LMFDB - Embedded newform 504.2.ch.a.341.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(269,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 1]))

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

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

chi := DirichletCharacter("504.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.ch (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.4857532416.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 7x^{6} - 2x^{5} + 98x^{4} - 98x^{3} + 67x^{2} - 30x + 9 $ x^8 - 2x^7 - 7x^6 - 2x^5 + 98x^4 - 98x^3 + 67x^2 - 30*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.1
Root			$2.91089 - 1.10325i$ of defining polynomial
Character	$\chi$	$=$	504.341
Dual form			504.2.ch.a.269.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-2.87228 - 1.65831i) q^{5} +(2.50000 + 0.866025i) q^{7} -2.82843i q^{8} +O(q^{10})$	\(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-2.87228 - 1.65831i) q^{5} +(2.50000 + 0.866025i) q^{7} -2.82843i q^{8} +(2.34521 + 4.06202i) q^{10} +(2.87228 + 4.97494i) q^{11} -4.69042 q^{13} +(-2.44949 - 2.82843i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(1.22474 + 2.12132i) q^{17} +(2.34521 - 4.06202i) q^{19} -6.63325i q^{20} -8.12404i q^{22} +(1.22474 + 0.707107i) q^{23} +(3.00000 + 5.19615i) q^{25} +(5.74456 + 3.31662i) q^{26} +(1.00000 + 5.19615i) q^{28} +5.74456 q^{29} +(4.50000 - 2.59808i) q^{31} +(4.89898 - 2.82843i) q^{32} -3.46410i q^{34} +(-5.74456 - 6.63325i) q^{35} +(7.03562 + 4.06202i) q^{37} +(-5.74456 + 3.31662i) q^{38} +(-4.69042 + 8.12404i) q^{40} +9.79796 q^{41} +8.12404i q^{43} +(-5.74456 + 9.94987i) q^{44} +(-1.00000 - 1.73205i) q^{46} +(-3.67423 + 6.36396i) q^{47} +(5.50000 + 4.33013i) q^{49} -8.48528i q^{50} +(-4.69042 - 8.12404i) q^{52} +(-2.87228 - 4.97494i) q^{53} -19.0526i q^{55} +(2.44949 - 7.07107i) q^{56} +(-7.03562 - 4.06202i) q^{58} +(2.87228 - 1.65831i) q^{59} +(2.34521 - 4.06202i) q^{61} -7.34847 q^{62} -8.00000 q^{64} +(13.4722 + 7.77817i) q^{65} +(-2.44949 + 4.24264i) q^{68} +(2.34521 + 12.1861i) q^{70} -1.41421i q^{71} +(-3.00000 + 1.73205i) q^{73} +(-5.74456 - 9.94987i) q^{74} +9.38083 q^{76} +(2.87228 + 14.9248i) q^{77} +(3.50000 - 6.06218i) q^{79} +(11.4891 - 6.63325i) q^{80} +(-12.0000 - 6.92820i) q^{82} +3.31662i q^{83} -8.12404i q^{85} +(5.74456 - 9.94987i) q^{86} +(14.0712 - 8.12404i) q^{88} +(-4.89898 + 8.48528i) q^{89} +(-11.7260 - 4.06202i) q^{91} +2.82843i q^{92} +(9.00000 - 5.19615i) q^{94} +(-13.4722 + 7.77817i) q^{95} +1.73205i q^{97} +(-3.67423 - 9.19239i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} + 20 q^{7}+O(q^{10}) $ 8 * q + 8 * q^4 + 20 * q^7	$ 8 q + 8 q^{4} + 20 q^{7} - 16 q^{16} + 24 q^{25} + 8 q^{28} + 36 q^{31} - 8 q^{46} + 44 q^{49} - 64 q^{64} - 24 q^{73} + 28 q^{79} - 96 q^{82} + 72 q^{94}+O(q^{100}) $ 8 * q + 8 * q^4 + 20 * q^7 - 16 * q^16 + 24 * q^25 + 8 * q^28 + 36 * q^31 - 8 * q^46 + 44 * q^49 - 64 * q^64 - 24 * q^73 + 28 * q^79 - 96 * q^82 + 72 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.22474	−	0.707107i	−0.866025	−	0.500000i
$2$	−1.22474	−	0.707107i	−0.866025	−	0.500000i
$3$		0			0
$3$		0			0
$4$	1.00000	+	1.73205i	0.500000	+	0.866025i
$5$	−2.87228	−	1.65831i	−1.28452	−	0.741620i	−0.306851	−	0.951757i	$-0.599275\pi$
$5$	−2.87228	−	1.65831i	−1.28452	−	0.741620i	−0.977672	+	0.210138i	$0.932609\pi$
$6$		0			0
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$8$		−	2.82843i		−	1.00000i
$9$		0			0
$10$	2.34521	+	4.06202i	0.741620	+	1.28452i
$11$	2.87228	+	4.97494i	0.866025	+	1.50000i	0.866025	+	0.500000i	$0.166667\pi$
$11$	2.87228	+	4.97494i	0.866025	+	1.50000i			1.00000i	$0.5\pi$
$12$		0			0
$13$	−4.69042			−1.30089			−0.650444	−	0.759555i	$-0.725417\pi$
$13$	−4.69042			−1.30089			−0.650444	+	0.759555i	$0.725417\pi$
$14$	−2.44949	−	2.82843i	−0.654654	−	0.755929i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$	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
$19$	2.34521	−	4.06202i	0.538028	−	0.931891i	−0.460983	−	0.887409i	$-0.652503\pi$
$19$	2.34521	−	4.06202i	0.538028	−	0.931891i	0.999010	−	0.0444819i	$-0.0141637\pi$
$20$		−	6.63325i		−	1.48324i
$21$		0			0
$22$		−	8.12404i		−	1.73205i
$23$	1.22474	+	0.707107i	0.255377	+	0.147442i	0.622224	−	0.782839i	$-0.286229\pi$
$23$	1.22474	+	0.707107i	0.255377	+	0.147442i	−0.366847	+	0.930281i	$0.619563\pi$
$24$		0			0
$25$	3.00000	+	5.19615i	0.600000	+	1.03923i
$26$	5.74456	+	3.31662i	1.12660	+	0.650444i
$27$		0			0
$28$	1.00000	+	5.19615i	0.188982	+	0.981981i
$29$	5.74456			1.06674			0.533369	−	0.845883i	$-0.320926\pi$
$29$	5.74456			1.06674			0.533369	+	0.845883i	$0.320926\pi$
$30$		0			0
$31$	4.50000	−	2.59808i	0.808224	−	0.466628i	−0.0381148	−	0.999273i	$-0.512135\pi$
$31$	4.50000	−	2.59808i	0.808224	−	0.466628i	0.846339	+	0.532645i	$0.178802\pi$
$32$	4.89898	−	2.82843i	0.866025	−	0.500000i
$33$		0			0
$34$		−	3.46410i		−	0.594089i
$35$	−5.74456	−	6.63325i	−0.971008	−	1.12122i
$36$		0			0
$37$	7.03562	+	4.06202i	1.15665	+	0.667792i	0.950499	−	0.310728i	$-0.100573\pi$
$37$	7.03562	+	4.06202i	1.15665	+	0.667792i	0.206151	+	0.978520i	$0.433906\pi$
$38$	−5.74456	+	3.31662i	−0.931891	+	0.538028i
$39$		0			0
$40$	−4.69042	+	8.12404i	−0.741620	+	1.28452i
$41$	9.79796			1.53018			0.765092	−	0.643921i	$-0.222693\pi$
$41$	9.79796			1.53018			0.765092	+	0.643921i	$0.222693\pi$
$42$		0			0
$43$			8.12404i			1.23890i	0.785034	+	0.619452i	$0.212645\pi$
$43$			8.12404i			1.23890i	−0.785034	+	0.619452i	$0.787355\pi$
$44$	−5.74456	+	9.94987i	−0.866025	+	1.50000i
$45$		0			0
$46$	−1.00000	−	1.73205i	−0.147442	−	0.255377i
$47$	−3.67423	+	6.36396i	−0.535942	+	0.928279i	0.463175	+	0.886267i	$0.346710\pi$
$47$	−3.67423	+	6.36396i	−0.535942	+	0.928279i	−0.999117	+	0.0420122i	$0.986623\pi$
$48$		0			0
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$		−	8.48528i		−	1.20000i
$51$		0			0
$52$	−4.69042	−	8.12404i	−0.650444	−	1.12660i
$53$	−2.87228	−	4.97494i	−0.394538	−	0.683360i	0.598504	−	0.801120i	$-0.295762\pi$
$53$	−2.87228	−	4.97494i	−0.394538	−	0.683360i	−0.993042	+	0.117760i	$0.962429\pi$
$54$		0			0
$55$		−	19.0526i		−	2.56905i
$56$	2.44949	−	7.07107i	0.327327	−	0.944911i
$57$		0			0
$58$	−7.03562	−	4.06202i	−0.923823	−	0.533369i
$59$	2.87228	−	1.65831i	0.373939	−	0.215894i	−0.301239	−	0.953549i	$-0.597400\pi$
$59$	2.87228	−	1.65831i	0.373939	−	0.215894i	0.675178	+	0.737655i	$0.264067\pi$
$60$		0			0
$61$	2.34521	−	4.06202i	0.300273	−	0.520088i	−0.675925	−	0.736971i	$-0.736256\pi$
$61$	2.34521	−	4.06202i	0.300273	−	0.520088i	0.976198	+	0.216883i	$0.0695889\pi$
$62$	−7.34847			−0.933257
$63$		0			0
$64$	−8.00000			−1.00000
$65$	13.4722	+	7.77817i	1.67102	+	0.964764i
$66$		0			0
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$	−2.44949	+	4.24264i	−0.297044	+	0.514496i
$69$		0			0
$70$	2.34521	+	12.1861i	0.280306	+	1.45651i
$71$		−	1.41421i		−	0.167836i	−0.996473	−	0.0839181i	$-0.973257\pi$
$71$		−	1.41421i		−	0.167836i	0.996473	−	0.0839181i	$-0.0267434\pi$
$72$		0			0
$73$	−3.00000	+	1.73205i	−0.351123	+	0.202721i	−0.665180	−	0.746683i	$-0.731645\pi$
