		0			0
$13$			1.38806i			0.384979i	0.981299	+	0.192490i	$0.0616562\pi$
$13$			1.38806i			0.384979i	−0.981299	+	0.192490i	$0.938344\pi$
$14$		0			0
$15$		−	1.00000i		−	0.258199i
$16$		0			0
$17$	3.91777	−	2.26192i	0.950198	−	0.548597i	0.0570555	−	0.998371i	$-0.481829\pi$
$17$	3.91777	−	2.26192i	0.950198	−	0.548597i	0.893142	+	0.449774i	$0.148495\pi$
$18$		0			0
$19$	−3.88789	+	6.73403i	−0.891944	+	1.54489i	−0.0544021	+	0.998519i	$0.517325\pi$
$19$	−3.88789	+	6.73403i	−0.891944	+	1.54489i	−0.837542	+	0.546373i	$0.816008\pi$
$20$		0			0
$21$	−2.46778	+	0.953976i	−0.538513	+	0.208175i
$22$		0			0
$23$	3.02783	+	1.74812i	0.631347	+	0.364508i	0.781274	−	0.624189i	$-0.214570\pi$
$23$	3.02783	+	1.74812i	0.631347	+	0.364508i	−0.149926	+	0.988697i	$0.547904\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	9.76080			1.81253			0.906267	−	0.422705i	$-0.138920\pi$
$29$	9.76080			1.81253			0.906267	+	0.422705i	$0.138920\pi$
$30$		0			0
$31$	1.90023	+	3.29129i	0.341291	+	0.591133i	0.984673	−	0.174413i	$-0.0558026\pi$
$31$	1.90023	+	3.29129i	0.341291	+	0.591133i	−0.643382	+	0.765545i	$0.722469\pi$
$32$		0			0
$33$	5.57010	+	3.21590i	0.969630	+	0.559816i
$34$		0			0
$35$	1.66017	−	2.06006i	0.280620	−	0.348213i
$36$		0			0
$37$	−4.66988	+	8.08846i	−0.767723	+	1.32973i	0.171072	+	0.985259i	$0.445277\pi$
$37$	−4.66988	+	8.08846i	−0.767723	+	1.32973i	−0.938795	+	0.344476i	$0.888056\pi$
$38$		0			0
$39$	1.20210	−	0.694031i	0.192490	−	0.111134i
$40$		0			0
$41$			7.82852i			1.22261i	0.791395	+	0.611304i	$0.209355\pi$
$41$			7.82852i			1.22261i	−0.791395	+	0.611304i	$0.790645\pi$
$42$		0			0
$43$			0.143761i			0.0219233i	0.999940	+	0.0109616i	$0.00348927\pi$
$43$			0.143761i			0.0219233i	−0.999940	+	0.0109616i	$0.996511\pi$
$44$		0			0
$45$	−0.866025	+	0.500000i	−0.129099	+	0.0745356i
$46$		0			0
$47$	4.69975	−	8.14020i	0.685529	−	1.18737i	−0.287742	−	0.957708i	$-0.592904\pi$
$47$	4.69975	−	8.14020i	0.685529	−	1.18737i	0.973270	−	0.229663i	$-0.0737622\pi$
$48$		0			0
$49$	−6.66753	−	2.13169i	−0.952504	−	0.304527i
$50$		0			0
$51$	−3.91777	−	2.26192i	−0.548597	−	0.316733i
$52$		0			0
$53$	−2.93556	−	5.08453i	−0.403230	−	0.698414i	0.590884	−	0.806757i	$-0.298779\pi$
$53$	−2.93556	−	5.08453i	−0.403230	−	0.698414i	−0.994114	+	0.108342i	$0.965446\pi$
$54$		0			0
$55$	−6.43180			−0.867264
$56$		0			0
$57$	7.77579			1.02993
$58$		0			0
$59$	−0.870353	−	1.50750i	−0.113310	−	0.196259i	0.803793	−	0.594909i	$-0.202812\pi$
$59$	−0.870353	−	1.50750i	−0.113310	−	0.196259i	−0.917103	+	0.398650i	$0.869479\pi$
$60$		0			0
$61$	8.62835	+	4.98158i	1.10475	+	0.637826i	0.937464	−	0.348083i	$-0.113167\pi$
$61$	8.62835	+	4.98158i	1.10475	+	0.637826i	0.167283	+	0.985909i	$0.446501\pi$
$62$		0			0
$63$	2.06006	+	1.66017i	0.259543	+	0.209162i
$64$		0			0
$65$	−0.694031	+	1.20210i	−0.0860840	+	0.149102i
$66$		0			0
$67$	4.20817	−	2.42959i	0.514110	−	0.296822i	−0.220411	−	0.975407i	$-0.570740\pi$
$67$	4.20817	−	2.42959i	0.514110	−	0.296822i	0.734522	+	0.678585i	$0.237407\pi$
$68$		0			0
$69$		−	3.49624i		−	0.420898i
$70$		0			0
$71$		−	1.97521i		−	0.234415i	−0.993107	−	0.117207i	$-0.962606\pi$
$71$		−	1.97521i		−	0.234415i	0.993107	−	0.117207i	$-0.0373942\pi$
$72$		0			0
$73$	5.53477	−	3.19550i	0.647796	−	0.374005i	−0.139815	−	0.990178i	$-0.544651\pi$
$73$	5.53477	−	3.19550i	0.647796	−	0.374005i	0.787611	+	0.616172i	$0.211318\pi$
$74$		0			0
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$		0			0
$77$	6.13578	+	15.8723i	0.699237	+	1.80881i
$78$		0			0
$79$	−2.49151	−	1.43848i	−0.280317	−	0.161841i	0.353250	−	0.935529i	$-0.385077\pi$
$79$	−2.49151	−	1.43848i	−0.280317	−	0.161841i	−0.633567	+	0.773688i	$0.718410\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	5.81544			0.638328			0.319164	−	0.947700i	$-0.396598\pi$
$83$	5.81544			0.638328			0.319164	+	0.947700i	$0.396598\pi$
$84$		0			0
$85$	4.52385			0.490680
$86$		0			0
$87$	−4.88040	−	8.45310i	−0.523234	−	0.906267i
$88$		0			0
$89$	1.02870	+	0.593918i	0.109042	+	0.0629552i	0.553529	−	0.832830i	$-0.313281\pi$
$89$	1.02870	+	0.593918i	0.109042	+	0.0629552i	−0.444487	+	0.895785i	$0.646614\pi$
$90$		0			0
$91$	3.62860	+	0.565943i	0.380381	+	0.0593269i
$92$		0			0
$93$	1.90023	−	3.29129i	0.197044	−	0.341291i
$94$		0			0
$95$	−6.73403	+	3.88789i	−0.690897	+	0.398889i
$96$		0			0
$97$			12.3645i			1.25543i	0.778444	+	0.627714i	$0.216009\pi$
$97$			12.3645i			1.25543i	−0.778444	+	0.627714i	$0.783991\pi$
$98$		0			0
$99$		−	6.43180i		−	0.646420i
$100$		0			0
$101$	−3.83564	+	2.21451i	−0.381661	+	0.220352i	−0.678541	−	0.734563i	$-0.737387\pi$
$101$	−3.83564	+	2.21451i	−0.381661	+	0.220352i	0.296880	+	0.954915i	$0.404054\pi$
$102$		0			0
$103$	−8.02040	+	13.8917i	−0.790274	+	1.36879i	0.135524	+	0.990774i	$0.456728\pi$
$103$	−8.02040	+	13.8917i	−0.790274	+	1.36879i	−0.925797	+	0.378020i	$0.876605\pi$
$104$		0			0
$105$	−2.61415	−	0.407721i	−0.255115	−	0.0397895i
$106$		0			0
$107$	10.6282	+	6.13618i	1.02747	+	0.593207i	0.916257	−	0.400590i	$-0.131195\pi$
$107$	10.6282	+	6.13618i	1.02747	+	0.593207i	0.111208	+	0.993797i	$0.464528\pi$
$108$		0			0
$109$	−2.20359	−	3.81672i	−0.211065	−	0.365576i	0.740983	−	0.671524i	$-0.234360\pi$
$109$	−2.20359	−	3.81672i	−0.211065	−	0.365576i	−0.952048	+	0.305948i	$0.901027\pi$
$110$		0			0
$111$	9.33975			0.886490
$112$		0			0
$113$	−14.3597			−1.35085			−0.675424	−	0.737429i	$-0.736039\pi$
$113$	−14.3597			−1.35085			−0.675424	+	0.737429i	$0.736039\pi$
$114$		0			0
$115$	1.74812	+	3.02783i	0.163013	+	0.282347i
$116$		0			0
$117$	−1.20210	−	0.694031i	−0.111134	−	0.0641632i
$118$		0			0
$119$	−4.31564	−	11.1638i	−0.395614	−	1.02339i
$120$		0			0
$121$	15.1840	−	26.2995i	1.38037	−	2.39086i
$122$		0			0
$123$	6.77969	−	3.91426i	0.611304	−	0.352937i
$124$		0			0
$125$			1.00000i			0.0894427i
$126$		0			0
$127$			20.1471i			1.78777i	0.448300	+	0.893883i	$0.352030\pi$
$127$			20.1471i			1.78777i	−0.448300	+	0.893883i	$0.647970\pi$
$128$		0			0
$129$	0.124500	−	0.0718803i	0.0109616	−	0.00632871i
$130$		0			0
