LMFDB - Embedded newform 504.2.ch.a.269.3

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			269.3
Root			$0.461396 - 0.310963i$ of defining polynomial
Character	$\chi$	$=$	504.269
Dual form			504.2.ch.a.341.3

$q$-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 $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

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

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	−0.977672	−	0.210138i	$-0.932609\pi$
$5$	−2.87228	+	1.65831i	−1.28452	+	0.741620i	−0.306851	+	0.951757i	$0.599275\pi$
$6$		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		−	1.00000i	$-0.5\pi$
$11$	2.87228	−	4.97494i	0.866025	−	1.50000i	0.866025	−	0.500000i	$-0.166667\pi$
$12$		0			0
$13$	4.69042			1.30089			0.650444	−	0.759555i	$-0.274583\pi$
$13$	4.69042			1.30089			0.650444	+	0.759555i	$0.274583\pi$
$14$	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	$-0.929334\pi$
$17$	−1.22474	+	2.12132i	−0.297044	+	0.514496i	0.678414	+	0.734680i	$0.262668\pi$
$18$		0			0
$19$	−2.34521	−	4.06202i	−0.538028	−	0.931891i	−0.999010	−	0.0444819i	$-0.985836\pi$
$19$	−2.34521	−	4.06202i	−0.538028	−	0.931891i	0.460983	−	0.887409i	$-0.347497\pi$
$20$			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	$-0.713771\pi$
$23$	−1.22474	+	0.707107i	−0.255377	+	0.147442i	0.366847	+	0.930281i	$0.380437\pi$
$24$		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	0.846339	−	0.532645i	$-0.178802\pi$
$31$	4.50000	+	2.59808i	0.808224	+	0.466628i	−0.0381148	+	0.999273i	$0.512135\pi$
$32$	−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	$-0.899427\pi$
$37$	−7.03562	+	4.06202i	−1.15665	+	0.667792i	−0.206151	+	0.978520i	$0.566094\pi$
$38$	−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	$-0.777307\pi$
$41$	−9.79796			−1.53018			−0.765092	+	0.643921i	$0.777307\pi$
$42$		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	0.999117	+	0.0420122i	$0.0133768\pi$
$47$	3.67423	+	6.36396i	0.535942	+	0.928279i	−0.463175	+	0.886267i	$0.653290\pi$
$48$		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	−0.993042	−	0.117760i	$-0.962429\pi$
$53$	−2.87228	+	4.97494i	−0.394538	+	0.683360i	0.598504	+	0.801120i	$0.295762\pi$
$54$		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	0.675178	−	0.737655i	$-0.264067\pi$
$59$	2.87228	+	1.65831i	0.373939	+	0.215894i	−0.301239	+	0.953549i	$0.597400\pi$
$60$		0			0
$61$	−2.34521	−	4.06202i	−0.300273	−	0.520088i	0.675925	−	0.736971i	$-0.263744\pi$
$61$	−2.34521	−	4.06202i	−0.300273	−	0.520088i	−0.976198	+	0.216883i	$0.930411\pi$
$62$	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	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$	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	0.314057	−	0.949404i	$-0.398312\pi$
$73$	−3.00000	−	1.73205i	−0.351123	−	0.202721i	−0.665180	+	0.746683i	$0.731645\pi$
$74$	−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	0.992945	−	0.118578i	$-0.0378336\pi$
$79$	3.50000	+	6.06218i	0.393781	+	0.682048i	−0.599164	+	0.800626i	$0.704500\pi$
$80$	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	$-0.941735\pi$
$83$		−	3.31662i		−	0.364047i	0.983294	−	0.182023i	$-0.0582647\pi$
$84$		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	0.999749	+	0.0224202i	$0.00713717\pi$
$89$	4.89898	+	8.48528i	0.519291	+	0.899438i	−0.480458	+	0.877018i	$0.659529\pi$
$90$		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	$-0.971974\pi$
$97$		−	1.73205i		−	0.175863i	0.996127	−	0.0879316i	$-0.0280257\pi$
