LMFDB - Embedded newform 567.2.h.g.352.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(298,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 4]))

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

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

chi := DirichletCharacter("567.298");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.h (of order $3$, 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			352.2
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	567.352
Dual form			567.2.h.g.298.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.44949 q^{2} +4.00000 q^{4} +(-1.22474 - 2.12132i) q^{5} +(2.50000 - 0.866025i) q^{7} +4.89898 q^{8} +O(q^{10})$	\(q+2.44949 q^{2} +4.00000 q^{4} +(-1.22474 - 2.12132i) q^{5} +(2.50000 - 0.866025i) q^{7} +4.89898 q^{8} +(-3.00000 - 5.19615i) q^{10} +(-2.44949 + 4.24264i) q^{11} +(2.00000 - 3.46410i) q^{13} +(6.12372 - 2.12132i) q^{14} +4.00000 q^{16} +(1.22474 + 2.12132i) q^{17} +(0.500000 - 0.866025i) q^{19} +(-4.89898 - 8.48528i) q^{20} +(-6.00000 + 10.3923i) q^{22} +(-1.22474 - 2.12132i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(4.89898 - 8.48528i) q^{26} +(10.0000 - 3.46410i) q^{28} +(3.67423 + 6.36396i) q^{29} -7.00000 q^{31} +(3.00000 + 5.19615i) q^{34} +(-4.89898 - 4.24264i) q^{35} +(-4.00000 + 6.92820i) q^{37} +(1.22474 - 2.12132i) q^{38} +(-6.00000 - 10.3923i) q^{40} +(-3.67423 + 6.36396i) q^{41} +(0.500000 + 0.866025i) q^{43} +(-9.79796 + 16.9706i) q^{44} +(-3.00000 - 5.19615i) q^{46} +2.44949 q^{47} +(5.50000 - 4.33013i) q^{49} +(-1.22474 + 2.12132i) q^{50} +(8.00000 - 13.8564i) q^{52} +(1.22474 + 2.12132i) q^{53} +12.0000 q^{55} +(12.2474 - 4.24264i) q^{56} +(9.00000 + 15.5885i) q^{58} -9.79796 q^{59} +5.00000 q^{61} -17.1464 q^{62} -8.00000 q^{64} -9.79796 q^{65} +2.00000 q^{67} +(4.89898 + 8.48528i) q^{68} +(-12.0000 - 10.3923i) q^{70} +(0.500000 + 0.866025i) q^{73} +(-9.79796 + 16.9706i) q^{74} +(2.00000 - 3.46410i) q^{76} +(-2.44949 + 12.7279i) q^{77} -4.00000 q^{79} +(-4.89898 - 8.48528i) q^{80} +(-9.00000 + 15.5885i) q^{82} +(-7.34847 - 12.7279i) q^{83} +(3.00000 - 5.19615i) q^{85} +(1.22474 + 2.12132i) q^{86} +(-12.0000 + 20.7846i) q^{88} +(-1.22474 + 2.12132i) q^{89} +(2.00000 - 10.3923i) q^{91} +(-4.89898 - 8.48528i) q^{92} +6.00000 q^{94} -2.44949 q^{95} +(0.500000 + 0.866025i) q^{97} +(13.4722 - 10.6066i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 16 q^{4} + 10 q^{7}+O(q^{10}) $ 4 * q + 16 * q^4 + 10 * q^7	$ 4 q + 16 q^{4} + 10 q^{7} - 12 q^{10} + 8 q^{13} + 16 q^{16} + 2 q^{19} - 24 q^{22} - 2 q^{25} + 40 q^{28} - 28 q^{31} + 12 q^{34} - 16 q^{37} - 24 q^{40} + 2 q^{43} - 12 q^{46} + 22 q^{49} + 32 q^{52} + 48 q^{55} + 36 q^{58} + 20 q^{61} - 32 q^{64} + 8 q^{67} - 48 q^{70} + 2 q^{73} + 8 q^{76} - 16 q^{79} - 36 q^{82} + 12 q^{85} - 48 q^{88} + 8 q^{91} + 24 q^{94} + 2 q^{97}+O(q^{100}) $ 4 * q + 16 * q^4 + 10 * q^7 - 12 * q^10 + 8 * q^13 + 16 * q^16 + 2 * q^19 - 24 * q^22 - 2 * q^25 + 40 * q^28 - 28 * q^31 + 12 * q^34 - 16 * q^37 - 24 * q^40 + 2 * q^43 - 12 * q^46 + 22 * q^49 + 32 * q^52 + 48 * q^55 + 36 * q^58 + 20 * q^61 - 32 * q^64 + 8 * q^67 - 48 * q^70 + 2 * q^73 + 8 * q^76 - 16 * q^79 - 36 * q^82 + 12 * q^85 - 48 * q^88 + 8 * q^91 + 24 * q^94 + 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2.44949			1.73205			0.866025	−	0.500000i	$-0.166667\pi$
$2$	2.44949			1.73205			0.866025	+	0.500000i	$0.166667\pi$
$3$		0			0
$3$		0			0
$4$	4.00000			2.00000
$5$	−1.22474	−	2.12132i	−0.547723	−	0.948683i	−0.998430	−	0.0560116i	$-0.982162\pi$
$5$	−1.22474	−	2.12132i	−0.547723	−	0.948683i	0.450708	−	0.892672i	$-0.351172\pi$
$6$		0			0
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$8$	4.89898			1.73205
$9$		0			0
$10$	−3.00000	−	5.19615i	−0.948683	−	1.64317i
$11$	−2.44949	+	4.24264i	−0.738549	+	1.27920i	0.214600	+	0.976702i	$0.431155\pi$
$11$	−2.44949	+	4.24264i	−0.738549	+	1.27920i	−0.953149	+	0.302502i	$0.902178\pi$
$12$		0			0
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	−0.443227	−	0.896410i	$-0.646166\pi$
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	0.997927	−	0.0643593i	$-0.0205004\pi$
$14$	6.12372	−	2.12132i	1.63663	−	0.566947i
$15$		0			0
$16$	4.00000			1.00000
$17$	1.22474	+	2.12132i	0.297044	+	0.514496i	0.975458	−	0.220184i	$-0.0706658\pi$
$17$	1.22474	+	2.12132i	0.297044	+	0.514496i	−0.678414	+	0.734680i	$0.737332\pi$
$18$		0			0
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	0.917663	+	0.397360i	$0.130073\pi$
$20$	−4.89898	−	8.48528i	−1.09545	−	1.89737i
$21$		0			0
$22$	−6.00000	+	10.3923i	−1.27920	+	2.21565i
$23$	−1.22474	−	2.12132i	−0.255377	−	0.442326i	0.709621	−	0.704584i	$-0.248866\pi$
$23$	−1.22474	−	2.12132i	−0.255377	−	0.442326i	−0.964998	+	0.262258i	$0.915533\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	4.89898	−	8.48528i	0.960769	−	1.66410i
$27$		0			0
$28$	10.0000	−	3.46410i	1.88982	−	0.654654i
$29$	3.67423	+	6.36396i	0.682288	+	1.18176i	0.974281	+	0.225337i	$0.0723484\pi$
$29$	3.67423	+	6.36396i	0.682288	+	1.18176i	−0.291993	+	0.956421i	$0.594318\pi$
$30$		0			0
$31$	−7.00000			−1.25724			−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000			−1.25724			−0.628619	+	0.777714i	$0.716379\pi$
$32$		0			0
$33$		0			0
$34$	3.00000	+	5.19615i	0.514496	+	0.891133i
$35$	−4.89898	−	4.24264i	−0.828079	−	0.717137i
$36$		0			0
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	0.323640	+	0.946180i	$0.395093\pi$
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	−0.981236	+	0.192809i	$0.938240\pi$
$38$	1.22474	−	2.12132i	0.198680	−	0.344124i
$39$		0			0
$40$	−6.00000	−	10.3923i	−0.948683	−	1.64317i
$41$	−3.67423	+	6.36396i	−0.573819	+	0.993884i	0.422350	+	0.906433i	$0.361205\pi$
$41$	−3.67423	+	6.36396i	−0.573819	+	0.993884i	−0.996169	+	0.0874508i	$0.972128\pi$
$42$		0			0
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$	−9.79796	+	16.9706i	−1.47710	+	2.55841i
$45$		0			0
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$	2.44949			0.357295			0.178647	−	0.983913i	$-0.442828\pi$
$47$	2.44949			0.357295			0.178647	+	0.983913i	$0.442828\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	−1.22474	+	2.12132i	−0.173205	+	0.300000i
$51$		0			0
$52$	8.00000	−	13.8564i	1.10940	−	1.92154i
$53$	1.22474	+	2.12132i	0.168232	+	0.291386i	0.937798	−	0.347181i	$-0.112861\pi$
$53$	1.22474	+	2.12132i	0.168232	+	0.291386i	−0.769567	+	0.638567i	$0.779528\pi$
$54$		0			0
$55$	12.0000			1.61808
$56$	12.2474	−	4.24264i	1.63663	−	0.566947i
$57$		0			0
$58$	9.00000	+	15.5885i	1.18176	+	2.04686i
$59$	−9.79796			−1.27559			−0.637793	−	0.770208i	$-0.720152\pi$
$59$	−9.79796			−1.27559			−0.637793	+	0.770208i	$0.720152\pi$
$60$		0			0
$61$	5.00000			0.640184			0.320092	−	0.947386i	$-0.396286\pi$
$61$	5.00000			0.640184			0.320092	+	0.947386i	$0.396286\pi$
$62$	−17.1464			−2.17760
$63$		0			0
$64$	−8.00000			−1.00000
$65$	−9.79796			−1.21529
$66$		0			0
$67$	2.00000			0.244339			0.122169	−	0.992509i	$-0.461015\pi$
$67$	2.00000			0.244339			0.122169	+	0.992509i	$0.461015\pi$
$68$	4.89898	+	8.48528i	0.594089	+	1.02899i
$69$		0			0
