LMFDB - Embedded newform 912.2.bn.k.65.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(65,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("912.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bn (of order $6$, degree $2$, not 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.2
Root			$1.68614 + 0.396143i$ of defining polynomial
Character	$\chi$	$=$	912.65
Dual form			912.2.bn.k.449.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.68614 - 0.396143i) q^{3} +(-0.813859 - 0.469882i) q^{5} -3.37228 q^{7} +(2.68614 - 1.33591i) q^{9} +O(q^{10})$	\(q+(1.68614 - 0.396143i) q^{3} +(-0.813859 - 0.469882i) q^{5} -3.37228 q^{7} +(2.68614 - 1.33591i) q^{9} -5.04868i q^{11} +(1.50000 - 0.866025i) q^{13} +(-1.55842 - 0.469882i) q^{15} +(5.18614 + 2.99422i) q^{17} +(-4.00000 - 1.73205i) q^{19} +(-5.68614 + 1.33591i) q^{21} +(-0.813859 + 0.469882i) q^{23} +(-2.05842 - 3.56529i) q^{25} +(4.00000 - 3.31662i) q^{27} +(-5.18614 - 8.98266i) q^{29} -2.37686i q^{31} +(-2.00000 - 8.51278i) q^{33} +(2.74456 + 1.58457i) q^{35} +5.84096i q^{37} +(2.18614 - 2.05446i) q^{39} +(3.55842 - 6.16337i) q^{41} +(0.872281 - 1.51084i) q^{43} +(-2.81386 - 0.174928i) q^{45} +(5.18614 - 2.99422i) q^{47} +4.37228 q^{49} +(9.93070 + 2.99422i) q^{51} +(0.813859 + 1.40965i) q^{53} +(-2.37228 + 4.10891i) q^{55} +(-7.43070 - 1.33591i) q^{57} +(-0.813859 + 1.40965i) q^{59} +(-0.872281 - 1.51084i) q^{61} +(-9.05842 + 4.50506i) q^{63} -1.62772 q^{65} +(1.50000 - 0.866025i) q^{67} +(-1.18614 + 1.11469i) q^{69} +(-3.55842 + 6.16337i) q^{71} +(-6.87228 + 11.9031i) q^{73} +(-4.88316 - 5.19615i) q^{75} +17.0256i q^{77} +(8.61684 + 4.97494i) q^{79} +(5.43070 - 7.17687i) q^{81} +1.87953i q^{83} +(-2.81386 - 4.87375i) q^{85} +(-12.3030 - 13.0916i) q^{87} +(0.813859 + 1.40965i) q^{89} +(-5.05842 + 2.92048i) q^{91} +(-0.941578 - 4.00772i) q^{93} +(2.44158 + 3.28917i) q^{95} +(10.6753 + 6.16337i) q^{97} +(-6.74456 - 13.5615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} - 9 q^{5} - 2 q^{7} + 5 q^{9}+O(q^{10}) $ 4 * q + q^3 - 9 * q^5 - 2 * q^7 + 5 * q^9	$ 4 q + q^{3} - 9 q^{5} - 2 q^{7} + 5 q^{9} + 6 q^{13} + 11 q^{15} + 15 q^{17} - 16 q^{19} - 17 q^{21} - 9 q^{23} + 9 q^{25} + 16 q^{27} - 15 q^{29} - 8 q^{33} - 12 q^{35} + 3 q^{39} - 3 q^{41} - 8 q^{43} - 17 q^{45} + 15 q^{47} + 6 q^{49} + 11 q^{51} + 9 q^{53} + 2 q^{55} - q^{57} - 9 q^{59} + 8 q^{61} - 19 q^{63} - 18 q^{65} + 6 q^{67} + q^{69} + 3 q^{71} - 16 q^{73} - 54 q^{75} - 7 q^{81} - 17 q^{85} - 9 q^{87} + 9 q^{89} - 3 q^{91} - 21 q^{93} + 27 q^{95} - 9 q^{97} - 4 q^{99}+O(q^{100}) $ 4 * q + q^3 - 9 * q^5 - 2 * q^7 + 5 * q^9 + 6 * q^13 + 11 * q^15 + 15 * q^17 - 16 * q^19 - 17 * q^21 - 9 * q^23 + 9 * q^25 + 16 * q^27 - 15 * q^29 - 8 * q^33 - 12 * q^35 + 3 * q^39 - 3 * q^41 - 8 * q^43 - 17 * q^45 + 15 * q^47 + 6 * q^49 + 11 * q^51 + 9 * q^53 + 2 * q^55 - q^57 - 9 * q^59 + 8 * q^61 - 19 * q^63 - 18 * q^65 + 6 * q^67 + q^69 + 3 * q^71 - 16 * q^73 - 54 * q^75 - 7 * q^81 - 17 * q^85 - 9 * q^87 + 9 * q^89 - 3 * q^91 - 21 * q^93 + 27 * q^95 - 9 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$1$

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
$3$	1.68614	−	0.396143i	0.973494	−	0.228714i
$3$	1.68614	−	0.396143i	0.973494	−	0.228714i
$4$		0			0
$5$	−0.813859	−	0.469882i	−0.363969	−	0.210138i	0.306851	−	0.951757i	$-0.400725\pi$
$5$	−0.813859	−	0.469882i	−0.363969	−	0.210138i	−0.670820	+	0.741620i	$0.734058\pi$
$6$		0			0
$7$	−3.37228			−1.27460			−0.637301	−	0.770615i	$-0.719949\pi$
$7$	−3.37228			−1.27460			−0.637301	+	0.770615i	$0.719949\pi$
$8$		0			0
$9$	2.68614	−	1.33591i	0.895380	−	0.445302i
$10$		0			0
$11$		−	5.04868i		−	1.52223i	−0.648615	−	0.761116i	$-0.724652\pi$
$11$		−	5.04868i		−	1.52223i	0.648615	−	0.761116i	$-0.275348\pi$
$12$		0			0
$13$	1.50000	−	0.866025i	0.416025	−	0.240192i	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	1.50000	−	0.866025i	0.416025	−	0.240192i	0.693375	+	0.720577i	$0.256123\pi$
$14$		0			0
$15$	−1.55842	−	0.469882i	−0.402383	−	0.121323i
$16$		0			0
$17$	5.18614	+	2.99422i	1.25782	+	0.726205i	0.972651	−	0.232271i	$-0.0746157\pi$
$17$	5.18614	+	2.99422i	1.25782	+	0.726205i	0.285173	+	0.958476i	$0.407949\pi$
$18$		0			0
$19$	−4.00000	−	1.73205i	−0.917663	−	0.397360i
$19$	−4.00000	−	1.73205i	−0.917663	−	0.397360i
$20$		0			0
$21$	−5.68614	+	1.33591i	−1.24082	+	0.291519i
$22$		0			0
$23$	−0.813859	+	0.469882i	−0.169701	+	0.0979772i	−0.582445	−	0.812870i	$-0.697904\pi$
$23$	−0.813859	+	0.469882i	−0.169701	+	0.0979772i	0.412744	+	0.910847i	$0.364571\pi$
$24$		0			0
$25$	−2.05842	−	3.56529i	−0.411684	−	0.713058i
$26$		0			0
$27$	4.00000	−	3.31662i	0.769800	−	0.638285i
$28$		0			0
$29$	−5.18614	−	8.98266i	−0.963042	−	1.66804i	−0.714786	−	0.699344i	$-0.753476\pi$
$29$	−5.18614	−	8.98266i	−0.963042	−	1.66804i	−0.248256	−	0.968694i	$-0.579858\pi$
$30$		0			0
$31$		−	2.37686i		−	0.426897i	−0.976954	−	0.213448i	$-0.931530\pi$
$31$		−	2.37686i		−	0.426897i	0.976954	−	0.213448i	$-0.0684695\pi$
$32$		0			0
$33$	−2.00000	−	8.51278i	−0.348155	−	1.48188i
$34$		0			0
$35$	2.74456	+	1.58457i	0.463916	+	0.267842i
$36$		0			0
$37$			5.84096i			0.960248i	0.877201	+	0.480124i	$0.159408\pi$
$37$			5.84096i			0.960248i	−0.877201	+	0.480124i	$0.840592\pi$
$38$		0			0
$39$	2.18614	−	2.05446i	0.350063	−	0.328976i
$40$		0			0
$41$	3.55842	−	6.16337i	0.555732	−	0.962556i	−0.442114	−	0.896959i	$-0.645771\pi$
$41$	3.55842	−	6.16337i	0.555732	−	0.962556i	0.997846	−	0.0655975i	$-0.0208953\pi$
$42$		0			0
$43$	0.872281	−	1.51084i	0.133022	−	0.230400i	−0.791818	−	0.610757i	$-0.790865\pi$
$43$	0.872281	−	1.51084i	0.133022	−	0.230400i	0.924840	+	0.380356i	$0.124199\pi$
$44$		0			0
$45$	−2.81386	−	0.174928i	−0.419465	−	0.0260768i
$46$		0			0
$47$	5.18614	−	2.99422i	0.756476	−	0.436752i	−0.0715528	−	0.997437i	$-0.522795\pi$
$47$	5.18614	−	2.99422i	0.756476	−	0.436752i	0.828029	+	0.560685i	$0.189462\pi$
$48$		0			0
$49$	4.37228			0.624612
$50$		0			0
$51$	9.93070	+	2.99422i	1.39058	+	0.419275i
$52$		0			0
$53$	0.813859	+	1.40965i	0.111792	+	0.193630i	0.916493	−	0.400051i	$-0.131008\pi$
$53$	0.813859	+	1.40965i	0.111792	+	0.193630i	−0.804701	+	0.593681i	$0.797674\pi$
$54$		0			0
$55$	−2.37228	+	4.10891i	−0.319878	+	0.554046i
$56$		0			0
$57$	−7.43070	−	1.33591i	−0.984221	−	0.176945i
$58$		0			0
$59$	−0.813859	+	1.40965i	−0.105955	+	0.183520i	−0.914128	−	0.405425i	$-0.867123\pi$
$59$	−0.813859	+	1.40965i	−0.105955	+	0.183520i	0.808173	+	0.588946i	$0.200457\pi$
$60$		0			0
$61$	−0.872281	−	1.51084i	−0.111684	−	0.193443i	0.804765	−	0.593593i	$-0.202291\pi$
$61$	−0.872281	−	1.51084i	−0.111684	−	0.193443i	−0.916449	+	0.400151i	$0.868958\pi$
$62$		0			0
$63$	−9.05842	+	4.50506i	−1.14125	+	0.567584i
