LMFDB - Embedded newform 828.2.c.f.323.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [828,2,Mod(323,828)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("828.323"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(828, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 828 = 2^{2} \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	828.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,4,0,4,0,0,0,4,0,-8,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$6.61161328736$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 7 x^{10} + 20 x^{9} + 49 x^{8} - 382 x^{7} - 235 x^{6} + 2192 x^{5} + 668 x^{4} + \cdots + 1516 $ x^12 - 6x^11 + 7x^10 + 20x^9 + 49x^8 - 382x^7 - 235x^6 + 2192x^5 + 668x^4 - 5508x^3 - 94x^2 + 3288*x + 1516
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.12
Root			$-1.64216 + 2.25841i$ of defining polynomial
Character	$\chi$	$=$	828.323
Dual form			828.2.c.f.323.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.38078 + 0.305697i) q^{2} +(1.81310 + 0.844199i) q^{4} +0.474164i q^{5} -1.17248i q^{7} +(2.24542 + 1.71991i) q^{8} +(-0.144950 + 0.654715i) q^{10} +4.48358 q^{11} -1.65813 q^{13} +(0.358422 - 1.61893i) q^{14} +(2.57466 + 3.06123i) q^{16} -3.66369i q^{17} +6.80758i q^{19} +(-0.400289 + 0.859706i) q^{20} +(6.19084 + 1.37062i) q^{22} +1.00000 q^{23} +4.77517 q^{25} +(-2.28951 - 0.506885i) q^{26} +(0.989803 - 2.12582i) q^{28} -2.70023i q^{29} -2.02533i q^{31} +(2.61922 + 5.01395i) q^{32} +(1.11998 - 5.05875i) q^{34} +0.555946 q^{35} -10.6773 q^{37} +(-2.08105 + 9.39976i) q^{38} +(-0.815519 + 1.06470i) q^{40} -0.885578i q^{41} +10.2545i q^{43} +(8.12918 + 3.78504i) q^{44} +(1.38078 + 0.305697i) q^{46} -0.864641 q^{47} +5.62530 q^{49} +(6.59345 + 1.45975i) q^{50} +(-3.00636 - 1.39979i) q^{52} -8.96892i q^{53} +2.12595i q^{55} +(2.01655 - 2.63270i) q^{56} +(0.825453 - 3.72843i) q^{58} -6.86425 q^{59} -1.83341 q^{61} +(0.619137 - 2.79654i) q^{62} +(2.08382 + 7.72384i) q^{64} -0.786226i q^{65} -8.35780i q^{67} +(3.09289 - 6.64264i) q^{68} +(0.767638 + 0.169951i) q^{70} +3.52273 q^{71} -11.3549 q^{73} +(-14.7429 - 3.26401i) q^{74} +(-5.74695 + 12.3428i) q^{76} -5.25690i q^{77} +3.32649i q^{79} +(-1.45153 + 1.22081i) q^{80} +(0.270718 - 1.22279i) q^{82} -3.78125 q^{83} +1.73719 q^{85} +(-3.13475 + 14.1591i) q^{86} +(10.0675 + 7.71136i) q^{88} -15.3168i q^{89} +1.94412i q^{91} +(1.81310 + 0.844199i) q^{92} +(-1.19388 - 0.264318i) q^{94} -3.22791 q^{95} -13.9816 q^{97} +(7.76729 + 1.71964i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 4 q^{4} + 4 q^{8} - 8 q^{10} + 12 q^{11} - 4 q^{13} - 12 q^{14} - 12 q^{16} + 20 q^{20} + 4 q^{22} + 12 q^{23} - 40 q^{25} + 8 q^{26} - 24 q^{28} + 44 q^{32} - 28 q^{34} + 40 q^{35} - 32 q^{37}+ \cdots - 20 q^{98}+O(q^{100}) $ 12 * q + 4 * q^2 + 4 * q^4 + 4 * q^8 - 8 * q^10 + 12 * q^11 - 4 * q^13 - 12 * q^14 - 12 * q^16 + 20 * q^20 + 4 * q^22 + 12 * q^23 - 40 * q^25 + 8 * q^26 - 24 * q^28 + 44 * q^32 - 28 * q^34 + 40 * q^35 - 32 * q^37 - 32 * q^38 - 12 * q^40 + 4 * q^44 + 4 * q^46 - 32 * q^49 - 20 * q^50 + 32 * q^52 - 8 * q^56 - 16 * q^58 - 24 * q^59 - 56 * q^61 + 28 * q^64 + 16 * q^68 + 64 * q^70 - 56 * q^71 + 8 * q^73 - 36 * q^74 - 28 * q^76 + 28 * q^80 + 24 * q^82 - 28 * q^83 - 12 * q^85 - 8 * q^86 + 4 * q^88 + 4 * q^92 + 16 * q^94 + 8 * q^95 - 4 * q^97 - 20 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/828\mathbb{Z}\right)^\times$.

$n$	$415$	$461$	$649$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	1.38078	+	0.305697i	0.976358	+	0.216160i
$2$	1.38078	+	0.305697i	0.976358	+	0.216160i
$3$		0			0
$3$		0			0
$4$	1.81310	+	0.844199i	0.906550	+	0.422099i
$5$			0.474164i			0.212053i	0.994363	+	0.106026i	$0.0338128\pi$
$5$			0.474164i			0.212053i	−0.994363	+	0.106026i	$0.966187\pi$
$6$		0			0
$7$		−	1.17248i		−	0.443154i	−0.975143	−	0.221577i	$-0.928880\pi$
$7$		−	1.17248i		−	0.443154i	0.975143	−	0.221577i	$-0.0711205\pi$
$8$	2.24542	+	1.71991i	0.793876	+	0.608080i
$9$		0			0
$10$	−0.144950	+	0.654715i	−0.0458373	+	0.207039i
$11$	4.48358			1.35185			0.675926	−	0.736970i	$-0.263744\pi$
$11$	4.48358			1.35185			0.675926	+	0.736970i	$0.263744\pi$
$12$		0			0
$13$	−1.65813			−0.459883			−0.229941	−	0.973204i	$-0.573853\pi$
$13$	−1.65813			−0.459883			−0.229941	+	0.973204i	$0.573853\pi$
$14$	0.358422	−	1.61893i	0.0957923	−	0.432677i
$15$		0			0
$16$	2.57466	+	3.06123i	0.643664	+	0.765308i
$17$		−	3.66369i		−	0.888576i	−0.895884	−	0.444288i	$-0.853457\pi$
$17$		−	3.66369i		−	0.888576i	0.895884	−	0.444288i	$-0.146543\pi$
$18$		0			0
$19$			6.80758i			1.56177i	0.624677	+	0.780883i	$0.285231\pi$
$19$			6.80758i			1.56177i	−0.624677	+	0.780883i	$0.714769\pi$
$20$	−0.400289	+	0.859706i	−0.0895073	+	0.192236i
$21$		0			0
$22$	6.19084	+	1.37062i	1.31989	+	0.292217i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$		0			0
$25$	4.77517			0.955034
$26$	−2.28951	−	0.506885i	−0.449010	−	0.0994084i
$27$		0			0
$28$	0.989803	−	2.12582i	0.187055	−	0.401741i
$29$		−	2.70023i		−	0.501421i	−0.968062	−	0.250710i	$-0.919336\pi$
$29$		−	2.70023i		−	0.501421i	0.968062	−	0.250710i	$-0.0806642\pi$
$30$		0			0
$31$		−	2.02533i		−	0.363760i	−0.983321	−	0.181880i	$-0.941782\pi$
$31$		−	2.02533i		−	0.363760i	0.983321	−	0.181880i	$-0.0582183\pi$
$32$	2.61922	+	5.01395i	0.463017	+	0.886349i
$33$		0			0
$34$	1.11998	−	5.05875i	0.192075	−	0.867569i
$35$	0.555946			0.0939720
$36$		0			0
$37$	−10.6773			−1.75533			−0.877666	−	0.479273i	$-0.840900\pi$
$37$	−10.6773			−1.75533			−0.877666	+	0.479273i	$0.840900\pi$
$38$	−2.08105	+	9.39976i	−0.337592	+	1.52484i
$39$		0			0
$40$	−0.815519	+	1.06470i	−0.128945	+	0.168343i
$41$		−	0.885578i		−	0.138304i	−0.997606	−	0.0691520i	$-0.977971\pi$
$41$		−	0.885578i		−	0.138304i	0.997606	−	0.0691520i	$-0.0220293\pi$
$42$		0			0
$43$			10.2545i			1.56379i	0.623410	+	0.781895i	$0.285747\pi$
$43$			10.2545i			1.56379i	−0.623410	+	0.781895i	$0.714253\pi$
$44$	8.12918	+	3.78504i	1.22552	+	0.570616i
$45$		0			0
$46$	1.38078	+	0.305697i	0.203585	+	0.0450725i
$47$	−0.864641			−0.126121			−0.0630604	−	0.998010i	$-0.520086\pi$
$47$	−0.864641			−0.126121			−0.0630604	+	0.998010i	$0.520086\pi$
$48$		0			0
$49$	5.62530			0.803614
$50$	6.59345	+	1.45975i	0.932455	+	0.206440i
$51$		0			0
$52$	−3.00636	−	1.39979i	−0.416907	−	0.194116i
$53$		−	8.96892i		−	1.23198i	−0.787756	−	0.615988i	$-0.788757\pi$
$53$		−	8.96892i		−	1.23198i	0.787756	−	0.615988i	$-0.211243\pi$
$54$		0			0
$55$			2.12595i			0.286664i
$56$	2.01655	−	2.63270i	0.269473	−	0.351809i
$57$		0			0
$58$	0.825453	−	3.72843i	0.108387	−	0.489566i
$59$	−6.86425			−0.893650			−0.446825	−	0.894621i	$-0.647445\pi$