$70$	−12.0000	−	10.3923i	−1.43427	−	1.24212i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	0.500000	+	0.866025i	0.0585206	+	0.101361i	0.893801	−	0.448463i	$-0.148028\pi$
$73$	0.500000	+	0.866025i	0.0585206	+	0.101361i	−0.835281	+	0.549823i	$0.814695\pi$
$74$	−9.79796	+	16.9706i	−1.13899	+	1.97279i
$75$		0			0
$76$	2.00000	−	3.46410i	0.229416	−	0.397360i
$77$	−2.44949	+	12.7279i	−0.279145	+	1.45048i
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$	−4.89898	−	8.48528i	−0.547723	−	0.948683i
$81$		0			0
$82$	−9.00000	+	15.5885i	−0.993884	+	1.72146i
$83$	−7.34847	−	12.7279i	−0.806599	−	1.39707i	−0.915206	−	0.402986i	$-0.867972\pi$
$83$	−7.34847	−	12.7279i	−0.806599	−	1.39707i	0.108607	−	0.994085i	$-0.465361\pi$
$84$		0			0
$85$	3.00000	−	5.19615i	0.325396	−	0.563602i
$86$	1.22474	+	2.12132i	0.132068	+	0.228748i
$87$		0			0
$88$	−12.0000	+	20.7846i	−1.27920	+	2.21565i
$89$	−1.22474	+	2.12132i	−0.129823	+	0.224860i	−0.923608	−	0.383339i	$-0.874774\pi$
$89$	−1.22474	+	2.12132i	−0.129823	+	0.224860i	0.793785	+	0.608198i	$0.208107\pi$
$90$		0			0
$91$	2.00000	−	10.3923i	0.209657	−	1.08941i
$92$	−4.89898	−	8.48528i	−0.510754	−	0.884652i
$93$		0			0
$94$	6.00000			0.618853
$95$	−2.44949			−0.251312
$96$		0			0
$97$	0.500000	+	0.866025i	0.0507673	+	0.0879316i	0.890292	−	0.455389i	$-0.150500\pi$
$97$	0.500000	+	0.866025i	0.0507673	+	0.0879316i	−0.839525	+	0.543321i	$0.817167\pi$
$98$	13.4722	−	10.6066i	1.36090	−	1.07143i
$99$		0			0
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	−2.44949	+	4.24264i	−0.243733	+	0.422159i	−0.961775	−	0.273842i	$-0.911706\pi$
$101$	−2.44949	+	4.24264i	−0.243733	+	0.422159i	0.718041	+	0.696000i	$0.245039\pi$
$102$		0			0
$103$	−1.00000	−	1.73205i	−0.0985329	−	0.170664i	0.812545	−	0.582899i	$-0.198082\pi$
$103$	−1.00000	−	1.73205i	−0.0985329	−	0.170664i	−0.911078	+	0.412235i	$0.864748\pi$
$104$	9.79796	−	16.9706i	0.960769	−	1.66410i
$105$		0			0
$106$	3.00000	+	5.19615i	0.291386	+	0.504695i
$107$	9.79796	−	16.9706i	0.947204	−	1.64061i	0.195928	−	0.980618i	$-0.437228\pi$
$107$	9.79796	−	16.9706i	0.947204	−	1.64061i	0.751276	−	0.659988i	$-0.229439\pi$
$108$		0			0
$109$	0.500000	+	0.866025i	0.0478913	+	0.0829502i	0.888977	−	0.457951i	$-0.151417\pi$
$109$	0.500000	+	0.866025i	0.0478913	+	0.0829502i	−0.841086	+	0.540901i	$0.818083\pi$
$110$	29.3939			2.80260
$111$		0			0
$112$	10.0000	−	3.46410i	0.944911	−	0.327327i
$113$	7.34847	−	12.7279i	0.691286	−	1.19734i	−0.280131	−	0.959962i	$-0.590378\pi$
$113$	7.34847	−	12.7279i	0.691286	−	1.19734i	0.971417	−	0.237380i	$-0.0762888\pi$
$114$		0			0
$115$	−3.00000	+	5.19615i	−0.279751	+	0.484544i
$116$	14.6969	+	25.4558i	1.36458	+	2.36352i
$117$		0			0
$118$	−24.0000			−2.20938
$119$	4.89898	+	4.24264i	0.449089	+	0.388922i
$120$		0			0
$121$	−6.50000	−	11.2583i	−0.590909	−	1.02348i
$122$	12.2474			1.10883
$123$		0			0
$124$	−28.0000			−2.51447
$125$	−9.79796			−0.876356
$126$		0			0
$127$	11.0000			0.976092			0.488046	−	0.872818i	$-0.337710\pi$
$127$	11.0000			0.976092			0.488046	+	0.872818i	$0.337710\pi$
$128$	−19.5959			−1.73205
$129$		0			0
$130$	−24.0000			−2.10494
$131$	−1.22474	−	2.12132i	−0.107006	−	0.185341i	0.807550	−	0.589799i	$-0.200793\pi$
$131$	−1.22474	−	2.12132i	−0.107006	−	0.185341i	−0.914556	+	0.404459i	$0.867460\pi$
$132$		0			0
$133$	0.500000	−	2.59808i	0.0433555	−	0.225282i
$134$	4.89898			0.423207
$135$		0			0
$136$	6.00000	+	10.3923i	0.514496	+	0.891133i
$137$	8.57321	−	14.8492i	0.732459	−	1.26866i	−0.223370	−	0.974734i	$-0.571706\pi$
$137$	8.57321	−	14.8492i	0.732459	−	1.26866i	0.955829	−	0.293923i	$-0.0949608\pi$
$138$		0			0
$139$	−7.00000	+	12.1244i	−0.593732	+	1.02837i	0.399992	+	0.916519i	$0.369013\pi$
$139$	−7.00000	+	12.1244i	−0.593732	+	1.02837i	−0.993724	+	0.111856i	$0.964321\pi$
$140$	−19.5959	−	16.9706i	−1.65616	−	1.43427i
$141$		0			0
$142$		0			0
$143$	9.79796	+	16.9706i	0.819346	+	1.41915i
$144$		0			0
$145$	9.00000	−	15.5885i	0.747409	−	1.29455i
$146$	1.22474	+	2.12132i	0.101361	+	0.175562i
$147$		0			0
$148$	−16.0000	+	27.7128i	−1.31519	+	2.27798i
$149$	−1.22474	−	2.12132i	−0.100335	−	0.173785i	0.811488	−	0.584370i	$-0.198658\pi$
$149$	−1.22474	−	2.12132i	−0.100335	−	0.173785i	−0.911823	+	0.410584i	$0.865325\pi$
$150$		0			0
$151$	−2.50000	+	4.33013i	−0.203447	+	0.352381i	−0.949637	−	0.313353i	$-0.898548\pi$
$151$	−2.50000	+	4.33013i	−0.203447	+	0.352381i	0.746190	+	0.665733i	$0.231881\pi$
$152$	2.44949	−	4.24264i	0.198680	−	0.344124i
$153$		0			0
$154$	−6.00000	+	31.1769i	−0.483494	+	2.51231i
$155$	8.57321	+	14.8492i	0.688617	+	1.19272i
$156$		0			0
$157$	20.0000			1.59617			0.798087	−	0.602542i	$-0.205846\pi$
$157$	20.0000			1.59617			0.798087	+	0.602542i	$0.205846\pi$
$158$	−9.79796			−0.779484
$159$		0			0
$160$		0			0
$161$	−4.89898	−	4.24264i	−0.386094	−	0.334367i
$162$		0			0
$163$	0.500000	−	0.866025i	0.0391630	−	0.0678323i	−0.845780	−	0.533533i	$-0.820864\pi$
$163$	0.500000	−	0.866025i	0.0391630	−	0.0678323i	0.884943	+	0.465700i	$0.154198\pi$
$164$	−14.6969	+	25.4558i	−1.14764	+	1.98777i
$165$		0			0
$166$	−18.0000	−	31.1769i	−1.39707	−	2.41980i
$167$	7.34847	−	12.7279i	0.568642	−	0.984916i	−0.428059	−	0.903751i	$-0.640802\pi$
$167$	7.34847	−	12.7279i	0.568642	−	0.984916i	0.996701	−	0.0811654i	$-0.0258642\pi$
$168$		0			0
$169$	−1.50000	−	2.59808i	−0.115385	−	0.199852i
$170$	7.34847	−	12.7279i	0.563602	−	0.976187i
$171$		0			0
$172$	2.00000	+	3.46410i	0.152499	+	0.264135i
$173$	2.44949			0.186231			0.0931156	−	0.995655i	$-0.470317\pi$
$173$	2.44949			0.186231			0.0931156	+	0.995655i	$0.470317\pi$
$174$		0			0
$175$	−0.500000	+	2.59808i	−0.0377964	+	0.196396i
$176$	−9.79796	+	16.9706i	−0.738549	+	1.27920i
$177$		0			0
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	1.22474	+	2.12132i	0.0915417	+	0.158555i	0.908160	−	0.418623i	$-0.137487\pi$
$179$	1.22474	+	2.12132i	0.0915417	+	0.158555i	−0.816618	+	0.577178i	$0.804154\pi$
$180$		0			0
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$	4.89898	−	25.4558i	0.363137	−	1.88691i
$183$		0			0
$184$	−6.00000	−	10.3923i	−0.442326	−	0.766131i
$185$	19.5959			1.44072
$186$		0			0
$187$	−12.0000			−0.877527
$188$	9.79796			0.714590
$189$		0			0
$190$	−6.00000			−0.435286
$191$	2.44949			0.177239			0.0886194	−	0.996066i	$-0.471755\pi$
$191$	2.44949			0.177239			0.0886194	+	0.996066i	$0.471755\pi$
$192$		0			0
$193$	20.0000			1.43963			0.719816	−	0.694165i	$-0.244226\pi$
$193$	20.0000			1.43963			0.719816	+	0.694165i	$0.244226\pi$
$194$	1.22474	+	2.12132i	0.0879316	+	0.152302i
$195$		0			0
$196$	22.0000	−	17.3205i	1.57143	−	1.23718i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$		0			0
$199$	9.50000	+	16.4545i	0.673437	+	1.16643i	0.976923	+	0.213591i	$0.0685161\pi$
$199$	9.50000	+	16.4545i	0.673437	+	1.16643i	−0.303486	+	0.952836i	$0.598151\pi$
$200$	−2.44949	+	4.24264i	−0.173205	+	0.300000i
$201$		0			0
$202$	−6.00000	+	10.3923i	−0.422159	+	0.731200i
$203$	14.6969	+	12.7279i	1.03152	+	0.893325i
$204$		0			0
$205$	18.0000			1.25717
$206$	−2.44949	−	4.24264i	−0.170664	−	0.295599i
$207$		0			0
$208$	8.00000	−	13.8564i	0.554700	−	0.960769i
