LMFDB - Embedded newform 912.2.bn.l.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:	$\Z[a_1, \ldots, a_{7}]$
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.l.449.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 1.65831i) q^{3} +(0.813859 + 0.469882i) q^{5} -3.37228 q^{7} +(-2.50000 + 1.65831i) q^{9} +O(q^{10})$	\(q+(0.500000 + 1.65831i) q^{3} +(0.813859 + 0.469882i) q^{5} -3.37228 q^{7} +(-2.50000 + 1.65831i) q^{9} +5.04868i q^{11} +(1.50000 - 0.866025i) q^{13} +(-0.372281 + 1.58457i) q^{15} +(-5.18614 - 2.99422i) q^{17} +(-4.00000 - 1.73205i) q^{19} +(-1.68614 - 5.59230i) q^{21} +(0.813859 - 0.469882i) q^{23} +(-2.05842 - 3.56529i) q^{25} +(-4.00000 - 3.31662i) q^{27} +(5.18614 + 8.98266i) q^{29} -2.37686i q^{31} +(-8.37228 + 2.52434i) q^{33} +(-2.74456 - 1.58457i) q^{35} +5.84096i q^{37} +(2.18614 + 2.05446i) q^{39} +(-3.55842 + 6.16337i) q^{41} +(0.872281 - 1.51084i) q^{43} +(-2.81386 + 0.174928i) q^{45} +(-5.18614 + 2.99422i) q^{47} +4.37228 q^{49} +(2.37228 - 10.0974i) q^{51} +(-0.813859 - 1.40965i) q^{53} +(-2.37228 + 4.10891i) q^{55} +(0.872281 - 7.49927i) q^{57} +(0.813859 - 1.40965i) q^{59} +(-0.872281 - 1.51084i) q^{61} +(8.43070 - 5.59230i) q^{63} +1.62772 q^{65} +(1.50000 - 0.866025i) q^{67} +(1.18614 + 1.11469i) q^{69} +(3.55842 - 6.16337i) q^{71} +(-6.87228 + 11.9031i) q^{73} +(4.88316 - 5.19615i) q^{75} -17.0256i q^{77} +(8.61684 + 4.97494i) q^{79} +(3.50000 - 8.29156i) q^{81} -1.87953i q^{83} +(-2.81386 - 4.87375i) q^{85} +(-12.3030 + 13.0916i) q^{87} +(-0.813859 - 1.40965i) q^{89} +(-5.05842 + 2.92048i) q^{91} +(3.94158 - 1.18843i) q^{93} +(-2.44158 - 3.28917i) q^{95} +(10.6753 + 6.16337i) q^{97} +(-8.37228 - 12.6217i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 9 q^{5} - 2 q^{7} - 10 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 9 * q^5 - 2 * q^7 - 10 * q^9	$ 4 q + 2 q^{3} + 9 q^{5} - 2 q^{7} - 10 q^{9} + 6 q^{13} + 10 q^{15} - 15 q^{17} - 16 q^{19} - q^{21} + 9 q^{23} + 9 q^{25} - 16 q^{27} + 15 q^{29} - 22 q^{33} + 12 q^{35} + 3 q^{39} + 3 q^{41} - 8 q^{43} - 17 q^{45} - 15 q^{47} + 6 q^{49} - 2 q^{51} - 9 q^{53} + 2 q^{55} - 8 q^{57} + 9 q^{59} + 8 q^{61} + 5 q^{63} + 18 q^{65} + 6 q^{67} - q^{69} - 3 q^{71} - 16 q^{73} + 54 q^{75} + 14 q^{81} - 17 q^{85} - 9 q^{87} - 9 q^{89} - 3 q^{91} + 33 q^{93} - 27 q^{95} - 9 q^{97} - 22 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 + 9 * q^5 - 2 * q^7 - 10 * q^9 + 6 * q^13 + 10 * q^15 - 15 * q^17 - 16 * q^19 - q^21 + 9 * q^23 + 9 * q^25 - 16 * q^27 + 15 * q^29 - 22 * q^33 + 12 * q^35 + 3 * q^39 + 3 * q^41 - 8 * q^43 - 17 * q^45 - 15 * q^47 + 6 * q^49 - 2 * q^51 - 9 * q^53 + 2 * q^55 - 8 * q^57 + 9 * q^59 + 8 * q^61 + 5 * q^63 + 18 * q^65 + 6 * q^67 - q^69 - 3 * q^71 - 16 * q^73 + 54 * q^75 + 14 * q^81 - 17 * q^85 - 9 * q^87 - 9 * q^89 - 3 * q^91 + 33 * q^93 - 27 * q^95 - 9 * q^97 - 22 * 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
$3$	0.500000	+	1.65831i	0.288675	+	0.957427i
$3$	0.500000	+	1.65831i	0.288675	+	0.957427i
$4$		0			0
$5$	0.813859	+	0.469882i	0.363969	+	0.210138i	0.670820	−	0.741620i	$-0.265942\pi$
$5$	0.813859	+	0.469882i	0.363969	+	0.210138i	−0.306851	+	0.951757i	$0.599275\pi$
$6$		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
$9$	−2.50000	+	1.65831i	−0.833333	+	0.552771i
$10$		0			0
$11$			5.04868i			1.52223i	0.648615	+	0.761116i	$0.275348\pi$
$11$			5.04868i			1.52223i	−0.648615	+	0.761116i	$0.724652\pi$
$12$		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
$15$	−0.372281	+	1.58457i	−0.0961226	+	0.409135i
$16$		0			0
$17$	−5.18614	−	2.99422i	−1.25782	−	0.726205i	−0.285173	−	0.958476i	$-0.592051\pi$
$17$	−5.18614	−	2.99422i	−1.25782	−	0.726205i	−0.972651	+	0.232271i	$0.925384\pi$
$18$		0			0
$19$	−4.00000	−	1.73205i	−0.917663	−	0.397360i
$19$	−4.00000	−	1.73205i	−0.917663	−	0.397360i
$20$		0			0
$21$	−1.68614	−	5.59230i	−0.367946	−	1.22034i
$22$		0			0
$23$	0.813859	−	0.469882i	0.169701	−	0.0979772i	−0.412744	−	0.910847i	$-0.635429\pi$
$23$	0.813859	−	0.469882i	0.169701	−	0.0979772i	0.582445	+	0.812870i	$0.302096\pi$
$24$		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	$0.246524\pi$