$59$	−6.86425			−0.893650			−0.446825	+	0.894621i	$0.647445\pi$
$60$		0			0
$61$	−1.83341			−0.234744			−0.117372	−	0.993088i	$-0.537447\pi$
$61$	−1.83341			−0.234744			−0.117372	+	0.993088i	$0.537447\pi$
$62$	0.619137	−	2.79654i	0.0786305	−	0.355160i
$63$		0			0
$64$	2.08382	+	7.72384i	0.260477	+	0.965480i
$65$		−	0.786226i		−	0.0975194i
$66$		0			0
$67$		−	8.35780i		−	1.02107i	−0.859858	−	0.510534i	$-0.829448\pi$
$67$		−	8.35780i		−	1.02107i	0.859858	−	0.510534i	$-0.170552\pi$
$68$	3.09289	−	6.64264i	0.375068	−	0.805538i
$69$		0			0
$70$	0.767638	+	0.169951i	0.0917503	+	0.0203130i
$71$	3.52273			0.418071			0.209035	−	0.977908i	$-0.432968\pi$
$71$	3.52273			0.418071			0.209035	+	0.977908i	$0.432968\pi$
$72$		0			0
$73$	−11.3549			−1.32899			−0.664497	−	0.747291i	$-0.731354\pi$
$73$	−11.3549			−1.32899			−0.664497	+	0.747291i	$0.731354\pi$
$74$	−14.7429	−	3.26401i	−1.71383	−	0.379433i
$75$		0			0
$76$	−5.74695	+	12.3428i	−0.659221	+	1.41582i
$77$		−	5.25690i		−	0.599079i
$78$		0			0
$79$			3.32649i			0.374259i	0.982335	+	0.187129i	$0.0599184\pi$
$79$			3.32649i			0.374259i	−0.982335	+	0.187129i	$0.940082\pi$
$80$	−1.45153	+	1.22081i	−0.162286	+	0.136491i
$81$		0			0
$82$	0.270718	−	1.22279i	0.0298958	−	0.135034i
$83$	−3.78125			−0.415046			−0.207523	−	0.978230i	$-0.566540\pi$
$83$	−3.78125			−0.415046			−0.207523	+	0.978230i	$0.566540\pi$
$84$		0			0
$85$	1.73719			0.188425
$86$	−3.13475	+	14.1591i	−0.338029	+	1.52682i
$87$		0			0
$88$	10.0675	+	7.71136i	1.07320	+	0.822034i
$89$		−	15.3168i		−	1.62357i	−0.583954	−	0.811786i	$-0.698495\pi$
$89$		−	15.3168i		−	1.62357i	0.583954	−	0.811786i	$-0.301505\pi$
$90$		0			0
$91$			1.94412i			0.203799i
$92$	1.81310	+	0.844199i	0.189029	+	0.0880138i
$93$		0			0
$94$	−1.19388	−	0.264318i	−0.123139	−	0.0272623i
$95$	−3.22791			−0.331176
$96$		0			0
$97$	−13.9816			−1.41962			−0.709810	−	0.704393i	$-0.751219\pi$
$97$	−13.9816			−1.41962			−0.709810	+	0.704393i	$0.751219\pi$
$98$	7.76729	+	1.71964i	0.784615	+	0.173709i
$99$		0			0
$100$	8.65785	+	4.03119i	0.865785	+	0.403119i
$101$		−	16.8609i		−	1.67772i	−0.544346	−	0.838861i	$-0.683222\pi$
$101$		−	16.8609i		−	1.67772i	0.544346	−	0.838861i	$-0.316778\pi$
$102$		0			0
$103$			1.99530i			0.196603i	0.995157	+	0.0983016i	$0.0313410\pi$
$103$			1.99530i			0.196603i	−0.995157	+	0.0983016i	$0.968659\pi$
$104$	−3.72320	−	2.85184i	−0.365090	−	0.279646i
$105$		0			0
$106$	2.74177	−	12.3841i	0.266304	−	1.20285i
$107$	−5.01845			−0.485152			−0.242576	−	0.970132i	$-0.577992\pi$
$107$	−5.01845			−0.485152			−0.242576	+	0.970132i	$0.577992\pi$
$108$		0			0
$109$	−6.47322			−0.620022			−0.310011	−	0.950733i	$-0.600333\pi$
$109$	−6.47322			−0.620022			−0.310011	+	0.950733i	$0.600333\pi$
$110$	−0.649897	+	2.93547i	−0.0619653	+	0.279886i
$111$		0			0
$112$	3.58922	−	3.01872i	0.339150	−	0.285242i
$113$			7.98937i			0.751576i	0.926706	+	0.375788i	$0.122628\pi$
$113$			7.98937i			0.751576i	−0.926706	+	0.375788i	$0.877372\pi$
$114$		0			0
$115$			0.474164i			0.0442160i
$116$	2.27953	−	4.89579i	0.211650	−	0.454563i
$117$		0			0
$118$	−9.47801	−	2.09838i	−0.872522	−	0.193171i
$119$	−4.29559			−0.393776
$120$		0			0
$121$	9.10253			0.827503
$122$	−2.53153	−	0.560467i	−0.229194	−	0.0507423i
$123$		0			0
$124$	1.70978	−	3.67213i	0.153543	−	0.329767i
$125$			4.63503i			0.414570i
$126$		0			0
$127$		−	4.91699i		−	0.436313i	−0.975914	−	0.218156i	$-0.929996\pi$
$127$		−	4.91699i		−	0.436313i	0.975914	−	0.218156i	$-0.0700043\pi$
$128$	0.516138	+	11.3019i	0.0456206	+	0.998959i
$129$		0			0
$130$	0.240347	−	1.08560i	0.0210798	−	0.0952138i
$131$	10.5541			0.922120			0.461060	−	0.887369i	$-0.347469\pi$
$131$	10.5541			0.922120			0.461060	+	0.887369i	$0.347469\pi$
$132$		0			0
$133$	7.98172			0.692103
$134$	2.55495	−	11.5403i	0.220714	−	0.996928i
$135$		0			0
$136$	6.30123	−	8.22653i	0.540326	−	0.705419i
$137$		−	1.58979i		−	0.135825i	−0.997691	−	0.0679123i	$-0.978366\pi$
$137$		−	1.58979i		−	0.135825i	0.997691	−	0.0679123i	$-0.0216338\pi$
$138$		0			0
$139$			11.4587i			0.971915i	0.873983	+	0.485957i	$0.161529\pi$
$139$			11.4587i			0.971915i	−0.873983	+	0.485957i	$0.838471\pi$
$140$	1.00798	+	0.469329i	0.0851903	+	0.0396655i
$141$		0			0
$142$	4.86410	+	1.07689i	0.408187	+	0.0903702i
$143$	−7.43437			−0.621693
$144$		0			0
$145$	1.28035			0.106328
$146$	−15.6786	−	3.47116i	−1.29757	−	0.287275i
$147$		0			0
$148$	−19.3589	−	9.01374i	−1.59130	−	0.740925i
$149$		−	4.11595i		−	0.337191i	−0.985685	−	0.168596i	$-0.946077\pi$
$149$		−	4.11595i		−	0.337191i	0.985685	−	0.168596i	$-0.0539232\pi$
$150$		0			0
$151$		−	13.1481i		−	1.06998i	−0.844859	−	0.534989i	$-0.820316\pi$
$151$		−	13.1481i		−	1.06998i	0.844859	−	0.534989i	$-0.179684\pi$
$152$	−11.7084	+	15.2859i	−0.949679	+	1.23985i
$153$		0			0
$154$	1.60702	−	7.25861i	0.129497	−	0.584915i
$155$	0.960340			0.0771363
$156$		0			0
$157$	−4.52908			−0.361460			−0.180730	−	0.983533i	$-0.557846\pi$
$157$	−4.52908			−0.361460			−0.180730	+	0.983533i	$0.557846\pi$
$158$	−1.01690	+	4.59314i	−0.0808999	+	0.365411i
$159$		0			0
$160$	−2.37743	+	1.24194i	−0.187953	+	0.0981840i
$161$		−	1.17248i		−	0.0924041i
$162$		0			0
$163$		−	2.28292i		−	0.178812i	−0.995995	−	0.0894062i	$-0.971503\pi$
$163$		−	2.28292i		−	0.178812i	0.995995	−	0.0894062i	$-0.0284969\pi$
$164$	0.747604	−	1.60564i	0.0583781	−	0.125379i
$165$		0			0
$166$	−5.22107	−	1.15592i	−0.405233	−	0.0897164i
$167$	−8.56827			−0.663033			−0.331516	−	0.943449i	$-0.607560\pi$
$167$	−8.56827			−0.663033			−0.331516	+	0.943449i	$0.607560\pi$
$168$		0			0
$169$	−10.2506			−0.788508
$170$	2.39868	+	0.531054i	0.183970	+	0.0407300i
$171$		0			0
$172$	−8.65680	+	18.5923i	−0.660075	+	1.41765i
$173$			23.6139i			1.79533i	0.440674	+	0.897667i	$0.354740\pi$
$173$			23.6139i			1.79533i	−0.440674	+	0.897667i	$0.645260\pi$
$174$		0			0
$175$		−	5.59877i		−	0.423227i
$176$	11.5437	+	13.7253i	0.870138	+	1.03458i
$177$		0			0
$178$	4.68228	−	21.1490i	0.350952	−	1.58519i
$179$	24.0655			1.79874			0.899370	−	0.437189i	$-0.144026\pi$
$179$	24.0655			1.79874			0.899370	+	0.437189i	$0.144026\pi$
$180$		0			0
$181$	−11.5751			−0.860369			−0.430185	−	0.902741i	$-0.641552\pi$
$181$	−11.5751			−0.860369			−0.430185	+	0.902741i	$0.641552\pi$
$182$	−0.594311	+	2.68440i	−0.0440533	+	0.198981i
$183$		0			0
$184$	2.24542	+	1.71991i	0.165535	+	0.126793i
$185$		−	5.06278i		−	0.372223i
$186$		0			0
$187$		−	16.4265i		−	1.20122i
$188$	−1.56768	−	0.729929i	−0.114335	−	0.0532355i
$189$		0			0
$190$	−4.45703	−	0.986761i	−0.323347	−	0.0715872i
$191$	−15.3632			−1.11164			−0.555822	−	0.831301i	$-0.687596\pi$
$191$	−15.3632			−1.11164			−0.555822	+	0.831301i	$0.687596\pi$