$73$	−3.00000	+	1.73205i	−0.351123	+	0.202721i	0.314057	+	0.949404i	$0.398312\pi$
$74$	−5.74456	−	9.94987i	−0.667792	−	1.15665i
$75$		0			0
$76$	9.38083			1.07606
$77$	2.87228	+	14.9248i	0.327327	+	1.70084i
$78$		0			0
$79$	3.50000	−	6.06218i	0.393781	−	0.682048i	−0.599164	−	0.800626i	$-0.704500\pi$
$79$	3.50000	−	6.06218i	0.393781	−	0.682048i	0.992945	+	0.118578i	$0.0378336\pi$
$80$	11.4891	−	6.63325i	1.28452	−	0.741620i
$81$		0			0
$82$	−12.0000	−	6.92820i	−1.32518	−	0.765092i
$83$			3.31662i			0.364047i	0.983294	+	0.182023i	$0.0582647\pi$
$83$			3.31662i			0.364047i	−0.983294	+	0.182023i	$0.941735\pi$
$84$		0			0
$85$		−	8.12404i		−	0.881176i
$86$	5.74456	−	9.94987i	0.619452	−	1.07292i
$87$		0			0
$88$	14.0712	−	8.12404i	1.50000	−	0.866025i
$89$	−4.89898	+	8.48528i	−0.519291	+	0.899438i	0.480458	+	0.877018i	$0.340471\pi$
$89$	−4.89898	+	8.48528i	−0.519291	+	0.899438i	−0.999749	+	0.0224202i	$0.992863\pi$
$90$		0			0
$91$	−11.7260	−	4.06202i	−1.22922	−	0.425815i
$92$			2.82843i			0.294884i
$93$		0			0
$94$	9.00000	−	5.19615i	0.928279	−	0.535942i
$95$	−13.4722	+	7.77817i	−1.38222	+	0.798024i
$96$		0			0
$97$			1.73205i			0.175863i	0.996127	+	0.0879316i	$0.0280257\pi$
$97$			1.73205i			0.175863i	−0.996127	+	0.0879316i	$0.971974\pi$
$98$	−3.67423	−	9.19239i	−0.371154	−	0.928571i
$99$		0			0
$100$	−6.00000	+	10.3923i	−0.600000	+	1.03923i
$101$	−5.74456	+	3.31662i	−0.571605	+	0.330017i	−0.757790	−	0.652498i	$-0.773721\pi$
$101$	−5.74456	+	3.31662i	−0.571605	+	0.330017i	0.186185	+	0.982515i	$0.440388\pi$
$102$		0			0
$103$	−6.00000	−	3.46410i	−0.591198	−	0.341328i	0.174373	−	0.984680i	$-0.444210\pi$
$103$	−6.00000	−	3.46410i	−0.591198	−	0.341328i	−0.765571	+	0.643352i	$0.777543\pi$
$104$			13.2665i			1.30089i
$105$		0			0
$106$			8.12404i			0.789076i
$107$	2.87228	−	4.97494i	0.277674	−	0.480945i	−0.693132	−	0.720810i	$-0.743770\pi$
$107$	2.87228	−	4.97494i	0.277674	−	0.480945i	0.970806	+	0.239865i	$0.0771032\pi$
$108$		0			0
$109$	−14.0712	+	8.12404i	−1.34778	+	0.778142i	−0.987935	−	0.154870i	$-0.950504\pi$
$109$	−14.0712	+	8.12404i	−1.34778	+	0.778142i	−0.359846	+	0.933012i	$0.617171\pi$
$110$	−13.4722	+	23.3345i	−1.28452	+	2.22486i
$111$		0			0
$112$	−8.00000	+	6.92820i	−0.755929	+	0.654654i
$113$		−	14.1421i		−	1.33038i	−0.746674	−	0.665190i	$-0.768350\pi$
$113$		−	14.1421i		−	1.33038i	0.746674	−	0.665190i	$-0.231650\pi$
$114$		0			0
$115$	−2.34521	−	4.06202i	−0.218692	−	0.378785i
$116$	5.74456	+	9.94987i	0.533369	+	0.923823i
$117$		0			0
$118$	−4.69042			−0.431788
$119$	1.22474	+	6.36396i	0.112272	+	0.583383i
$120$		0			0
$121$	−11.0000	+	19.0526i	−1.00000	+	1.73205i
$122$	−5.74456	+	3.31662i	−0.520088	+	0.300273i
$123$		0			0
$124$	9.00000	+	5.19615i	0.808224	+	0.466628i
$125$		−	3.31662i		−	0.296648i
$126$		0			0
$127$	−13.0000			−1.15356			−0.576782	−	0.816898i	$-0.695692\pi$
$127$	−13.0000			−1.15356			−0.576782	+	0.816898i	$0.695692\pi$
$128$	9.79796	+	5.65685i	0.866025	+	0.500000i
$129$		0			0
$130$	−11.0000	−	19.0526i	−0.964764	−	1.67102i
$131$	−2.87228	−	1.65831i	−0.250952	−	0.144887i	0.369248	−	0.929331i	$-0.379615\pi$
$131$	−2.87228	−	1.65831i	−0.250952	−	0.144887i	−0.620200	+	0.784444i	$0.712949\pi$
$132$		0			0
$133$	9.38083	−	8.12404i	0.813421	−	0.704443i
$134$		0			0
$135$		0			0
$136$	6.00000	−	3.46410i	0.514496	−	0.297044i
$137$	−12.2474	+	7.07107i	−1.04637	+	0.604122i	−0.921631	−	0.388067i	$-0.873143\pi$
$137$	−12.2474	+	7.07107i	−1.04637	+	0.604122i	−0.124739	+	0.992190i	$0.539809\pi$
$138$		0			0
$139$	9.38083			0.795672			0.397836	−	0.917457i	$-0.369761\pi$
$139$	9.38083			0.795672			0.397836	+	0.917457i	$0.369761\pi$
$140$	5.74456	−	16.5831i	0.485504	−	1.40153i
$141$		0			0
$142$	−1.00000	+	1.73205i	−0.0839181	+	0.145350i
$143$	−13.4722	−	23.3345i	−1.12660	−	1.95133i
$144$		0			0
$145$	−16.5000	−	9.52628i	−1.37025	−	0.791114i
$146$	4.89898			0.405442
$147$		0			0
$148$			16.2481i			1.33558i
$149$	5.74456	−	9.94987i	0.470613	−	0.815125i	−0.528822	−	0.848733i	$-0.677366\pi$
$149$	5.74456	−	9.94987i	0.470613	−	0.815125i	0.999435	+	0.0336072i	$0.0106995\pi$
$150$		0			0
$151$	0.500000	+	0.866025i	0.0406894	+	0.0704761i	0.885653	−	0.464348i	$-0.153711\pi$
$151$	0.500000	+	0.866025i	0.0406894	+	0.0704761i	−0.844963	+	0.534824i	$0.820378\pi$
$152$	−11.4891	−	6.63325i	−0.931891	−	0.538028i
$153$		0			0
$154$	7.03562	−	20.3101i	0.566947	−	1.63663i
$155$	−17.2337			−1.38424
$156$		0			0
$157$	9.38083	+	16.2481i	0.748672	+	1.29674i	0.948459	+	0.316898i	$0.102641\pi$
$157$	9.38083	+	16.2481i	0.748672	+	1.29674i	−0.199788	+	0.979839i	$0.564025\pi$
$158$	−8.57321	+	4.94975i	−0.682048	+	0.393781i
$159$		0			0
$160$	−18.7617			−1.48324
$161$	2.44949	+	2.82843i	0.193047	+	0.222911i
$162$		0			0
$163$	7.03562	+	4.06202i	0.551073	+	0.318162i	0.749554	−	0.661943i	$-0.230268\pi$
$163$	7.03562	+	4.06202i	0.551073	+	0.318162i	−0.198482	+	0.980105i	$0.563601\pi$
$164$	9.79796	+	16.9706i	0.765092	+	1.32518i
$165$		0			0
$166$	2.34521	−	4.06202i	0.182023	−	0.315274i
$167$	−4.89898			−0.379094			−0.189547	−	0.981872i	$-0.560702\pi$
$167$	−4.89898			−0.379094			−0.189547	+	0.981872i	$0.560702\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$	−5.74456	+	9.94987i	−0.440588	+	0.763121i
$171$		0			0
$172$	−14.0712	+	8.12404i	−1.07292	+	0.619452i
$173$	5.74456	+	3.31662i	0.436751	+	0.252158i	0.702219	−	0.711961i	$-0.252193\pi$
$173$	5.74456	+	3.31662i	0.436751	+	0.252158i	−0.265467	+	0.964120i	$0.585526\pi$
$174$		0			0
$175$	3.00000	+	15.5885i	0.226779	+	1.17838i
$176$	−22.9783			−1.73205
$177$		0			0
$178$	12.0000	−	6.92820i	0.899438	−	0.519291i
$179$	5.74456	+	9.94987i	0.429369	+	0.743689i	0.996817	−	0.0797204i	$-0.0254027\pi$
$179$	5.74456	+	9.94987i	0.429369	+	0.743689i	−0.567448	+	0.823409i	$0.692069\pi$
$180$		0			0
$181$	9.38083			0.697272			0.348636	−	0.937258i	$-0.386645\pi$
$181$	9.38083			0.697272			0.348636	+	0.937258i	$0.386645\pi$
$182$	11.4891	+	13.2665i	0.851631	+	0.983378i
$183$		0			0
$184$	2.00000	−	3.46410i	0.147442	−	0.255377i
$185$	−13.4722	−	23.3345i	−0.990495	−	1.71559i
$186$		0			0
$187$	−7.03562	+	12.1861i	−0.514496	+	0.891133i
$188$	−14.6969			−1.07188
$189$		0			0
$190$	22.0000			1.59605
$191$	4.89898	+	2.82843i	0.354478	+	0.204658i	0.666656	−	0.745366i	$-0.267725\pi$
$191$	4.89898	+	2.82843i	0.354478	+	0.204658i	−0.312178	+	0.950024i	$0.601059\pi$
$192$		0			0
$193$	0.500000	+	0.866025i	0.0359908	+	0.0623379i	0.883460	−	0.468507i	$-0.155208\pi$
$193$	0.500000	+	0.866025i	0.0359908	+	0.0623379i	−0.847469	+	0.530845i	$0.821875\pi$
$194$	1.22474	−	2.12132i	0.0879316	−	0.152302i
$195$		0			0
$196$	−2.00000	+	13.8564i	−0.142857	+	0.989743i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$		0			0
$199$	6.00000	−	3.46410i	0.425329	−	0.245564i	−0.272026	−	0.962290i	$-0.587694\pi$
$199$	6.00000	−	3.46410i	0.425329	−	0.245564i	0.697355	+	0.716726i	$0.254360\pi$
$200$	14.6969	−	8.48528i	1.03923	−	0.600000i
$201$		0			0
$202$	9.38083			0.660033
$203$	14.3614	+	4.97494i	1.00797	+	0.349172i
$204$		0			0
$205$	−28.1425	−	16.2481i	−1.96556	−	1.13481i