$131$	1.76419	−	3.05567i	0.154138	−	0.266975i	−0.778607	−	0.627512i	$-0.784073\pi$
$131$	1.76419	−	3.05567i	0.154138	−	0.266975i	0.932745	+	0.360537i	$0.117407\pi$
$132$		0			0
$133$	16.0186	+	12.9091i	1.38899	+	1.11936i
$134$		0			0
$135$	0.866025	+	0.500000i	0.0745356	+	0.0430331i
$136$		0			0
$137$	6.71754	+	11.6351i	0.573918	+	0.994055i	0.996158	+	0.0875713i	$0.0279105\pi$
$137$	6.71754	+	11.6351i	0.573918	+	0.994055i	−0.422240	+	0.906484i	$0.638756\pi$
$138$		0			0
$139$	2.02416			0.171687			0.0858437	−	0.996309i	$-0.472641\pi$
$139$	2.02416			0.171687			0.0858437	+	0.996309i	$0.472641\pi$
$140$		0			0
$141$	−9.39950			−0.791580
$142$		0			0
$143$	−4.46387	−	7.73165i	−0.373288	−	0.646553i
$144$		0			0
$145$	8.45310	+	4.88040i	0.701991	+	0.405295i
$146$		0			0
$147$	1.48767	+	6.84009i	0.122701	+	0.564161i
$148$		0			0
$149$	−5.53998	+	9.59553i	−0.453853	+	0.786096i	−0.998621	−	0.0524903i	$-0.983284\pi$
$149$	−5.53998	+	9.59553i	−0.453853	+	0.786096i	0.544769	+	0.838586i	$0.316617\pi$
$150$		0			0
$151$	−3.19701	+	1.84580i	−0.260169	+	0.150209i	−0.624412	−	0.781095i	$-0.714661\pi$
$151$	−3.19701	+	1.84580i	−0.260169	+	0.150209i	0.364243	+	0.931304i	$0.381328\pi$
$152$		0			0
$153$			4.52385i			0.365731i
$154$		0			0
$155$			3.80045i			0.305260i
$156$		0			0
$157$	−6.60934	+	3.81591i	−0.527483	+	0.304542i	−0.739991	−	0.672617i	$-0.765170\pi$
$157$	−6.60934	+	3.81591i	−0.527483	+	0.304542i	0.212508	+	0.977159i	$0.431837\pi$
$158$		0			0
$159$	−2.93556	+	5.08453i	−0.232805	+	0.403230i
$160$		0			0
$161$	5.80436	−	7.20246i	0.457448	−	0.567633i
$162$		0			0
$163$	13.0726	+	7.54749i	1.02393	+	0.591165i	0.915239	−	0.402910i	$-0.132001\pi$
$163$	13.0726	+	7.54749i	1.02393	+	0.591165i	0.108689	+	0.994076i	$0.465335\pi$
$164$		0			0
$165$	3.21590	+	5.57010i	0.250357	+	0.433632i
$166$		0			0
$167$	−6.08701			−0.471027			−0.235514	−	0.971871i	$-0.575677\pi$
$167$	−6.08701			−0.471027			−0.235514	+	0.971871i	$0.575677\pi$
$168$		0			0
$169$	11.0733			0.851791
$170$		0			0
$171$	−3.88789	−	6.73403i	−0.297315	−	0.514964i
$172$		0			0
$173$	0.0409579	+	0.0236471i	0.00311397	+	0.00179785i	0.501556	−	0.865125i	$-0.332761\pi$
$173$	0.0409579	+	0.0236471i	0.00311397	+	0.00179785i	−0.498442	+	0.866923i	$0.666094\pi$
$174$		0			0
$175$	2.46778	−	0.953976i	0.186546	−	0.0721138i
$176$		0			0
$177$	−0.870353	+	1.50750i	−0.0654197	+	0.113310i
$178$		0			0
$179$	−0.0149916	+	0.00865543i	−0.00112053	+	0.000646937i	−0.500560	−	0.865702i	$-0.666873\pi$
$179$	−0.0149916	+	0.00865543i	−0.00112053	+	0.000646937i	0.499440	+	0.866349i	$0.333539\pi$
$180$		0			0
$181$			12.7350i			0.946584i	0.880905	+	0.473292i	$0.156935\pi$
$181$			12.7350i			0.946584i	−0.880905	+	0.473292i	$0.843065\pi$
$182$		0			0
$183$		−	9.96316i		−	0.736498i
$184$		0			0
$185$	−8.08846	+	4.66988i	−0.594676	+	0.343336i
$186$		0			0
$187$	−14.5482	+	25.1983i	−1.06387	+	1.84268i
$188$		0			0
$189$	0.407721	−	2.61415i	0.0296574	−	0.190151i
$190$		0			0
$191$	18.2428	+	10.5325i	1.32000	+	0.762105i	0.983729	−	0.179658i	$-0.0574993\pi$
$191$	18.2428	+	10.5325i	1.32000	+	0.762105i	0.336276	+	0.941764i	$0.390833\pi$
$192$		0			0
$193$	−6.41058	−	11.1035i	−0.461444	−	0.799244i	0.537589	−	0.843207i	$-0.319335\pi$
$193$	−6.41058	−	11.1035i	−0.461444	−	0.799244i	−0.999033	+	0.0439627i	$0.986002\pi$
$194$		0			0
$195$	1.38806			0.0994012
$196$		0			0
$197$	9.93803			0.708056			0.354028	−	0.935235i	$-0.384812\pi$
$197$	9.93803			0.708056			0.354028	+	0.935235i	$0.384812\pi$
$198$		0			0
$199$	−4.22790	−	7.32293i	−0.299708	−	0.519109i	0.676361	−	0.736570i	$-0.263556\pi$
$199$	−4.22790	−	7.32293i	−0.299708	−	0.519109i	−0.976069	+	0.217461i	$0.930222\pi$
$200$		0			0
$201$	−4.20817	−	2.42959i	−0.296822	−	0.171370i
$202$		0			0
$203$	3.97969	−	25.5162i	0.279319	−	1.79088i
$204$		0			0
$205$	−3.91426	+	6.77969i	−0.273384	+	0.473514i
$206$		0			0
$207$	−3.02783	+	1.74812i	−0.210449	+	0.121503i
$208$		0			0
$209$		−	50.0123i		−	3.45942i
$210$		0			0
$211$		−	2.61292i		−	0.179881i	−0.995947	−	0.0899403i	$-0.971332\pi$
$211$		−	2.61292i		−	0.179881i	0.995947	−	0.0899403i	$-0.0286676\pi$
$212$		0			0
$213$	−1.71058	+	0.987606i	−0.117207	+	0.0676697i
$214$		0			0
$215$	−0.0718803	+	0.124500i	−0.00490220	+	0.00849086i
$216$		0			0
$217$	9.37867	−	3.62554i	0.636666	−	0.246118i
$218$		0			0
$219$	−5.53477	−	3.19550i	−0.374005	−	0.215932i
$220$		0			0
$221$	3.13969	+	5.43811i	0.211199	+	0.365807i
$222$		0			0
$223$	1.55133			0.103885			0.0519423	−	0.998650i	$-0.483459\pi$
$223$	1.55133			0.103885			0.0519423	+	0.998650i	$0.483459\pi$
$224$		0			0
$225$	−1.00000			−0.0666667
$226$		0			0
$227$	−10.3235	−	17.8808i	−0.685196	−	1.18679i	−0.973375	−	0.229217i	$-0.926383\pi$
$227$	−10.3235	−	17.8808i	−0.685196	−	1.18679i	0.288180	−	0.957576i	$-0.406950\pi$
$228$		0			0
$229$	−20.8104	−	12.0149i	−1.37519	−	0.793966i	−0.383613	−	0.923494i	$-0.625320\pi$
$229$	−20.8104	−	12.0149i	−1.37519	−	0.793966i	−0.991576	+	0.129528i	$0.958654\pi$
$230$		0			0
$231$	10.6779	−	13.2499i	0.702553	−	0.871778i
$232$		0			0
$233$	11.8446	−	20.5155i	0.775969	−	1.34402i	−0.158280	−	0.987394i	$-0.550595\pi$
$233$	11.8446	−	20.5155i	0.775969	−	1.34402i	0.934248	−	0.356623i	$-0.116072\pi$
$234$		0			0
$235$	8.14020	−	4.69975i	0.531008	−	0.306578i
$236$		0			0
$237$			2.87695i			0.186878i
$238$		0			0
$239$		−	22.3450i		−	1.44538i	−0.691173	−	0.722689i	$-0.742906\pi$
$239$		−	22.3450i		−	1.44538i	0.691173	−	0.722689i	$-0.257094\pi$
$240$		0			0
$241$	−22.1999	+	12.8171i	−1.43002	+	0.825623i	−0.997122	−	0.0758196i	$-0.975843\pi$
$241$	−22.1999	+	12.8171i	−1.43002	+	0.825623i	−0.432899	+	0.901442i	$0.642509\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	−4.70840	−	5.17986i	−0.300809	−	0.330929i
$246$		0			0
$247$	−9.34726	−	5.39664i	−0.594752	−	0.343380i
$248$		0			0
$249$	−2.90772	−	5.03632i	−0.184269	−	0.319164i
$250$		0			0
$251$	−24.0041			−1.51513			−0.757563	−	0.652762i	$-0.773610\pi$
$251$	−24.0041			−1.51513			−0.757563	+	0.652762i	$0.773610\pi$
$252$		0			0
$253$	−22.4871			−1.41375
$254$		0			0