$29$	5.18614	+	8.98266i	0.963042	+	1.66804i	0.248256	+	0.968694i	$0.420142\pi$
$30$		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
$33$	−8.37228	+	2.52434i	−1.45743	+	0.439431i
$34$		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	$0.354229\pi$
$41$	−3.55842	+	6.16337i	−0.555732	+	0.962556i	−0.997846	+	0.0655975i	$0.979105\pi$
$42$		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	−0.828029	−	0.560685i	$-0.810538\pi$
$47$	−5.18614	+	2.99422i	−0.756476	+	0.436752i	0.0715528	+	0.997437i	$0.477205\pi$
$48$		0			0
$49$	4.37228			0.624612
$50$		0			0
$51$	2.37228	−	10.0974i	0.332186	−	1.41391i
$52$		0			0
$53$	−0.813859	−	1.40965i	−0.111792	−	0.193630i	0.804701	−	0.593681i	$-0.202326\pi$
$53$	−0.813859	−	1.40965i	−0.111792	−	0.193630i	−0.916493	+	0.400051i	$0.868992\pi$
$54$		0			0
$55$	−2.37228	+	4.10891i	−0.319878	+	0.554046i
$56$		0			0
$57$	0.872281	−	7.49927i	0.115536	−	0.993303i
$58$		0			0
$59$	0.813859	−	1.40965i	0.105955	−	0.183520i	−0.808173	−	0.588946i	$-0.799543\pi$
$59$	0.813859	−	1.40965i	0.105955	−	0.183520i	0.914128	+	0.405425i	$0.132877\pi$
$60$		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
$63$	8.43070	−	5.59230i	1.06217	−	0.704563i
$64$		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	−0.573858	−	0.818955i	$-0.694554\pi$
$71$	3.55842	−	6.16337i	0.422307	−	0.731457i	0.996165	+	0.0874978i	$0.0278871\pi$
$72$		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
$81$	3.50000	−	8.29156i	0.388889	−	0.921285i
$82$		0			0
$83$		−	1.87953i		−	0.206305i	−0.994666	−	0.103152i	$-0.967107\pi$
$83$		−	1.87953i		−	0.206305i	0.994666	−	0.103152i	$-0.0328930\pi$
$84$		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	0.819662	−	0.572847i	$-0.194161\pi$
$89$	−0.813859	−	1.40965i	−0.0862689	−	0.149422i	−0.905931	+	0.423425i	$0.860828\pi$
$90$		0			0
$91$	−5.05842	+	2.92048i	−0.530267	+	0.306150i
$92$		0			0
$93$	3.94158	−	1.18843i	0.408723	−	0.123235i
$94$		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
$99$	−8.37228	−	12.6217i	−0.841446	−	1.26853i
$100$		0			0
$101$	−13.9307	+	8.04290i	−1.38616	+	0.800298i	−0.992880	−	0.119122i	$-0.961992\pi$
$101$	−13.9307	+	8.04290i	−1.38616	+	0.800298i	−0.393277	+	0.919420i	$0.628659\pi$
$102$		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
$105$	1.25544	−	5.34363i	0.122518	−	0.521485i
$106$		0			0
$107$	−17.4891			−1.69074			−0.845369	−	0.534183i	$-0.820619\pi$
$107$	−17.4891			−1.69074			−0.845369	+	0.534183i	$0.820619\pi$
$108$		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
$111$	−9.68614	+	2.92048i	−0.919368	+	0.277200i
$112$		0			0
$113$	8.74456			0.822619			0.411310	−	0.911496i	$-0.365071\pi$
$113$	8.74456			0.822619			0.411310	+	0.911496i	$0.365071\pi$
$114$		0			0
$115$	0.883156			0.0823547
$116$		0			0
$117$	−2.31386	+	4.65253i	−0.213916	+	0.430127i
$118$		0			0
$119$	17.4891	+	10.0974i	1.60323	+	0.925623i
$120$		0			0
$121$	−14.4891			−1.31719
$122$		0			0
$123$	−12.0000	−	2.81929i	−1.08200	−	0.254207i
$124$		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
$129$	2.94158	+	0.691097i	0.258992	+	0.0608477i
$130$		0			0
$131$	5.18614	+	2.99422i	0.453115	+	0.261606i	0.709145	−	0.705063i	$-0.249081\pi$
$131$	5.18614	+	2.99422i	0.453115	+	0.261606i	−0.256030	+	0.966669i	$0.582415\pi$
$132$		0			0
$133$	13.4891	+	5.84096i	1.16966	+	0.506476i
$134$		0			0
$135$	−1.69702	−	4.57879i	−0.146056	−	0.394080i
$136$		0			0
$137$	0.302985	−	0.174928i	0.0258857	−	0.0149451i	−0.487001	−	0.873401i	$-0.661909\pi$
$137$	0.302985	−	0.174928i	0.0258857	−	0.0149451i	0.512887	+	0.858456i	$0.328576\pi$
$138$		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
$147$	2.18614	+	7.25061i	0.180310	+	0.598020i
$148$		0			0
$149$	15.0475	+	8.68771i	1.23274	+	0.711725i	0.967601	−	0.252485i	$-0.0812478\pi$
$149$	15.0475	+	8.68771i	1.23274	+	0.711725i	0.265142	+	0.964209i	$0.414581\pi$
$150$		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
$165$	−8.00000	−	1.87953i	−0.622799	−	0.146321i
$166$		0			0
$167$	7.93070	+	13.7364i	0.613696	+	1.06295i	0.990612	+	0.136705i	$0.0436514\pi$
$167$	7.93070	+	13.7364i	0.613696	+	1.06295i	−0.376915	+	0.926248i	$0.623015\pi$
