LMFDB - Embedded newform 648.2.n.n.541.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [648,2,Mod(109,648)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(648, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("648.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.n (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:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.49787136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			541.1
Root			$-1.09445 + 0.895644i$ of defining polynomial
Character	$\chi$	$=$	648.541
Dual form			648.2.n.n.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09445 + 0.895644i) q^{2} +(0.395644 - 1.96048i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(1.32288 + 2.50000i) q^{8} +O(q^{10})$	\(q+(-1.09445 + 0.895644i) q^{2} +(0.395644 - 1.96048i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(1.32288 + 2.50000i) q^{8} +(0.500000 - 1.32288i) q^{10} +(2.59808 + 1.50000i) q^{11} +(4.58258 - 2.64575i) q^{13} +(-0.228425 - 1.39564i) q^{14} +(-3.68693 - 1.55130i) q^{16} -5.29150 q^{17} -5.29150i q^{19} +(0.637600 + 1.89564i) q^{20} +(-4.18693 + 0.685275i) q^{22} +(2.64575 + 4.58258i) q^{23} +(-2.00000 + 3.46410i) q^{25} +(-2.64575 + 7.00000i) q^{26} +(1.50000 + 1.32288i) q^{28} +(5.19615 + 3.00000i) q^{29} +(3.50000 + 6.06218i) q^{31} +(5.42458 - 1.60436i) q^{32} +(5.79129 - 4.73930i) q^{34} -1.00000i q^{35} +5.29150i q^{37} +(4.73930 + 5.79129i) q^{38} +(-2.39564 - 1.50363i) q^{40} +(-2.64575 - 4.58258i) q^{41} +(9.16515 + 5.29150i) q^{43} +(3.96863 - 4.50000i) q^{44} +(-7.00000 - 2.64575i) q^{46} +(3.00000 + 5.19615i) q^{49} +(-0.913701 - 5.58258i) q^{50} +(-3.37386 - 10.0308i) q^{52} +9.00000i q^{53} -3.00000 q^{55} +(-2.82650 - 0.104356i) q^{56} +(-8.37386 + 1.37055i) q^{58} +(3.46410 - 2.00000i) q^{59} +(-9.26013 - 3.50000i) q^{62} +(-4.50000 + 6.61438i) q^{64} +(-2.64575 + 4.58258i) q^{65} +(-2.09355 + 10.3739i) q^{68} +(0.895644 + 1.09445i) q^{70} +15.8745 q^{71} +3.00000 q^{73} +(-4.73930 - 5.79129i) q^{74} +(-10.3739 - 2.09355i) q^{76} +(-2.59808 + 1.50000i) q^{77} +(-2.00000 + 3.46410i) q^{79} +(3.96863 - 0.500000i) q^{80} +(7.00000 + 2.64575i) q^{82} +(-6.06218 - 3.50000i) q^{83} +(4.58258 - 2.64575i) q^{85} +(-14.7701 + 2.41742i) q^{86} +(-0.313068 + 8.47950i) q^{88} -10.5830 q^{89} +5.29150i q^{91} +(10.0308 - 3.37386i) q^{92} +(2.64575 + 4.58258i) q^{95} +(-3.50000 + 6.06218i) q^{97} +(-7.93725 - 3.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{4} - 4 q^{7}+O(q^{10}) $ 8 * q - 6 * q^4 - 4 * q^7	$ 8 q - 6 q^{4} - 4 q^{7} + 4 q^{10} - 2 q^{16} - 6 q^{22} - 16 q^{25} + 12 q^{28} + 28 q^{31} + 28 q^{34} - 10 q^{40} - 56 q^{46} + 24 q^{49} + 28 q^{52} - 24 q^{55} - 12 q^{58} - 36 q^{64} - 2 q^{70} + 24 q^{73} - 28 q^{76} - 16 q^{79} + 56 q^{82} - 30 q^{88} - 28 q^{97}+O(q^{100}) $ 8 * q - 6 * q^4 - 4 * q^7 + 4 * q^10 - 2 * q^16 - 6 * q^22 - 16 * q^25 + 12 * q^28 + 28 * q^31 + 28 * q^34 - 10 * q^40 - 56 * q^46 + 24 * q^49 + 28 * q^52 - 24 * q^55 - 12 * q^58 - 36 * q^64 - 2 * q^70 + 24 * q^73 - 28 * q^76 - 16 * q^79 + 56 * q^82 - 30 * q^88 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.09445	+	0.895644i	−0.773893	+	0.633316i
$2$	−1.09445	+	0.895644i	−0.773893	+	0.633316i
$3$		0			0
$3$		0			0
$4$	0.395644	−	1.96048i	0.197822	−	0.980238i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i	−0.680989	−	0.732294i	$-0.738450\pi$
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i	0.293691	+	0.955901i	$0.405116\pi$
$6$		0			0
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i	0.755929	+	0.654654i	$0.227186\pi$
$8$	1.32288	+	2.50000i	0.467707	+	0.883883i
$9$		0			0
$10$	0.500000	−	1.32288i	0.158114	−	0.418330i
$11$	2.59808	+	1.50000i	0.783349	+	0.452267i	0.837616	−	0.546259i	$-0.183949\pi$
$11$	2.59808	+	1.50000i	0.783349	+	0.452267i	−0.0542666	+	0.998526i	$0.517282\pi$
$12$		0			0
$13$	4.58258	−	2.64575i	1.27098	−	0.733799i	0.295806	−	0.955248i	$-0.404412\pi$
$13$	4.58258	−	2.64575i	1.27098	−	0.733799i	0.975172	+	0.221449i	$0.0710785\pi$
$14$	−0.228425	−	1.39564i	−0.0610492	−	0.373002i
$15$		0			0
$16$	−3.68693	−	1.55130i	−0.921733	−	0.387825i
$17$	−5.29150			−1.28338			−0.641689	−	0.766965i	$-0.721766\pi$
$17$	−5.29150			−1.28338			−0.641689	+	0.766965i	$0.721766\pi$
$18$		0			0
$19$		−	5.29150i		−	1.21395i	−0.794719	−	0.606977i	$-0.792382\pi$
$19$		−	5.29150i		−	1.21395i	0.794719	−	0.606977i	$-0.207618\pi$
$20$	0.637600	+	1.89564i	0.142572	+	0.423879i
$21$		0			0
$22$	−4.18693	+	0.685275i	−0.892657	+	0.146101i
$23$	2.64575	+	4.58258i	0.551677	+	0.955533i	0.998154	+	0.0607377i	$0.0193453\pi$
$23$	2.64575	+	4.58258i	0.551677	+	0.955533i	−0.446476	+	0.894795i	$0.647321\pi$
$24$		0			0
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$	−2.64575	+	7.00000i	−0.518875	+	1.37281i
$27$		0			0
$28$	1.50000	+	1.32288i	0.283473	+	0.250000i
$29$	5.19615	+	3.00000i	0.964901	+	0.557086i	0.897678	−	0.440652i	$-0.145253\pi$
$29$	5.19615	+	3.00000i	0.964901	+	0.557086i	0.0672232	+	0.997738i	$0.478586\pi$
$30$		0			0
$31$	3.50000	+	6.06218i	0.628619	+	1.08880i	0.987829	+	0.155543i	$0.0497126\pi$
$31$	3.50000	+	6.06218i	0.628619	+	1.08880i	−0.359211	+	0.933257i	$0.616954\pi$
$32$	5.42458	−	1.60436i	0.958939	−	0.283613i
$33$		0			0
$34$	5.79129	−	4.73930i	0.993198	−	0.812784i
$35$		−	1.00000i		−	0.169031i
$36$		0			0
$37$			5.29150i			0.869918i	0.900450	+	0.434959i	$0.143237\pi$
$37$			5.29150i			0.869918i	−0.900450	+	0.434959i	$0.856763\pi$
$38$	4.73930	+	5.79129i	0.768816	+	0.939471i
$39$		0			0
$40$	−2.39564	−	1.50363i	−0.378785	−	0.237744i
$41$	−2.64575	−	4.58258i	−0.413197	−	0.715678i	0.582040	−	0.813160i	$-0.302255\pi$
$41$	−2.64575	−	4.58258i	−0.413197	−	0.715678i	−0.995237	+	0.0974818i	$0.968921\pi$
$42$		0			0
$43$	9.16515	+	5.29150i	1.39767	+	0.806947i	0.994148	−	0.108022i	$-0.0344518\pi$
$43$	9.16515	+	5.29150i	1.39767	+	0.806947i	0.403524	+	0.914969i	$0.367785\pi$
$44$	3.96863	−	4.50000i	0.598293	−	0.678401i
$45$		0			0
$46$	−7.00000	−	2.64575i	−1.03209	−	0.390095i
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$	−0.913701	−	5.58258i	−0.129217	−	0.789495i
$51$		0			0
$52$	−3.37386	−	10.0308i	−0.467871	−	1.39102i
$53$			9.00000i			1.23625i	0.786082	+	0.618123i	$0.212106\pi$
$53$			9.00000i			1.23625i	−0.786082	+	0.618123i	$0.787894\pi$
$54$		0			0
$55$	−3.00000			−0.404520
$56$	−2.82650	−	0.104356i	−0.377707	−	0.0139452i
$57$		0			0
$58$	−8.37386	+	1.37055i	−1.09954	+	0.179962i
$59$	3.46410	−	2.00000i	0.450988	−	0.260378i	−0.257260	−	0.966342i	$-0.582820\pi$
$59$	3.46410	−	2.00000i	0.450988	−	0.260378i	0.708247	+	0.705965i	$0.249486\pi$
$60$		0			0
$61$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$61$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$62$	−9.26013	−	3.50000i	−1.17604	−	0.444500i
$63$		0			0
$64$	−4.50000	+	6.61438i	−0.562500	+	0.826797i
$65$	−2.64575	+	4.58258i	−0.328165	+	0.568399i
$66$		0			0
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$	−2.09355	+	10.3739i	−0.253880	+	1.25802i
$69$		0			0
$70$	0.895644	+	1.09445i	0.107050	+	0.130812i
$71$	15.8745			1.88396			0.941979	−	0.335673i	$-0.108964\pi$
$71$	15.8745			1.88396			0.941979	+	0.335673i	$0.108964\pi$
$72$		0			0
$73$	3.00000			0.351123			0.175562	−	0.984468i	$-0.443826\pi$
$73$	3.00000			0.351123			0.175562	+	0.984468i	$0.443826\pi$