$206$	4.89898	+	8.48528i	0.341328	+	0.591198i
$207$		0			0
$208$	9.38083	−	16.2481i	0.650444	−	1.12660i
$209$	26.9444			1.86378
$210$		0			0
$211$		−	8.12404i		−	0.559282i	−0.960105	−	0.279641i	$-0.909785\pi$
$211$		−	8.12404i		−	0.559282i	0.960105	−	0.279641i	$-0.0902154\pi$
$212$	5.74456	−	9.94987i	0.394538	−	0.683360i
$213$		0			0
$214$	−7.03562	+	4.06202i	−0.480945	+	0.277674i
$215$	13.4722	−	23.3345i	0.918796	−	1.59140i
$216$		0			0
$217$	13.5000	−	2.59808i	0.916440	−	0.176369i
$218$	22.9783			1.55628
$219$		0			0
$220$	33.0000	−	19.0526i	2.22486	−	1.28452i
$221$	−5.74456	−	9.94987i	−0.386421	−	0.669301i
$222$		0			0
$223$		−	19.0526i		−	1.27585i	−0.770097	−	0.637927i	$-0.779792\pi$
$223$		−	19.0526i		−	1.27585i	0.770097	−	0.637927i	$-0.220208\pi$
$224$	14.6969	−	2.82843i	0.981981	−	0.188982i
$225$		0			0
$226$	−10.0000	+	17.3205i	−0.665190	+	1.15214i
$227$	20.1060	−	11.6082i	1.33448	−	0.770462i	0.348497	−	0.937310i	$-0.386692\pi$
$227$	20.1060	−	11.6082i	1.33448	−	0.770462i	0.985983	+	0.166847i	$0.0533587\pi$
$228$		0			0
$229$	−4.69042	+	8.12404i	−0.309951	+	0.536852i	−0.978351	−	0.206950i	$-0.933646\pi$
$229$	−4.69042	+	8.12404i	−0.309951	+	0.536852i	0.668400	+	0.743802i	$0.266979\pi$
$230$			6.63325i			0.437384i
$231$		0			0
$232$		−	16.2481i		−	1.06674i
$233$	−6.12372	−	3.53553i	−0.401179	−	0.231621i	0.285814	−	0.958285i	$-0.407736\pi$
$233$	−6.12372	−	3.53553i	−0.401179	−	0.231621i	−0.686992	+	0.726665i	$0.741069\pi$
$234$		0			0
$235$	21.1069	−	12.1861i	1.37686	−	0.794931i
$236$	5.74456	+	3.31662i	0.373939	+	0.215894i
$237$		0			0
$238$	3.00000	−	8.66025i	0.194461	−	0.561361i
$239$		−	1.41421i		−	0.0914779i	−0.998953	−	0.0457389i	$-0.985436\pi$
$239$		−	1.41421i		−	0.0914779i	0.998953	−	0.0457389i	$-0.0145642\pi$
$240$		0			0
$241$	−10.5000	+	6.06218i	−0.676364	+	0.390499i	−0.798484	−	0.602016i	$-0.794364\pi$
$241$	−10.5000	+	6.06218i	−0.676364	+	0.390499i	0.122119	+	0.992515i	$0.461031\pi$
$242$	26.9444	−	15.5563i	1.73205	−	1.00000i
$243$		0			0
$244$	9.38083			0.600546
$245$	−8.61684	−	21.5581i	−0.550510	−	1.37729i
$246$		0			0
$247$	−11.0000	+	19.0526i	−0.699913	+	1.21229i
$248$	−7.34847	−	12.7279i	−0.466628	−	0.808224i
$249$		0			0
$250$	−2.34521	+	4.06202i	−0.148324	+	0.256905i
$251$			3.31662i			0.209344i	0.994507	+	0.104672i	$0.0333792\pi$
$251$			3.31662i			0.209344i	−0.994507	+	0.104672i	$0.966621\pi$
$252$		0			0
$253$			8.12404i			0.510754i
$254$	15.9217	+	9.19239i	0.999015	+	0.576782i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	4.89898	−	8.48528i	0.305590	−	0.529297i	−0.671803	−	0.740730i	$-0.734480\pi$
$257$	4.89898	−	8.48528i	0.305590	−	0.529297i	0.977393	+	0.211433i	$0.0678130\pi$
$258$		0			0
$259$	14.0712	+	16.2481i	0.874345	+	1.00961i
$260$			31.1127i			1.92953i
$261$		0			0
$262$	2.34521	+	4.06202i	0.144887	+	0.250952i
$263$	−8.57321	+	4.94975i	−0.528647	+	0.305215i	−0.740465	−	0.672095i	$-0.765395\pi$
$263$	−8.57321	+	4.94975i	−0.528647	+	0.305215i	0.211818	+	0.977309i	$0.432061\pi$
$264$		0			0
$265$			19.0526i			1.17039i
$266$	−17.2337	+	3.31662i	−1.05667	+	0.203355i
$267$		0			0
$268$		0			0
$269$	−14.3614	+	8.29156i	−0.875630	+	0.505545i	−0.869215	−	0.494434i	$-0.835375\pi$
$269$	−14.3614	+	8.29156i	−0.875630	+	0.505545i	−0.00641522	+	0.999979i	$0.502042\pi$
$270$		0			0
$271$	1.50000	+	0.866025i	0.0911185	+	0.0526073i	0.544867	−	0.838523i	$-0.316580\pi$
$271$	1.50000	+	0.866025i	0.0911185	+	0.0526073i	−0.453748	+	0.891130i	$0.649914\pi$
$272$	−9.79796			−0.594089
$273$		0			0
$274$	20.0000			1.20824
$275$	−17.2337	+	29.8496i	−1.03923	+	1.80000i
$276$		0			0
$277$	14.0712	−	8.12404i	0.845459	−	0.488126i	−0.0136569	−	0.999907i	$-0.504347\pi$
$277$	14.0712	−	8.12404i	0.845459	−	0.488126i	0.859116	+	0.511781i	$0.171014\pi$
$278$	−11.4891	−	6.63325i	−0.689072	−	0.397836i
$279$		0			0
$280$	−18.7617	+	16.2481i	−1.12122	+	0.971008i
$281$		−	22.6274i		−	1.34984i	−0.737892	−	0.674919i	$-0.764178\pi$
$281$		−	22.6274i		−	1.34984i	0.737892	−	0.674919i	$-0.235822\pi$
$282$		0			0
$283$	−11.7260	−	20.3101i	−0.697041	−	1.20731i	−0.969488	−	0.245139i	$-0.921166\pi$
$283$	−11.7260	−	20.3101i	−0.697041	−	1.20731i	0.272447	−	0.962171i	$-0.412167\pi$
$284$	2.44949	−	1.41421i	0.145350	−	0.0839181i
$285$		0			0
$286$			38.1051i			2.25320i
$287$	24.4949	+	8.48528i	1.44589	+	0.500870i
$288$		0			0
$289$	5.50000	−	9.52628i	0.323529	−	0.560369i
$290$	13.4722	+	23.3345i	0.791114	+	1.37025i
$291$		0			0
$292$	−6.00000	−	3.46410i	−0.351123	−	0.202721i
$293$			3.31662i			0.193759i	0.995296	+	0.0968796i	$0.0308862\pi$
$293$			3.31662i			0.193759i	−0.995296	+	0.0968796i	$0.969114\pi$
$294$		0			0
$295$	−11.0000			−0.640445
$296$	11.4891	−	19.8997i	0.667792	−	1.15665i
$297$		0			0
$298$	−14.0712	+	8.12404i	−0.815125	+	0.470613i
$299$	−5.74456	−	3.31662i	−0.332217	−	0.191805i
$300$		0			0
$301$	−7.03562	+	20.3101i	−0.405527	+	1.17065i
$302$		−	1.41421i		−	0.0813788i
$303$		0			0
$304$	9.38083	+	16.2481i	0.538028	+	0.931891i
$305$	−13.4722	+	7.77817i	−0.771416	+	0.445377i
$306$		0			0
$307$	−32.8329			−1.87387			−0.936937	−	0.349499i	$-0.886352\pi$
$307$	−32.8329			−1.87387			−0.936937	+	0.349499i	$0.886352\pi$
$308$	−22.9783	+	19.8997i	−1.30931	+	1.13389i
$309$		0			0
$310$	21.1069	+	12.1861i	1.19879	+	0.692122i
$311$	−14.6969	−	25.4558i	−0.833387	−	1.44347i	−0.895337	−	0.445389i	$-0.853065\pi$
$311$	−14.6969	−	25.4558i	−0.833387	−	1.44347i	0.0619501	−	0.998079i	$-0.480268\pi$
$312$		0			0
$313$	−22.5000	−	12.9904i	−1.27178	−	0.734260i	−0.296453	−	0.955047i	$-0.595804\pi$
$313$	−22.5000	−	12.9904i	−1.27178	−	0.734260i	−0.975322	+	0.220788i	$0.929137\pi$
$314$		−	26.5330i		−	1.49734i
$315$		0			0
$316$	14.0000			0.787562
$317$	−8.61684	+	14.9248i	−0.483970	+	0.838261i	−0.999830	−	0.0184118i	$-0.994139\pi$
$317$	−8.61684	+	14.9248i	−0.483970	+	0.838261i	0.515860	+	0.856673i	$0.327472\pi$
$318$		0			0
$319$	16.5000	+	28.5788i	0.923823	+	1.60011i
$320$	22.9783	+	13.2665i	1.28452	+	0.741620i
$321$		0			0
$322$	−1.00000	−	5.19615i	−0.0557278	−	0.289570i
$323$	11.4891			0.639272
$324$		0			0
$325$	−14.0712	−	24.3721i	−0.780532	−	1.35192i
$326$	−5.74456	−	9.94987i	−0.318162	−	0.551073i
$327$		0			0
$328$		−	27.7128i		−	1.53018i
$329$	−14.6969	+	12.7279i	−0.810268	+	0.701713i
$330$		0			0
$331$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$331$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$332$	−5.74456	+	3.31662i	−0.315274	+	0.182023i
$333$		0			0
$334$	6.00000	+	3.46410i	0.328305	+	0.189547i
$335$		0			0
$336$		0			0
$337$	29.0000			1.57973			0.789865	−	0.613280i	$-0.210150\pi$
$337$	29.0000			1.57973			0.789865	+	0.613280i	$0.210150\pi$
$338$	−11.0227	−	6.36396i	−0.599556	−	0.346154i
$339$		0			0
$340$	14.0712	−	8.12404i	0.763121	−	0.440588i
$341$	25.8505	+	14.9248i	1.39988	+	0.808224i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	22.9783			1.23890
$345$		0			0
$346$	−4.69042	−	8.12404i	−0.252158	−	0.436751i
$347$	−17.2337	−	29.8496i	−0.925153	−	1.60241i	−0.791315	−	0.611408i	$-0.790603\pi$
$347$	−17.2337	−	29.8496i	−0.925153	−	1.60241i	−0.133838	−	0.991003i	$-0.542730\pi$