$192$		0			0
$193$	−1.37290			−0.0988238			−0.0494119	−	0.998778i	$-0.515735\pi$
$193$	−1.37290			−0.0988238			−0.0494119	+	0.998778i	$0.515735\pi$
$194$	−19.3055	−	4.27414i	−1.38606	−	0.306865i
$195$		0			0
$196$	10.1992	+	4.74887i	0.728516	+	0.339205i
$197$			9.80742i			0.698750i	0.936983	+	0.349375i	$0.113606\pi$
$197$			9.80742i			0.698750i	−0.936983	+	0.349375i	$0.886394\pi$
$198$		0			0
$199$		−	12.4427i		−	0.882038i	−0.897498	−	0.441019i	$-0.854617\pi$
$199$		−	12.4427i		−	0.882038i	0.897498	−	0.441019i	$-0.145383\pi$
$200$	10.7223	+	8.21286i	0.758178	+	0.580737i
$201$		0			0
$202$	5.15432	−	23.2812i	0.362657	−	1.63806i
$203$	−3.16596			−0.222207
$204$		0			0
$205$	0.419909			0.0293277
$206$	−0.609958	+	2.75507i	−0.0424978	+	0.191955i
$207$		0			0
$208$	−4.26912	−	5.07593i	−0.296010	−	0.351952i
$209$			30.5224i			2.11128i
$210$		0			0
$211$			4.32567i			0.297792i	0.988853	+	0.148896i	$0.0475719\pi$
$211$			4.32567i			0.297792i	−0.988853	+	0.148896i	$0.952428\pi$
$212$	7.57155	−	16.2615i	0.520016	−	1.11685i
$213$		0			0
$214$	−6.92937	−	1.53412i	−0.473682	−	0.104871i
$215$	−4.86229			−0.331606
$216$		0			0
$217$	−2.37465			−0.161202
$218$	−8.93808	−	1.97884i	−0.605363	−	0.134024i
$219$		0			0
$220$	−1.79473	+	3.85457i	−0.121001	+	0.259875i
$221$			6.07489i			0.408641i
$222$		0			0
$223$		−	25.3012i		−	1.69429i	−0.531359	−	0.847147i	$-0.678319\pi$
$223$		−	25.3012i		−	1.69429i	0.531359	−	0.847147i	$-0.321681\pi$
$224$	5.87873	−	3.07097i	0.392789	−	0.205188i
$225$		0			0
$226$	−2.44232	+	11.0315i	−0.162461	+	0.733808i
$227$	−25.4220			−1.68732			−0.843659	−	0.536879i	$-0.819603\pi$
$227$	−25.4220			−1.68732			−0.843659	+	0.536879i	$0.819603\pi$
$228$		0			0
$229$	21.1997			1.40091			0.700456	−	0.713695i	$-0.252980\pi$
$229$	21.1997			1.40091			0.700456	+	0.713695i	$0.252980\pi$
$230$	−0.144950	+	0.654715i	−0.00955774	+	0.0431707i
$231$		0			0
$232$	4.64416	−	6.06316i	0.304904	−	0.398066i
$233$			11.5905i			0.759322i	0.925126	+	0.379661i	$0.123959\pi$
$233$			11.5905i			0.759322i	−0.925126	+	0.379661i	$0.876041\pi$
$234$		0			0
$235$		−	0.409982i		−	0.0267442i
$236$	−12.4456	−	5.79479i	−0.810138	−	0.377209i
$237$		0			0
$238$	−5.93126	−	1.31315i	−0.384467	−	0.0851188i
$239$	18.2731			1.18199			0.590993	−	0.806677i	$-0.298736\pi$
$239$	18.2731			1.18199			0.590993	+	0.806677i	$0.298736\pi$
$240$		0			0
$241$	1.96823			0.126785			0.0633926	−	0.997989i	$-0.479808\pi$
$241$	1.96823			0.126785			0.0633926	+	0.997989i	$0.479808\pi$
$242$	12.5686	+	2.78261i	0.807939	+	0.178873i
$243$		0			0
$244$	−3.32415	−	1.54776i	−0.212807	−	0.0990853i
$245$			2.66731i			0.170408i
$246$		0			0
$247$		−	11.2879i		−	0.718229i
$248$	3.48339	−	4.54772i	0.221195	−	0.288781i
$249$		0			0
$250$	−1.41691	+	6.39995i	−0.0896135	+	0.404769i
$251$	0.00646928			0.000408337			0.000204169	−	1.00000i	$-0.499935\pi$
$251$	0.00646928			0.000408337			0.000204169		1.00000i	$0.499935\pi$
$252$		0			0
$253$	4.48358			0.281881
$254$	1.50311	−	6.78928i	0.0943134	−	0.425997i
$255$		0			0
$256$	−2.74229	+	15.7632i	−0.171393	+	0.985203i
$257$		−	15.1727i		−	0.946448i	−0.880942	−	0.473224i	$-0.843090\pi$
$257$		−	15.1727i		−	0.946448i	0.880942	−	0.473224i	$-0.156910\pi$
$258$		0			0
$259$			12.5188i			0.777883i
$260$	0.663731	−	1.42551i	0.0411629	−	0.0884061i
$261$		0			0
$262$	14.5729	+	3.22637i	0.900319	+	0.199326i
$263$	−11.4792			−0.707837			−0.353918	−	0.935276i	$-0.615151\pi$
$263$	−11.4792			−0.707837			−0.353918	+	0.935276i	$0.615151\pi$
$264$		0			0
$265$	4.25274			0.261244
$266$	11.0210	+	2.43999i	0.675740	+	0.149605i
$267$		0			0
$268$	7.05565	−	15.1535i	0.430992	−	0.925648i
$269$			22.0371i			1.34363i	0.740720	+	0.671814i	$0.234485\pi$
$269$			22.0371i			1.34363i	−0.740720	+	0.671814i	$0.765515\pi$
$270$		0			0
$271$			32.5653i			1.97820i	0.147232	+	0.989102i	$0.452963\pi$
$271$			32.5653i			1.97820i	−0.147232	+	0.989102i	$0.547037\pi$
$272$	11.2154	−	9.43275i	0.680035	−	0.571945i
$273$		0			0
$274$	0.485993	−	2.19514i	0.0293599	−	0.132614i
$275$	21.4099			1.29106
$276$		0			0
$277$	20.8770			1.25438			0.627188	−	0.778868i	$-0.284206\pi$
$277$	20.8770			1.25438			0.627188	+	0.778868i	$0.284206\pi$
$278$	−3.50289	+	15.8219i	−0.210089	+	0.948937i
$279$		0			0
$280$	1.24833	+	0.956177i	0.0746021	+	0.0571425i
$281$		−	18.1369i		−	1.08195i	−0.841037	−	0.540977i	$-0.818055\pi$
$281$		−	18.1369i		−	1.08195i	0.841037	−	0.540977i	$-0.181945\pi$
$282$		0			0
$283$		−	8.17536i		−	0.485975i	−0.970029	−	0.242987i	$-0.921873\pi$
$283$		−	8.17536i		−	0.485975i	0.970029	−	0.242987i	$-0.0781274\pi$
$284$	6.38705	+	2.97388i	0.379002	+	0.176467i
$285$		0			0
$286$	−10.2652	−	2.27266i	−0.606995	−	0.134385i
$287$	−1.03832			−0.0612900
$288$		0			0
$289$	3.57735			0.210432
$290$	1.76789	+	0.391400i	0.103814	+	0.0229838i
$291$		0			0
$292$	−20.5876	−	9.58581i	−1.20480	−	0.560967i
$293$		−	7.65429i		−	0.447169i	−0.974685	−	0.223584i	$-0.928224\pi$
$293$		−	7.65429i		−	0.447169i	0.974685	−	0.223584i	$-0.0717758\pi$
$294$		0			0
$295$		−	3.25478i		−	0.189501i
$296$	−23.9749	−	18.3639i	−1.39352	−	1.06738i
$297$		0			0
$298$	1.25823	−	5.68321i	0.0728874	−	0.329219i
$299$	−1.65813			−0.0958922
$300$		0			0
$301$	12.0231			0.693000
$302$	4.01933	−	18.1546i	0.231286	−	1.04468i
$303$		0			0
$304$	−20.8396	+	17.5272i	−1.19523	+	1.00525i
$305$		−	0.869337i		−	0.0497781i
$306$		0			0
$307$			13.4496i			0.767612i	0.923414	+	0.383806i	$0.125387\pi$
$307$			13.4496i			0.767612i	−0.923414	+	0.383806i	$0.874613\pi$
$308$	4.43787	−	9.53127i	0.252871	−	0.543095i
$309$		0			0
$310$	1.32602	+	0.293573i	0.0753127	+	0.0166738i
$311$	6.22993			0.353267			0.176633	−	0.984277i	$-0.443479\pi$
$311$	6.22993			0.353267			0.176633	+	0.984277i	$0.443479\pi$
$312$		0			0
$313$	2.38737			0.134942			0.0674710	−	0.997721i	$-0.478507\pi$
$313$	2.38737			0.134942			0.0674710	+	0.997721i	$0.478507\pi$
$314$	−6.25366	−	1.38453i	−0.352914	−	0.0781333i
$315$		0			0
$316$	−2.80822	+	6.03125i	−0.157974	+	0.339284i
$317$			14.7728i			0.829720i	0.909885	+	0.414860i	$0.136170\pi$
$317$			14.7728i			0.829720i	−0.909885	+	0.414860i	$0.863830\pi$
$318$		0			0
$319$		−	12.1067i		−	0.677847i
$320$	−3.66237	+	0.988071i	−0.204733	+	0.0552349i
$321$		0			0
$322$	0.358422	−	1.61893i	0.0199741	−	0.0902194i
$323$	24.9409			1.38775
$324$		0			0
$325$	−7.91786			−0.439204
$326$	0.697882	−	3.15221i	0.0386521	−	0.174585i
$327$		0			0
$328$	1.52311	−	1.98849i	0.0840999	−	0.109796i
$329$			1.01377i			0.0558910i
$330$		0			0
$331$			17.3959i			0.956164i	0.878315	+	0.478082i	$0.158668\pi$
$331$			17.3959i			0.956164i	−0.878315	+	0.478082i	$0.841332\pi$