$74$	−4.73930	−	5.79129i	−0.550933	−	0.673224i
$75$		0			0
$76$	−10.3739	−	2.09355i	−1.18996	−	0.240147i
$77$	−2.59808	+	1.50000i	−0.296078	+	0.170941i
$78$		0			0
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	−0.956325	−	0.292306i	$-0.905577\pi$
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	0.731307	+	0.682048i	$0.238911\pi$
$80$	3.96863	−	0.500000i	0.443706	−	0.0559017i
$81$		0			0
$82$	7.00000	+	2.64575i	0.773021	+	0.292174i
$83$	−6.06218	−	3.50000i	−0.665410	−	0.384175i	0.128925	−	0.991654i	$-0.458847\pi$
$83$	−6.06218	−	3.50000i	−0.665410	−	0.384175i	−0.794335	+	0.607479i	$0.792181\pi$
$84$		0			0
$85$	4.58258	−	2.64575i	0.497050	−	0.286972i
$86$	−14.7701	+	2.41742i	−1.59270	+	0.260678i
$87$		0			0
$88$	−0.313068	+	8.47950i	−0.0333732	+	0.903918i
$89$	−10.5830			−1.12180			−0.560898	−	0.827885i	$-0.689544\pi$
$89$	−10.5830			−1.12180			−0.560898	+	0.827885i	$0.689544\pi$
$90$		0			0
$91$			5.29150i			0.554700i
$92$	10.0308	−	3.37386i	1.04578	−	0.351750i
$93$		0			0
$94$		0			0
$95$	2.64575	+	4.58258i	0.271448	+	0.470162i
$96$		0			0
$97$	−3.50000	+	6.06218i	−0.355371	+	0.615521i	−0.987181	−	0.159602i	$-0.948979\pi$
$97$	−3.50000	+	6.06218i	−0.355371	+	0.615521i	0.631810	+	0.775123i	$0.282312\pi$
$98$	−7.93725	−	3.00000i	−0.801784	−	0.303046i
$99$		0			0
$100$	6.00000	+	5.29150i	0.600000	+	0.529150i
$101$	−14.7224	−	8.50000i	−1.46494	−	0.845782i	−0.465704	−	0.884941i	$-0.654199\pi$
$101$	−14.7224	−	8.50000i	−1.46494	−	0.845782i	−0.999233	+	0.0391591i	$0.987532\pi$
$102$		0			0
$103$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$103$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$104$	12.6766	+	7.95644i	1.24304	+	0.780193i
$105$		0			0
$106$	−8.06080	−	9.85005i	−0.782934	−	0.956722i
$107$		−	3.00000i		−	0.290021i	−0.989430	−	0.145010i	$-0.953678\pi$
$107$		−	3.00000i		−	0.290021i	0.989430	−	0.145010i	$-0.0463216\pi$
$108$		0			0
$109$		−	5.29150i		−	0.506834i	−0.967357	−	0.253417i	$-0.918446\pi$
$109$		−	5.29150i		−	0.506834i	0.967357	−	0.253417i	$-0.0815545\pi$
$110$	3.28335	−	2.68693i	0.313055	−	0.256189i
$111$		0			0
$112$	3.18693	−	2.41733i	0.301137	−	0.228416i
$113$	−7.93725	−	13.7477i	−0.746674	−	1.29328i	−0.949409	−	0.314044i	$-0.898316\pi$
$113$	−7.93725	−	13.7477i	−0.746674	−	1.29328i	0.202735	−	0.979234i	$-0.435017\pi$
$114$		0			0
$115$	−4.58258	−	2.64575i	−0.427327	−	0.246718i
$116$	7.93725	−	9.00000i	0.736956	−	0.835629i
$117$		0			0
$118$	−2.00000	+	5.29150i	−0.184115	+	0.487122i
$119$	2.64575	−	4.58258i	0.242536	−	0.420084i
$120$		0			0
$121$	−1.00000	−	1.73205i	−0.0909091	−	0.157459i
$122$		0			0
$123$		0			0
$124$	13.2695	−	4.46320i	1.19164	−	0.400807i
$125$		−	9.00000i		−	0.804984i
$126$		0			0
$127$	13.0000			1.15356			0.576782	−	0.816898i	$-0.304308\pi$
$127$	13.0000			1.15356			0.576782	+	0.816898i	$0.304308\pi$
$128$	−0.999100	−	11.2695i	−0.0883088	−	0.996093i
$129$		0			0
$130$	−1.20871	−	7.38505i	−0.106011	−	0.647712i
$131$	6.06218	−	3.50000i	0.529655	−	0.305796i	−0.211221	−	0.977438i	$-0.567744\pi$
$131$	6.06218	−	3.50000i	0.529655	−	0.305796i	0.740876	+	0.671642i	$0.234411\pi$
$132$		0			0
$133$	4.58258	+	2.64575i	0.397360	+	0.229416i
$134$		0			0
$135$		0			0
$136$	−7.00000	−	13.2288i	−0.600245	−	1.13436i
$137$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$137$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$138$		0			0
$139$	9.16515	−	5.29150i	0.777378	−	0.448819i	−0.0581222	−	0.998309i	$-0.518511\pi$
$139$	9.16515	−	5.29150i	0.777378	−	0.448819i	0.835500	+	0.549490i	$0.185178\pi$
$140$	−1.96048	−	0.395644i	−0.165690	−	0.0334380i
$141$		0			0
$142$	−17.3739	+	14.2179i	−1.45798	+	1.19314i
$143$	15.8745			1.32749
$144$		0			0
$145$	−6.00000			−0.498273
$146$	−3.28335	+	2.68693i	−0.271732	+	0.222372i
$147$		0			0
$148$	10.3739	+	2.09355i	0.852726	+	0.172089i
$149$	2.59808	−	1.50000i	0.212843	−	0.122885i	−0.389789	−	0.920904i	$-0.627452\pi$
$149$	2.59808	−	1.50000i	0.212843	−	0.122885i	0.602632	+	0.798019i	$0.294119\pi$
$150$		0			0
$151$	−1.50000	+	2.59808i	−0.122068	+	0.211428i	−0.920583	−	0.390547i	$-0.872286\pi$
$151$	−1.50000	+	2.59808i	−0.122068	+	0.211428i	0.798515	+	0.601975i	$0.205619\pi$
$152$	13.2288	−	7.00000i	1.07299	−	0.567775i
$153$		0			0
$154$	1.50000	−	3.96863i	0.120873	−	0.319801i
$155$	−6.06218	−	3.50000i	−0.486926	−	0.281127i
$156$		0			0
$157$	−9.16515	+	5.29150i	−0.731459	+	0.422308i	−0.818956	−	0.573857i	$-0.805447\pi$
$157$	−9.16515	+	5.29150i	−0.731459	+	0.422308i	0.0874969	+	0.996165i	$0.472113\pi$
$158$	−0.913701	−	5.58258i	−0.0726901	−	0.444126i
$159$		0			0
$160$	−3.89564	+	4.10170i	−0.307978	+	0.324268i
$161$	−5.29150			−0.417029
$162$		0			0
$163$			5.29150i			0.414462i	0.978292	+	0.207231i	$0.0664452\pi$
$163$			5.29150i			0.414462i	−0.978292	+	0.207231i	$0.933555\pi$
$164$	−10.0308	+	3.37386i	−0.783274	+	0.263454i
$165$		0			0
$166$	9.76951	−	1.59898i	0.758261	−	0.124105i
$167$	5.29150	+	9.16515i	0.409469	+	0.709221i	0.994830	−	0.101552i	$-0.0323807\pi$
$167$	5.29150	+	9.16515i	0.409469	+	0.709221i	−0.585361	+	0.810772i	$0.699047\pi$
$168$		0			0
$169$	7.50000	−	12.9904i	0.576923	−	0.999260i
$170$	−2.64575	+	7.00000i	−0.202920	+	0.536875i
$171$		0			0
$172$	14.0000	−	15.8745i	1.06749	−	1.21042i
$173$	12.9904	+	7.50000i	0.987640	+	0.570214i	0.904568	−	0.426329i	$-0.140193\pi$
$173$	12.9904	+	7.50000i	0.987640	+	0.570214i	0.0830722	+	0.996544i	$0.473527\pi$
$174$		0			0
$175$	−2.00000	−	3.46410i	−0.151186	−	0.261861i
$176$	−7.25198	−	9.56080i	−0.546638	−	0.720672i
$177$		0			0
$178$	11.5826	−	9.47860i	0.868151	−	0.710451i
$179$		−	23.0000i		−	1.71910i	−0.511051	−	0.859550i	$-0.670744\pi$
$179$		−	23.0000i		−	1.71910i	0.511051	−	0.859550i	$-0.329256\pi$
$180$		0			0
$181$		−	21.1660i		−	1.57326i	−0.617426	−	0.786629i	$-0.711825\pi$
$181$		−	21.1660i		−	1.57326i	0.617426	−	0.786629i	$-0.288175\pi$
$182$	−4.73930	−	5.79129i	−0.351300	−	0.429279i
$183$		0			0
$184$	−7.95644	+	12.6766i	−0.586556	+	0.934528i
$185$	−2.64575	−	4.58258i	−0.194520	−	0.336918i
$186$		0			0
$187$	−13.7477	−	7.93725i	−1.00533	−	0.580429i
$188$		0			0
$189$		0			0
$190$	−7.00000	−	2.64575i	−0.507833	−	0.191943i
$191$	2.64575	−	4.58258i	0.191440	−	0.331584i	−0.754288	−	0.656544i	$-0.772018\pi$
$191$	2.64575	−	4.58258i	0.191440	−	0.331584i	0.945728	+	0.324960i	$0.105351\pi$
$192$		0			0
$193$	1.50000	+	2.59808i	0.107972	+	0.187014i	0.914949	−	0.403570i	$-0.132231\pi$
$193$	1.50000	+	2.59808i	0.107972	+	0.187014i	−0.806976	+	0.590584i	$0.798898\pi$
$194$	−1.59898	−	9.76951i	−0.114800	−	0.701410i
$195$		0			0
$196$	11.3739	−	3.82560i	0.812419	−	0.273257i
$197$			13.0000i			0.926212i	0.886303	+	0.463106i	$0.153265\pi$
$197$			13.0000i			0.926212i	−0.886303	+	0.463106i	$0.846735\pi$
$198$		0			0
$199$	−17.0000			−1.20510			−0.602549	−	0.798082i	$-0.705848\pi$
$199$	−17.0000			−1.20510			−0.602549	+	0.798082i	$0.705848\pi$
$200$	−11.3060	−	0.417424i	−0.799455	−	0.0295164i
$201$		0			0
$202$	23.7259	−	3.88323i	1.66935	−	0.273223i
$203$	−5.19615	+	3.00000i	−0.364698	+	0.210559i
$204$		0			0
$205$	4.58258	+	2.64575i	0.320061	+	0.184787i
$206$		0			0
$207$		0			0
$208$	−21.0000	+	2.64575i	−1.45609	+	0.183450i
$209$	7.93725	−	13.7477i	0.549031	−	0.950950i
$210$		0			0
$211$	4.58258	−	2.64575i	0.315478	−	0.182141i	−0.333897	−	0.942609i	$-0.608364\pi$