$168$		0			0
$169$	−5.00000	+	8.66025i	−0.384615	+	0.666173i
$170$		0			0
$171$	12.8723	−	2.30312i	0.984368	−	0.176124i
$172$		0			0
$173$	5.18614	−	8.98266i	0.394295	−	0.682939i	−0.598716	−	0.800961i	$-0.704322\pi$
$173$	5.18614	−	8.98266i	0.394295	−	0.682939i	0.993011	+	0.118023i	$0.0376555\pi$
$174$		0			0
$175$	6.94158	+	12.0232i	0.524734	+	0.908866i
$176$		0			0
$177$	2.74456	+	0.644810i	0.206294	+	0.0484669i
$178$		0			0
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		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	$-0.633546\pi$
$191$		−	25.2434i		−	1.82655i	0.407347	−	0.913273i	$-0.366454\pi$
$192$		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
$195$	0.813859	+	2.69927i	0.0582817	+	0.193298i
$196$		0			0
$197$			17.0256i			1.21302i	0.795076	+	0.606510i	$0.207431\pi$
$197$			17.0256i			1.21302i	−0.795076	+	0.606510i	$0.792569\pi$
$198$		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
$207$	−1.25544	+	2.52434i	−0.0872589	+	0.175454i
$208$		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
$213$	12.0000	+	2.81929i	0.822226	+	0.193175i
$214$		0			0
$215$	1.41983	−	0.819738i	0.0968315	−	0.0559057i
$216$		0			0
$217$			8.01544i			0.544124i
$218$		0			0
$219$	−23.1753	−	5.44482i	−1.56604	−	0.367927i
$220$		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
$225$	11.0584	+	5.49972i	0.737228	+	0.366648i
$226$		0			0
$227$	−22.9783			−1.52512			−0.762560	−	0.646917i	$-0.776058\pi$
$227$	−22.9783			−1.52512			−0.762560	+	0.646917i	$0.776058\pi$
$228$		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
$231$	28.2337	−	8.51278i	1.85764	−	0.560100i
$232$		0			0
$233$	6.81386	+	3.93398i	0.446391	+	0.257724i	0.706305	−	0.707908i	$-0.250361\pi$
$233$	6.81386	+	3.93398i	0.446391	+	0.257724i	−0.259914	+	0.965632i	$0.583694\pi$
$234$		0			0
$235$	−5.62772			−0.367112
$236$		0			0
$237$	−3.94158	+	16.7769i	−0.256033	+	1.08978i
$238$		0			0
$239$			5.04868i			0.326572i	0.986579	+	0.163286i	$0.0522093\pi$
$239$			5.04868i			0.326572i	−0.986579	+	0.163286i	$0.947791\pi$
$240$		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
$243$	15.5000	+	1.65831i	0.994325	+	0.106381i
$244$		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
$249$	3.11684	−	0.939764i	0.197522	−	0.0595551i
$250$		0			0
$251$	−17.1861	+	9.92242i	−1.08478	+	0.626298i	−0.932182	−	0.361991i	$-0.882097\pi$
$251$	−17.1861	+	9.92242i	−1.08478	+	0.626298i	−0.152598	+	0.988288i	$0.548764\pi$
$252$		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	$-0.963328\pi$
$257$	−9.55842	−	16.5557i	−0.596238	−	1.03271i	0.397133	−	0.917761i	$-0.370005\pi$
$258$		0			0
$259$		−	19.6974i		−	1.22393i
$260$		0			0
$261$	−27.8614	−	13.8564i	−1.72458	−	0.857690i
$262$		0			0
$263$	17.1861	+	9.92242i	1.05974	+	0.611843i	0.925361	−	0.379087i	$-0.123762\pi$
$263$	17.1861	+	9.92242i	1.05974	+	0.611843i	0.134382	+	0.990930i	$0.457095\pi$
$264$		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	−0.889769	−	0.456410i	$-0.849135\pi$
$269$	−0.813859	+	1.40965i	−0.0496219	+	0.0859476i	0.840148	+	0.542358i	$0.182468\pi$
$270$		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
$279$	3.94158	+	5.94215i	0.235976	+	0.355747i
$280$		0			0
$281$	7.93070	+	13.7364i	0.473106	+	0.819444i	0.999526	−	0.0307808i	$-0.00979939\pi$
$281$	7.93070	+	13.7364i	0.473106	+	0.819444i	−0.526420	+	0.850225i	$0.676466\pi$
$282$		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
$285$	4.23369	−	5.69349i	0.250782	−	0.337253i
$286$		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
$291$	−4.88316	+	20.7846i	−0.286256	+	1.21842i
$292$		0			0
$293$	−14.2337			−0.831541			−0.415770	−	0.909470i	$-0.636488\pi$
$293$	−14.2337			−0.831541			−0.415770	+	0.909470i	$0.636488\pi$
$294$		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
$309$	−26.9198	+	8.11663i	−1.53142	+	0.461739i
$310$		0			0
$311$			18.9051i			1.07201i	0.844215	+	0.536004i	$0.180067\pi$
$311$			18.9051i			1.07201i	−0.844215	+	0.536004i	$0.819933\pi$
$312$		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	$-0.986279\pi$
$317$	−9.55842	−	16.5557i	−0.536854	−	0.929859i	0.462217	−	0.886767i	$-0.347054\pi$