$255$	−2.26192	−	3.91777i	−0.141647	−	0.245340i
$256$		0			0
$257$	2.44375	+	1.41090i	0.152437	+	0.0880095i	0.574278	−	0.818660i	$-0.305283\pi$
$257$	2.44375	+	1.41090i	0.152437	+	0.0880095i	−0.421841	+	0.906670i	$0.638616\pi$
$258$		0			0
$259$	19.2404	+	15.5056i	1.19554	+	0.963470i
$260$		0			0
$261$	−4.88040	+	8.45310i	−0.302089	+	0.523234i
$262$		0			0
$263$	6.51271	−	3.76012i	0.401591	−	0.231859i	−0.285579	−	0.958355i	$-0.592186\pi$
$263$	6.51271	−	3.76012i	0.401591	−	0.231859i	0.687170	+	0.726496i	$0.258853\pi$
$264$		0			0
$265$		−	5.87111i		−	0.360660i
$266$		0			0
$267$		−	1.18784i		−	0.0726943i
$268$		0			0
$269$	−15.7270	+	9.08000i	−0.958893	+	0.553617i	−0.895832	−	0.444393i	$-0.853420\pi$
$269$	−15.7270	+	9.08000i	−0.958893	+	0.553617i	−0.0630608	+	0.998010i	$0.520086\pi$
$270$		0			0
$271$	−8.68872	+	15.0493i	−0.527802	+	0.914180i	0.471673	+	0.881774i	$0.343650\pi$
$271$	−8.68872	+	15.0493i	−0.527802	+	0.914180i	−0.999475	+	0.0324063i	$0.989683\pi$
$272$		0			0
$273$	−1.32418	−	3.42543i	−0.0801430	−	0.207317i
$274$		0			0
$275$	−5.57010	−	3.21590i	−0.335890	−	0.193926i
$276$		0			0
$277$	5.26098	+	9.11229i	0.316102	+	0.547504i	0.979671	−	0.200610i	$-0.0642926\pi$
$277$	5.26098	+	9.11229i	0.316102	+	0.547504i	−0.663569	+	0.748115i	$0.730959\pi$
$278$		0			0
$279$	−3.80045			−0.227527
$280$		0			0
$281$	19.5202			1.16448			0.582240	−	0.813017i	$-0.302176\pi$
$281$	19.5202			1.16448			0.582240	+	0.813017i	$0.302176\pi$
$282$		0			0
$283$	−1.59612	−	2.76456i	−0.0948793	−	0.164336i	0.814679	−	0.579912i	$-0.196913\pi$
$283$	−1.59612	−	2.76456i	−0.0948793	−	0.164336i	−0.909558	+	0.415577i	$0.863580\pi$
$284$		0			0
$285$	6.73403	+	3.88789i	0.398889	+	0.230299i
$286$		0			0
$287$	20.4649	+	3.19185i	1.20800	+	0.188409i
$288$		0			0
$289$	1.73259	−	3.00094i	0.101917	−	0.176526i
$290$		0			0
$291$	10.7080	−	6.18227i	0.627714	−	0.362411i
$292$		0			0
$293$		−	14.0026i		−	0.818041i	−0.912525	−	0.409020i	$-0.865870\pi$
$293$		−	14.0026i		−	0.818041i	0.912525	−	0.409020i	$-0.134130\pi$
$294$		0			0
$295$		−	1.74071i		−	0.101348i
$296$		0			0
$297$	−5.57010	+	3.21590i	−0.323210	+	0.186605i
$298$		0			0
$299$	−2.42650	+	4.20283i	−0.140328	+	0.243056i
$300$		0			0
$301$	0.375811	+	0.0586143i	0.0216614	+	0.00337847i
$302$		0			0
$303$	3.83564	+	2.21451i	0.220352	+	0.127220i
$304$		0			0
$305$	4.98158	+	8.62835i	0.285244	+	0.494058i
$306$		0			0
$307$	−25.2166			−1.43919			−0.719593	−	0.694396i	$-0.755672\pi$
$307$	−25.2166			−1.43919			−0.719593	+	0.694396i	$0.755672\pi$
$308$		0			0
$309$	16.0408			0.912529
$310$		0			0
$311$	−5.19981	−	9.00634i	−0.294854	−	0.510703i	0.680097	−	0.733122i	$-0.261938\pi$
$311$	−5.19981	−	9.00634i	−0.294854	−	0.510703i	−0.974951	+	0.222420i	$0.928604\pi$
$312$		0			0
$313$	−26.4986	−	15.2990i	−1.49779	−	0.864750i	−0.497794	−	0.867296i	$-0.665856\pi$
$313$	−26.4986	−	15.2990i	−1.49779	−	0.864750i	−0.999997	+	0.00254595i	$0.999190\pi$
$314$		0			0
$315$	0.953976	+	2.46778i	0.0537505	+	0.139044i
$316$		0			0
$317$	−9.87861	+	17.1103i	−0.554838	+	0.961008i	0.443078	+	0.896483i	$0.353886\pi$
$317$	−9.87861	+	17.1103i	−0.554838	+	0.961008i	−0.997916	+	0.0645246i	$0.979447\pi$
$318$		0			0
$319$	−54.3686	+	31.3897i	−3.04406	+	1.75749i
$320$		0			0
$321$		−	12.2724i		−	0.684977i
$322$		0			0
$323$			35.1765i			1.95727i
$324$		0			0
$325$	−1.20210	+	0.694031i	−0.0666804	+	0.0384979i
$326$		0			0
$327$	−2.20359	+	3.81672i	−0.121859	+	0.211065i
$328$		0			0
$329$	−19.3635	−	15.6048i	−1.06754	−	0.860319i
$330$		0			0
$331$	27.8018	+	16.0514i	1.52813	+	0.882265i	0.999440	+	0.0334483i	$0.0106489\pi$
$331$	27.8018	+	16.0514i	1.52813	+	0.882265i	0.528687	+	0.848817i	$0.322684\pi$
$332$		0			0
$333$	−4.66988	−	8.08846i	−0.255908	−	0.443245i
$334$		0			0
$335$	4.85918			0.265485
$336$		0			0
$337$	−14.2949			−0.778693			−0.389346	−	0.921091i	$-0.627299\pi$
$337$	−14.2949			−0.778693			−0.389346	+	0.921091i	$0.627299\pi$
$338$		0			0
$339$	7.17986	+	12.4359i	0.389956	+	0.675424i
$340$		0			0
$341$	−21.1689	−	12.2219i	−1.14636	−	0.661851i
$342$		0			0
$343$	−8.29104	+	16.5608i	−0.447674	+	0.894197i
$344$		0			0
$345$	1.74812	−	3.02783i	0.0941157	−	0.163013i
$346$		0			0
$347$	4.25012	−	2.45381i	0.228158	−	0.131727i	−0.381564	−	0.924343i	$-0.624614\pi$
$347$	4.25012	−	2.45381i	0.228158	−	0.131727i	0.609722	+	0.792615i	$0.291281\pi$
$348$		0			0
$349$		−	25.2236i		−	1.35019i	−0.737732	−	0.675093i	$-0.764103\pi$
$349$		−	25.2236i		−	1.35019i	0.737732	−	0.675093i	$-0.235897\pi$
$350$		0			0
$351$			1.38806i			0.0740893i
$352$		0			0
$353$	−9.39006	+	5.42135i	−0.499783	+	0.288550i	−0.728624	−	0.684914i	$-0.759840\pi$
$353$	−9.39006	+	5.42135i	−0.499783	+	0.288550i	0.228841	+	0.973464i	$0.426506\pi$
$354$		0			0
$355$	0.987606	−	1.71058i	0.0524167	−	0.0907884i
$356$		0			0
$357$	−7.51036	+	9.31938i	−0.397490	+	0.493234i
$358$		0			0
$359$	23.8674	+	13.7799i	1.25967	+	0.727273i	0.973011	−	0.230758i	$-0.0741206\pi$
$359$	23.8674	+	13.7799i	1.25967	+	0.727273i	0.286663	+	0.958031i	$0.407454\pi$
$360$		0			0
$361$	−20.7314	−	35.9079i	−1.09113	−	1.88989i
$362$		0			0
$363$	−30.3680			−1.59391
$364$		0			0
$365$	6.39100			0.334520
$366$		0			0
$367$	8.67211	+	15.0205i	0.452681	+	0.784066i	0.998552	−	0.0538035i	$-0.0171344\pi$
$367$	8.67211	+	15.0205i	0.452681	+	0.784066i	−0.545871	+	0.837869i	$0.683801\pi$
$368$		0			0
$369$	−6.77969	−	3.91426i	−0.352937	−	0.203768i
$370$		0			0
$371$	−14.4886	+	5.60090i	−0.752211	+	0.290784i
$372$		0			0
$373$	7.17323	−	12.4244i	0.371416	−	0.643311i	−0.618368	−	0.785889i	$-0.712206\pi$
$373$	7.17323	−	12.4244i	0.371416	−	0.643311i	0.989784	+	0.142578i	$0.0455390\pi$
$374$		0			0
$375$	0.866025	−	0.500000i	0.0447214	−	0.0258199i
$376$		0			0
$377$			13.5486i			0.697788i
$378$		0			0
$379$			2.88120i			0.147998i	0.997258	+	0.0739988i	$0.0235761\pi$
$379$			2.88120i			0.147998i	−0.997258	+	0.0739988i	$0.976424\pi$
$380$		0			0
$381$	17.4479	−	10.0735i	0.893883	−	0.516084i
$382$		0			0
$383$	−7.27219	+	12.5958i	−0.371592	+	0.643616i	−0.989811	−	0.142390i	$-0.954521\pi$