$348$		0			0
$349$	9.38083			0.502144			0.251072	−	0.967968i	$-0.419217\pi$
$349$	9.38083			0.502144			0.251072	+	0.967968i	$0.419217\pi$
$350$	7.34847	−	21.2132i	0.392792	−	1.13389i
$351$		0			0
$352$	28.1425	+	16.2481i	1.50000	+	0.866025i
$353$	−4.89898	−	8.48528i	−0.260746	−	0.451626i	0.705694	−	0.708517i	$-0.250635\pi$
$353$	−4.89898	−	8.48528i	−0.260746	−	0.451626i	−0.966440	+	0.256891i	$0.917302\pi$
$354$		0			0
$355$	−2.34521	+	4.06202i	−0.124471	+	0.215590i
$356$	−19.5959			−1.03858
$357$		0			0
$358$		−	16.2481i		−	0.858738i
$359$	4.89898	+	2.82843i	0.258558	+	0.149279i	0.623677	−	0.781682i	$-0.285638\pi$
$359$	4.89898	+	2.82843i	0.258558	+	0.149279i	−0.365118	+	0.930961i	$0.618972\pi$
$360$		0			0
$361$	−1.50000	−	2.59808i	−0.0789474	−	0.136741i
$362$	−11.4891	−	6.63325i	−0.603855	−	0.348636i
$363$		0			0
$364$	−4.69042	−	24.3721i	−0.245845	−	1.27745i
$365$	11.4891			0.601368
$366$		0			0
$367$	−19.5000	+	11.2583i	−1.01789	+	0.587680i	−0.913493	−	0.406855i	$-0.866625\pi$
$367$	−19.5000	+	11.2583i	−1.01789	+	0.587680i	−0.104399	+	0.994535i	$0.533292\pi$
$368$	−4.89898	+	2.82843i	−0.255377	+	0.147442i
$369$		0			0
$370$			38.1051i			1.98099i
$371$	−2.87228	−	14.9248i	−0.149121	−	0.774858i
$372$		0			0
$373$	14.0712	+	8.12404i	0.728582	+	0.420647i	0.817903	−	0.575356i	$-0.195137\pi$
$373$	14.0712	+	8.12404i	0.728582	+	0.420647i	−0.0893215	+	0.996003i	$0.528470\pi$
$374$	17.2337	−	9.94987i	0.891133	−	0.514496i
$375$		0			0
$376$	18.0000	+	10.3923i	0.928279	+	0.535942i
$377$	−26.9444			−1.38771
$378$		0			0
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$	−26.9444	−	15.5563i	−1.38222	−	0.798024i
$381$		0			0
$382$	−4.00000	−	6.92820i	−0.204658	−	0.354478i
$383$	4.89898	−	8.48528i	0.250326	−	0.433578i	−0.713289	−	0.700870i	$-0.752795\pi$
$383$	4.89898	−	8.48528i	0.250326	−	0.433578i	0.963616	+	0.267292i	$0.0861288\pi$
$384$		0			0
$385$	16.5000	−	47.6314i	0.840918	−	2.42752i
$386$		−	1.41421i		−	0.0719816i
$387$		0			0
$388$	−3.00000	+	1.73205i	−0.152302	+	0.0879316i
$389$	11.4891	+	19.8997i	0.582522	+	1.00896i	0.995179	+	0.0980711i	$0.0312673\pi$
$389$	11.4891	+	19.8997i	0.582522	+	1.00896i	−0.412658	+	0.910886i	$0.635399\pi$
$390$		0			0
$391$			3.46410i			0.175187i
$392$	12.2474	−	15.5563i	0.618590	−	0.785714i
$393$		0			0
$394$		0			0
$395$	−20.1060	+	11.6082i	−1.01164	+	0.584071i
$396$		0			0
$397$	9.38083	−	16.2481i	0.470810	−	0.815468i	−0.528632	−	0.848851i	$-0.677295\pi$
$397$	9.38083	−	16.2481i	0.470810	−	0.815468i	0.999443	+	0.0333834i	$0.0106282\pi$
$398$	−9.79796			−0.491127
$399$		0			0
$400$	−24.0000			−1.20000
$401$	12.2474	+	7.07107i	0.611608	+	0.353112i	0.773595	−	0.633681i	$-0.218457\pi$
$401$	12.2474	+	7.07107i	0.611608	+	0.353112i	−0.161986	+	0.986793i	$0.551790\pi$
$402$		0			0
$403$	−21.1069	+	12.1861i	−1.05141	+	0.607031i
$404$	−11.4891	−	6.63325i	−0.571605	−	0.330017i
$405$		0			0
$406$	−14.0712	−	16.2481i	−0.698344	−	0.806379i
$407$			46.6690i			2.31330i
$408$		0			0
$409$	−22.5000	+	12.9904i	−1.11255	+	0.642333i	−0.939490	−	0.342578i	$-0.888700\pi$
$409$	−22.5000	+	12.9904i	−1.11255	+	0.642333i	−0.173064	+	0.984911i	$0.555367\pi$
$410$	22.9783	+	39.7995i	1.13481	+	1.96556i
$411$		0			0
$412$		−	13.8564i		−	0.682656i
$413$	8.61684	−	1.65831i	0.424007	−	0.0816002i
$414$		0			0
$415$	5.50000	−	9.52628i	0.269984	−	0.467627i
$416$	−22.9783	+	13.2665i	−1.12660	+	0.650444i
$417$		0			0
$418$	−33.0000	−	19.0526i	−1.61408	−	0.931891i
$419$		−	26.5330i		−	1.29622i	−0.761546	−	0.648111i	$-0.775559\pi$
$419$		−	26.5330i		−	1.29622i	0.761546	−	0.648111i	$-0.224441\pi$
$420$		0			0
$421$			8.12404i			0.395941i	0.980208	+	0.197971i	$0.0634351\pi$
$421$			8.12404i			0.395941i	−0.980208	+	0.197971i	$0.936565\pi$
$422$	−5.74456	+	9.94987i	−0.279641	+	0.484352i
$423$		0			0
$424$	−14.0712	+	8.12404i	−0.683360	+	0.394538i
$425$	−7.34847	+	12.7279i	−0.356453	+	0.617395i
$426$		0			0
$427$	9.38083	−	8.12404i	0.453970	−	0.393150i
$428$	11.4891			0.555348
$429$		0			0
$430$	−33.0000	+	19.0526i	−1.59140	+	0.918796i
$431$	24.4949	−	14.1421i	1.17988	−	0.681203i	0.223891	−	0.974614i	$-0.428124\pi$
$431$	24.4949	−	14.1421i	1.17988	−	0.681203i	0.955986	+	0.293411i	$0.0947906\pi$
$432$		0			0
$433$		−	31.1769i		−	1.49827i	−0.662419	−	0.749133i	$-0.730470\pi$
$433$		−	31.1769i		−	1.49827i	0.662419	−	0.749133i	$-0.269530\pi$
$434$	−18.3712	−	6.36396i	−0.881845	−	0.305480i
$435$		0			0
$436$	−28.1425	−	16.2481i	−1.34778	−	0.778142i
$437$	5.74456	−	3.31662i	0.274800	−	0.158656i
$438$		0			0
$439$	22.5000	+	12.9904i	1.07387	+	0.619997i	0.929235	−	0.369489i	$-0.120467\pi$
$439$	22.5000	+	12.9904i	1.07387	+	0.619997i	0.144631	+	0.989486i	$0.453800\pi$
$440$	−53.8888			−2.56905
$441$		0			0
$442$			16.2481i			0.772842i
$443$	8.61684	−	14.9248i	0.409399	−	0.709099i	−0.585424	−	0.810727i	$-0.699072\pi$
$443$	8.61684	−	14.9248i	0.409399	−	0.709099i	0.994822	+	0.101628i	$0.0324052\pi$
$444$		0			0
$445$	28.1425	−	16.2481i	1.33408	−	0.770233i
$446$	−13.4722	+	23.3345i	−0.637927	+	1.10492i
$447$		0			0
$448$	−20.0000	−	6.92820i	−0.944911	−	0.327327i
$449$			24.0416i			1.13459i	0.823513	+	0.567297i	$0.192011\pi$
$449$			24.0416i			1.13459i	−0.823513	+	0.567297i	$0.807989\pi$
$450$		0			0
$451$	28.1425	+	48.7442i	1.32518	+	2.29528i
$452$	24.4949	−	14.1421i	1.15214	−	0.665190i
$453$		0			0
$454$	−32.8329			−1.54092
$455$	26.9444	+	31.1127i	1.26317	+	1.45859i
$456$		0			0
$457$	12.5000	−	21.6506i	0.584725	−	1.01277i	−0.410184	−	0.912003i	$-0.634536\pi$
$457$	12.5000	−	21.6506i	0.584725	−	1.01277i	0.994910	−	0.100771i	$-0.0321310\pi$
$458$	11.4891	−	6.63325i	0.536852	−	0.309951i
$459$		0			0
$460$	4.69042	−	8.12404i	0.218692	−	0.378785i
$461$		−	6.63325i		−	0.308941i	−0.987997	−	0.154471i	$-0.950633\pi$
$461$		−	6.63325i		−	0.308941i	0.987997	−	0.154471i	$-0.0493672\pi$
$462$		0			0
$463$	−22.0000			−1.02243			−0.511213	−	0.859454i	$-0.670804\pi$
$463$	−22.0000			−1.02243			−0.511213	+	0.859454i	$0.670804\pi$
$464$	−11.4891	+	19.8997i	−0.533369	+	0.923823i
$465$		0			0
$466$	5.00000	+	8.66025i	0.231621	+	0.401179i
$467$	5.74456	+	3.31662i	0.265827	+	0.153475i	0.626990	−	0.779028i	$-0.284287\pi$
$467$	5.74456	+	3.31662i	0.265827	+	0.153475i	−0.361163	+	0.932503i	$0.617620\pi$
$468$		0			0
$469$		0			0
$470$	−34.4674			−1.58986
$471$		0			0
$472$	−4.69042	−	8.12404i	−0.215894	−	0.373939i
$473$	−40.4166	+	23.3345i	−1.85836	+	1.07292i
$474$		0			0
$475$	28.1425			1.29127
$476$	−9.79796	+	8.48528i	−0.449089	+	0.388922i
$477$		0			0
$478$	−1.00000	+	1.73205i	−0.0457389	+	0.0792222i
$479$	13.4722	+	23.3345i	0.615560	+	1.06618i	0.990286	+	0.139046i	$0.0444036\pi$
$479$	13.4722	+	23.3345i	0.615560	+	1.06618i	−0.374726	+	0.927136i	$0.622263\pi$
$480$		0			0
$481$	−33.0000	−	19.0526i	−1.50467	−	0.868722i
$482$	17.1464			0.780998
$483$		0			0
$484$	−44.0000			−2.00000
$485$	2.87228	−	4.97494i	0.130424	−	0.225900i
$486$		0			0
$487$	12.5000	+	21.6506i	0.566429	+	0.981084i	0.996915	+	0.0784867i	$0.0250088\pi$
$487$	12.5000	+	21.6506i	0.566429	+	0.981084i	−0.430486	+	0.902597i	$0.641658\pi$
