LMFDB - Embedded newform 441.2.i.d.68.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(68,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 5]))

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

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

chi := DirichletCharacter("441.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			68.19
Character	$\chi$	$=$	441.68
Dual form			441.2.i.d.227.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.86894i q^{2} +(-1.72324 - 0.174470i) q^{3} -1.49292 q^{4} +(1.25287 + 2.17003i) q^{5} +(0.326074 - 3.22063i) q^{6} +0.947692i q^{8} +(2.93912 + 0.601309i) q^{9} +O(q^{10})$	\(q+1.86894i q^{2} +(-1.72324 - 0.174470i) q^{3} -1.49292 q^{4} +(1.25287 + 2.17003i) q^{5} +(0.326074 - 3.22063i) q^{6} +0.947692i q^{8} +(2.93912 + 0.601309i) q^{9} +(-4.05565 + 2.34153i) q^{10} +(4.85803 + 2.80479i) q^{11} +(2.57267 + 0.260471i) q^{12} +(0.384312 + 0.221883i) q^{13} +(-1.78039 - 3.95807i) q^{15} -4.75703 q^{16} +(-1.53885 - 2.66536i) q^{17} +(-1.12381 + 5.49303i) q^{18} +(-2.22932 - 1.28710i) q^{19} +(-1.87044 - 3.23969i) q^{20} +(-5.24197 + 9.07935i) q^{22} +(-6.83476 + 3.94605i) q^{23} +(0.165344 - 1.63310i) q^{24} +(-0.639351 + 1.10739i) q^{25} +(-0.414685 + 0.718255i) q^{26} +(-4.95990 - 1.54899i) q^{27} +(2.71041 - 1.56485i) q^{29} +(7.39739 - 3.32743i) q^{30} +10.4669i q^{31} -6.99520i q^{32} +(-7.88221 - 5.68091i) q^{33} +(4.98140 - 2.87601i) q^{34} +(-4.38788 - 0.897709i) q^{36} +(0.708168 - 1.22658i) q^{37} +(2.40550 - 4.16645i) q^{38} +(-0.623551 - 0.449409i) q^{39} +(-2.05652 + 1.18733i) q^{40} +(1.64665 - 2.85208i) q^{41} +(-4.75676 - 8.23894i) q^{43} +(-7.25268 - 4.18733i) q^{44} +(2.37747 + 7.13134i) q^{45} +(-7.37492 - 12.7737i) q^{46} +2.14380 q^{47} +(8.19750 + 0.829960i) q^{48} +(-2.06964 - 1.19491i) q^{50} +(2.18678 + 4.86155i) q^{51} +(-0.573749 - 0.331254i) q^{52} +(4.20379 - 2.42706i) q^{53} +(2.89496 - 9.26974i) q^{54} +14.0561i q^{55} +(3.61709 + 2.60693i) q^{57} +(2.92461 + 5.06558i) q^{58} +7.30991 q^{59} +(2.65798 + 5.90910i) q^{60} +8.55576i q^{61} -19.5619 q^{62} +3.55953 q^{64} +1.11196i q^{65} +(10.6173 - 14.7314i) q^{66} -1.86888 q^{67} +(2.29739 + 3.97919i) q^{68} +(12.4664 - 5.60753i) q^{69} +2.95338i q^{71} +(-0.569856 + 2.78538i) q^{72} +(7.37804 - 4.25971i) q^{73} +(2.29241 + 1.32352i) q^{74} +(1.29496 - 1.79675i) q^{75} +(3.32820 + 1.92154i) q^{76} +(0.839916 - 1.16538i) q^{78} -0.574261 q^{79} +(-5.95992 - 10.3229i) q^{80} +(8.27686 + 3.53464i) q^{81} +(5.33036 + 3.07748i) q^{82} +(4.23521 + 7.33560i) q^{83} +(3.85595 - 6.67870i) q^{85} +(15.3981 - 8.89008i) q^{86} +(-4.94370 + 2.22373i) q^{87} +(-2.65807 + 4.60392i) q^{88} +(3.78929 - 6.56325i) q^{89} +(-13.3280 + 4.44334i) q^{90} +(10.2038 - 5.89115i) q^{92} +(1.82616 - 18.0369i) q^{93} +4.00663i q^{94} -6.45024i q^{95} +(-1.22045 + 12.0544i) q^{96} +(-3.22662 + 1.86289i) q^{97} +(12.5918 + 11.1648i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4} - 8 q^{9}+O(q^{10}) $ 48 * q - 48 * q^4 - 8 * q^9	$ 48 q - 48 q^{4} - 8 q^{9} + 24 q^{11} - 40 q^{15} + 48 q^{16} - 16 q^{18} + 48 q^{23} - 24 q^{25} - 24 q^{30} - 8 q^{36} - 56 q^{39} - 96 q^{44} + 48 q^{50} - 24 q^{51} - 48 q^{53} + 80 q^{57} + 168 q^{60} - 48 q^{64} - 88 q^{72} + 168 q^{74} - 88 q^{78} + 48 q^{79} - 24 q^{81} - 24 q^{85} - 24 q^{86} - 144 q^{92} + 16 q^{93} - 72 q^{99}+O(q^{100}) $ 48 * q - 48 * q^4 - 8 * q^9 + 24 * q^11 - 40 * q^15 + 48 * q^16 - 16 * q^18 + 48 * q^23 - 24 * q^25 - 24 * q^30 - 8 * q^36 - 56 * q^39 - 96 * q^44 + 48 * q^50 - 24 * q^51 - 48 * q^53 + 80 * q^57 + 168 * q^60 - 48 * q^64 - 88 * q^72 + 168 * q^74 - 88 * q^78 + 48 * q^79 - 24 * q^81 - 24 * q^85 - 24 * q^86 - 144 * q^92 + 16 * q^93 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$			1.86894i			1.32154i	0.750589	+	0.660769i	$0.229770\pi$
$2$			1.86894i			1.32154i	−0.750589	+	0.660769i	$0.770230\pi$
$3$	−1.72324	−	0.174470i	−0.994914	−	0.100730i
$3$	−1.72324	−	0.174470i	−0.994914	−	0.100730i
$4$	−1.49292			−0.746462
$5$	1.25287	+	2.17003i	0.560299	+	0.970467i	0.997470	+	0.0710881i	$0.0226472\pi$
$5$	1.25287	+	2.17003i	0.560299	+	0.970467i	−0.437171	+	0.899378i	$0.644020\pi$
$6$	0.326074	−	3.22063i	0.133119	−	1.31482i
$7$		0			0
$7$		0			0
$8$			0.947692i			0.335060i
$9$	2.93912	+	0.601309i	0.979707	+	0.200436i
$10$	−4.05565	+	2.34153i	−1.28251	+	0.740457i
$11$	4.85803	+	2.80479i	1.46475	+	0.845675i	0.999225	−	0.0393590i	$-0.0125316\pi$
$11$	4.85803	+	2.80479i	1.46475	+	0.845675i	0.465527	+	0.885034i	$0.345865\pi$
$12$	2.57267	+	0.260471i	0.742666	+	0.0751915i
$13$	0.384312	+	0.221883i	0.106589	+	0.0615392i	0.552347	−	0.833614i	$-0.313732\pi$
$13$	0.384312	+	0.221883i	0.106589	+	0.0615392i	−0.445758	+	0.895154i	$0.647066\pi$
$14$		0			0
$15$	−1.78039	−	3.95807i	−0.459694	−	1.02197i
$16$	−4.75703			−1.18926
$17$	−1.53885	−	2.66536i	−0.373226	−	0.646446i	0.616834	−	0.787093i	$-0.288415\pi$
$17$	−1.53885	−	2.66536i	−0.373226	−	0.646446i	−0.990060	+	0.140647i	$0.955082\pi$
$18$	−1.12381	+	5.49303i	−0.264884	+	1.29472i
$19$	−2.22932	−	1.28710i	−0.511440	−	0.295280i	0.221985	−	0.975050i	$-0.428746\pi$
$19$	−2.22932	−	1.28710i	−0.511440	−	0.295280i	−0.733425	+	0.679770i	$0.762080\pi$
$20$	−1.87044	−	3.23969i	−0.418242	−	0.724417i
$21$		0			0
$22$	−5.24197	+	9.07935i	−1.11759	+	1.93572i
$23$	−6.83476	+	3.94605i	−1.42515	+	0.822808i	−0.996732	−	0.0807749i	$-0.974261\pi$
$23$	−6.83476	+	3.94605i	−1.42515	+	0.822808i	−0.428413	+	0.903583i	$0.640927\pi$
$24$	0.165344	−	1.63310i	0.0337507	−	0.333355i
$25$	−0.639351	+	1.10739i	−0.127870	+	0.221478i
$26$	−0.414685	+	0.718255i	−0.0813264	+	0.140861i
$27$	−4.95990	−	1.54899i	−0.954534	−	0.298103i
$28$		0			0
$29$	2.71041	−	1.56485i	0.503310	−	0.290586i	−0.226770	−	0.973948i	$-0.572816\pi$
$29$	2.71041	−	1.56485i	0.503310	−	0.290586i	0.730079	+	0.683362i	$0.239483\pi$
$30$	7.39739	−	3.32743i	1.35057	−	0.607503i
$31$			10.4669i			1.87990i	0.341306	+	0.939952i	$0.389131\pi$
$31$			10.4669i			1.87990i	−0.341306	+	0.939952i	$0.610869\pi$
$32$		−	6.99520i		−	1.23659i
$33$	−7.88221	−	5.68091i	−1.37212	−	0.988919i
$34$	4.98140	−	2.87601i	0.854303	−	0.493232i
$35$		0			0
$36$	−4.38788	−	0.897709i	−0.731314	−	0.149618i
$37$	0.708168	−	1.22658i	0.116422	−	0.201649i	−0.801925	−	0.597424i	$-0.796191\pi$
$37$	0.708168	−	1.22658i	0.116422	−	0.201649i	0.918347	+	0.395775i	$0.129524\pi$
$38$	2.40550	−	4.16645i	0.390224	−	0.675887i
$39$	−0.623551	−	0.449409i	−0.0998480	−	0.0719630i
$40$	−2.05652	+	1.18733i	−0.325164	+	0.187734i
$41$	1.64665	−	2.85208i	0.257163	−	0.445420i	−0.708318	−	0.705894i	$-0.750545\pi$
$41$	1.64665	−	2.85208i	0.257163	−	0.445420i	0.965481	+	0.260474i	$0.0838788\pi$
$42$		0			0
$43$	−4.75676	−	8.23894i	−0.725398	−	1.25643i	−0.958810	−	0.284049i	$-0.908322\pi$
$43$	−4.75676	−	8.23894i	−0.725398	−	1.25643i	0.233411	−	0.972378i	$-0.425011\pi$
$44$	−7.25268	−	4.18733i	−1.09338	−	0.631264i
$45$	2.37747	+	7.13134i	0.354412	+	1.06308i
$46$	−7.37492	−	12.7737i	−1.08737	−	1.88338i
$47$	2.14380			0.312706			0.156353	−	0.987701i	$-0.450026\pi$
$47$	2.14380			0.312706			0.156353	+	0.987701i	$0.450026\pi$
$48$	8.19750	+	0.829960i	1.18321	+	0.119794i
$49$		0			0
$50$	−2.06964	−	1.19491i	−0.292691	−	0.168985i
$51$	2.18678	+	4.86155i	0.306211	+	0.680753i
$52$	−0.573749	−	0.331254i	−0.0795647	−	0.0459367i
$53$	4.20379	−	2.42706i	0.577435	−	0.333382i	−0.182678	−	0.983173i	$-0.558477\pi$
$53$	4.20379	−	2.42706i	0.577435	−	0.333382i	0.760113	+	0.649791i	$0.225143\pi$
$54$	2.89496	−	9.26974i	0.393955	−	1.26145i
$55$			14.0561i			1.89532i
$56$		0			0
$57$	3.61709	+	2.60693i	0.479095	+	0.345296i
$58$	2.92461	+	5.06558i	0.384020	+	0.665143i
$59$	7.30991			0.951669			0.475835	−	0.879535i	$-0.342146\pi$
$59$	7.30991			0.951669			0.475835	+	0.879535i	$0.342146\pi$
$60$	2.65798	+	5.90910i	0.343144	+	0.762862i
$61$			8.55576i			1.09545i	0.836658	+	0.547726i	$0.184506\pi$
$61$			8.55576i			1.09545i	−0.836658	+	0.547726i	$0.815494\pi$
$62$	−19.5619			−2.48437
$63$		0			0
$64$	3.55953			0.444941
$65$			1.11196i			0.137921i
$66$	10.6173	−	14.7314i	1.30689	−	1.81330i
$67$	−1.86888			−0.228321			−0.114160	−	0.993462i	$-0.536418\pi$
$67$	−1.86888			−0.228321			−0.114160	+	0.993462i	$0.536418\pi$
$68$	2.29739	+	3.97919i	0.278599	+	0.482548i
$69$	12.4664	−	5.60753i	1.50078	−	0.675067i
$70$		0			0