$211$	4.58258	−	2.64575i	0.315478	−	0.182141i	0.649375	+	0.760468i	$0.275031\pi$
$212$	17.6443	+	3.56080i	1.21181	+	0.244556i
$213$		0			0
$214$	2.68693	+	3.28335i	0.183675	+	0.224445i
$215$	−10.5830			−0.721755
$216$		0			0
$217$	−7.00000			−0.475191
$218$	4.73930	+	5.79129i	0.320986	+	0.392236i
$219$		0			0
$220$	−1.18693	+	5.88143i	−0.0800229	+	0.396526i
$221$	−24.2487	+	14.0000i	−1.63114	+	0.941742i
$222$		0			0
$223$	8.00000	−	13.8564i	0.535720	−	0.927894i	−0.463409	−	0.886145i	$-0.653374\pi$
$223$	8.00000	−	13.8564i	0.535720	−	0.927894i	0.999128	−	0.0417488i	$-0.0132929\pi$
$224$	−1.32288	+	5.50000i	−0.0883883	+	0.367484i
$225$		0			0
$226$	21.0000	+	7.93725i	1.39690	+	0.527978i
$227$	3.46410	+	2.00000i	0.229920	+	0.132745i	0.610535	−	0.791989i	$-0.290954\pi$
$227$	3.46410	+	2.00000i	0.229920	+	0.132745i	−0.380615	+	0.924734i	$0.624288\pi$
$228$		0			0
$229$	−18.3303	+	10.5830i	−1.21130	+	0.699345i	−0.963043	−	0.269349i	$-0.913191\pi$
$229$	−18.3303	+	10.5830i	−1.21130	+	0.699345i	−0.248258	+	0.968694i	$0.579858\pi$
$230$	7.38505	−	1.20871i	0.486956	−	0.0797001i
$231$		0			0
$232$	−0.626136	+	16.9590i	−0.0411079	+	1.11341i
$233$	−10.5830			−0.693316			−0.346658	−	0.937992i	$-0.612684\pi$
$233$	−10.5830			−0.693316			−0.346658	+	0.937992i	$0.612684\pi$
$234$		0			0
$235$		0			0
$236$	−2.55040	−	7.58258i	−0.166017	−	0.493584i
$237$		0			0
$238$	1.20871	+	7.38505i	0.0783492	+	0.478702i
$239$	7.93725	+	13.7477i	0.513418	+	0.889267i	0.999879	+	0.0155640i	$0.00495438\pi$
$239$	7.93725	+	13.7477i	0.513418	+	0.889267i	−0.486461	+	0.873703i	$0.661712\pi$
$240$		0			0
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	−0.658838	−	0.752285i	$-0.728952\pi$
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	0.980917	+	0.194429i	$0.0622852\pi$
$242$	2.64575	+	1.00000i	0.170075	+	0.0642824i
$243$		0			0
$244$		0			0
$245$	−5.19615	−	3.00000i	−0.331970	−	0.191663i
$246$		0			0
$247$	−14.0000	−	24.2487i	−0.890799	−	1.54291i
$248$	−10.5254	+	16.7695i	−0.668362	+	1.06486i
$249$		0			0
$250$	8.06080	+	9.85005i	0.509809	+	0.622972i
$251$			12.0000i			0.757433i	0.925513	+	0.378717i	$0.123635\pi$
$251$			12.0000i			0.757433i	−0.925513	+	0.378717i	$0.876365\pi$
$252$		0			0
$253$			15.8745i			0.998022i
$254$	−14.2279	+	11.6434i	−0.892735	+	0.730570i
$255$		0			0
$256$	11.1869	+	11.4391i	0.699183	+	0.714943i
$257$	7.93725	+	13.7477i	0.495112	+	0.857560i	0.999984	−	0.00563467i	$-0.00179358\pi$
$257$	7.93725	+	13.7477i	0.495112	+	0.857560i	−0.504872	+	0.863194i	$0.668460\pi$
$258$		0			0
$259$	−4.58258	−	2.64575i	−0.284747	−	0.164399i
$260$	7.93725	+	7.00000i	0.492248	+	0.434122i
$261$		0			0
$262$	−3.50000	+	9.26013i	−0.216231	+	0.572093i
$263$	−2.64575	+	4.58258i	−0.163144	+	0.282574i	−0.935995	−	0.352014i	$-0.885497\pi$
$263$	−2.64575	+	4.58258i	−0.163144	+	0.282574i	0.772851	+	0.634588i	$0.218830\pi$
$264$		0			0
$265$	−4.50000	−	7.79423i	−0.276433	−	0.478796i
$266$	−7.38505	+	1.20871i	−0.452807	+	0.0741109i
$267$		0			0
$268$		0			0
$269$		−	18.0000i		−	1.09748i	−0.835993	−	0.548740i	$-0.815108\pi$
$269$		−	18.0000i		−	1.09748i	0.835993	−	0.548740i	$-0.184892\pi$
$270$		0			0
$271$	15.0000			0.911185			0.455593	−	0.890188i	$-0.349427\pi$
$271$	15.0000			0.911185			0.455593	+	0.890188i	$0.349427\pi$
$272$	19.5094	+	8.20871i	1.18293	+	0.497726i
$273$		0			0
$274$		0			0
$275$	−10.3923	+	6.00000i	−0.626680	+	0.361814i
$276$		0			0
$277$	−9.16515	−	5.29150i	−0.550681	−	0.317936i	0.198716	−	0.980057i	$-0.436323\pi$
$277$	−9.16515	−	5.29150i	−0.550681	−	0.317936i	−0.749396	+	0.662122i	$0.769656\pi$
$278$	−5.29150	+	14.0000i	−0.317363	+	0.839664i
$279$		0			0
$280$	2.50000	−	1.32288i	0.149404	−	0.0790569i
$281$	−7.93725	+	13.7477i	−0.473497	+	0.820121i	−0.999540	−	0.0303374i	$-0.990342\pi$
$281$	−7.93725	+	13.7477i	−0.473497	+	0.820121i	0.526043	+	0.850458i	$0.323675\pi$
$282$		0			0
$283$	−22.9129	+	13.2288i	−1.36203	+	0.786368i	−0.989894	−	0.141810i	$-0.954708\pi$
$283$	−22.9129	+	13.2288i	−1.36203	+	0.786368i	−0.372135	+	0.928178i	$0.621374\pi$
$284$	6.28065	−	31.1216i	0.372688	−	1.84673i
$285$		0			0
$286$	−17.3739	+	14.2179i	−1.02734	+	0.840722i
$287$	5.29150			0.312348
$288$		0			0
$289$	11.0000			0.647059
$290$	6.56670	−	5.37386i	0.385610	−	0.315564i
$291$		0			0
$292$	1.18693	−	5.88143i	0.0694599	−	0.344185i
$293$	25.9808	−	15.0000i	1.51781	−	0.876309i	0.518032	−	0.855361i	$-0.326665\pi$
$293$	25.9808	−	15.0000i	1.51781	−	0.876309i	0.999781	−	0.0209480i	$-0.00666844\pi$
$294$		0			0
$295$	−2.00000	+	3.46410i	−0.116445	+	0.201688i
$296$	−13.2288	+	7.00000i	−0.768906	+	0.406867i
$297$		0			0
$298$	−1.50000	+	3.96863i	−0.0868927	+	0.229896i
$299$	24.2487	+	14.0000i	1.40234	+	0.809641i
$300$		0			0
$301$	−9.16515	+	5.29150i	−0.528271	+	0.304997i
$302$	−0.685275	−	4.18693i	−0.0394332	−	0.240931i
$303$		0			0
$304$	−8.20871	+	19.5094i	−0.470802	+	1.11894i
$305$		0			0
$306$		0			0
$307$			15.8745i			0.906006i	0.891509	+	0.453003i	$0.149647\pi$
$307$			15.8745i			0.906006i	−0.891509	+	0.453003i	$0.850353\pi$
$308$	1.91280	+	5.68693i	0.108992	+	0.324043i
$309$		0			0
$310$	9.76951	−	1.59898i	0.554871	−	0.0908157i
$311$	−13.2288	−	22.9129i	−0.750134	−	1.29927i	−0.947757	−	0.318992i	$-0.896656\pi$
$311$	−13.2288	−	22.9129i	−0.750134	−	1.29927i	0.197623	−	0.980278i	$-0.436678\pi$
$312$		0			0
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	−0.851549	−	0.524276i	$-0.824336\pi$
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	0.879810	+	0.475325i	$0.157669\pi$
$314$	5.29150	−	14.0000i	0.298617	−	0.790066i
$315$		0			0
$316$	6.00000	+	5.29150i	0.337526	+	0.297670i
$317$	11.2583	+	6.50000i	0.632331	+	0.365076i	0.781654	−	0.623712i	$-0.214376\pi$
$317$	11.2583	+	6.50000i	0.632331	+	0.365076i	−0.149323	+	0.988788i	$0.547710\pi$
$318$		0			0
$319$	9.00000	+	15.5885i	0.503903	+	0.872786i
$320$	0.589925	−	7.97822i	0.0329778	−	0.445996i
$321$		0			0
$322$	5.79129	−	4.73930i	0.322736	−	0.264111i
$323$			28.0000i			1.55796i
$324$		0			0
$325$			21.1660i			1.17408i
$326$	−4.73930	−	5.79129i	−0.262486	−	0.320750i
$327$		0			0
$328$	7.95644	−	12.6766i	0.439321	−	0.699946i
$329$		0			0
$330$		0			0
$331$	−18.3303	−	10.5830i	−1.00752	−	0.581695i	−0.0970586	−	0.995279i	$-0.530943\pi$
$331$	−18.3303	−	10.5830i	−1.00752	−	0.581695i	−0.910466	+	0.413584i	$0.864277\pi$
$332$	−9.26013	+	10.5000i	−0.508216	+	0.576262i
$333$		0			0
$334$	−14.0000	−	5.29150i	−0.766046	−	0.289538i
$335$		0			0
$336$		0			0
$337$	−17.0000	−	29.4449i	−0.926049	−	1.60396i	−0.789865	−	0.613280i	$-0.789850\pi$
$337$	−17.0000	−	29.4449i	−0.926049	−	1.60396i	−0.136184	−	0.990684i	$-0.543484\pi$
$338$	3.42638	+	20.9347i	0.186370	+	1.13870i
$339$		0			0
$340$	−3.37386	−	10.0308i	−0.182973	−	0.543997i
$341$			21.0000i			1.13721i
$342$		0			0
$343$	−13.0000			−0.701934
$344$	−1.10440	+	29.9129i	−0.0595453	+	1.61279i
$345$		0			0
$346$	−20.9347	+	3.42638i	−1.12545	+	0.184203i
$347$	19.9186	−	11.5000i	1.06929	−	0.617352i	0.141299	−	0.989967i	$-0.454872\pi$
$347$	19.9186	−	11.5000i	1.06929	−	0.617352i	0.927986	+	0.372615i	$0.121539\pi$
$348$		0			0
$349$	−4.58258	−	2.64575i	−0.245300	−	0.141624i	0.372310	−	0.928108i	$-0.378566\pi$
$349$	−4.58258	−	2.64575i	−0.245300	−	0.141624i	−0.617610	+	0.786484i	$0.711899\pi$
$350$	5.29150	+	2.00000i	0.282843	+	0.106904i
$351$		0			0