$383$	−7.27219	+	12.5958i	−0.371592	+	0.643616i	0.618219	+	0.786006i	$0.287854\pi$
$384$		0			0
$385$	−2.62238	+	16.8137i	−0.133649	+	0.856904i
$386$		0			0
$387$	−0.124500	−	0.0718803i	−0.00632871	−	0.00365388i
$388$		0			0
$389$	−10.3553	−	17.9358i	−0.525032	−	0.909383i	−0.999575	−	0.0291501i	$-0.990720\pi$
$389$	−10.3553	−	17.9358i	−0.525032	−	0.909383i	0.474543	−	0.880232i	$-0.342613\pi$
$390$		0			0
$391$	15.8165			0.799873
$392$		0			0
$393$	−3.52838			−0.177983
$394$		0			0
$395$	−1.43848	−	2.49151i	−0.0723776	−	0.125362i
$396$		0			0
$397$	23.1074	+	13.3411i	1.15973	+	0.669570i	0.951239	−	0.308455i	$-0.0998119\pi$
$397$	23.1074	+	13.3411i	1.15973	+	0.669570i	0.208490	+	0.978025i	$0.433145\pi$
$398$		0			0
$399$	3.17035	−	20.3270i	0.158716	−	1.01763i
$400$		0			0
$401$	1.56396	−	2.70887i	0.0781007	−	0.135274i	−0.824330	−	0.566110i	$-0.808448\pi$
$401$	1.56396	−	2.70887i	0.0781007	−	0.135274i	0.902430	+	0.430836i	$0.141781\pi$
$402$		0			0
$403$	−4.56851	+	2.63763i	−0.227574	+	0.131390i
$404$		0			0
$405$		−	1.00000i		−	0.0496904i
$406$		0			0
$407$		−	60.0714i		−	2.97763i
$408$		0			0
$409$	19.2645	−	11.1224i	0.952570	−	0.549967i	0.0586917	−	0.998276i	$-0.481307\pi$
$409$	19.2645	−	11.1224i	0.952570	−	0.549967i	0.893878	+	0.448310i	$0.147974\pi$
$410$		0			0
$411$	6.71754	−	11.6351i	0.331352	−	0.573918i
$412$		0			0
$413$	−4.29568	+	1.66059i	−0.211376	+	0.0817124i
$414$		0			0
$415$	5.03632	+	2.90772i	0.247223	+	0.142734i
$416$		0			0
$417$	−1.01208	−	1.75298i	−0.0495619	−	0.0858437i
$418$		0			0
$419$	−16.7928			−0.820380			−0.410190	−	0.912000i	$-0.634538\pi$
$419$	−16.7928			−0.820380			−0.410190	+	0.912000i	$0.634538\pi$
$420$		0			0
$421$	−26.8579			−1.30897			−0.654487	−	0.756073i	$-0.727115\pi$
$421$	−26.8579			−1.30897			−0.654487	+	0.756073i	$0.727115\pi$
$422$		0			0
$423$	4.69975	+	8.14020i	0.228510	+	0.395790i
$424$		0			0
$425$	3.91777	+	2.26192i	0.190040	+	0.109719i
$426$		0			0
$427$	16.5405	−	20.5247i	0.800453	−	0.993259i
$428$		0			0
$429$	−4.46387	+	7.73165i	−0.215518	+	0.373288i
$430$		0			0
$431$	5.68521	−	3.28236i	0.273847	−	0.158106i	−0.356788	−	0.934186i	$-0.616128\pi$
$431$	5.68521	−	3.28236i	0.273847	−	0.158106i	0.630635	+	0.776080i	$0.282795\pi$
$432$		0			0
$433$			3.02710i			0.145473i	0.997351	+	0.0727365i	$0.0231732\pi$
$433$			3.02710i			0.145473i	−0.997351	+	0.0727365i	$0.976827\pi$
$434$		0			0
$435$		−	9.76080i		−	0.467994i
$436$		0			0
$437$	−23.5438	+	13.5930i	−1.12625	+	0.650242i
$438$		0			0
$439$	4.45148	−	7.71020i	0.212458	−	0.367988i	−0.740025	−	0.672579i	$-0.765187\pi$
$439$	4.45148	−	7.71020i	0.212458	−	0.367988i	0.952483	+	0.304591i	$0.0985199\pi$
$440$		0			0
$441$	5.17986	−	4.70840i	0.246660	−	0.224210i
$442$		0			0
$443$	−12.8791	−	7.43576i	−0.611905	−	0.353283i	0.161806	−	0.986823i	$-0.448268\pi$
$443$	−12.8791	−	7.43576i	−0.611905	−	0.353283i	−0.773711	+	0.633539i	$0.781602\pi$
$444$		0			0
$445$	0.593918	+	1.02870i	0.0281544	+	0.0487649i
$446$		0			0
$447$	11.0800			0.524064
$448$		0			0
$449$	−15.4308			−0.728226			−0.364113	−	0.931355i	$-0.618628\pi$
$449$	−15.4308			−0.728226			−0.364113	+	0.931355i	$0.618628\pi$
$450$		0			0
$451$	−25.1757	−	43.6056i	−1.18548	−	2.05331i
$452$		0			0
$453$	3.19701	+	1.84580i	0.150209	+	0.0867231i
$454$		0			0
$455$	2.85949	+	2.30442i	0.134055	+	0.108033i
$456$		0			0
$457$	7.35418	−	12.7378i	0.344014	−	0.595849i	−0.641160	−	0.767407i	$-0.721547\pi$
$457$	7.35418	−	12.7378i	0.344014	−	0.595849i	0.985174	+	0.171558i	$0.0548800\pi$
$458$		0			0
$459$	3.91777	−	2.26192i	0.182866	−	0.105578i
$460$		0			0
$461$			6.60397i			0.307577i	0.988104	+	0.153789i	$0.0491475\pi$
$461$			6.60397i			0.307577i	−0.988104	+	0.153789i	$0.950852\pi$
$462$		0			0
$463$		−	20.7567i		−	0.964645i	−0.875994	−	0.482322i	$-0.839793\pi$
$463$		−	20.7567i		−	0.964645i	0.875994	−	0.482322i	$-0.160207\pi$
$464$		0			0
$465$	3.29129	−	1.90023i	0.152630	−	0.0881209i
$466$		0			0
$467$	1.77566	−	3.07554i	0.0821679	−	0.142319i	−0.822013	−	0.569469i	$-0.807149\pi$
$467$	1.77566	−	3.07554i	0.0821679	−	0.142319i	0.904181	+	0.427150i	$0.140482\pi$
$468$		0			0
$469$	−4.63554	−	11.9914i	−0.214049	−	0.553710i
$470$		0			0
$471$	6.60934	+	3.81591i	0.304542	+	0.175828i
$472$		0			0
$473$	−0.462320	−	0.800761i	−0.0212575	−	0.0368191i
$474$		0			0
$475$	−7.77579			−0.356778
$476$		0			0
$477$	5.87111			0.268820
$478$		0			0
$479$	10.2286	+	17.7165i	0.467358	+	0.809488i	0.999304	−	0.0372900i	$-0.0118725\pi$
$479$	10.2286	+	17.7165i	0.467358	+	0.809488i	−0.531946	+	0.846778i	$0.678539\pi$
$480$		0			0
$481$	−11.2273	−	6.48208i	−0.511921	−	0.295557i
$482$		0			0
$483$	−9.13969	−	1.42549i	−0.415870	−	0.0648622i
$484$		0			0
$485$	−6.18227	+	10.7080i	−0.280722	+	0.486225i
$486$		0			0
$487$	7.36027	−	4.24945i	0.333525	−	0.192561i	−0.323880	−	0.946098i	$-0.604987\pi$
$487$	7.36027	−	4.24945i	0.333525	−	0.192561i	0.657405	+	0.753537i	$0.271654\pi$
$488$		0			0
$489$		−	15.0950i		−	0.682619i
$490$		0			0
$491$			14.9445i			0.674436i	0.941426	+	0.337218i	$0.109486\pi$
$491$			14.9445i			0.674436i	−0.941426	+	0.337218i	$0.890514\pi$
$492$		0			0
$493$	38.2405	−	22.0782i	1.72227	−	0.994351i
$494$		0			0
$495$	3.21590	−	5.57010i	0.144544	−	0.250357i
$496$		0			0
$497$	−5.16349	−	0.805336i	−0.231614	−	0.0361243i
$498$		0			0
$499$	30.3188	+	17.5046i	1.35726	+	0.783613i	0.989253	−	0.146211i	$-0.0467079\pi$
$499$	30.3188	+	17.5046i	1.35726	+	0.783613i	0.368004	+	0.929824i	$0.380041\pi$
$500$		0			0
$501$	3.04351	+	5.27151i	0.135974	+	0.235514i
$502$		0			0
$503$	9.36092			0.417383			0.208691	−	0.977982i	$-0.433080\pi$
$503$	9.36092			0.417383			0.208691	+	0.977982i	$0.433080\pi$
$504$		0			0
$505$	−4.42902			−0.197089
$506$		0			0
$507$	−5.53664	−	9.58974i	−0.245891	−	0.425895i
$508$		0			0
$509$	10.1976	+	5.88758i	0.452000	+	0.260963i	0.708675	−	0.705535i	$-0.249293\pi$
$509$	10.1976	+	5.88758i	0.452000	+	0.260963i	−0.256674	+	0.966498i	$0.582627\pi$
$510$		0			0
$511$	−6.09686	−	15.7716i	−0.269709	−	0.697693i