$71$			2.95338i			0.350501i	0.984524	+	0.175251i	$0.0560736\pi$
$71$			2.95338i			0.350501i	−0.984524	+	0.175251i	$0.943926\pi$
$72$	−0.569856	+	2.78538i	−0.0671581	+	0.328260i
$73$	7.37804	−	4.25971i	0.863534	−	0.498562i	−0.00165984	−	0.999999i	$-0.500528\pi$
$73$	7.37804	−	4.25971i	0.863534	−	0.498562i	0.865194	+	0.501437i	$0.167195\pi$
$74$	2.29241	+	1.32352i	0.266487	+	0.153856i
$75$	1.29496	−	1.79675i	0.149529	−	0.207471i
$76$	3.32820	+	1.92154i	0.381771	+	0.220415i
$77$		0			0
$78$	0.839916	−	1.16538i	0.0951018	−	0.131953i
$79$	−0.574261			−0.0646094			−0.0323047	−	0.999478i	$-0.510285\pi$
$79$	−0.574261			−0.0646094			−0.0323047	+	0.999478i	$0.510285\pi$
$80$	−5.95992	−	10.3229i	−0.666339	−	1.15413i
$81$	8.27686	+	3.53464i	0.919651	+	0.392738i
$82$	5.33036	+	3.07748i	0.588639	+	0.339851i
$83$	4.23521	+	7.33560i	0.464875	+	0.805186i	0.999196	−	0.0400951i	$-0.0127661\pi$
$83$	4.23521	+	7.33560i	0.464875	+	0.805186i	−0.534321	+	0.845281i	$0.679433\pi$
$84$		0			0
$85$	3.85595	−	6.67870i	0.418236	−	0.724406i
$86$	15.3981	−	8.89008i	1.66042	−	0.958642i
$87$	−4.94370	+	2.22373i	−0.530021	+	0.238409i
$88$	−2.65807	+	4.60392i	−0.283352	+	0.490779i
$89$	3.78929	−	6.56325i	0.401664	−	0.695703i	−0.592263	−	0.805745i	$-0.701765\pi$
$89$	3.78929	−	6.56325i	0.401664	−	0.695703i	0.993927	+	0.110042i	$0.0350986\pi$
$90$	−13.3280	+	4.44334i	−1.40490	+	0.468369i
$91$		0			0
$92$	10.2038	−	5.89115i	1.06382	−	0.614195i
$93$	1.82616	−	18.0369i	0.189364	−	1.87034i
$94$			4.00663i			0.413252i
$95$		−	6.45024i		−	0.661781i
$96$	−1.22045	+	12.0544i	−0.124562	+	1.23030i
$97$	−3.22662	+	1.86289i	−0.327614	+	0.189148i	−0.654781	−	0.755818i	$-0.727239\pi$
$97$	−3.22662	+	1.86289i	−0.327614	+	0.189148i	0.327167	+	0.944966i	$0.393906\pi$
$98$		0			0
$99$	12.5918	+	11.1648i	1.26552	+	1.12210i
$100$	0.954503	−	1.65325i	0.0954503	−	0.165325i
$101$	−3.76725	+	6.52506i	−0.374855	+	0.649268i	−0.990305	−	0.138908i	$-0.955641\pi$
$101$	−3.76725	+	6.52506i	−0.374855	+	0.649268i	0.615450	+	0.788176i	$0.288974\pi$
$102$	−9.08593	+	4.08696i	−0.899641	+	0.404669i
$103$	12.4045	−	7.16173i	1.22225	−	0.705666i	0.256853	−	0.966451i	$-0.417315\pi$
$103$	12.4045	−	7.16173i	1.22225	−	0.705666i	0.965397	+	0.260784i	$0.0839812\pi$
$104$	−0.210276	+	0.364210i	−0.0206193	+	0.0357137i
$105$		0			0
$106$	4.53602	+	7.85662i	0.440577	+	0.763102i
$107$	−11.6798	−	6.74331i	−1.12912	−	0.651900i	−0.185410	−	0.982661i	$-0.559361\pi$
$107$	−11.6798	−	6.74331i	−1.12912	−	0.651900i	−0.943715	+	0.330761i	$0.892695\pi$
$108$	7.40476	+	2.31252i	0.712523	+	0.222523i
$109$	0.459348	+	0.795613i	0.0439975	+	0.0762059i	0.887186	−	0.461413i	$-0.152657\pi$
$109$	0.459348	+	0.795613i	0.0439975	+	0.0762059i	−0.843188	+	0.537619i	$0.819324\pi$
$110$	−26.2700			−2.50474
$111$	−1.43435	+	1.99014i	−0.136142	+	0.188896i
$112$		0			0
$113$	4.10412	+	2.36952i	0.386083	+	0.222905i	0.680462	−	0.732784i	$-0.261779\pi$
$113$	4.10412	+	2.36952i	0.386083	+	0.222905i	−0.294378	+	0.955689i	$0.595113\pi$
$114$	−4.87218	+	6.76011i	−0.456321	+	0.633142i
$115$	−17.1261	−	9.88775i	−1.59702	−	0.922037i
$116$	−4.04643	+	2.33621i	−0.375702	+	0.216912i
$117$	0.996120	+	0.883231i	0.0920913	+	0.0816547i
$118$			13.6618i			1.25767i
$119$		0			0
$120$	3.75103	−	1.68726i	0.342421	−	0.154025i
$121$	10.2337	+	17.7252i	0.930332	+	1.61138i
$122$	−15.9902			−1.44768
$123$	−3.33518	+	4.62753i	−0.300723	+	0.417250i
$124$		−	15.6262i		−	1.40328i
$125$	9.32458			0.834016
$126$		0			0
$127$	7.37245			0.654200			0.327100	−	0.944990i	$-0.393929\pi$
$127$	7.37245			0.654200			0.327100	+	0.944990i	$0.393929\pi$
$128$		−	7.33786i		−	0.648581i
$129$	6.75959	+	15.0276i	0.595148	+	1.32311i
$130$	−2.07818			−0.182268
$131$	3.93150	+	6.80955i	0.343497	+	0.594953i	0.985079	−	0.172100i	$-0.0550553\pi$
$131$	3.93150	+	6.80955i	0.343497	+	0.594953i	−0.641583	+	0.767054i	$0.721722\pi$
$132$	11.7675	+	8.48116i	1.02423	+	0.738191i
$133$		0			0
$134$		−	3.49283i		−	0.301734i
$135$	−2.85275	−	12.7038i	−0.245525	−	1.09337i
$136$	2.52594	−	1.45835i	0.216598	−	0.125053i
$137$	10.0198	+	5.78491i	0.856046	+	0.494238i	0.862686	−	0.505740i	$-0.168780\pi$
$137$	10.0198	+	5.78491i	0.856046	+	0.494238i	−0.00664016	+	0.999978i	$0.502114\pi$
$138$	10.4801	+	23.2989i	0.892127	+	1.98334i
$139$	−16.9741	−	9.79999i	−1.43972	−	0.831224i	−0.441893	−	0.897068i	$-0.645693\pi$
$139$	−16.9741	−	9.79999i	−1.43972	−	0.831224i	−0.997830	+	0.0658437i	$0.979026\pi$
$140$		0			0
$141$	−3.69429	−	0.374030i	−0.311115	−	0.0314990i
$142$	−5.51968			−0.463201
$143$	1.24467	+	2.15583i	0.104084	+	0.180279i
$144$	−13.9815	−	2.86044i	−1.16512	−	0.238370i
$145$	6.79156	+	3.92111i	0.564008	+	0.325630i
$146$	7.96114	+	13.7891i	0.658868	+	1.14119i
$147$		0			0
$148$	−1.05724	+	1.83120i	−0.0869047	+	0.150523i
$149$	13.6315	−	7.87012i	1.11673	−	0.644746i	0.176167	−	0.984360i	$-0.443630\pi$
$149$	13.6315	−	7.87012i	1.11673	−	0.644746i	0.940565	+	0.339615i	$0.110297\pi$
$150$	3.35801	+	2.42020i	0.274181	+	0.197609i
$151$	0.991353	−	1.71707i	0.0806752	−	0.139734i	−0.822865	−	0.568237i	$-0.807626\pi$
$151$	0.991353	−	1.71707i	0.0806752	−	0.139734i	0.903540	+	0.428503i	$0.140959\pi$
$152$	1.21977	−	2.11270i	0.0989364	−	0.171363i
$153$	−2.92015	−	8.75915i	−0.236081	−	0.708135i
$154$		0			0
$155$	−22.7134	+	13.1136i	−1.82438	+	1.05331i
$156$	0.930914	+	0.670933i	0.0745328	+	0.0537176i
$157$		−	8.39224i		−	0.669774i	−0.942258	−	0.334887i	$-0.891302\pi$
$157$		−	8.39224i		−	0.669774i	0.942258	−	0.334887i	$-0.108698\pi$
$158$		−	1.07326i		−	0.0853837i
$159$	−7.66759	+	3.44897i	−0.608080	+	0.273521i
$160$	15.1798	−	8.76405i	1.20007	−	0.692859i
$161$		0			0
$162$	−6.60602	+	15.4689i	−0.519018	+	1.21535i
$163$	0.537054	−	0.930204i	0.0420653	−	0.0728592i	−0.844226	−	0.535987i	$-0.819940\pi$
$163$	0.537054	−	0.930204i	0.0420653	−	0.0728592i	0.886291	+	0.463128i	$0.153273\pi$
$164$	−2.45832	+	4.25794i	−0.191963	+	0.332489i
$165$	2.45237	−	24.2220i	0.190917	−	1.88568i
$166$	−13.7098	+	7.91534i	−1.06408	+	0.614349i
$167$	−3.99731	+	6.92354i	−0.309321	+	0.535760i	−0.978214	−	0.207599i	$-0.933435\pi$
$167$	−3.99731	+	6.92354i	−0.309321	+	0.535760i	0.668893	+	0.743359i	$0.266768\pi$
$168$		0			0
$169$	−6.40154	−	11.0878i	−0.492426	−	0.852907i
$170$	12.4821	+	7.20652i	0.957330	+	0.552715i
$171$	−5.77828	−	5.12344i	−0.441876	−	0.391799i
$172$	7.10148	+	12.3001i	0.541483	+	0.937875i
$173$	1.00349			0.0762938			0.0381469	−	0.999272i	$-0.487855\pi$
$173$	1.00349			0.0762938			0.0381469	+	0.999272i	$0.487855\pi$
$174$	−4.15602	−	9.23947i	−0.315067	−	0.700442i
$175$		0			0
$176$	−23.1098	−	13.3424i	−1.74197	−	1.00572i
$177$	−12.5967	−	1.27536i	−0.946829	−	0.0958621i
$178$	12.2663	+	7.08195i	0.919398	+	0.530814i
$179$	−1.27773	+	0.737695i	−0.0955017	+	0.0551379i	−0.546990	−	0.837139i	$-0.684227\pi$
$179$	−1.27773	+	0.737695i	−0.0955017	+	0.0551379i	0.451489	+	0.892277i	$0.350893\pi$
$180$	−3.54938	−	10.6465i	−0.264555	−	0.793547i
$181$		−	15.0440i		−	1.11821i	−0.829096	−	0.559106i	$-0.811145\pi$
$181$		−	15.0440i		−	1.11821i	0.829096	−	0.559106i	$-0.188855\pi$
$182$		0			0
$183$	1.49273	−	14.7436i	0.110345	−	1.08988i
$184$	−3.73964	−	6.47724i	−0.275690	−	0.477509i
$185$	3.54896			0.260925
$186$	33.7099	+	3.41297i	2.47173	+	0.250251i
$187$		−	17.2646i		−	1.26251i
$188$	−3.20054			−0.233423
$189$		0			0
$190$	12.0551			0.874568
$191$			13.2237i			0.956836i	0.878132	+	0.478418i	$0.158790\pi$
$191$			13.2237i			0.956836i	−0.878132	+	0.478418i	$0.841210\pi$
$192$	−6.13392	−	0.621032i	−0.442678	−	0.0448191i
$193$	−1.55571			−0.111982			−0.0559912	−	0.998431i	$-0.517832\pi$
$193$	−1.55571			−0.111982			−0.0559912	+	0.998431i	$0.517832\pi$
$194$	−3.48163	−	6.03035i	−0.249966	−	0.432954i
$195$	0.194004	−	1.91617i	0.0138929	−	0.137220i
$196$		0			0
$197$			4.96185i			0.353517i	0.984254	+	0.176759i	$0.0565612\pi$
$197$			4.96185i			0.353517i	−0.984254	+	0.176759i	$0.943439\pi$
$198$	−20.8663	+	23.5333i	−1.48290	+	1.67244i
$199$	9.69273	−	5.59610i	0.687100	−	0.396697i	−0.115425	−	0.993316i	$-0.536823\pi$
$199$	9.69273	−	5.59610i	0.687100	−	0.396697i	0.802525	+	0.596619i	$0.203490\pi$
$200$	−1.04946	−	0.605908i	−0.0742083	−	0.0428442i
$201$	3.22054	+	0.326065i	0.227159	+	0.0229988i
$202$	−12.1949	−	7.04074i	−0.858032	−	0.495385i
$203$		0			0
$204$	−3.26470	−	7.25793i	−0.228575	−	0.508157i
$205$	8.25213			0.576354
$206$	13.3848	+	23.1832i	0.932565	+	1.61525i