$488$	−11.4891	−	6.63325i	−0.520088	−	0.300273i
$489$		0			0
$490$	−4.69042	+	32.4962i	−0.211891	+	1.46803i
$491$	28.7228			1.29624			0.648121	−	0.761537i	$-0.275555\pi$
$491$	28.7228			1.29624			0.648121	+	0.761537i	$0.275555\pi$
$492$		0			0
$493$	7.03562	+	12.1861i	0.316869	+	0.548832i
$494$	26.9444	−	15.5563i	1.21229	−	0.699913i
$495$		0			0
$496$			20.7846i			0.933257i
$497$	1.22474	−	3.53553i	0.0549373	−	0.158590i
$498$		0			0
$499$	−28.1425	−	16.2481i	−1.25983	−	0.727364i	−0.286790	−	0.957994i	$-0.592588\pi$
$499$	−28.1425	−	16.2481i	−1.25983	−	0.727364i	−0.973042	+	0.230630i	$0.925921\pi$
$500$	5.74456	−	3.31662i	0.256905	−	0.148324i
$501$		0			0
$502$	2.34521	−	4.06202i	0.104672	−	0.181297i
$503$	−7.34847			−0.327652			−0.163826	−	0.986489i	$-0.552384\pi$
$503$	−7.34847			−0.327652			−0.163826	+	0.986489i	$0.552384\pi$
$504$		0			0
$505$	22.0000			0.978987
$506$	5.74456	−	9.94987i	0.255377	−	0.442326i
$507$		0			0
$508$	−13.0000	−	22.5167i	−0.576782	−	0.999015i
$509$	−37.3397	−	21.5581i	−1.65505	−	0.955544i	−0.974949	−	0.222427i	$-0.928602\pi$
$509$	−37.3397	−	21.5581i	−1.65505	−	0.955544i	−0.680102	−	0.733118i	$-0.738064\pi$
$510$		0			0
$511$	−9.00000	+	1.73205i	−0.398137	+	0.0766214i
$512$			22.6274i			1.00000i
$513$		0			0
$514$	−12.0000	+	6.92820i	−0.529297	+	0.305590i
$515$	11.4891	+	19.8997i	0.506271	+	0.876888i
$516$		0			0
$517$	−42.2137			−1.85656
$518$	−5.74456	−	29.8496i	−0.252402	−	1.31152i
$519$		0			0
$520$	22.0000	−	38.1051i	0.964764	−	1.67102i
$521$	8.57321	+	14.8492i	0.375599	+	0.650557i	0.990417	−	0.138113i	$-0.0441036\pi$
$521$	8.57321	+	14.8492i	0.375599	+	0.650557i	−0.614817	+	0.788670i	$0.710770\pi$
$522$		0			0
$523$	2.34521	−	4.06202i	0.102549	−	0.177620i	−0.810185	−	0.586174i	$-0.800634\pi$
$523$	2.34521	−	4.06202i	0.102549	−	0.177620i	0.912734	+	0.408554i	$0.133967\pi$
$524$		−	6.63325i		−	0.289775i
$525$		0			0
$526$	14.0000			0.610429
$527$	11.0227	+	6.36396i	0.480157	+	0.277218i
$528$		0			0
$529$	−10.5000	−	18.1865i	−0.456522	−	0.790719i
$530$	13.4722	−	23.3345i	0.585195	−	1.01359i
$531$		0			0
$532$	23.4521	+	8.12404i	1.01678	+	0.352222i
$533$	−45.9565			−1.99060
$534$		0			0
$535$	−16.5000	+	9.52628i	−0.713357	+	0.411857i
$536$		0			0
$537$		0			0
$538$	23.4521			1.01109
$539$	−5.74456	+	39.7995i	−0.247436	+	1.71429i
$540$		0			0
$541$	7.03562	+	4.06202i	0.302485	+	0.174640i	0.643559	−	0.765397i	$-0.277457\pi$
$541$	7.03562	+	4.06202i	0.302485	+	0.174640i	−0.341074	+	0.940037i	$0.610791\pi$
$542$	−1.22474	−	2.12132i	−0.0526073	−	0.0911185i
$543$		0			0
$544$	12.0000	+	6.92820i	0.514496	+	0.297044i
$545$	53.8888			2.30834
$546$		0			0
$547$		−	40.6202i		−	1.73679i	−0.495870	−	0.868397i	$-0.665151\pi$
$547$		−	40.6202i		−	1.73679i	0.495870	−	0.868397i	$-0.334849\pi$
$548$	−24.4949	−	14.1421i	−1.04637	−	0.604122i
$549$		0			0
$550$	42.2137	−	24.3721i	1.80000	−	1.03923i
$551$	13.4722	−	23.3345i	0.573935	−	0.994084i
$552$		0			0
$553$	14.0000	−	12.1244i	0.595341	−	0.515580i
$554$	−22.9783			−0.976252
$555$		0			0
$556$	9.38083	+	16.2481i	0.397836	+	0.689072i
$557$	−2.87228	−	4.97494i	−0.121702	−	0.210795i	0.798737	−	0.601681i	$-0.205502\pi$
$557$	−2.87228	−	4.97494i	−0.121702	−	0.210795i	−0.920439	+	0.390886i	$0.872169\pi$
$558$		0			0
$559$		−	38.1051i		−	1.61167i
$560$	34.4674	−	6.63325i	1.45651	−	0.280306i
$561$		0			0
$562$	−16.0000	+	27.7128i	−0.674919	+	1.16899i
$563$	−31.5951	+	18.2414i	−1.33157	+	0.768785i	−0.985541	−	0.169437i	$-0.945805\pi$
$563$	−31.5951	+	18.2414i	−1.33157	+	0.768785i	−0.346034	+	0.938222i	$0.612472\pi$
$564$		0			0
$565$	−23.4521	+	40.6202i	−0.986636	+	1.70890i
$566$			33.1662i			1.39408i
$567$		0			0
$568$	−4.00000			−0.167836
$569$	−13.4722	−	7.77817i	−0.564784	−	0.326078i	0.190280	−	0.981730i	$-0.439061\pi$
$569$	−13.4722	−	7.77817i	−0.564784	−	0.326078i	−0.755063	+	0.655652i	$0.772394\pi$
$570$		0			0
$571$	−21.1069	+	12.1861i	−0.883295	+	0.509971i	−0.871743	−	0.489963i	$-0.837010\pi$
$571$	−21.1069	+	12.1861i	−0.883295	+	0.509971i	−0.0115516	+	0.999933i	$0.503677\pi$
$572$	26.9444	−	46.6690i	1.12660	−	1.95133i
$573$		0			0
$574$	−24.0000	−	27.7128i	−1.00174	−	1.15671i
$575$			8.48528i			0.353861i
$576$		0			0
$577$	10.5000	−	6.06218i	0.437121	−	0.252372i	−0.265255	−	0.964178i	$-0.585456\pi$
$577$	10.5000	−	6.06218i	0.437121	−	0.252372i	0.702376	+	0.711807i	$0.252123\pi$
$578$	−13.4722	+	7.77817i	−0.560369	+	0.323529i
$579$		0			0
$580$		−	38.1051i		−	1.58223i
$581$	−2.87228	+	8.29156i	−0.119162	+	0.343992i
$582$		0			0
$583$	16.5000	−	28.5788i	0.683360	−	1.18361i
$584$	4.89898	+	8.48528i	0.202721	+	0.351123i
$585$		0			0
$586$	2.34521	−	4.06202i	0.0968796	−	0.167800i
$587$			23.2164i			0.958242i	0.877749	+	0.479121i	$0.159045\pi$
$587$			23.2164i			0.958242i	−0.877749	+	0.479121i	$0.840955\pi$
$588$		0			0
$589$		−	24.3721i		−	1.00424i
$590$	13.4722	+	7.77817i	0.554641	+	0.320222i
$591$		0			0
$592$	−28.1425	+	16.2481i	−1.15665	+	0.667792i
$593$	−8.57321	+	14.8492i	−0.352060	+	0.609785i	−0.986610	−	0.163096i	$-0.947852\pi$
$593$	−8.57321	+	14.8492i	−0.352060	+	0.609785i	0.634550	+	0.772881i	$0.281185\pi$
$594$		0			0
$595$	7.03562	−	20.3101i	0.288432	−	0.832633i
$596$	22.9783			0.941226
$597$		0			0
$598$	4.69042	+	8.12404i	0.191805	+	0.332217i
$599$	−12.2474	+	7.07107i	−0.500417	+	0.288916i	−0.728886	−	0.684635i	$-0.759961\pi$
$599$	−12.2474	+	7.07107i	−0.500417	+	0.288916i	0.228469	+	0.973551i	$0.426628\pi$
$600$		0			0
$601$			43.3013i			1.76630i	0.469095	+	0.883148i	$0.344580\pi$
$601$			43.3013i			1.76630i	−0.469095	+	0.883148i	$0.655420\pi$
$602$	22.9783	−	19.8997i	0.936524	−	0.811053i
$603$		0			0
$604$	−1.00000	+	1.73205i	−0.0406894	+	0.0704761i
$605$	63.1902	−	36.4829i	2.56905	−	1.48324i
$606$		0			0
$607$	34.5000	+	19.9186i	1.40031	+	0.808470i	0.994424	−	0.105453i	$-0.0336291\pi$
$607$	34.5000	+	19.9186i	1.40031	+	0.808470i	0.405887	+	0.913923i	$0.366962\pi$
$608$		−	26.5330i		−	1.07606i
$609$		0			0
$610$	22.0000			0.890754
$611$	17.2337	−	29.8496i	0.697200	−	1.20759i
$612$		0			0
$613$	−35.1781	+	20.3101i	−1.42083	+	0.820317i	−0.996370	−	0.0851292i	$-0.972870\pi$
$613$	−35.1781	+	20.3101i	−1.42083	+	0.820317i	−0.424461	+	0.905446i	$0.639536\pi$
$614$	40.2119	+	23.2164i	1.62282	+	0.936937i
$615$		0			0
$616$	42.2137	−	8.12404i	1.70084	−	0.327327i
$617$		−	18.3848i		−	0.740143i	−0.929003	−	0.370072i	$-0.879333\pi$
$617$		−	18.3848i		−	0.740143i	0.929003	−	0.370072i	$-0.120667\pi$
$618$		0			0
$619$	−11.7260	−	20.3101i	−0.471309	−	0.816332i	0.528152	−	0.849150i	$-0.322885\pi$
$619$	−11.7260	−	20.3101i	−0.471309	−	0.816332i	−0.999461	+	0.0328182i	$0.989552\pi$
$620$	−17.2337	−	29.8496i	−0.692122	−	1.19879i
$621$		0			0
$622$			41.5692i			1.66677i
$623$	−19.5959	+	16.9706i	−0.785094	+	0.679911i
$624$		0			0
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$	18.3712	+	31.8198i	0.734260	+	1.27178i
$627$		0			0
$628$	−18.7617	+	32.4962i	−0.748672	+	1.29674i
$629$			19.8997i			0.793455i
$630$		0			0
$631$	−31.0000			−1.23409			−0.617045	−	0.786928i	$-0.711670\pi$
$631$	−31.0000			−1.23409			−0.617045	+	0.786928i	$0.711670\pi$
