LMFDB - Embedded newform 828.2.c.e.323.1

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			323.1
Root			$-1.64216 - 2.25841i$ of defining polynomial
Character	$\chi$	$=$	828.323
Dual form			828.2.c.e.323.4

$q$-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	$-0.966187\pi$
$5$		−	0.474164i		−	0.212053i	0.994363	−	0.106026i	$-0.0338128\pi$
$6$		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	$-0.736256\pi$
$11$	−4.48358			−1.35185			−0.675926	+	0.736970i	$0.736256\pi$
$12$		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	$0.146543\pi$
$17$			3.66369i			0.888576i	−0.895884	+	0.444288i	$0.853457\pi$
$18$		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	$0.0806642\pi$
$29$			2.70023i			0.501421i	−0.968062	+	0.250710i	$0.919336\pi$
$30$		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	$0.0220293\pi$
$41$			0.885578i			0.138304i	−0.997606	+	0.0691520i	$0.977971\pi$
$42$		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	$-0.479914\pi$
$47$	0.864641			0.126121			0.0630604	+	0.998010i	$0.479914\pi$
$48$		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	$0.211243\pi$
$53$			8.96892i			1.23198i	−0.787756	+	0.615988i	$0.788757\pi$
$54$		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	$-0.352555\pi$
$59$	6.86425			0.893650			0.446825	+	0.894621i	$0.352555\pi$
$60$		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	$-0.567032\pi$
$71$	−3.52273			−0.418071			−0.209035	+	0.977908i	$0.567032\pi$
$72$		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	$-0.433460\pi$
$83$	3.78125			0.415046			0.207523	+	0.978230i	$0.433460\pi$
$84$		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	$0.301505\pi$
$89$			15.3168i			1.62357i	−0.583954	+	0.811786i	$0.698495\pi$
$90$		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	$0.316778\pi$
$101$			16.8609i			1.67772i	−0.544346	+	0.838861i	$0.683222\pi$
$102$		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	$-0.422008\pi$
$107$	5.01845			0.485152			0.242576	+	0.970132i	$0.422008\pi$
$108$		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	$-0.877372\pi$
$113$		−	7.98937i		−	0.751576i	0.926706	−	0.375788i	$-0.122628\pi$
$114$		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	$-0.652531\pi$
$131$	−10.5541			−0.922120			−0.461060	+	0.887369i	$0.652531\pi$
$132$		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	$0.0216338\pi$
$137$			1.58979i			0.135825i	−0.997691	+	0.0679123i	$0.978366\pi$
$138$		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	$0.0539232\pi$
$149$			4.11595i			0.337191i	−0.985685	+	0.168596i	$0.946077\pi$
$150$		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	$-0.392440\pi$
$167$	8.56827			0.663033			0.331516	+	0.943449i	$0.392440\pi$
$168$		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	$-0.645260\pi$
$173$		−	23.6139i		−	1.79533i	0.440674	−	0.897667i	$-0.354740\pi$
$174$		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	$-0.855974\pi$
$179$	−24.0655			−1.79874			−0.899370	+	0.437189i	$0.855974\pi$
$180$		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	$-0.312404\pi$
$191$	15.3632			1.11164			0.555822	+	0.831301i	$0.312404\pi$
$192$		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	$-0.886394\pi$
$197$		−	9.80742i		−	0.698750i	0.936983	−	0.349375i	$-0.113606\pi$
$198$		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	$-0.180397\pi$
$227$	25.4220			1.68732			0.843659	+	0.536879i	$0.180397\pi$
$228$		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	$-0.876041\pi$
$233$		−	11.5905i		−	0.759322i	0.925126	−	0.379661i	$-0.123959\pi$
$234$		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	$-0.701264\pi$
$239$	−18.2731			−1.18199			−0.590993	+	0.806677i	$0.701264\pi$
$240$		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	$-0.500065\pi$
$251$	−0.00646928			−0.000408337			−0.000204169		1.00000i	$0.500065\pi$
$252$		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	$0.156910\pi$
$257$			15.1727i			0.946448i	−0.880942	+	0.473224i	$0.843090\pi$
$258$		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	$-0.384849\pi$
$263$	11.4792			0.707837			0.353918	+	0.935276i	$0.384849\pi$