$318$		0			0
$319$	−45.3505	+	26.1831i	−2.53914	+	1.46597i
$320$		0			0
$321$	−8.74456	−	29.0024i	−0.488074	−	1.61876i
$322$		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
$327$	−1.11684	+	4.75372i	−0.0617616	+	0.262881i
$328$		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
$333$	−9.68614	−	14.6024i	−0.530797	−	0.800207i
$334$		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
$339$	4.37228	+	14.5012i	0.237470	+	0.787598i
$340$		0			0
$341$	12.0000			0.649836
$342$		0			0
$343$	8.86141			0.478471
$344$		0			0
$345$	0.441578	+	1.46455i	0.0237738	+	0.0788486i
$346$		0			0
$347$	−0.813859	−	0.469882i	−0.0436903	−	0.0252246i	0.477996	−	0.878362i	$-0.341363\pi$
$347$	−0.813859	−	0.469882i	−0.0436903	−	0.0252246i	−0.521686	+	0.853138i	$0.674697\pi$
$348$		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
$351$	−8.87228	−	1.51084i	−0.473567	−	0.0806424i
$352$		0			0
$353$		−	13.2665i		−	0.706105i	−0.935604	−	0.353052i	$-0.885144\pi$
$353$		−	13.2665i		−	0.706105i	0.935604	−	0.353052i	$-0.114856\pi$
$354$		0			0
$355$	5.79211	−	3.34408i	0.307413	−	0.177485i
$356$		0			0
$357$	−8.00000	+	34.0511i	−0.423405	+	1.80218i
$358$		0			0
$359$	−18.8139	−	10.8622i	−0.992958	−	0.573284i	−0.0868005	−	0.996226i	$-0.527664\pi$
$359$	−18.8139	−	10.8622i	−0.992958	−	0.573284i	−0.906157	+	0.422941i	$0.860998\pi$
$360$		0			0
$361$	13.0000	+	13.8564i	0.684211	+	0.729285i
$362$		0			0
$363$	−7.24456	−	24.0275i	−0.380241	−	1.26112i
$364$		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
$375$	14.2079	−	4.28384i	0.733692	−	0.221217i
$376$		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	−0.844483	−	0.535582i	$-0.820092\pi$
$383$	0.813859	−	1.40965i	0.0415863	−	0.0720295i	0.886069	+	0.463553i	$0.153426\pi$
$384$		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	−0.393279	−	0.919419i	$-0.628659\pi$
$389$	4.06930	−	2.34941i	0.206322	−	0.119120i	0.599601	+	0.800299i	$0.295326\pi$
$390$		0			0
$391$	−5.62772			−0.284606
$392$		0			0
$393$	−2.37228	+	10.0974i	−0.119666	+	0.509344i
$394$		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
$399$	−2.94158	+	25.2897i	−0.147263	+	1.26607i
$400$		0			0
$401$	−6.30298	+	10.9171i	−0.314756	+	0.545173i	−0.979386	−	0.202000i	$-0.935256\pi$
$401$	−6.30298	+	10.9171i	−0.314756	+	0.545173i	0.664630	+	0.747173i	$0.268589\pi$
$402$		0			0
$403$	−2.05842	−	3.56529i	−0.102537	−	0.177600i
$404$		0			0
$405$	6.74456	−	5.10358i	0.335140	−	0.253599i
$406$		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	$0.152791\pi$
$419$			18.9051i			0.923574i	−0.886991	+	0.461787i	$0.847209\pi$
$420$		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
$423$	8.00000	−	16.0858i	0.388973	−	0.782118i
$424$		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	0.994508	−	0.104659i	$-0.0333752\pi$
$431$	8.44158	+	14.6212i	0.406617	+	0.704280i	−0.587892	+	0.808940i	$0.700042\pi$
$432$		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
$435$	−16.1644	+	4.87375i	−0.775023	+	0.233678i
$436$		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
$441$	−10.9307	+	7.25061i	−0.520510	+	0.345267i
$442$		0			0
$443$	18.8139	−	10.8622i	0.893873	−	0.516078i	0.0186659	−	0.999826i	$-0.494058\pi$
$443$	18.8139	−	10.8622i	0.893873	−	0.516078i	0.875207	+	0.483748i	$0.160725\pi$
$444$		0			0
$445$		−	1.52967i		−	0.0725134i
$446$		0			0
$447$	−6.88316	+	29.2974i	−0.325562	+	1.38572i
$448$		0			0
$449$	−20.7446			−0.978996			−0.489498	−	0.872004i	$-0.662820\pi$
$449$	−20.7446			−0.978996			−0.489498	+	0.872004i	$0.662820\pi$
$450$		0			0
$451$	−31.1168	−	17.9653i	−1.46523	−	0.845954i
$452$		0			0
$453$	5.74456	−	1.73205i	0.269903	−	0.0813788i
$454$		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
$459$	10.8139	+	29.1774i	0.504748	+	1.36188i
$460$		0			0
$461$	−13.4198	−	7.74794i	−0.625024	−	0.360858i	0.153799	−	0.988102i	$-0.450849\pi$
$461$	−13.4198	−	7.74794i	−0.625024	−	0.360858i	−0.778822	+	0.627245i	$0.784183\pi$
$462$		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
$465$	3.76631	+	0.884861i	0.174659	+	0.0410344i
$466$		0			0
$467$		−	18.3152i		−	0.847525i	−0.905773	−	0.423763i	$-0.860709\pi$