$512$		0			0
$513$	−3.88789	+	6.73403i	−0.171655	+	0.297315i
$514$		0			0
$515$	−13.8917	+	8.02040i	−0.612143	+	0.353421i
$516$		0			0
$517$			60.4557i			2.65884i
$518$		0			0
$519$		−	0.0472942i		−	0.00207598i
$520$		0			0
$521$	14.6470	−	8.45646i	0.641698	−	0.370484i	−0.143570	−	0.989640i	$-0.545858\pi$
$521$	14.6470	−	8.45646i	0.641698	−	0.370484i	0.785268	+	0.619156i	$0.212525\pi$
$522$		0			0
$523$	0.921114	−	1.59542i	0.0402775	−	0.0697626i	−0.845184	−	0.534476i	$-0.820509\pi$
$523$	0.921114	−	1.59542i	0.0402775	−	0.0697626i	0.885461	+	0.464713i	$0.153842\pi$
$524$		0			0
$525$	−2.06006	−	1.66017i	−0.0899082	−	0.0724558i
$526$		0			0
$527$	14.8893	+	8.59633i	0.648587	+	0.374462i
$528$		0			0
$529$	−5.38814	−	9.33254i	−0.234267	−	0.405763i
$530$		0			0
$531$	1.74071			0.0755402
$532$		0			0
$533$	−10.8665			−0.470679
$534$		0			0
$535$	6.13618	+	10.6282i	0.265290	+	0.459496i
$536$		0			0
$537$	0.0149916	+	0.00865543i	0.000646937	+	0.000373509i
$538$		0			0
$539$	43.9941	−	9.56838i	1.89496	−	0.412139i
$540$		0			0
$541$	−14.5908	+	25.2719i	−0.627305	+	1.08652i	0.360785	+	0.932649i	$0.382509\pi$
$541$	−14.5908	+	25.2719i	−0.627305	+	1.08652i	−0.988090	+	0.153876i	$0.950824\pi$
$542$		0			0
$543$	11.0288	−	6.36750i	0.473292	−	0.273255i
$544$		0			0
$545$		−	4.40717i		−	0.188783i
$546$		0			0
$547$		−	8.27812i		−	0.353947i	−0.984216	−	0.176974i	$-0.943369\pi$
$547$		−	8.27812i		−	0.353947i	0.984216	−	0.176974i	$-0.0566307\pi$
$548$		0			0
$549$	−8.62835	+	4.98158i	−0.368249	+	0.212609i
$550$		0			0
$551$	−37.9489	+	65.7295i	−1.61668	+	2.80017i
$552$		0			0
$553$	−4.77623	+	5.92669i	−0.203106	+	0.252028i
$554$		0			0
$555$	8.08846	+	4.66988i	0.343336	+	0.198225i
$556$		0			0
$557$	−3.00849	−	5.21086i	−0.127474	−	0.220791i	0.795223	−	0.606317i	$-0.207354\pi$
$557$	−3.00849	−	5.21086i	−0.127474	−	0.220791i	−0.922697	+	0.385525i	$0.874020\pi$
$558$		0			0
$559$	−0.199549			−0.00844002
$560$		0			0
$561$	29.0965			1.22845
$562$		0			0
$563$	−17.8362	−	30.8931i	−0.751704	−	1.30199i	−0.946996	−	0.321245i	$-0.895899\pi$
$563$	−17.8362	−	30.8931i	−0.751704	−	1.30199i	0.195292	−	0.980745i	$-0.437435\pi$
$564$		0			0
$565$	−12.4359	−	7.17986i	−0.523181	−	0.302059i
$566$		0			0
$567$	−2.46778	+	0.953976i	−0.103637	+	0.0400632i
$568$		0			0
$569$	15.9914	−	27.6979i	0.670394	−	1.16116i	−0.307398	−	0.951581i	$-0.599458\pi$
$569$	15.9914	−	27.6979i	0.670394	−	1.16116i	0.977792	−	0.209576i	$-0.0672083\pi$
$570$		0			0
$571$	−0.773374	+	0.446508i	−0.0323647	+	0.0186858i	−0.516095	−	0.856531i	$-0.672615\pi$
$571$	−0.773374	+	0.446508i	−0.0323647	+	0.0186858i	0.483730	+	0.875217i	$0.339282\pi$
$572$		0			0
$573$		−	21.0650i		−	0.880003i
$574$		0			0
$575$			3.49624i			0.145803i
$576$		0			0
$577$	33.8200	−	19.5260i	1.40795	−	0.812878i	0.412756	−	0.910841i	$-0.364566\pi$
$577$	33.8200	−	19.5260i	1.40795	−	0.812878i	0.995190	+	0.0979632i	$0.0312327\pi$
$578$		0			0
$579$	−6.41058	+	11.1035i	−0.266415	+	0.461444i
$580$		0			0
$581$	2.37108	−	15.2024i	0.0983690	−	0.630703i
$582$		0			0
$583$	32.7027	+	18.8809i	1.35441	+	0.781967i
$584$		0			0
$585$	−0.694031	−	1.20210i	−0.0286947	−	0.0497006i
$586$		0			0
$587$	38.1746			1.57563			0.787817	−	0.615909i	$-0.211211\pi$
$587$	38.1746			1.57563			0.787817	+	0.615909i	$0.211211\pi$
$588$		0			0
$589$	−29.5515			−1.21765
$590$		0			0
$591$	−4.96902	−	8.60659i	−0.204398	−	0.354028i
$592$		0			0
$593$	7.69309	+	4.44160i	0.315917	+	0.182395i	0.649571	−	0.760301i	$-0.274948\pi$
$593$	7.69309	+	4.44160i	0.315917	+	0.182395i	−0.333654	+	0.942696i	$0.608282\pi$
$594$		0			0
$595$	1.84447	−	11.8260i	0.0756159	−	0.484819i
$596$		0			0
$597$	−4.22790	+	7.32293i	−0.173036	+	0.299708i
$598$		0			0
$599$	33.2013	−	19.1688i	1.35657	−	0.783215i	0.367409	−	0.930059i	$-0.380245\pi$
$599$	33.2013	−	19.1688i	1.35657	−	0.783215i	0.989160	+	0.146844i	$0.0469115\pi$
$600$		0			0
$601$			18.4807i			0.753845i	0.926245	+	0.376922i	$0.123018\pi$
$601$			18.4807i			0.753845i	−0.926245	+	0.376922i	$0.876982\pi$
$602$		0			0
$603$			4.85918i			0.197881i
$604$		0			0
$605$	26.2995	−	15.1840i	1.06923	−	0.617318i
$606$		0			0
$607$	−20.1917	+	34.9731i	−0.819556	+	1.41951i	0.0864536	+	0.996256i	$0.472447\pi$
$607$	−20.1917	+	34.9731i	−0.819556	+	1.41951i	−0.906010	+	0.423257i	$0.860887\pi$
$608$		0			0
$609$	−24.0875	+	9.31157i	−0.976074	+	0.377324i
$610$		0			0
$611$	11.2991	+	6.52355i	0.457113	+	0.263914i
$612$		0			0
$613$	−7.43842	−	12.8837i	−0.300435	−	0.520368i	0.675800	−	0.737085i	$-0.263798\pi$
$613$	−7.43842	−	12.8837i	−0.300435	−	0.520368i	−0.976234	+	0.216717i	$0.930465\pi$
$614$		0			0
$615$	7.82852			0.315676
$616$		0			0
$617$	13.6805			0.550755			0.275377	−	0.961336i	$-0.411197\pi$
$617$	13.6805			0.550755			0.275377	+	0.961336i	$0.411197\pi$
$618$		0			0
$619$	−11.3724	−	19.6975i	−0.457094	−	0.791710i	0.541712	−	0.840564i	$-0.317776\pi$
$619$	−11.3724	−	19.6975i	−0.457094	−	0.791710i	−0.998806	+	0.0488543i	$0.984443\pi$
$620$		0			0
$621$	3.02783	+	1.74812i	0.121503	+	0.0701497i
$622$		0			0
$623$	1.97201	−	2.44701i	0.0790069	−	0.0980373i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−43.3119	+	25.0062i	−1.72971	+	0.998649i
$628$		0			0
$629$			42.2516i			1.68468i
$630$		0			0
$631$			16.1342i			0.642293i	0.947030	+	0.321146i	$0.104068\pi$
$631$			16.1342i			0.642293i	−0.947030	+	0.321146i	$0.895932\pi$
$632$		0			0
$633$	−2.26285	+	1.30646i	−0.0899403	+	0.0519271i
$634$		0			0
$635$	−10.0735	+	17.4479i	−0.399757	+	0.692399i
$636$		0			0
$637$	2.95892	−	9.25495i	0.117237	−	0.366694i
$638$		0			0
$639$	1.71058	+	0.987606i	0.0676697	+	0.0390691i
$640$		0			0
$641$	−6.99921	−	12.1230i	−0.276452	−	0.478829i	0.694048	−	0.719928i	$-0.255825\pi$
$641$	−6.99921	−	12.1230i	−0.276452	−	0.478829i	−0.970500	+	0.241099i	$0.922492\pi$
$642$		0			0
$643$	−16.5420			−0.652354			−0.326177	−	0.945309i	$-0.605761\pi$
$643$	−16.5420			−0.652354			−0.326177	+	0.945309i	$0.605761\pi$
$644$		0			0
$645$	0.143761			0.00566057
$646$		0			0