$264$		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	$-0.765515\pi$
$269$		−	22.0371i		−	1.34363i	0.740720	−	0.671814i	$-0.234485\pi$
$270$		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	$0.181945\pi$
$281$			18.1369i			1.08195i	−0.841037	+	0.540977i	$0.818055\pi$
$282$		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	$0.0717758\pi$
$293$			7.65429i			0.447169i	−0.974685	+	0.223584i	$0.928224\pi$
$294$		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	$-0.556521\pi$
$311$	−6.22993			−0.353267			−0.176633	+	0.984277i	$0.556521\pi$
$312$		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	$-0.863830\pi$
$317$		−	14.7728i		−	0.829720i	0.909885	−	0.414860i	$-0.136170\pi$
$318$		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	$-0.799880\pi$
$347$	−30.1324			−1.61759			−0.808796	+	0.588090i	$0.799880\pi$
$348$		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	$-0.837519\pi$
$353$		−	18.3588i		−	0.977140i	0.872525	−	0.488570i	$-0.162481\pi$
$354$		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	$-0.450665\pi$
$359$	5.84979			0.308740			0.154370	+	0.988013i	$0.450665\pi$
$360$		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	$-0.828712\pi$
$383$	−33.6092			−1.71735			−0.858676	+	0.512519i	$0.828712\pi$
$384$		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	$-0.816025\pi$
$389$		−	21.5506i		−	1.09266i	0.837570	−	0.546330i	$-0.183975\pi$
$390$		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	$-0.961093\pi$
$401$		−	4.88307i		−	0.243849i	0.992539	−	0.121924i	$-0.0389065\pi$
$402$		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	$-0.317961\pi$
$419$	22.1571			1.08245			0.541224	+	0.840879i	$0.317961\pi$
$420$		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	$-0.455943\pi$
$431$	5.72851			0.275932			0.137966	+	0.990437i	$0.455943\pi$
$432$		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	$-0.669236\pi$
$443$	−21.3411			−1.01395			−0.506974	+	0.861961i	$0.669236\pi$
$444$		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	$0.285327\pi$
$449$			33.1013i			1.56214i	−0.624440	+	0.781072i	$0.714673\pi$
$450$		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	$0.0302180\pi$
$461$			4.07046i			0.189580i	−0.995497	+	0.0947902i	$0.969782\pi$
$462$		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	$-0.379383\pi$
$467$	15.9883			0.739852			0.369926	+	0.929061i	$0.379383\pi$
$468$		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	$-0.482328\pi$
$479$	2.42884			0.110976			0.0554882	+	0.998459i	$0.482328\pi$
$480$		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	$-0.554577\pi$
$491$	−7.56139			−0.341241			−0.170620	+	0.985337i	$0.554577\pi$
$492$		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	$-0.675080\pi$
$503$	−23.4464			−1.04542			−0.522712	+	0.852510i	$0.675080\pi$
$504$		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	$0.183467\pi$
$509$			24.5911i			1.08998i	−0.838442	+	0.544991i	$0.816533\pi$
$510$		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	$-0.644489\pi$
$521$		−	41.0279i		−	1.79746i	0.438498	−	0.898732i	$-0.355511\pi$
$522$		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	$0.194493\pi$
$557$			27.0797i			1.14740i	−0.819064	+	0.573702i	$0.805507\pi$
$558$		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	$-0.673484\pi$
$563$	−24.6024			−1.03687			−0.518433	+	0.855118i	$0.673484\pi$
$564$		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	$-0.862329\pi$
$569$		−	19.9964i		−	0.838294i	0.907918	−	0.419147i	$-0.137671\pi$
$570$		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	$-0.736941\pi$
$587$	−32.8296			−1.35502			−0.677511	+	0.735513i	$0.736941\pi$
$588$		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	$-0.963547\pi$
$593$		−	5.56526i		−	0.228538i	0.993450	−	0.114269i	$-0.0364526\pi$
$594$		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	$-0.283932\pi$
$599$	30.7329			1.25571			0.627857	+	0.778329i	$0.283932\pi$
$600$		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	$0.167536\pi$
$617$			24.9569i			1.00473i	−0.864656	+	0.502364i	$0.832464\pi$
$618$		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	$-0.860957\pi$
$641$		−	21.4219i		−	0.846114i	0.906103	−	0.423057i	$-0.139043\pi$