$467$		−	18.3152i		−	0.847525i	0.905773	−	0.423763i	$-0.139291\pi$
$468$		0			0
$469$	−5.05842	+	2.92048i	−0.233576	+	0.134855i
$470$		0			0
$471$	35.8030	+	8.41159i	1.64971	+	0.387585i
$472$		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
$477$	4.37228	+	2.17448i	0.200193	+	0.0995627i
$478$		0			0
$479$	−17.1861	+	9.92242i	−0.785255	+	0.453367i	−0.838289	−	0.545226i	$-0.816444\pi$
$479$	−17.1861	+	9.92242i	−0.785255	+	0.453367i	0.0530345	+	0.998593i	$0.483111\pi$
$480$		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
$489$	−3.05842	−	10.1436i	−0.138307	−	0.458711i
$490$		0			0
$491$	−18.8139	−	10.8622i	−0.849058	−	0.490204i	0.0112752	−	0.999936i	$-0.496411\pi$
$491$	−18.8139	−	10.8622i	−0.849058	−	0.490204i	−0.860333	+	0.509733i	$0.829744\pi$
$492$		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	−0.656211	−	0.754577i	$-0.727842\pi$
$503$	−7.41983	+	4.28384i	−0.330834	+	0.191007i	0.325377	+	0.945584i	$0.394509\pi$
$504$		0			0
$505$	−15.1168			−0.672691
$506$		0			0
$507$	−16.8614	−	3.96143i	−0.748841	−	0.175934i
$508$		0			0
$509$	10.6753	+	18.4901i	0.473173	+	0.819559i	0.999528	−	0.0307051i	$-0.00977527\pi$
$509$	10.6753	+	18.4901i	0.473173	+	0.819559i	−0.526356	+	0.850265i	$0.676442\pi$
$510$		0			0
$511$	23.1753	−	40.1407i	1.02521	−	1.77572i
$512$		0			0
$513$	10.2554	+	20.1947i	0.452789	+	0.891618i
$514$		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
$519$	17.4891	+	4.10891i	0.767687	+	0.180361i
$520$		0			0
$521$	−32.7446			−1.43457			−0.717283	−	0.696782i	$-0.754614\pi$
$521$	−32.7446			−1.43457			−0.717283	+	0.696782i	$0.754614\pi$
$522$		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
$537$	6.00000	+	19.8997i	0.258919	+	0.858738i
$538$		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
$549$	4.68614	+	2.33057i	0.200000	+	0.0994665i
$550$		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
$555$	−9.25544	−	2.17448i	−0.392871	−	0.0923016i
$556$		0			0
$557$	24.3030	−	14.0313i	1.02975	−	0.594527i	0.112837	−	0.993613i	$-0.464006\pi$
$557$	24.3030	−	14.0313i	1.02975	−	0.594527i	0.916913	+	0.399087i	$0.130673\pi$
$558$		0			0
$559$		−	3.02167i		−	0.127803i
$560$		0			0
$561$	50.9783	+	11.9769i	2.15230	+	0.505664i
$562$		0			0
$563$	−17.4891			−0.737079			−0.368539	−	0.929612i	$-0.620142\pi$
$563$	−17.4891			−0.737079			−0.368539	+	0.929612i	$0.620142\pi$
$564$		0			0
$565$	7.11684	+	4.10891i	0.299408	+	0.172863i
$566$		0			0
$567$	−11.8030	+	27.9615i	−0.495679	+	1.17427i
$568$		0			0
$569$	−44.7446			−1.87579			−0.937895	−	0.346920i	$-0.887228\pi$
$569$	−44.7446			−1.87579			−0.937895	+	0.346920i	$0.887228\pi$
$570$		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
$573$	41.8614	−	12.6217i	1.74879	−	0.527279i
$574$		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
$579$	4.80298	−	20.4434i	0.199605	−	0.849597i
$580$		0			0
$581$			6.33830i			0.262957i
$582$		0			0
$583$	7.11684	−	4.10891i	0.294750	−	0.170174i
$584$		0			0
$585$	−4.06930	+	2.69927i	−0.168245	+	0.111601i
$586$		0			0
$587$	25.4198	+	14.6761i	1.04919	+	0.605749i	0.922422	−	0.386183i	$-0.126207\pi$
$587$	25.4198	+	14.6761i	1.04919	+	0.605749i	0.126767	+	0.991933i	$0.459540\pi$
$588$		0			0
$589$	−4.11684	+	9.50744i	−0.169632	+	0.391747i
$590$		0			0
$591$	−28.2337	+	8.51278i	−1.16138	+	0.350169i
$592$		0			0
$593$	4.06930	−	2.34941i	0.167106	−	0.0964787i	−0.414115	−	0.910225i	$-0.635909\pi$
$593$	4.06930	−	2.34941i	0.167106	−	0.0964787i	0.581221	+	0.813746i	$0.302575\pi$
$594$		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	$-0.991270\pi$
$599$	−12.8139	−	22.1943i	−0.523560	−	0.906833i	0.476064	−	0.879411i	$-0.342063\pi$
$600$		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
$603$	−2.31386	+	4.65253i	−0.0942276	+	0.189466i
$604$		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	−0.140352	−	0.990102i	$-0.544823\pi$
$617$	16.0693	−	9.27761i	0.646926	−	0.373503i	0.787277	+	0.616599i	$0.211490\pi$
$618$		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
$621$	−4.81386	−	0.819738i	−0.193174	−	0.0328950i
$622$		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