$332$	−6.85578	−	3.19213i	−0.376260	−	0.175191i
$333$		0			0
$334$	−11.8309	−	2.61929i	−0.647357	−	0.143321i
$335$	3.96297			0.216520
$336$		0			0
$337$	18.5231			1.00902			0.504508	−	0.863407i	$-0.331674\pi$
$337$	18.5231			1.00902			0.504508	+	0.863407i	$0.331674\pi$
$338$	−14.1538	−	3.13357i	−0.769866	−	0.170444i
$339$		0			0
$340$	3.14970	+	1.46654i	0.170817	+	0.0795341i
$341$		−	9.08075i		−	0.491750i
$342$		0			0
$343$		−	14.8029i		−	0.799279i
$344$	−17.6367	+	23.0256i	−0.950909	+	1.24145i
$345$		0			0
$346$	−7.21870	+	32.6056i	−0.388080	+	1.75289i
$347$	30.1324			1.61759			0.808796	−	0.588090i	$-0.200120\pi$
$347$	30.1324			1.61759			0.808796	+	0.588090i	$0.200120\pi$
$348$		0			0
$349$	21.7858			1.16617			0.583084	−	0.812412i	$-0.301846\pi$
$349$	21.7858			1.16617			0.583084	+	0.812412i	$0.301846\pi$
$350$	1.71153	−	7.73066i	0.0914849	−	0.413221i
$351$		0			0
$352$	11.7435	+	22.4805i	0.625931	+	1.19821i
$353$			18.3588i			0.977140i	0.872525	+	0.488570i	$0.162481\pi$
$353$			18.3588i			0.977140i	−0.872525	+	0.488570i	$0.837519\pi$
$354$		0			0
$355$			1.67035i			0.0886530i
$356$	12.9304	−	27.7708i	0.685309	−	1.47185i
$357$		0			0
$358$	33.2291	+	7.35674i	1.75621	+	0.388816i
$359$	−5.84979			−0.308740			−0.154370	−	0.988013i	$-0.549335\pi$
$359$	−5.84979			−0.308740			−0.154370	+	0.988013i	$0.549335\pi$
$360$		0			0
$361$	−27.3431			−1.43911
$362$	−15.9826	−	3.53846i	−0.840028	−	0.185978i
$363$		0			0
$364$	−1.64122	+	3.52488i	−0.0860235	+	0.184754i
$365$		−	5.38410i		−	0.281816i
$366$		0			0
$367$			19.9655i			1.04219i	0.853499	+	0.521094i	$0.174476\pi$
$367$			19.9655i			1.04219i	−0.853499	+	0.521094i	$0.825524\pi$
$368$	2.57466	+	3.06123i	0.134213	+	0.159578i
$369$		0			0
$370$	1.54767	−	6.99057i	0.0804597	−	0.363423i
$371$	−10.5158			−0.545955
$372$		0			0
$373$	9.60019			0.497079			0.248539	−	0.968622i	$-0.420049\pi$
$373$	9.60019			0.497079			0.248539	+	0.968622i	$0.420049\pi$
$374$	5.02152	−	22.6813i	0.259657	−	1.17282i
$375$		0			0
$376$	−1.94148	−	1.48710i	−0.100124	−	0.0766916i
$377$			4.47734i			0.230595i
$378$		0			0
$379$			35.6214i			1.82975i	0.403739	+	0.914874i	$0.367710\pi$
$379$			35.6214i			1.82975i	−0.403739	+	0.914874i	$0.632290\pi$
$380$	−5.85252	−	2.72500i	−0.300228	−	0.139789i
$381$		0			0
$382$	−21.2132	−	4.69649i	−1.08536	−	0.240293i
$383$	33.6092			1.71735			0.858676	−	0.512519i	$-0.171288\pi$
$383$	33.6092			1.71735			0.858676	+	0.512519i	$0.171288\pi$
$384$		0			0
$385$	2.49263			0.127036
$386$	−1.89568	−	0.419692i	−0.0964874	−	0.0213618i
$387$		0			0
$388$	−25.3501	−	11.8033i	−1.28696	−	0.599221i
$389$			21.5506i			1.09266i	0.837570	+	0.546330i	$0.183975\pi$
$389$			21.5506i			1.09266i	−0.837570	+	0.546330i	$0.816025\pi$
$390$		0			0
$391$		−	3.66369i		−	0.185281i
$392$	12.6312	+	9.67501i	0.637970	+	0.488662i
$393$		0			0
$394$	−2.99810	+	13.5419i	−0.151042	+	0.682230i
$395$	−1.57730			−0.0793625
$396$		0			0
$397$	−19.7043			−0.988931			−0.494466	−	0.869197i	$-0.664636\pi$
$397$	−19.7043			−0.988931			−0.494466	+	0.869197i	$0.664636\pi$
$398$	3.80369	−	17.1806i	0.190662	−	0.861185i
$399$		0			0
$400$	12.2944	+	14.6179i	0.614721	+	0.730895i
$401$			4.88307i			0.243849i	0.992539	+	0.121924i	$0.0389065\pi$
$401$			4.88307i			0.243849i	−0.992539	+	0.121924i	$0.961093\pi$
$402$		0			0
$403$			3.35827i			0.167287i
$404$	14.2340	−	30.5705i	0.708166	−	1.52094i
$405$		0			0
$406$	−4.37149	−	0.967824i	−0.216953	−	0.0480323i
$407$	−47.8724			−2.37295
$408$		0			0
$409$	37.9064			1.87435			0.937175	−	0.348860i	$-0.113431\pi$
$409$	37.9064			1.87435			0.937175	+	0.348860i	$0.113431\pi$
$410$	0.579801	+	0.128365i	0.0286344	+	0.00633949i
$411$		0			0
$412$	−1.68443	+	3.61768i	−0.0829861	+	0.178230i
$413$			8.04817i			0.396025i
$414$		0			0
$415$		−	1.79293i		−	0.0880116i
$416$	−4.34301	−	8.31379i	−0.212934	−	0.407617i
$417$		0			0
$418$	−9.33058	+	42.1446i	−0.456374	+	2.06136i
$419$	−22.1571			−1.08245			−0.541224	−	0.840879i	$-0.682039\pi$
$419$	−22.1571			−1.08245			−0.541224	+	0.840879i	$0.682039\pi$
$420$		0			0
$421$	−16.8313			−0.820306			−0.410153	−	0.912017i	$-0.634525\pi$
$421$	−16.8313			−0.820306			−0.410153	+	0.912017i	$0.634525\pi$
$422$	−1.32234	+	5.97280i	−0.0643707	+	0.290751i
$423$		0			0
$424$	15.4257	−	20.1390i	0.749140	−	0.978036i
$425$		−	17.4948i		−	0.848620i
$426$		0			0
$427$			2.14963i			0.104028i
$428$	−9.09895	−	4.23657i	−0.439814	−	0.204782i
$429$		0			0
$430$	−6.71375	−	1.48639i	−0.323766	−	0.0716800i
$431$	−5.72851			−0.275932			−0.137966	−	0.990437i	$-0.544057\pi$
$431$	−5.72851			−0.275932			−0.137966	+	0.990437i	$0.544057\pi$
$432$		0			0
$433$	19.0597			0.915952			0.457976	−	0.888965i	$-0.348575\pi$
$433$	19.0597			0.915952			0.457976	+	0.888965i	$0.348575\pi$
$434$	−3.27887	−	0.725924i	−0.157391	−	0.0348455i
$435$		0			0
$436$	−11.7366	−	5.46468i	−0.562081	−	0.261711i
$437$			6.80758i			0.325651i
$438$		0			0
$439$		−	16.8772i		−	0.805503i	−0.915309	−	0.402751i	$-0.868054\pi$
$439$		−	16.8772i		−	0.805503i	0.915309	−	0.402751i	$-0.131946\pi$
$440$	−3.65645	+	4.77366i	−0.174314	+	0.227575i
$441$		0			0
$442$	−1.85707	+	8.38807i	−0.0883319	+	0.398980i
$443$	21.3411			1.01395			0.506974	−	0.861961i	$-0.330764\pi$
$443$	21.3411			1.01395			0.506974	+	0.861961i	$0.330764\pi$
$444$		0			0
$445$	7.26265			0.344283
$446$	7.73449	−	34.9353i	0.366239	−	1.65424i
$447$		0			0
$448$	9.05602	−	2.44323i	0.427857	−	0.115432i
$449$		−	33.1013i		−	1.56214i	−0.624440	−	0.781072i	$-0.714673\pi$
$449$		−	33.1013i		−	1.56214i	0.624440	−	0.781072i	$-0.285327\pi$
$450$		0			0
$451$		−	3.97056i		−	0.186966i
$452$	−6.74462	+	14.4855i	−0.317240	+	0.681341i
$453$		0			0
$454$	−35.1022	−	7.77143i	−1.64743	−	0.364731i
$455$	−0.921831			−0.0432161
$456$		0			0
$457$	−27.4032			−1.28187			−0.640933	−	0.767597i	$-0.721452\pi$
$457$	−27.4032			−1.28187			−0.640933	+	0.767597i	$0.721452\pi$
$458$	29.2720	+	6.48066i	1.36779	+	0.302822i
$459$		0			0
$460$	−0.400289	+	0.859706i	−0.0186636	+	0.0400840i
$461$		−	4.07046i		−	0.189580i	−0.995497	−	0.0947902i	$-0.969782\pi$
$461$		−	4.07046i		−	0.189580i	0.995497	−	0.0947902i	$-0.0302180\pi$
$462$		0			0
$463$		−	3.79483i		−	0.176361i	−0.996105	−	0.0881803i	$-0.971895\pi$
$463$		−	3.79483i		−	0.176361i	0.996105	−	0.0881803i	$-0.0281052\pi$
$464$	8.26605	−	6.95217i	0.383742	−	0.322747i
$465$		0			0
$466$	−3.54319	+	16.0040i	−0.164135	+	0.741370i
$467$	−15.9883			−0.739852			−0.369926	−	0.929061i	$-0.620617\pi$
$467$	−15.9883			−0.739852			−0.369926	+	0.929061i	$0.620617\pi$
$468$		0			0
$469$	−9.79932			−0.452491
$470$	0.125330	−	0.566094i	0.00578104	−	0.0261120i
$471$		0			0