$98$	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	0.186185	−	0.982515i	$-0.440388\pi$
$101$	−5.74456	−	3.31662i	−0.571605	−	0.330017i	−0.757790	+	0.652498i	$0.773721\pi$
$102$		0			0
$103$	−6.00000	+	3.46410i	−0.591198	+	0.341328i	−0.765571	−	0.643352i	$-0.777543\pi$
$103$	−6.00000	+	3.46410i	−0.591198	+	0.341328i	0.174373	+	0.984680i	$0.444210\pi$
$104$		−	13.2665i		−	1.30089i
$105$		0			0
$106$			8.12404i			0.789076i
$107$	2.87228	+	4.97494i	0.277674	+	0.480945i	0.970806	−	0.239865i	$-0.0771032\pi$
$107$	2.87228	+	4.97494i	0.277674	+	0.480945i	−0.693132	+	0.720810i	$0.743770\pi$
$108$		0			0
$109$	14.0712	+	8.12404i	1.34778	+	0.778142i	0.987935	−	0.154870i	$-0.0494958\pi$
$109$	14.0712	+	8.12404i	1.34778	+	0.778142i	0.359846	+	0.933012i	$0.382829\pi$
$110$	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	−0.620200	−	0.784444i	$-0.712949\pi$
$131$	−2.87228	+	1.65831i	−0.250952	+	0.144887i	0.369248	+	0.929331i	$0.379615\pi$
$132$		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	$-0.126857\pi$
$137$	12.2474	+	7.07107i	1.04637	+	0.604122i	0.124739	+	0.992190i	$0.460191\pi$
$138$		0			0
$139$	−9.38083			−0.795672			−0.397836	−	0.917457i	$-0.630239\pi$
$139$	−9.38083			−0.795672			−0.397836	+	0.917457i	$0.630239\pi$
$140$	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	0.999435	−	0.0336072i	$-0.0106995\pi$
$149$	5.74456	+	9.94987i	0.470613	+	0.815125i	−0.528822	+	0.848733i	$0.677366\pi$
$150$		0			0
$151$	0.500000	−	0.866025i	0.0406894	−	0.0704761i	−0.844963	−	0.534824i	$-0.820378\pi$
$151$	0.500000	−	0.866025i	0.0406894	−	0.0704761i	0.885653	+	0.464348i	$0.153711\pi$
$152$	−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	0.199788	+	0.979839i	$0.435975\pi$
$157$	−9.38083	+	16.2481i	−0.748672	+	1.29674i	−0.948459	+	0.316898i	$0.897359\pi$
$158$	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	$-0.769732\pi$
$163$	−7.03562	+	4.06202i	−0.551073	+	0.318162i	0.198482	+	0.980105i	$0.436399\pi$
$164$	−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	$-0.439298\pi$
$167$	4.89898			0.379094			0.189547	+	0.981872i	$0.439298\pi$
$168$		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	−0.265467	−	0.964120i	$-0.585526\pi$
$173$	5.74456	−	3.31662i	0.436751	−	0.252158i	0.702219	+	0.711961i	$0.252193\pi$
$174$		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	−0.567448	−	0.823409i	$-0.692069\pi$
$179$	5.74456	−	9.94987i	0.429369	−	0.743689i	0.996817	+	0.0797204i	$0.0254027\pi$
$180$		0			0
$181$	−9.38083			−0.697272			−0.348636	−	0.937258i	$-0.613355\pi$
$181$	−9.38083			−0.697272			−0.348636	+	0.937258i	$0.613355\pi$
$182$	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	$-0.732275\pi$
$191$	−4.89898	+	2.82843i	−0.354478	+	0.204658i	0.312178	+	0.950024i	$0.398941\pi$
$192$		0			0
$193$	0.500000	−	0.866025i	0.0359908	−	0.0623379i	−0.847469	−	0.530845i	$-0.821875\pi$
$193$	0.500000	−	0.866025i	0.0359908	−	0.0623379i	0.883460	+	0.468507i	$0.155208\pi$
$194$	−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	0.697355	−	0.716726i	$-0.254360\pi$
$199$	6.00000	+	3.46410i	0.425329	+	0.245564i	−0.272026	+	0.962290i	$0.587694\pi$
$200$	−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	$0.220208\pi$
$223$			19.0526i			1.27585i	−0.770097	+	0.637927i	$0.779792\pi$
$224$	−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	0.985983	−	0.166847i	$-0.0533587\pi$
$227$	20.1060	+	11.6082i	1.33448	+	0.770462i	0.348497	+	0.937310i	$0.386692\pi$
$228$		0			0
$229$	4.69042	+	8.12404i	0.309951	+	0.536852i	0.978351	−	0.206950i	$-0.0663539\pi$