$632$	−17.1464	−	9.89949i	−0.682048	−	0.393781i
$633$		0			0
$634$	21.1069	−	12.1861i	0.838261	−	0.483970i
$635$	37.3397	+	21.5581i	1.48178	+	0.855506i
$636$		0			0
$637$	−25.7973	−	20.3101i	−1.02213	−	0.804715i
$638$		−	46.6690i		−	1.84765i
$639$		0			0
$640$	−18.7617	−	32.4962i	−0.741620	−	1.28452i
$641$	35.5176	−	20.5061i	1.40286	−	0.809942i	0.408176	−	0.912903i	$-0.366165\pi$
$641$	35.5176	−	20.5061i	1.40286	−	0.809942i	0.994685	+	0.102961i	$0.0328318\pi$
$642$		0			0
$643$	37.5233			1.47978			0.739888	−	0.672730i	$-0.234879\pi$
$643$	37.5233			1.47978			0.739888	+	0.672730i	$0.234879\pi$
$644$	−2.44949	+	7.07107i	−0.0965234	+	0.278639i
$645$		0			0
$646$	−14.0712	−	8.12404i	−0.553626	−	0.319636i
$647$	1.22474	+	2.12132i	0.0481497	+	0.0833977i	0.889096	−	0.457721i	$-0.151334\pi$
$647$	1.22474	+	2.12132i	0.0481497	+	0.0833977i	−0.840946	+	0.541119i	$0.818001\pi$
$648$		0			0
$649$	16.5000	+	9.52628i	0.647682	+	0.373939i
$650$			39.7995i			1.56106i
$651$		0			0
$652$			16.2481i			0.636324i
$653$	−2.87228	+	4.97494i	−0.112401	+	0.194684i	−0.916738	−	0.399489i	$-0.869187\pi$
$653$	−2.87228	+	4.97494i	−0.112401	+	0.194684i	0.804337	+	0.594174i	$0.202521\pi$
$654$		0			0
$655$	5.50000	+	9.52628i	0.214903	+	0.372223i
$656$	−19.5959	+	33.9411i	−0.765092	+	1.32518i
$657$		0			0
$658$	27.0000	−	5.19615i	1.05257	−	0.202567i
$659$	−11.4891			−0.447553			−0.223776	−	0.974641i	$-0.571839\pi$
$659$	−11.4891			−0.447553			−0.223776	+	0.974641i	$0.571839\pi$
$660$		0			0
$661$	−11.7260	−	20.3101i	−0.456090	−	0.789971i	0.542660	−	0.839952i	$-0.317417\pi$
$661$	−11.7260	−	20.3101i	−0.456090	−	0.789971i	−0.998750	+	0.0499812i	$0.984084\pi$
$662$		0			0
$663$		0			0
$664$	9.38083			0.364047
$665$	−40.4166	+	7.77817i	−1.56729	+	0.301625i
$666$		0			0
$667$	7.03562	+	4.06202i	0.272420	+	0.157282i
$668$	−4.89898	−	8.48528i	−0.189547	−	0.328305i
$669$		0			0
$670$		0			0
$671$	26.9444			1.04018
$672$		0			0
$673$	17.0000			0.655302			0.327651	−	0.944799i	$-0.393743\pi$
$673$	17.0000			0.655302			0.327651	+	0.944799i	$0.393743\pi$
$674$	−35.5176	−	20.5061i	−1.36809	−	0.789865i
$675$		0			0
$676$	9.00000	+	15.5885i	0.346154	+	0.599556i
$677$	−20.1060	−	11.6082i	−0.772735	−	0.446139i	0.0611143	−	0.998131i	$-0.480535\pi$
$677$	−20.1060	−	11.6082i	−0.772735	−	0.446139i	−0.833849	+	0.551992i	$0.813868\pi$
$678$		0			0
$679$	−1.50000	+	4.33013i	−0.0575647	+	0.166175i
$680$	−22.9783			−0.881176
$681$		0			0
$682$	−21.1069	−	36.5582i	−0.808224	−	1.39988i
$683$	−20.1060	−	34.8246i	−0.769334	−	1.33252i	−0.937925	−	0.346839i	$-0.887255\pi$
$683$	−20.1060	−	34.8246i	−0.769334	−	1.33252i	0.168591	−	0.985686i	$-0.446078\pi$
$684$		0			0
$685$	46.9042			1.79212
$686$	−1.22474	−	26.1630i	−0.0467610	−	0.998906i
$687$		0			0
$688$	−28.1425	−	16.2481i	−1.07292	−	0.619452i
$689$	13.4722	+	23.3345i	0.513250	+	0.888975i
$690$		0			0
$691$	23.4521	−	40.6202i	0.892159	−	1.54526i	0.0548775	−	0.998493i	$-0.482523\pi$
$691$	23.4521	−	40.6202i	0.892159	−	1.54526i	0.837282	−	0.546772i	$-0.184143\pi$
$692$			13.2665i			0.504317i
$693$		0			0
$694$			48.7442i			1.85031i
$695$	−26.9444	−	15.5563i	−1.02206	−	0.590086i
$696$		0			0
$697$	12.0000	+	20.7846i	0.454532	+	0.787273i
$698$	−11.4891	−	6.63325i	−0.434870	−	0.251072i
$699$		0			0
$700$	−24.0000	+	20.7846i	−0.907115	+	0.785584i
$701$	−17.2337			−0.650907			−0.325454	−	0.945558i	$-0.605517\pi$
$701$	−17.2337			−0.650907			−0.325454	+	0.945558i	$0.605517\pi$
$702$		0			0
$703$	33.0000	−	19.0526i	1.24462	−	0.718581i
$704$	−22.9783	−	39.7995i	−0.866025	−	1.50000i
$705$		0			0
$706$			13.8564i			0.521493i
$707$	−17.2337	+	3.31662i	−0.648140	+	0.124735i
$708$		0			0
$709$	42.2137	+	24.3721i	1.58537	+	0.915314i	0.994056	+	0.108873i	$0.0347242\pi$
$709$	42.2137	+	24.3721i	1.58537	+	0.915314i	0.591315	+	0.806441i	$0.298609\pi$
$710$	5.74456	−	3.31662i	0.215590	−	0.124471i
$711$		0			0
$712$	24.0000	+	13.8564i	0.899438	+	0.519291i
$713$	7.34847			0.275202
$714$		0			0
$715$			89.3644i			3.34204i
$716$	−11.4891	+	19.8997i	−0.429369	+	0.743689i
$717$		0			0
$718$	−4.00000	−	6.92820i	−0.149279	−	0.258558i
$719$	17.1464	−	29.6985i	0.639454	−	1.10757i	−0.346099	−	0.938198i	$-0.612494\pi$
$719$	17.1464	−	29.6985i	0.639454	−	1.10757i	0.985553	−	0.169369i	$-0.0541728\pi$
$720$		0			0
$721$	−12.0000	−	13.8564i	−0.446903	−	0.516040i
$722$			4.24264i			0.157895i
$723$		0			0
$724$	9.38083	+	16.2481i	0.348636	+	0.603855i
$725$	17.2337	+	29.8496i	0.640043	+	1.10859i
$726$		0			0
$727$			12.1244i			0.449667i	0.974397	+	0.224834i	$0.0721839\pi$
$727$			12.1244i			0.449667i	−0.974397	+	0.224834i	$0.927816\pi$
$728$	−11.4891	+	33.1662i	−0.425815	+	1.22922i
$729$		0			0
$730$	−14.0712	−	8.12404i	−0.520800	−	0.300684i
$731$	−17.2337	+	9.94987i	−0.637411	+	0.368009i
$732$		0			0
$733$	16.4165	−	28.4341i	0.606356	−	1.05024i	−0.385480	−	0.922716i	$-0.625964\pi$
$733$	16.4165	−	28.4341i	0.606356	−	1.05024i	0.991836	−	0.127523i	$-0.0407025\pi$
$734$	31.8434			1.17536
$735$		0			0
$736$	8.00000			0.294884
$737$		0			0
$738$		0			0
$739$	−14.0712	+	8.12404i	−0.517619	+	0.298848i	−0.735960	−	0.677025i	$-0.763269\pi$
$739$	−14.0712	+	8.12404i	−0.517619	+	0.298848i	0.218341	+	0.975873i	$0.429936\pi$
$740$	26.9444	−	46.6690i	0.990495	−	1.71559i
$741$		0			0
$742$	−7.03562	+	20.3101i	−0.258286	+	0.745607i
$743$			19.7990i			0.726354i	0.931720	+	0.363177i	$0.118308\pi$
$743$			19.7990i			0.726354i	−0.931720	+	0.363177i	$0.881692\pi$
$744$		0			0
$745$	−33.0000	+	19.0526i	−1.20903	+	0.698032i
$746$	−11.4891	−	19.8997i	−0.420647	−	0.728582i
$747$		0			0
$748$	−28.1425			−1.02899
$749$	11.4891	−	9.94987i	0.419804	−	0.363560i
$750$		0			0
$751$	−2.50000	+	4.33013i	−0.0912263	+	0.158009i	−0.908027	−	0.418911i	$-0.862412\pi$
$751$	−2.50000	+	4.33013i	−0.0912263	+	0.158009i	0.816801	+	0.576919i	$0.195745\pi$
$752$	−14.6969	−	25.4558i	−0.535942	−	0.928279i
$753$		0			0
$754$	33.0000	+	19.0526i	1.20179	+	0.693853i
$755$		−	3.31662i		−	0.120704i
$756$		0			0
$757$			24.3721i			0.885820i	0.896566	+	0.442910i	$0.146054\pi$
$757$			24.3721i			0.885820i	−0.896566	+	0.442910i	$0.853946\pi$
$758$		0			0
$759$		0			0
$760$	22.0000	+	38.1051i	0.798024	+	1.38222i
$761$	8.57321	−	14.8492i	0.310779	−	0.538285i	−0.667752	−	0.744383i	$-0.732744\pi$
$761$	8.57321	−	14.8492i	0.310779	−	0.538285i	0.978531	+	0.206099i	$0.0660768\pi$
$762$		0			0
$763$	−42.2137	+	8.12404i	−1.52824	+	0.294110i
$764$			11.3137i			0.409316i
$765$		0			0
$766$	−12.0000	+	6.92820i	−0.433578	+	0.250326i
$767$	−13.4722	+	7.77817i	−0.486453	+	0.280854i
$768$		0			0
$769$			39.8372i			1.43657i	0.695752	+	0.718283i	$0.255071\pi$
$769$			39.8372i			1.43657i	−0.695752	+	0.718283i	$0.744929\pi$
$770$	−53.8888	+	46.6690i	−1.94202	+	1.68184i
$771$		0			0
$772$	−1.00000	+	1.73205i	−0.0359908	+	0.0623379i
$773$	11.4891	−	6.63325i	0.413235	−	0.238581i	−0.278944	−	0.960307i	$-0.589984\pi$
$773$	11.4891	−	6.63325i	0.413235	−	0.238581i	0.692179	+	0.721726i	$0.256651\pi$
$774$		0			0
$775$	27.0000	+	15.5885i	0.969869	+	0.559954i
$776$	4.89898			0.175863