$472$	−15.4131	−	11.8059i	−0.709447	−	0.543411i
$473$			45.9767i			2.11401i
$474$		0			0
$475$			32.5073i			1.49154i
$476$	−7.78834	−	3.62634i	−0.356978	−	0.166213i
$477$		0			0
$478$	25.2311	+	5.58602i	1.15404	+	0.255498i
$479$	−2.42884			−0.110976			−0.0554882	−	0.998459i	$-0.517672\pi$
$479$	−2.42884			−0.110976			−0.0554882	+	0.998459i	$0.517672\pi$
$480$		0			0
$481$	17.7043			0.807247
$482$	2.71770	+	0.601683i	0.123788	+	0.0274059i
$483$		0			0
$484$	16.5038	+	7.68434i	0.750172	+	0.349288i
$485$		−	6.62959i		−	0.301034i
$486$		0			0
$487$		−	31.8827i		−	1.44474i	−0.691505	−	0.722371i	$-0.743052\pi$
$487$		−	31.8827i		−	1.44474i	0.691505	−	0.722371i	$-0.256948\pi$
$488$	−4.11677	−	3.15330i	−0.186358	−	0.142743i
$489$		0			0
$490$	−0.815389	+	3.68297i	−0.0368355	+	0.166380i
$491$	7.56139			0.341241			0.170620	−	0.985337i	$-0.445423\pi$
$491$	7.56139			0.341241			0.170620	+	0.985337i	$0.445423\pi$
$492$		0			0
$493$	−9.89283			−0.445551
$494$	3.45066	−	15.5860i	0.155253	−	0.701249i
$495$		0			0
$496$	6.20001	−	5.21453i	0.278389	−	0.234140i
$497$		−	4.13031i		−	0.185270i
$498$		0			0
$499$		−	23.4350i		−	1.04910i	−0.851381	−	0.524548i	$-0.824234\pi$
$499$		−	23.4350i		−	1.04910i	0.851381	−	0.524548i	$-0.175766\pi$
$500$	−3.91289	+	8.40377i	−0.174990	+	0.375828i
$501$		0			0
$502$	0.00893264	+	0.00197764i	0.000398683	+	8.82663e-5i
$503$	23.4464			1.04542			0.522712	−	0.852510i	$-0.324920\pi$
$503$	23.4464			1.04542			0.522712	+	0.852510i	$0.324920\pi$
$504$		0			0
$505$	7.99483			0.355765
$506$	6.19084	+	1.37062i	0.275216	+	0.0609314i
$507$		0			0
$508$	4.15092	−	8.91500i	0.184167	−	0.395539i
$509$		−	24.5911i		−	1.08998i	−0.838442	−	0.544991i	$-0.816533\pi$
$509$		−	24.5911i		−	1.08998i	0.838442	−	0.544991i	$-0.183467\pi$
$510$		0			0
$511$			13.3134i			0.588949i
$512$	−8.60527	+	20.9272i	−0.380303	+	0.924862i
$513$		0			0
$514$	4.63825	−	20.9502i	0.204584	−	0.924072i
$515$	−0.946101			−0.0416902
$516$		0			0
$517$	−3.87669			−0.170497
$518$	−3.82697	+	17.2857i	−0.168147	+	0.759492i
$519$		0			0
$520$	1.35224	−	1.76541i	0.0592996	−	0.0774182i
$521$			41.0279i			1.79746i	0.438498	+	0.898732i	$0.355511\pi$
$521$			41.0279i			1.79746i	−0.438498	+	0.898732i	$0.644489\pi$
$522$		0			0
$523$			31.5714i			1.38052i	0.723562	+	0.690259i	$0.242504\pi$
$523$			31.5714i			1.38052i	−0.723562	+	0.690259i	$0.757496\pi$
$524$	19.1357	+	8.90980i	0.835948	+	0.389227i
$525$		0			0
$526$	−15.8502	−	3.50915i	−0.691102	−	0.153006i
$527$	−7.42020			−0.323229
$528$		0			0
$529$	1.00000			0.0434783
$530$	5.87209	+	1.30005i	0.255067	+	0.0564705i
$531$		0			0
$532$	14.4717	+	6.73816i	0.627426	+	0.292136i
$533$			1.46840i			0.0636037i
$534$		0			0
$535$		−	2.37957i		−	0.102878i
$536$	14.3747	−	18.7668i	0.620891	−	0.810601i
$537$		0			0
$538$	−6.73668	+	30.4284i	−0.290439	+	1.31186i
$539$	25.2215			1.08637
$540$		0			0
$541$	24.7212			1.06285			0.531424	−	0.847106i	$-0.321657\pi$
$541$	24.7212			1.06285			0.531424	+	0.847106i	$0.321657\pi$
$542$	−9.95512	+	44.9655i	−0.427609	+	1.93143i
$543$		0			0
$544$	18.3696	−	9.59603i	0.787589	−	0.411426i
$545$		−	3.06937i		−	0.131477i
$546$		0			0
$547$			19.3996i			0.829466i	0.909943	+	0.414733i	$0.136125\pi$
$547$			19.3996i			0.829466i	−0.909943	+	0.414733i	$0.863875\pi$
$548$	1.34210	−	2.88244i	0.0573315	−	0.123132i
$549$		0			0
$550$	29.5623	+	6.54493i	1.26054	+	0.279077i
$551$	18.3821			0.783102
$552$		0			0
$553$	3.90022			0.165854
$554$	28.8265	+	6.38202i	1.22472	+	0.271146i
$555$		0			0
$556$	−9.67343	+	20.7758i	−0.410245	+	0.881089i
$557$		−	27.0797i		−	1.14740i	−0.819064	−	0.573702i	$-0.805507\pi$
$557$		−	27.0797i		−	1.14740i	0.819064	−	0.573702i	$-0.194493\pi$
$558$		0			0
$559$		−	17.0032i		−	0.719160i
$560$	1.43137	+	1.70188i	0.0604864	+	0.0719175i
$561$		0			0
$562$	5.54438	−	25.0430i	0.233875	−	1.05637i
$563$	24.6024			1.03687			0.518433	−	0.855118i	$-0.326516\pi$
$563$	24.6024			1.03687			0.518433	+	0.855118i	$0.326516\pi$
$564$		0			0
$565$	−3.78827			−0.159374
$566$	2.49918	−	11.2884i	0.105048	−	0.474485i
$567$		0			0
$568$	7.91000	+	6.05877i	0.331896	+	0.254220i
$569$			19.9964i			0.838294i	0.907918	+	0.419147i	$0.137671\pi$
$569$			19.9964i			0.838294i	−0.907918	+	0.419147i	$0.862329\pi$
$570$		0			0
$571$			27.1896i			1.13785i	0.822390	+	0.568924i	$0.192640\pi$
$571$			27.1896i			1.13785i	−0.822390	+	0.568924i	$0.807360\pi$
$572$	−13.4793	−	6.27609i	−0.563596	−	0.262416i
$573$		0			0
$574$	−1.43369	−	0.317411i	−0.0598410	−	0.0132485i
$575$	4.77517			0.199138
$576$		0			0
$577$	−5.42816			−0.225977			−0.112989	−	0.993596i	$-0.536042\pi$
$577$	−5.42816			−0.225977			−0.112989	+	0.993596i	$0.536042\pi$
$578$	4.93952	+	1.09358i	0.205457	+	0.0454870i
$579$		0			0
$580$	2.32141	+	1.08087i	0.0963912	+	0.0448808i
$581$			4.43342i			0.183929i
$582$		0			0
$583$		−	40.2129i		−	1.66545i
$584$	−25.4966	−	19.5295i	−1.05506	−	0.808134i
$585$		0			0
$586$	2.33989	−	10.5689i	0.0966601	−	0.436597i
$587$	32.8296			1.35502			0.677511	−	0.735513i	$-0.263059\pi$
$587$	32.8296			1.35502			0.677511	+	0.735513i	$0.263059\pi$
$588$		0			0
$589$	13.7876			0.568109
$590$	0.994976	−	4.49413i	0.0409625	−	0.185021i
$591$		0			0
$592$	−27.4903	−	32.6856i	−1.12984	−	1.34337i
$593$			5.56526i			0.228538i	0.993450	+	0.114269i	$0.0364526\pi$
$593$			5.56526i			0.228538i	−0.993450	+	0.114269i	$0.963547\pi$
$594$		0			0
$595$		−	2.03682i		−	0.0835013i
$596$	3.47468	−	7.46262i	0.142328	−	0.305681i
$597$		0			0
$598$	−2.28951	−	0.506885i	−0.0936251	−	0.0207281i
$599$	−30.7329			−1.25571			−0.627857	−	0.778329i	$-0.716068\pi$
$599$	−30.7329			−1.25571			−0.627857	+	0.778329i	$0.716068\pi$
$600$		0			0
$601$	−19.9150			−0.812349			−0.406175	−	0.913795i	$-0.633138\pi$
$601$	−19.9150			−0.812349			−0.406175	+	0.913795i	$0.633138\pi$
$602$	16.6012	+	3.67542i	0.676616	+	0.149799i
$603$		0			0
$604$	11.0996	−	23.8388i	0.451637	−	0.969987i
$605$			4.31609i			0.175474i
$606$		0			0
$607$			29.9003i			1.21362i	0.794849	+	0.606808i	$0.207550\pi$
$607$			29.9003i			1.21362i	−0.794849	+	0.606808i	$0.792450\pi$
$608$	−34.1329	+	17.8306i	−1.38427	+	0.723125i
$609$		0			0
$610$	0.265753	−	1.20036i	0.0107600	−	0.0486012i
$611$	1.43369			0.0580008
$612$		0			0
$613$	36.9033			1.49051			0.745256	−	0.666779i	$-0.232327\pi$
$613$	36.9033			1.49051			0.745256	+	0.666779i	$0.232327\pi$
$614$	−4.11151	+	18.5710i	−0.165927	+	0.749464i
$615$		0			0
$616$	9.04139	−	11.8039i	0.364288	−	0.475594i
$617$		−	24.9569i		−	1.00473i	−0.864656	−	0.502364i	$-0.832464\pi$
$617$		−	24.9569i		−	1.00473i	0.864656	−	0.502364i	$-0.167536\pi$
$618$		0			0
$619$		−	31.6234i		−	1.27105i	−0.772079	−	0.635527i	$-0.780783\pi$