$229$	4.69042	+	8.12404i	0.309951	+	0.536852i	−0.668400	+	0.743802i	$0.733021\pi$
$230$		−	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	$-0.592264\pi$
$233$	6.12372	−	3.53553i	0.401179	−	0.231621i	0.686992	+	0.726665i	$0.258931\pi$
$234$		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	0.122119	−	0.992515i	$-0.461031\pi$
$241$	−10.5000	−	6.06218i	−0.676364	−	0.390499i	−0.798484	+	0.602016i	$0.794364\pi$
$242$	−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	$-0.966621\pi$
$251$		−	3.31662i		−	0.209344i	0.994507	−	0.104672i	$-0.0333792\pi$
$252$		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	$-0.265520\pi$
$257$	−4.89898	−	8.48528i	−0.305590	−	0.529297i	−0.977393	+	0.211433i	$0.932187\pi$
$258$		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	$-0.234605\pi$
$263$	8.57321	+	4.94975i	0.528647	+	0.305215i	−0.211818	+	0.977309i	$0.567939\pi$
$264$		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	−0.00641522	−	0.999979i	$-0.502042\pi$
$269$	−14.3614	−	8.29156i	−0.875630	−	0.505545i	−0.869215	+	0.494434i	$0.835375\pi$
$270$		0			0
$271$	1.50000	−	0.866025i	0.0911185	−	0.0526073i	−0.453748	−	0.891130i	$-0.649914\pi$
$271$	1.50000	−	0.866025i	0.0911185	−	0.0526073i	0.544867	+	0.838523i	$0.316580\pi$
$272$	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	$-0.495653\pi$
$277$	−14.0712	−	8.12404i	−0.845459	−	0.488126i	−0.859116	+	0.511781i	$0.828986\pi$
$278$	−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	−0.272447	−	0.962171i	$-0.587833\pi$
$283$	11.7260	−	20.3101i	0.697041	−	1.20731i	0.969488	−	0.245139i	$-0.0788337\pi$
$284$	−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	$-0.969114\pi$
$293$		−	3.31662i		−	0.193759i	0.995296	−	0.0968796i	$-0.0308862\pi$
$294$		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	$-0.113648\pi$
$307$	32.8329			1.87387			0.936937	+	0.349499i	$0.113648\pi$
$308$	−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	−0.0619501	−	0.998079i	$-0.519732\pi$
$311$	14.6969	−	25.4558i	0.833387	−	1.44347i	0.895337	−	0.445389i	$-0.146935\pi$
$312$		0			0
$313$	−22.5000	+	12.9904i	−1.27178	+	0.734260i	−0.975322	−	0.220788i	$-0.929137\pi$
$313$	−22.5000	+	12.9904i	−1.27178	+	0.734260i	−0.296453	+	0.955047i	$0.595804\pi$
$314$			26.5330i			1.49734i
$315$		0			0
$316$	14.0000			0.787562
$317$	−8.61684	−	14.9248i	−0.483970	−	0.838261i	0.515860	−	0.856673i	$-0.327472\pi$
$317$	−8.61684	−	14.9248i	−0.483970	−	0.838261i	−0.999830	+	0.0184118i	$0.994139\pi$
$318$		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	$-0.666667\pi$
$331$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$332$	−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	−0.133838	+	0.991003i	$0.542730\pi$
$347$	−17.2337	+	29.8496i	−0.925153	+	1.60241i	−0.791315	+	0.611408i	$0.790603\pi$
$348$		0			0
$349$	−9.38083			−0.502144			−0.251072	−	0.967968i	$-0.580783\pi$
$349$	−9.38083			−0.502144			−0.251072	+	0.967968i	$0.580783\pi$
$350$	−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	$-0.749365\pi$
$353$	4.89898	−	8.48528i	0.260746	−	0.451626i	0.966440	+	0.256891i	$0.0826980\pi$
$354$		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	$-0.714362\pi$
$359$	−4.89898	+	2.82843i	−0.258558	+	0.149279i	0.365118	+	0.930961i	$0.381028\pi$
$360$		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	−0.104399	−	0.994535i	$-0.533292\pi$
$367$	−19.5000	−	11.2583i	−1.01789	−	0.587680i	−0.913493	+	0.406855i	$0.866625\pi$
$368$	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	$-0.804863\pi$