$647$	−5.85475	−	10.1407i	−0.230174	−	0.398673i	0.727685	−	0.685911i	$-0.240596\pi$
$647$	−5.85475	−	10.1407i	−0.230174	−	0.398673i	−0.957859	+	0.287238i	$0.907263\pi$
$648$		0			0
$649$	9.69591	+	5.59794i	0.380598	+	0.219738i
$650$		0			0
$651$	−7.82915	−	6.30940i	−0.306848	−	0.247285i
$652$		0			0
$653$	12.6616	−	21.9305i	0.495486	−	0.858207i	−0.504500	−	0.863412i	$-0.668323\pi$
$653$	12.6616	−	21.9305i	0.495486	−	0.858207i	0.999986	+	0.00520419i	$0.00165655\pi$
$654$		0			0
$655$	3.05567	−	1.76419i	0.119395	−	0.0689327i
$656$		0			0
$657$			6.39100i			0.249337i
$658$		0			0
$659$		−	25.0183i		−	0.974574i	−0.873242	−	0.487287i	$-0.837987\pi$
$659$		−	25.0183i		−	0.974574i	0.873242	−	0.487287i	$-0.162013\pi$
$660$		0			0
$661$	9.42113	−	5.43929i	0.366439	−	0.211564i	−0.305462	−	0.952204i	$-0.598811\pi$
$661$	9.42113	−	5.43929i	0.366439	−	0.211564i	0.671902	+	0.740640i	$0.265478\pi$
$662$		0			0
$663$	3.13969	−	5.43811i	0.121936	−	0.211199i
$664$		0			0
$665$	7.41792	+	19.1889i	0.287654	+	0.744114i
$666$		0			0
$667$	29.5541	+	17.0631i	1.14434	+	0.660684i
$668$		0			0
$669$	−0.775663	−	1.34349i	−0.0299889	−	0.0519423i
$670$		0			0
$671$	−64.0810			−2.47382
$672$		0			0
$673$	−21.9568			−0.846371			−0.423186	−	0.906043i	$-0.639088\pi$
$673$	−21.9568			−0.846371			−0.423186	+	0.906043i	$0.639088\pi$
$674$		0			0
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$		0			0
$677$	11.1776	+	6.45337i	0.429589	+	0.248023i	0.699171	−	0.714954i	$-0.253552\pi$
$677$	11.1776	+	6.45337i	0.429589	+	0.248023i	−0.269583	+	0.962977i	$0.586886\pi$
$678$		0			0
$679$	32.3227	+	5.04129i	1.24043	+	0.193467i
$680$		0			0
$681$	−10.3235	+	17.8808i	−0.395598	+	0.685196i
$682$		0			0
$683$	24.8995	−	14.3757i	0.952753	−	0.550072i	0.0588179	−	0.998269i	$-0.481267\pi$
$683$	24.8995	−	14.3757i	0.952753	−	0.550072i	0.893935	+	0.448197i	$0.147934\pi$
$684$		0			0
$685$			13.4351i			0.513328i
$686$		0			0
$687$			24.0298i			0.916793i
$688$		0			0
$689$	7.05765	−	4.07474i	0.268875	−	0.155235i
$690$		0			0
$691$	13.2400	−	22.9323i	0.503672	−	0.872386i	−0.496319	−	0.868141i	$-0.665315\pi$
$691$	13.2400	−	22.9323i	0.503672	−	0.872386i	0.999991	−	0.00424581i	$-0.00135149\pi$
$692$		0			0
$693$	−16.8137	−	2.62238i	−0.638698	−	0.0996161i
$694$		0			0
$695$	1.75298	+	1.01208i	0.0664942	+	0.0383905i
$696$		0			0
$697$	17.7075	+	30.6703i	0.670720	+	1.16172i
$698$		0			0
$699$	−23.6893			−0.896012
$700$		0			0
$701$	−14.1098			−0.532918			−0.266459	−	0.963846i	$-0.585854\pi$
$701$	−14.1098			−0.532918			−0.266459	+	0.963846i	$0.585854\pi$
$702$		0			0
$703$	−36.3120	−	62.8942i	−1.36953	−	2.37210i
$704$		0			0
$705$	−8.14020	−	4.69975i	−0.306578	−	0.177003i
$706$		0			0
$707$	4.22518	+	10.9298i	0.158904	+	0.411059i
$708$		0			0
$709$	20.9840	−	36.3453i	0.788070	−	1.36498i	−0.139077	−	0.990282i	$-0.544414\pi$
$709$	20.9840	−	36.3453i	0.788070	−	1.36498i	0.927148	−	0.374696i	$-0.122253\pi$
$710$		0			0
$711$	2.49151	−	1.43848i	0.0934391	−	0.0539471i
$712$		0			0
$713$			13.2873i			0.497613i
$714$		0			0
$715$		−	8.92774i		−	0.333879i
$716$		0			0
$717$	−19.3513	+	11.1725i	−0.722689	+	0.417245i
$718$		0			0
$719$	−6.06491	+	10.5047i	−0.226183	+	0.391761i	−0.956674	−	0.291162i	$-0.905958\pi$
$719$	−6.06491	+	10.5047i	−0.226183	+	0.391761i	0.730491	+	0.682923i	$0.239291\pi$
$720$		0			0
$721$	33.0450	+	26.6305i	1.23066	+	0.991770i
$722$		0			0
$723$	22.1999	+	12.8171i	0.825623	+	0.476674i
$724$		0			0
$725$	4.88040	+	8.45310i	0.181253	+	0.313940i
$726$		0			0
$727$	−35.2582			−1.30766			−0.653828	−	0.756643i	$-0.726838\pi$
$727$	−35.2582			−1.30766			−0.653828	+	0.756643i	$0.726838\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	0.325176	+	0.563221i	0.0120271	+	0.0208315i
$732$		0			0
$733$	41.3079	+	23.8491i	1.52574	+	0.880887i	0.999534	+	0.0305304i	$0.00971964\pi$
$733$	41.3079	+	23.8491i	1.52574	+	0.880887i	0.526207	+	0.850357i	$0.323614\pi$
$734$		0			0
$735$	−2.13169	+	6.66753i	−0.0786285	+	0.245935i
$736$		0			0
$737$	−15.6266	+	27.0661i	−0.575614	+	0.996993i
$738$		0			0
$739$	6.91840	−	3.99434i	0.254497	−	0.146934i	−0.367324	−	0.930093i	$-0.619726\pi$
$739$	6.91840	−	3.99434i	0.254497	−	0.146934i	0.621822	+	0.783159i	$0.286393\pi$
$740$		0			0
$741$			10.7933i			0.396501i
$742$		0			0
$743$		−	9.51187i		−	0.348957i	−0.984661	−	0.174478i	$-0.944176\pi$
$743$		−	9.51187i		−	0.348957i	0.984661	−	0.174478i	$-0.0558239\pi$
$744$		0			0
$745$	−9.59553	+	5.53998i	−0.351553	+	0.202969i
$746$		0			0
$747$	−2.90772	+	5.03632i	−0.106388	+	0.184269i
$748$		0			0
$749$	20.3742	−	25.2818i	0.744458	−	0.923776i
$750$		0			0
$751$	−18.8028	−	10.8558i	−0.686125	−	0.396134i	0.116034	−	0.993245i	$-0.462982\pi$
$751$	−18.8028	−	10.8558i	−0.686125	−	0.396134i	−0.802159	+	0.597111i	$0.796315\pi$
$752$		0			0
$753$	12.0021	+	20.7882i	0.437379	+	0.757563i
$754$		0			0
$755$	−3.69159			−0.134351
$756$		0			0
$757$	−0.255827			−0.00929819			−0.00464909	−	0.999989i	$-0.501480\pi$
$757$	−0.255827			−0.00929819			−0.00464909	+	0.999989i	$0.501480\pi$
$758$		0			0
$759$	11.2436	+	19.4744i	0.408116	+	0.706877i
$760$		0			0
$761$	−8.11750	−	4.68664i	−0.294259	−	0.169891i	0.345602	−	0.938381i	$-0.387675\pi$
$761$	−8.11750	−	4.68664i	−0.294259	−	0.169891i	−0.639861	+	0.768491i	$0.721008\pi$
$762$		0			0
$763$	−10.8759	+	4.20434i	−0.393735	+	0.152207i
$764$		0			0
$765$	−2.26192	+	3.91777i	−0.0817800	+	0.141647i
$766$		0			0
$767$	2.09250	−	1.20810i	0.0755558	−	0.0436221i
$768$		0			0
$769$			36.8290i			1.32809i	0.747693	+	0.664044i	$0.231161\pi$
$769$			36.8290i			1.32809i	−0.747693	+	0.664044i	$0.768839\pi$
$770$		0			0
$771$		−	2.82180i		−	0.101625i
$772$		0			0
$773$	8.39905	−	4.84920i	0.302093	−	0.174413i	−0.341290	−	0.939958i	$-0.610864\pi$
$773$	8.39905	−	4.84920i	0.302093	−	0.174413i	0.643383	+	0.765545i	$0.277530\pi$
$774$		0			0
$775$	−1.90023	+	3.29129i	−0.0682581	+	0.118227i
$776$		0			0
$777$	3.80802	−	24.4155i	0.136612	−	0.875901i
$778$		0			0
$779$	−52.7175	−	30.4364i	−1.88880	−	1.09050i
$780$		0			0
$781$	6.35208	+	11.0021i	0.227295	+	0.393687i