$619$		−	31.6234i		−	1.27105i	0.772079	−	0.635527i	$-0.219217\pi$
$620$	1.74119	+	0.810718i	0.0699279	+	0.0325592i
$621$		0			0
$622$	8.60215	+	1.90447i	0.344915	+	0.0763623i
$623$	−17.9585			−0.719493
$624$		0			0
$625$	21.6781			0.867123
$626$	3.29643	+	0.729810i	0.131752	+	0.0291691i
$627$		0			0
$628$	−8.21168	−	3.82345i	−0.327682	−	0.152572i
$629$			39.1182i			1.55975i
$630$		0			0
$631$			35.0879i			1.39683i	0.715693	+	0.698415i	$0.246111\pi$
$631$			35.0879i			1.39683i	−0.715693	+	0.698415i	$0.753889\pi$
$632$	−5.72126	+	7.46935i	−0.227579	+	0.297115i
$633$		0			0
$634$	−4.51598	+	20.3979i	−0.179353	+	0.810104i
$635$	2.33146			0.0925212
$636$		0			0
$637$	−9.32749			−0.369568
$638$	3.70099	−	16.7167i	0.146523	−	0.661821i
$639$		0			0
$640$	−5.35897	+	0.244734i	−0.211832	+	0.00967396i
$641$			21.4219i			0.846114i	0.906103	+	0.423057i	$0.139043\pi$
$641$			21.4219i			0.846114i	−0.906103	+	0.423057i	$0.860957\pi$
$642$		0			0
$643$			0.476123i			0.0187765i	0.999956	+	0.00938824i	$0.00298841\pi$
$643$			0.476123i			0.0187765i	−0.999956	+	0.00938824i	$0.997012\pi$
$644$	0.989803	−	2.12582i	0.0390037	−	0.0837689i
$645$		0			0
$646$	34.4378	+	7.62435i	1.35494	+	0.299976i
$647$	−39.8244			−1.56566			−0.782830	−	0.622236i	$-0.786224\pi$
$647$	−39.8244			−1.56566			−0.782830	+	0.622236i	$0.786224\pi$
$648$		0			0
$649$	−30.7765			−1.20808
$650$	−10.9328	−	2.42046i	−0.428820	−	0.0949384i
$651$		0			0
$652$	1.92724	−	4.13917i	0.0754766	−	0.162102i
$653$		−	26.3437i		−	1.03091i	−0.856917	−	0.515455i	$-0.827623\pi$
$653$		−	26.3437i		−	1.03091i	0.856917	−	0.515455i	$-0.172377\pi$
$654$		0			0
$655$			5.00440i			0.195538i
$656$	2.71096	−	2.28006i	0.105845	−	0.0890213i
$657$		0			0
$658$	−0.309906	+	1.39979i	−0.0120814	+	0.0545696i
$659$	8.57952			0.334211			0.167105	−	0.985939i	$-0.446558\pi$
$659$	8.57952			0.334211			0.167105	+	0.985939i	$0.446558\pi$
$660$		0			0
$661$	−14.5774			−0.566994			−0.283497	−	0.958973i	$-0.591495\pi$
$661$	−14.5774			−0.566994			−0.283497	+	0.958973i	$0.591495\pi$
$662$	−5.31786	+	24.0199i	−0.206685	+	0.933558i
$663$		0			0
$664$	−8.49049	−	6.50341i	−0.329495	−	0.252381i
$665$			3.78465i			0.146762i
$666$		0			0
$667$		−	2.70023i		−	0.104553i
$668$	−15.5351	−	7.23333i	−0.601072	−	0.279866i
$669$		0			0
$670$	5.47198	+	1.21147i	0.211401	+	0.0468030i
$671$	−8.22024			−0.317339
$672$		0			0
$673$	−13.0282			−0.502202			−0.251101	−	0.967961i	$-0.580793\pi$
$673$	−13.0282			−0.502202			−0.251101	+	0.967961i	$0.580793\pi$
$674$	25.5763	+	5.66244i	0.985161	+	0.218109i
$675$		0			0
$676$	−18.5854	−	8.65355i	−0.714821	−	0.332829i
$677$		−	41.9381i		−	1.61181i	−0.592044	−	0.805906i	$-0.701679\pi$
$677$		−	41.9381i		−	1.61181i	0.592044	−	0.805906i	$-0.298321\pi$
$678$		0			0
$679$			16.3931i			0.629111i
$680$	3.90072	+	2.98781i	0.149586	+	0.114577i
$681$		0			0
$682$	2.77596	−	12.5385i	0.106297	−	0.480124i
$683$	−16.7889			−0.642410			−0.321205	−	0.947010i	$-0.604088\pi$
$683$	−16.7889			−0.642410			−0.321205	+	0.947010i	$0.604088\pi$
$684$		0			0
$685$	0.753820			0.0288020
$686$	4.52519	−	20.4395i	0.172772	−	0.780383i
$687$		0			0
$688$	−31.3913	+	26.4017i	−1.19678	+	1.00656i
$689$			14.8716i			0.566565i
$690$		0			0
$691$			19.1954i			0.730227i	0.930963	+	0.365113i	$0.118970\pi$
$691$			19.1954i			0.730227i	−0.930963	+	0.365113i	$0.881030\pi$
$692$	−19.9349	+	42.8144i	−0.757810	+	1.62756i
$693$		0			0
$694$	41.6062	+	9.21137i	1.57935	+	0.349659i
$695$	−5.43330			−0.206097
$696$		0			0
$697$	−3.24449			−0.122894
$698$	30.0814	+	6.65986i	1.13860	+	0.252079i
$699$		0			0
$700$	4.72648	−	10.1511i	0.178644	−	0.383676i
$701$		−	50.9433i		−	1.92410i	−0.272872	−	0.962050i	$-0.587974\pi$
$701$		−	50.9433i		−	1.92410i	0.272872	−	0.962050i	$-0.412026\pi$
$702$		0			0
$703$		−	72.6864i		−	2.74142i
$704$	9.34297	+	34.6305i	0.352126	+	1.30519i
$705$		0			0
$706$	−5.61222	+	25.3494i	−0.211219	+	0.954039i
$707$	−19.7690			−0.743490
$708$		0			0
$709$	−24.0242			−0.902249			−0.451125	−	0.892461i	$-0.648977\pi$
$709$	−24.0242			−0.902249			−0.451125	+	0.892461i	$0.648977\pi$
$710$	−0.510620	+	2.30638i	−0.0191632	+	0.0865570i
$711$		0			0
$712$	26.3434	−	34.3925i	0.987262	−	1.28891i
$713$		−	2.02533i		−	0.0758493i
$714$		0			0
$715$		−	3.52511i		−	0.131832i
$716$	43.6331	+	20.3161i	1.63065	+	0.759247i
$717$		0			0
$718$	−8.07726	−	1.78826i	−0.301441	−	0.0667373i
$719$	−18.0272			−0.672302			−0.336151	−	0.941808i	$-0.609125\pi$
$719$	−18.0272			−0.672302			−0.336151	+	0.941808i	$0.609125\pi$
$720$		0			0
$721$	2.33945			0.0871255
$722$	−37.7548	−	8.35871i	−1.40509	−	0.311079i
$723$		0			0
$724$	−20.9868	−	9.77167i	−0.779967	−	0.363161i
$725$		−	12.8941i		−	0.478874i
$726$		0			0
$727$		−	25.0299i		−	0.928307i	−0.885755	−	0.464154i	$-0.846359\pi$
$727$		−	25.0299i		−	0.928307i	0.885755	−	0.464154i	$-0.153641\pi$
$728$	−3.34371	+	4.36536i	−0.123926	+	0.161791i
$729$		0			0
$730$	1.64590	−	7.43424i	0.0609175	−	0.275154i
$731$	37.5692			1.38955
$732$		0			0
$733$	7.21556			0.266513			0.133256	−	0.991082i	$-0.457457\pi$
$733$	7.21556			0.266513			0.133256	+	0.991082i	$0.457457\pi$
$734$	−6.10337	+	27.5679i	−0.225280	+	1.01755i
$735$		0			0
$736$	2.61922	+	5.01395i	0.0965458	+	0.184817i
$737$		−	37.4729i		−	1.38033i
$738$		0			0
$739$		−	53.2281i		−	1.95803i	−0.203793	−	0.979014i	$-0.565327\pi$
$739$		−	53.2281i		−	1.95803i	0.203793	−	0.979014i	$-0.434673\pi$
$740$	4.27399	−	9.17931i	0.157115	−	0.337438i
$741$		0			0
$742$	−14.5200	−	3.21466i	−0.533048	−	0.118014i
$743$	−11.8795			−0.435816			−0.217908	−	0.975969i	$-0.569923\pi$
$743$	−11.8795			−0.435816			−0.217908	+	0.975969i	$0.569923\pi$
$744$		0			0
$745$	1.95163			0.0715023
$746$	13.2557	+	2.93475i	0.485327	+	0.107449i
$747$		0			0
$748$	13.8672	−	29.7828i	0.507036	−	1.08897i
$749$			5.88401i			0.214997i
$750$		0			0
$751$		−	42.0501i		−	1.53443i	−0.641389	−	0.767216i	$-0.721642\pi$
$751$		−	42.0501i		−	1.53443i	0.641389	−	0.767216i	$-0.278358\pi$
$752$	−2.22615	−	2.64687i	−0.0811794	−	0.0965213i
$753$		0			0
$754$	−1.36871	+	6.18222i	−0.0498454	+	0.225143i
$755$	6.23435			0.226891
$756$		0			0
$757$	−48.0113			−1.74500			−0.872500	−	0.488614i	$-0.837503\pi$
$757$	−48.0113			−1.74500			−0.872500	+	0.488614i	$0.837503\pi$
$758$	−10.8893	+	49.1853i	−0.395519	+	1.78649i
$759$		0			0
$760$	−7.24801	−	5.55171i	−0.262913	−	0.201382i
$761$		−	6.75256i		−	0.244780i	−0.992482	−	0.122390i	$-0.960944\pi$
$761$		−	6.75256i		−	0.244780i	0.992482	−	0.122390i	$-0.0390559\pi$
$762$		0			0
$763$			7.58969i			0.274765i
$764$	−27.8550	−	12.9696i	−1.00776	−	0.469224i
$765$		0			0