$207$	−22.4610	+	7.48811i	−1.56115	+	0.520460i
$208$	−1.82818	−	1.05550i	−0.126762	−	0.0731859i
$209$	−7.22006	−	12.5055i	−0.499422	−	0.865024i
$210$		0			0
$211$	7.68026	−	13.3026i	0.528731	−	0.915789i	−0.470708	−	0.882289i	$-0.656001\pi$
$211$	7.68026	−	13.3026i	0.528731	−	0.915789i	0.999439	−	0.0334999i	$-0.0106654\pi$
$212$	−6.27594	+	3.62342i	−0.431033	+	0.248857i
$213$	0.515277	−	5.08938i	0.0353062	−	0.348719i
$214$	12.6028	−	21.8287i	0.861511	−	1.49218i
$215$	11.9192	−	20.6446i	0.812880	−	1.40795i
$216$	1.46796	−	4.70046i	0.0998824	−	0.319826i
$217$		0			0
$218$	−1.48695	+	0.858492i	−0.100709	+	0.0581444i
$219$	−13.4573	+	6.05327i	−0.909363	+	0.409042i
$220$		−	20.9847i		−	1.41479i
$221$		−	1.36578i		−	0.0918721i
$222$	−3.71945	−	2.68070i	−0.249633	−	0.179917i
$223$	2.76845	−	1.59837i	0.185389	−	0.107034i	−0.404433	−	0.914568i	$-0.632531\pi$
$223$	2.76845	−	1.59837i	0.185389	−	0.107034i	0.589822	+	0.807533i	$0.299198\pi$
$224$		0			0
$225$	−2.54501	+	2.87030i	−0.169668	+	0.191353i
$226$	−4.42848	+	7.67035i	−0.294578	+	0.510224i
$227$	7.33494	−	12.7045i	0.486837	−	0.843227i	−0.513048	−	0.858360i	$-0.671484\pi$
$227$	7.33494	−	12.7045i	0.486837	−	0.843227i	0.999885	+	0.0151329i	$0.00481714\pi$
$228$	−5.40004	−	3.89194i	−0.357626	−	0.257750i
$229$	2.92550	−	1.68904i	0.193322	−	0.111615i	−0.400215	−	0.916421i	$-0.631064\pi$
$229$	2.92550	−	1.68904i	0.193322	−	0.111615i	0.593537	+	0.804807i	$0.297731\pi$
$230$	18.4796	−	32.0076i	1.21851	−	2.11052i
$231$		0			0
$232$	1.48300	+	2.56863i	0.0973637	+	0.168639i
$233$	−4.22628	−	2.44005i	−0.276873	−	0.159853i	0.355134	−	0.934815i	$-0.384435\pi$
$233$	−4.22628	−	2.44005i	−0.276873	−	0.159853i	−0.632007	+	0.774963i	$0.717769\pi$
$234$	−1.65070	+	1.86168i	−0.107910	+	0.121702i
$235$	2.68590	+	4.65211i	0.175209	+	0.303470i
$236$	−10.9131			−0.710385
$237$	0.989589	+	0.100191i	0.0642807	+	0.00650813i
$238$		0			0
$239$	13.6253	+	7.86657i	0.881347	+	0.508846i	0.871102	−	0.491101i	$-0.163406\pi$
$239$	13.6253	+	7.86657i	0.881347	+	0.508846i	0.0102448	+	0.999948i	$0.496739\pi$
$240$	8.46934	+	18.8286i	0.546694	+	1.21538i
$241$	−0.666305	−	0.384691i	−0.0429205	−	0.0247801i	0.478386	−	0.878150i	$-0.341222\pi$
$241$	−0.666305	−	0.384691i	−0.0429205	−	0.0247801i	−0.521307	+	0.853369i	$0.674555\pi$
$242$	−33.1273	+	19.1260i	−2.12950	+	1.22947i
$243$	−13.6463	−	7.53510i	−0.875412	−	0.483377i
$244$		−	12.7731i		−	0.817714i
$245$		0			0
$246$	−8.64856	−	6.23323i	−0.551412	−	0.397416i
$247$	−0.571169	−	0.989293i	−0.0363426	−	0.0629472i
$248$	−9.91936			−0.629880
$249$	−6.01844	−	13.3799i	−0.381403	−	0.847918i
$250$			17.4271i			1.10218i
$251$	−1.14544			−0.0722996			−0.0361498	−	0.999346i	$-0.511509\pi$
$251$	−1.14544			−0.0722996			−0.0361498	+	0.999346i	$0.511509\pi$
$252$		0			0
$253$	−44.2713			−2.78331
$254$			13.7787i			0.864549i
$255$	−7.80996	+	10.8363i	−0.489079	+	0.678593i
$256$	20.8331			1.30207
$257$	14.4917	+	25.1004i	0.903969	+	1.56572i	0.822295	+	0.569061i	$0.192693\pi$
$257$	14.4917	+	25.1004i	0.903969	+	1.56572i	0.0816738	+	0.996659i	$0.473973\pi$
$258$	−28.0856	+	12.6332i	−1.74853	+	0.786511i
$259$		0			0
$260$		−	1.66007i		−	0.102953i
$261$	8.90717	−	2.96950i	0.551340	−	0.183808i
$262$	−12.7266	+	7.34772i	−0.786254	+	0.453944i
$263$	−11.8643	−	6.84988i	−0.731586	−	0.422381i	0.0874160	−	0.996172i	$-0.472139\pi$
$263$	−11.8643	−	6.84988i	−0.731586	−	0.422381i	−0.819002	+	0.573790i	$0.805472\pi$
$264$	5.38375	−	7.46991i	0.331347	−	0.459741i
$265$	10.5336	+	6.08156i	0.647072	+	0.373587i
$266$		0			0
$267$	−7.67496	+	10.6489i	−0.469700	+	0.651704i
$268$	2.79010			0.170433
$269$	5.23973	+	9.07548i	0.319472	+	0.553342i	0.980378	−	0.197127i	$-0.0631611\pi$
$269$	5.23973	+	9.07548i	0.319472	+	0.553342i	−0.660906	+	0.750469i	$0.729828\pi$
$270$	23.7426	−	5.33160i	1.44493	−	0.324471i
$271$	−5.66907	−	3.27304i	−0.344371	−	0.198823i	0.317832	−	0.948147i	$-0.397045\pi$
$271$	−5.66907	−	3.27304i	−0.344371	−	0.198823i	−0.662203	+	0.749324i	$0.730379\pi$
$272$	7.32034	+	12.6792i	0.443861	+	0.768790i
$273$		0			0
$274$	−10.8116	+	18.7263i	−0.653155	+	1.13130i
$275$	−6.21198	+	3.58649i	−0.374596	+	0.216273i
$276$	−18.6114	+	8.37162i	−1.12027	+	0.503912i
$277$	−11.2156	+	19.4261i	−0.673883	+	1.16720i	0.302911	+	0.953019i	$0.402041\pi$
$277$	−11.2156	+	19.4261i	−0.673883	+	1.16720i	−0.976794	+	0.214181i	$0.931292\pi$
$278$	18.3156	−	31.7235i	1.09849	−	1.90265i
$279$	−6.29382	+	30.7634i	−0.376801	+	1.84176i
$280$		0			0
$281$	19.3552	−	11.1747i	1.15463	−	0.666627i	0.204621	−	0.978841i	$-0.434404\pi$
$281$	19.3552	−	11.1747i	1.15463	−	0.666627i	0.950012	+	0.312214i	$0.101071\pi$
$282$	0.699038	−	6.90439i	0.0416271	−	0.411151i
$283$			18.9713i			1.12772i	0.825869	+	0.563862i	$0.190685\pi$
$283$			18.9713i			1.12772i	−0.825869	+	0.563862i	$0.809315\pi$
$284$		−	4.40917i		−	0.261636i
$285$	−1.12538	+	11.1153i	−0.0666615	+	0.658415i
$286$	−4.02910	+	2.32620i	−0.238246	+	0.137551i
$287$		0			0
$288$	4.20627	−	20.5597i	0.247857	−	1.21149i
$289$	3.76389	−	6.51924i	0.221405	−	0.383485i
$290$	−7.32830	+	12.6930i	−0.430333	+	0.745358i
$291$	5.88527	−	2.64726i	0.345000	−	0.155185i
$292$	−11.0149	+	6.35943i	−0.644596	+	0.372158i
$293$	4.41136	−	7.64069i	0.257714	−	0.446374i	−0.707915	−	0.706298i	$-0.750364\pi$
$293$	4.41136	−	7.64069i	0.257714	−	0.446374i	0.965629	+	0.259924i	$0.0836974\pi$
$294$		0			0
$295$	9.15835	+	15.8627i	0.533220	+	0.923563i
$296$	1.16242	+	0.671125i	0.0675644	+	0.0390083i
$297$	−19.7508	−	21.4365i	−1.14606	−	1.24387i
$298$	14.7088	+	25.4763i	0.852056	+	1.47580i
$299$	−3.50224			−0.202540
$300$	−1.93328	+	2.68241i	−0.111618	+	0.154869i
$301$		0			0
$302$	3.20910	+	1.85278i	0.184663	+	0.106615i
$303$	7.63030	−	10.5870i	0.438349	−	0.608206i
$304$	10.6049	+	6.12275i	0.608233	+	0.351164i
$305$	−18.5662	+	10.7192i	−1.06310	+	0.613781i
$306$	16.3703	−	5.45758i	0.935828	−	0.311989i
$307$		−	28.7533i		−	1.64104i	−0.571620	−	0.820519i	$-0.693685\pi$
$307$		−	28.7533i		−	1.64104i	0.571620	−	0.820519i	$-0.306315\pi$
$308$		0			0
$309$	−22.6254	+	10.1772i	−1.28712	+	0.578959i
$310$	−24.5085	−	42.4499i	−1.39199	−	2.41099i
$311$	13.2859			0.753373			0.376687	−	0.926341i	$-0.377063\pi$
$311$	13.2859			0.753373			0.376687	+	0.926341i	$0.377063\pi$
$312$	0.425901	−	0.590934i	0.0241119	−	0.0334550i
$313$			31.5495i			1.78329i	0.452740	+	0.891643i	$0.350447\pi$
$313$			31.5495i			1.78329i	−0.452740	+	0.891643i	$0.649553\pi$
$314$	15.6846			0.885132
$315$		0			0
$316$	0.857328			0.0482285
$317$			20.0709i			1.12729i	0.826016	+	0.563646i	$0.190602\pi$
$317$			20.0709i			1.12729i	−0.826016	+	0.563646i	$0.809398\pi$
$318$	−6.44591	−	14.3302i	−0.361469	−	0.803600i
$319$	17.5563			0.982965
$320$	4.45961	+	7.72428i	0.249300	+	0.431800i
$321$	18.9505	+	13.6581i	1.05772	+	0.762322i
$322$		0			0
$323$			7.92259i			0.440824i
$324$	−12.3567	−	5.27695i	−0.686484	−	0.293164i
$325$	−0.491421	+	0.283722i	−0.0272591	+	0.0157381i
$326$	1.73849	+	1.00372i	0.0962862	+	0.0555909i
$327$	−0.652756	−	1.45118i	−0.0360975	−	0.0802502i
$328$	2.70289	+	1.56052i	0.149242	+	0.0861651i
$329$		0			0
$330$	45.2695	+	4.58333i	2.49200	+	0.252304i
$331$	1.24791			0.0685915			0.0342958	−	0.999412i	$-0.489081\pi$
$331$	1.24791			0.0685915			0.0342958	+	0.999412i	$0.489081\pi$
$332$	−6.32285	−	10.9515i	−0.347011	−	0.601041i
$333$	2.81895	−	3.17925i	0.154477	−	0.174222i
$334$	−12.9397	−	7.47072i	−0.708027	−	0.408780i
$335$	−2.34146	−	4.05553i	−0.127928	−	0.221577i
$336$		0			0
$337$	6.58745	−	11.4098i	0.358842	−	0.621532i	−0.628926	−	0.777465i	$-0.716505\pi$
$337$	6.58745	−	11.4098i	0.358842	−	0.621532i	0.987768	+	0.155933i	$0.0498385\pi$
$338$	20.7224	−	11.9641i	1.12715	−	0.650759i
$339$	−6.65898	−	4.79930i	−0.361666	−	0.260662i
$340$	−5.75664	+	9.97079i	−0.312198	+	0.540742i
$341$	−29.3573	+	50.8484i	−1.58979	+	2.75359i
$342$	9.57538	−	10.7992i	0.517777	−	0.583956i
$343$		0			0
$344$	7.80798	−	4.50794i	0.420978	−	0.243052i
$345$	27.7873	+	20.0270i	1.49602	+	1.07822i
$346$			1.87545i			0.100825i
$347$			27.0675i			1.45306i	0.687136	+	0.726529i	$0.258868\pi$
$347$			27.0675i			1.45306i	−0.687136	+	0.726529i	$0.741132\pi$
$348$	7.38058	−	3.31987i	0.395640	−	0.177964i
$349$	−30.3413	+	17.5176i	−1.62413	+	0.937694i	−0.638336	+	0.769758i	$0.720377\pi$
$349$	−30.3413	+	17.5176i	−1.62413	+	0.937694i	−0.985798	+	0.167936i	$0.946290\pi$