$782$		0			0
$783$	9.76080			0.348822
$784$		0			0
$785$	−7.63181			−0.272391
$786$		0			0
$787$	19.7098	+	34.1383i	0.702577	+	1.21690i	0.967559	+	0.252646i	$0.0813007\pi$
$787$	19.7098	+	34.1383i	0.702577	+	1.21690i	−0.264982	+	0.964253i	$0.585366\pi$
$788$		0			0
$789$	−6.51271	−	3.76012i	−0.231859	−	0.133864i
$790$		0			0
$791$	−5.85476	+	37.5384i	−0.208171	+	1.33471i
$792$		0			0
$793$	−6.91475	+	11.9767i	−0.245550	+	0.425305i
$794$		0			0
$795$	−5.08453	+	2.93556i	−0.180330	+	0.104113i
$796$		0			0
$797$		−	24.9449i		−	0.883593i	−0.897115	−	0.441797i	$-0.854341\pi$
$797$		−	24.9449i		−	0.883593i	0.897115	−	0.441797i	$-0.145659\pi$
$798$		0			0
$799$		−	42.5219i		−	1.50432i
$800$		0			0
$801$	−1.02870	+	0.593918i	−0.0363472	+	0.0209851i
$802$		0			0
$803$	−20.5528	+	35.5985i	−0.725293	+	1.25624i
$804$		0			0
$805$	8.62795	−	3.33533i	0.304095	−	0.117555i
$806$		0			0
$807$	15.7270	+	9.08000i	0.553617	+	0.319631i
$808$		0			0
$809$	11.0968	+	19.2201i	0.390141	+	0.675744i	0.992468	−	0.122506i	$-0.0390929\pi$
$809$	11.0968	+	19.2201i	0.390141	+	0.675744i	−0.602327	+	0.798250i	$0.705760\pi$
$810$		0			0
$811$	25.9516			0.911283			0.455642	−	0.890163i	$-0.349410\pi$
$811$	25.9516			0.911283			0.455642	+	0.890163i	$0.349410\pi$
$812$		0			0
$813$	17.3774			0.609453
$814$		0			0
$815$	7.54749	+	13.0726i	0.264377	+	0.457915i
$816$		0			0
$817$	−0.968089	−	0.558926i	−0.0338691	−	0.0195544i
$818$		0			0
$819$	−2.30442	+	2.85949i	−0.0805230	+	0.0999186i
$820$		0			0
$821$	−25.0678	+	43.4187i	−0.874871	+	1.51532i	−0.0179718	+	0.999838i	$0.505721\pi$
$821$	−25.0678	+	43.4187i	−0.874871	+	1.51532i	−0.856900	+	0.515483i	$0.827612\pi$
$822$		0			0
$823$	−14.5241	+	8.38549i	−0.506278	+	0.292300i	−0.731302	−	0.682053i	$-0.761087\pi$
$823$	−14.5241	+	8.38549i	−0.506278	+	0.292300i	0.225024	+	0.974353i	$0.427754\pi$
$824$		0			0
$825$			6.43180i			0.223927i
$826$		0			0
$827$			17.7882i			0.618555i	0.950972	+	0.309278i	$0.100087\pi$
$827$			17.7882i			0.618555i	−0.950972	+	0.309278i	$0.899913\pi$
$828$		0			0
$829$	−10.8454	+	6.26160i	−0.376676	+	0.217474i	−0.676371	−	0.736561i	$-0.736448\pi$
$829$	−10.8454	+	6.26160i	−0.376676	+	0.217474i	0.299695	+	0.954035i	$0.403115\pi$
$830$		0			0
$831$	5.26098	−	9.11229i	0.182501	−	0.316102i
$832$		0			0
$833$	−30.9435	+	6.72998i	−1.07213	+	0.233180i
$834$		0			0
$835$	−5.27151	−	3.04351i	−0.182428	−	0.105325i
$836$		0			0
$837$	1.90023	+	3.29129i	0.0656814	+	0.113764i
$838$		0			0
$839$	13.2933			0.458935			0.229467	−	0.973316i	$-0.426302\pi$
$839$	13.2933			0.458935			0.229467	+	0.973316i	$0.426302\pi$
$840$		0			0
$841$	66.2731			2.28528
$842$		0			0
$843$	−9.76012	−	16.9050i	−0.336156	−	0.582240i
$844$		0			0
$845$	9.58974	+	5.53664i	0.329897	+	0.190466i
$846$		0			0
$847$	−62.5599	−	50.4161i	−2.14958	−	1.73232i
$848$		0			0
$849$	−1.59612	+	2.76456i	−0.0547786	+	0.0948793i
$850$		0			0
$851$	−28.2792	+	16.3270i	−0.969399	+	0.559683i
$852$		0			0
$853$		−	29.0157i		−	0.993480i	−0.867899	−	0.496740i	$-0.834530\pi$
$853$		−	29.0157i		−	0.993480i	0.867899	−	0.496740i	$-0.165470\pi$
$854$		0			0
$855$		−	7.77579i		−	0.265926i
$856$		0			0
$857$	4.84421	−	2.79680i	0.165475	−	0.0955370i	−0.414975	−	0.909833i	$-0.636210\pi$
$857$	4.84421	−	2.79680i	0.165475	−	0.0955370i	0.580450	+	0.814296i	$0.302877\pi$
$858$		0			0
$859$	16.7480	−	29.0083i	0.571433	−	0.989751i	−0.424986	−	0.905200i	$-0.639721\pi$
$859$	16.7480	−	29.0083i	0.571433	−	0.989751i	0.996419	−	0.0845513i	$-0.0269457\pi$
$860$		0			0
$861$	−7.46822	−	19.3190i	−0.254516	−	0.658391i
$862$		0			0
$863$	14.7957	+	8.54228i	0.503650	+	0.290783i	0.730220	−	0.683212i	$-0.239418\pi$
$863$	14.7957	+	8.54228i	0.503650	+	0.290783i	−0.226570	+	0.973995i	$0.572751\pi$
$864$		0			0
$865$	0.0236471	+	0.0409579i	0.000804025	+	0.00139261i
$866$		0			0
$867$	−3.46519			−0.117684
$868$		0			0
$869$	18.5040			0.627705
$870$		0			0
$871$	3.37242	+	5.84121i	0.114270	+	0.197922i
$872$		0			0
$873$	−10.7080	−	6.18227i	−0.362411	−	0.209238i
$874$		0			0
$875$	2.61415	+	0.407721i	0.0883743	+	0.0137835i
$876$		0			0
$877$	11.7758	−	20.3963i	0.397640	−	0.688733i	−0.595794	−	0.803137i	$-0.703163\pi$
$877$	11.7758	−	20.3963i	0.397640	−	0.688733i	0.993434	+	0.114404i	$0.0364959\pi$
$878$		0			0
$879$	−12.1266	+	7.00130i	−0.409020	+	0.236148i
$880$		0			0
$881$		−	54.8901i		−	1.84929i	−0.380825	−	0.924647i	$-0.624360\pi$
$881$		−	54.8901i		−	1.84929i	0.380825	−	0.924647i	$-0.375640\pi$
$882$		0			0
$883$			22.4675i			0.756092i	0.925787	+	0.378046i	$0.123404\pi$
$883$			22.4675i			0.756092i	−0.925787	+	0.378046i	$0.876596\pi$
$884$		0			0
$885$	−1.50750	+	0.870353i	−0.0506739	+	0.0292566i
$886$		0			0
$887$	5.53075	−	9.57954i	0.185704	−	0.321650i	−0.758109	−	0.652128i	$-0.773877\pi$
$887$	5.53075	−	9.57954i	0.185704	−	0.321650i	0.943814	+	0.330478i	$0.107210\pi$
$888$		0			0
$889$	52.6675	+	8.21440i	1.76641	+	0.275502i
$890$		0			0
$891$	5.57010	+	3.21590i	0.186605	+	0.107737i
$892$		0			0
$893$	36.5442	+	63.2965i	1.22291	+	2.11814i
$894$		0			0
$895$	−0.0173109			−0.000578638
$896$		0			0
$897$	4.85300			0.162037
$898$		0			0
$899$	18.5477	+	32.1256i	0.618601	+	1.07145i
$900$		0			0
$901$	−23.0016	−	13.2800i	−0.766296	−	0.442421i
$902$		0			0
$903$	−0.137144	−	0.354769i	−0.00456388	−	0.0118060i
$904$		0			0
$905$	−6.36750	+	11.0288i	−0.211663	+	0.366611i
$906$		0			0
$907$	40.5349	−	23.4029i	1.34594	−	0.777079i	0.358269	−	0.933618i	$-0.383367\pi$
$907$	40.5349	−	23.4029i	1.34594	−	0.777079i	0.987672	+	0.156539i	$0.0500338\pi$
$908$		0			0
$909$		−	4.42902i		−	0.146901i
$910$		0			0
$911$		−	23.9321i		−	0.792906i	−0.918055	−	0.396453i	$-0.870241\pi$
$911$		−	23.9321i		−	0.792906i	0.918055	−	0.396453i	$-0.129759\pi$
$912$		0			0
$913$	−32.3926	+	18.7019i	−1.07204	+	0.618942i
$914$		0			0
$915$	4.98158	−	8.62835i	0.164686	−	0.285244i
$916$		0			0
$917$	−7.26867	−	5.85772i	−0.240033	−	0.193439i
$918$		0			0
$919$	−17.4110	−	10.0522i	−0.574336	−	0.331593i	0.184543	−	0.982824i	$-0.440919\pi$