$627$	37.8614	+	4.40387i	1.51204	+	0.175873i
$628$		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
$633$	−11.3139	+	48.1562i	−0.449686	+	1.91404i
$634$		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	−0.574453	−	0.818537i	$-0.694785\pi$
$641$	10.6753	−	18.4901i	0.421648	−	0.730315i	0.996101	+	0.0882223i	$0.0281186\pi$
$642$		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	$-0.899898\pi$
$647$		−	15.7359i		−	0.618643i	0.950957	−	0.309322i	$-0.100102\pi$
$648$		0			0
$649$	7.11684	+	4.10891i	0.279361	+	0.161289i
$650$		0			0
$651$	−13.2921	+	4.00772i	−0.520959	+	0.157075i
$652$		0			0
$653$		−	20.1947i		−	0.790280i	−0.918621	−	0.395140i	$-0.870696\pi$
$653$		−	20.1947i		−	0.790280i	0.918621	−	0.395140i	$-0.129304\pi$
$654$		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	0.942603	−	0.333915i	$-0.108370\pi$
$659$	4.67527	+	8.09780i	0.182123	+	0.315445i	−0.760481	+	0.649361i	$0.775037\pi$
$660$		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
$663$	−5.18614	−	17.2005i	−0.201413	−	0.668011i
$664$		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
$669$	−1.19702	+	5.09496i	−0.0462793	+	0.196983i
$670$		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
$675$	−3.59105	+	21.0882i	−0.138219	+	0.811684i
$676$		0			0
$677$	9.76631			0.375350			0.187675	−	0.982231i	$-0.439905\pi$
$677$	9.76631			0.375350			0.187675	+	0.982231i	$0.439905\pi$
$678$		0			0
$679$	−36.0000	−	20.7846i	−1.38155	−	0.797640i
$680$		0			0
$681$	−11.4891	−	38.1051i	−0.440264	−	1.46019i
$682$		0			0
$683$	40.4674			1.54844			0.774221	−	0.632916i	$-0.218142\pi$
$683$	40.4674			1.54844			0.774221	+	0.632916i	$0.218142\pi$
$684$		0			0
$685$	0.328782			0.0125621
$686$		0			0
$687$	−1.31386	−	4.35758i	−0.0501269	−	0.166252i
$688$		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
$693$	28.2337	+	42.5639i	1.07251	+	1.61687i
$694$		0			0
$695$			15.9760i			0.606004i
$696$		0			0
$697$	36.9090	−	21.3094i	1.39803	−	0.807151i
$698$		0			0
$699$	−3.11684	+	13.2665i	−0.117890	+	0.501785i
$700$		0			0
$701$	−25.4198	−	14.6761i	−0.960094	−	0.554310i	−0.0638918	−	0.997957i	$-0.520351\pi$
$701$	−25.4198	−	14.6761i	−0.960094	−	0.554310i	−0.896202	+	0.443646i	$0.853685\pi$
$702$		0			0
$703$	10.1168	−	23.3639i	0.381564	−	0.881184i
$704$		0			0
$705$	−2.81386	−	9.33252i	−0.105976	−	0.351483i
$706$		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
$717$	−8.37228	+	2.52434i	−0.312669	+	0.0942731i
$718$		0			0
$719$	25.4198	+	14.6761i	0.948000	+	0.547328i	0.892459	−	0.451129i	$-0.148978\pi$
$719$	25.4198	+	14.6761i	0.948000	+	0.547328i	0.0555407	+	0.998456i	$0.482312\pi$
$720$		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
$735$	−1.62772	+	6.92820i	−0.0600393	+	0.255551i
$736$		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
$741$	−5.18614	−	12.0043i	−0.190518	−	0.440990i
$742$		0			0
$743$	−14.4416	+	25.0135i	−0.529810	+	0.917658i	0.469585	+	0.882887i	$0.344403\pi$
$743$	−14.4416	+	25.0135i	−0.529810	+	0.917658i	−0.999395	+	0.0347709i	$0.988930\pi$
$744$		0			0
$745$	8.16439	+	14.1411i	0.299120	+	0.518091i
$746$		0			0
$747$	3.11684	+	4.69882i	0.114039	+	0.171921i
$748$		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	$-0.922703\pi$
$761$		−	13.2665i		−	0.480910i	0.970660	−	0.240455i	$-0.0772967\pi$
$762$		0			0
$763$	−8.23369	−	4.75372i	−0.298080	−	0.172096i
$764$		0			0
$765$	15.1168	+	7.51811i	0.546551	+	0.271818i
$766$		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	$0.000387012\pi$
$773$	13.9307	+	24.1287i	0.501053	+	0.867849i	−0.498947	+	0.866633i	$0.666280\pi$
$774$		0			0
$775$	−8.47420	+	4.89258i	−0.304402	+	0.175747i
$776$		0			0
$777$	32.6644	−	9.84868i	1.17183	−	0.353320i
$778$		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
$783$	9.04755	−	53.1311i	0.323333	−	1.89875i
$784$		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
$789$	−7.86141	+	33.4612i	−0.279873	+	1.19125i
$790$		0			0
$791$	−29.4891			−1.04851
$792$		0			0
$793$	−2.61684	−	1.51084i	−0.0929269	−	0.0536513i
$794$		0			0
$795$	2.53667	−	0.764836i	0.0899665	−	0.0271259i
$796$		0			0
$797$	−38.2337			−1.35431			−0.677153	−	0.735842i	$-0.736787\pi$