$64$		0			0
$65$	−1.62772			−0.201894
$66$		0			0
$67$	1.50000	−	0.866025i	0.183254	−	0.105802i	−0.405567	−	0.914066i	$-0.632926\pi$
$67$	1.50000	−	0.866025i	0.183254	−	0.105802i	0.588821	+	0.808264i	$0.299592\pi$
$68$		0			0
$69$	−1.18614	+	1.11469i	−0.142795	+	0.134193i
$70$		0			0
$71$	−3.55842	+	6.16337i	−0.422307	+	0.731457i	−0.996165	−	0.0874978i	$-0.972113\pi$
$71$	−3.55842	+	6.16337i	−0.422307	+	0.731457i	0.573858	+	0.818955i	$0.305446\pi$
$72$		0			0
$73$	−6.87228	+	11.9031i	−0.804340	+	1.39316i	0.112396	+	0.993663i	$0.464147\pi$
$73$	−6.87228	+	11.9031i	−0.804340	+	1.39316i	−0.916736	+	0.399494i	$0.869186\pi$
$74$		0			0
$75$	−4.88316	−	5.19615i	−0.563858	−	0.600000i
$76$		0			0
$77$			17.0256i			1.94024i
$78$		0			0
$79$	8.61684	+	4.97494i	0.969471	+	0.559724i	0.899075	−	0.437795i	$-0.144240\pi$
$79$	8.61684	+	4.97494i	0.969471	+	0.559724i	0.0703959	+	0.997519i	$0.477574\pi$
$80$		0			0
$81$	5.43070	−	7.17687i	0.603411	−	0.797430i
$82$		0			0
$83$			1.87953i			0.206305i	0.994666	+	0.103152i	$0.0328930\pi$
$83$			1.87953i			0.206305i	−0.994666	+	0.103152i	$0.967107\pi$
$84$		0			0
$85$	−2.81386	−	4.87375i	−0.305206	−	0.528632i
$86$		0			0
$87$	−12.3030	−	13.0916i	−1.31902	−	1.40356i
$88$		0			0
$89$	0.813859	+	1.40965i	0.0862689	+	0.149422i	0.905931	−	0.423425i	$-0.139172\pi$
$89$	0.813859	+	1.40965i	0.0862689	+	0.149422i	−0.819662	+	0.572847i	$0.805839\pi$
$90$		0			0
$91$	−5.05842	+	2.92048i	−0.530267	+	0.306150i
$92$		0			0
$93$	−0.941578	−	4.00772i	−0.0976371	−	0.415581i
$94$		0			0
$95$	2.44158	+	3.28917i	0.250501	+	0.337462i
$96$		0			0
$97$	10.6753	+	6.16337i	1.08391	+	0.625795i	0.931948	−	0.362591i	$-0.118108\pi$
$97$	10.6753	+	6.16337i	1.08391	+	0.625795i	0.151961	+	0.988387i	$0.451441\pi$
$98$		0			0
$99$	−6.74456	−	13.5615i	−0.677854	−	1.36298i
$100$		0			0
$101$	13.9307	−	8.04290i	1.38616	−	0.800298i	0.393277	−	0.919420i	$-0.371341\pi$
$101$	13.9307	−	8.04290i	1.38616	−	0.800298i	0.992880	+	0.119122i	$0.0380080\pi$
$102$		0			0
$103$			16.2333i			1.59951i	0.600326	+	0.799756i	$0.295038\pi$
$103$			16.2333i			1.59951i	−0.600326	+	0.799756i	$0.704962\pi$
$104$		0			0
$105$	5.25544	+	1.58457i	0.512878	+	0.154639i
$106$		0			0
$107$	17.4891			1.69074			0.845369	−	0.534183i	$-0.179381\pi$
$107$	17.4891			1.69074			0.845369	+	0.534183i	$0.179381\pi$
$108$		0			0
$109$	2.44158	+	1.40965i	0.233861	+	0.135020i	0.612352	−	0.790585i	$-0.290224\pi$
$109$	2.44158	+	1.40965i	0.233861	+	0.135020i	−0.378491	+	0.925605i	$0.623557\pi$
$110$		0			0
$111$	2.31386	+	9.84868i	0.219622	+	0.934796i
$112$		0			0
$113$	−8.74456			−0.822619			−0.411310	−	0.911496i	$-0.634929\pi$
$113$	−8.74456			−0.822619			−0.411310	+	0.911496i	$0.634929\pi$
$114$		0			0
$115$	0.883156			0.0823547
$116$		0			0
$117$	2.87228	−	4.33013i	0.265543	−	0.400320i
$118$		0			0
$119$	−17.4891	−	10.0974i	−1.60323	−	0.925623i
$120$		0			0
$121$	−14.4891			−1.31719
$122$		0			0
$123$	3.55842	−	11.8020i	0.320852	−	1.06415i
$124$		0			0
$125$			8.56768i			0.766317i
$126$		0			0
$127$	6.55842	−	3.78651i	0.581966	−	0.335998i	−0.179948	−	0.983676i	$-0.557593\pi$
$127$	6.55842	−	3.78651i	0.581966	−	0.335998i	0.761914	+	0.647678i	$0.224260\pi$
$128$		0			0
$129$	0.872281	−	2.89303i	0.0768001	−	0.254717i
$130$		0			0
$131$	−5.18614	−	2.99422i	−0.453115	−	0.261606i	0.256030	−	0.966669i	$-0.417585\pi$
$131$	−5.18614	−	2.99422i	−0.453115	−	0.261606i	−0.709145	+	0.705063i	$0.750919\pi$
$132$		0			0
$133$	13.4891	+	5.84096i	1.16966	+	0.506476i
$134$		0			0
$135$	−4.81386	+	0.819738i	−0.414311	+	0.0705519i
$136$		0			0
$137$	−0.302985	+	0.174928i	−0.0258857	+	0.0149451i	−0.512887	−	0.858456i	$-0.671424\pi$
$137$	−0.302985	+	0.174928i	−0.0258857	+	0.0149451i	0.487001	+	0.873401i	$0.338091\pi$
$138$		0			0
$139$	8.50000	+	14.7224i	0.720961	+	1.24874i	0.960615	+	0.277882i	$0.0896325\pi$
$139$	8.50000	+	14.7224i	0.720961	+	1.24874i	−0.239655	+	0.970858i	$0.577034\pi$
$140$		0			0
$141$	7.55842	−	7.10313i	0.636534	−	0.598192i
$142$		0			0
$143$	−4.37228	−	7.57301i	−0.365629	−	0.633287i
$144$		0			0
$145$			9.74749i			0.809485i
$146$		0			0
$147$	7.37228	−	1.73205i	0.608056	−	0.142857i
$148$		0			0
$149$	−15.0475	−	8.68771i	−1.23274	−	0.711725i	−0.265142	−	0.964209i	$-0.585419\pi$
$149$	−15.0475	−	8.68771i	−1.23274	−	0.711725i	−0.967601	+	0.252485i	$0.918752\pi$
$150$		0			0
$151$		−	3.46410i		−	0.281905i	−0.990016	−	0.140952i	$-0.954984\pi$
$151$		−	3.46410i		−	0.281905i	0.990016	−	0.140952i	$-0.0450164\pi$
$152$		0			0
$153$	17.9307	+	1.11469i	1.44961	+	0.0901175i
$154$		0			0
$155$	−1.11684	+	1.93443i	−0.0897071	+	0.155377i
$156$		0			0
$157$	10.6168	−	18.3889i	0.847316	−	1.46760i	−0.0362779	−	0.999342i	$-0.511550\pi$
$157$	10.6168	−	18.3889i	0.847316	−	1.46760i	0.883594	−	0.468253i	$-0.155117\pi$
$158$		0			0
$159$	1.93070	+	2.05446i	0.153115	+	0.162929i
$160$		0			0
$161$	2.74456	−	1.58457i	0.216302	−	0.124882i
$162$		0			0
$163$	−6.11684			−0.479108			−0.239554	−	0.970883i	$-0.577001\pi$
$163$	−6.11684			−0.479108			−0.239554	+	0.970883i	$0.577001\pi$
$164$		0			0
$165$	−2.37228	+	7.86797i	−0.184682	+	0.612520i
$166$		0			0
$167$	−7.93070	−	13.7364i	−0.613696	−	1.06295i	−0.990612	−	0.136705i	$-0.956349\pi$
$167$	−7.93070	−	13.7364i	−0.613696	−	1.06295i	0.376915	−	0.926248i	$-0.376985\pi$
$168$		0			0
$169$	−5.00000	+	8.66025i	−0.384615	+	0.666173i
$170$		0			0
$171$	−13.0584	+	0.691097i	−0.998602	+	0.0528495i
$172$		0			0
$173$	−5.18614	+	8.98266i	−0.394295	+	0.682939i	−0.993011	−	0.118023i	$-0.962345\pi$
$173$	−5.18614	+	8.98266i	−0.394295	+	0.682939i	0.598716	+	0.800961i	$0.295678\pi$
$174$		0			0
$175$	6.94158	+	12.0232i	0.524734	+	0.908866i
$176$		0			0
$177$	−0.813859	+	2.69927i	−0.0611734	+	0.202889i
$178$		0			0
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$		0			0
$181$	−9.55842	+	5.51856i	−0.710472	+	0.410191i	−0.811236	−	0.584719i	$-0.801205\pi$
$181$	−9.55842	+	5.51856i	−0.710472	+	0.410191i	0.100764	+	0.994910i	$0.467871\pi$
$182$		0			0
$183$	−2.06930	−	2.20193i	−0.152967	−	0.162772i
$184$		0			0
$185$	2.74456	−	4.75372i	0.201784	−	0.349501i
$186$		0			0
$187$	15.1168	−	26.1831i	1.10545	−	1.91470i
$188$		0			0
$189$	−13.4891	+	11.1846i	−0.981189	+	0.813559i
$190$		0			0
$191$			25.2434i			1.82655i	0.407347	+	0.913273i	$0.366454\pi$
$191$			25.2434i			1.82655i	−0.407347	+	0.913273i	$0.633546\pi$
$192$		0			0
$193$	−10.5000	−	6.06218i	−0.755807	−	0.436365i	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	−10.5000	−	6.06218i	−0.755807	−	0.436365i	−0.827788	+	0.561041i	$0.810401\pi$
$194$		0			0
$195$	−2.74456	+	0.644810i	−0.196542	+	0.0461758i
$196$		0			0
$197$		−	17.0256i		−	1.21302i	−0.795076	−	0.606510i	$-0.792569\pi$