$766$	46.4069	+	10.2742i	1.67675	+	0.371223i
$767$	11.3818			0.410974
$768$		0			0
$769$	−0.717958			−0.0258902			−0.0129451	−	0.999916i	$-0.504121\pi$
$769$	−0.717958			−0.0258902			−0.0129451	+	0.999916i	$0.504121\pi$
$770$	3.44177	+	0.761989i	0.124033	+	0.0274602i
$771$		0			0
$772$	−2.48921	−	1.15900i	−0.0895887	−	0.0417135i
$773$			39.3429i			1.41507i	0.706680	+	0.707533i	$0.250192\pi$
$773$			39.3429i			1.41507i	−0.706680	+	0.707533i	$0.749808\pi$
$774$		0			0
$775$		−	9.67130i		−	0.347403i
$776$	−31.3946	−	24.0472i	−1.12700	−	0.863242i
$777$		0			0
$778$	−6.58795	+	29.7566i	−0.236190	+	1.06683i
$779$	6.02864			0.215999
$780$		0			0
$781$	15.7944			0.565169
$782$	1.11998	−	5.05875i	0.0400504	−	0.180901i
$783$		0			0
$784$	14.4832	+	17.2204i	0.517258	+	0.615013i
$785$		−	2.14753i		−	0.0766486i
$786$		0			0
$787$		−	19.6796i		−	0.701501i	−0.936469	−	0.350750i	$-0.885927\pi$
$787$		−	19.6796i		−	0.701501i	0.936469	−	0.350750i	$-0.114073\pi$
$788$	−8.27941	+	17.7818i	−0.294942	+	0.633451i
$789$		0			0
$790$	−2.17790	−	0.482175i	−0.0774862	−	0.0171550i
$791$	9.36734			0.333064
$792$		0			0
$793$	3.04003			0.107955
$794$	−27.2073	−	6.02354i	−0.965551	−	0.213768i
$795$		0			0
$796$	10.5041	−	22.5598i	0.372308	−	0.799612i
$797$			12.6856i			0.449348i	0.974434	+	0.224674i	$0.0721316\pi$
$797$			12.6856i			0.449348i	−0.974434	+	0.224674i	$0.927868\pi$
$798$		0			0
$799$			3.16778i			0.112068i
$800$	12.5072	+	23.9424i	0.442197	+	0.846493i
$801$		0			0
$802$	−1.49274	+	6.74243i	−0.0527104	+	0.238084i
$803$	−50.9108			−1.79660
$804$		0			0
$805$	0.555946			0.0195945
$806$	−1.02661	+	4.63702i	−0.0361608	+	0.163332i
$807$		0			0
$808$	28.9992	−	37.8598i	1.02019	−	1.33190i
$809$			32.1609i			1.13072i	0.824845	+	0.565359i	$0.191262\pi$
$809$			32.1609i			1.13072i	−0.824845	+	0.565359i	$0.808738\pi$
$810$		0			0
$811$			3.13861i			0.110212i	0.998481	+	0.0551058i	$0.0175496\pi$
$811$			3.13861i			0.110212i	−0.998481	+	0.0551058i	$0.982450\pi$
$812$	−5.74020	−	2.67270i	−0.201441	−	0.0937934i
$813$		0			0
$814$	−66.1012	−	14.6344i	−2.31685	−	0.512937i
$815$	1.08248			0.0379176
$816$		0			0
$817$	−69.8080			−2.44227
$818$	52.3403	+	11.5879i	1.83004	+	0.405160i
$819$		0			0
$820$	0.761337	+	0.354487i	0.0265870	+	0.0123792i
$821$		−	38.8138i		−	1.35461i	−0.735702	−	0.677305i	$-0.763148\pi$
$821$		−	38.8138i		−	1.35461i	0.735702	−	0.677305i	$-0.236852\pi$
$822$		0			0
$823$			14.8738i			0.518467i	0.965815	+	0.259234i	$0.0834699\pi$
$823$			14.8738i			0.518467i	−0.965815	+	0.259234i	$0.916530\pi$
$824$	−3.43174	+	4.48029i	−0.119550	+	0.156078i
$825$		0			0
$826$	−2.46030	+	11.1127i	−0.0856048	+	0.386662i
$827$	14.5906			0.507365			0.253683	−	0.967288i	$-0.418358\pi$
$827$	14.5906			0.507365			0.253683	+	0.967288i	$0.418358\pi$
$828$		0			0
$829$	−47.0677			−1.63473			−0.817364	−	0.576121i	$-0.804566\pi$
$829$	−47.0677			−1.63473			−0.817364	+	0.576121i	$0.804566\pi$
$830$	0.548094	−	2.47564i	0.0190246	−	0.0859308i
$831$		0			0
$832$	−3.45524	−	12.8071i	−0.119789	−	0.444008i
$833$		−	20.6094i		−	0.714073i
$834$		0			0
$835$		−	4.06277i		−	0.140598i
$836$	−25.7669	+	55.3401i	−0.891168	+	1.91398i
$837$		0			0
$838$	−30.5941	−	6.77336i	−1.05686	−	0.233982i
$839$	−36.6970			−1.26692			−0.633461	−	0.773775i	$-0.718366\pi$
$839$	−36.6970			−1.26692			−0.633461	+	0.773775i	$0.718366\pi$
$840$		0			0
$841$	21.7087			0.748577
$842$	−23.2403	−	5.14527i	−0.800912	−	0.177318i
$843$		0			0
$844$	−3.65173	+	7.84287i	−0.125698	+	0.269963i
$845$		−	4.86047i		−	0.167205i
$846$		0			0
$847$		−	10.6725i		−	0.366711i
$848$	27.4559	−	23.0919i	0.942841	−	0.792978i
$849$		0			0
$850$	5.34809	−	24.1564i	0.183438	−	0.828557i
$851$	−10.6773			−0.366012
$852$		0			0
$853$	13.3936			0.458588			0.229294	−	0.973357i	$-0.426358\pi$
$853$	13.3936			0.458588			0.229294	+	0.973357i	$0.426358\pi$
$854$	−0.657134	+	2.96816i	−0.0224867	+	0.101568i
$855$		0			0
$856$	−11.2685	−	8.63129i	−0.385150	−	0.295011i
$857$		−	35.5685i		−	1.21500i	−0.794320	−	0.607499i	$-0.792173\pi$
$857$		−	35.5685i		−	1.21500i	0.794320	−	0.607499i	$-0.207827\pi$
$858$		0			0
$859$			4.83116i			0.164837i	0.996598	+	0.0824186i	$0.0262644\pi$
$859$			4.83116i			0.164837i	−0.996598	+	0.0824186i	$0.973736\pi$
$860$	−8.81582	−	4.10474i	−0.300617	−	0.139971i
$861$		0			0
$862$	−7.90980	−	1.75119i	−0.269409	−	0.0596456i
$863$	−41.5509			−1.41441			−0.707204	−	0.707009i	$-0.750044\pi$
$863$	−41.5509			−1.41441			−0.707204	+	0.707009i	$0.750044\pi$
$864$		0			0
$865$	−11.1969			−0.380705
$866$	26.3173	+	5.82649i	0.894297	+	0.197992i
$867$		0			0
$868$	−4.30548	−	2.00468i	−0.146138	−	0.0680433i
$869$			14.9146i			0.505942i
$870$		0			0
$871$			13.8583i			0.469572i
$872$	−14.5351	−	11.1334i	−0.492220	−	0.377023i
$873$		0			0
$874$	−2.08105	+	9.39976i	−0.0703927	+	0.317952i
$875$	5.43446			0.183718
$876$		0			0
$877$	−39.4773			−1.33306			−0.666528	−	0.745480i	$-0.732220\pi$
$877$	−39.4773			−1.33306			−0.666528	+	0.745480i	$0.732220\pi$
$878$	5.15929	−	23.3036i	0.174118	−	0.786459i
$879$		0			0
$880$	−6.50804	+	5.47360i	−0.219386	+	0.184515i
$881$		−	13.1178i		−	0.441951i	−0.975279	−	0.220975i	$-0.929076\pi$
$881$		−	13.1178i		−	0.441951i	0.975279	−	0.220975i	$-0.0709240\pi$
$882$		0			0
$883$			32.9057i			1.10736i	0.832728	+	0.553682i	$0.186778\pi$
$883$			32.9057i			1.10736i	−0.832728	+	0.553682i	$0.813222\pi$
$884$	−5.12841	+	11.0144i	−0.172487	+	0.370453i
$885$		0			0
$886$	29.4674	+	6.52392i	0.989976	+	0.219175i
$887$	−49.1905			−1.65165			−0.825827	−	0.563923i	$-0.809292\pi$
$887$	−49.1905			−1.65165			−0.825827	+	0.563923i	$0.809292\pi$
$888$		0			0
$889$	−5.76506			−0.193354
$890$	10.0281	+	2.22017i	0.336143	+	0.0744202i
$891$		0			0
$892$	21.3592	−	45.8736i	0.715160	−	1.53596i
$893$		−	5.88611i		−	0.196971i
$894$		0			0
$895$			11.4110i			0.381427i
$896$	13.2512	−	0.605159i	0.442693	−	0.0202169i
$897$		0			0
$898$	10.1189	−	45.7055i	0.337674	−	1.52521i
$899$	−5.46887			−0.182397
$900$		0			0
$901$	−32.8594			−1.09470
$902$	1.21379	−	5.48247i	0.0404147	−	0.182546i
$903$		0			0
$904$	−13.7410	+	17.9395i	−0.457019	+	0.596658i
$905$		−	5.48849i		−	0.182443i
$906$		0			0
$907$			52.4548i			1.74173i	0.491520	+	0.870866i	$0.336442\pi$
$907$			52.4548i			1.74173i	−0.491520	+	0.870866i	$0.663558\pi$
$908$	−46.0926	−	21.4612i	−1.52964	−	0.712216i
$909$		0			0
$910$	−1.27285	−	0.281801i	−0.0421944	−	0.00934161i
$911$	−1.90599			−0.0631482			−0.0315741	−	0.999501i	$-0.510052\pi$
$911$	−1.90599			−0.0631482			−0.0315741	+	0.999501i	$0.510052\pi$
$912$		0			0
$913$	−16.9536			−0.561081
$914$	−37.8377	−	8.37706i	−1.25156	−	0.277088i
$915$		0			0
$916$	38.4371	+	17.8967i	1.27000	+	0.591324i