$350$		0			0
$351$	−1.56246	−	1.69581i	−0.0833978	−	0.0905158i
$352$	19.6200	−	33.9829i	1.04575	−	1.81129i
$353$	−1.26256	+	2.18682i	−0.0671992	+	0.116392i	−0.897667	−	0.440674i	$-0.854740\pi$
$353$	−1.26256	+	2.18682i	−0.0671992	+	0.116392i	0.830468	+	0.557066i	$0.188073\pi$
$354$	2.38357	−	23.5425i	0.126685	−	1.25127i
$355$	−6.40892	+	3.70019i	−0.340150	+	0.196386i
$356$	−5.65713	+	9.79843i	−0.299827	+	0.519316i
$357$		0			0
$358$	−1.37871	−	2.38799i	−0.0728669	−	0.126209i
$359$	−6.29395	−	3.63381i	−0.332182	−	0.191785i	0.324628	−	0.945842i	$-0.394761\pi$
$359$	−6.29395	−	3.63381i	−0.332182	−	0.191785i	−0.656809	+	0.754057i	$0.728094\pi$
$360$	−6.75831	+	2.25311i	−0.356194	+	0.118749i
$361$	−6.18677	−	10.7158i	−0.325619	−	0.563989i
$362$	28.1163			1.47776
$363$	−14.5425	−	32.3303i	−0.763285	−	1.69690i
$364$		0			0
$365$	18.4874	+	10.6737i	0.967675	+	0.558688i
$366$	27.5549	+	2.78981i	1.44032	+	0.145826i
$367$	−11.6714	−	6.73848i	−0.609242	−	0.351746i	0.163427	−	0.986555i	$-0.447745\pi$
$367$	−11.6714	−	6.73848i	−0.609242	−	0.351746i	−0.772669	+	0.634809i	$0.781079\pi$
$368$	32.5131	−	18.7715i	1.69486	−	0.978530i
$369$	6.55468	−	7.39246i	0.341223	−	0.384836i
$370$			6.63278i			0.344822i
$371$		0			0
$372$	−2.72632	+	26.9278i	−0.141353	+	1.39614i
$373$	−11.8820	−	20.5801i	−0.615224	−	1.06560i	−0.990345	−	0.138624i	$-0.955732\pi$
$373$	−11.8820	−	20.5801i	−0.615224	−	1.06560i	0.375121	−	0.926976i	$-0.377601\pi$
$374$	32.2664			1.66846
$375$	−16.0685	−	1.62686i	−0.829774	−	0.0840108i
$376$			2.03166i			0.104775i
$377$	1.38886			0.0715297
$378$		0			0
$379$	21.2283			1.09042			0.545211	−	0.838299i	$-0.316449\pi$
$379$	21.2283			1.09042			0.545211	+	0.838299i	$0.316449\pi$
$380$			9.62972i			0.493994i
$381$	−12.7045	−	1.28627i	−0.650872	−	0.0658978i
$382$	−24.7143			−1.26450
$383$	−6.47930	−	11.2225i	−0.331077	−	0.573442i	0.651646	−	0.758523i	$-0.274079\pi$
$383$	−6.47930	−	11.2225i	−0.331077	−	0.573442i	−0.982723	+	0.185081i	$0.940745\pi$
$384$	−1.28024	+	12.6449i	−0.0653319	+	0.645282i
$385$		0			0
$386$		−	2.90752i		−	0.147989i
$387$	−9.02653	−	27.0755i	−0.458844	−	1.37633i
$388$	4.81710	−	2.78116i	0.244551	−	0.141192i
$389$	−9.48037	−	5.47350i	−0.480674	−	0.277517i	0.240023	−	0.970767i	$-0.422845\pi$
$389$	−9.48037	−	5.47350i	−0.480674	−	0.277517i	−0.720697	+	0.693250i	$0.756178\pi$
$390$	3.58121	+	0.362581i	0.181341	+	0.0183600i
$391$	21.0353	+	12.1447i	1.06380	+	0.614186i
$392$		0			0
$393$	−5.58685	−	12.4204i	−0.281819	−	0.626528i
$394$	−9.27338			−0.467186
$395$	−0.719472	−	1.24616i	−0.0362006	−	0.0627012i
$396$	−18.7986	−	16.6682i	−0.944665	−	0.837607i
$397$	−25.8856	−	14.9451i	−1.29916	−	0.750071i	−0.318901	−	0.947788i	$-0.603314\pi$
$397$	−25.8856	−	14.9451i	−1.29916	−	0.750071i	−0.980259	+	0.197717i	$0.936647\pi$
$398$	10.4588	+	18.1151i	0.524250	+	0.908028i
$399$		0			0
$400$	3.04141	−	5.26788i	0.152071	−	0.263394i
$401$	−16.6233	+	9.59744i	−0.830126	+	0.479273i	−0.853896	−	0.520444i	$-0.825766\pi$
$401$	−16.6233	+	9.59744i	−0.830126	+	0.479273i	0.0237698	+	0.999717i	$0.492433\pi$
$402$	−0.609395	+	6.01898i	−0.0303938	+	0.300200i
$403$	−2.32242	+	4.02254i	−0.115688	+	0.200377i
$404$	5.62421	−	9.74142i	0.279815	−	0.484654i
$405$	2.69953	+	22.3894i	0.134141	+	1.11254i
$406$		0			0
$407$	6.88060	−	3.97252i	0.341059	−	0.196910i
$408$	−4.60725	+	2.07239i	−0.228093	+	0.102599i
$409$		−	28.8372i		−	1.42591i	−0.701212	−	0.712953i	$-0.747357\pi$
$409$		−	28.8372i		−	1.42591i	0.701212	−	0.712953i	$-0.252643\pi$
$410$			15.4227i			0.761673i
$411$	−16.2572	−	11.7170i	−0.801907	−	0.577955i
$412$	−18.5190	+	10.6919i	−0.912363	+	0.526753i
$413$		0			0
$414$	−13.9948	−	41.9781i	−0.687807	−	2.06311i
$415$	−10.6123	+	18.3811i	−0.520938	+	0.902290i
$416$	1.55211	−	2.68834i	0.0760986	−	0.131807i
$417$	27.5406	+	19.8492i	1.34867	+	0.972020i
$418$	23.3720	−	13.4938i	1.14316	−	0.660005i
$419$	−5.06390	+	8.77094i	−0.247388	+	0.428488i	−0.962800	−	0.270214i	$-0.912906\pi$
$419$	−5.06390	+	8.77094i	−0.247388	+	0.428488i	0.715412	+	0.698702i	$0.246239\pi$
$420$		0			0
$421$	12.7094	+	22.0134i	0.619419	+	1.07287i	0.989592	+	0.143902i	$0.0459651\pi$
$421$	12.7094	+	22.0134i	0.619419	+	1.07287i	−0.370173	+	0.928963i	$0.620702\pi$
$422$	24.8617	+	14.3539i	1.21025	+	0.698738i
$423$	6.30089	+	1.28909i	0.306360	+	0.0626776i
$424$	2.30010	+	3.98390i	0.111703	+	0.193475i
$425$	3.93546			0.190898
$426$	9.51173	+	0.963020i	0.460845	+	0.0466585i
$427$		0			0
$428$	17.4370	+	10.0673i	0.842849	+	0.486619i
$429$	−1.76873	−	3.93217i	−0.0853953	−	0.189847i
$430$	38.5834	+	22.2762i	1.86066	+	1.07425i
$431$	−9.39066	+	5.42170i	−0.452332	+	0.261154i	−0.708815	−	0.705395i	$-0.750770\pi$
$431$	−9.39066	+	5.42170i	−0.452332	+	0.261154i	0.256482	+	0.966549i	$0.417436\pi$
$432$	23.5944	+	7.36858i	1.13519	+	0.354521i
$433$			13.0519i			0.627233i	0.949550	+	0.313616i	$0.101541\pi$
$433$			13.0519i			0.627233i	−0.949550	+	0.313616i	$0.898459\pi$
$434$		0			0
$435$	−11.0194	−	7.94194i	−0.528338	−	0.380787i
$436$	−0.685771	−	1.18779i	−0.0328425	−	0.0568849i
$437$	20.3158			0.971835
$438$	−11.3132	−	25.1509i	−0.540564	−	1.20176i
$439$		−	31.9547i		−	1.52511i	−0.646922	−	0.762557i	$-0.723944\pi$
$439$		−	31.9547i		−	1.52511i	0.646922	−	0.762557i	$-0.276056\pi$
$440$	−13.3208			−0.635046
$441$		0			0
$442$	2.55255			0.121412
$443$			24.7969i			1.17814i	0.808083	+	0.589068i	$0.200505\pi$
$443$			24.7969i			1.17814i	−0.808083	+	0.589068i	$0.799495\pi$
$444$	2.14137	−	2.97113i	0.101625	−	0.141004i
$445$	18.9899			0.900208
$446$	2.98724	+	5.17406i	0.141450	+	0.244999i
$447$	−24.8634	+	11.1838i	−1.17600	+	0.528977i
$448$		0			0
$449$		−	13.7710i		−	0.649892i	−0.945733	−	0.324946i	$-0.894654\pi$
$449$		−	13.7710i		−	0.649892i	0.945733	−	0.324946i	$-0.105346\pi$
$450$	−5.36441	−	4.75647i	−0.252881	−	0.224222i
$451$	15.9989	−	9.23700i	0.753361	−	0.434953i
$452$	−6.12715	−	3.53751i	−0.288197	−	0.166390i
$453$	−2.00792	+	2.78597i	−0.0943403	+	0.130896i
$454$	23.7439	+	13.7085i	1.11436	+	0.643374i
$455$		0			0
$456$	−2.47056	+	3.42789i	−0.115695	+	0.160525i
$457$	27.3107			1.27754			0.638771	−	0.769397i	$-0.279443\pi$
$457$	27.3107			1.27754			0.638771	+	0.769397i	$0.279443\pi$
$458$	3.15670	+	5.46757i	0.147503	+	0.255483i
$459$	3.50392	+	15.6036i	0.163549	+	0.728314i
$460$	25.5680	+	14.7617i	1.19211	+	0.688266i
$461$	5.51822	+	9.55784i	0.257009	+	0.445153i	0.965439	−	0.260628i	$-0.0839296\pi$
$461$	5.51822	+	9.55784i	0.257009	+	0.445153i	−0.708430	+	0.705781i	$0.750596\pi$
$462$		0			0
$463$	−12.2346	+	21.1910i	−0.568591	+	0.984829i	0.428115	+	0.903724i	$0.359178\pi$
$463$	−12.2346	+	21.1910i	−0.568591	+	0.984829i	−0.996706	+	0.0811042i	$0.974155\pi$
$464$	−12.8935	+	7.44405i	−0.598564	+	0.345581i
$465$	41.4286	−	18.6351i	1.92121	−	0.864180i
$466$	4.56029	−	7.89866i	0.211251	−	0.365898i
$467$	7.95241	−	13.7740i	0.367994	−	0.637384i	−0.621258	−	0.783606i	$-0.713378\pi$
$467$	7.95241	−	13.7740i	0.367994	−	0.637384i	0.989252	+	0.146222i	$0.0467114\pi$
$468$	−1.48713	−	1.31860i	−0.0687427	−	0.0609521i
$469$		0			0
$470$	−8.69451	+	5.01978i	−0.401048	+	0.231545i
$471$	−1.46420	+	14.4619i	−0.0674667	+	0.666367i
$472$			6.92754i			0.318866i
$473$		−	53.3667i		−	2.45380i
$474$	−0.187251	+	1.84948i	−0.00860074	+	0.0849494i
$475$	2.85063	−	1.64581i	0.130796	−	0.0755151i
$476$		0			0
$477$	13.8149	−	4.60564i	0.632539	−	0.210878i
$478$	−14.7021	+	25.4648i	−0.672459	+	1.16473i
$479$	6.92685	−	11.9976i	0.316496	−	0.548187i	−0.663259	−	0.748390i	$-0.730827\pi$
$479$	6.92685	−	11.9976i	0.316496	−	0.548187i	0.979754	+	0.200204i	$0.0641604\pi$
$480$	−27.6875	+	12.4542i	−1.26376	+	0.568452i
$481$	0.544315	−	0.314261i	0.0248186	−	0.0143290i
$482$	0.718964	−	1.24528i	0.0327479	−	0.0567210i
$483$		0			0
$484$	−15.2781	−	26.4624i	−0.694458	−	1.20284i
$485$	−8.08506	−	4.66791i	−0.367123	−	0.211959i
$486$	14.0826	−	25.5041i	0.638801	−	1.15689i
$487$	−14.3993	−	24.9404i	−0.652496	−	1.13016i	−0.982515	−	0.186182i	$-0.940389\pi$
$487$	−14.3993	−	24.9404i	−0.652496	−	1.13016i	0.330020	−	0.943974i	$-0.392945\pi$
$488$	−8.10822			−0.367042
$489$	−1.08777	+	1.50927i	−0.0491905	+	0.0682514i
$490$		0			0
$491$	−33.5627	−	19.3774i	−1.51466	−	0.874492i	−0.999852	−	0.0171884i	$-0.994528\pi$
$491$	−33.5627	−	19.3774i	−1.51466	−	0.874492i	−0.514812	−	0.857303i	$-0.672138\pi$