$197$		−	17.0256i		−	1.21302i	0.795076	−	0.606510i	$-0.207431\pi$
$198$		0			0
$199$	3.87228	+	6.70699i	0.274499	+	0.475446i	0.970009	−	0.243071i	$-0.0781548\pi$
$199$	3.87228	+	6.70699i	0.274499	+	0.475446i	−0.695510	+	0.718517i	$0.744821\pi$
$200$		0			0
$201$	2.18614	−	2.05446i	0.154198	−	0.144910i
$202$		0			0
$203$	17.4891	+	30.2921i	1.22750	+	2.12609i
$204$		0			0
$205$	−5.79211	+	3.34408i	−0.404539	+	0.233560i
$206$		0			0
$207$	−1.55842	+	2.34941i	−0.108318	+	0.163295i
$208$		0			0
$209$	−8.74456	+	20.1947i	−0.604874	+	1.39690i
$210$		0			0
$211$	24.7337	+	14.2800i	1.70274	+	0.983076i	0.942968	+	0.332883i	$0.108021\pi$
$211$	24.7337	+	14.2800i	1.70274	+	0.983076i	0.759769	+	0.650193i	$0.225312\pi$
$212$		0			0
$213$	−3.55842	+	11.8020i	−0.243819	+	0.808656i
$214$		0			0
$215$	−1.41983	+	0.819738i	−0.0968315	+	0.0559057i
$216$		0			0
$217$			8.01544i			0.544124i
$218$		0			0
$219$	−6.87228	+	22.7928i	−0.464386	+	1.54019i
$220$		0			0
$221$	10.3723			0.697715
$222$		0			0
$223$	2.61684	+	1.51084i	0.175237	+	0.101173i	0.585053	−	0.810995i	$-0.301074\pi$
$223$	2.61684	+	1.51084i	0.175237	+	0.101173i	−0.409816	+	0.912168i	$0.634407\pi$
$224$		0			0
$225$	−10.2921	−	6.82701i	−0.686141	−	0.455134i
$226$		0			0
$227$	22.9783			1.52512			0.762560	−	0.646917i	$-0.223942\pi$
$227$	22.9783			1.52512			0.762560	+	0.646917i	$0.223942\pi$
$228$		0			0
$229$	−2.62772			−0.173645			−0.0868223	−	0.996224i	$-0.527671\pi$
$229$	−2.62772			−0.173645			−0.0868223	+	0.996224i	$0.527671\pi$
$230$		0			0
$231$	6.74456	+	28.7075i	0.443760	+	1.88881i
$232$		0			0
$233$	−6.81386	−	3.93398i	−0.446391	−	0.257724i	0.259914	−	0.965632i	$-0.416306\pi$
$233$	−6.81386	−	3.93398i	−0.446391	−	0.257724i	−0.706305	+	0.707908i	$0.749639\pi$
$234$		0			0
$235$	−5.62772			−0.367112
$236$		0			0
$237$	16.5000	+	4.97494i	1.07179	+	0.323157i
$238$		0			0
$239$		−	5.04868i		−	0.326572i	−0.986579	−	0.163286i	$-0.947791\pi$
$239$		−	5.04868i		−	0.326572i	0.986579	−	0.163286i	$-0.0522093\pi$
$240$		0			0
$241$	5.61684	−	3.24289i	0.361813	−	0.208893i	−0.308063	−	0.951366i	$-0.599681\pi$
$241$	5.61684	−	3.24289i	0.361813	−	0.208893i	0.669876	+	0.742473i	$0.266347\pi$
$242$		0			0
$243$	6.31386	−	14.2525i	0.405034	−	0.914302i
$244$		0			0
$245$	−3.55842	−	2.05446i	−0.227339	−	0.131254i
$246$		0			0
$247$	−7.50000	+	0.866025i	−0.477214	+	0.0551039i
$248$		0			0
$249$	0.744563	+	3.16915i	0.0471847	+	0.200837i
$250$		0			0
$251$	17.1861	−	9.92242i	1.08478	−	0.626298i	0.152598	−	0.988288i	$-0.451236\pi$
$251$	17.1861	−	9.92242i	1.08478	−	0.626298i	0.932182	+	0.361991i	$0.117903\pi$
$252$		0			0
$253$	2.37228	+	4.10891i	0.149144	+	0.258325i
$254$		0			0
$255$	−6.67527	−	7.10313i	−0.418021	−	0.444815i
$256$		0			0
$257$	9.55842	+	16.5557i	0.596238	+	1.03271i	0.993371	+	0.114953i	$0.0366719\pi$
$257$	9.55842	+	16.5557i	0.596238	+	1.03271i	−0.397133	+	0.917761i	$0.629995\pi$
$258$		0			0
$259$		−	19.6974i		−	1.22393i
$260$		0			0
$261$	−25.9307	−	17.2005i	−1.60507	−	1.06468i
$262$		0			0
$263$	−17.1861	−	9.92242i	−1.05974	−	0.611843i	−0.134382	−	0.990930i	$-0.542905\pi$
$263$	−17.1861	−	9.92242i	−1.05974	−	0.611843i	−0.925361	+	0.379087i	$0.876238\pi$
$264$		0			0
$265$		−	1.52967i		−	0.0939669i
$266$		0			0
$267$	1.93070	+	2.05446i	0.118157	+	0.125731i
$268$		0			0
$269$	0.813859	−	1.40965i	0.0496219	−	0.0859476i	−0.840148	−	0.542358i	$-0.817532\pi$
$269$	0.813859	−	1.40965i	0.0496219	−	0.0859476i	0.889769	+	0.456410i	$0.150865\pi$
$270$		0			0
$271$	−5.55842	+	9.62747i	−0.337650	+	0.584827i	−0.983990	−	0.178222i	$-0.942965\pi$
$271$	−5.55842	+	9.62747i	−0.337650	+	0.584827i	0.646340	+	0.763049i	$0.276299\pi$
$272$		0			0
$273$	−7.37228	+	6.92820i	−0.446191	+	0.419314i
$274$		0			0
$275$	−18.0000	+	10.3923i	−1.08544	+	0.626680i
$276$		0			0
$277$	31.4891			1.89200			0.945999	−	0.324169i	$-0.105085\pi$
$277$	31.4891			1.89200			0.945999	+	0.324169i	$0.105085\pi$
$278$		0			0
$279$	−3.17527	−	6.38458i	−0.190098	−	0.382235i
$280$		0			0
$281$	−7.93070	−	13.7364i	−0.473106	−	0.819444i	0.526420	−	0.850225i	$-0.323534\pi$
$281$	−7.93070	−	13.7364i	−0.473106	−	0.819444i	−0.999526	+	0.0307808i	$0.990201\pi$
$282$		0			0
$283$	−2.81386	+	4.87375i	−0.167267	+	0.289714i	−0.937458	−	0.348099i	$-0.886827\pi$
$283$	−2.81386	+	4.87375i	−0.167267	+	0.289714i	0.770191	+	0.637813i	$0.220161\pi$
$284$		0			0
$285$	5.41983	+	4.57879i	0.321043	+	0.271224i
$286$		0			0
$287$	−12.0000	+	20.7846i	−0.708338	+	1.22688i
$288$		0			0
$289$	9.43070	+	16.3345i	0.554747	+	0.960850i
$290$		0			0
$291$	20.4416	+	6.16337i	1.19831	+	0.361303i
$292$		0			0
$293$	14.2337			0.831541			0.415770	−	0.909470i	$-0.363512\pi$
$293$	14.2337			0.831541			0.415770	+	0.909470i	$0.363512\pi$
$294$		0			0
$295$	1.32473	−	0.764836i	0.0771290	−	0.0445304i
$296$		0			0
$297$	−16.7446	−	20.1947i	−0.971618	−	1.17182i
$298$		0			0
$299$	−0.813859	+	1.40965i	−0.0470667	+	0.0815219i
$300$		0			0
$301$	−2.94158	+	5.09496i	−0.169550	+	0.293669i
$302$		0			0
$303$	20.3030	−	19.0800i	1.16638	−	1.09612i
$304$		0			0
$305$			1.63948i			0.0938762i
$306$		0			0
$307$	−18.5584	−	10.7147i	−1.05919	−	0.611521i	−0.133978	−	0.990984i	$-0.542775\pi$
$307$	−18.5584	−	10.7147i	−1.05919	−	0.611521i	−0.925207	+	0.379463i	$0.876109\pi$
$308$		0			0
$309$	6.43070	+	27.3716i	0.365830	+	1.55711i
$310$		0			0
$311$		−	18.9051i		−	1.07201i	−0.844215	−	0.536004i	$-0.819933\pi$
$311$		−	18.9051i		−	1.07201i	0.844215	−	0.536004i	$-0.180067\pi$
$312$		0			0
$313$	−10.5584	−	18.2877i	−0.596797	−	1.03368i	−0.993291	−	0.115646i	$-0.963106\pi$
$313$	−10.5584	−	18.2877i	−0.596797	−	1.03368i	0.396493	−	0.918038i	$-0.370227\pi$
$314$		0			0
$315$	9.48913	+	0.589907i	0.534652	+	0.0332375i
$316$		0			0
$317$	9.55842	+	16.5557i	0.536854	+	0.929859i	0.999071	+	0.0430922i	$0.0137209\pi$
$317$	9.55842	+	16.5557i	0.536854	+	0.929859i	−0.462217	+	0.886767i	$0.652946\pi$
$318$		0			0
$319$	−45.3505	+	26.1831i	−2.53914	+	1.46597i
$320$		0			0
$321$	29.4891	−	6.92820i	1.64592	−	0.386695i
$322$		0			0
$323$	−15.5584	−	20.9595i	−0.865694	−	1.16622i
$324$		0			0
$325$	−6.17527	−	3.56529i	−0.342542	−	0.197767i
$326$		0			0
$327$	4.67527	+	1.40965i	0.258543	+	0.0779536i
$328$		0			0
$329$	−17.4891	+	10.0974i	−0.964207	+	0.556685i
$330$		0			0
$331$		−	4.55134i		−	0.250164i	−0.992146	−	0.125082i	$-0.960081\pi$
$331$		−	4.55134i		−	0.250164i	0.992146	−	0.125082i	$-0.0399195\pi$
$332$		0			0
$333$	7.80298	+	15.6896i	0.427601	+	0.859787i
$334$		0			0
$335$	−1.62772			−0.0889318
$336$		0			0
$337$	7.50000	+	4.33013i	0.408551	+	0.235877i	0.690167	−	0.723650i	$-0.257537\pi$
$337$	7.50000	+	4.33013i	0.408551	+	0.235877i	−0.281616	+	0.959527i	$0.590870\pi$
$338$		0			0