$209$	2.44949	+	4.24264i	0.169435	+	0.293470i
$210$		0			0
$211$	−2.50000	+	4.33013i	−0.172107	+	0.298098i	−0.939156	−	0.343490i	$-0.888391\pi$
$211$	−2.50000	+	4.33013i	−0.172107	+	0.298098i	0.767049	+	0.641588i	$0.221724\pi$
$212$	4.89898	+	8.48528i	0.336463	+	0.582772i
$213$		0			0
$214$	24.0000	−	41.5692i	1.64061	−	2.84161i
$215$	1.22474	−	2.12132i	0.0835269	−	0.144673i
$216$		0			0
$217$	−17.5000	+	6.06218i	−1.18798	+	0.411527i
$218$	1.22474	+	2.12132i	0.0829502	+	0.143674i
$219$		0			0
$220$	48.0000			3.23616
$221$	9.79796			0.659082
$222$		0			0
$223$	−13.0000	−	22.5167i	−0.870544	−	1.50783i	−0.861435	−	0.507869i	$-0.830434\pi$
$223$	−13.0000	−	22.5167i	−0.870544	−	1.50783i	−0.00910984	−	0.999959i	$-0.502900\pi$
$224$		0			0
$225$		0			0
$226$	18.0000	−	31.1769i	1.19734	−	2.07386i
$227$	8.57321	−	14.8492i	0.569024	−	0.985579i	−0.427639	−	0.903950i	$-0.640654\pi$
$227$	8.57321	−	14.8492i	0.569024	−	0.985579i	0.996663	−	0.0816290i	$-0.0260123\pi$
$228$		0			0
$229$	3.50000	+	6.06218i	0.231287	+	0.400600i	0.958187	−	0.286143i	$-0.0923732\pi$
$229$	3.50000	+	6.06218i	0.231287	+	0.400600i	−0.726900	+	0.686743i	$0.759040\pi$
$230$	−7.34847	+	12.7279i	−0.484544	+	0.839254i
$231$		0			0
$232$	18.0000	+	31.1769i	1.18176	+	2.04686i
$233$	−1.22474	+	2.12132i	−0.0802357	+	0.138972i	−0.903351	−	0.428902i	$-0.858901\pi$
$233$	−1.22474	+	2.12132i	−0.0802357	+	0.138972i	0.823115	+	0.567874i	$0.192234\pi$
$234$		0			0
$235$	−3.00000	−	5.19615i	−0.195698	−	0.338960i
$236$	−39.1918			−2.55117
$237$		0			0
$238$	12.0000	+	10.3923i	0.777844	+	0.673633i
$239$	−3.67423	+	6.36396i	−0.237666	+	0.411650i	−0.960044	−	0.279848i	$-0.909716\pi$
$239$	−3.67423	+	6.36396i	−0.237666	+	0.411650i	0.722378	+	0.691499i	$0.243049\pi$
$240$		0			0
$241$	6.50000	−	11.2583i	0.418702	−	0.725213i	−0.577107	−	0.816668i	$-0.695819\pi$
$241$	6.50000	−	11.2583i	0.418702	−	0.725213i	0.995809	+	0.0914555i	$0.0291519\pi$
$242$	−15.9217	−	27.5772i	−1.02348	−	1.77273i
$243$		0			0
$244$	20.0000			1.28037
$245$	−15.9217	−	6.36396i	−1.01720	−	0.406579i
$246$		0			0
$247$	−2.00000	−	3.46410i	−0.127257	−	0.220416i
$248$	−34.2929			−2.17760
$249$		0			0
$250$	−24.0000			−1.51789
$251$	−22.0454			−1.39149			−0.695747	−	0.718287i	$-0.744926\pi$
$251$	−22.0454			−1.39149			−0.695747	+	0.718287i	$0.744926\pi$
$252$		0			0
$253$	12.0000			0.754434
$254$	26.9444			1.69064
$255$		0			0
$256$	−32.0000			−2.00000
$257$	−12.2474	−	21.2132i	−0.763975	−	1.32324i	−0.940787	−	0.338999i	$-0.889912\pi$
$257$	−12.2474	−	21.2132i	−0.763975	−	1.32324i	0.176812	−	0.984245i	$-0.443422\pi$
$258$		0			0
$259$	−4.00000	+	20.7846i	−0.248548	+	1.29149i
$260$	−39.1918			−2.43057
$261$		0			0
$262$	−3.00000	−	5.19615i	−0.185341	−	0.321019i
$263$	−2.44949	+	4.24264i	−0.151042	+	0.261612i	−0.931611	−	0.363457i	$-0.881596\pi$
$263$	−2.44949	+	4.24264i	−0.151042	+	0.261612i	0.780569	+	0.625070i	$0.214930\pi$
$264$		0			0
$265$	3.00000	−	5.19615i	0.184289	−	0.319197i
$266$	1.22474	−	6.36396i	0.0750939	−	0.390199i
$267$		0			0
$268$	8.00000			0.488678
$269$	12.2474	+	21.2132i	0.746740	+	1.29339i	0.949377	+	0.314138i	$0.101715\pi$
$269$	12.2474	+	21.2132i	0.746740	+	1.29339i	−0.202637	+	0.979254i	$0.564951\pi$
$270$		0			0
$271$	0.500000	−	0.866025i	0.0303728	−	0.0526073i	−0.850439	−	0.526073i	$-0.823664\pi$
$271$	0.500000	−	0.866025i	0.0303728	−	0.0526073i	0.880812	+	0.473466i	$0.156997\pi$
$272$	4.89898	+	8.48528i	0.297044	+	0.514496i
$273$		0			0
$274$	21.0000	−	36.3731i	1.26866	−	2.19738i
$275$	−2.44949	−	4.24264i	−0.147710	−	0.255841i
$276$		0			0
$277$	−11.5000	+	19.9186i	−0.690968	+	1.19679i	0.280553	+	0.959839i	$0.409482\pi$
$277$	−11.5000	+	19.9186i	−0.690968	+	1.19679i	−0.971521	+	0.236953i	$0.923851\pi$
$278$	−17.1464	+	29.6985i	−1.02837	+	1.78120i
$279$		0			0
$280$	−24.0000	−	20.7846i	−1.43427	−	1.24212i
$281$	−7.34847	−	12.7279i	−0.438373	−	0.759284i	0.559191	−	0.829039i	$-0.311112\pi$
$281$	−7.34847	−	12.7279i	−0.438373	−	0.759284i	−0.997564	+	0.0697545i	$0.977778\pi$
$282$		0			0
$283$	−25.0000			−1.48610			−0.743048	−	0.669238i	$-0.766621\pi$
$283$	−25.0000			−1.48610			−0.743048	+	0.669238i	$0.766621\pi$
$284$		0			0
$285$		0			0
$286$	24.0000	+	41.5692i	1.41915	+	2.45804i
$287$	−3.67423	+	19.0919i	−0.216883	+	1.12696i
$288$		0			0
$289$	5.50000	−	9.52628i	0.323529	−	0.560369i
$290$	22.0454	−	38.1838i	1.29455	−	2.24223i
$291$		0			0
$292$	2.00000	+	3.46410i	0.117041	+	0.202721i
$293$	−14.6969	+	25.4558i	−0.858604	+	1.48715i	0.0146561	+	0.999893i	$0.495335\pi$
$293$	−14.6969	+	25.4558i	−0.858604	+	1.48715i	−0.873260	+	0.487254i	$0.837999\pi$
$294$		0			0
$295$	12.0000	+	20.7846i	0.698667	+	1.21013i
$296$	−19.5959	+	33.9411i	−1.13899	+	1.97279i
$297$		0			0
$298$	−3.00000	−	5.19615i	−0.173785	−	0.301005i
$299$	−9.79796			−0.566631
$300$		0			0
$301$	2.00000	+	1.73205i	0.115278	+	0.0998337i
$302$	−6.12372	+	10.6066i	−0.352381	+	0.610341i
$303$		0			0
$304$	2.00000	−	3.46410i	0.114708	−	0.198680i
$305$	−6.12372	−	10.6066i	−0.350643	−	0.607332i
$306$		0			0
$307$	−25.0000			−1.42683			−0.713413	−	0.700744i	$-0.752851\pi$
$307$	−25.0000			−1.42683			−0.713413	+	0.700744i	$0.752851\pi$
$308$	−9.79796	+	50.9117i	−0.558291	+	2.90096i
$309$		0			0
$310$	21.0000	+	36.3731i	1.19272	+	2.06585i
$311$	34.2929			1.94457			0.972285	−	0.233800i	$-0.0751161\pi$
$311$	34.2929			1.94457			0.972285	+	0.233800i	$0.0751161\pi$
$312$		0			0
$313$	23.0000			1.30004			0.650018	−	0.759918i	$-0.274761\pi$
$313$	23.0000			1.30004			0.650018	+	0.759918i	$0.274761\pi$
$314$	48.9898			2.76465
$315$		0			0
$316$	−16.0000			−0.900070
$317$	24.4949			1.37577			0.687885	−	0.725819i	$-0.258539\pi$
$317$	24.4949			1.37577			0.687885	+	0.725819i	$0.258539\pi$
$318$		0			0
$319$	−36.0000			−2.01561
$320$	9.79796	+	16.9706i	0.547723	+	0.948683i
$321$		0			0
$322$	−12.0000	−	10.3923i	−0.668734	−	0.579141i
$323$	2.44949			0.136293
$324$		0			0
$325$	2.00000	+	3.46410i	0.110940	+	0.192154i
$326$	1.22474	−	2.12132i	0.0678323	−	0.117489i
$327$		0			0
$328$	−18.0000	+	31.1769i	−0.993884	+	1.72146i
$329$	6.12372	−	2.12132i	0.337612	−	0.116952i
$330$		0			0
$331$	−13.0000			−0.714545			−0.357272	−	0.934000i	$-0.616293\pi$
$331$	−13.0000			−0.714545			−0.357272	+	0.934000i	$0.616293\pi$
$332$	−29.3939	−	50.9117i	−1.61320	−	2.79414i
$333$		0			0
$334$	18.0000	−	31.1769i	0.984916	−	1.70592i
$335$	−2.44949	−	4.24264i	−0.133830	−	0.231800i
$336$		0			0
$337$	−2.50000	+	4.33013i	−0.136184	+	0.235877i	−0.926049	−	0.377403i	$-0.876817\pi$
$337$	−2.50000	+	4.33013i	−0.136184	+	0.235877i	0.789865	+	0.613280i	$0.210150\pi$
$338$	−3.67423	−	6.36396i	−0.199852	−	0.346154i
$339$		0			0
$340$	12.0000	−	20.7846i	0.650791	−	1.12720i
$341$	17.1464	−	29.6985i	0.928531	−	1.60826i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	2.44949	+	4.24264i	0.132068	+	0.228748i
$345$		0			0
$346$	6.00000			0.322562
$347$	−9.79796			−0.525982			−0.262991	−	0.964798i	$-0.584709\pi$
$347$	−9.79796			−0.525982			−0.262991	+	0.964798i	$0.584709\pi$
$348$		0			0
$349$	−17.5000	−	30.3109i	−0.936754	−	1.62250i	−0.771477	−	0.636257i	$-0.780482\pi$