$492$	4.97917	−	6.90855i	0.224478	−	0.311462i
$493$	−8.34181	−	4.81615i	−0.375696	−	0.216908i
$494$	1.84893	−	1.06748i	0.0831872	−	0.0480281i
$495$	−8.45206	+	41.3126i	−0.379892	+	1.85686i
$496$		−	49.7911i		−	2.23569i
$497$		0			0
$498$	25.0062	−	11.2481i	1.12056	−	0.504039i
$499$	1.73333	+	3.00222i	0.0775946	+	0.134398i	0.902212	−	0.431294i	$-0.141943\pi$
$499$	1.73333	+	3.00222i	0.0775946	+	0.134398i	−0.824617	+	0.565691i	$0.808609\pi$
$500$	−13.9209			−0.622561
$501$	8.09628	−	11.2335i	0.361715	−	0.501877i
$502$		−	2.14076i		−	0.0955467i
$503$	28.2202			1.25828			0.629138	−	0.777293i	$-0.283408\pi$
$503$	28.2202			1.25828			0.629138	+	0.777293i	$0.283408\pi$
$504$		0			0
$505$	−18.8794			−0.840124
$506$		−	82.7403i		−	3.67825i
$507$	9.09690	+	20.2238i	0.404008	+	0.898171i
$508$	−11.0065			−0.488335
$509$	−17.9062	−	31.0144i	−0.793678	−	1.37469i	−0.923675	−	0.383176i	$-0.874830\pi$
$509$	−17.9062	−	31.0144i	−0.793678	−	1.37469i	0.129997	−	0.991514i	$-0.458503\pi$
$510$	−20.2523	−	14.5963i	−0.896786	−	0.646336i
$511$		0			0
$512$			24.2599i			1.07215i
$513$	9.06349	+	9.83706i	0.400163	+	0.434317i
$514$	−46.9111	+	27.0841i	−2.06916	+	1.19463i
$515$	31.0823	+	17.9454i	1.36965	+	0.790768i
$516$	−10.0916	−	22.4351i	−0.444256	−	0.987649i
$517$	10.4147	+	6.01291i	0.458036	+	0.264447i
$518$		0			0
$519$	−1.72925	−	0.175079i	−0.0759057	−	0.00768511i
$520$	−1.05379			−0.0462119
$521$	−13.4608	−	23.3148i	−0.589729	−	1.02144i	−0.994268	−	0.106920i	$-0.965901\pi$
$521$	−13.4608	−	23.3148i	−0.589729	−	1.02144i	0.404538	−	0.914521i	$-0.367432\pi$
$522$	5.54981	+	16.6469i	0.242909	+	0.728617i
$523$	−7.82181	−	4.51593i	−0.342024	−	0.197468i	0.319143	−	0.947707i	$-0.396605\pi$
$523$	−7.82181	−	4.51593i	−0.342024	−	0.197468i	−0.661167	+	0.750239i	$0.729938\pi$
$524$	−5.86943	−	10.1662i	−0.256407	−	0.444110i
$525$		0			0
$526$	12.8020	−	22.1737i	0.558193	−	0.966819i
$527$	27.8980	−	16.1069i	1.21526	−	0.701629i
$528$	37.4959	+	27.0242i	1.63180	+	1.17608i
$529$	19.6426	−	34.0220i	0.854026	−	1.47922i
$530$	−11.3661	+	19.6866i	−0.493710	+	0.855131i
$531$	21.4847	+	4.39552i	0.932357	+	0.190749i
$532$		0			0
$533$	1.26565	−	0.730726i	0.0548216	−	0.0316513i
$534$	−19.9022	−	14.3440i	−0.861252	−	0.620726i
$535$		−	33.7939i		−	1.46104i
$536$		−	1.77113i		−	0.0765010i
$537$	2.33054	−	1.04830i	0.100570	−	0.0452376i
$538$	−16.9615	+	9.79273i	−0.731262	+	0.422195i
$539$		0			0
$540$	4.25893	+	18.9658i	0.183275	+	0.816159i
$541$	−5.66792	+	9.81713i	−0.243683	+	0.422071i	−0.961760	−	0.273892i	$-0.911689\pi$
$541$	−5.66792	+	9.81713i	−0.243683	+	0.422071i	0.718078	+	0.695963i	$0.245022\pi$
$542$	6.11710	−	10.5951i	0.262752	−	0.455100i
$543$	−2.62473	+	25.9244i	−0.112638	+	1.11252i
$544$	−18.6447	+	10.7646i	−0.799387	+	0.461526i
$545$	−1.15100	+	1.99360i	−0.0493035	+	0.0853962i
$546$		0			0
$547$	19.4246	+	33.6444i	0.830537	+	1.43853i	0.897613	+	0.440784i	$0.145300\pi$
$547$	19.4246	+	33.6444i	0.830537	+	1.43853i	−0.0670762	+	0.997748i	$0.521367\pi$
$548$	−14.9587	−	8.63644i	−0.639006	−	0.368930i
$549$	−5.14465	+	25.1464i	−0.219568	+	1.07322i
$550$	−6.70292	−	11.6098i	−0.285813	−	0.495043i
$551$	−8.05647			−0.343217
$552$	5.31421	+	11.8143i	0.226188	+	0.502850i
$553$		0			0
$554$	−36.3061	−	20.9613i	−1.54250	−	0.890562i
$555$	−6.11572	−	0.619188i	−0.259598	−	0.0262831i
$556$	25.3410	+	14.6306i	1.07470	+	0.620478i
$557$	−6.29167	+	3.63249i	−0.266586	+	0.153914i	−0.627335	−	0.778749i	$-0.715854\pi$
$557$	−6.29167	+	3.63249i	−0.266586	+	0.153914i	0.360749	+	0.932663i	$0.382521\pi$
$558$	−57.4948	−	11.7628i	−2.43395	−	0.497957i
$559$		−	4.22177i		−	0.178562i
$560$		0			0
$561$	−3.01216	+	29.7510i	−0.127173	+	1.25609i
$562$	20.8848	+	36.1736i	0.880973	+	1.52589i
$563$	−23.0818			−0.972780			−0.486390	−	0.873742i	$-0.661687\pi$
$563$	−23.0818			−0.972780			−0.486390	+	0.873742i	$0.661687\pi$
$564$	5.51529	+	0.558399i	0.232236	+	0.0235128i
$565$			11.8748i			0.499575i
$566$	−35.4561			−1.49033
$567$		0			0
$568$	−2.79889			−0.117439
$569$		−	17.9535i		−	0.752651i	−0.926487	−	0.376326i	$-0.877187\pi$
$569$		−	17.9535i		−	0.752651i	0.926487	−	0.376326i	$-0.122813\pi$
$570$	−20.7738	−	2.10326i	−0.870120	−	0.0880957i
$571$	−14.0847			−0.589425			−0.294713	−	0.955586i	$-0.595224\pi$
$571$	−14.0847			−0.589425			−0.294713	+	0.955586i	$0.595224\pi$
$572$	−1.85819	−	3.21849i	−0.0776950	−	0.134572i
$573$	2.30715	−	22.7877i	0.0963826	−	0.951969i
$574$		0			0
$575$		−	10.0916i		−	0.420851i
$576$	10.4619	+	2.14038i	0.435912	+	0.0891823i
$577$	−26.0392	+	15.0337i	−1.08403	+	0.625862i	−0.931979	−	0.362511i	$-0.881919\pi$
$577$	−26.0392	+	15.0337i	−1.08403	+	0.625862i	−0.152046	+	0.988373i	$0.548586\pi$
$578$	12.1841	+	7.03447i	0.506790	+	0.292595i
$579$	2.68086	+	0.271425i	0.111413	+	0.0112800i
$580$	−10.1393	−	5.85392i	−0.421011	−	0.243071i
$581$		0			0
$582$	4.94756	+	10.9992i	0.205083	+	0.455931i
$583$	27.2295			1.12773
$584$	4.03690	+	6.99211i	0.167048	+	0.289336i
$585$	−0.668631	+	3.26818i	−0.0276445	+	0.135123i
$586$	14.2800	+	8.24455i	0.589900	+	0.340579i
$587$	−18.0979	−	31.3465i	−0.746981	−	1.29381i	−0.949264	−	0.314481i	$-0.898169\pi$
$587$	−18.0979	−	31.3465i	−0.746981	−	1.29381i	0.202283	−	0.979327i	$-0.435164\pi$
$588$		0			0
$589$	13.4719	−	23.3339i	0.555098	−	0.961459i
$590$	−29.6464	+	17.1164i	−1.22052	+	0.704670i
$591$	0.865695	−	8.55046i	0.0356099	−	0.351719i
$592$	−3.36877	+	5.83489i	−0.138456	+	0.239812i
$593$	−1.02158	+	1.76943i	−0.0419514	+	0.0726620i	−0.886239	−	0.463229i	$-0.846691\pi$
$593$	−1.02158	+	1.76943i	−0.0419514	+	0.0726620i	0.844287	+	0.535891i	$0.180024\pi$
$594$	40.0635	−	36.9130i	1.64382	−	1.51456i
$595$		0			0
$596$	−20.3507	+	11.7495i	−0.833598	+	0.481278i
$597$	−17.6793	+	7.95234i	−0.723564	+	0.325468i
$598$		−	6.54547i		−	0.267664i
$599$			18.2296i			0.744840i	0.928064	+	0.372420i	$0.121472\pi$
$599$			18.2296i			0.744840i	−0.928064	+	0.372420i	$0.878528\pi$
$600$	1.70277	+	1.22723i	0.0695151	+	0.0501013i
$601$	32.1713	−	18.5741i	1.31230	−	0.757654i	0.329820	−	0.944044i	$-0.393012\pi$
$601$	32.1713	−	18.5741i	1.31230	−	0.757654i	0.982476	+	0.186390i	$0.0596787\pi$
$602$		0			0
$603$	−5.49287	−	1.12378i	−0.223687	−	0.0457637i
$604$	−1.48002	+	2.56346i	−0.0602210	+	0.104306i
$605$	−25.6428	+	44.4146i	−1.04253	+	1.80571i
$606$	19.7864	+	14.2606i	0.803768	+	0.579295i
$607$	17.1730	−	9.91482i	0.697030	−	0.402430i	−0.109211	−	0.994019i	$-0.534832\pi$
$607$	17.1730	−	9.91482i	0.697030	−	0.402430i	0.806240	+	0.591588i	$0.201499\pi$
$608$	−9.00349	+	15.5945i	−0.365140	+	0.632440i
$609$		0			0
$610$	−20.0336	−	34.6991i	−0.811135	−	1.40493i
$611$	0.823890	+	0.475673i	0.0333310	+	0.0192437i
$612$	4.35957	+	13.0768i	0.176225	+	0.528596i
$613$	6.34412	+	10.9883i	0.256237	+	0.443815i	0.965231	−	0.261400i	$-0.0841840\pi$
$613$	6.34412	+	10.9883i	0.256237	+	0.443815i	−0.708994	+	0.705214i	$0.750851\pi$
$614$	53.7381			2.16869
$615$	−14.2204	−	1.43975i	−0.573422	−	0.0580564i
$616$		0			0
$617$	4.37247	+	2.52445i	0.176029	+	0.101630i	0.585426	−	0.810726i	$-0.300927\pi$
$617$	4.37247	+	2.52445i	0.176029	+	0.101630i	−0.409397	+	0.912357i	$0.634261\pi$
$618$	−19.0205	−	42.2855i	−0.765116	−	1.70097i
$619$	0.231999	+	0.133945i	0.00932485	+	0.00538370i	0.504655	−	0.863321i	$-0.331620\pi$
$619$	0.231999	+	0.133945i	0.00932485	+	0.00538370i	−0.495330	+	0.868705i	$0.664953\pi$
$620$	33.9094	−	19.5776i	1.36183	−	0.786255i
$621$	40.0121	−	8.98505i	1.60563	−	0.360558i
$622$			24.8305i			0.995611i
$623$		0			0
$624$	2.96625	+	2.13785i	0.118745	+	0.0855824i
$625$	14.8792	+	25.7716i	0.595169	+	1.03086i
$626$	−58.9641			−2.35668
$627$	10.2601	+	22.8097i	0.409747	+	0.910931i
$628$			12.5290i			0.499961i
$629$	−4.35905			−0.173807
$630$		0			0
$631$	37.7899			1.50439			0.752197	−	0.658938i	$-0.228994\pi$
$631$	37.7899			1.50439			0.752197	+	0.658938i	$0.228994\pi$
$632$		−	0.544222i		−	0.0216480i
$633$	−15.5559	+	21.5836i	−0.618290	+	0.857872i
$634$	−37.5112			−1.48976
$635$	9.23671	+	15.9984i	0.366547	+	0.634879i
$636$	11.4471	−	5.14905i	0.453908	−	0.204173i
$637$		0			0
$638$			32.8117i			1.29903i
$639$	−1.77589	+	8.68033i	−0.0702532	+	0.343389i
$640$	15.9234	−	9.19336i	0.629426	−	0.363400i
$641$	−29.7991	−	17.2045i	−1.17699	−	0.679537i	−0.221676	−	0.975120i	$-0.571153\pi$
$641$	−29.7991	−	17.2045i	−1.17699	−	0.679537i	−0.955317	+	0.295583i	$0.904486\pi$