$339$	−14.7446	+	3.46410i	−0.800815	+	0.188144i
$340$		0			0
$341$	−12.0000			−0.649836
$342$		0			0
$343$	8.86141			0.478471
$344$		0			0
$345$	1.48913	−	0.349857i	0.0801718	−	0.0188356i
$346$		0			0
$347$	0.813859	+	0.469882i	0.0436903	+	0.0252246i	0.521686	−	0.853138i	$-0.325303\pi$
$347$	0.813859	+	0.469882i	0.0436903	+	0.0252246i	−0.477996	+	0.878362i	$0.658637\pi$
$348$		0			0
$349$	26.8614			1.43786			0.718929	−	0.695083i	$-0.244633\pi$
$349$	26.8614			1.43786			0.718929	+	0.695083i	$0.244633\pi$
$350$		0			0
$351$	3.12772	−	8.43904i	0.166945	−	0.450443i
$352$		0			0
$353$			13.2665i			0.706105i	0.935604	+	0.353052i	$0.114856\pi$
$353$			13.2665i			0.706105i	−0.935604	+	0.353052i	$0.885144\pi$
$354$		0			0
$355$	5.79211	−	3.34408i	0.307413	−	0.177485i
$356$		0			0
$357$	−33.4891	−	10.0974i	−1.77243	−	0.534408i
$358$		0			0
$359$	18.8139	+	10.8622i	0.992958	+	0.573284i	0.906157	−	0.422941i	$-0.139002\pi$
$359$	18.8139	+	10.8622i	0.992958	+	0.573284i	0.0868005	+	0.996226i	$0.472336\pi$
$360$		0			0
$361$	13.0000	+	13.8564i	0.684211	+	0.729285i
$362$		0			0
$363$	−24.4307	+	5.73977i	−1.28228	+	0.301260i
$364$		0			0
$365$	11.1861	−	6.45832i	0.585509	−	0.338044i
$366$		0			0
$367$	−3.50000	−	6.06218i	−0.182699	−	0.316443i	0.760100	−	0.649806i	$-0.225150\pi$
$367$	−3.50000	−	6.06218i	−0.182699	−	0.316443i	−0.942799	+	0.333363i	$0.891817\pi$
$368$		0			0
$369$	1.32473	−	21.3094i	0.0689629	−	1.10932i
$370$		0			0
$371$	−2.74456	−	4.75372i	−0.142491	−	0.246801i
$372$		0			0
$373$		−	20.7846i		−	1.07619i	−0.842885	−	0.538093i	$-0.819145\pi$
$373$		−	20.7846i		−	1.07619i	0.842885	−	0.538093i	$-0.180855\pi$
$374$		0			0
$375$	3.39403	+	14.4463i	0.175267	+	0.746004i
$376$		0			0
$377$	−15.5584	−	8.98266i	−0.801299	−	0.462630i
$378$		0			0
$379$		−	14.0588i		−	0.722151i	−0.932537	−	0.361076i	$-0.882410\pi$
$379$		−	14.0588i		−	0.722151i	0.932537	−	0.361076i	$-0.117590\pi$
$380$		0			0
$381$	9.55842	−	8.98266i	0.489693	−	0.460196i
$382$		0			0
$383$	−0.813859	+	1.40965i	−0.0415863	+	0.0720295i	−0.886069	−	0.463553i	$-0.846574\pi$
$383$	−0.813859	+	1.40965i	−0.0415863	+	0.0720295i	0.844483	+	0.535582i	$0.179908\pi$
$384$		0			0
$385$	8.00000	−	13.8564i	0.407718	−	0.706188i
$386$		0			0
$387$	0.324734	−	5.22360i	0.0165072	−	0.265531i
$388$		0			0
$389$	−4.06930	+	2.34941i	−0.206322	+	0.119120i	−0.599601	−	0.800299i	$-0.704674\pi$
$389$	−4.06930	+	2.34941i	−0.206322	+	0.119120i	0.393279	+	0.919419i	$0.371341\pi$
$390$		0			0
$391$	−5.62772			−0.284606
$392$		0			0
$393$	−9.93070	−	2.99422i	−0.500938	−	0.151038i
$394$		0			0
$395$	−4.67527	−	8.09780i	−0.235238	−	0.407444i
$396$		0			0
$397$	0.500000	−	0.866025i	0.0250943	−	0.0434646i	−0.853206	−	0.521575i	$-0.825345\pi$
$397$	0.500000	−	0.866025i	0.0250943	−	0.0434646i	0.878300	+	0.478110i	$0.158678\pi$
$398$		0			0
$399$	25.0584	+	4.50506i	1.25449	+	0.225535i
$400$		0			0
$401$	6.30298	−	10.9171i	0.314756	−	0.545173i	−0.664630	−	0.747173i	$-0.731411\pi$
$401$	6.30298	−	10.9171i	0.314756	−	0.545173i	0.979386	+	0.202000i	$0.0647440\pi$
$402$		0			0
$403$	−2.05842	−	3.56529i	−0.102537	−	0.177600i
$404$		0			0
$405$	−7.79211	+	3.28917i	−0.387193	+	0.163440i
$406$		0			0
$407$	29.4891			1.46172
$408$		0			0
$409$	−27.5584	+	15.9109i	−1.36268	+	0.786742i	−0.989979	−	0.141212i	$-0.954900\pi$
$409$	−27.5584	+	15.9109i	−1.36268	+	0.786742i	−0.372697	+	0.927953i	$0.621567\pi$
$410$		0			0
$411$	−0.441578	+	0.414979i	−0.0217814	+	0.0204694i
$412$		0			0
$413$	2.74456	−	4.75372i	0.135051	−	0.233915i
$414$		0			0
$415$	0.883156	−	1.52967i	0.0433524	−	0.0750886i
$416$		0			0
$417$	20.1644	+	21.4569i	0.987454	+	1.05075i
$418$		0			0
$419$		−	18.9051i		−	0.923574i	−0.886991	−	0.461787i	$-0.847209\pi$
$419$		−	18.9051i		−	0.923574i	0.886991	−	0.461787i	$-0.152791\pi$
$420$		0			0
$421$	−11.7921	−	6.80818i	−0.574712	−	0.331810i	0.184317	−	0.982867i	$-0.440993\pi$
$421$	−11.7921	−	6.80818i	−0.574712	−	0.331810i	−0.759029	+	0.651057i	$0.774326\pi$
$422$		0			0
$423$	9.93070	−	14.9711i	0.482847	−	0.727920i
$424$		0			0
$425$		−	24.6535i		−	1.19587i
$426$		0			0
$427$	2.94158	+	5.09496i	0.142353	+	0.246563i
$428$		0			0
$429$	−10.3723	−	11.0371i	−0.500778	−	0.532877i
$430$		0			0
$431$	−8.44158	−	14.6212i	−0.406617	−	0.704280i	0.587892	−	0.808940i	$-0.299958\pi$
$431$	−8.44158	−	14.6212i	−0.406617	−	0.704280i	−0.994508	+	0.104659i	$0.966625\pi$
$432$		0			0
$433$	9.73369	−	5.61975i	0.467771	−	0.270068i	−0.247535	−	0.968879i	$-0.579621\pi$
$433$	9.73369	−	5.61975i	0.467771	−	0.270068i	0.715306	+	0.698811i	$0.246287\pi$
$434$		0			0
$435$	3.86141	+	16.4356i	0.185140	+	0.788029i
$436$		0			0
$437$	4.06930	−	0.469882i	0.194661	−	0.0224775i
$438$		0			0
$439$	−11.6168	−	6.70699i	−0.554442	−	0.320107i	0.196470	−	0.980510i	$-0.437052\pi$
$439$	−11.6168	−	6.70699i	−0.554442	−	0.320107i	−0.750912	+	0.660403i	$0.770386\pi$
$440$		0			0
$441$	11.7446	−	5.84096i	0.559265	−	0.278141i
$442$		0			0
$443$	−18.8139	+	10.8622i	−0.893873	+	0.516078i	−0.875207	−	0.483748i	$-0.839275\pi$
$443$	−18.8139	+	10.8622i	−0.893873	+	0.516078i	−0.0186659	+	0.999826i	$0.505942\pi$
$444$		0			0
$445$		−	1.52967i		−	0.0725134i
$446$		0			0
$447$	−28.8139	−	8.68771i	−1.36285	−	0.410914i
$448$		0			0
$449$	20.7446			0.978996			0.489498	−	0.872004i	$-0.337180\pi$
$449$	20.7446			0.978996			0.489498	+	0.872004i	$0.337180\pi$
$450$		0			0
$451$	−31.1168	−	17.9653i	−1.46523	−	0.845954i
$452$		0			0
$453$	−1.37228	−	5.84096i	−0.0644754	−	0.274432i
$454$		0			0
$455$	5.48913			0.257334
$456$		0			0
$457$	−28.3505			−1.32618			−0.663091	−	0.748539i	$-0.730756\pi$
$457$	−28.3505			−1.32618			−0.663091	+	0.748539i	$0.730756\pi$
$458$		0			0
$459$	30.6753	−	5.22360i	1.43180	−	0.243817i
$460$		0			0
$461$	13.4198	+	7.74794i	0.625024	+	0.360858i	0.778822	−	0.627245i	$-0.215817\pi$
$461$	13.4198	+	7.74794i	0.625024	+	0.360858i	−0.153799	+	0.988102i	$0.549151\pi$
$462$		0			0
$463$	8.62772			0.400964			0.200482	−	0.979697i	$-0.435749\pi$
$463$	8.62772			0.400964			0.200482	+	0.979697i	$0.435749\pi$
$464$		0			0
$465$	−1.11684	+	3.70415i	−0.0517924	+	0.171776i
$466$		0			0
$467$			18.3152i			0.847525i	0.905773	+	0.423763i	$0.139291\pi$
$467$			18.3152i			0.847525i	−0.905773	+	0.423763i	$0.860709\pi$
$468$		0			0
$469$	−5.05842	+	2.92048i	−0.233576	+	0.134855i
$470$		0			0
$471$	10.6168	−	35.2121i	0.489198	−	1.62249i
$472$		0			0
$473$	−7.62772	−	4.40387i	−0.350723	−	0.202490i
$474$		0			0
$475$	2.05842	+	17.8265i	0.0944469	+	0.817934i
$476$		0			0
$477$	4.06930	+	2.69927i	0.186320	+	0.123591i
$478$		0			0
$479$	17.1861	−	9.92242i	0.785255	−	0.453367i	−0.0530345	−	0.998593i	$-0.516889\pi$
$479$	17.1861	−	9.92242i	0.785255	−	0.453367i	0.838289	+	0.545226i	$0.183556\pi$