$797$	−38.2337			−1.35431			−0.677153	+	0.735842i	$0.736787\pi$
$798$		0			0
$799$	35.8614			1.26869
$800$		0			0
$801$	4.37228	+	2.17448i	0.154487	+	0.0768315i
$802$		0			0
$803$	−60.0951	−	34.6959i	−2.12071	−	1.22439i
$804$		0			0
$805$	−2.97825			−0.104970
$806$		0			0
$807$	−2.74456	−	0.644810i	−0.0966132	−	0.0226984i
$808$		0			0
$809$			47.3176i			1.66360i	0.555077	+	0.831799i	$0.312689\pi$
$809$			47.3176i			1.66360i	−0.555077	+	0.831799i	$0.687311\pi$
$810$		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
$813$	−18.7446	−	4.40387i	−0.657401	−	0.154450i
$814$		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
$819$	7.80298	−	15.6896i	0.272658	−	0.548241i
$820$		0			0
$821$	−1.93070	+	1.11469i	−0.0673820	+	0.0389030i	−0.533313	−	0.845918i	$-0.679053\pi$
$821$	−1.93070	+	1.11469i	−0.0673820	+	0.0389030i	0.465930	+	0.884821i	$0.345720\pi$
$822$		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	0.860709	−	0.509097i	$-0.170020\pi$
$827$	−0.302985	−	0.524785i	−0.0105358	−	0.0182486i	−0.871245	+	0.490848i	$0.836687\pi$
$828$		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
$831$	15.7446	+	52.2188i	0.546173	+	1.81145i
$832$		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	$-0.566126\pi$
$839$	21.5584	−	37.3403i	0.744279	−	1.28913i	0.950531	−	0.310631i	$-0.100540\pi$
$840$		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
$849$	−9.48913	−	2.22938i	−0.325666	−	0.0765123i
$850$		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
$855$	11.5584	+	4.17403i	0.395290	+	0.142749i
$856$		0			0
$857$	−12.3030	+	21.3094i	−0.420262	+	0.727915i	−0.995965	−	0.0897439i	$-0.971395\pi$
$857$	−12.3030	+	21.3094i	−0.420262	+	0.727915i	0.575703	+	0.817659i	$0.304728\pi$
$858$		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
$861$	40.4674	+	9.50744i	1.37912	+	0.324013i
$862$		0			0
$863$	−28.4674			−0.969041			−0.484520	−	0.874780i	$-0.661006\pi$
$863$	−28.4674			−0.969041			−0.484520	+	0.874780i	$0.661006\pi$
$864$		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
$879$	−7.11684	−	23.6039i	−0.240045	−	0.796140i
$880$		0			0
$881$		−	27.1229i		−	0.913794i	−0.889520	−	0.456897i	$-0.848961\pi$
$881$		−	27.1229i		−	0.913794i	0.889520	−	0.456897i	$-0.151039\pi$
$882$		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	0.999850	−	0.0173482i	$-0.00552239\pi$
$887$	14.4416	+	25.0135i	0.484901	+	0.839873i	−0.514949	+	0.857221i	$0.672189\pi$
$888$		0			0
$889$	−22.1168	+	12.7692i	−0.741775	+	0.428264i
$890$		0			0
$891$	41.8614	+	17.6704i	1.40241	+	0.591979i
$892$		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
$897$	2.74456	+	0.644810i	0.0916383	+	0.0215296i
$898$		0			0
$899$	21.3505	−	12.3267i	0.712080	−	0.411120i
$900$		0			0
$901$			9.74749i			0.324736i
$902$		0			0
$903$	−9.91983	−	2.33057i	−0.330111	−	0.0775566i
$904$		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
$909$	21.4891	−	43.2087i	0.712749	−	1.43314i
$910$		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
$915$	2.71876	−	0.819738i	0.0898796	−	0.0270997i
$916$		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
$921$	8.48913	−	36.1330i	0.279726	−	1.19062i
$922$		0			0
$923$		−	12.3267i		−	0.405739i
$924$		0			0
$925$	20.8247	−	12.0232i	0.684713	−	0.395319i
$926$		0			0
$927$	−26.9198	−	40.5832i	−0.884163	−	1.33293i
$928$		0			0
$929$	17.2812	+	9.97733i	0.566979	+	0.327345i	0.755942	−	0.654639i	$-0.227179\pi$
$929$	17.2812	+	9.97733i	0.566979	+	0.327345i	−0.188963	+	0.981984i	$0.560513\pi$
$930$		0			0
$931$	−17.4891	−	7.57301i	−0.573183	−	0.248195i
$932$		0			0
$933$	−31.3505	+	9.45254i	−1.02637	+	0.309462i
$934$		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	$0.153922\pi$
$941$	25.9307	+	44.9133i	0.845317	+	1.46413i	−0.0400291	+	0.999199i	$0.512745\pi$
$942$		0			0
$943$			6.68815i			0.217796i
$944$		0			0
$945$	5.72281	+	15.4410i	0.186163	+	0.502295i
$946$		0			0
$947$	7.41983	+	4.28384i	0.241112	+	0.139206i	0.615688	−	0.787990i	$-0.288878\pi$
$947$	7.41983	+	4.28384i	0.241112	+	0.139206i	−0.374576	+	0.927196i	$0.622212\pi$
$948$		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	$-0.609933\pi$