$352$	16.5000	+	3.96863i	0.879453	+	0.211529i
$353$	−7.93725	+	13.7477i	−0.422457	+	0.731718i	−0.996179	−	0.0873325i	$-0.972166\pi$
$353$	−7.93725	+	13.7477i	−0.422457	+	0.731718i	0.573722	+	0.819050i	$0.305499\pi$
$354$		0			0
$355$	−13.7477	+	7.93725i	−0.729654	+	0.421266i
$356$	−4.18710	+	20.7477i	−0.221916	+	1.09963i
$357$		0			0
$358$	20.5998	+	25.1724i	1.08873	+	1.33040i
$359$	−21.1660			−1.11710			−0.558550	−	0.829471i	$-0.688642\pi$
$359$	−21.1660			−1.11710			−0.558550	+	0.829471i	$0.688642\pi$
$360$		0			0
$361$	−9.00000			−0.473684
$362$	18.9572	+	23.1652i	0.996369	+	1.21753i
$363$		0			0
$364$	10.3739	+	2.09355i	0.543738	+	0.109732i
$365$	−2.59808	+	1.50000i	−0.135990	+	0.0785136i
$366$		0			0
$367$	1.50000	−	2.59808i	0.0782994	−	0.135618i	−0.824217	−	0.566274i	$-0.808384\pi$
$367$	1.50000	−	2.59808i	0.0782994	−	0.135618i	0.902516	+	0.430656i	$0.141718\pi$
$368$	−2.64575	−	21.0000i	−0.137919	−	1.09470i
$369$		0			0
$370$	7.00000	+	2.64575i	0.363913	+	0.137546i
$371$	−7.79423	−	4.50000i	−0.404656	−	0.233628i
$372$		0			0
$373$	22.9129	−	13.2288i	1.18638	−	0.684959i	0.228901	−	0.973450i	$-0.426487\pi$
$373$	22.9129	−	13.2288i	1.18638	−	0.684959i	0.957483	+	0.288491i	$0.0931534\pi$
$374$	22.1552	−	3.62614i	1.14562	−	0.187503i
$375$		0			0
$376$		0			0
$377$	31.7490			1.63516
$378$		0			0
$379$		−	21.1660i		−	1.08722i	−0.839336	−	0.543612i	$-0.817056\pi$
$379$		−	21.1660i		−	1.08722i	0.839336	−	0.543612i	$-0.182944\pi$
$380$	10.0308	−	3.37386i	0.514569	−	0.173076i
$381$		0			0
$382$	1.20871	+	7.38505i	0.0618431	+	0.377852i
$383$	−7.93725	−	13.7477i	−0.405575	−	0.702476i	0.588813	−	0.808269i	$-0.299595\pi$
$383$	−7.93725	−	13.7477i	−0.405575	−	0.702476i	−0.994388	+	0.105793i	$0.966262\pi$
$384$		0			0
$385$	1.50000	−	2.59808i	0.0764471	−	0.132410i
$386$	−3.96863	−	1.50000i	−0.201998	−	0.0763480i
$387$		0			0
$388$	10.5000	+	9.26013i	0.533057	+	0.470112i
$389$	4.33013	+	2.50000i	0.219546	+	0.126755i	0.605740	−	0.795663i	$-0.292877\pi$
$389$	4.33013	+	2.50000i	0.219546	+	0.126755i	−0.386194	+	0.922418i	$0.626210\pi$
$390$		0			0
$391$	−14.0000	−	24.2487i	−0.708010	−	1.22631i
$392$	−9.02175	+	14.3739i	−0.455667	+	0.725990i
$393$		0			0
$394$	−11.6434	−	14.2279i	−0.586585	−	0.716789i
$395$		−	4.00000i		−	0.201262i
$396$		0			0
$397$		−	5.29150i		−	0.265573i	−0.991145	−	0.132786i	$-0.957608\pi$
$397$		−	5.29150i		−	0.265573i	0.991145	−	0.132786i	$-0.0423924\pi$
$398$	18.6057	−	15.2259i	0.932617	−	0.763208i
$399$		0			0
$400$	12.7477	−	9.66930i	0.637386	−	0.483465i
$401$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$401$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$402$		0			0
$403$	32.0780	+	18.5203i	1.59792	+	0.922560i
$404$	−22.4889	+	25.5000i	−1.11886	+	1.26867i
$405$		0			0
$406$	3.00000	−	7.93725i	0.148888	−	0.393919i
$407$	−7.93725	+	13.7477i	−0.393435	+	0.681450i
$408$		0			0
$409$	5.50000	+	9.52628i	0.271957	+	0.471044i	0.969363	−	0.245633i	$-0.0789957\pi$
$409$	5.50000	+	9.52628i	0.271957	+	0.471044i	−0.697406	+	0.716677i	$0.745662\pi$
$410$	−7.38505	+	1.20871i	−0.364722	+	0.0596940i
$411$		0			0
$412$		0			0
$413$			4.00000i			0.196827i
$414$		0			0
$415$	7.00000			0.343616
$416$	20.6138	−	21.7042i	1.01068	−	1.06413i
$417$		0			0
$418$	3.62614	+	22.1552i	0.177360	+	1.08364i
$419$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$419$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$420$		0			0
$421$	−9.16515	−	5.29150i	−0.446682	−	0.257892i	0.259746	−	0.965677i	$-0.416361\pi$
$421$	−9.16515	−	5.29150i	−0.446682	−	0.257892i	−0.706428	+	0.707785i	$0.749695\pi$
$422$	−2.64575	+	7.00000i	−0.128793	+	0.340755i
$423$		0			0
$424$	−22.5000	+	11.9059i	−1.09270	+	0.578201i
$425$	10.5830	−	18.3303i	0.513351	−	0.889150i
$426$		0			0
$427$		0			0
$428$	−5.88143	−	1.18693i	−0.284290	−	0.0573725i
$429$		0			0
$430$	11.5826	−	9.47860i	0.558561	−	0.457099i
$431$	−31.7490			−1.52930			−0.764648	−	0.644448i	$-0.777087\pi$
$431$	−31.7490			−1.52930			−0.764648	+	0.644448i	$0.777087\pi$
$432$		0			0
$433$	5.00000			0.240285			0.120142	−	0.992757i	$-0.461665\pi$
$433$	5.00000			0.240285			0.120142	+	0.992757i	$0.461665\pi$
$434$	7.66115	−	6.26951i	0.367747	−	0.300946i
$435$		0			0
$436$	−10.3739	−	2.09355i	−0.496818	−	0.100263i
$437$	24.2487	−	14.0000i	1.15997	−	0.669711i
$438$		0			0
$439$	10.5000	−	18.1865i	0.501138	−	0.867996i	−0.498861	−	0.866682i	$-0.666248\pi$
$439$	10.5000	−	18.1865i	0.501138	−	0.867996i	0.999999	−	0.00131415i	$-0.000418308\pi$
$440$	−3.96863	−	7.50000i	−0.189197	−	0.357548i
$441$		0			0
$442$	14.0000	−	37.0405i	0.665912	−	1.76184i
$443$	−20.7846	−	12.0000i	−0.987507	−	0.570137i	−0.0829786	−	0.996551i	$-0.526443\pi$
$443$	−20.7846	−	12.0000i	−0.987507	−	0.570137i	−0.904528	+	0.426414i	$0.859777\pi$
$444$		0			0
$445$	9.16515	−	5.29150i	0.434470	−	0.250841i
$446$	3.65480	+	22.3303i	0.173060	+	1.05737i
$447$		0			0
$448$	−3.47822	−	7.20430i	−0.164330	−	0.340371i
$449$	15.8745			0.749164			0.374582	−	0.927194i	$-0.377786\pi$
$449$	15.8745			0.749164			0.374582	+	0.927194i	$0.377786\pi$
$450$		0			0
$451$		−	15.8745i		−	0.747501i
$452$	−30.0924	+	10.1216i	−1.41543	+	0.476080i
$453$		0			0
$454$	−5.58258	+	0.913701i	−0.262003	+	0.0428821i
$455$	−2.64575	−	4.58258i	−0.124035	−	0.214834i
$456$		0			0
$457$	−8.50000	+	14.7224i	−0.397613	+	0.688686i	−0.993431	−	0.114433i	$-0.963495\pi$
$457$	−8.50000	+	14.7224i	−0.397613	+	0.688686i	0.595818	+	0.803120i	$0.296828\pi$
$458$	10.5830	−	28.0000i	0.494511	−	1.30835i
$459$		0			0
$460$	−7.00000	+	7.93725i	−0.326377	+	0.370076i
$461$	−7.79423	−	4.50000i	−0.363013	−	0.209586i	0.307388	−	0.951584i	$-0.400545\pi$
$461$	−7.79423	−	4.50000i	−0.363013	−	0.209586i	−0.670402	+	0.741998i	$0.733878\pi$
$462$		0			0
$463$	20.5000	+	35.5070i	0.952716	+	1.65015i	0.739511	+	0.673145i	$0.235057\pi$
$463$	20.5000	+	35.5070i	0.952716	+	1.65015i	0.213205	+	0.977007i	$0.431610\pi$
$464$	−14.5040	−	19.1216i	−0.673329	−	0.887698i
$465$		0			0
$466$	11.5826	−	9.47860i	0.536552	−	0.439088i
$467$		−	1.00000i		−	0.0462745i	−0.999732	−	0.0231372i	$-0.992635\pi$
$467$		−	1.00000i		−	0.0462745i	0.999732	−	0.0231372i	$-0.00736547\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	9.58258	+	6.01450i	0.441074	+	0.276840i
$473$	15.8745	+	27.4955i	0.729911	+	1.26424i
$474$		0			0
$475$	18.3303	+	10.5830i	0.841052	+	0.485582i
$476$	−7.93725	−	7.00000i	−0.363803	−	0.320844i
$477$		0			0
$478$	−21.0000	−	7.93725i	−0.960518	−	0.363042i
$479$	−10.5830	+	18.3303i	−0.483550	+	0.837533i	−0.999822	−	0.0188920i	$-0.993986\pi$
$479$	−10.5830	+	18.3303i	−0.483550	+	0.837533i	0.516272	+	0.856425i	$0.327319\pi$
$480$		0			0
$481$	14.0000	+	24.2487i	0.638345	+	1.10565i
$482$	2.28425	+	13.9564i	0.104045	+	0.635698i
$483$		0			0
$484$	−3.79129	+	1.27520i	−0.172331	+	0.0579637i
$485$		−	7.00000i		−	0.317854i
$486$		0			0
$487$	−40.0000			−1.81257			−0.906287	−	0.422664i	$-0.861095\pi$
$487$	−40.0000			−1.81257			−0.906287	+	0.422664i	$0.861095\pi$
$488$		0			0
$489$		0			0
$490$	8.37386	−	1.37055i	0.378293	−	0.0619152i
$491$	−25.1147	+	14.5000i	−1.13341	+	0.654376i	−0.944791	−	0.327674i	$-0.893735\pi$
$491$	−25.1147	+	14.5000i	−1.13341	+	0.654376i	−0.188621	+	0.982050i	$0.560402\pi$
$492$		0			0
$493$	−27.4955	−	15.8745i	−1.23833	−	0.714952i
$494$	37.0405	+	14.0000i	1.66653	+	0.629890i