$480$		0			0
$481$	5.05842	+	8.76144i	0.230644	+	0.399487i
$482$		0			0
$483$	4.00000	−	3.75906i	0.182006	−	0.171043i
$484$		0			0
$485$	−5.79211	−	10.0322i	−0.263006	−	0.455540i
$486$		0			0
$487$		−	40.6844i		−	1.84358i	−0.387684	−	0.921792i	$-0.626725\pi$
$487$		−	40.6844i		−	1.84358i	0.387684	−	0.921792i	$-0.373275\pi$
$488$		0			0
$489$	−10.3139	+	2.42315i	−0.466409	+	0.109579i
$490$		0			0
$491$	18.8139	+	10.8622i	0.849058	+	0.490204i	0.860333	−	0.509733i	$-0.170256\pi$
$491$	18.8139	+	10.8622i	0.849058	+	0.490204i	−0.0112752	+	0.999936i	$0.503589\pi$
$492$		0			0
$493$		−	62.1138i		−	2.79746i
$494$		0			0
$495$	−0.883156	+	14.2063i	−0.0396949	+	0.638524i
$496$		0			0
$497$	12.0000	−	20.7846i	0.538274	−	0.932317i
$498$		0			0
$499$	0.872281	−	1.51084i	0.0390487	−	0.0676343i	−0.845841	−	0.533436i	$-0.820901\pi$
$499$	0.872281	−	1.51084i	0.0390487	−	0.0676343i	0.884889	+	0.465802i	$0.154234\pi$
$500$		0			0
$501$	−18.8139	−	20.0198i	−0.840541	−	0.894418i
$502$		0			0
$503$	7.41983	−	4.28384i	0.330834	−	0.191007i	−0.325377	−	0.945584i	$-0.605491\pi$
$503$	7.41983	−	4.28384i	0.330834	−	0.191007i	0.656211	+	0.754577i	$0.272158\pi$
$504$		0			0
$505$	−15.1168			−0.672691
$506$		0			0
$507$	−5.00000	+	16.5831i	−0.222058	+	0.736482i
$508$		0			0
$509$	−10.6753	−	18.4901i	−0.473173	−	0.819559i	0.526356	−	0.850265i	$-0.323558\pi$
$509$	−10.6753	−	18.4901i	−0.473173	−	0.819559i	−0.999528	+	0.0307051i	$0.990225\pi$
$510$		0			0
$511$	23.1753	−	40.1407i	1.02521	−	1.77572i
$512$		0			0
$513$	−21.7446	+	6.33830i	−0.960046	+	0.279843i
$514$		0			0
$515$	7.62772	−	13.2116i	0.336117	−	0.582172i
$516$		0			0
$517$	−15.1168	−	26.1831i	−0.664838	−	1.15153i
$518$		0			0
$519$	−5.18614	+	17.2005i	−0.227646	+	0.755017i
$520$		0			0
$521$	32.7446			1.43457			0.717283	−	0.696782i	$-0.245386\pi$
$521$	32.7446			1.43457			0.717283	+	0.696782i	$0.245386\pi$
$522$		0			0
$523$	13.5000	−	7.79423i	0.590314	−	0.340818i	−0.174908	−	0.984585i	$-0.555963\pi$
$523$	13.5000	−	7.79423i	0.590314	−	0.340818i	0.765222	+	0.643767i	$0.222629\pi$
$524$		0			0
$525$	16.4674	+	17.5229i	0.718695	+	0.764762i
$526$		0			0
$527$	7.11684	−	12.3267i	0.310015	−	0.536961i
$528$		0			0
$529$	−11.0584	+	19.1537i	−0.480801	+	0.832772i
$530$		0			0
$531$	−0.302985	+	4.87375i	−0.0131484	+	0.211503i
$532$		0			0
$533$		−	12.3267i		−	0.533930i
$534$		0			0
$535$	−14.2337	−	8.21782i	−0.615376	−	0.355287i
$536$		0			0
$537$	−20.2337	+	4.75372i	−0.873148	+	0.205138i
$538$		0			0
$539$		−	22.0742i		−	0.950804i
$540$		0			0
$541$	−1.38316	−	2.39570i	−0.0594665	−	0.102999i	0.834760	−	0.550615i	$-0.185607\pi$
$541$	−1.38316	−	2.39570i	−0.0594665	−	0.102999i	−0.894226	+	0.447616i	$0.852273\pi$
$542$		0			0
$543$	−13.9307	+	13.0916i	−0.597824	+	0.561813i
$544$		0			0
$545$	−1.32473	−	2.29451i	−0.0567454	−	0.0982859i
$546$		0			0
$547$	−14.6168	+	8.43904i	−0.624971	+	0.360827i	−0.778802	−	0.627270i	$-0.784172\pi$
$547$	−14.6168	+	8.43904i	−0.624971	+	0.360827i	0.153831	+	0.988097i	$0.450839\pi$
$548$		0			0
$549$	−4.36141	−	2.89303i	−0.186140	−	0.123472i
$550$		0			0
$551$	5.18614	+	44.9133i	0.220937	+	1.91337i
$552$		0			0
$553$	−29.0584	−	16.7769i	−1.23569	−	0.713426i
$554$		0			0
$555$	2.74456	−	9.10268i	0.116500	−	0.386387i
$556$		0			0
$557$	−24.3030	+	14.0313i	−1.02975	+	0.594527i	−0.916913	−	0.399087i	$-0.869327\pi$
$557$	−24.3030	+	14.0313i	−1.02975	+	0.594527i	−0.112837	+	0.993613i	$0.535994\pi$
$558$		0			0
$559$		−	3.02167i		−	0.127803i
$560$		0			0
$561$	15.1168	−	50.1369i	0.638234	−	2.11678i
$562$		0			0
$563$	17.4891			0.737079			0.368539	−	0.929612i	$-0.379858\pi$
$563$	17.4891			0.737079			0.368539	+	0.929612i	$0.379858\pi$
$564$		0			0
$565$	7.11684	+	4.10891i	0.299408	+	0.172863i
$566$		0			0
$567$	−18.3139	+	24.2024i	−0.769110	+	1.01641i
$568$		0			0
$569$	44.7446			1.87579			0.937895	−	0.346920i	$-0.112772\pi$
$569$	44.7446			1.87579			0.937895	+	0.346920i	$0.112772\pi$
$570$		0			0
$571$	−6.11684			−0.255982			−0.127991	−	0.991775i	$-0.540853\pi$
$571$	−6.11684			−0.255982			−0.127991	+	0.991775i	$0.540853\pi$
$572$		0			0
$573$	10.0000	+	42.5639i	0.417756	+	1.77813i
$574$		0			0
$575$	3.35053	+	1.93443i	0.139727	+	0.0806713i
$576$		0			0
$577$	−20.9783			−0.873336			−0.436668	−	0.899623i	$-0.643842\pi$
$577$	−20.9783			−0.873336			−0.436668	+	0.899623i	$0.643842\pi$
$578$		0			0
$579$	−20.1060	−	6.06218i	−0.835576	−	0.251936i
$580$		0			0
$581$		−	6.33830i		−	0.262957i
$582$		0			0
$583$	7.11684	−	4.10891i	0.294750	−	0.170174i
$584$		0			0
$585$	−4.37228	+	2.17448i	−0.180772	+	0.0899037i
$586$		0			0
$587$	−25.4198	−	14.6761i	−1.04919	−	0.605749i	−0.126767	−	0.991933i	$-0.540460\pi$
$587$	−25.4198	−	14.6761i	−1.04919	−	0.605749i	−0.922422	+	0.386183i	$0.873793\pi$
$588$		0			0
$589$	−4.11684	+	9.50744i	−0.169632	+	0.391747i
$590$		0			0
$591$	−6.74456	−	28.7075i	−0.277434	−	1.18087i
$592$		0			0
$593$	−4.06930	+	2.34941i	−0.167106	+	0.0964787i	−0.581221	−	0.813746i	$-0.697425\pi$
$593$	−4.06930	+	2.34941i	−0.167106	+	0.0964787i	0.414115	+	0.910225i	$0.364091\pi$
$594$		0			0
$595$	9.48913	+	16.4356i	0.389016	+	0.673796i
$596$		0			0
$597$	9.18614	+	9.77495i	0.375964	+	0.400062i
$598$		0			0
$599$	12.8139	+	22.1943i	0.523560	+	0.906833i	0.999624	+	0.0274220i	$0.00872978\pi$
$599$	12.8139	+	22.1943i	0.523560	+	0.906833i	−0.476064	+	0.879411i	$0.657937\pi$
$600$		0			0
$601$		−	10.5947i		−	0.432166i	−0.976375	−	0.216083i	$-0.930672\pi$
$601$		−	10.5947i		−	0.432166i	0.976375	−	0.216083i	$-0.0693282\pi$
$602$		0			0
$603$	2.87228	−	4.33013i	0.116968	−	0.176336i
$604$		0			0
$605$	11.7921	+	6.80818i	0.479417	+	0.276792i
$606$		0			0
$607$		−	9.30506i		−	0.377681i	−0.982008	−	0.188840i	$-0.939527\pi$
$607$		−	9.30506i		−	0.377681i	0.982008	−	0.188840i	$-0.0604729\pi$
$608$		0			0
$609$	41.4891	+	44.1485i	1.68122	+	1.78899i
$610$		0			0
$611$	5.18614	−	8.98266i	0.209809	−	0.363399i
$612$		0			0
$613$	16.1861	−	28.0352i	0.653752	−	1.13233i	−0.328453	−	0.944520i	$-0.606527\pi$
$613$	16.1861	−	28.0352i	0.653752	−	1.13233i	0.982205	−	0.187811i	$-0.0601394\pi$
$614$		0			0
$615$	−8.44158	+	7.93309i	−0.340397	+	0.319893i
$616$		0			0
$617$	−16.0693	+	9.27761i	−0.646926	+	0.373503i	−0.787277	−	0.616599i	$-0.788510\pi$
$617$	−16.0693	+	9.27761i	−0.646926	+	0.373503i	0.140352	+	0.990102i	$0.455177\pi$
$618$		0			0
$619$	38.1168			1.53205			0.766023	−	0.642814i	$-0.222233\pi$
$619$	38.1168			1.53205			0.766023	+	0.642814i	$0.222233\pi$
$620$		0			0
$621$	−1.69702	+	4.57879i	−0.0680989	+	0.183741i
$622$		0			0
$623$	−2.74456	−	4.75372i	−0.109959	−	0.190454i
$624$		0			0
$625$	−6.26631	+	10.8536i	−0.250652	+	0.434143i
$626$		0			0
$627$	−6.74456	+	37.5152i	−0.269352	+	1.49821i