$919$	−17.4110	−	10.0522i	−0.574336	−	0.331593i	−0.758879	+	0.651231i	$0.774253\pi$
$920$		0			0
$921$	12.6083	+	21.8382i	0.415457	+	0.719593i
$922$		0			0
$923$	2.74172			0.0902448
$924$		0			0
$925$	−9.33975			−0.307089
$926$		0			0
$927$	−8.02040	−	13.8917i	−0.263425	−	0.456265i
$928$		0			0
$929$	−5.21975	−	3.01362i	−0.171254	−	0.0988737i	0.411923	−	0.911219i	$-0.364857\pi$
$929$	−5.21975	−	3.01362i	−0.171254	−	0.0988737i	−0.583177	+	0.812345i	$0.698191\pi$
$930$		0			0
$931$	40.2775	−	36.6115i	1.32004	−	1.19989i
$932$		0			0
$933$	−5.19981	+	9.00634i	−0.170234	+	0.294854i
$934$		0			0
$935$	−25.1983	+	14.5482i	−0.824072	+	0.475778i
$936$		0			0
$937$		−	0.141626i		−	0.00462671i	−0.999997	−	0.00231336i	$-0.999264\pi$
$937$		−	0.141626i		−	0.00462671i	0.999997	−	0.00231336i	$-0.000736365\pi$
$938$		0			0
$939$			30.5980i			0.998527i
$940$		0			0
$941$	−4.35563	+	2.51472i	−0.141989	+	0.0819777i	−0.569312	−	0.822122i	$-0.692790\pi$
$941$	−4.35563	+	2.51472i	−0.141989	+	0.0819777i	0.427322	+	0.904099i	$0.359457\pi$
$942$		0			0
$943$	−13.6852	+	23.7035i	−0.445651	+	0.771891i
$944$		0			0
$945$	1.66017	−	2.06006i	0.0540053	−	0.0670137i
$946$		0			0
$947$	12.7646	+	7.36967i	0.414795	+	0.239482i	0.692848	−	0.721084i	$-0.256356\pi$
$947$	12.7646	+	7.36967i	0.414795	+	0.239482i	−0.278053	+	0.960566i	$0.589689\pi$
$948$		0			0
$949$	4.43556	+	7.68261i	0.143984	+	0.249388i
$950$		0			0
$951$	19.7572			0.640672
$952$		0			0
$953$	49.9423			1.61779			0.808895	−	0.587953i	$-0.200066\pi$
$953$	49.9423			1.61779			0.808895	+	0.587953i	$0.200066\pi$
$954$		0			0
$955$	10.5325	+	18.2428i	0.340824	+	0.590324i
$956$		0			0
$957$	54.3686	+	31.3897i	1.75749	+	1.01469i
$958$		0			0
$959$	33.1548	−	12.8167i	1.07062	−	0.413874i
$960$		0			0
$961$	8.27829	−	14.3384i	0.267041	−	0.462529i
$962$		0			0
$963$	−10.6282	+	6.13618i	−0.342488	+	0.197736i
$964$		0			0
$965$		−	12.8212i		−	0.412728i
$966$		0			0
$967$		−	13.5753i		−	0.436551i	−0.975887	−	0.218276i	$-0.929957\pi$
$967$		−	13.5753i		−	0.436551i	0.975887	−	0.218276i	$-0.0700432\pi$
$968$		0			0
$969$	30.4637	−	17.5882i	0.978636	−	0.565015i
$970$		0			0
$971$	−12.1793	+	21.0952i	−0.390852	+	0.676976i	−0.992562	−	0.121739i	$-0.961153\pi$
$971$	−12.1793	+	21.0952i	−0.390852	+	0.676976i	0.601710	+	0.798715i	$0.294486\pi$
$972$		0			0
$973$	0.825295	−	5.29146i	0.0264577	−	0.169636i
$974$		0			0
$975$	1.20210	+	0.694031i	0.0384979	+	0.0222268i
$976$		0			0
$977$	22.6843	+	39.2903i	0.725735	+	1.25701i	0.958671	+	0.284517i	$0.0918332\pi$
$977$	22.6843	+	39.2903i	0.725735	+	1.25701i	−0.232936	+	0.972492i	$0.574833\pi$
$978$		0			0
$979$	−7.63992			−0.244173
$980$		0			0
$981$	4.40717			0.140710
$982$		0			0
$983$	−17.9519	−	31.0936i	−0.572577	−	0.991733i	−0.996300	−	0.0859411i	$-0.972610\pi$
$983$	−17.9519	−	31.0936i	−0.572577	−	0.991733i	0.423723	−	0.905792i	$-0.360723\pi$
$984$		0			0
$985$	8.60659	+	4.96902i	0.274229	+	0.158326i
$986$		0			0
$987$	−3.83238	+	24.5717i	−0.121986	+	0.782125i
$988$		0			0
$989$	−0.251311	+	0.435284i	−0.00799123	+	0.0138412i
$990$		0			0
$991$	51.6371	−	29.8127i	1.64031	−	0.947031i	0.659583	−	0.751632i	$-0.270733\pi$
$991$	51.6371	−	29.8127i	1.64031	−	0.947031i	0.980724	−	0.195400i	$-0.0626004\pi$
$992$		0			0
$993$		−	32.1028i		−	1.01875i
$994$		0			0
$995$		−	8.45579i		−	0.268067i
$996$		0			0
$997$	−35.1476	+	20.2925i	−1.11314	+	0.642670i	−0.939640	−	0.342165i	$-0.888840\pi$
$997$	−35.1476	+	20.2925i	−1.11314	+	0.642670i	−0.173497	+	0.984834i	$0.555507\pi$
$998$		0			0
$999$	−4.66988	+	8.08846i	−0.147748	+	0.255908i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.dx.f.271.5	yes	12
4.3	odd	2		1680.2.dx.h.271.5	yes	12
7.3	odd	6		1680.2.dx.h.31.5	yes	12
28.3	even	6	inner	1680.2.dx.f.31.5	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1680.2.dx.f.31.5	✓	12	28.3	even	6	inner
1680.2.dx.f.271.5	yes	12	1.1	even	1	trivial
1680.2.dx.h.31.5	yes	12	7.3	odd	6
1680.2.dx.h.271.5	yes	12	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.dx (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +(0.866025 + 0.500000i) q^{5} +(0.407721 - 2.61415i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-5.57010 + 3.21590i) q^{11} +1.38806i q^{13} -1.00000i q^{15} +(3.91777 - 2.26192i) q^{17} +(-3.88789 + 6.73403i) q^{19} +(-2.46778 + 0.953976i) q^{21} +(3.02783 + 1.74812i) q^{23} +(0.500000 + 0.866025i) q^{25} +1.00000 q^{27} +9.76080 q^{29} +(1.90023 + 3.29129i) q^{31} +(5.57010 + 3.21590i) q^{33} +(1.66017 - 2.06006i) q^{35} +(-4.66988 + 8.08846i) q^{37} +(1.20210 - 0.694031i) q^{39} +7.82852i q^{41} +0.143761i q^{43} +(-0.866025 + 0.500000i) q^{45} +(4.69975 - 8.14020i) q^{47} +(-6.66753 - 2.13169i) q^{49} +(-3.91777 - 2.26192i) q^{51} +(-2.93556 - 5.08453i) q^{53} -6.43180 q^{55} +7.77579 q^{57} +(-0.870353 - 1.50750i) q^{59} +(8.62835 + 4.98158i) q^{61} +(2.06006 + 1.66017i) q^{63} +(-0.694031 + 1.20210i) q^{65} +(4.20817 - 2.42959i) q^{67} -3.49624i q^{69} -1.97521i q^{71} +(5.53477 - 3.19550i) q^{73} +(0.500000 - 0.866025i) q^{75} +(6.13578 + 15.8723i) q^{77} +(-2.49151 - 1.43848i) q^{79} +(-0.500000 - 0.866025i) q^{81} +5.81544 q^{83} +4.52385 q^{85} +(-4.88040 - 8.45310i) q^{87} +(1.02870 + 0.593918i) q^{89} +(3.62860 + 0.565943i) q^{91} +(1.90023 - 3.29129i) q^{93} +(-6.73403 + 3.88789i) q^{95} +12.3645i q^{97} -6.43180i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 2 q^{7} - 6 q^{9} - 10 q^{19} - 4 q^{21} - 12 q^{23} + 6 q^{25} + 12 q^{27} + 8 q^{29} + 2 q^{31} + 4 q^{35} - 10 q^{37} - 6 q^{39} + 2 q^{49} + 16 q^{53} + 20 q^{57} + 24 q^{61} + 2 q^{63}+ \cdots - 24 q^{95}+O(q^{100}) \) 12 * q - 6 * q^3 + 2 * q^7 - 6 * q^9 - 10 * q^19 - 4 * q^21 - 12 * q^23 + 6 * q^25 + 12 * q^27 + 8 * q^29 + 2 * q^31 + 4 * q^35 - 10 * q^37 - 6 * q^39 + 2 * q^49 + 16 * q^53 + 20 * q^57 + 24 * q^61 + 2 * q^63 + 4 * q^65 + 6 * q^67 + 30 * q^73 + 6 * q^75 + 36 * q^77 - 42 * q^79 - 6 * q^81 + 64 * q^83 - 8 * q^85 - 4 * q^87 - 14 * q^91 + 2 * q^93 - 24 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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