$495$		0			0
$496$	−3.50000	−	27.7804i	−0.157155	−	1.24738i
$497$	−7.93725	+	13.7477i	−0.356034	+	0.616670i
$498$		0			0
$499$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$499$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$500$	−17.6443	−	3.56080i	−0.789076	−	0.159244i
$501$		0			0
$502$	−10.7477	−	13.1334i	−0.479695	−	0.586173i
$503$	15.8745			0.707809			0.353905	−	0.935282i	$-0.384854\pi$
$503$	15.8745			0.707809			0.353905	+	0.935282i	$0.384854\pi$
$504$		0			0
$505$	17.0000			0.756490
$506$	−14.2179	−	17.3739i	−0.632063	−	0.772362i
$507$		0			0
$508$	5.14337	−	25.4862i	0.228200	−	1.13077i
$509$	−18.1865	+	10.5000i	−0.806104	+	0.465404i	−0.845601	−	0.533815i	$-0.820758\pi$
$509$	−18.1865	+	10.5000i	−0.806104	+	0.465404i	0.0394971	+	0.999220i	$0.487424\pi$
$510$		0			0
$511$	−1.50000	+	2.59808i	−0.0663561	+	0.114932i
$512$	−22.4889	−	2.50000i	−0.993878	−	0.110485i
$513$		0			0
$514$	−21.0000	−	7.93725i	−0.926270	−	0.350097i
$515$		0			0
$516$		0			0
$517$		0			0
$518$	7.38505	−	1.20871i	0.324481	−	0.0531078i
$519$		0			0
$520$	−14.9564	−	0.552200i	−0.655883	−	0.0242156i
$521$	15.8745			0.695475			0.347737	−	0.937592i	$-0.386950\pi$
$521$	15.8745			0.695475			0.347737	+	0.937592i	$0.386950\pi$
$522$		0			0
$523$		−	15.8745i		−	0.694144i	−0.937839	−	0.347072i	$-0.887176\pi$
$523$		−	15.8745i		−	0.694144i	0.937839	−	0.347072i	$-0.112824\pi$
$524$	−4.46320	−	13.2695i	−0.194976	−	0.579681i
$525$		0			0
$526$	−1.20871	−	7.38505i	−0.0527024	−	0.322004i
$527$	−18.5203	−	32.0780i	−0.806755	−	1.39734i
$528$		0			0
$529$	−2.50000	+	4.33013i	−0.108696	+	0.188266i
$530$	11.9059	+	4.50000i	0.517158	+	0.195468i
$531$		0			0
$532$	7.00000	−	7.93725i	0.303488	−	0.344124i
$533$	−24.2487	−	14.0000i	−1.05033	−	0.606407i
$534$		0			0
$535$	1.50000	+	2.59808i	0.0648507	+	0.112325i
$536$		0			0
$537$		0			0
$538$	16.1216	+	19.7001i	0.695051	+	0.849332i
$539$			18.0000i			0.775315i
$540$		0			0
$541$		−	10.5830i		−	0.454999i	−0.973778	−	0.227499i	$-0.926945\pi$
$541$		−	10.5830i		−	0.454999i	0.973778	−	0.227499i	$-0.0730550\pi$
$542$	−16.4168	+	13.4347i	−0.705160	+	0.577068i
$543$		0			0
$544$	−28.7042	+	8.48945i	−1.23068	+	0.363982i
$545$	2.64575	+	4.58258i	0.113332	+	0.196296i
$546$		0			0
$547$	4.58258	+	2.64575i	0.195937	+	0.113124i	0.594759	−	0.803904i	$-0.297248\pi$
$547$	4.58258	+	2.64575i	0.195937	+	0.113124i	−0.398822	+	0.917028i	$0.630581\pi$
$548$		0			0
$549$		0			0
$550$	6.00000	−	15.8745i	0.255841	−	0.676891i
$551$	15.8745	−	27.4955i	0.676277	−	1.17135i
$552$		0			0
$553$	−2.00000	−	3.46410i	−0.0850487	−	0.147309i
$554$	14.7701	−	2.41742i	0.627522	−	0.102707i
$555$		0			0
$556$	−6.74773	−	20.0616i	−0.286167	−	0.850802i
$557$		−	39.0000i		−	1.65248i	−0.563316	−	0.826242i	$-0.690475\pi$
$557$		−	39.0000i		−	1.65248i	0.563316	−	0.826242i	$-0.309525\pi$
$558$		0			0
$559$	56.0000			2.36855
$560$	−1.55130	+	3.68693i	−0.0655544	+	0.155801i
$561$		0			0
$562$	−3.62614	−	22.1552i	−0.152959	−	0.934559i
$563$	−2.59808	+	1.50000i	−0.109496	+	0.0632175i	−0.553748	−	0.832684i	$-0.686803\pi$
$563$	−2.59808	+	1.50000i	−0.109496	+	0.0632175i	0.444252	+	0.895902i	$0.353470\pi$
$564$		0			0
$565$	13.7477	+	7.93725i	0.578371	+	0.333923i
$566$	13.2288	−	35.0000i	0.556046	−	1.47116i
$567$		0			0
$568$	21.0000	+	39.6863i	0.881140	+	1.66520i
$569$	15.8745	−	27.4955i	0.665494	−	1.15267i	−0.313657	−	0.949536i	$-0.601554\pi$
$569$	15.8745	−	27.4955i	0.665494	−	1.15267i	0.979151	−	0.203133i	$-0.0651124\pi$
$570$		0			0
$571$	22.9129	−	13.2288i	0.958874	−	0.553606i	0.0630478	−	0.998011i	$-0.479918\pi$
$571$	22.9129	−	13.2288i	0.958874	−	0.553606i	0.895826	+	0.444404i	$0.146585\pi$
$572$	6.28065	−	31.1216i	0.262607	−	1.30126i
$573$		0			0
$574$	−5.79129	+	4.73930i	−0.241724	+	0.197815i
$575$	−21.1660			−0.882684
$576$		0			0
$577$	−18.0000			−0.749350			−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000			−0.749350			−0.374675	+	0.927156i	$0.622246\pi$
$578$	−12.0390	+	9.85208i	−0.500755	+	0.409793i
$579$		0			0
$580$	−2.37386	+	11.7629i	−0.0985693	+	0.488426i
$581$	6.06218	−	3.50000i	0.251502	−	0.145204i
$582$		0			0
$583$	−13.5000	+	23.3827i	−0.559113	+	0.968412i
$584$	3.96863	+	7.50000i	0.164223	+	0.310352i
$585$		0			0
$586$	−15.0000	+	39.6863i	−0.619644	+	1.63942i
$587$	19.9186	+	11.5000i	0.822128	+	0.474656i	0.851150	−	0.524923i	$-0.175906\pi$
$587$	19.9186	+	11.5000i	0.822128	+	0.474656i	−0.0290218	+	0.999579i	$0.509239\pi$
$588$		0			0
$589$	32.0780	−	18.5203i	1.32175	−	0.763114i
$590$	−0.913701	−	5.58258i	−0.0376165	−	0.229831i
$591$		0			0
$592$	8.20871	−	19.5094i	0.337376	−	0.801832i
$593$	31.7490			1.30378			0.651888	−	0.758315i	$-0.273977\pi$
$593$	31.7490			1.30378			0.651888	+	0.758315i	$0.273977\pi$
$594$		0			0
$595$			5.29150i			0.216930i
$596$	−1.91280	−	5.68693i	−0.0783514	−	0.232946i
$597$		0			0
$598$	−39.0780	+	6.39590i	−1.59802	+	0.261548i
$599$	10.5830	+	18.3303i	0.432410	+	0.748956i	0.997080	−	0.0763606i	$-0.0243300\pi$
$599$	10.5830	+	18.3303i	0.432410	+	0.748956i	−0.564670	+	0.825317i	$0.690997\pi$
$600$		0			0
$601$	−2.50000	+	4.33013i	−0.101977	+	0.176630i	−0.912499	−	0.409079i	$-0.865850\pi$
$601$	−2.50000	+	4.33013i	−0.101977	+	0.176630i	0.810522	+	0.585708i	$0.199184\pi$
$602$	5.29150	−	14.0000i	0.215666	−	0.570597i
$603$		0			0
$604$	4.50000	+	3.96863i	0.183102	+	0.161481i
$605$	1.73205	+	1.00000i	0.0704179	+	0.0406558i
$606$		0			0
$607$	4.00000	+	6.92820i	0.162355	+	0.281207i	0.935713	−	0.352763i	$-0.114758\pi$
$607$	4.00000	+	6.92820i	0.162355	+	0.281207i	−0.773358	+	0.633970i	$0.781424\pi$
$608$	−8.48945	−	28.7042i	−0.344293	−	1.16411i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$			10.5830i			0.427444i	0.976895	+	0.213722i	$0.0685586\pi$
$613$			10.5830i			0.427444i	−0.976895	+	0.213722i	$0.931441\pi$
$614$	−14.2179	−	17.3739i	−0.573788	−	0.701152i
$615$		0			0
$616$	−7.18693	−	4.51088i	−0.289570	−	0.181748i
$617$	2.64575	+	4.58258i	0.106514	+	0.184488i	0.914356	−	0.404912i	$-0.132698\pi$
$617$	2.64575	+	4.58258i	0.106514	+	0.184488i	−0.807842	+	0.589399i	$0.799364\pi$
$618$		0			0
$619$	13.7477	+	7.93725i	0.552568	+	0.319025i	0.750157	−	0.661260i	$-0.229978\pi$
$619$	13.7477	+	7.93725i	0.552568	+	0.319025i	−0.197589	+	0.980285i	$0.563311\pi$
$620$	−9.26013	+	10.5000i	−0.371896	+	0.421690i
$621$		0			0
$622$	35.0000	+	13.2288i	1.40337	+	0.530425i
$623$	5.29150	−	9.16515i	0.212000	−	0.367194i
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	0.228425	+	1.39564i	0.00912970	+	0.0557811i
$627$		0			0
$628$	6.74773	+	20.0616i	0.269264	+	0.800545i
$629$		−	28.0000i		−	1.11643i
$630$		0			0
$631$	−23.0000			−0.915616			−0.457808	−	0.889051i	$-0.651365\pi$
$631$	−23.0000			−0.915616			−0.457808	+	0.889051i	$0.651365\pi$
$632$	−11.3060	−	0.417424i	−0.449729	−	0.0166042i
$633$		0			0
$634$	−18.1434	+	2.96953i	−0.720565	+	0.117935i
$635$	−11.2583	+	6.50000i	−0.446773	+	0.257945i
$636$		0			0
$637$	27.4955	+	15.8745i	1.08941	+	0.628971i
$638$	−23.8118	−	9.00000i	−0.942717	−	0.356313i
$639$		0			0
$640$	6.50000	+	9.26013i	0.256935	+	0.366039i
$641$	18.5203	−	32.0780i	0.731506	−	1.26701i	−0.224733	−	0.974420i	$-0.572151\pi$
$641$	18.5203	−	32.0780i	0.731506	−	1.26701i	0.956239	−	0.292586i	$-0.0945157\pi$
$642$		0			0
$643$	18.3303	−	10.5830i	0.722877	−	0.417353i	−0.0929339	−	0.995672i	$-0.529625\pi$