$642$		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	$-0.213776\pi$
$647$	39.8244			1.56566			0.782830	+	0.622236i	$0.213776\pi$
$648$		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	$0.172377\pi$
$653$			26.3437i			1.03091i	−0.856917	+	0.515455i	$0.827623\pi$
$654$		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	$-0.553442\pi$
$659$	−8.57952			−0.334211			−0.167105	+	0.985939i	$0.553442\pi$
$660$		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	$0.298321\pi$
$677$			41.9381i			1.61181i	−0.592044	+	0.805906i	$0.701679\pi$
$678$		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	$-0.395912\pi$
$683$	16.7889			0.642410			0.321205	+	0.947010i	$0.395912\pi$
$684$		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	$0.412026\pi$
$701$			50.9433i			1.92410i	−0.272872	+	0.962050i	$0.587974\pi$
$702$		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	$-0.390875\pi$
$719$	18.0272			0.672302			0.336151	+	0.941808i	$0.390875\pi$
$720$		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	$-0.430077\pi$
$743$	11.8795			0.435816			0.217908	+	0.975969i	$0.430077\pi$
$744$		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	$0.0390559\pi$
$761$			6.75256i			0.244780i	−0.992482	+	0.122390i	$0.960944\pi$
$762$		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	$-0.749808\pi$
$773$		−	39.3429i		−	1.41507i	0.706680	−	0.707533i	$-0.250192\pi$
$774$		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	$-0.927868\pi$
$797$		−	12.6856i		−	0.449348i	0.974434	−	0.224674i	$-0.0721316\pi$
$798$		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	$-0.808738\pi$
$809$		−	32.1609i		−	1.13072i	0.824845	−	0.565359i	$-0.191262\pi$
$810$		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	$0.236852\pi$
$821$			38.8138i			1.35461i	−0.735702	+	0.677305i	$0.763148\pi$
$822$		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	$-0.581642\pi$
$827$	−14.5906			−0.507365			−0.253683	+	0.967288i	$0.581642\pi$
$828$		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	$-0.281634\pi$
$839$	36.6970			1.26692			0.633461	+	0.773775i	$0.281634\pi$
$840$		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	$0.207827\pi$
$857$			35.5685i			1.21500i	−0.794320	+	0.607499i	$0.792173\pi$
$858$		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	$-0.249956\pi$
$863$	41.5509			1.41441			0.707204	+	0.707009i	$0.249956\pi$
$864$		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	$0.0709240\pi$
$881$			13.1178i			0.441951i	−0.975279	+	0.220975i	$0.929076\pi$
$882$		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	$-0.190708\pi$
$887$	49.1905			1.65165			0.825827	+	0.563923i	$0.190708\pi$
$888$		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	$-0.489948\pi$
$911$	1.90599			0.0631482			0.0315741	+	0.999501i	$0.489948\pi$
$912$		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	$0.415093\pi$
$929$			58.8031i			1.92927i	−0.263592	+	0.964634i	$0.584907\pi$
$930$		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	$0.0403971\pi$
$941$			7.76530i			0.253142i	−0.991958	+	0.126571i	$0.959603\pi$
$942$		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	$-0.501989\pi$
$947$	−0.384626			−0.0124987			−0.00624934	+	0.999980i	$0.501989\pi$
$948$		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	$0.276430\pi$
$953$			47.1282i			1.52663i	−0.646025	+	0.763316i	$0.723570\pi$
$954$		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	$-0.429422\pi$
$971$	13.7054			0.439829			0.219914	+	0.975519i	$0.429422\pi$
$972$		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	$0.0479230\pi$
$977$			9.37625i			0.299973i	−0.988688	+	0.149986i	$0.952077\pi$
$978$		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	$-0.734899\pi$
$983$	−42.1869			−1.34555			−0.672777	+	0.739846i	$0.734899\pi$
$984$		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.e.323.1	✓	12
3.2	odd	2		828.2.c.f.323.12	yes	12
4.3	odd	2		828.2.c.f.323.9	yes	12
12.11	even	2	inner	828.2.c.e.323.4	yes	12

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
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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