$777$		0			0
$778$		−	32.4962i		−	1.16504i
$779$	22.9783	−	39.7995i	0.823281	−	1.42596i
$780$		0			0
$781$	7.03562	−	4.06202i	0.251754	−	0.145350i
$782$	2.44949	−	4.24264i	0.0875936	−	0.151717i
$783$		0			0
$784$	−26.0000	+	10.3923i	−0.928571	+	0.371154i
$785$		−	62.2254i		−	2.22092i
$786$		0			0
$787$	16.4165	+	28.4341i	0.585183	+	1.01357i	0.994853	+	0.101333i	$0.0323108\pi$
$787$	16.4165	+	28.4341i	0.585183	+	1.01357i	−0.409669	+	0.912234i	$0.634356\pi$
$788$		0			0
$789$		0			0
$790$	32.8329			1.16814
$791$	12.2474	−	35.3553i	0.435469	−	1.25709i
$792$		0			0
$793$	−11.0000	+	19.0526i	−0.390621	+	0.676576i
$794$	−22.9783	+	13.2665i	−0.815468	+	0.470810i
$795$		0			0
$796$	12.0000	+	6.92820i	0.425329	+	0.245564i
$797$			3.31662i			0.117481i	0.998273	+	0.0587404i	$0.0187084\pi$
$797$			3.31662i			0.117481i	−0.998273	+	0.0587404i	$0.981292\pi$
$798$		0			0
$799$	−18.0000			−0.636794
$800$	29.3939	+	16.9706i	1.03923	+	0.600000i
$801$		0			0
$802$	−10.0000	−	17.3205i	−0.353112	−	0.611608i
$803$	−17.2337	−	9.94987i	−0.608164	−	0.351123i
$804$		0			0
$805$	−2.34521	−	12.1861i	−0.0826577	−	0.429502i
$806$	34.4674			1.21406
$807$		0			0
$808$	9.38083	+	16.2481i	0.330017	+	0.571605i
$809$	−19.5959	+	11.3137i	−0.688956	+	0.397769i	−0.803221	−	0.595682i	$-0.796882\pi$
$809$	−19.5959	+	11.3137i	−0.688956	+	0.397769i	0.114265	+	0.993450i	$0.463549\pi$
$810$		0			0
$811$	−46.9042			−1.64703			−0.823514	−	0.567296i	$-0.807989\pi$
$811$	−46.9042			−1.64703			−0.823514	+	0.567296i	$0.807989\pi$
$812$	5.74456	+	29.8496i	0.201595	+	1.04752i
$813$		0			0
$814$	33.0000	−	57.1577i	1.15665	−	2.00338i
$815$	−13.4722	−	23.3345i	−0.471910	−	0.817373i
$816$		0			0
$817$	33.0000	+	19.0526i	1.15452	+	0.666565i
$818$	36.7423			1.28467
$819$		0			0
$820$		−	64.9923i		−	2.26963i
$821$	−8.61684	+	14.9248i	−0.300730	+	0.520880i	−0.976301	−	0.216415i	$-0.930564\pi$
$821$	−8.61684	+	14.9248i	−0.300730	+	0.520880i	0.675572	+	0.737294i	$0.263897\pi$
$822$		0			0
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	0.717847	−	0.696201i	$-0.245128\pi$
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	−0.961851	+	0.273573i	$0.911795\pi$
$824$	−9.79796	+	16.9706i	−0.341328	+	0.591198i
$825$		0			0
$826$	−11.7260	−	4.06202i	−0.408001	−	0.141336i
$827$	17.2337			0.599274			0.299637	−	0.954053i	$-0.403134\pi$
$827$	17.2337			0.599274			0.299637	+	0.954053i	$0.403134\pi$
$828$		0			0
$829$	−11.7260	−	20.3101i	−0.407262	−	0.705399i	0.587320	−	0.809355i	$-0.300183\pi$
$829$	−11.7260	−	20.3101i	−0.407262	−	0.705399i	−0.994582	+	0.103956i	$0.966850\pi$
$830$	−13.4722	+	7.77817i	−0.467627	+	0.269984i
$831$		0			0
$832$	37.5233			1.30089
$833$	−2.44949	+	16.9706i	−0.0848698	+	0.587995i
$834$		0			0
$835$	14.0712	+	8.12404i	0.486956	+	0.281144i
$836$	26.9444	+	46.6690i	0.931891	+	1.61408i
$837$		0			0
$838$	−18.7617	+	32.4962i	−0.648111	+	1.12256i
$839$	−46.5403			−1.60675			−0.803375	−	0.595474i	$-0.796964\pi$
$839$	−46.5403			−1.60675			−0.803375	+	0.595474i	$0.796964\pi$
$840$		0			0
$841$	4.00000			0.137931
$842$	5.74456	−	9.94987i	0.197971	−	0.342895i
$843$		0			0
$844$	14.0712	−	8.12404i	0.484352	−	0.279641i
$845$	−25.8505	−	14.9248i	−0.889285	−	0.513429i
$846$		0			0
$847$	−44.0000	+	38.1051i	−1.51186	+	1.30931i
$848$	22.9783			0.789076
$849$		0			0
$850$	18.0000	−	10.3923i	0.617395	−	0.356453i
$851$	5.74456	+	9.94987i	0.196921	+	0.341077i
$852$		0			0
$853$	−18.7617			−0.642387			−0.321194	−	0.947014i	$-0.604084\pi$
$853$	−18.7617			−0.642387			−0.321194	+	0.947014i	$0.604084\pi$
$854$	−17.2337	+	3.31662i	−0.589725	+	0.113493i
$855$		0			0
$856$	−14.0712	−	8.12404i	−0.480945	−	0.277674i
$857$	−8.57321	−	14.8492i	−0.292855	−	0.507240i	0.681628	−	0.731699i	$-0.261272\pi$
$857$	−8.57321	−	14.8492i	−0.292855	−	0.507240i	−0.974484	+	0.224458i	$0.927939\pi$
$858$		0			0
$859$	2.34521	−	4.06202i	0.0800175	−	0.138594i	−0.823240	−	0.567694i	$-0.807836\pi$
$859$	2.34521	−	4.06202i	0.0800175	−	0.138594i	0.903257	+	0.429100i	$0.141169\pi$
$860$	53.8888			1.83759
$861$		0			0
$862$	−40.0000			−1.36241
$863$	−17.1464	−	9.89949i	−0.583671	−	0.336983i	0.178920	−	0.983864i	$-0.442740\pi$
$863$	−17.1464	−	9.89949i	−0.583671	−	0.336983i	−0.762591	+	0.646881i	$0.776073\pi$
$864$		0			0
$865$	−11.0000	−	19.0526i	−0.374011	−	0.647806i
$866$	−22.0454	+	38.1838i	−0.749133	+	1.29754i
$867$		0			0
$868$	18.0000	+	20.7846i	0.610960	+	0.705476i
$869$	40.2119			1.36410
$870$		0			0
$871$		0			0
$872$	22.9783	+	39.7995i	0.778142	+	1.34778i
$873$		0			0
$874$	−9.38083			−0.317311
$875$	2.87228	−	8.29156i	0.0971008	−	0.280306i
$876$		0			0
$877$	14.0712	+	8.12404i	0.475152	+	0.274329i	0.718394	−	0.695636i	$-0.244878\pi$
$877$	14.0712	+	8.12404i	0.475152	+	0.274329i	−0.243242	+	0.969966i	$0.578211\pi$
$878$	−18.3712	−	31.8198i	−0.619997	−	1.07387i
$879$		0			0
$880$	66.0000	+	38.1051i	2.22486	+	1.28452i
$881$	44.0908			1.48546			0.742729	−	0.669593i	$-0.233531\pi$
$881$	44.0908			1.48546			0.742729	+	0.669593i	$0.233531\pi$
$882$		0			0
$883$		−	48.7442i		−	1.64037i	−0.572096	−	0.820187i	$-0.693869\pi$
$883$		−	48.7442i		−	1.64037i	0.572096	−	0.820187i	$-0.306131\pi$
$884$	11.4891	−	19.8997i	0.386421	−	0.669301i
$885$		0			0
$886$	−21.1069	+	12.1861i	−0.709099	+	0.409399i
$887$	−6.12372	+	10.6066i	−0.205615	+	0.356135i	−0.950328	−	0.311249i	$-0.899253\pi$
$887$	−6.12372	+	10.6066i	−0.205615	+	0.356135i	0.744714	+	0.667384i	$0.232586\pi$
$888$		0			0
$889$	−32.5000	−	11.2583i	−1.09002	−	0.377592i
$890$	−45.9565			−1.54047
$891$		0			0
$892$	33.0000	−	19.0526i	1.10492	−	0.637927i
$893$	17.2337	+	29.8496i	0.576703	+	0.998880i
$894$		0			0
$895$		−	38.1051i		−	1.27371i
$896$	19.5959	+	22.6274i	0.654654	+	0.755929i
$897$		0			0
$898$	17.0000	−	29.4449i	0.567297	−	0.982588i
$899$	25.8505	−	14.9248i	0.862164	−	0.497770i
$900$		0			0
$901$	7.03562	−	12.1861i	0.234391	−	0.405976i
$902$		−	79.5990i		−	2.65036i
$903$		0			0
$904$	−40.0000			−1.33038
$905$	−26.9444	−	15.5563i	−0.895662	−	0.517111i
$906$		0			0
$907$	35.1781	−	20.3101i	1.16807	−	0.674386i	0.214845	−	0.976648i	$-0.431075\pi$
$907$	35.1781	−	20.3101i	1.16807	−	0.674386i	0.953225	+	0.302262i	$0.0977419\pi$
$908$	40.2119	+	23.2164i	1.33448	+	0.770462i
$909$		0			0
$910$	−11.0000	−	57.1577i	−0.364646	−	1.89476i
$911$		−	35.3553i		−	1.17137i	−0.810537	−	0.585687i	$-0.800825\pi$
$911$		−	35.3553i		−	1.17137i	0.810537	−	0.585687i	$-0.199175\pi$
$912$		0			0
$913$	−16.5000	+	9.52628i	−0.546070	+	0.315274i
$914$	−30.6186	+	17.6777i	−1.01277	+	0.584725i
$915$		0			0
$916$	−18.7617			−0.619903
$917$	−5.74456	−	6.63325i	−0.189702	−	0.219049i
$918$		0			0
$919$	17.0000	−	29.4449i	0.560778	−	0.971296i	−0.436650	−	0.899631i	$-0.643835\pi$
$919$	17.0000	−	29.4449i	0.560778	−	0.971296i	0.997429	−	0.0716652i	$-0.0228313\pi$
$920$	−11.4891	+	6.63325i	−0.378785	+	0.218692i
$921$		0			0
$922$	−4.69042	+	8.12404i	−0.154471	+	0.267551i
$923$			6.63325i			0.218336i
$924$		0			0
$925$			48.7442i			1.60270i
$926$	26.9444	+	15.5563i	0.885448	+	0.511213i
$927$		0			0
$928$	28.1425	−	16.2481i	0.923823	−	0.533369i