$349$	−17.5000	−	30.3109i	−0.936754	−	1.62250i	−0.165277	−	0.986247i	$-0.552852\pi$
$350$	−1.22474	+	6.36396i	−0.0654654	+	0.340168i
$351$		0			0
$352$		0			0
$353$	−2.44949	+	4.24264i	−0.130373	+	0.225813i	−0.923820	−	0.382826i	$-0.874951\pi$
$353$	−2.44949	+	4.24264i	−0.130373	+	0.225813i	0.793447	+	0.608639i	$0.208284\pi$
$354$		0			0
$355$		0			0
$356$	−4.89898	+	8.48528i	−0.259645	+	0.449719i
$357$		0			0
$358$	3.00000	+	5.19615i	0.158555	+	0.274625i
$359$	9.79796	−	16.9706i	0.517116	−	0.895672i	−0.482686	−	0.875794i	$-0.660339\pi$
$359$	9.79796	−	16.9706i	0.517116	−	0.895672i	0.999802	−	0.0198785i	$-0.00632794\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	−17.1464			−0.901196
$363$		0			0
$364$	8.00000	−	41.5692i	0.419314	−	2.17882i
$365$	1.22474	−	2.12132i	0.0641061	−	0.111035i
$366$		0			0
$367$	6.50000	−	11.2583i	0.339297	−	0.587680i	−0.645003	−	0.764180i	$-0.723144\pi$
$367$	6.50000	−	11.2583i	0.339297	−	0.587680i	0.984301	+	0.176500i	$0.0564774\pi$
$368$	−4.89898	−	8.48528i	−0.255377	−	0.442326i
$369$		0			0
$370$	48.0000			2.49540
$371$	4.89898	+	4.24264i	0.254342	+	0.220267i
$372$		0			0
$373$	−5.50000	−	9.52628i	−0.284779	−	0.493252i	0.687776	−	0.725923i	$-0.258587\pi$
$373$	−5.50000	−	9.52628i	−0.284779	−	0.493252i	−0.972556	+	0.232671i	$0.925254\pi$
$374$	−29.3939			−1.51992
$375$		0			0
$376$	12.0000			0.618853
$377$	29.3939			1.51386
$378$		0			0
$379$	−34.0000			−1.74646			−0.873231	−	0.487306i	$-0.837980\pi$
$379$	−34.0000			−1.74646			−0.873231	+	0.487306i	$0.837980\pi$
$380$	−9.79796			−0.502625
$381$		0			0
$382$	6.00000			0.306987
$383$	9.79796	+	16.9706i	0.500652	+	0.867155i	1.00000		0.000753393i	$0.000239813\pi$
$383$	9.79796	+	16.9706i	0.500652	+	0.867155i	−0.499347	+	0.866402i	$0.666427\pi$
$384$		0			0
$385$	30.0000	−	10.3923i	1.52894	−	0.529641i
$386$	48.9898			2.49351
$387$		0			0
$388$	2.00000	+	3.46410i	0.101535	+	0.175863i
$389$	8.57321	−	14.8492i	0.434679	−	0.752886i	−0.562590	−	0.826736i	$-0.690195\pi$
$389$	8.57321	−	14.8492i	0.434679	−	0.752886i	0.997269	+	0.0738494i	$0.0235284\pi$
$390$		0			0
$391$	3.00000	−	5.19615i	0.151717	−	0.262781i
$392$	26.9444	−	21.2132i	1.36090	−	1.07143i
$393$		0			0
$394$		0			0
$395$	4.89898	+	8.48528i	0.246494	+	0.426941i
$396$		0			0
$397$	−8.50000	+	14.7224i	−0.426603	+	0.738898i	−0.996569	−	0.0827707i	$-0.973623\pi$
$397$	−8.50000	+	14.7224i	−0.426603	+	0.738898i	0.569966	+	0.821668i	$0.306956\pi$
$398$	23.2702	+	40.3051i	1.16643	+	2.02031i
$399$		0			0
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	−12.2474	−	21.2132i	−0.611608	−	1.05934i	−0.990969	−	0.134088i	$-0.957189\pi$
$401$	−12.2474	−	21.2132i	−0.611608	−	1.05934i	0.379361	−	0.925249i	$-0.376144\pi$
$402$		0			0
$403$	−14.0000	+	24.2487i	−0.697390	+	1.20791i
$404$	−9.79796	+	16.9706i	−0.487467	+	0.844317i
$405$		0			0
$406$	36.0000	+	31.1769i	1.78665	+	1.54728i
$407$	−19.5959	−	33.9411i	−0.971334	−	1.68240i
$408$		0			0
$409$	20.0000			0.988936			0.494468	−	0.869196i	$-0.335363\pi$
$409$	20.0000			0.988936			0.494468	+	0.869196i	$0.335363\pi$
$410$	44.0908			2.17749
$411$		0			0
$412$	−4.00000	−	6.92820i	−0.197066	−	0.341328i
$413$	−24.4949	+	8.48528i	−1.20532	+	0.417533i
$414$		0			0
$415$	−18.0000	+	31.1769i	−0.883585	+	1.53041i
$416$		0			0
$417$		0			0
$418$	6.00000	+	10.3923i	0.293470	+	0.508304i
$419$	−3.67423	+	6.36396i	−0.179498	+	0.310900i	−0.941709	−	0.336429i	$-0.890781\pi$
$419$	−3.67423	+	6.36396i	−0.179498	+	0.310900i	0.762211	+	0.647329i	$0.224114\pi$
$420$		0			0
$421$	−17.5000	−	30.3109i	−0.852898	−	1.47726i	−0.878582	−	0.477592i	$-0.841510\pi$
$421$	−17.5000	−	30.3109i	−0.852898	−	1.47726i	0.0256838	−	0.999670i	$-0.491824\pi$
$422$	−6.12372	+	10.6066i	−0.298098	+	0.516321i
$423$		0			0
$424$	6.00000	+	10.3923i	0.291386	+	0.504695i
$425$	−2.44949			−0.118818
$426$		0			0
$427$	12.5000	−	4.33013i	0.604917	−	0.209550i
$428$	39.1918	−	67.8823i	1.89441	−	3.28121i
$429$		0			0
$430$	3.00000	−	5.19615i	0.144673	−	0.250581i
$431$	−9.79796	−	16.9706i	−0.471951	−	0.817443i	0.527534	−	0.849534i	$-0.323117\pi$
$431$	−9.79796	−	16.9706i	−0.471951	−	0.817443i	−0.999485	+	0.0320907i	$0.989783\pi$
$432$		0			0
$433$	−7.00000			−0.336399			−0.168199	−	0.985753i	$-0.553795\pi$
$433$	−7.00000			−0.336399			−0.168199	+	0.985753i	$0.553795\pi$
$434$	−42.8661	+	14.8492i	−2.05764	+	0.712786i
$435$		0			0
$436$	2.00000	+	3.46410i	0.0957826	+	0.165900i
$437$	−2.44949			−0.117175
$438$		0			0
$439$	14.0000			0.668184			0.334092	−	0.942541i	$-0.391570\pi$
$439$	14.0000			0.668184			0.334092	+	0.942541i	$0.391570\pi$
$440$	58.7878			2.80260
$441$		0			0
$442$	24.0000			1.14156
$443$	2.44949			0.116379			0.0581894	−	0.998306i	$-0.481467\pi$
$443$	2.44949			0.116379			0.0581894	+	0.998306i	$0.481467\pi$
$444$		0			0
$445$	6.00000			0.284427
$446$	−31.8434	−	55.1543i	−1.50783	−	2.61163i
$447$		0			0
$448$	−20.0000	+	6.92820i	−0.944911	+	0.327327i
$449$	22.0454			1.04039			0.520194	−	0.854048i	$-0.325860\pi$
$449$	22.0454			1.04039			0.520194	+	0.854048i	$0.325860\pi$
$450$		0			0
$451$	−18.0000	−	31.1769i	−0.847587	−	1.46806i
$452$	29.3939	−	50.9117i	1.38257	−	2.39468i
$453$		0			0
$454$	21.0000	−	36.3731i	0.985579	−	1.70707i
$455$	−24.4949	+	8.48528i	−1.14834	+	0.397796i
$456$		0			0
$457$	23.0000			1.07589			0.537947	−	0.842978i	$-0.319200\pi$
$457$	23.0000			1.07589			0.537947	+	0.842978i	$0.319200\pi$
$458$	8.57321	+	14.8492i	0.400600	+	0.693860i
$459$		0			0
$460$	−12.0000	+	20.7846i	−0.559503	+	0.969087i
$461$	14.6969	+	25.4558i	0.684505	+	1.18560i	0.973592	+	0.228294i	$0.0733148\pi$
$461$	14.6969	+	25.4558i	0.684505	+	1.18560i	−0.289088	+	0.957303i	$0.593352\pi$
$462$		0			0
$463$	−11.5000	+	19.9186i	−0.534450	+	0.925695i	0.464739	+	0.885448i	$0.346148\pi$
$463$	−11.5000	+	19.9186i	−0.534450	+	0.925695i	−0.999190	+	0.0402476i	$0.987185\pi$
$464$	14.6969	+	25.4558i	0.682288	+	1.18176i
$465$		0			0
$466$	−3.00000	+	5.19615i	−0.138972	+	0.240707i
$467$	−12.2474	+	21.2132i	−0.566744	+	0.981630i	0.430141	+	0.902762i	$0.358464\pi$
$467$	−12.2474	+	21.2132i	−0.566744	+	0.981630i	−0.996885	+	0.0788681i	$0.974869\pi$
$468$		0			0
$469$	5.00000	−	1.73205i	0.230879	−	0.0799787i
$470$	−7.34847	−	12.7279i	−0.338960	−	0.587095i
$471$		0			0
$472$	−48.0000			−2.20938
$473$	−4.89898			−0.225255
$474$		0			0
$475$	0.500000	+	0.866025i	0.0229416	+	0.0397360i
$476$	19.5959	+	16.9706i	0.898177	+	0.777844i
$477$		0			0
$478$	−9.00000	+	15.5885i	−0.411650	+	0.712999i
$479$	−13.4722	+	23.3345i	−0.615560	+	1.06618i	0.374726	+	0.927136i	$0.377737\pi$
$479$	−13.4722	+	23.3345i	−0.615560	+	1.06618i	−0.990286	+	0.139046i	$0.955596\pi$
$480$		0			0
$481$	16.0000	+	27.7128i	0.729537	+	1.26360i
$482$	15.9217	−	27.5772i	0.725213	−	1.25611i
$483$		0			0
$484$	−26.0000	−	45.0333i	−1.18182	−	2.04697i
$485$	1.22474	−	2.12132i	0.0556128	−	0.0963242i
$486$		0			0
$487$	9.50000	+	16.4545i	0.430486	+	0.745624i	0.996915	−	0.0784867i	$-0.0250088\pi$
$487$	9.50000	+	16.4545i	0.430486	+	0.745624i	−0.566429	+	0.824110i	$0.691675\pi$
$488$	24.4949			1.10883
$489$		0			0
$490$	−39.0000	−	15.5885i	−1.76184	−	0.704215i