$628$		0			0
$629$	−17.4891	+	30.2921i	−0.697337	+	1.20782i
$630$		0			0
$631$	13.9891	+	24.2299i	0.556898	+	0.964576i	0.997753	+	0.0669977i	$0.0213420\pi$
$631$	13.9891	+	24.2299i	0.556898	+	0.964576i	−0.440855	+	0.897578i	$0.645325\pi$
$632$		0			0
$633$	47.3614	+	14.2800i	1.88245	+	0.567579i
$634$		0			0
$635$	−7.11684			−0.282423
$636$		0			0
$637$	6.55842	−	3.78651i	0.259854	−	0.150027i
$638$		0			0
$639$	−1.32473	+	21.3094i	−0.0524057	+	0.842987i
$640$		0			0
$641$	−10.6753	+	18.4901i	−0.421648	+	0.730315i	−0.996101	−	0.0882223i	$-0.971881\pi$
$641$	−10.6753	+	18.4901i	−0.421648	+	0.730315i	0.574453	+	0.818537i	$0.305215\pi$
$642$		0			0
$643$	−9.24456	+	16.0121i	−0.364570	+	0.631454i	−0.988707	−	0.149861i	$-0.952117\pi$
$643$	−9.24456	+	16.0121i	−0.364570	+	0.631454i	0.624137	+	0.781315i	$0.285451\pi$
$644$		0			0
$645$	−2.06930	+	1.94465i	−0.0814785	+	0.0765705i
$646$		0			0
$647$			15.7359i			0.618643i	0.950957	+	0.309322i	$0.100102\pi$
$647$			15.7359i			0.618643i	−0.950957	+	0.309322i	$0.899898\pi$
$648$		0			0
$649$	7.11684	+	4.10891i	0.279361	+	0.161289i
$650$		0			0
$651$	3.17527	+	13.5152i	0.124448	+	0.529701i
$652$		0			0
$653$			20.1947i			0.790280i	0.918621	+	0.395140i	$0.129304\pi$
$653$			20.1947i			0.790280i	−0.918621	+	0.395140i	$0.870696\pi$
$654$		0			0
$655$	2.81386	+	4.87375i	0.109947	+	0.190433i
$656$		0			0
$657$	−2.55842	+	41.1542i	−0.0998135	+	1.60558i
$658$		0			0
$659$	−4.67527	−	8.09780i	−0.182123	−	0.315445i	0.760481	−	0.649361i	$-0.224963\pi$
$659$	−4.67527	−	8.09780i	−0.182123	−	0.315445i	−0.942603	+	0.333915i	$0.891630\pi$
$660$		0			0
$661$	−23.7921	+	13.7364i	−0.925406	+	0.534283i	−0.885356	−	0.464914i	$-0.846085\pi$
$661$	−23.7921	+	13.7364i	−0.925406	+	0.534283i	−0.0400502	+	0.999198i	$0.512752\pi$
$662$		0			0
$663$	17.4891	−	4.10891i	0.679221	−	0.159577i
$664$		0			0
$665$	−8.23369	−	11.0920i	−0.319289	−	0.430130i
$666$		0			0
$667$	8.44158	+	4.87375i	0.326859	+	0.188712i
$668$		0			0
$669$	5.01087	+	1.51084i	0.193732	+	0.0584123i
$670$		0			0
$671$	−7.62772	+	4.40387i	−0.294465	+	0.170009i
$672$		0			0
$673$		−	1.08724i		−	0.0419100i	−0.999780	−	0.0209550i	$-0.993329\pi$
$673$		−	1.08724i		−	0.0419100i	0.999780	−	0.0209550i	$-0.00667068\pi$
$674$		0			0
$675$	−20.0584	−	7.43415i	−0.772049	−	0.286141i
$676$		0			0
$677$	−9.76631			−0.375350			−0.187675	−	0.982231i	$-0.560095\pi$
$677$	−9.76631			−0.375350			−0.187675	+	0.982231i	$0.560095\pi$
$678$		0			0
$679$	−36.0000	−	20.7846i	−1.38155	−	0.797640i
$680$		0			0
$681$	38.7446	−	9.10268i	1.48469	−	0.348816i
$682$		0			0
$683$	−40.4674			−1.54844			−0.774221	−	0.632916i	$-0.781858\pi$
$683$	−40.4674			−1.54844			−0.774221	+	0.632916i	$0.781858\pi$
$684$		0			0
$685$	0.328782			0.0125621
$686$		0			0
$687$	−4.43070	+	1.04095i	−0.169042	+	0.0397149i
$688$		0			0
$689$	2.44158	+	1.40965i	0.0930167	+	0.0537032i
$690$		0			0
$691$	−36.4674			−1.38728			−0.693642	−	0.720320i	$-0.743995\pi$
$691$	−36.4674			−1.38728			−0.693642	+	0.720320i	$0.743995\pi$
$692$		0			0
$693$	22.7446	+	45.7330i	0.863994	+	1.73725i
$694$		0			0
$695$		−	15.9760i		−	0.606004i
$696$		0			0
$697$	36.9090	−	21.3094i	1.39803	−	0.807151i
$698$		0			0
$699$	−13.0475	−	3.93398i	−0.493504	−	0.148797i
$700$		0			0
$701$	25.4198	+	14.6761i	0.960094	+	0.554310i	0.896202	−	0.443646i	$-0.146315\pi$
$701$	25.4198	+	14.6761i	0.960094	+	0.554310i	0.0638918	+	0.997957i	$0.479649\pi$
$702$		0			0
$703$	10.1168	−	23.3639i	0.381564	−	0.881184i
$704$		0			0
$705$	−9.48913	+	2.22938i	−0.357381	+	0.0839635i
$706$		0			0
$707$	−46.9783	+	27.1229i	−1.76680	+	1.02006i
$708$		0			0
$709$	4.61684	+	7.99661i	0.173389	+	0.300319i	0.939603	−	0.342267i	$-0.111195\pi$
$709$	4.61684	+	7.99661i	0.173389	+	0.300319i	−0.766213	+	0.642586i	$0.777861\pi$
$710$		0			0
$711$	29.7921	+	1.85208i	1.11729	+	0.0694583i
$712$		0			0
$713$	1.11684	+	1.93443i	0.0418261	+	0.0724450i
$714$		0			0
$715$			8.21782i			0.307329i
$716$		0			0
$717$	−2.00000	−	8.51278i	−0.0746914	−	0.317915i
$718$		0			0
$719$	−25.4198	−	14.6761i	−0.948000	−	0.547328i	−0.0555407	−	0.998456i	$-0.517688\pi$
$719$	−25.4198	−	14.6761i	−0.948000	−	0.547328i	−0.892459	+	0.451129i	$0.851022\pi$
$720$		0			0
$721$		−	54.7431i		−	2.03874i
$722$		0			0
$723$	8.18614	−	7.69304i	0.304446	−	0.286107i
$724$		0			0
$725$	−21.3505	+	36.9802i	−0.792939	+	1.37341i
$726$		0			0
$727$	11.5000	−	19.9186i	0.426511	−	0.738739i	−0.570049	−	0.821611i	$-0.693076\pi$
$727$	11.5000	−	19.9186i	0.426511	−	0.738739i	0.996560	+	0.0828714i	$0.0264091\pi$
$728$		0			0
$729$	5.00000	−	26.5330i	0.185185	−	0.982704i
$730$		0			0
$731$	9.04755	−	5.22360i	0.334636	−	0.193202i
$732$		0			0
$733$	2.00000			0.0738717			0.0369358	−	0.999318i	$-0.488240\pi$
$733$	2.00000			0.0738717			0.0369358	+	0.999318i	$0.488240\pi$
$734$		0			0
$735$	−6.81386	−	2.05446i	−0.251333	−	0.0757797i
$736$		0			0
$737$	−4.37228	−	7.57301i	−0.161055	−	0.278956i
$738$		0			0
$739$	−6.50000	+	11.2583i	−0.239106	+	0.414144i	−0.960458	−	0.278425i	$-0.910188\pi$
$739$	−6.50000	+	11.2583i	−0.239106	+	0.414144i	0.721352	+	0.692569i	$0.243521\pi$
$740$		0			0
$741$	−12.3030	+	4.43132i	−0.451961	+	0.162788i
$742$		0			0
$743$	14.4416	−	25.0135i	0.529810	−	0.917658i	−0.469585	−	0.882887i	$-0.655597\pi$
$743$	14.4416	−	25.0135i	0.529810	−	0.917658i	0.999395	−	0.0347709i	$-0.0110701\pi$
$744$		0			0
$745$	8.16439	+	14.1411i	0.299120	+	0.518091i
$746$		0			0
$747$	2.51087	+	5.04868i	0.0918681	+	0.184721i
$748$		0			0
$749$	−58.9783			−2.15502
$750$		0			0
$751$	31.8505	−	18.3889i	1.16224	−	0.671021i	0.210402	−	0.977615i	$-0.432523\pi$
$751$	31.8505	−	18.3889i	1.16224	−	0.671021i	0.951840	+	0.306594i	$0.0991894\pi$
$752$		0			0
$753$	25.0475	−	23.5388i	0.912783	−	0.857801i
$754$		0			0
$755$	−1.62772	+	2.81929i	−0.0592387	+	0.102605i
$756$		0			0
$757$	−11.5000	+	19.9186i	−0.417975	+	0.723953i	−0.995736	−	0.0922527i	$-0.970593\pi$
$757$	−11.5000	+	19.9186i	−0.417975	+	0.723953i	0.577761	+	0.816206i	$0.303927\pi$
$758$		0			0
$759$	5.62772	+	5.98844i	0.204273	+	0.217367i
$760$		0			0
$761$			13.2665i			0.480910i	0.970660	+	0.240455i	$0.0772967\pi$
$761$			13.2665i			0.480910i	−0.970660	+	0.240455i	$0.922703\pi$
$762$		0			0
$763$	−8.23369	−	4.75372i	−0.298080	−	0.172096i
$764$		0			0
$765$	−14.0693	−	9.33252i	−0.508676	−	0.337418i
$766$		0			0
$767$			2.81929i			0.101799i
$768$		0			0
$769$	−12.3614	−	21.4106i	−0.445764	−	0.772085i	0.552341	−	0.833618i	$-0.313735\pi$
$769$	−12.3614	−	21.4106i	−0.445764	−	0.772085i	−0.998105	+	0.0615326i	$0.980401\pi$
$770$		0			0
$771$	22.6753	+	24.1287i	0.816630	+	0.868973i
$772$		0			0
$773$	−13.9307	−	24.1287i	−0.501053	−	0.867849i	−0.999999	−	0.00121583i	$-0.999613\pi$