$643$	18.3303	−	10.5830i	0.722877	−	0.417353i	0.815811	+	0.578319i	$0.196291\pi$
$644$	−2.09355	+	10.3739i	−0.0824975	+	0.408787i
$645$		0			0
$646$	−25.0780	−	30.6446i	−0.986682	−	1.20570i
$647$	−31.7490			−1.24818			−0.624091	−	0.781351i	$-0.714531\pi$
$647$	−31.7490			−1.24818			−0.624091	+	0.781351i	$0.714531\pi$
$648$		0			0
$649$	12.0000			0.471041
$650$	−18.9572	−	23.1652i	−0.743563	−	0.908612i
$651$		0			0
$652$	10.3739	+	2.09355i	0.406272	+	0.0819898i
$653$	−2.59808	+	1.50000i	−0.101671	+	0.0586995i	−0.549973	−	0.835182i	$-0.685362\pi$
$653$	−2.59808	+	1.50000i	−0.101671	+	0.0586995i	0.448303	+	0.893882i	$0.352029\pi$
$654$		0			0
$655$	−3.50000	+	6.06218i	−0.136756	+	0.236869i
$656$	2.64575	+	21.0000i	0.103299	+	0.819912i
$657$		0			0
$658$		0			0
$659$	12.9904	+	7.50000i	0.506033	+	0.292159i	0.731202	−	0.682161i	$-0.238960\pi$
$659$	12.9904	+	7.50000i	0.506033	+	0.292159i	−0.225168	+	0.974320i	$0.572293\pi$
$660$		0			0
$661$	−22.9129	+	13.2288i	−0.891208	+	0.514539i	−0.874337	−	0.485319i	$-0.838704\pi$
$661$	−22.9129	+	13.2288i	−0.891208	+	0.514539i	−0.0168704	+	0.999858i	$0.505370\pi$
$662$	29.5402	−	4.83485i	1.14811	−	0.187912i
$663$		0			0
$664$	0.730493	−	19.7855i	0.0283486	−	0.767827i
$665$	−5.29150			−0.205196
$666$		0			0
$667$			31.7490i			1.22933i
$668$	20.0616	−	6.74773i	0.776207	−	0.261077i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−14.5000	+	25.1147i	−0.558934	+	0.968102i	0.438652	+	0.898657i	$0.355456\pi$
$673$	−14.5000	+	25.1147i	−0.558934	+	0.968102i	−0.997586	+	0.0694449i	$0.977877\pi$
$674$	44.9778	+	17.0000i	1.73248	+	0.654816i
$675$		0			0
$676$	−22.5000	−	19.8431i	−0.865385	−	0.763197i
$677$	5.19615	+	3.00000i	0.199704	+	0.115299i	0.596518	−	0.802600i	$-0.296551\pi$
$677$	5.19615	+	3.00000i	0.199704	+	0.115299i	−0.396813	+	0.917899i	$0.629884\pi$
$678$		0			0
$679$	−3.50000	−	6.06218i	−0.134318	−	0.232645i
$680$	12.6766	+	7.95644i	0.486124	+	0.305116i
$681$		0			0
$682$	−18.8085	−	22.9835i	−0.720216	−	0.880082i
$683$		−	44.0000i		−	1.68361i	−0.539779	−	0.841807i	$-0.681492\pi$
$683$		−	44.0000i		−	1.68361i	0.539779	−	0.841807i	$-0.318508\pi$
$684$		0			0
$685$		0			0
$686$	14.2279	−	11.6434i	0.543222	−	0.444546i
$687$		0			0
$688$	−25.5826	−	33.7273i	−0.975327	−	1.28584i
$689$	23.8118	+	41.2432i	0.907156	+	1.57124i
$690$		0			0
$691$	−36.6606	−	21.1660i	−1.39464	−	0.805193i	−0.400811	−	0.916161i	$-0.631272\pi$
$691$	−36.6606	−	21.1660i	−1.39464	−	0.805193i	−0.993824	+	0.110968i	$0.964605\pi$
$692$	19.8431	−	22.5000i	0.754323	−	0.855322i
$693$		0			0
$694$	−11.5000	+	30.4261i	−0.436534	+	1.15496i
$695$	−5.29150	+	9.16515i	−0.200718	+	0.347654i
$696$		0			0
$697$	14.0000	+	24.2487i	0.530288	+	0.918485i
$698$	7.38505	−	1.20871i	0.279528	−	0.0457504i
$699$		0			0
$700$	−7.58258	+	2.55040i	−0.286594	+	0.0963961i
$701$		−	1.00000i		−	0.0377695i	−0.999822	−	0.0188847i	$-0.993988\pi$
$701$		−	1.00000i		−	0.0377695i	0.999822	−	0.0188847i	$-0.00601156\pi$
$702$		0			0
$703$	28.0000			1.05604
$704$	−21.6129	+	10.4347i	−0.814567	+	0.393271i
$705$		0			0
$706$	−3.62614	−	22.1552i	−0.136471	−	0.833820i
$707$	14.7224	−	8.50000i	0.553694	−	0.319675i
$708$		0			0
$709$	18.3303	+	10.5830i	0.688409	+	0.397453i	0.803016	−	0.595958i	$-0.203227\pi$
$709$	18.3303	+	10.5830i	0.688409	+	0.397453i	−0.114607	+	0.993411i	$0.536561\pi$
$710$	7.93725	−	21.0000i	0.297880	−	0.788116i
$711$		0			0
$712$	−14.0000	−	26.4575i	−0.524672	−	0.991537i
$713$	−18.5203	+	32.0780i	−0.693589	+	1.20133i
$714$		0			0
$715$	−13.7477	+	7.93725i	−0.514136	+	0.296836i
$716$	−45.0909	−	9.09981i	−1.68513	−	0.340076i
$717$		0			0
$718$	23.1652	−	18.9572i	0.864516	−	0.707477i
$719$	−21.1660			−0.789359			−0.394679	−	0.918819i	$-0.629144\pi$
$719$	−21.1660			−0.789359			−0.394679	+	0.918819i	$0.629144\pi$
$720$		0			0
$721$		0			0
$722$	9.85005	−	8.06080i	0.366581	−	0.299992i
$723$		0			0
$724$	−41.4955	−	8.37420i	−1.54217	−	0.311225i
$725$	−20.7846	+	12.0000i	−0.771921	+	0.445669i
$726$		0			0
$727$	−16.5000	+	28.5788i	−0.611951	+	1.05993i	0.378960	+	0.925413i	$0.376282\pi$
$727$	−16.5000	+	28.5788i	−0.611951	+	1.05993i	−0.990911	+	0.134517i	$0.957052\pi$
$728$	−13.2288	+	7.00000i	−0.490290	+	0.259437i
$729$		0			0
$730$	1.50000	−	3.96863i	0.0555175	−	0.146885i
$731$	−48.4974	−	28.0000i	−1.79374	−	1.03562i
$732$		0			0
$733$	4.58258	−	2.64575i	0.169261	−	0.0977231i	−0.412976	−	0.910742i	$-0.635511\pi$
$733$	4.58258	−	2.64575i	0.169261	−	0.0977231i	0.582237	+	0.813019i	$0.302177\pi$
$734$	0.685275	+	4.18693i	0.0252940	+	0.154542i
$735$		0			0
$736$	21.7042	+	20.6138i	0.800026	+	0.759835i
$737$		0			0
$738$		0			0
$739$			5.29150i			0.194651i	0.995253	+	0.0973255i	$0.0310288\pi$
$739$			5.29150i			0.194651i	−0.995253	+	0.0973255i	$0.968971\pi$
$740$	−10.0308	+	3.37386i	−0.368740	+	0.124026i
$741$		0			0
$742$	12.5608	−	2.05583i	0.461121	−	0.0754718i
$743$	−18.5203	−	32.0780i	−0.679442	−	1.17683i	−0.975149	−	0.221550i	$-0.928888\pi$
$743$	−18.5203	−	32.0780i	−0.679442	−	1.17683i	0.295707	−	0.955279i	$-0.404445\pi$
$744$		0			0
$745$	−1.50000	+	2.59808i	−0.0549557	+	0.0951861i
$746$	−13.2288	+	35.0000i	−0.484339	+	1.28144i
$747$		0			0
$748$	−21.0000	+	23.8118i	−0.767836	+	0.870644i
$749$	2.59808	+	1.50000i	0.0949316	+	0.0548088i
$750$		0			0
$751$	15.5000	+	26.8468i	0.565603	+	0.979653i	0.996993	+	0.0774878i	$0.0246899\pi$
$751$	15.5000	+	26.8468i	0.565603	+	0.979653i	−0.431390	+	0.902165i	$0.641977\pi$
$752$		0			0
$753$		0			0
$754$	−34.7477	+	28.4358i	−1.26544	+	1.03557i
$755$		−	3.00000i		−	0.109181i
$756$		0			0
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$	18.9572	+	23.1652i	0.688557	+	0.841396i
$759$		0			0
$760$	−7.95644	+	12.6766i	−0.288610	+	0.459827i
$761$	−5.29150	−	9.16515i	−0.191817	−	0.332236i	0.754036	−	0.656834i	$-0.228105\pi$
$761$	−5.29150	−	9.16515i	−0.191817	−	0.332236i	−0.945852	+	0.324597i	$0.894771\pi$
$762$		0			0
$763$	4.58258	+	2.64575i	0.165900	+	0.0957826i
$764$	−7.93725	−	7.00000i	−0.287160	−	0.253251i
$765$		0			0
$766$	21.0000	+	7.93725i	0.758761	+	0.286785i
$767$	10.5830	−	18.3303i	0.382130	−	0.661869i
$768$		0			0
$769$	17.5000	+	30.3109i	0.631066	+	1.09304i	0.987334	+	0.158655i	$0.0507157\pi$
$769$	17.5000	+	30.3109i	0.631066	+	1.09304i	−0.356268	+	0.934384i	$0.615951\pi$
$770$	0.685275	+	4.18693i	0.0246956	+	0.150887i
$771$		0			0
$772$	5.68693	−	1.91280i	0.204677	−	0.0688432i
$773$			14.0000i			0.503545i	0.967786	+	0.251773i	$0.0810135\pi$
$773$			14.0000i			0.503545i	−0.967786	+	0.251773i	$0.918987\pi$
$774$		0			0
$775$	−28.0000			−1.00579
$776$	−19.7855	−	0.730493i	−0.710258	−	0.0262232i
$777$		0			0
$778$	−6.97822	+	1.14213i	−0.250181	+	0.0409472i
$779$	−24.2487	+	14.0000i	−0.868800	+	0.501602i
$780$		0			0
$781$	41.2432	+	23.8118i	1.47580	+	0.852052i
$782$	37.0405	+	14.0000i	1.32457	+	0.500639i
$783$		0			0
$784$	−3.00000	−	23.8118i	−0.107143	−	0.850420i
$785$	5.29150	−	9.16515i	0.188862	−	0.327118i
$786$		0			0
$787$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$787$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$788$	25.4862	+	5.14337i	0.907908	+	0.183225i
$789$		0			0
$790$	3.58258	+	4.37780i	0.127462	+	0.155755i
$791$	15.8745			0.564433
$792$		0			0
$793$		0			0
$794$	4.73930	+	5.79129i	0.168192	+	0.205525i
$795$		0			0