$642$	−25.5262	+	35.4173i	−1.00744	+	1.39781i
$643$	−0.676278	−	0.390449i	−0.0266698	−	0.0153978i	0.486606	−	0.873622i	$-0.338235\pi$
$643$	−0.676278	−	0.390449i	−0.0266698	−	0.0153978i	−0.513276	+	0.858224i	$0.671568\pi$
$644$		0			0
$645$	−24.1415	+	33.4961i	−0.950569	+	1.31891i
$646$	−14.8068			−0.582566
$647$	−9.82182	−	17.0119i	−0.386136	−	0.668807i	0.605790	−	0.795624i	$-0.292857\pi$
$647$	−9.82182	−	17.0119i	−0.386136	−	0.668807i	−0.991926	+	0.126818i	$0.959524\pi$
$648$	−3.34975	+	7.84391i	−0.131591	+	0.308138i
$649$	35.5118	+	20.5027i	1.39396	+	0.804803i
$650$	−0.530259	−	0.918435i	−0.0207985	−	0.0360240i
$651$		0			0
$652$	−0.801781	+	1.38872i	−0.0314001	+	0.0543867i
$653$	−2.77600	+	1.60272i	−0.108633	+	0.0627194i	−0.553332	−	0.832961i	$-0.686644\pi$
$653$	−2.77600	+	1.60272i	−0.108633	+	0.0627194i	0.444699	+	0.895680i	$0.353311\pi$
$654$	2.71216	−	1.21996i	0.106054	−	0.0477042i
$655$	−9.85129	+	17.0629i	−0.384922	+	0.666704i
$656$	−7.83315	+	13.5674i	−0.305833	+	0.529719i
$657$	24.2464	−	8.08333i	0.945940	−	0.315361i
$658$		0			0
$659$	−24.2959	+	14.0273i	−0.946435	+	0.546425i	−0.891972	−	0.452091i	$-0.850678\pi$
$659$	−24.2959	+	14.0273i	−0.946435	+	0.546425i	−0.0544636	+	0.998516i	$0.517345\pi$
$660$	−3.66121	+	36.1617i	−0.142512	+	1.40759i
$661$			32.3882i			1.25976i	0.776694	+	0.629878i	$0.216895\pi$
$661$			32.3882i			1.25976i	−0.776694	+	0.629878i	$0.783105\pi$
$662$			2.33227i			0.0906463i
$663$	−0.238287	+	2.35356i	−0.00925432	+	0.0914048i
$664$	−6.95189	+	4.01367i	−0.269785	+	0.155761i
$665$		0			0
$666$	5.94181	+	5.26843i	0.230240	+	0.204148i
$667$	−12.3500	+	21.3908i	−0.478193	+	0.828255i
$668$	5.96768	−	10.3363i	0.230897	−	0.399925i
$669$	−5.04957	+	2.27136i	−0.195228	+	0.0878157i
$670$	7.57953	−	4.37605i	0.292823	−	0.169061i
$671$	−23.9971	+	41.5641i	−0.926397	+	1.60457i
$672$		0			0
$673$	−10.3088	−	17.8554i	−0.397375	−	0.688273i	0.596026	−	0.802965i	$-0.296745\pi$
$673$	−10.3088	−	17.8554i	−0.397375	−	0.688273i	−0.993401	+	0.114692i	$0.963412\pi$
$674$	21.3242	+	12.3115i	0.821378	+	0.474223i
$675$	4.88645	−	4.50219i	0.188080	−	0.173289i
$676$	9.55701	+	16.5532i	0.367577	+	0.636663i
$677$	−50.3311			−1.93438			−0.967190	−	0.254053i	$-0.918236\pi$
$677$	−50.3311			−1.93438			−0.967190	+	0.254053i	$0.918236\pi$
$678$	8.96958	−	12.4452i	0.344475	−	0.477956i
$679$		0			0
$680$	6.32935	+	3.65425i	0.242719	+	0.140134i
$681$	−14.8564	+	20.6132i	−0.569300	+	0.789899i
$682$	−95.0324	−	54.8670i	−3.63898	−	2.10097i
$683$	11.9031	−	6.87227i	0.455460	−	0.262960i	−0.254673	−	0.967027i	$-0.581968\pi$
$683$	11.9031	−	6.87227i	0.455460	−	0.262960i	0.710133	+	0.704067i	$0.248635\pi$
$684$	8.62654	+	7.64891i	0.329844	+	0.292463i
$685$			28.9909i			1.10769i
$686$		0			0
$687$	−5.33602	+	2.40020i	−0.203582	+	0.0915735i
$688$	22.6280	+	39.1929i	0.862685	+	1.49421i
$689$	2.15409			0.0820643
$690$	−37.4291	+	51.9326i	−1.42490	+	1.97704i
$691$		−	29.3673i		−	1.11719i	−0.829442	−	0.558593i	$-0.811342\pi$
$691$		−	29.3673i		−	1.11719i	0.829442	−	0.558593i	$-0.188658\pi$
$692$	−1.49813			−0.0569504
$693$		0			0
$694$	−50.5874			−1.92027
$695$		−	49.1123i		−	1.86294i
$696$	−2.10742	−	4.68511i	−0.0798814	−	0.177589i
$697$	−10.1358			−0.383920
$698$	−32.7392	−	56.7060i	−1.23920	−	2.14635i
$699$	6.85719	+	4.94215i	0.259363	+	0.186929i
$700$		0			0
$701$		−	44.2011i		−	1.66945i	−0.550666	−	0.834726i	$-0.685626\pi$
$701$		−	44.2011i		−	1.66945i	0.550666	−	0.834726i	$-0.314374\pi$
$702$	3.16937	−	2.92013i	0.119620	−	0.110213i
$703$	−3.15746	+	1.82296i	−0.119086	+	0.0687542i
$704$	17.2923	+	9.98371i	0.651728	+	0.376275i
$705$	−3.81680	−	8.48532i	−0.143749	−	0.319576i
$706$	−4.08702	−	2.35964i	−0.153817	−	0.0888063i
$707$		0			0
$708$	18.8060	+	1.90402i	0.706772	+	0.0715575i
$709$	−11.3326			−0.425604			−0.212802	−	0.977095i	$-0.568259\pi$
$709$	−11.3326			−0.425604			−0.212802	+	0.977095i	$0.568259\pi$
$710$	−6.91542	−	11.9779i	−0.259531	−	0.449521i
$711$	−1.68782	−	0.345308i	−0.0632982	−	0.0129501i
$712$	6.21994	+	3.59108i	0.233102	+	0.134581i
$713$	−41.3028	−	71.5385i	−1.54680	−	2.67914i
$714$		0			0
$715$	−3.11881	+	5.40193i	−0.116637	+	0.202021i
$716$	1.90755	−	1.10132i	0.0712884	−	0.0411584i
$717$	−22.1072	−	15.9332i	−0.825608	−	0.595036i
$718$	6.79136	−	11.7630i	0.253451	−	0.438991i
$719$	−18.0647	+	31.2890i	−0.673700	+	1.16688i	0.303147	+	0.952944i	$0.401963\pi$
$719$	−18.0647	+	31.2890i	−0.673700	+	1.16688i	−0.976847	+	0.213939i	$0.931371\pi$
$720$	−11.3097	−	33.9240i	−0.421487	−	1.26427i
$721$		0			0
$722$	20.0271	−	11.5627i	0.745333	−	0.430318i
$723$	1.08109	+	0.779166i	0.0402061	+	0.0289775i
$724$			22.4596i			0.834703i
$725$			4.00197i			0.148629i
$726$	60.4232	−	27.1791i	2.24252	−	1.00871i
$727$	6.20547	−	3.58273i	0.230148	−	0.132876i	−0.380492	−	0.924784i	$-0.624245\pi$
$727$	6.20547	−	3.58273i	0.230148	−	0.132876i	0.610640	+	0.791908i	$0.290912\pi$
$728$		0			0
$729$	22.2013	+	15.3657i	0.822269	+	0.569099i
$730$	−19.9485	+	34.5518i	−0.738327	+	1.27882i
$731$	−14.6399	+	25.3570i	−0.541475	+	0.937862i
$732$	−2.22853	+	22.0111i	−0.0823687	+	0.813555i
$733$	41.4391	−	23.9249i	1.53059	−	0.883685i	0.531253	−	0.847213i	$-0.321721\pi$
$733$	41.4391	−	23.9249i	1.53059	−	0.883685i	0.999335	−	0.0364726i	$-0.0116122\pi$
$734$	12.5938	−	21.8131i	0.464846	−	0.805136i
$735$		0			0
$736$	27.6034	+	47.8105i	1.01747	+	1.76232i
$737$	−9.07910	−	5.24182i	−0.334433	−	0.193085i
$738$	13.8160	+	12.2503i	0.508575	+	0.450939i
$739$	−7.67416	−	13.2920i	−0.282299	−	0.488956i	0.689652	−	0.724141i	$-0.257764\pi$
$739$	−7.67416	−	13.2920i	−0.282299	−	0.488956i	−0.971951	+	0.235185i	$0.924430\pi$
$740$	−5.29833			−0.194771
$741$	0.811659	+	1.80444i	0.0298170	+	0.0662879i
$742$		0			0
$743$	34.9422	+	20.1739i	1.28191	+	0.740109i	0.977197	−	0.212337i	$-0.0681073\pi$
$743$	34.9422	+	20.1739i	1.28191	+	0.740109i	0.304709	+	0.952445i	$0.401441\pi$
$744$	17.0935	+	1.73063i	0.626677	+	0.0634481i
$745$	34.1568	+	19.7204i	1.25141	+	0.722501i
$746$	38.4630	−	22.2066i	1.40823	−	0.813042i
$747$	8.03683	+	24.1069i	0.294052	+	0.882024i
$748$			25.7747i			0.942417i
$749$		0			0
$750$	3.04050	−	30.0310i	0.111023	−	1.09658i
$751$	−16.9449	−	29.3494i	−0.618327	−	1.07097i	−0.989791	−	0.142527i	$-0.954477\pi$
$751$	−16.9449	−	29.3494i	−0.618327	−	1.07097i	0.371463	−	0.928448i	$-0.378856\pi$
$752$	−10.1981			−0.371887
$753$	1.97387	+	0.199846i	0.0719319	+	0.00728277i
$754$			2.59568i			0.0945293i
$755$	4.96814			0.180809
$756$		0			0
$757$	−5.73237			−0.208346			−0.104173	−	0.994559i	$-0.533220\pi$
$757$	−5.73237			−0.208346			−0.104173	+	0.994559i	$0.533220\pi$
$758$			39.6743i			1.44103i
$759$	76.2901	+	7.72403i	2.76916	+	0.280364i
$760$	6.11284			0.221736
$761$	−13.2666	−	22.9784i	−0.480914	−	0.832968i	0.518846	−	0.854868i	$-0.326362\pi$
$761$	−13.2666	−	22.9784i	−0.480914	−	0.832968i	−0.999760	+	0.0218999i	$0.993028\pi$
$762$	2.40397	−	23.7439i	0.0870865	−	0.860152i
$763$		0			0
$764$		−	19.7420i		−	0.714242i
$765$	15.3490	−	17.3109i	0.554946	−	0.625876i
$766$	20.9741	−	12.1094i	0.757825	−	0.437531i
$767$	2.80929	+	1.62194i	0.101438	+	0.0585650i
$768$	−35.9004	−	3.63475i	−1.29544	−	0.131158i
$769$	−23.3944	−	13.5068i	−0.843623	−	0.487066i	0.0148711	−	0.999889i	$-0.495266\pi$
$769$	−23.3944	−	13.5068i	−0.843623	−	0.487066i	−0.858494	+	0.512823i	$0.828600\pi$
$770$		0			0
$771$	−20.5935	−	45.7824i	−0.741655	−	1.64881i
$772$	2.32256			0.0835906
$773$	−11.3009	−	19.5737i	−0.406464	−	0.704016i	0.588027	−	0.808841i	$-0.299905\pi$
$773$	−11.3009	−	19.5737i	−0.406464	−	0.704016i	−0.994491	+	0.104826i	$0.966572\pi$
$774$	50.6024	−	16.8700i	1.81887	−	0.606380i
$775$	−11.5909	−	6.69201i	−0.416357	−	0.240384i
$776$	−1.76545	−	3.05784i	−0.0633758	−	0.109770i
$777$		0			0
$778$	10.2296	−	17.7182i	0.366750	−	0.635229i
$779$	−7.34180	+	4.23879i	−0.263047	+	0.151870i
$780$	−0.289633	+	2.86070i	−0.0103705	+	0.102430i
$781$	−8.28359	+	14.3476i	−0.296410	+	0.513398i
$782$	−22.6978	+	39.3137i	−0.811670	+	1.40585i
$783$	−15.8673	+	3.56313i	−0.567051	+	0.127336i
$784$		0			0
$785$	18.2114	−	10.5144i	0.649993	−	0.375274i
$786$	23.2130	−	10.4415i	0.827980	−	0.372435i
$787$			26.1960i			0.933787i	0.884314	+	0.466893i	$0.154627\pi$
$787$			26.1960i			0.933787i	−0.884314	+	0.466893i	$0.845373\pi$
$788$		−	7.40767i		−	0.263887i
$789$	19.2500	+	13.8740i	0.685318	+	0.493926i
$790$	2.32900	−	1.34465i	0.0828620	−	0.0478404i