$773$	−13.9307	−	24.1287i	−0.501053	−	0.867849i	0.498947	−	0.866633i	$-0.333720\pi$
$774$		0			0
$775$	−8.47420	+	4.89258i	−0.304402	+	0.175747i
$776$		0			0
$777$	−7.80298	−	33.2125i	−0.279931	−	1.19149i
$778$		0			0
$779$	−24.9090	+	18.4901i	−0.892456	+	0.662477i
$780$		0			0
$781$	31.1168	+	17.9653i	1.11345	+	0.642850i
$782$		0			0
$783$	−50.5367	−	18.7302i	−1.80603	−	0.669361i
$784$		0			0
$785$	−17.2812	+	9.97733i	−0.616794	+	0.356106i
$786$		0			0
$787$			7.13058i			0.254178i	0.991891	+	0.127089i	$0.0405634\pi$
$787$			7.13058i			0.254178i	−0.991891	+	0.127089i	$0.959437\pi$
$788$		0			0
$789$	−32.9090	−	9.92242i	−1.17159	−	0.353248i
$790$		0			0
$791$	29.4891			1.04851
$792$		0			0
$793$	−2.61684	−	1.51084i	−0.0929269	−	0.0536513i
$794$		0			0
$795$	−0.605969	−	2.57924i	−0.0214915	−	0.0914762i
$796$		0			0
$797$	38.2337			1.35431			0.677153	−	0.735842i	$-0.263213\pi$
$797$	38.2337			1.35431			0.677153	+	0.735842i	$0.263213\pi$
$798$		0			0
$799$	35.8614			1.26869
$800$		0			0
$801$	4.06930	+	2.69927i	0.143782	+	0.0953739i
$802$		0			0
$803$	60.0951	+	34.6959i	2.12071	+	1.22439i
$804$		0			0
$805$	−2.97825			−0.104970
$806$		0			0
$807$	0.813859	−	2.69927i	0.0286492	−	0.0950187i
$808$		0			0
$809$		−	47.3176i		−	1.66360i	−0.555077	−	0.831799i	$-0.687311\pi$
$809$		−	47.3176i		−	1.66360i	0.555077	−	0.831799i	$-0.312689\pi$
$810$		0			0
$811$	−21.9090	+	12.6491i	−0.769327	+	0.444171i	−0.832635	−	0.553823i	$-0.813169\pi$
$811$	−21.9090	+	12.6491i	−0.769327	+	0.444171i	0.0633072	+	0.997994i	$0.479835\pi$
$812$		0			0
$813$	−5.55842	+	18.4352i	−0.194942	+	0.646551i
$814$		0			0
$815$	4.97825	+	2.87419i	0.174381	+	0.100679i
$816$		0			0
$817$	−6.10597	+	4.53251i	−0.213621	+	0.158572i
$818$		0			0
$819$	−9.68614	+	14.6024i	−0.338461	+	0.510249i
$820$		0			0
$821$	1.93070	−	1.11469i	0.0673820	−	0.0389030i	−0.465930	−	0.884821i	$-0.654280\pi$
$821$	1.93070	−	1.11469i	0.0673820	−	0.0389030i	0.533313	+	0.845918i	$0.320947\pi$
$822$		0			0
$823$	1.55842	+	2.69927i	0.0543232	+	0.0940905i	0.891908	−	0.452216i	$-0.149367\pi$
$823$	1.55842	+	2.69927i	0.0543232	+	0.0940905i	−0.837585	+	0.546307i	$0.816033\pi$
$824$		0			0
$825$	−26.2337	+	24.6535i	−0.913340	+	0.858324i
$826$		0			0
$827$	0.302985	+	0.524785i	0.0105358	+	0.0182486i	0.871245	−	0.490848i	$-0.163313\pi$
$827$	0.302985	+	0.524785i	0.0105358	+	0.0182486i	−0.860709	+	0.509097i	$0.829980\pi$
$828$		0			0
$829$		−	24.4511i		−	0.849221i	−0.905376	−	0.424611i	$-0.860411\pi$
$829$		−	24.4511i		−	0.849221i	0.905376	−	0.424611i	$-0.139589\pi$
$830$		0			0
$831$	53.0951	−	12.4742i	1.84185	−	0.432726i
$832$		0			0
$833$	22.6753	+	13.0916i	0.785651	+	0.453596i
$834$		0			0
$835$			14.9060i			0.515843i
$836$		0			0
$837$	−7.88316	−	9.50744i	−0.272482	−	0.328625i
$838$		0			0
$839$	−21.5584	+	37.3403i	−0.744279	+	1.28913i	0.206251	+	0.978499i	$0.433874\pi$
$839$	−21.5584	+	37.3403i	−0.744279	+	1.28913i	−0.950531	+	0.310631i	$0.899460\pi$
$840$		0			0
$841$	−39.2921	+	68.0559i	−1.35490	+	2.34676i
$842$		0			0
$843$	−18.8139	−	20.0198i	−0.647984	−	0.689518i
$844$		0			0
$845$	8.13859	−	4.69882i	0.279976	−	0.161644i
$846$		0			0
$847$	48.8614			1.67890
$848$		0			0
$849$	−2.81386	+	9.33252i	−0.0965714	+	0.320291i
$850$		0			0
$851$	−2.74456	−	4.75372i	−0.0940824	−	0.162955i
$852$		0			0
$853$	−7.73369	+	13.3951i	−0.264796	+	0.458641i	−0.967510	−	0.252832i	$-0.918638\pi$
$853$	−7.73369	+	13.3951i	−0.264796	+	0.458641i	0.702714	+	0.711473i	$0.251971\pi$
$854$		0			0
$855$	10.9525	+	5.57346i	0.374566	+	0.190608i
$856$		0			0
$857$	12.3030	−	21.3094i	0.420262	−	0.727915i	−0.575703	−	0.817659i	$-0.695272\pi$
$857$	12.3030	−	21.3094i	0.420262	−	0.727915i	0.995965	+	0.0897439i	$0.0286049\pi$
$858$		0			0
$859$	18.1060	+	31.3605i	0.617768	+	1.07001i	0.989892	+	0.141822i	$0.0452961\pi$
$859$	18.1060	+	31.3605i	0.617768	+	1.07001i	−0.372124	+	0.928183i	$0.621371\pi$
$860$		0			0
$861$	−12.0000	+	39.7995i	−0.408959	+	1.35636i
$862$		0			0
$863$	28.4674			0.969041			0.484520	−	0.874780i	$-0.338994\pi$
$863$	28.4674			0.969041			0.484520	+	0.874780i	$0.338994\pi$
$864$		0			0
$865$	8.44158	−	4.87375i	0.287022	−	0.165712i
$866$		0			0
$867$	22.3723	+	23.8063i	0.759803	+	0.808504i
$868$		0			0
$869$	25.1168	−	43.5036i	0.852031	−	1.47576i
$870$		0			0
$871$	1.50000	−	2.59808i	0.0508256	−	0.0880325i
$872$		0			0
$873$	36.9090	+	2.29451i	1.24918	+	0.0776573i
$874$		0			0
$875$		−	28.8926i		−	0.976749i
$876$		0			0
$877$	39.7337	+	22.9403i	1.34171	+	0.774637i	0.987058	−	0.160361i	$-0.0512657\pi$
$877$	39.7337	+	22.9403i	1.34171	+	0.774637i	0.354653	+	0.934998i	$0.384599\pi$
$878$		0			0
$879$	24.0000	−	5.63858i	0.809500	−	0.190185i
$880$		0			0
$881$			27.1229i			0.913794i	0.889520	+	0.456897i	$0.151039\pi$
$881$			27.1229i			0.913794i	−0.889520	+	0.456897i	$0.848961\pi$
$882$		0			0
$883$	13.1277	+	22.7379i	0.441783	+	0.765190i	0.997822	−	0.0659658i	$-0.0210128\pi$
$883$	13.1277	+	22.7379i	0.441783	+	0.765190i	−0.556039	+	0.831156i	$0.687679\pi$
$884$		0			0
$885$	1.93070	−	1.81441i	0.0648999	−	0.0609906i
$886$		0			0
$887$	−14.4416	−	25.0135i	−0.484901	−	0.839873i	0.514949	−	0.857221i	$-0.327811\pi$
$887$	−14.4416	−	25.0135i	−0.484901	−	0.839873i	−0.999850	+	0.0173482i	$0.994478\pi$
$888$		0			0
$889$	−22.1168	+	12.7692i	−0.741775	+	0.428264i
$890$		0			0
$891$	−36.2337	−	27.4179i	−1.21387	−	0.918533i
$892$		0			0
$893$	−25.9307	+	2.99422i	−0.867738	+	0.100198i
$894$		0			0
$895$	9.76631	+	5.63858i	0.326452	+	0.188477i
$896$		0			0
$897$	−0.813859	+	2.69927i	−0.0271740	+	0.0901259i
$898$		0			0
$899$	−21.3505	+	12.3267i	−0.712080	+	0.411120i
$900$		0			0
$901$			9.74749i			0.324736i
$902$		0			0
$903$	−2.94158	+	9.75611i	−0.0978896	+	0.324663i
$904$		0			0
$905$	10.3723			0.344786
$906$		0			0
$907$	−10.3247	−	5.96099i	−0.342827	−	0.197931i	0.318694	−	0.947858i	$-0.396756\pi$
$907$	−10.3247	−	5.96099i	−0.342827	−	0.197931i	−0.661522	+	0.749926i	$0.730089\pi$
$908$		0			0
$909$	26.6753	−	40.2145i	0.884763	−	1.33383i
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$	9.48913			0.314044
$914$		0			0
$915$	0.649468	+	2.76439i	0.0214708	+	0.0913879i
$916$		0			0
$917$	17.4891	+	10.0974i	0.577542	+	0.333444i
$918$		0			0
$919$	−18.1168			−0.597620			−0.298810	−	0.954313i	$-0.596590\pi$
$919$	−18.1168			−0.597620			−0.298810	+	0.954313i	$0.596590\pi$
$920$		0			0
$921$	−35.5367	−	10.7147i	−1.17097	−	0.353062i
$922$		0			0
$923$			12.3267i			0.405739i
$924$		0			0
$925$	20.8247	−	12.0232i	0.684713	−	0.395319i
$926$		0			0
$927$	21.6861	+	43.6048i	0.712266	+	1.43217i
$928$		0			0
$929$	−17.2812	−	9.97733i	−0.566979	−	0.327345i	0.188963	−	0.981984i	$-0.439487\pi$