$929$	3.67423	−	6.36396i	0.120548	−	0.208795i	−0.799436	−	0.600751i	$-0.794868\pi$
$929$	3.67423	−	6.36396i	0.120548	−	0.208795i	0.919984	+	0.391956i	$0.128202\pi$
$930$		0			0
$931$	30.4877	−	12.1861i	0.999194	−	0.399382i
$932$		−	14.1421i		−	0.463241i
$933$		0			0
$934$	−4.69042	−	8.12404i	−0.153475	−	0.265827i
$935$	40.4166	−	23.3345i	1.32176	−	0.763121i
$936$		0			0
$937$			36.3731i			1.18826i	0.804370	+	0.594128i	$0.202503\pi$
$937$			36.3731i			1.18826i	−0.804370	+	0.594128i	$0.797497\pi$
$938$		0			0
$939$		0			0
$940$	42.2137	+	24.3721i	1.37686	+	0.794931i
$941$	−31.5951	+	18.2414i	−1.02997	+	0.594654i	−0.916976	−	0.398942i	$-0.869378\pi$
$941$	−31.5951	+	18.2414i	−1.02997	+	0.594654i	−0.112994	+	0.993596i	$0.536044\pi$
$942$		0			0
$943$	12.0000	+	6.92820i	0.390774	+	0.225613i
$944$			13.2665i			0.431788i
$945$		0			0
$946$	66.0000			2.14585
$947$	−17.2337	+	29.8496i	−0.560020	+	0.969982i	0.437474	+	0.899231i	$0.355873\pi$
$947$	−17.2337	+	29.8496i	−0.560020	+	0.969982i	−0.997494	+	0.0707515i	$0.977460\pi$
$948$		0			0
$949$	14.0712	−	8.12404i	0.456772	−	0.263717i
$950$	−34.4674	−	19.8997i	−1.11827	−	0.645633i
$951$		0			0
$952$	18.0000	−	3.46410i	0.583383	−	0.112272i
$953$			7.07107i			0.229054i	0.993420	+	0.114527i	$0.0365353\pi$
$953$			7.07107i			0.229054i	−0.993420	+	0.114527i	$0.963465\pi$
$954$		0			0
$955$	−9.38083	−	16.2481i	−0.303557	−	0.525775i
$956$	2.44949	−	1.41421i	0.0792222	−	0.0457389i
$957$		0			0
$958$		−	38.1051i		−	1.23112i
$959$	−36.7423	+	7.07107i	−1.18647	+	0.228337i
$960$		0			0
$961$	−2.00000	+	3.46410i	−0.0645161	+	0.111745i
$962$	26.9444	+	46.6690i	0.868722	+	1.50467i
$963$		0			0
$964$	−21.0000	−	12.1244i	−0.676364	−	0.390499i
$965$		−	3.31662i		−	0.106766i
$966$		0			0
$967$	−13.0000			−0.418052			−0.209026	−	0.977910i	$-0.567029\pi$
$967$	−13.0000			−0.418052			−0.209026	+	0.977910i	$0.567029\pi$
$968$	53.8888	+	31.1127i	1.73205	+	1.00000i
$969$		0			0
$970$	−7.03562	+	4.06202i	−0.225900	+	0.130424i
$971$	−37.3397	−	21.5581i	−1.19829	−	0.691831i	−0.238114	−	0.971237i	$-0.576529\pi$
$971$	−37.3397	−	21.5581i	−1.19829	−	0.691831i	−0.960173	+	0.279406i	$0.909862\pi$
$972$		0			0
$973$	23.4521	+	8.12404i	0.751839	+	0.260445i
$974$		−	35.3553i		−	1.13286i
$975$		0			0
$976$	9.38083	+	16.2481i	0.300273	+	0.520088i
$977$	20.8207	−	12.0208i	0.666112	−	0.384580i	−0.128490	−	0.991711i	$-0.541013\pi$
$977$	20.8207	−	12.0208i	0.666112	−	0.384580i	0.794602	+	0.607131i	$0.207680\pi$
$978$		0			0
$979$	−56.2850			−1.79888
$980$	28.7228	−	36.4829i	0.917517	−	1.16540i
$981$		0			0
$982$	−35.1781	−	20.3101i	−1.12258	−	0.648121i
$983$	−4.89898	−	8.48528i	−0.156253	−	0.270638i	0.777261	−	0.629178i	$-0.216608\pi$
$983$	−4.89898	−	8.48528i	−0.156253	−	0.270638i	−0.933515	+	0.358539i	$0.883275\pi$
$984$		0			0
$985$		0			0
$986$		−	19.8997i		−	0.633737i
$987$		0			0
$988$	−44.0000			−1.39983
$989$	−5.74456	+	9.94987i	−0.182666	+	0.316388i
$990$		0			0
$991$	−17.5000	−	30.3109i	−0.555906	−	0.962857i	−0.997832	−	0.0658059i	$-0.979038\pi$
$991$	−17.5000	−	30.3109i	−0.555906	−	0.962857i	0.441927	−	0.897051i	$-0.354295\pi$
$992$	14.6969	−	25.4558i	0.466628	−	0.808224i
$993$		0			0
$994$	−4.00000	+	3.46410i	−0.126872	+	0.109875i
$995$	−22.9783			−0.728460
$996$		0			0
$997$	9.38083	+	16.2481i	0.297094	+	0.514582i	0.975470	−	0.220133i	$-0.0706492\pi$
$997$	9.38083	+	16.2481i	0.297094	+	0.514582i	−0.678376	+	0.734715i	$0.737316\pi$
$998$	22.9783	+	39.7995i	0.727364	+	1.25983i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.ch.a.341.1	yes	8
3.2	odd	2	inner	504.2.ch.a.341.4	yes	8
4.3	odd	2		2016.2.cp.a.593.1		8
7.3	odd	6	inner	504.2.ch.a.269.3	yes	8
8.3	odd	2		2016.2.cp.a.593.4		8
8.5	even	2	inner	504.2.ch.a.341.2	yes	8
12.11	even	2		2016.2.cp.a.593.3		8
21.17	even	6	inner	504.2.ch.a.269.2	yes	8
24.5	odd	2	inner	504.2.ch.a.341.3	yes	8
24.11	even	2		2016.2.cp.a.593.2		8
28.3	even	6		2016.2.cp.a.17.2		8
56.3	even	6		2016.2.cp.a.17.3		8
56.45	odd	6	inner	504.2.ch.a.269.4	yes	8
84.59	odd	6		2016.2.cp.a.17.4		8
168.59	odd	6		2016.2.cp.a.17.1		8
168.101	even	6	inner	504.2.ch.a.269.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.ch.a.269.1	✓	8	168.101	even	6	inner
504.2.ch.a.269.2	yes	8	21.17	even	6	inner
504.2.ch.a.269.3	yes	8	7.3	odd	6	inner
504.2.ch.a.269.4	yes	8	56.45	odd	6	inner
504.2.ch.a.341.1	yes	8	1.1	even	1	trivial
504.2.ch.a.341.2	yes	8	8.5	even	2	inner
504.2.ch.a.341.3	yes	8	24.5	odd	2	inner
504.2.ch.a.341.4	yes	8	3.2	odd	2	inner
2016.2.cp.a.17.1		8	168.59	odd	6
2016.2.cp.a.17.2		8	28.3	even	6
2016.2.cp.a.17.3		8	56.3	even	6
2016.2.cp.a.17.4		8	84.59	odd	6
2016.2.cp.a.593.1		8	4.3	odd	2
2016.2.cp.a.593.2		8	24.11	even	2
2016.2.cp.a.593.3		8	12.11	even	2
2016.2.cp.a.593.4		8	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.ch (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-2.87228 - 1.65831i) q^{5} +(2.50000 + 0.866025i) q^{7} -2.82843i q^{8} +O(q^{10})\)	\(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-2.87228 - 1.65831i) q^{5} +(2.50000 + 0.866025i) q^{7} -2.82843i q^{8} +(2.34521 + 4.06202i) q^{10} +(2.87228 + 4.97494i) q^{11} -4.69042 q^{13} +(-2.44949 - 2.82843i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(1.22474 + 2.12132i) q^{17} +(2.34521 - 4.06202i) q^{19} -6.63325i q^{20} -8.12404i q^{22} +(1.22474 + 0.707107i) q^{23} +(3.00000 + 5.19615i) q^{25} +(5.74456 + 3.31662i) q^{26} +(1.00000 + 5.19615i) q^{28} +5.74456 q^{29} +(4.50000 - 2.59808i) q^{31} +(4.89898 - 2.82843i) q^{32} -3.46410i q^{34} +(-5.74456 - 6.63325i) q^{35} +(7.03562 + 4.06202i) q^{37} +(-5.74456 + 3.31662i) q^{38} +(-4.69042 + 8.12404i) q^{40} +9.79796 q^{41} +8.12404i q^{43} +(-5.74456 + 9.94987i) q^{44} +(-1.00000 - 1.73205i) q^{46} +(-3.67423 + 6.36396i) q^{47} +(5.50000 + 4.33013i) q^{49} -8.48528i q^{50} +(-4.69042 - 8.12404i) q^{52} +(-2.87228 - 4.97494i) q^{53} -19.0526i q^{55} +(2.44949 - 7.07107i) q^{56} +(-7.03562 - 4.06202i) q^{58} +(2.87228 - 1.65831i) q^{59} +(2.34521 - 4.06202i) q^{61} -7.34847 q^{62} -8.00000 q^{64} +(13.4722 + 7.77817i) q^{65} +(-2.44949 + 4.24264i) q^{68} +(2.34521 + 12.1861i) q^{70} -1.41421i q^{71} +(-3.00000 + 1.73205i) q^{73} +(-5.74456 - 9.94987i) q^{74} +9.38083 q^{76} +(2.87228 + 14.9248i) q^{77} +(3.50000 - 6.06218i) q^{79} +(11.4891 - 6.63325i) q^{80} +(-12.0000 - 6.92820i) q^{82} +3.31662i q^{83} -8.12404i q^{85} +(5.74456 - 9.94987i) q^{86} +(14.0712 - 8.12404i) q^{88} +(-4.89898 + 8.48528i) q^{89} +(-11.7260 - 4.06202i) q^{91} +2.82843i q^{92} +(9.00000 - 5.19615i) q^{94} +(-13.4722 + 7.77817i) q^{95} +1.73205i q^{97} +(-3.67423 - 9.19239i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} + 20 q^{7}+O(q^{10}) \) 8 * q + 8 * q^4 + 20 * q^7	\( 8 q + 8 q^{4} + 20 q^{7} - 16 q^{16} + 24 q^{25} + 8 q^{28} + 36 q^{31} - 8 q^{46} + 44 q^{49} - 64 q^{64} - 24 q^{73} + 28 q^{79} - 96 q^{82} + 72 q^{94}+O(q^{100}) \) 8 * q + 8 * q^4 + 20 * q^7 - 16 * q^16 + 24 * q^25 + 8 * q^28 + 36 * q^31 - 8 * q^46 + 44 * q^49 - 64 * q^64 - 24 * q^73 + 28 * q^79 - 96 * q^82 + 72 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more