$791$		0			0
$792$	−10.5808	+	11.9331i	−0.375971	+	0.424026i
$793$	−1.89838	+	3.28808i	−0.0674133	+	0.116763i
$794$	27.9314	−	48.3785i	0.991247	−	1.71689i
$795$	−17.0908	−	12.3178i	−0.606150	−	0.436867i
$796$	−14.4705	+	8.35456i	−0.512894	+	0.296120i
$797$	5.96560	−	10.3327i	0.211312	−	0.366004i	−0.740813	−	0.671711i	$-0.765560\pi$
$797$	5.96560	−	10.3327i	0.211312	−	0.366004i	0.952126	+	0.305707i	$0.0988929\pi$
$798$		0			0
$799$	−3.29899	−	5.71402i	−0.116710	−	0.202147i
$800$	7.74640	+	4.47239i	0.273877	+	0.158123i
$801$	15.0837	−	17.0116i	0.532957	−	0.601077i
$802$	−17.9370	−	31.0678i	−0.633378	−	1.09704i
$803$	47.7904			1.68648
$804$	−4.80802	−	0.486790i	−0.169566	−	0.0171678i
$805$		0			0
$806$	−7.51788	−	4.34045i	−0.264806	−	0.152886i
$807$	−7.44592	−	16.5534i	−0.262109	−	0.582708i
$808$	−6.18375	−	3.57019i	−0.217543	−	0.125599i
$809$	22.9399	−	13.2443i	0.806522	−	0.465646i	−0.0392244	−	0.999230i	$-0.512489\pi$
$809$	22.9399	−	13.2443i	0.806522	−	0.465646i	0.845747	+	0.533585i	$0.179155\pi$
$810$	−41.8445	+	5.04525i	−1.47026	+	0.177272i
$811$		−	13.7419i		−	0.482544i	−0.970458	−	0.241272i	$-0.922435\pi$
$811$		−	13.7419i		−	0.482544i	0.970458	−	0.241272i	$-0.0775646\pi$
$812$		0			0
$813$	9.19812	+	6.62932i	0.322592	+	0.232500i
$814$	7.42439	+	12.8594i	0.260225	+	0.450722i
$815$	2.69143			0.0942766
$816$	−10.4026	−	23.1265i	−0.364163	−	0.809590i
$817$			24.4896i			0.856783i
$818$	53.8949			1.88439
$819$		0			0
$820$	−12.3198			−0.430226
$821$		−	13.5669i		−	0.473489i	−0.971572	−	0.236744i	$-0.923920\pi$
$821$		−	13.5669i		−	0.473489i	0.971572	−	0.236744i	$-0.0760804\pi$
$822$	21.8982	−	30.3836i	0.763789	−	1.05975i
$823$	14.6971			0.512310			0.256155	−	0.966636i	$-0.417544\pi$
$823$	14.6971			0.512310			0.256155	+	0.966636i	$0.417544\pi$
$824$	6.78711	+	11.7556i	0.236440	+	0.409527i
$825$	11.3305	−	5.09658i	0.394476	−	0.177440i
$826$		0			0
$827$		−	40.8787i		−	1.42149i	−0.703449	−	0.710746i	$-0.748358\pi$
$827$		−	40.8787i		−	1.42149i	0.703449	−	0.710746i	$-0.251642\pi$
$828$	33.5325	−	11.1792i	1.16534	−	0.388504i
$829$	17.7189	−	10.2300i	0.615402	−	0.355302i	−0.159675	−	0.987170i	$-0.551045\pi$
$829$	17.7189	−	10.2300i	0.615402	−	0.355302i	0.775077	+	0.631867i	$0.217711\pi$
$830$	−34.3530	−	19.8337i	−1.19241	−	0.688439i
$831$	22.7165	−	31.5190i	0.788028	−	1.09338i
$832$	1.36797	+	0.789798i	0.0474258	+	0.0273813i
$833$		0			0
$834$	−37.0969	+	51.4717i	−1.28456	+	1.78232i
$835$	−20.0324			−0.693249
$836$	10.7790	+	18.6698i	0.372800	+	0.645708i
$837$	16.2131	−	51.9146i	0.560406	−	1.79443i
$838$	−16.3923	−	9.46412i	−0.566264	−	0.326932i
$839$	27.3475	+	47.3673i	0.944141	+	1.63530i	0.757462	+	0.652880i	$0.226439\pi$
$839$	27.3475	+	47.3673i	0.944141	+	1.63530i	0.186680	+	0.982421i	$0.440227\pi$
$840$		0			0
$841$	−9.60247	+	16.6320i	−0.331120	+	0.573516i
$842$	−41.1416	+	23.7531i	−1.41783	+	0.818586i
$843$	−35.3033	+	15.8798i	−1.21591	+	0.546930i
$844$	−11.4661	+	19.8598i	−0.394678	+	0.683602i
$845$	16.0405	−	27.7830i	0.551812	−	0.955766i
$846$	−2.40922	+	11.7760i	−0.0828308	+	0.404866i
$847$		0			0
$848$	−19.9975	+	11.5456i	−0.686718	+	0.396477i
$849$	3.30992	−	32.6921i	0.113596	−	1.12199i
$850$			7.35513i			0.252279i
$851$			11.1779i			0.383172i
$852$	−0.769269	+	7.59806i	−0.0263547	+	0.260305i
$853$	11.0684	−	6.39037i	0.378976	−	0.218802i	−0.298396	−	0.954442i	$-0.596452\pi$
$853$	11.0684	−	6.39037i	0.378976	−	0.218802i	0.677373	+	0.735640i	$0.263118\pi$
$854$		0			0
$855$	3.87859	−	18.9580i	0.132645	−	0.648351i
$856$	6.39058	−	11.0688i	0.218426	−	0.378324i
$857$	9.16200	−	15.8691i	0.312968	−	0.542077i	−0.666035	−	0.745920i	$-0.732010\pi$
$857$	9.16200	−	15.8691i	0.312968	−	0.542077i	0.979003	+	0.203844i	$0.0653434\pi$
$858$	7.34897	−	3.30565i	0.250890	−	0.112853i
$859$	−33.4579	+	19.3169i	−1.14157	+	0.659085i	−0.946819	−	0.321768i	$-0.895723\pi$
$859$	−33.4579	+	19.3169i	−1.14157	+	0.659085i	−0.194750	+	0.980853i	$0.562390\pi$
$860$	−17.7944	+	30.8208i	−0.606784	+	1.05098i
$861$		0			0
$862$	−10.1328	−	17.5505i	−0.345125	−	0.597774i
$863$	−14.4626	−	8.35001i	−0.492314	−	0.284238i	0.233220	−	0.972424i	$-0.425074\pi$
$863$	−14.4626	−	8.35001i	−0.492314	−	0.284238i	−0.725534	+	0.688186i	$0.758407\pi$
$864$	−10.8355	+	34.6955i	−0.368631	+	1.18036i
$865$	1.25724	+	2.17760i	0.0427473	+	0.0740405i
$866$	−24.3931			−0.828912
$867$	−7.62350	+	10.5775i	−0.258908	+	0.359232i
$868$		0			0
$869$	−2.78978	−	1.61068i	−0.0946367	−	0.0546385i
$870$	14.8430	−	20.5945i	0.503224	−	0.698219i
$871$	−0.718235	−	0.414673i	−0.0243365	−	0.0140507i
$872$	−0.753996	+	0.435320i	−0.0255335	+	0.0147418i
$873$	−10.6036	+	3.53506i	−0.358878	+	0.119644i
$874$			37.9689i			1.28432i
$875$		0			0
$876$	20.0908	−	9.03707i	0.678805	−	0.305334i
$877$	−16.7617	−	29.0321i	−0.566002	−	0.980345i	−0.996956	−	0.0779707i	$-0.975156\pi$
$877$	−16.7617	−	29.0321i	−0.566002	−	0.980345i	0.430953	−	0.902374i	$-0.358177\pi$
$878$	59.7213			2.01549
$879$	−8.93491	+	12.3971i	−0.301367	+	0.418144i
$880$		−	66.8652i		−	2.25403i
$881$	−28.6657			−0.965771			−0.482885	−	0.875684i	$-0.660411\pi$
$881$	−28.6657			−0.965771			−0.482885	+	0.875684i	$0.660411\pi$
$882$		0			0
$883$	−38.2091			−1.28584			−0.642919	−	0.765935i	$-0.722277\pi$
$883$	−38.2091			−1.28584			−0.642919	+	0.765935i	$0.722277\pi$
$884$			2.03900i			0.0685790i
$885$	−13.0145	−	28.9332i	−0.437476	−	0.972577i
$886$	−46.3439			−1.55695
$887$	17.5914	+	30.4692i	0.590662	+	1.02306i	0.994143	+	0.108069i	$0.0344666\pi$
$887$	17.5914	+	30.4692i	0.590662	+	1.02306i	−0.403481	+	0.914988i	$0.632200\pi$
$888$	−1.88604	−	1.35932i	−0.0632915	−	0.0456157i
$889$		0			0
$890$			35.4910i			1.18966i
$891$	30.2953	+	40.3862i	1.01493	+	1.35299i
$892$	−4.13309	+	2.38624i	−0.138386	+	0.0798972i
$893$	−4.77921	−	2.75928i	−0.159930	−	0.0923358i
$894$	−20.9019	−	46.4681i	−0.699063	−	1.55413i
$895$	−3.20164	−	1.84847i	−0.107019	−	0.0617875i
$896$		0			0
$897$	6.03521	+	0.611037i	0.201510	+	0.0204019i
$898$	25.7371			0.858857
$899$	16.3791	+	28.3695i	0.546274	+	0.946174i
$900$	3.79951	−	4.28514i	0.126650	−	0.142838i
$901$	−12.9380	−	7.46975i	−0.431027	−	0.248854i
$902$	17.2634	+	29.9010i	0.574807	+	0.995595i
$903$		0			0
$904$	−2.24557	+	3.88944i	−0.0746866	+	0.129361i
$905$	32.6459	−	18.8481i	1.08519	−	0.626533i
$906$	−5.20680	−	3.75267i	−0.172984	−	0.124674i
$907$	21.2977	−	36.8887i	0.707179	−	1.22487i	−0.258720	−	0.965952i	$-0.583301\pi$
$907$	21.2977	−	36.8887i	0.707179	−	1.22487i	0.965899	−	0.258918i	$-0.0833660\pi$
$908$	−10.9505	+	18.9669i	−0.363406	+	0.629437i
$909$	−14.9960	+	16.9127i	−0.497385	+	0.560958i
$910$		0			0
$911$	−43.5221	+	25.1275i	−1.44195	+	0.832510i	−0.997980	−	0.0635313i	$-0.979764\pi$
$911$	−43.5221	+	25.1275i	−1.44195	+	0.832510i	−0.443970	+	0.896042i	$0.646430\pi$
$912$	−17.2066	−	12.4012i	−0.569767	−	0.410645i
$913$			47.5154i			1.57253i
$914$			51.0420i			1.68832i
$915$	33.8643	−	15.2326i	1.11952	−	0.503573i
$916$	−4.36754	+	2.52160i	−0.144308	+	0.0833161i
$917$		0			0
$918$	−29.1622	+	6.54860i	−0.962495	+	0.216136i
$919$	29.3486	−	50.8333i	0.968121	−	1.67684i	0.267137	−	0.963658i	$-0.413922\pi$
$919$	29.3486	−	50.8333i	0.968121	−	1.67684i	0.700984	−	0.713177i	$-0.252744\pi$
$920$	9.37054	−	16.2303i	0.308938	−	0.535096i
$921$	−5.01660	+	49.5489i	−0.165302	+	1.63269i
$922$	−17.8630	+	10.3132i	−0.588287	+	0.339647i
$923$	−0.655304	+	1.13502i	−0.0215696	+	0.0373596i
$924$		0			0
$925$	0.905536	+	1.56843i	0.0297738	+	0.0515698i
$926$	−39.6046	−	22.8657i	−1.30149	−	0.751415i
$927$	40.7647	−	13.5903i	1.33889	−	0.446363i
$928$	−10.9465	−	18.9598i	−0.359335	−	0.622387i
$929$	14.3823			0.471868			0.235934	−	0.971769i	$-0.424185\pi$
$929$	14.3823			0.471868			0.235934	+	0.971769i	$0.424185\pi$
$930$	34.8278	+	77.4275i	1.14205	+	2.53895i
$931$		0			0
$932$	6.30952	+	3.64281i	0.206675	+	0.119324i
$933$	−22.8948	−	2.31799i	−0.749542	−	0.0758877i
$934$	25.7427	+	14.8626i	0.842327	+	0.486318i
$935$	37.4646	−	21.6302i	1.22522	−	0.707384i
$936$	−0.837030	+	0.944015i	−0.0273592	+	0.0308561i
$937$			44.2981i			1.44716i	0.690243	+	0.723578i	$0.257504\pi$
$937$			44.2981i			1.44716i	−0.690243	+	0.723578i	$0.742496\pi$
$938$		0			0
$939$	5.50446	−	54.3675i	0.179631	−	1.77422i
$940$	−4.00985	−	6.94526i	−0.130787	−	0.226529i
$941$	14.8880			0.485335			0.242667	−	0.970110i	$-0.421978\pi$