$491$	7.34847	−	12.7279i	0.331632	−	0.574403i	−0.651200	−	0.758906i	$-0.725734\pi$
$491$	7.34847	−	12.7279i	0.331632	−	0.574403i	0.982832	+	0.184503i	$0.0590675\pi$
$492$		0			0
$493$	−9.00000	+	15.5885i	−0.405340	+	0.702069i
$494$	−4.89898	−	8.48528i	−0.220416	−	0.381771i
$495$		0			0
$496$	−28.0000			−1.25724
$497$		0			0
$498$		0			0
$499$	3.50000	+	6.06218i	0.156682	+	0.271380i	0.933670	−	0.358134i	$-0.116587\pi$
$499$	3.50000	+	6.06218i	0.156682	+	0.271380i	−0.776989	+	0.629515i	$0.783254\pi$
$500$	−39.1918			−1.75271
$501$		0			0
$502$	−54.0000			−2.41014
$503$	−22.0454			−0.982956			−0.491478	−	0.870890i	$-0.663543\pi$
$503$	−22.0454			−0.982956			−0.491478	+	0.870890i	$0.663543\pi$
$504$		0			0
$505$	12.0000			0.533993
$506$	29.3939			1.30672
$507$		0			0
$508$	44.0000			1.95218
$509$	9.79796	+	16.9706i	0.434287	+	0.752207i	0.997237	−	0.0742838i	$-0.0236671\pi$
$509$	9.79796	+	16.9706i	0.434287	+	0.752207i	−0.562950	+	0.826491i	$0.690334\pi$
$510$		0			0
$511$	2.00000	+	1.73205i	0.0884748	+	0.0766214i
$512$	−39.1918			−1.73205
$513$		0			0
$514$	−30.0000	−	51.9615i	−1.32324	−	2.29192i
$515$	−2.44949	+	4.24264i	−0.107937	+	0.186953i
$516$		0			0
$517$	−6.00000	+	10.3923i	−0.263880	+	0.457053i
$518$	−9.79796	+	50.9117i	−0.430498	+	2.23693i
$519$		0			0
$520$	−48.0000			−2.10494
$521$	−9.79796	−	16.9706i	−0.429256	−	0.743494i	0.567551	−	0.823338i	$-0.307891\pi$
$521$	−9.79796	−	16.9706i	−0.429256	−	0.743494i	−0.996807	+	0.0798444i	$0.974558\pi$
$522$		0			0
$523$	−4.00000	+	6.92820i	−0.174908	+	0.302949i	−0.940129	−	0.340818i	$-0.889296\pi$
$523$	−4.00000	+	6.92820i	−0.174908	+	0.302949i	0.765222	+	0.643767i	$0.222629\pi$
$524$	−4.89898	−	8.48528i	−0.214013	−	0.370681i
$525$		0			0
$526$	−6.00000	+	10.3923i	−0.261612	+	0.453126i
$527$	−8.57321	−	14.8492i	−0.373455	−	0.646843i
$528$		0			0
$529$	8.50000	−	14.7224i	0.369565	−	0.640106i
$530$	7.34847	−	12.7279i	0.319197	−	0.552866i
$531$		0			0
$532$	2.00000	−	10.3923i	0.0867110	−	0.450564i
$533$	14.6969	+	25.4558i	0.636595	+	1.10262i
$534$		0			0
$535$	−48.0000			−2.07522
$536$	9.79796			0.423207
$537$		0			0
$538$	30.0000	+	51.9615i	1.29339	+	2.24022i
$539$	4.89898	+	33.9411i	0.211014	+	1.46195i
$540$		0			0
$541$	−17.5000	+	30.3109i	−0.752384	+	1.30317i	0.194281	+	0.980946i	$0.437763\pi$
$541$	−17.5000	+	30.3109i	−0.752384	+	1.30317i	−0.946664	+	0.322221i	$0.895571\pi$
$542$	1.22474	−	2.12132i	0.0526073	−	0.0911185i
$543$		0			0
$544$		0			0
$545$	1.22474	−	2.12132i	0.0524623	−	0.0908674i
$546$		0			0
$547$	18.5000	+	32.0429i	0.791003	+	1.37006i	0.925347	+	0.379122i	$0.123774\pi$
$547$	18.5000	+	32.0429i	0.791003	+	1.37006i	−0.134344	+	0.990935i	$0.542893\pi$
$548$	34.2929	−	59.3970i	1.46492	−	2.53731i
$549$		0			0
$550$	−6.00000	−	10.3923i	−0.255841	−	0.443129i
$551$	7.34847			0.313055
$552$		0			0
$553$	−10.0000	+	3.46410i	−0.425243	+	0.147309i
$554$	−28.1691	+	48.7904i	−1.19679	+	2.07290i
$555$		0			0
$556$	−28.0000	+	48.4974i	−1.18746	+	2.05675i
$557$	−20.8207	−	36.0624i	−0.882200	−	1.52801i	−0.848890	−	0.528570i	$-0.822728\pi$
$557$	−20.8207	−	36.0624i	−0.882200	−	1.52801i	−0.0333100	−	0.999445i	$-0.510605\pi$
$558$		0			0
$559$	4.00000			0.169182
$560$	−19.5959	−	16.9706i	−0.828079	−	0.717137i
$561$		0			0
$562$	−18.0000	−	31.1769i	−0.759284	−	1.31512i
$563$	12.2474			0.516168			0.258084	−	0.966122i	$-0.416909\pi$
$563$	12.2474			0.516168			0.258084	+	0.966122i	$0.416909\pi$
$564$		0			0
$565$	−36.0000			−1.51453
$566$	−61.2372			−2.57399
$567$		0			0
$568$		0			0
$569$	−19.5959			−0.821504			−0.410752	−	0.911747i	$-0.634734\pi$
$569$	−19.5959			−0.821504			−0.410752	+	0.911747i	$0.634734\pi$
$570$		0			0
$571$	29.0000			1.21361			0.606806	−	0.794850i	$-0.292450\pi$
$571$	29.0000			1.21361			0.606806	+	0.794850i	$0.292450\pi$
$572$	39.1918	+	67.8823i	1.63869	+	2.83830i
$573$		0			0
$574$	−9.00000	+	46.7654i	−0.375653	+	1.95195i
$575$	2.44949			0.102151
$576$		0			0
$577$	−4.00000	−	6.92820i	−0.166522	−	0.288425i	0.770673	−	0.637231i	$-0.219920\pi$
$577$	−4.00000	−	6.92820i	−0.166522	−	0.288425i	−0.937195	+	0.348806i	$0.886587\pi$
$578$	13.4722	−	23.3345i	0.560369	−	0.970588i
$579$		0			0
$580$	36.0000	−	62.3538i	1.49482	−	2.58910i
$581$	−29.3939	−	25.4558i	−1.21946	−	1.05609i
$582$		0			0
$583$	−12.0000			−0.496989
$584$	2.44949	+	4.24264i	0.101361	+	0.175562i
$585$		0			0
$586$	−36.0000	+	62.3538i	−1.48715	+	2.57581i
$587$	3.67423	+	6.36396i	0.151652	+	0.262669i	0.931835	−	0.362883i	$-0.118207\pi$
$587$	3.67423	+	6.36396i	0.151652	+	0.262669i	−0.780183	+	0.625551i	$0.784874\pi$
$588$		0			0
$589$	−3.50000	+	6.06218i	−0.144215	+	0.249788i
$590$	29.3939	+	50.9117i	1.21013	+	2.09600i
$591$		0			0
$592$	−16.0000	+	27.7128i	−0.657596	+	1.13899i
$593$	−12.2474	+	21.2132i	−0.502942	+	0.871122i	0.497052	+	0.867721i	$0.334416\pi$
$593$	−12.2474	+	21.2132i	−0.502942	+	0.871122i	−0.999994	+	0.00340097i	$0.998917\pi$
$594$		0			0
$595$	3.00000	−	15.5885i	0.122988	−	0.639064i
$596$	−4.89898	−	8.48528i	−0.200670	−	0.347571i
$597$		0			0
$598$	−24.0000			−0.981433
$599$	−31.8434			−1.30108			−0.650542	−	0.759470i	$-0.725458\pi$
$599$	−31.8434			−1.30108			−0.650542	+	0.759470i	$0.725458\pi$
$600$		0			0
$601$	−8.50000	−	14.7224i	−0.346722	−	0.600541i	0.638943	−	0.769254i	$-0.279372\pi$
$601$	−8.50000	−	14.7224i	−0.346722	−	0.600541i	−0.985665	+	0.168714i	$0.946039\pi$
$602$	4.89898	+	4.24264i	0.199667	+	0.172917i
$603$		0			0
$604$	−10.0000	+	17.3205i	−0.406894	+	0.704761i
$605$	−15.9217	+	27.5772i	−0.647308	+	1.12117i
$606$		0			0
$607$	−14.5000	−	25.1147i	−0.588537	−	1.01938i	−0.994424	−	0.105453i	$-0.966371\pi$
$607$	−14.5000	−	25.1147i	−0.588537	−	1.01938i	0.405887	−	0.913923i	$-0.366962\pi$
$608$		0			0
$609$		0			0
$610$	−15.0000	−	25.9808i	−0.607332	−	1.05193i
$611$	4.89898	−	8.48528i	0.198191	−	0.343278i
$612$		0			0
$613$	−8.50000	−	14.7224i	−0.343312	−	0.594633i	0.641734	−	0.766927i	$-0.278215\pi$
$613$	−8.50000	−	14.7224i	−0.343312	−	0.594633i	−0.985046	+	0.172294i	$0.944882\pi$
$614$	−61.2372			−2.47133
$615$		0			0
$616$	−12.0000	+	62.3538i	−0.483494	+	2.51231i
$617$	−14.6969	+	25.4558i	−0.591676	+	1.02481i	0.402330	+	0.915495i	$0.368200\pi$
$617$	−14.6969	+	25.4558i	−0.591676	+	1.02481i	−0.994007	+	0.109319i	$0.965133\pi$
$618$		0			0
$619$	−7.00000	+	12.1244i	−0.281354	+	0.487319i	−0.971718	−	0.236143i	$-0.924117\pi$
$619$	−7.00000	+	12.1244i	−0.281354	+	0.487319i	0.690365	+	0.723462i	$0.257450\pi$
$620$	34.2929	+	59.3970i	1.37723	+	2.38544i
$621$		0			0
$622$	84.0000			3.36809
$623$	−1.22474	+	6.36396i	−0.0490684	+	0.254967i
$624$		0			0
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	56.3383			2.25173
$627$		0			0
$628$	80.0000			3.19235
$629$	−19.5959			−0.781340
$630$		0			0
$631$	−25.0000			−0.995234			−0.497617	−	0.867397i	$-0.665792\pi$
$631$	−25.0000			−0.995234			−0.497617	+	0.867397i	$0.665792\pi$
$632$	−19.5959			−0.779484
$633$		0			0
$634$	60.0000			2.38290
$635$	−13.4722	−	23.3345i	−0.534628	−	0.926002i
$636$		0			0
$637$	−4.00000	−	27.7128i	−0.158486	−	1.09802i
$638$	−88.1816			−3.49114