$953$	19.9307	−	34.5210i	0.645619	−	1.11824i	0.984158	−	0.177292i	$-0.0567338\pi$
$954$		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
$963$	43.7228	−	29.0024i	1.40895	−	0.934590i
$964$		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
$969$	−26.9783	+	36.2805i	−0.866666	+	1.16550i
$970$		0			0
$971$	10.0693	−	17.4405i	0.323139	−	0.559693i	−0.657995	−	0.753022i	$-0.728595\pi$
$971$	10.0693	−	17.4405i	0.323139	−	0.559693i	0.981134	+	0.193329i	$0.0619285\pi$
$972$		0			0
$973$	−28.6644	−	49.6482i	−0.918938	−	1.59165i
$974$		0			0
$975$	2.82473	−	12.0232i	0.0904639	−	0.385049i
$976$		0			0
$977$	27.2554			0.871979			0.435989	−	0.899952i	$-0.356399\pi$
$977$	27.2554			0.871979			0.435989	+	0.899952i	$0.356399\pi$
$978$		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	$0.416589\pi$
$983$	−22.1644	+	38.3899i	−0.706934	+	1.22445i	−0.965989	+	0.258583i	$0.916744\pi$
$984$		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
$993$	7.54755	−	2.27567i	0.239514	−	0.0722162i
$994$		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.l.65.2		4
3.2	odd	2		912.2.bn.k.65.2		4
4.3	odd	2		228.2.p.c.65.1	✓	4
12.11	even	2		228.2.p.d.65.1	yes	4
19.12	odd	6		912.2.bn.k.449.2		4
57.50	even	6	inner	912.2.bn.l.449.1		4
76.31	even	6		228.2.p.d.221.1	yes	4
228.107	odd	6		228.2.p.c.221.2	yes	4

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 + 1.65831i) q^{3} +(0.813859 + 0.469882i) q^{5} -3.37228 q^{7} +(-2.50000 + 1.65831i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 1.65831i) q^{3} +(0.813859 + 0.469882i) q^{5} -3.37228 q^{7} +(-2.50000 + 1.65831i) q^{9} +5.04868i q^{11} +(1.50000 - 0.866025i) q^{13} +(-0.372281 + 1.58457i) q^{15} +(-5.18614 - 2.99422i) q^{17} +(-4.00000 - 1.73205i) q^{19} +(-1.68614 - 5.59230i) q^{21} +(0.813859 - 0.469882i) q^{23} +(-2.05842 - 3.56529i) q^{25} +(-4.00000 - 3.31662i) q^{27} +(5.18614 + 8.98266i) q^{29} -2.37686i q^{31} +(-8.37228 + 2.52434i) q^{33} +(-2.74456 - 1.58457i) q^{35} +5.84096i q^{37} +(2.18614 + 2.05446i) q^{39} +(-3.55842 + 6.16337i) q^{41} +(0.872281 - 1.51084i) q^{43} +(-2.81386 + 0.174928i) q^{45} +(-5.18614 + 2.99422i) q^{47} +4.37228 q^{49} +(2.37228 - 10.0974i) q^{51} +(-0.813859 - 1.40965i) q^{53} +(-2.37228 + 4.10891i) q^{55} +(0.872281 - 7.49927i) q^{57} +(0.813859 - 1.40965i) q^{59} +(-0.872281 - 1.51084i) q^{61} +(8.43070 - 5.59230i) q^{63} +1.62772 q^{65} +(1.50000 - 0.866025i) q^{67} +(1.18614 + 1.11469i) q^{69} +(3.55842 - 6.16337i) q^{71} +(-6.87228 + 11.9031i) q^{73} +(4.88316 - 5.19615i) q^{75} -17.0256i q^{77} +(8.61684 + 4.97494i) q^{79} +(3.50000 - 8.29156i) q^{81} -1.87953i q^{83} +(-2.81386 - 4.87375i) q^{85} +(-12.3030 + 13.0916i) q^{87} +(-0.813859 - 1.40965i) q^{89} +(-5.05842 + 2.92048i) q^{91} +(3.94158 - 1.18843i) q^{93} +(-2.44158 - 3.28917i) q^{95} +(10.6753 + 6.16337i) q^{97} +(-8.37228 - 12.6217i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 9 q^{5} - 2 q^{7} - 10 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 9 * q^5 - 2 * q^7 - 10 * q^9	\( 4 q + 2 q^{3} + 9 q^{5} - 2 q^{7} - 10 q^{9} + 6 q^{13} + 10 q^{15} - 15 q^{17} - 16 q^{19} - q^{21} + 9 q^{23} + 9 q^{25} - 16 q^{27} + 15 q^{29} - 22 q^{33} + 12 q^{35} + 3 q^{39} + 3 q^{41} - 8 q^{43} - 17 q^{45} - 15 q^{47} + 6 q^{49} - 2 q^{51} - 9 q^{53} + 2 q^{55} - 8 q^{57} + 9 q^{59} + 8 q^{61} + 5 q^{63} + 18 q^{65} + 6 q^{67} - q^{69} - 3 q^{71} - 16 q^{73} + 54 q^{75} + 14 q^{81} - 17 q^{85} - 9 q^{87} - 9 q^{89} - 3 q^{91} + 33 q^{93} - 27 q^{95} - 9 q^{97} - 22 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 + 9 * q^5 - 2 * q^7 - 10 * q^9 + 6 * q^13 + 10 * q^15 - 15 * q^17 - 16 * q^19 - q^21 + 9 * q^23 + 9 * q^25 - 16 * q^27 + 15 * q^29 - 22 * q^33 + 12 * q^35 + 3 * q^39 + 3 * q^41 - 8 * q^43 - 17 * q^45 - 15 * q^47 + 6 * q^49 - 2 * q^51 - 9 * q^53 + 2 * q^55 - 8 * q^57 + 9 * q^59 + 8 * q^61 + 5 * q^63 + 18 * q^65 + 6 * q^67 - q^69 - 3 * q^71 - 16 * q^73 + 54 * q^75 + 14 * q^81 - 17 * q^85 - 9 * q^87 - 9 * q^89 - 3 * q^91 + 33 * q^93 - 27 * q^95 - 9 * q^97 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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