$941$	14.8880			0.485335			0.242667	+	0.970110i	$0.421978\pi$
$942$	−27.0283	−	2.73649i	−0.880630	−	0.0891598i
$943$			25.9910i			0.846384i
$944$	−34.7734			−1.13178
$945$		0			0
$946$	99.7390			3.24280
$947$			41.9552i			1.36336i	0.731650	+	0.681681i	$0.238751\pi$
$947$			41.9552i			1.36336i	−0.731650	+	0.681681i	$0.761249\pi$
$948$	−1.47738	−	0.149578i	−0.0479832	−	0.00485808i
$949$	3.78063			0.122724
$950$	3.07592	+	5.32765i	0.0997960	+	0.172852i
$951$	3.50177	−	34.5869i	0.113553	−	1.12156i
$952$		0			0
$953$			13.9821i			0.452926i	0.974020	+	0.226463i	$0.0727162\pi$
$953$			13.9821i			0.452926i	−0.974020	+	0.226463i	$0.927284\pi$
$954$	8.60765	+	25.8191i	0.278683	+	0.835924i
$955$	−28.6959	+	16.5676i	−0.928578	+	0.536115i
$956$	−20.3415	−	11.7442i	−0.657892	−	0.379834i
$957$	−30.2538	−	3.06306i	−0.977966	−	0.0990146i
$958$	22.4228	+	12.9458i	0.724449	+	0.418261i
$959$		0			0
$960$	−6.33733	−	14.0889i	−0.204537	−	0.454716i
$961$	−78.5553			−2.53404
$962$	0.587333	+	1.01729i	0.0189364	+	0.0327988i
$963$	−30.2734	−	26.8425i	−0.975546	−	0.864989i
$964$	0.994743	+	0.574315i	0.0320385	+	0.0184974i
$965$	−1.94910	−	3.37593i	−0.0627436	−	0.108675i
$966$		0			0
$967$	−11.5757	+	20.0497i	−0.372249	+	0.644754i	−0.989911	−	0.141690i	$-0.954746\pi$
$967$	−11.5757	+	20.0497i	−0.372249	+	0.644754i	0.617662	+	0.786443i	$0.288080\pi$
$968$	−16.7980	+	9.69835i	−0.539909	+	0.311717i
$969$	1.38226	−	13.6525i	0.0444045	−	0.438582i
$970$	8.72403	−	15.1105i	0.280112	−	0.485168i
$971$	21.6869	−	37.5628i	0.695965	−	1.20545i	−0.273890	−	0.961761i	$-0.588310\pi$
$971$	21.6869	−	37.5628i	0.695965	−	1.20545i	0.969854	−	0.243685i	$-0.0783564\pi$
$972$	20.3729	+	11.2493i	0.653462	+	0.360823i
$973$		0			0
$974$	46.6120	−	26.9114i	1.49354	−	0.862298i
$975$	0.896338	−	0.403183i	0.0287058	−	0.0129122i
$976$		−	40.7000i		−	1.30277i
$977$			12.0331i			0.384974i	0.981300	+	0.192487i	$0.0616553\pi$
$977$			12.0331i			0.384974i	−0.981300	+	0.192487i	$0.938345\pi$
$978$	−2.82072	−	2.03297i	−0.0901968	−	0.0650071i
$979$	36.8170	−	21.2563i	1.17668	−	0.679355i
$980$		0			0
$981$	0.871668	+	2.61461i	0.0278302	+	0.0834782i
$982$	36.2152	−	62.7266i	1.15567	−	2.00169i
$983$	3.14829	−	5.45300i	0.100415	−	0.173924i	−0.811441	−	0.584435i	$-0.801316\pi$
$983$	3.14829	−	5.45300i	0.100415	−	0.173924i	0.911856	+	0.410511i	$0.134650\pi$
$984$	−4.38547	−	3.16072i	−0.139804	−	0.100760i
$985$	−10.7674	+	6.21654i	−0.343077	+	0.198075i
$986$	9.00108	−	15.5903i	0.286653	−	0.496497i
$987$		0			0
$988$	0.852712	+	1.47694i	0.0271284	+	0.0469877i
$989$	65.0225	+	37.5408i	2.06760	+	1.19373i
$990$	−77.2106	−	15.7964i	−2.45391	−	0.502041i
$991$	−16.7814	−	29.0662i	−0.533078	−	0.923317i	−0.999254	−	0.0386256i	$-0.987702\pi$
$991$	−16.7814	−	29.0662i	−0.533078	−	0.923317i	0.466176	−	0.884692i	$-0.345631\pi$
$992$	73.2178			2.32467
$993$	−2.15046	−	0.217724i	−0.0682427	−	0.00690926i
$994$		0			0
$995$	24.2874	+	14.0223i	0.769963	+	0.444538i
$996$	8.98508	+	19.9752i	0.284703	+	0.632939i
$997$	9.74838	+	5.62823i	0.308734	+	0.178248i	0.646360	−	0.763033i	$-0.276290\pi$
$997$	9.74838	+	5.62823i	0.308734	+	0.178248i	−0.337626	+	0.941280i	$0.609624\pi$
$998$	−5.61096	+	3.23949i	−0.177612	+	0.102544i
$999$	−5.41241	+	4.98679i	−0.171241	+	0.157775i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.i.d.68.19		48
3.2	odd	2		1323.2.i.d.1097.22		48
7.2	even	3		441.2.o.e.293.20	yes	48
7.3	odd	6		441.2.s.d.374.5		48
7.4	even	3		441.2.s.d.374.6		48
7.5	odd	6		441.2.o.e.293.19	yes	48
7.6	odd	2	inner	441.2.i.d.68.20		48
9.2	odd	6		441.2.s.d.362.5		48
9.7	even	3		1323.2.s.d.656.19		48
21.2	odd	6		1323.2.o.e.881.5		48
21.5	even	6		1323.2.o.e.881.6		48
21.11	odd	6		1323.2.s.d.962.20		48
21.17	even	6		1323.2.s.d.962.19		48
21.20	even	2		1323.2.i.d.1097.7		48
63.2	odd	6		441.2.o.e.146.19	✓	48
63.11	odd	6	inner	441.2.i.d.227.6		48
63.16	even	3		1323.2.o.e.440.6		48
63.20	even	6		441.2.s.d.362.6		48
63.25	even	3		1323.2.i.d.521.7		48
63.34	odd	6		1323.2.s.d.656.20		48
63.38	even	6	inner	441.2.i.d.227.5		48
63.47	even	6		441.2.o.e.146.20	yes	48
63.52	odd	6		1323.2.i.d.521.22		48
63.61	odd	6		1323.2.o.e.440.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.19		48	1.1	even	1	trivial
441.2.i.d.68.20		48	7.6	odd	2	inner
441.2.i.d.227.5		48	63.38	even	6	inner
441.2.i.d.227.6		48	63.11	odd	6	inner
441.2.o.e.146.19	✓	48	63.2	odd	6
441.2.o.e.146.20	yes	48	63.47	even	6
441.2.o.e.293.19	yes	48	7.5	odd	6
441.2.o.e.293.20	yes	48	7.2	even	3
441.2.s.d.362.5		48	9.2	odd	6
441.2.s.d.362.6		48	63.20	even	6
441.2.s.d.374.5		48	7.3	odd	6
441.2.s.d.374.6		48	7.4	even	3
1323.2.i.d.521.7		48	63.25	even	3
1323.2.i.d.521.22		48	63.52	odd	6
1323.2.i.d.1097.7		48	21.20	even	2
1323.2.i.d.1097.22		48	3.2	odd	2
1323.2.o.e.440.5		48	63.61	odd	6
1323.2.o.e.440.6		48	63.16	even	3
1323.2.o.e.881.5		48	21.2	odd	6
1323.2.o.e.881.6		48	21.5	even	6
1323.2.s.d.656.19		48	9.7	even	3
1323.2.s.d.656.20		48	63.34	odd	6
1323.2.s.d.962.19		48	21.17	even	6
1323.2.s.d.962.20		48	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.86894i q^{2} +(-1.72324 - 0.174470i) q^{3} -1.49292 q^{4} +(1.25287 + 2.17003i) q^{5} +(0.326074 - 3.22063i) q^{6} +0.947692i q^{8} +(2.93912 + 0.601309i) q^{9} +O(q^{10})\)	\(q+1.86894i q^{2} +(-1.72324 - 0.174470i) q^{3} -1.49292 q^{4} +(1.25287 + 2.17003i) q^{5} +(0.326074 - 3.22063i) q^{6} +0.947692i q^{8} +(2.93912 + 0.601309i) q^{9} +(-4.05565 + 2.34153i) q^{10} +(4.85803 + 2.80479i) q^{11} +(2.57267 + 0.260471i) q^{12} +(0.384312 + 0.221883i) q^{13} +(-1.78039 - 3.95807i) q^{15} -4.75703 q^{16} +(-1.53885 - 2.66536i) q^{17} +(-1.12381 + 5.49303i) q^{18} +(-2.22932 - 1.28710i) q^{19} +(-1.87044 - 3.23969i) q^{20} +(-5.24197 + 9.07935i) q^{22} +(-6.83476 + 3.94605i) q^{23} +(0.165344 - 1.63310i) q^{24} +(-0.639351 + 1.10739i) q^{25} +(-0.414685 + 0.718255i) q^{26} +(-4.95990 - 1.54899i) q^{27} +(2.71041 - 1.56485i) q^{29} +(7.39739 - 3.32743i) q^{30} +10.4669i q^{31} -6.99520i q^{32} +(-7.88221 - 5.68091i) q^{33} +(4.98140 - 2.87601i) q^{34} +(-4.38788 - 0.897709i) q^{36} +(0.708168 - 1.22658i) q^{37} +(2.40550 - 4.16645i) q^{38} +(-0.623551 - 0.449409i) q^{39} +(-2.05652 + 1.18733i) q^{40} +(1.64665 - 2.85208i) q^{41} +(-4.75676 - 8.23894i) q^{43} +(-7.25268 - 4.18733i) q^{44} +(2.37747 + 7.13134i) q^{45} +(-7.37492 - 12.7737i) q^{46} +2.14380 q^{47} +(8.19750 + 0.829960i) q^{48} +(-2.06964 - 1.19491i) q^{50} +(2.18678 + 4.86155i) q^{51} +(-0.573749 - 0.331254i) q^{52} +(4.20379 - 2.42706i) q^{53} +(2.89496 - 9.26974i) q^{54} +14.0561i q^{55} +(3.61709 + 2.60693i) q^{57} +(2.92461 + 5.06558i) q^{58} +7.30991 q^{59} +(2.65798 + 5.90910i) q^{60} +8.55576i q^{61} -19.5619 q^{62} +3.55953 q^{64} +1.11196i q^{65} +(10.6173 - 14.7314i) q^{66} -1.86888 q^{67} +(2.29739 + 3.97919i) q^{68} +(12.4664 - 5.60753i) q^{69} +2.95338i q^{71} +(-0.569856 + 2.78538i) q^{72} +(7.37804 - 4.25971i) q^{73} +(2.29241 + 1.32352i) q^{74} +(1.29496 - 1.79675i) q^{75} +(3.32820 + 1.92154i) q^{76} +(0.839916 - 1.16538i) q^{78} -0.574261 q^{79} +(-5.95992 - 10.3229i) q^{80} +(8.27686 + 3.53464i) q^{81} +(5.33036 + 3.07748i) q^{82} +(4.23521 + 7.33560i) q^{83} +(3.85595 - 6.67870i) q^{85} +(15.3981 - 8.89008i) q^{86} +(-4.94370 + 2.22373i) q^{87} +(-2.65807 + 4.60392i) q^{88} +(3.78929 - 6.56325i) q^{89} +(-13.3280 + 4.44334i) q^{90} +(10.2038 - 5.89115i) q^{92} +(1.82616 - 18.0369i) q^{93} +4.00663i q^{94} -6.45024i q^{95} +(-1.22045 + 12.0544i) q^{96} +(-3.22662 + 1.86289i) q^{97} +(12.5918 + 11.1648i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} - 8 q^{9}+O(q^{10}) \) 48 * q - 48 * q^4 - 8 * q^9	\( 48 q - 48 q^{4} - 8 q^{9} + 24 q^{11} - 40 q^{15} + 48 q^{16} - 16 q^{18} + 48 q^{23} - 24 q^{25} - 24 q^{30} - 8 q^{36} - 56 q^{39} - 96 q^{44} + 48 q^{50} - 24 q^{51} - 48 q^{53} + 80 q^{57} + 168 q^{60} - 48 q^{64} - 88 q^{72} + 168 q^{74} - 88 q^{78} + 48 q^{79} - 24 q^{81} - 24 q^{85} - 24 q^{86} - 144 q^{92} + 16 q^{93} - 72 q^{99}+O(q^{100}) \) 48 * q - 48 * q^4 - 8 * q^9 + 24 * q^11 - 40 * q^15 + 48 * q^16 - 16 * q^18 + 48 * q^23 - 24 * q^25 - 24 * q^30 - 8 * q^36 - 56 * q^39 - 96 * q^44 + 48 * q^50 - 24 * q^51 - 48 * q^53 + 80 * q^57 + 168 * q^60 - 48 * q^64 - 88 * q^72 + 168 * q^74 - 88 * q^78 + 48 * q^79 - 24 * q^81 - 24 * q^85 - 24 * q^86 - 144 * q^92 + 16 * q^93 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more