$639$		0			0
$640$	24.0000	+	41.5692i	0.948683	+	1.64317i
$641$	−13.4722	+	23.3345i	−0.532120	+	0.921658i	0.467177	+	0.884164i	$0.345271\pi$
$641$	−13.4722	+	23.3345i	−0.532120	+	0.921658i	−0.999297	+	0.0374946i	$0.988062\pi$
$642$		0			0
$643$	−2.50000	+	4.33013i	−0.0985904	+	0.170764i	−0.911101	−	0.412182i	$-0.864767\pi$
$643$	−2.50000	+	4.33013i	−0.0985904	+	0.170764i	0.812511	+	0.582946i	$0.198100\pi$
$644$	−19.5959	−	16.9706i	−0.772187	−	0.668734i
$645$		0			0
$646$	6.00000			0.236067
$647$	−9.79796	−	16.9706i	−0.385198	−	0.667182i	0.606599	−	0.795008i	$-0.292533\pi$
$647$	−9.79796	−	16.9706i	−0.385198	−	0.667182i	−0.991797	+	0.127826i	$0.959200\pi$
$648$		0			0
$649$	24.0000	−	41.5692i	0.942082	−	1.63173i
$650$	4.89898	+	8.48528i	0.192154	+	0.332820i
$651$		0			0
$652$	2.00000	−	3.46410i	0.0783260	−	0.135665i
$653$	−1.22474	−	2.12132i	−0.0479280	−	0.0830137i	0.841066	−	0.540932i	$-0.181928\pi$
$653$	−1.22474	−	2.12132i	−0.0479280	−	0.0830137i	−0.888994	+	0.457919i	$0.848595\pi$
$654$		0			0
$655$	−3.00000	+	5.19615i	−0.117220	+	0.203030i
$656$	−14.6969	+	25.4558i	−0.573819	+	0.993884i
$657$		0			0
$658$	15.0000	−	5.19615i	0.584761	−	0.202567i
$659$	3.67423	+	6.36396i	0.143128	+	0.247905i	0.928673	−	0.370900i	$-0.120951\pi$
$659$	3.67423	+	6.36396i	0.143128	+	0.247905i	−0.785545	+	0.618804i	$0.787617\pi$
$660$		0			0
$661$	11.0000			0.427850			0.213925	−	0.976850i	$-0.431375\pi$
$661$	11.0000			0.427850			0.213925	+	0.976850i	$0.431375\pi$
$662$	−31.8434			−1.23763
$663$		0			0
$664$	−36.0000	−	62.3538i	−1.39707	−	2.41980i
$665$	−6.12372	+	2.12132i	−0.237468	+	0.0822613i
$666$		0			0
$667$	9.00000	−	15.5885i	0.348481	−	0.603587i
$668$	29.3939	−	50.9117i	1.13728	−	1.96983i
$669$		0			0
$670$	−6.00000	−	10.3923i	−0.231800	−	0.401490i
$671$	−12.2474	+	21.2132i	−0.472808	+	0.818927i
$672$		0			0
$673$	−8.50000	−	14.7224i	−0.327651	−	0.567508i	0.654394	−	0.756153i	$-0.272924\pi$
$673$	−8.50000	−	14.7224i	−0.327651	−	0.567508i	−0.982045	+	0.188645i	$0.939590\pi$
$674$	−6.12372	+	10.6066i	−0.235877	+	0.408551i
$675$		0			0
$676$	−6.00000	−	10.3923i	−0.230769	−	0.399704i
$677$	−19.5959			−0.753132			−0.376566	−	0.926390i	$-0.622895\pi$
$677$	−19.5959			−0.753132			−0.376566	+	0.926390i	$0.622895\pi$
$678$		0			0
$679$	2.00000	+	1.73205i	0.0767530	+	0.0664700i
$680$	14.6969	−	25.4558i	0.563602	−	0.976187i
$681$		0			0
$682$	42.0000	−	72.7461i	1.60826	−	2.78559i
$683$	12.2474	+	21.2132i	0.468636	+	0.811701i	0.999357	−	0.0358455i	$-0.0114124\pi$
$683$	12.2474	+	21.2132i	0.468636	+	0.811701i	−0.530722	+	0.847546i	$0.678079\pi$
$684$		0			0
$685$	−42.0000			−1.60474
$686$	24.4949	−	38.1838i	0.935220	−	1.45786i
$687$		0			0
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$	9.79796			0.373273
$690$		0			0
$691$	41.0000			1.55971			0.779857	−	0.625958i	$-0.215292\pi$
$691$	41.0000			1.55971			0.779857	+	0.625958i	$0.215292\pi$
$692$	9.79796			0.372463
$693$		0			0
$694$	−24.0000			−0.911028
$695$	34.2929			1.30080
$696$		0			0
$697$	−18.0000			−0.681799
$698$	−42.8661	−	74.2462i	−1.62250	−	2.81026i
$699$		0			0
$700$	−2.00000	+	10.3923i	−0.0755929	+	0.392792i
$701$	22.0454			0.832644			0.416322	−	0.909217i	$-0.363319\pi$
$701$	22.0454			0.832644			0.416322	+	0.909217i	$0.363319\pi$
$702$		0			0
$703$	4.00000	+	6.92820i	0.150863	+	0.261302i
$704$	19.5959	−	33.9411i	0.738549	−	1.27920i
$705$		0			0
$706$	−6.00000	+	10.3923i	−0.225813	+	0.391120i
$707$	−2.44949	+	12.7279i	−0.0921225	+	0.478683i
$708$		0			0
$709$	−49.0000			−1.84023			−0.920117	−	0.391644i	$-0.871906\pi$
$709$	−49.0000			−1.84023			−0.920117	+	0.391644i	$0.871906\pi$
$710$		0			0
$711$		0			0
$712$	−6.00000	+	10.3923i	−0.224860	+	0.389468i
$713$	8.57321	+	14.8492i	0.321069	+	0.556108i
$714$		0			0
$715$	24.0000	−	41.5692i	0.897549	−	1.55460i
$716$	4.89898	+	8.48528i	0.183083	+	0.317110i
$717$		0			0
$718$	24.0000	−	41.5692i	0.895672	−	1.55135i
$719$	9.79796	−	16.9706i	0.365402	−	0.632895i	−0.623438	−	0.781872i	$-0.714265\pi$
$719$	9.79796	−	16.9706i	0.365402	−	0.632895i	0.988841	+	0.148977i	$0.0475981\pi$
$720$		0			0
$721$	−4.00000	−	3.46410i	−0.148968	−	0.129010i
$722$	22.0454	+	38.1838i	0.820445	+	1.42105i
$723$		0			0
$724$	−28.0000			−1.04061
$725$	−7.34847			−0.272915
$726$		0			0
$727$	9.50000	+	16.4545i	0.352335	+	0.610263i	0.986658	−	0.162805i	$-0.0520543\pi$
$727$	9.50000	+	16.4545i	0.352335	+	0.610263i	−0.634323	+	0.773068i	$0.718721\pi$
$728$	9.79796	−	50.9117i	0.363137	−	1.88691i
$729$		0			0
$730$	3.00000	−	5.19615i	0.111035	−	0.192318i
$731$	−1.22474	+	2.12132i	−0.0452988	+	0.0784599i
$732$		0			0
$733$	−5.50000	−	9.52628i	−0.203147	−	0.351861i	0.746394	−	0.665505i	$-0.231784\pi$
$733$	−5.50000	−	9.52628i	−0.203147	−	0.351861i	−0.949541	+	0.313644i	$0.898450\pi$
$734$	15.9217	−	27.5772i	0.587680	−	1.01789i
$735$		0			0
$736$		0			0
$737$	−4.89898	+	8.48528i	−0.180456	+	0.312559i
$738$		0			0
$739$	9.50000	+	16.4545i	0.349463	+	0.605288i	0.986154	−	0.165831i	$-0.0530307\pi$
$739$	9.50000	+	16.4545i	0.349463	+	0.605288i	−0.636691	+	0.771119i	$0.719697\pi$
$740$	78.3837			2.88144
$741$		0			0
$742$	12.0000	+	10.3923i	0.440534	+	0.381514i
$743$	−3.67423	+	6.36396i	−0.134795	+	0.233471i	−0.925519	−	0.378701i	$-0.876371\pi$
$743$	−3.67423	+	6.36396i	−0.134795	+	0.233471i	0.790724	+	0.612172i	$0.209704\pi$
$744$		0			0
$745$	−3.00000	+	5.19615i	−0.109911	+	0.190372i
$746$	−13.4722	−	23.3345i	−0.493252	−	0.854338i
$747$		0			0
$748$	−48.0000			−1.75505
$749$	9.79796	−	50.9117i	0.358010	−	1.86027i
$750$		0			0
$751$	21.5000	+	37.2391i	0.784546	+	1.35887i	0.929270	+	0.369402i	$0.120437\pi$
$751$	21.5000	+	37.2391i	0.784546	+	1.35887i	−0.144724	+	0.989472i	$0.546229\pi$
$752$	9.79796			0.357295
$753$		0			0
$754$	72.0000			2.62209
$755$	12.2474			0.445730
$756$		0			0
$757$	47.0000			1.70824			0.854122	−	0.520073i	$-0.174095\pi$
$757$	47.0000			1.70824			0.854122	+	0.520073i	$0.174095\pi$
$758$	−83.2827			−3.02496
$759$		0			0
$760$	−12.0000			−0.435286
$761$	9.79796	+	16.9706i	0.355176	+	0.615182i	0.987148	−	0.159809i	$-0.0510877\pi$
$761$	9.79796	+	16.9706i	0.355176	+	0.615182i	−0.631972	+	0.774991i	$0.717754\pi$
$762$		0			0
$763$	2.00000	+	1.73205i	0.0724049	+	0.0627044i
$764$	9.79796			0.354478
$765$		0			0
$766$	24.0000	+	41.5692i	0.867155	+	1.50196i
$767$	−19.5959	+	33.9411i	−0.707568	+	1.22554i
$768$		0			0
$769$	−2.50000	+	4.33013i	−0.0901523	+	0.156148i	−0.907575	−	0.419890i	$-0.862069\pi$
$769$	−2.50000	+	4.33013i	−0.0901523	+	0.156148i	0.817423	+	0.576038i	$0.195402\pi$
$770$	73.4847	−	25.4558i	2.64820	−	0.917365i
$771$		0			0
$772$	80.0000			2.87926
$773$	23.2702	+	40.3051i	0.836969	+	1.44967i	0.892417	+	0.451212i	$0.149008\pi$
$773$	23.2702	+	40.3051i	0.836969	+	1.44967i	−0.0554478	+	0.998462i	$0.517659\pi$
$774$		0			0
$775$	3.50000	−	6.06218i	0.125724	−	0.217760i
$776$	2.44949	+	4.24264i	0.0879316	+	0.152302i
$777$		0			0
$778$	21.0000	−	36.3731i	0.752886	−	1.30404i
$779$	3.67423	+	6.36396i	0.131643	+	0.228013i
$780$		0			0
$781$		0			0
$782$	7.34847	−	12.7279i	0.262781	−	0.455150i
$783$		0			0
$784$	22.0000	−	17.3205i	0.785714	−	0.618590i