$917$		−	12.3745i		−	0.408642i
$918$		0			0
$919$			45.0613i			1.48643i	0.669050	+	0.743217i	$0.266701\pi$
$919$			45.0613i			1.48643i	−0.669050	+	0.743217i	$0.733299\pi$
$920$	−0.815519	+	1.06470i	−0.0268869	+	0.0351020i
$921$		0			0
$922$	1.24433	−	5.62041i	0.0409797	−	0.185098i
$923$	−5.84114			−0.192264
$924$		0			0
$925$	−50.9858			−1.67640
$926$	1.16007	−	5.23982i	0.0381222	−	0.172191i
$927$		0			0
$928$	13.5388	−	7.07251i	0.444434	−	0.232167i
$929$		−	58.8031i		−	1.92927i	−0.263592	−	0.964634i	$-0.584907\pi$
$929$		−	58.8031i		−	1.92927i	0.263592	−	0.964634i	$-0.415093\pi$
$930$		0			0
$931$			38.2947i			1.25506i
$932$	−9.78473	+	21.0148i	−0.320509	+	0.688363i
$933$		0			0
$934$	−22.0763	−	4.88758i	−0.722360	−	0.159927i
$935$	7.78885			0.254722
$936$		0			0
$937$	−9.50851			−0.310630			−0.155315	−	0.987865i	$-0.549639\pi$
$937$	−9.50851			−0.310630			−0.155315	+	0.987865i	$0.549639\pi$
$938$	−13.5307	−	2.99562i	−0.441793	−	0.0978105i
$939$		0			0
$940$	0.346106	−	0.743337i	0.0112887	−	0.0242450i
$941$		−	7.76530i		−	0.253142i	−0.991958	−	0.126571i	$-0.959603\pi$
$941$		−	7.76530i		−	0.253142i	0.991958	−	0.126571i	$-0.0403971\pi$
$942$		0			0
$943$		−	0.885578i		−	0.0288384i
$944$	−17.6731	−	21.0131i	−0.575210	−	0.683917i
$945$		0			0
$946$	−14.0549	+	63.4837i	−0.456965	+	2.06403i
$947$	0.384626			0.0124987			0.00624934	−	0.999980i	$-0.498011\pi$
$947$	0.384626			0.0124987			0.00624934	+	0.999980i	$0.498011\pi$
$948$		0			0
$949$	18.8280			0.611181
$950$	−9.93739	+	44.8854i	−0.322411	+	1.45628i
$951$		0			0
$952$	−9.64541	−	7.38804i	−0.312610	−	0.239448i
$953$		−	47.1282i		−	1.52663i	−0.646025	−	0.763316i	$-0.723570\pi$
$953$		−	47.1282i		−	1.52663i	0.646025	−	0.763316i	$-0.276430\pi$
$954$		0			0
$955$		−	7.28469i		−	0.235727i
$956$	33.1309	+	15.4261i	1.07153	+	0.498916i
$957$		0			0
$958$	−3.35369	−	0.742488i	−0.108353	−	0.0239887i
$959$	−1.86399			−0.0601913
$960$		0			0
$961$	26.8980			0.867678
$962$	24.4457	+	5.41215i	0.788162	+	0.174495i
$963$		0			0
$964$	3.56860	+	1.66158i	0.114937	+	0.0535159i
$965$		−	0.650982i		−	0.0209558i
$966$		0			0
$967$		−	34.3587i		−	1.10490i	−0.833546	−	0.552451i	$-0.813693\pi$
$967$		−	34.3587i		−	1.10490i	0.833546	−	0.552451i	$-0.186307\pi$
$968$	20.4390	+	15.6555i	0.656934	+	0.503188i
$969$		0			0
$970$	2.02664	−	9.15399i	0.0650716	−	0.293917i
$971$	−13.7054			−0.439829			−0.219914	−	0.975519i	$-0.570578\pi$
$971$	−13.7054			−0.439829			−0.219914	+	0.975519i	$0.570578\pi$
$972$		0			0
$973$	13.4351			0.430708
$974$	9.74643	−	44.0229i	0.312296	−	1.41059i
$975$		0			0
$976$	−4.72040	−	5.61249i	−0.151096	−	0.179651i
$977$		−	9.37625i		−	0.299973i	−0.988688	−	0.149986i	$-0.952077\pi$
$977$		−	9.37625i		−	0.299973i	0.988688	−	0.149986i	$-0.0479230\pi$
$978$		0			0
$979$		−	68.6740i		−	2.19483i
$980$	−2.25174	+	4.83611i	−0.0719293	+	0.154484i
$981$		0			0
$982$	10.4406	+	2.31149i	0.333173	+	0.0737626i
$983$	42.1869			1.34555			0.672777	−	0.739846i	$-0.265101\pi$
$983$	42.1869			1.34555			0.672777	+	0.739846i	$0.265101\pi$
$984$		0			0
$985$	−4.65033			−0.148172
$986$	−13.6598	−	3.02421i	−0.435017	−	0.0963103i
$987$		0			0
$988$	9.52920	−	20.4660i	0.303164	−	0.651111i
$989$			10.2545i			0.326073i
$990$		0			0
$991$			27.8097i			0.883403i	0.897162	+	0.441702i	$0.145625\pi$
$991$			27.8097i			0.883403i	−0.897162	+	0.441702i	$0.854375\pi$
$992$	10.1549	−	5.30479i	0.322419	−	0.168427i
$993$		0			0
$994$	1.26262	−	5.70305i	0.0400480	−	0.180890i
$995$	5.89987			0.187039
$996$		0			0
$997$	43.3065			1.37153			0.685765	−	0.727823i	$-0.259468\pi$
$997$	43.3065			1.37153			0.685765	+	0.727823i	$0.259468\pi$
$998$	7.16401	−	32.3586i	0.226773	−	1.02429i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	828.2.c.f.323.12	yes	12
3.2	odd	2		828.2.c.e.323.1	✓	12
4.3	odd	2		828.2.c.e.323.4	yes	12
12.11	even	2	inner	828.2.c.f.323.9	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
828.2.c.e.323.1	✓	12	3.2	odd	2
828.2.c.e.323.4	yes	12	4.3	odd	2
828.2.c.f.323.9	yes	12	12.11	even	2	inner
828.2.c.f.323.12	yes	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	828.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38078 + 0.305697i) q^{2} +(1.81310 + 0.844199i) q^{4} +0.474164i q^{5} -1.17248i q^{7} +(2.24542 + 1.71991i) q^{8} +(-0.144950 + 0.654715i) q^{10} +4.48358 q^{11} -1.65813 q^{13} +(0.358422 - 1.61893i) q^{14} +(2.57466 + 3.06123i) q^{16} -3.66369i q^{17} +6.80758i q^{19} +(-0.400289 + 0.859706i) q^{20} +(6.19084 + 1.37062i) q^{22} +1.00000 q^{23} +4.77517 q^{25} +(-2.28951 - 0.506885i) q^{26} +(0.989803 - 2.12582i) q^{28} -2.70023i q^{29} -2.02533i q^{31} +(2.61922 + 5.01395i) q^{32} +(1.11998 - 5.05875i) q^{34} +0.555946 q^{35} -10.6773 q^{37} +(-2.08105 + 9.39976i) q^{38} +(-0.815519 + 1.06470i) q^{40} -0.885578i q^{41} +10.2545i q^{43} +(8.12918 + 3.78504i) q^{44} +(1.38078 + 0.305697i) q^{46} -0.864641 q^{47} +5.62530 q^{49} +(6.59345 + 1.45975i) q^{50} +(-3.00636 - 1.39979i) q^{52} -8.96892i q^{53} +2.12595i q^{55} +(2.01655 - 2.63270i) q^{56} +(0.825453 - 3.72843i) q^{58} -6.86425 q^{59} -1.83341 q^{61} +(0.619137 - 2.79654i) q^{62} +(2.08382 + 7.72384i) q^{64} -0.786226i q^{65} -8.35780i q^{67} +(3.09289 - 6.64264i) q^{68} +(0.767638 + 0.169951i) q^{70} +3.52273 q^{71} -11.3549 q^{73} +(-14.7429 - 3.26401i) q^{74} +(-5.74695 + 12.3428i) q^{76} -5.25690i q^{77} +3.32649i q^{79} +(-1.45153 + 1.22081i) q^{80} +(0.270718 - 1.22279i) q^{82} -3.78125 q^{83} +1.73719 q^{85} +(-3.13475 + 14.1591i) q^{86} +(10.0675 + 7.71136i) q^{88} -15.3168i q^{89} +1.94412i q^{91} +(1.81310 + 0.844199i) q^{92} +(-1.19388 - 0.264318i) q^{94} -3.22791 q^{95} -13.9816 q^{97} +(7.76729 + 1.71964i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 4 q^{4} + 4 q^{8} - 8 q^{10} + 12 q^{11} - 4 q^{13} - 12 q^{14} - 12 q^{16} + 20 q^{20} + 4 q^{22} + 12 q^{23} - 40 q^{25} + 8 q^{26} - 24 q^{28} + 44 q^{32} - 28 q^{34} + 40 q^{35} - 32 q^{37}+ \cdots - 20 q^{98}+O(q^{100}) \) 12 * q + 4 * q^2 + 4 * q^4 + 4 * q^8 - 8 * q^10 + 12 * q^11 - 4 * q^13 - 12 * q^14 - 12 * q^16 + 20 * q^20 + 4 * q^22 + 12 * q^23 - 40 * q^25 + 8 * q^26 - 24 * q^28 + 44 * q^32 - 28 * q^34 + 40 * q^35 - 32 * q^37 - 32 * q^38 - 12 * q^40 + 4 * q^44 + 4 * q^46 - 32 * q^49 - 20 * q^50 + 32 * q^52 - 8 * q^56 - 16 * q^58 - 24 * q^59 - 56 * q^61 + 28 * q^64 + 16 * q^68 + 64 * q^70 - 56 * q^71 + 8 * q^73 - 36 * q^74 - 28 * q^76 + 28 * q^80 + 24 * q^82 - 28 * q^83 - 12 * q^85 - 8 * q^86 + 4 * q^88 + 4 * q^92 + 16 * q^94 + 8 * q^95 - 4 * q^97 - 20 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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