$929$	−17.2812	−	9.97733i	−0.566979	−	0.327345i	−0.755942	+	0.654639i	$0.772821\pi$
$930$		0			0
$931$	−17.4891	−	7.57301i	−0.573183	−	0.248195i
$932$		0			0
$933$	−7.48913	−	31.8766i	−0.245183	−	1.04359i
$934$		0			0
$935$	−24.6060	+	14.2063i	−0.804701	+	0.464594i
$936$		0			0
$937$	20.7337	+	35.9118i	0.677340	+	1.17319i	0.975779	+	0.218759i	$0.0702007\pi$
$937$	20.7337	+	35.9118i	0.677340	+	1.17319i	−0.298439	+	0.954429i	$0.596466\pi$
$938$		0			0
$939$	−25.0475	−	26.6530i	−0.817396	−	0.869789i
$940$		0			0
$941$	−25.9307	−	44.9133i	−0.845317	−	1.46413i	−0.885346	−	0.464933i	$-0.846078\pi$
$941$	−25.9307	−	44.9133i	−0.845317	−	1.46413i	0.0400291	−	0.999199i	$-0.487255\pi$
$942$		0			0
$943$			6.68815i			0.217796i
$944$		0			0
$945$	16.2337	−	2.76439i	0.528082	−	0.0899256i
$946$		0			0
$947$	−7.41983	−	4.28384i	−0.241112	−	0.139206i	0.374576	−	0.927196i	$-0.377788\pi$
$947$	−7.41983	−	4.28384i	−0.241112	−	0.139206i	−0.615688	+	0.787990i	$0.711122\pi$
$948$		0			0
$949$			23.8063i			0.772785i
$950$		0			0
$951$	22.6753	+	24.1287i	0.735296	+	0.782426i
$952$		0			0
$953$	−19.9307	+	34.5210i	−0.645619	+	1.11824i	0.338539	+	0.940952i	$0.390067\pi$
$953$	−19.9307	+	34.5210i	−0.645619	+	1.11824i	−0.984158	+	0.177292i	$0.943266\pi$
$954$		0			0
$955$	11.8614	−	20.5446i	0.383826	−	0.664806i
$956$		0			0
$957$	−66.0951	+	62.1138i	−2.13655	+	2.00785i
$958$		0			0
$959$	1.02175	−	0.589907i	0.0329940	−	0.0190491i
$960$		0			0
$961$	25.3505			0.817759
$962$		0			0
$963$	46.9783	−	23.3639i	1.51385	−	0.752890i
$964$		0			0
$965$	5.69702	+	9.86752i	0.183393	+	0.317647i
$966$		0			0
$967$	−14.7337	+	25.5195i	−0.473803	+	0.820652i	−0.999550	−	0.0299895i	$-0.990453\pi$
$967$	−14.7337	+	25.5195i	−0.473803	+	0.820652i	0.525747	+	0.850641i	$0.323786\pi$
$968$		0			0
$969$	−34.5367	−	29.1774i	−1.10948	−	0.937312i
$970$		0			0
$971$	−10.0693	+	17.4405i	−0.323139	+	0.559693i	−0.981134	−	0.193329i	$-0.938072\pi$
$971$	−10.0693	+	17.4405i	−0.323139	+	0.559693i	0.657995	+	0.753022i	$0.271405\pi$
$972$		0			0
$973$	−28.6644	−	49.6482i	−0.918938	−	1.59165i
$974$		0			0
$975$	−11.8247	−	3.56529i	−0.378695	−	0.114181i
$976$		0			0
$977$	−27.2554			−0.871979			−0.435989	−	0.899952i	$-0.643601\pi$
$977$	−27.2554			−0.871979			−0.435989	+	0.899952i	$0.643601\pi$
$978$		0			0
$979$	7.11684	−	4.10891i	0.227455	−	0.131321i
$980$		0			0
$981$	8.44158	+	0.524785i	0.269519	+	0.0167551i
$982$		0			0
$983$	22.1644	−	38.3899i	0.706934	−	1.22445i	−0.259055	−	0.965863i	$-0.583411\pi$
$983$	22.1644	−	38.3899i	0.706934	−	1.22445i	0.965989	−	0.258583i	$-0.0832557\pi$
$984$		0			0
$985$	−8.00000	+	13.8564i	−0.254901	+	0.441502i
$986$		0			0
$987$	−25.4891	+	23.9538i	−0.811328	+	0.762457i
$988$		0			0
$989$			1.63948i			0.0521323i
$990$		0			0
$991$	−17.2663	−	9.96871i	−0.548482	−	0.316667i	0.200027	−	0.979790i	$-0.435897\pi$
$991$	−17.2663	−	9.96871i	−0.548482	−	0.316667i	−0.748510	+	0.663124i	$0.769230\pi$
$992$		0			0
$993$	−1.80298	−	7.67420i	−0.0572160	−	0.243533i
$994$		0			0
$995$		−	7.27806i		−	0.230730i
$996$		0			0
$997$	−15.6168	−	27.0492i	−0.494590	−	0.856656i	0.505390	−	0.862891i	$-0.331349\pi$
$997$	−15.6168	−	27.0492i	−0.494590	−	0.856656i	−0.999981	+	0.00623523i	$0.998015\pi$
$998$		0			0
$999$	19.3723	+	23.3639i	0.612912	+	0.739200i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bn.k.65.2		4
3.2	odd	2		912.2.bn.l.65.2		4
4.3	odd	2		228.2.p.d.65.1	yes	4
12.11	even	2		228.2.p.c.65.1	✓	4
19.12	odd	6		912.2.bn.l.449.1		4
57.50	even	6	inner	912.2.bn.k.449.2		4
76.31	even	6		228.2.p.c.221.2	yes	4
228.107	odd	6		228.2.p.d.221.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.p.c.65.1	✓	4	12.11	even	2
228.2.p.c.221.2	yes	4	76.31	even	6
228.2.p.d.65.1	yes	4	4.3	odd	2
228.2.p.d.221.1	yes	4	228.107	odd	6
912.2.bn.k.65.2		4	1.1	even	1	trivial
912.2.bn.k.449.2		4	57.50	even	6	inner
912.2.bn.l.65.2		4	3.2	odd	2
912.2.bn.l.449.1		4	19.12	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bn (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.68614 - 0.396143i) q^{3} +(-0.813859 - 0.469882i) q^{5} -3.37228 q^{7} +(2.68614 - 1.33591i) q^{9} +O(q^{10})\)	\(q+(1.68614 - 0.396143i) q^{3} +(-0.813859 - 0.469882i) q^{5} -3.37228 q^{7} +(2.68614 - 1.33591i) q^{9} -5.04868i q^{11} +(1.50000 - 0.866025i) q^{13} +(-1.55842 - 0.469882i) q^{15} +(5.18614 + 2.99422i) q^{17} +(-4.00000 - 1.73205i) q^{19} +(-5.68614 + 1.33591i) q^{21} +(-0.813859 + 0.469882i) q^{23} +(-2.05842 - 3.56529i) q^{25} +(4.00000 - 3.31662i) q^{27} +(-5.18614 - 8.98266i) q^{29} -2.37686i q^{31} +(-2.00000 - 8.51278i) q^{33} +(2.74456 + 1.58457i) q^{35} +5.84096i q^{37} +(2.18614 - 2.05446i) q^{39} +(3.55842 - 6.16337i) q^{41} +(0.872281 - 1.51084i) q^{43} +(-2.81386 - 0.174928i) q^{45} +(5.18614 - 2.99422i) q^{47} +4.37228 q^{49} +(9.93070 + 2.99422i) q^{51} +(0.813859 + 1.40965i) q^{53} +(-2.37228 + 4.10891i) q^{55} +(-7.43070 - 1.33591i) q^{57} +(-0.813859 + 1.40965i) q^{59} +(-0.872281 - 1.51084i) q^{61} +(-9.05842 + 4.50506i) q^{63} -1.62772 q^{65} +(1.50000 - 0.866025i) q^{67} +(-1.18614 + 1.11469i) q^{69} +(-3.55842 + 6.16337i) q^{71} +(-6.87228 + 11.9031i) q^{73} +(-4.88316 - 5.19615i) q^{75} +17.0256i q^{77} +(8.61684 + 4.97494i) q^{79} +(5.43070 - 7.17687i) q^{81} +1.87953i q^{83} +(-2.81386 - 4.87375i) q^{85} +(-12.3030 - 13.0916i) q^{87} +(0.813859 + 1.40965i) q^{89} +(-5.05842 + 2.92048i) q^{91} +(-0.941578 - 4.00772i) q^{93} +(2.44158 + 3.28917i) q^{95} +(10.6753 + 6.16337i) q^{97} +(-6.74456 - 13.5615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} - 9 q^{5} - 2 q^{7} + 5 q^{9}+O(q^{10}) \) 4 * q + q^3 - 9 * q^5 - 2 * q^7 + 5 * q^9	\( 4 q + q^{3} - 9 q^{5} - 2 q^{7} + 5 q^{9} + 6 q^{13} + 11 q^{15} + 15 q^{17} - 16 q^{19} - 17 q^{21} - 9 q^{23} + 9 q^{25} + 16 q^{27} - 15 q^{29} - 8 q^{33} - 12 q^{35} + 3 q^{39} - 3 q^{41} - 8 q^{43} - 17 q^{45} + 15 q^{47} + 6 q^{49} + 11 q^{51} + 9 q^{53} + 2 q^{55} - q^{57} - 9 q^{59} + 8 q^{61} - 19 q^{63} - 18 q^{65} + 6 q^{67} + q^{69} + 3 q^{71} - 16 q^{73} - 54 q^{75} - 7 q^{81} - 17 q^{85} - 9 q^{87} + 9 q^{89} - 3 q^{91} - 21 q^{93} + 27 q^{95} - 9 q^{97} - 4 q^{99}+O(q^{100}) \) 4 * q + q^3 - 9 * q^5 - 2 * q^7 + 5 * q^9 + 6 * q^13 + 11 * q^15 + 15 * q^17 - 16 * q^19 - 17 * q^21 - 9 * q^23 + 9 * q^25 + 16 * q^27 - 15 * q^29 - 8 * q^33 - 12 * q^35 + 3 * q^39 - 3 * q^41 - 8 * q^43 - 17 * q^45 + 15 * q^47 + 6 * q^49 + 11 * q^51 + 9 * q^53 + 2 * q^55 - q^57 - 9 * q^59 + 8 * q^61 - 19 * q^63 - 18 * q^65 + 6 * q^67 + q^69 + 3 * q^71 - 16 * q^73 - 54 * q^75 - 7 * q^81 - 17 * q^85 - 9 * q^87 + 9 * q^89 - 3 * q^91 - 21 * q^93 + 27 * q^95 - 9 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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