$785$	−24.4949	−	42.4264i	−0.874260	−	1.51426i
$786$		0			0
$787$	−7.00000			−0.249523			−0.124762	−	0.992187i	$-0.539817\pi$
$787$	−7.00000			−0.249523			−0.124762	+	0.992187i	$0.539817\pi$
$788$		0			0
$789$		0			0
$790$	12.0000	+	20.7846i	0.426941	+	0.739483i
$791$	7.34847	−	38.1838i	0.261281	−	1.35766i
$792$		0			0
$793$	10.0000	−	17.3205i	0.355110	−	0.615069i
$794$	−20.8207	+	36.0624i	−0.738898	+	1.27981i
$795$		0			0
$796$	38.0000	+	65.8179i	1.34687	+	2.33285i
$797$	7.34847	−	12.7279i	0.260296	−	0.450846i	−0.706024	−	0.708187i	$-0.749513\pi$
$797$	7.34847	−	12.7279i	0.260296	−	0.450846i	0.966321	+	0.257341i	$0.0828465\pi$
$798$		0			0
$799$	3.00000	+	5.19615i	0.106132	+	0.183827i
$800$		0			0
$801$		0			0
$802$	−30.0000	−	51.9615i	−1.05934	−	1.83483i
$803$	−4.89898			−0.172881
$804$		0			0
$805$	−3.00000	+	15.5885i	−0.105736	+	0.549421i
$806$	−34.2929	+	59.3970i	−1.20791	+	2.09217i
$807$		0			0
$808$	−12.0000	+	20.7846i	−0.422159	+	0.731200i
$809$	12.2474	+	21.2132i	0.430597	+	0.745817i	0.996925	−	0.0783638i	$-0.0249696\pi$
$809$	12.2474	+	21.2132i	0.430597	+	0.745817i	−0.566327	+	0.824180i	$0.691636\pi$
$810$		0			0
$811$	2.00000			0.0702295			0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000			0.0702295			0.0351147	+	0.999383i	$0.488820\pi$
$812$	58.7878	+	50.9117i	2.06305	+	1.78665i
$813$		0			0
$814$	−48.0000	−	83.1384i	−1.68240	−	2.91400i
$815$	−2.44949			−0.0858019
$816$		0			0
$817$	1.00000			0.0349856
$818$	48.9898			1.71289
$819$		0			0
$820$	72.0000			2.51435
$821$	−19.5959			−0.683902			−0.341951	−	0.939718i	$-0.611088\pi$
$821$	−19.5959			−0.683902			−0.341951	+	0.939718i	$0.611088\pi$
$822$		0			0
$823$	−25.0000			−0.871445			−0.435723	−	0.900081i	$-0.643507\pi$
$823$	−25.0000			−0.871445			−0.435723	+	0.900081i	$0.643507\pi$
$824$	−4.89898	−	8.48528i	−0.170664	−	0.295599i
$825$		0			0
$826$	−60.0000	+	20.7846i	−2.08767	+	0.723189i
$827$	44.0908			1.53319			0.766594	−	0.642132i	$-0.221950\pi$
$827$	44.0908			1.53319			0.766594	+	0.642132i	$0.221950\pi$
$828$		0			0
$829$	27.5000	+	47.6314i	0.955114	+	1.65431i	0.734106	+	0.679035i	$0.237602\pi$
$829$	27.5000	+	47.6314i	0.955114	+	1.65431i	0.221009	+	0.975272i	$0.429065\pi$
$830$	−44.0908	+	76.3675i	−1.53041	+	2.65076i
$831$		0			0
$832$	−16.0000	+	27.7128i	−0.554700	+	0.960769i
$833$	15.9217	+	6.36396i	0.551654	+	0.220498i
$834$		0			0
$835$	−36.0000			−1.24583
$836$	9.79796	+	16.9706i	0.338869	+	0.586939i
$837$		0			0
$838$	−9.00000	+	15.5885i	−0.310900	+	0.538494i
$839$	−7.34847	−	12.7279i	−0.253697	−	0.439417i	0.710844	−	0.703350i	$-0.248313\pi$
$839$	−7.34847	−	12.7279i	−0.253697	−	0.439417i	−0.964541	+	0.263933i	$0.914980\pi$
$840$		0			0
$841$	−12.5000	+	21.6506i	−0.431034	+	0.746574i
$842$	−42.8661	−	74.2462i	−1.47726	−	2.55869i
$843$		0			0
$844$	−10.0000	+	17.3205i	−0.344214	+	0.596196i
$845$	−3.67423	+	6.36396i	−0.126398	+	0.218927i
$846$		0			0
$847$	−26.0000	−	22.5167i	−0.893371	−	0.773682i
$848$	4.89898	+	8.48528i	0.168232	+	0.291386i
$849$		0			0
$850$	−6.00000			−0.205798
$851$	19.5959			0.671739
$852$		0			0
$853$	9.50000	+	16.4545i	0.325274	+	0.563391i	0.981568	−	0.191115i	$-0.0612102\pi$
$853$	9.50000	+	16.4545i	0.325274	+	0.563391i	−0.656294	+	0.754505i	$0.727877\pi$
$854$	30.6186	−	10.6066i	1.04775	−	0.362950i
$855$		0			0
$856$	48.0000	−	83.1384i	1.64061	−	2.84161i
$857$	19.5959	−	33.9411i	0.669384	−	1.15941i	−0.308693	−	0.951162i	$-0.599892\pi$
$857$	19.5959	−	33.9411i	0.669384	−	1.15941i	0.978077	−	0.208245i	$-0.0667751\pi$
$858$		0			0
$859$	12.5000	+	21.6506i	0.426494	+	0.738710i	0.996559	−	0.0828900i	$-0.0264150\pi$
$859$	12.5000	+	21.6506i	0.426494	+	0.738710i	−0.570064	+	0.821600i	$0.693082\pi$
$860$	4.89898	−	8.48528i	0.167054	−	0.289346i
$861$		0			0
$862$	−24.0000	−	41.5692i	−0.817443	−	1.41585i
$863$	−1.22474	+	2.12132i	−0.0416908	+	0.0722106i	−0.886118	−	0.463460i	$-0.846608\pi$
$863$	−1.22474	+	2.12132i	−0.0416908	+	0.0722106i	0.844427	+	0.535671i	$0.179941\pi$
$864$		0			0
$865$	−3.00000	−	5.19615i	−0.102003	−	0.176674i
$866$	−17.1464			−0.582659
$867$		0			0
$868$	−70.0000	+	24.2487i	−2.37595	+	0.823055i
$869$	9.79796	−	16.9706i	0.332373	−	0.575687i
$870$		0			0
$871$	4.00000	−	6.92820i	0.135535	−	0.234753i
$872$	2.44949	+	4.24264i	0.0829502	+	0.143674i
$873$		0			0
$874$	−6.00000			−0.202953
$875$	−24.4949	+	8.48528i	−0.828079	+	0.286855i
$876$		0			0
$877$	−23.5000	−	40.7032i	−0.793539	−	1.37445i	−0.923763	−	0.382965i	$-0.874903\pi$
$877$	−23.5000	−	40.7032i	−0.793539	−	1.37445i	0.130224	−	0.991485i	$-0.458430\pi$
$878$	34.2929			1.15733
$879$		0			0
$880$	48.0000			1.61808
$881$	−22.0454			−0.742729			−0.371364	−	0.928487i	$-0.621110\pi$
$881$	−22.0454			−0.742729			−0.371364	+	0.928487i	$0.621110\pi$
$882$		0			0
$883$	−7.00000			−0.235569			−0.117784	−	0.993039i	$-0.537579\pi$
$883$	−7.00000			−0.235569			−0.117784	+	0.993039i	$0.537579\pi$
$884$	39.1918			1.31816
$885$		0			0
$886$	6.00000			0.201574
$887$	9.79796	+	16.9706i	0.328983	+	0.569816i	0.982310	−	0.187260i	$-0.0599607\pi$
$887$	9.79796	+	16.9706i	0.328983	+	0.569816i	−0.653327	+	0.757076i	$0.726627\pi$
$888$		0			0
$889$	27.5000	−	9.52628i	0.922320	−	0.319501i
$890$	14.6969			0.492642
$891$		0			0
$892$	−52.0000	−	90.0666i	−1.74109	−	3.01565i
$893$	1.22474	−	2.12132i	0.0409845	−	0.0709873i
$894$		0			0
$895$	3.00000	−	5.19615i	0.100279	−	0.173688i
$896$	−48.9898	+	16.9706i	−1.63663	+	0.566947i
$897$		0			0
$898$	54.0000			1.80200
$899$	−25.7196	−	44.5477i	−0.857798	−	1.48575i
$900$		0			0
$901$	−3.00000	+	5.19615i	−0.0999445	+	0.173109i
$902$	−44.0908	−	76.3675i	−1.46806	−	2.54276i
$903$		0			0
$904$	36.0000	−	62.3538i	1.19734	−	2.07386i
$905$	8.57321	+	14.8492i	0.284983	+	0.493606i
$906$		0			0
$907$	−16.0000	+	27.7128i	−0.531271	+	0.920189i	0.468063	+	0.883695i	$0.344952\pi$
$907$	−16.0000	+	27.7128i	−0.531271	+	0.920189i	−0.999334	+	0.0364935i	$0.988381\pi$
$908$	34.2929	−	59.3970i	1.13805	−	1.97116i
$909$		0			0
$910$	−60.0000	+	20.7846i	−1.98898	+	0.689003i
$911$	3.67423	+	6.36396i	0.121733	+	0.210847i	0.920451	−	0.390858i	$-0.127822\pi$
$911$	3.67423	+	6.36396i	0.121733	+	0.210847i	−0.798718	+	0.601705i	$0.794488\pi$
$912$		0			0
$913$	72.0000			2.38285
$914$	56.3383			1.86350
$915$		0			0
$916$	14.0000	+	24.2487i	0.462573	+	0.801200i
$917$	−4.89898	−	4.24264i	−0.161779	−	0.140104i
$918$		0			0
$919$	0.500000	−	0.866025i	0.0164935	−	0.0285675i	−0.857661	−	0.514216i	$-0.828083\pi$
$919$	0.500000	−	0.866025i	0.0164935	−	0.0285675i	0.874154	+	0.485648i	$0.161416\pi$
$920$	−14.6969	+	25.4558i	−0.484544	+	0.839254i
$921$		0			0
$922$	36.0000	+	62.3538i	1.18560	+	2.05351i
$923$		0			0
$924$		0			0
$925$	−4.00000	−	6.92820i	−0.131519	−	0.227798i
$926$	−28.1691	+	48.7904i	−0.925695	+	1.60335i
$927$		0			0
$928$		0			0
$929$	46.5403			1.52694			0.763469	−	0.645845i	$-0.223495\pi$
$929$	46.5403			1.52694			0.763469	+	0.645845i	$0.223495\pi$
$930$		0			0
$931$	−1.00000	−	6.92820i	−0.0327737	−	0.227063i
$932$	−4.89898	+	8.48528i	−0.160471	+	0.277945i
$933$		0			0
$934$	−30.0000	+	51.9615i	−0.981630	+	1.70023i