$796$	−6.72595	+	33.3281i	−0.238395	+	1.18128i
$797$	42.4352	−	24.5000i	1.50313	−	0.867835i	0.503140	−	0.864205i	$-0.332178\pi$
$797$	42.4352	−	24.5000i	1.50313	−	0.867835i	0.999993	−	0.00362965i	$-0.00115536\pi$
$798$		0			0
$799$		0			0
$800$	−5.29150	+	22.0000i	−0.187083	+	0.777817i
$801$		0			0
$802$		0			0
$803$	7.79423	+	4.50000i	0.275052	+	0.158802i
$804$		0			0
$805$	4.58258	−	2.64575i	0.161515	−	0.0932505i
$806$	−51.6954	+	8.46099i	−1.82089	+	0.298025i
$807$		0			0
$808$	1.77405	−	48.0505i	0.0624110	−	1.69041i
$809$	31.7490			1.11624			0.558118	−	0.829762i	$-0.311524\pi$
$809$	31.7490			1.11624			0.558118	+	0.829762i	$0.311524\pi$
$810$		0			0
$811$			37.0405i			1.30067i	0.759648	+	0.650334i	$0.225371\pi$
$811$			37.0405i			1.30067i	−0.759648	+	0.650334i	$0.774629\pi$
$812$	3.82560	+	11.3739i	0.134252	+	0.399144i
$813$		0			0
$814$	−3.62614	−	22.1552i	−0.127096	−	0.776538i
$815$	−2.64575	−	4.58258i	−0.0926766	−	0.160521i
$816$		0			0
$817$	28.0000	−	48.4974i	0.979596	−	1.69671i
$818$	−14.5516	−	5.50000i	−0.508786	−	0.192303i
$819$		0			0
$820$	7.00000	−	7.93725i	0.244451	−	0.277181i
$821$	8.66025	+	5.00000i	0.302245	+	0.174501i	0.643451	−	0.765487i	$-0.277502\pi$
$821$	8.66025	+	5.00000i	0.302245	+	0.174501i	−0.341206	+	0.939989i	$0.610835\pi$
$822$		0			0
$823$	−11.5000	−	19.9186i	−0.400865	−	0.694318i	0.592966	−	0.805228i	$-0.297957\pi$
$823$	−11.5000	−	19.9186i	−0.400865	−	0.694318i	−0.993831	+	0.110910i	$0.964624\pi$
$824$		0			0
$825$		0			0
$826$	−3.58258	−	4.37780i	−0.124654	−	0.152323i
$827$			36.0000i			1.25184i	0.779886	+	0.625921i	$0.215277\pi$
$827$			36.0000i			1.25184i	−0.779886	+	0.625921i	$0.784723\pi$
$828$		0			0
$829$		−	21.1660i		−	0.735126i	−0.929999	−	0.367563i	$-0.880192\pi$
$829$		−	21.1660i		−	0.735126i	0.929999	−	0.367563i	$-0.119808\pi$
$830$	−7.66115	+	6.26951i	−0.265923	+	0.217618i
$831$		0			0
$832$	−3.12159	+	42.2168i	−0.108222	+	1.46360i
$833$	−15.8745	−	27.4955i	−0.550019	−	0.952661i
$834$		0			0
$835$	−9.16515	−	5.29150i	−0.317173	−	0.183120i
$836$	−23.8118	−	21.0000i	−0.823547	−	0.726300i
$837$		0			0
$838$		0			0
$839$	−18.5203	+	32.0780i	−0.639390	+	1.10746i	0.346176	+	0.938169i	$0.387480\pi$
$839$	−18.5203	+	32.0780i	−0.639390	+	1.10746i	−0.985567	+	0.169287i	$0.945853\pi$
$840$		0			0
$841$	3.50000	+	6.06218i	0.120690	+	0.209041i
$842$	14.7701	−	2.41742i	0.509012	−	0.0833099i
$843$		0			0
$844$	−3.37386	−	10.0308i	−0.116133	−	0.345275i
$845$			15.0000i			0.516016i
$846$		0			0
$847$	2.00000			0.0687208
$848$	13.9617	−	33.1824i	0.479447	−	1.13949i
$849$		0			0
$850$	4.83485	+	29.5402i	0.165834	+	1.01322i
$851$	−24.2487	+	14.0000i	−0.831235	+	0.479914i
$852$		0			0
$853$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$853$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$854$		0			0
$855$		0			0
$856$	7.50000	−	3.96863i	0.256345	−	0.135645i
$857$	−7.93725	+	13.7477i	−0.271131	+	0.469613i	−0.969152	−	0.246464i	$-0.920731\pi$
$857$	−7.93725	+	13.7477i	−0.271131	+	0.469613i	0.698020	+	0.716078i	$0.254064\pi$
$858$		0			0
$859$	45.8258	−	26.4575i	1.56355	−	0.902719i	0.566662	−	0.823951i	$-0.308235\pi$
$859$	45.8258	−	26.4575i	1.56355	−	0.902719i	0.996893	−	0.0787681i	$-0.0250987\pi$
$860$	−4.18710	+	20.7477i	−0.142779	+	0.707492i
$861$		0			0
$862$	34.7477	−	28.4358i	1.18351	−	0.968528i
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$		0			0
$865$	−15.0000			−0.510015
$866$	−5.47225	+	4.47822i	−0.185955	+	0.152176i
$867$		0			0
$868$	−2.76951	+	13.7233i	−0.0940032	+	0.465800i
$869$	−10.3923	+	6.00000i	−0.352535	+	0.203536i
$870$		0			0
$871$		0			0
$872$	13.2288	−	7.00000i	0.447982	−	0.237050i
$873$		0			0
$874$	−14.0000	+	37.0405i	−0.473557	+	1.25291i
$875$	7.79423	+	4.50000i	0.263493	+	0.152128i
$876$		0			0
$877$	−45.8258	+	26.4575i	−1.54743	+	0.893407i	−0.549089	+	0.835764i	$0.685025\pi$
$877$	−45.8258	+	26.4575i	−1.54743	+	0.893407i	−0.998337	+	0.0576426i	$0.981642\pi$
$878$	4.79693	+	29.3085i	0.161888	+	0.989115i
$879$		0			0
$880$	11.0608	+	4.65390i	0.372859	+	0.156883i
$881$	−26.4575			−0.891376			−0.445688	−	0.895188i	$-0.647041\pi$
$881$	−26.4575			−0.891376			−0.445688	+	0.895188i	$0.647041\pi$
$882$		0			0
$883$		−	58.2065i		−	1.95881i	−0.201916	−	0.979403i	$-0.564717\pi$
$883$		−	58.2065i		−	1.95881i	0.201916	−	0.979403i	$-0.435283\pi$
$884$	17.8528	+	53.0780i	0.600455	+	1.78521i
$885$		0			0
$886$	33.4955	−	5.48220i	1.12530	−	0.184178i
$887$	7.93725	+	13.7477i	0.266507	+	0.461603i	0.967957	−	0.251115i	$-0.0807972\pi$
$887$	7.93725	+	13.7477i	0.266507	+	0.461603i	−0.701450	+	0.712718i	$0.747464\pi$
$888$		0			0
$889$	−6.50000	+	11.2583i	−0.218003	+	0.377592i
$890$	−5.29150	+	14.0000i	−0.177372	+	0.469281i
$891$		0			0
$892$	−24.0000	−	21.1660i	−0.803579	−	0.708690i
$893$		0			0
$894$		0			0
$895$	11.5000	+	19.9186i	0.384403	+	0.665805i
$896$	10.2592	+	4.76951i	0.342737	+	0.159338i
$897$		0			0
$898$	−17.3739	+	14.2179i	−0.579773	+	0.474458i
$899$			42.0000i			1.40078i
$900$		0			0
$901$		−	47.6235i		−	1.58657i
$902$	14.2179	+	17.3739i	0.473405	+	0.578486i
$903$		0			0
$904$	23.8693	−	38.0297i	0.793882	−	1.26485i
$905$	10.5830	+	18.3303i	0.351791	+	0.609320i
$906$		0			0
$907$	4.58258	+	2.64575i	0.152162	+	0.0878507i	0.574148	−	0.818752i	$-0.305333\pi$
$907$	4.58258	+	2.64575i	0.152162	+	0.0878507i	−0.421986	+	0.906602i	$0.638667\pi$
$908$	5.29150	−	6.00000i	0.175605	−	0.199117i
$909$		0			0
$910$	7.00000	+	2.64575i	0.232048	+	0.0877058i
$911$	−15.8745	+	27.4955i	−0.525946	+	0.910965i	0.473597	+	0.880742i	$0.342955\pi$
$911$	−15.8745	+	27.4955i	−0.525946	+	0.910965i	−0.999543	+	0.0302235i	$0.990378\pi$
$912$		0			0
$913$	−10.5000	−	18.1865i	−0.347499	−	0.601886i
$914$	−3.88323	−	23.7259i	−0.128446	−	0.784785i
$915$		0			0
$916$	13.4955	+	40.1232i	0.445902	+	1.32571i
$917$			7.00000i			0.231160i
$918$		0			0
$919$	3.00000			0.0989609			0.0494804	−	0.998775i	$-0.484243\pi$
$919$	3.00000			0.0989609			0.0494804	+	0.998775i	$0.484243\pi$
$920$	0.552200	−	14.9564i	0.0182055	−	0.493099i
$921$		0			0
$922$	12.5608	−	2.05583i	0.413668	−	0.0677050i
$923$	72.7461	−	42.0000i	2.39447	−	1.38245i
$924$		0			0
$925$	−18.3303	−	10.5830i	−0.602697	−	0.347967i
$926$	−54.2379	−	20.5000i	−1.78237	−	0.673672i
$927$		0			0
$928$	33.0000	+	7.93725i	1.08328	+	0.260553i
$929$	−5.29150	+	9.16515i	−0.173609	+	0.300699i	−0.939679	−	0.342058i	$-0.888876\pi$
$929$	−5.29150	+	9.16515i	−0.173609	+	0.300699i	0.766070	+	0.642757i	$0.222209\pi$
$930$		0			0
$931$	27.4955	−	15.8745i	0.901127	−	0.520266i
$932$	−4.18710	+	20.7477i	−0.137153	+	0.679614i
$933$		0			0
$934$	0.895644	+	1.09445i	0.0293064	+	0.0358115i
$935$	15.8745			0.519152
$936$		0			0
$937$	−19.0000			−0.620703			−0.310351	−	0.950622i	$-0.600447\pi$
$937$	−19.0000			−0.620703			−0.310351	+	0.950622i	$0.600447\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	18.1865	−	10.5000i	0.592864	−	0.342290i	−0.173365	−	0.984858i	$-0.555464\pi$
$941$	18.1865	−	10.5000i	0.592864	−	0.342290i	0.766229	+	0.642567i	$0.222131\pi$
$942$		0			0
$943$	14.0000	−	24.2487i	0.455903	−	0.789647i
$944$	−15.8745	+	2.00000i	−0.516671	+	0.0650945i
$945$		0			0
$946$	−42.0000	−	15.8745i	−1.36554	−	0.516125i
$947$	33.7750	+	19.5000i	1.09754	+	0.633665i	0.935574	−	0.353131i	$-0.114883\pi$
$947$	33.7750	+	19.5000i	1.09754	+	0.633665i	0.161966	+	0.986796i	$0.448217\pi$