$935$	14.6969	+	25.4558i	0.480641	+	0.832495i
$936$		0			0
$937$	−16.0000			−0.522697			−0.261349	−	0.965244i	$-0.584167\pi$
$937$	−16.0000			−0.522697			−0.261349	+	0.965244i	$0.584167\pi$
$938$	12.2474	−	4.24264i	0.399893	−	0.138527i
$939$		0			0
$940$	−12.0000	−	20.7846i	−0.391397	−	0.677919i
$941$	−9.79796			−0.319404			−0.159702	−	0.987165i	$-0.551053\pi$
$941$	−9.79796			−0.319404			−0.159702	+	0.987165i	$0.551053\pi$
$942$		0			0
$943$	18.0000			0.586161
$944$	−39.1918			−1.27559
$945$		0			0
$946$	−12.0000			−0.390154
$947$	46.5403			1.51236			0.756178	−	0.654366i	$-0.227064\pi$
$947$	46.5403			1.51236			0.756178	+	0.654366i	$0.227064\pi$
$948$		0			0
$949$	4.00000			0.129845
$950$	1.22474	+	2.12132i	0.0397360	+	0.0688247i
$951$		0			0
$952$	24.0000	+	20.7846i	0.777844	+	0.673633i
$953$	−22.0454			−0.714121			−0.357060	−	0.934081i	$-0.616221\pi$
$953$	−22.0454			−0.714121			−0.357060	+	0.934081i	$0.616221\pi$
$954$		0			0
$955$	−3.00000	−	5.19615i	−0.0970777	−	0.168144i
$956$	−14.6969	+	25.4558i	−0.475333	+	0.823301i
$957$		0			0
$958$	−33.0000	+	57.1577i	−1.06618	+	1.84668i
$959$	8.57321	−	44.5477i	0.276844	−	1.43852i
$960$		0			0
$961$	18.0000			0.580645
$962$	39.1918	+	67.8823i	1.26360	+	2.18861i
$963$		0			0
$964$	26.0000	−	45.0333i	0.837404	−	1.45043i
$965$	−24.4949	−	42.4264i	−0.788519	−	1.36575i
$966$		0			0
$967$	11.0000	−	19.0526i	0.353736	−	0.612689i	−0.633165	−	0.774017i	$-0.718244\pi$
$967$	11.0000	−	19.0526i	0.353736	−	0.612689i	0.986901	+	0.161328i	$0.0515777\pi$
$968$	−31.8434	−	55.1543i	−1.02348	−	1.77273i
$969$		0			0
$970$	3.00000	−	5.19615i	0.0963242	−	0.166838i
$971$	20.8207	−	36.0624i	0.668167	−	1.15730i	−0.310249	−	0.950655i	$-0.600413\pi$
$971$	20.8207	−	36.0624i	0.668167	−	1.15730i	0.978416	−	0.206644i	$-0.0662541\pi$
$972$		0			0
$973$	−7.00000	+	36.3731i	−0.224410	+	1.16607i
$974$	23.2702	+	40.3051i	0.745624	+	1.29146i
$975$		0			0
$976$	20.0000			0.640184
$977$	−9.79796			−0.313464			−0.156732	−	0.987641i	$-0.550096\pi$
$977$	−9.79796			−0.313464			−0.156732	+	0.987641i	$0.550096\pi$
$978$		0			0
$979$	−6.00000	−	10.3923i	−0.191761	−	0.332140i
$980$	−63.6867	−	25.4558i	−2.03440	−	0.813157i
$981$		0			0
$982$	18.0000	−	31.1769i	0.574403	−	0.994895i
$983$	19.5959	−	33.9411i	0.625013	−	1.08255i	−0.363526	−	0.931584i	$-0.618427\pi$
$983$	19.5959	−	33.9411i	0.625013	−	1.08255i	0.988538	−	0.150970i	$-0.0482396\pi$
$984$		0			0
$985$		0			0
$986$	−22.0454	+	38.1838i	−0.702069	+	1.21602i
$987$		0			0
$988$	−8.00000	−	13.8564i	−0.254514	−	0.440831i
$989$	1.22474	−	2.12132i	0.0389446	−	0.0674541i
$990$		0			0
$991$	5.00000	+	8.66025i	0.158830	+	0.275102i	0.934447	−	0.356102i	$-0.115894\pi$
$991$	5.00000	+	8.66025i	0.158830	+	0.275102i	−0.775617	+	0.631204i	$0.782561\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	23.2702	−	40.3051i	0.737713	−	1.27776i
$996$		0			0
$997$	−20.5000	+	35.5070i	−0.649242	+	1.12452i	0.334063	+	0.942551i	$0.391580\pi$
$997$	−20.5000	+	35.5070i	−0.649242	+	1.12452i	−0.983304	+	0.181968i	$0.941753\pi$
$998$	8.57321	+	14.8492i	0.271380	+	0.470045i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.h.g.352.2		4
3.2	odd	2	inner	567.2.h.g.352.1		4
7.4	even	3		567.2.g.g.109.1		4
9.2	odd	6		567.2.g.g.541.2		4
9.4	even	3		189.2.e.d.163.1	yes	4
9.5	odd	6		189.2.e.d.163.2	yes	4
9.7	even	3		567.2.g.g.541.1		4
21.11	odd	6		567.2.g.g.109.2		4
63.4	even	3		189.2.e.d.109.1	✓	4
63.5	even	6		1323.2.a.u.1.1		2
63.11	odd	6	inner	567.2.h.g.298.1		4
63.23	odd	6		1323.2.a.v.1.1		2
63.25	even	3	inner	567.2.h.g.298.2		4
63.32	odd	6		189.2.e.d.109.2	yes	4
63.40	odd	6		1323.2.a.u.1.2		2
63.58	even	3		1323.2.a.v.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.e.d.109.1	✓	4	63.4	even	3
189.2.e.d.109.2	yes	4	63.32	odd	6
189.2.e.d.163.1	yes	4	9.4	even	3
189.2.e.d.163.2	yes	4	9.5	odd	6
567.2.g.g.109.1		4	7.4	even	3
567.2.g.g.109.2		4	21.11	odd	6
567.2.g.g.541.1		4	9.7	even	3
567.2.g.g.541.2		4	9.2	odd	6
567.2.h.g.298.1		4	63.11	odd	6	inner
567.2.h.g.298.2		4	63.25	even	3	inner
567.2.h.g.352.1		4	3.2	odd	2	inner
567.2.h.g.352.2		4	1.1	even	1	trivial
1323.2.a.u.1.1		2	63.5	even	6
1323.2.a.u.1.2		2	63.40	odd	6
1323.2.a.v.1.1		2	63.23	odd	6
1323.2.a.v.1.2		2	63.58	even	3

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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.44949 q^{2} +4.00000 q^{4} +(-1.22474 - 2.12132i) q^{5} +(2.50000 - 0.866025i) q^{7} +4.89898 q^{8} +O(q^{10})\)	\(q+2.44949 q^{2} +4.00000 q^{4} +(-1.22474 - 2.12132i) q^{5} +(2.50000 - 0.866025i) q^{7} +4.89898 q^{8} +(-3.00000 - 5.19615i) q^{10} +(-2.44949 + 4.24264i) q^{11} +(2.00000 - 3.46410i) q^{13} +(6.12372 - 2.12132i) q^{14} +4.00000 q^{16} +(1.22474 + 2.12132i) q^{17} +(0.500000 - 0.866025i) q^{19} +(-4.89898 - 8.48528i) q^{20} +(-6.00000 + 10.3923i) q^{22} +(-1.22474 - 2.12132i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(4.89898 - 8.48528i) q^{26} +(10.0000 - 3.46410i) q^{28} +(3.67423 + 6.36396i) q^{29} -7.00000 q^{31} +(3.00000 + 5.19615i) q^{34} +(-4.89898 - 4.24264i) q^{35} +(-4.00000 + 6.92820i) q^{37} +(1.22474 - 2.12132i) q^{38} +(-6.00000 - 10.3923i) q^{40} +(-3.67423 + 6.36396i) q^{41} +(0.500000 + 0.866025i) q^{43} +(-9.79796 + 16.9706i) q^{44} +(-3.00000 - 5.19615i) q^{46} +2.44949 q^{47} +(5.50000 - 4.33013i) q^{49} +(-1.22474 + 2.12132i) q^{50} +(8.00000 - 13.8564i) q^{52} +(1.22474 + 2.12132i) q^{53} +12.0000 q^{55} +(12.2474 - 4.24264i) q^{56} +(9.00000 + 15.5885i) q^{58} -9.79796 q^{59} +5.00000 q^{61} -17.1464 q^{62} -8.00000 q^{64} -9.79796 q^{65} +2.00000 q^{67} +(4.89898 + 8.48528i) q^{68} +(-12.0000 - 10.3923i) q^{70} +(0.500000 + 0.866025i) q^{73} +(-9.79796 + 16.9706i) q^{74} +(2.00000 - 3.46410i) q^{76} +(-2.44949 + 12.7279i) q^{77} -4.00000 q^{79} +(-4.89898 - 8.48528i) q^{80} +(-9.00000 + 15.5885i) q^{82} +(-7.34847 - 12.7279i) q^{83} +(3.00000 - 5.19615i) q^{85} +(1.22474 + 2.12132i) q^{86} +(-12.0000 + 20.7846i) q^{88} +(-1.22474 + 2.12132i) q^{89} +(2.00000 - 10.3923i) q^{91} +(-4.89898 - 8.48528i) q^{92} +6.00000 q^{94} -2.44949 q^{95} +(0.500000 + 0.866025i) q^{97} +(13.4722 - 10.6066i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 16 q^{4} + 10 q^{7}+O(q^{10}) \) 4 * q + 16 * q^4 + 10 * q^7	\( 4 q + 16 q^{4} + 10 q^{7} - 12 q^{10} + 8 q^{13} + 16 q^{16} + 2 q^{19} - 24 q^{22} - 2 q^{25} + 40 q^{28} - 28 q^{31} + 12 q^{34} - 16 q^{37} - 24 q^{40} + 2 q^{43} - 12 q^{46} + 22 q^{49} + 32 q^{52} + 48 q^{55} + 36 q^{58} + 20 q^{61} - 32 q^{64} + 8 q^{67} - 48 q^{70} + 2 q^{73} + 8 q^{76} - 16 q^{79} - 36 q^{82} + 12 q^{85} - 48 q^{88} + 8 q^{91} + 24 q^{94} + 2 q^{97}+O(q^{100}) \) 4 * q + 16 * q^4 + 10 * q^7 - 12 * q^10 + 8 * q^13 + 16 * q^16 + 2 * q^19 - 24 * q^22 - 2 * q^25 + 40 * q^28 - 28 * q^31 + 12 * q^34 - 16 * q^37 - 24 * q^40 + 2 * q^43 - 12 * q^46 + 22 * q^49 + 32 * q^52 + 48 * q^55 + 36 * q^58 + 20 * q^61 - 32 * q^64 + 8 * q^67 - 48 * q^70 + 2 * q^73 + 8 * q^76 - 16 * q^79 - 36 * q^82 + 12 * q^85 - 48 * q^88 + 8 * q^91 + 24 * q^94 + 2 * q^97

Introduction

L-functions

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