$948$		0			0
$949$	13.7477	−	7.93725i	0.446270	−	0.257654i
$950$	−29.5402	+	4.83485i	−0.958411	+	0.156863i
$951$		0			0
$952$	14.9564	+	0.552200i	0.484741	+	0.0178969i
$953$	−31.7490			−1.02845			−0.514226	−	0.857655i	$-0.671921\pi$
$953$	−31.7490			−1.02845			−0.514226	+	0.857655i	$0.671921\pi$
$954$		0			0
$955$			5.29150i			0.171229i
$956$	30.0924	−	10.1216i	0.973258	−	0.327356i
$957$		0			0
$958$	−4.83485	−	29.5402i	−0.156207	−	0.954401i
$959$		0			0
$960$		0			0
$961$	−9.00000	+	15.5885i	−0.290323	+	0.502853i
$962$	−37.0405	−	14.0000i	−1.19423	−	0.451378i
$963$		0			0
$964$	−15.0000	−	13.2288i	−0.483117	−	0.426070i
$965$	−2.59808	−	1.50000i	−0.0836350	−	0.0482867i
$966$		0			0
$967$	−20.5000	−	35.5070i	−0.659236	−	1.14183i	−0.980814	−	0.194946i	$-0.937547\pi$
$967$	−20.5000	−	35.5070i	−0.659236	−	1.14183i	0.321578	−	0.946883i	$-0.395787\pi$
$968$	3.00725	−	4.79129i	0.0966567	−	0.153998i
$969$		0			0
$970$	6.26951	+	7.66115i	0.201302	+	0.245985i
$971$		−	15.0000i		−	0.481373i	−0.970603	−	0.240686i	$-0.922627\pi$
$971$		−	15.0000i		−	0.481373i	0.970603	−	0.240686i	$-0.0773725\pi$
$972$		0			0
$973$			10.5830i			0.339276i
$974$	43.7780	−	35.8258i	1.40274	−	1.14793i
$975$		0			0
$976$		0			0
$977$	−5.29150	−	9.16515i	−0.169290	−	0.293219i	0.768880	−	0.639393i	$-0.220814\pi$
$977$	−5.29150	−	9.16515i	−0.169290	−	0.293219i	−0.938170	+	0.346174i	$0.887481\pi$
$978$		0			0
$979$	−27.4955	−	15.8745i	−0.878759	−	0.507351i
$980$	−7.93725	+	9.00000i	−0.253546	+	0.287494i
$981$		0			0
$982$	14.5000	−	38.3634i	0.462714	−	1.22423i
$983$	21.1660	−	36.6606i	0.675091	−	1.16929i	−0.301351	−	0.953513i	$-0.597438\pi$
$983$	21.1660	−	36.6606i	0.675091	−	1.16929i	0.976442	−	0.215779i	$-0.0692289\pi$
$984$		0			0
$985$	−6.50000	−	11.2583i	−0.207107	−	0.358720i
$986$	44.3103	−	7.25227i	1.41113	−	0.230959i
$987$		0			0
$988$	−53.0780	+	17.8528i	−1.68864	+	0.567973i
$989$			56.0000i			1.78070i
$990$		0			0
$991$	47.0000			1.49300			0.746502	−	0.665383i	$-0.231732\pi$
$991$	47.0000			1.49300			0.746502	+	0.665383i	$0.231732\pi$
$992$	28.7119	+	27.2695i	0.911604	+	0.865808i
$993$		0			0
$994$	−3.62614	−	22.1552i	−0.115014	−	0.702719i
$995$	14.7224	−	8.50000i	0.466732	−	0.269468i
$996$		0			0
$997$	−13.7477	−	7.93725i	−0.435395	−	0.251375i	0.266247	−	0.963905i	$-0.414216\pi$
$997$	−13.7477	−	7.93725i	−0.435395	−	0.251375i	−0.701642	+	0.712529i	$0.747550\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.n.n.541.1		8
3.2	odd	2	inner	648.2.n.n.541.4		8
4.3	odd	2		2592.2.r.p.2161.2		8
8.3	odd	2		2592.2.r.p.2161.3		8
8.5	even	2	inner	648.2.n.n.541.2		8
9.2	odd	6		216.2.d.b.109.1	✓	4
9.4	even	3	inner	648.2.n.n.109.2		8
9.5	odd	6	inner	648.2.n.n.109.3		8
9.7	even	3		216.2.d.b.109.4	yes	4
12.11	even	2		2592.2.r.p.2161.4		8
24.5	odd	2	inner	648.2.n.n.541.3		8
24.11	even	2		2592.2.r.p.2161.1		8
36.7	odd	6		864.2.d.a.433.2		4
36.11	even	6		864.2.d.a.433.4		4
36.23	even	6		2592.2.r.p.433.1		8
36.31	odd	6		2592.2.r.p.433.3		8
72.5	odd	6	inner	648.2.n.n.109.4		8
72.11	even	6		864.2.d.a.433.1		4
72.13	even	6	inner	648.2.n.n.109.1		8
72.29	odd	6		216.2.d.b.109.2	yes	4
72.43	odd	6		864.2.d.a.433.3		4
72.59	even	6		2592.2.r.p.433.4		8
72.61	even	6		216.2.d.b.109.3	yes	4
72.67	odd	6		2592.2.r.p.433.2		8
144.11	even	12		6912.2.a.bd.1.2		2
144.29	odd	12		6912.2.a.bu.1.1		2
144.43	odd	12		6912.2.a.bv.1.2		2
144.61	even	12		6912.2.a.bc.1.1		2
144.83	even	12		6912.2.a.bv.1.1		2
144.101	odd	12		6912.2.a.bc.1.2		2
144.115	odd	12		6912.2.a.bd.1.1		2
144.133	even	12		6912.2.a.bu.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.d.b.109.1	✓	4	9.2	odd	6
216.2.d.b.109.2	yes	4	72.29	odd	6
216.2.d.b.109.3	yes	4	72.61	even	6
216.2.d.b.109.4	yes	4	9.7	even	3
648.2.n.n.109.1		8	72.13	even	6	inner
648.2.n.n.109.2		8	9.4	even	3	inner
648.2.n.n.109.3		8	9.5	odd	6	inner
648.2.n.n.109.4		8	72.5	odd	6	inner
648.2.n.n.541.1		8	1.1	even	1	trivial
648.2.n.n.541.2		8	8.5	even	2	inner
648.2.n.n.541.3		8	24.5	odd	2	inner
648.2.n.n.541.4		8	3.2	odd	2	inner
864.2.d.a.433.1		4	72.11	even	6
864.2.d.a.433.2		4	36.7	odd	6
864.2.d.a.433.3		4	72.43	odd	6
864.2.d.a.433.4		4	36.11	even	6
2592.2.r.p.433.1		8	36.23	even	6
2592.2.r.p.433.2		8	72.67	odd	6
2592.2.r.p.433.3		8	36.31	odd	6
2592.2.r.p.433.4		8	72.59	even	6
2592.2.r.p.2161.1		8	24.11	even	2
2592.2.r.p.2161.2		8	4.3	odd	2
2592.2.r.p.2161.3		8	8.3	odd	2
2592.2.r.p.2161.4		8	12.11	even	2
6912.2.a.bc.1.1		2	144.61	even	12
6912.2.a.bc.1.2		2	144.101	odd	12
6912.2.a.bd.1.1		2	144.115	odd	12
6912.2.a.bd.1.2		2	144.11	even	12
6912.2.a.bu.1.1		2	144.29	odd	12
6912.2.a.bu.1.2		2	144.133	even	12
6912.2.a.bv.1.1		2	144.83	even	12
6912.2.a.bv.1.2		2	144.43	odd	12

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:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.09445 + 0.895644i) q^{2} +(0.395644 - 1.96048i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(1.32288 + 2.50000i) q^{8} +O(q^{10})\)	\(q+(-1.09445 + 0.895644i) q^{2} +(0.395644 - 1.96048i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(1.32288 + 2.50000i) q^{8} +(0.500000 - 1.32288i) q^{10} +(2.59808 + 1.50000i) q^{11} +(4.58258 - 2.64575i) q^{13} +(-0.228425 - 1.39564i) q^{14} +(-3.68693 - 1.55130i) q^{16} -5.29150 q^{17} -5.29150i q^{19} +(0.637600 + 1.89564i) q^{20} +(-4.18693 + 0.685275i) q^{22} +(2.64575 + 4.58258i) q^{23} +(-2.00000 + 3.46410i) q^{25} +(-2.64575 + 7.00000i) q^{26} +(1.50000 + 1.32288i) q^{28} +(5.19615 + 3.00000i) q^{29} +(3.50000 + 6.06218i) q^{31} +(5.42458 - 1.60436i) q^{32} +(5.79129 - 4.73930i) q^{34} -1.00000i q^{35} +5.29150i q^{37} +(4.73930 + 5.79129i) q^{38} +(-2.39564 - 1.50363i) q^{40} +(-2.64575 - 4.58258i) q^{41} +(9.16515 + 5.29150i) q^{43} +(3.96863 - 4.50000i) q^{44} +(-7.00000 - 2.64575i) q^{46} +(3.00000 + 5.19615i) q^{49} +(-0.913701 - 5.58258i) q^{50} +(-3.37386 - 10.0308i) q^{52} +9.00000i q^{53} -3.00000 q^{55} +(-2.82650 - 0.104356i) q^{56} +(-8.37386 + 1.37055i) q^{58} +(3.46410 - 2.00000i) q^{59} +(-9.26013 - 3.50000i) q^{62} +(-4.50000 + 6.61438i) q^{64} +(-2.64575 + 4.58258i) q^{65} +(-2.09355 + 10.3739i) q^{68} +(0.895644 + 1.09445i) q^{70} +15.8745 q^{71} +3.00000 q^{73} +(-4.73930 - 5.79129i) q^{74} +(-10.3739 - 2.09355i) q^{76} +(-2.59808 + 1.50000i) q^{77} +(-2.00000 + 3.46410i) q^{79} +(3.96863 - 0.500000i) q^{80} +(7.00000 + 2.64575i) q^{82} +(-6.06218 - 3.50000i) q^{83} +(4.58258 - 2.64575i) q^{85} +(-14.7701 + 2.41742i) q^{86} +(-0.313068 + 8.47950i) q^{88} -10.5830 q^{89} +5.29150i q^{91} +(10.0308 - 3.37386i) q^{92} +(2.64575 + 4.58258i) q^{95} +(-3.50000 + 6.06218i) q^{97} +(-7.93725 - 3.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{4} - 4 q^{7}+O(q^{10}) \) 8 * q - 6 * q^4 - 4 * q^7	\( 8 q - 6 q^{4} - 4 q^{7} + 4 q^{10} - 2 q^{16} - 6 q^{22} - 16 q^{25} + 12 q^{28} + 28 q^{31} + 28 q^{34} - 10 q^{40} - 56 q^{46} + 24 q^{49} + 28 q^{52} - 24 q^{55} - 12 q^{58} - 36 q^{64} - 2 q^{70} + 24 q^{73} - 28 q^{76} - 16 q^{79} + 56 q^{82} - 30 q^{88} - 28 q^{97}+O(q^{100}) \) 8 * q - 6 * q^4 - 4 * q^7 + 4 * q^10 - 2 * q^16 - 6 * q^22 - 16 * q^25 + 12 * q^28 + 28 * q^31 + 28 * q^34 - 10 * q^40 - 56 * q^46 + 24 * q^49 + 28 * q^52 - 24 * q^55 - 12 * q^58 - 36 * q^64 - 2 * q^70 + 24 * q^73 - 28 * q^76 - 16 * q^79 + 56 * q^82 - 30 * q^88 - 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more