$373$	−14.0712	+	8.12404i	−0.728582	+	0.420647i	0.0893215	+	0.996003i	$0.471530\pi$
$374$	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	$-0.247205\pi$
$383$	−4.89898	−	8.48528i	−0.250326	−	0.433578i	−0.963616	+	0.267292i	$0.913871\pi$
$384$		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	−0.412658	−	0.910886i	$-0.635399\pi$
$389$	11.4891	−	19.8997i	0.582522	−	1.00896i	0.995179	−	0.0980711i	$-0.0312673\pi$
$390$		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	$-0.322705\pi$
$397$	−9.38083	−	16.2481i	−0.470810	−	0.815468i	−0.999443	+	0.0333834i	$0.989372\pi$
$398$	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	$-0.781543\pi$
$401$	−12.2474	+	7.07107i	−0.611608	+	0.353112i	0.161986	+	0.986793i	$0.448210\pi$
$402$		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	−0.173064	−	0.984911i	$-0.555367\pi$
$409$	−22.5000	−	12.9904i	−1.11255	−	0.642333i	−0.939490	+	0.342578i	$0.888700\pi$
$410$	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	$0.224441\pi$
$419$			26.5330i			1.29622i	−0.761546	+	0.648111i	$0.775559\pi$
$420$		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	$-0.571876\pi$
$431$	−24.4949	−	14.1421i	−1.17988	−	0.681203i	−0.955986	+	0.293411i	$0.905209\pi$
$432$		0			0
$433$			31.1769i			1.49827i	0.662419	+	0.749133i	$0.269530\pi$
$433$			31.1769i			1.49827i	−0.662419	+	0.749133i	$0.730470\pi$
$434$	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	0.144631	−	0.989486i	$-0.453800\pi$
$439$	22.5000	−	12.9904i	1.07387	−	0.619997i	0.929235	+	0.369489i	$0.120467\pi$
$440$	53.8888			2.56905
$441$		0			0
$442$			16.2481i			0.772842i
$443$	8.61684	+	14.9248i	0.409399	+	0.709099i	0.994822	−	0.101628i	$-0.0324052\pi$
$443$	8.61684	+	14.9248i	0.409399	+	0.709099i	−0.585424	+	0.810727i	$0.699072\pi$
$444$		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	0.994910	+	0.100771i	$0.0321310\pi$
$457$	12.5000	+	21.6506i	0.584725	+	1.01277i	−0.410184	+	0.912003i	$0.634536\pi$
$458$	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	$0.0493672\pi$
$461$			6.63325i			0.308941i	−0.987997	+	0.154471i	$0.950633\pi$
$462$		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	−0.361163	−	0.932503i	$-0.617620\pi$
$467$	5.74456	−	3.31662i	0.265827	−	0.153475i	0.626990	+	0.779028i	$0.284287\pi$
$468$		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	0.374726	+	0.927136i	$0.377737\pi$
$479$	−13.4722	+	23.3345i	−0.615560	+	1.06618i	−0.990286	+	0.139046i	$0.955596\pi$
$480$		0			0
$481$	−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	−0.430486	−	0.902597i	$-0.641658\pi$
$487$	12.5000	−	21.6506i	0.566429	−	0.981084i	0.996915	−	0.0784867i	$-0.0250088\pi$
$488$	−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	$-0.407412\pi$
$499$	28.1425	−	16.2481i	1.25983	−	0.727364i	0.973042	+	0.230630i	$0.0740786\pi$
$500$	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	$-0.447616\pi$
$503$	7.34847			0.327652			0.163826	+	0.986489i	$0.447616\pi$
$504$		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	−0.680102	+	0.733118i	$0.738064\pi$
$509$	−37.3397	+	21.5581i	−1.65505	+	0.955544i	−0.974949	+	0.222427i	$0.928602\pi$
$510$		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	$-0.955896\pi$
$521$	−8.57321	+	14.8492i	−0.375599	+	0.650557i	0.614817	+	0.788670i	$0.289230\pi$
$522$		0			0
$523$	−2.34521	−	4.06202i	−0.102549	−	0.177620i	0.810185	−	0.586174i	$-0.199366\pi$
$523$	−2.34521	−	4.06202i	−0.102549	−	0.177620i	−0.912734	+	0.408554i	$0.866033\pi$
$524$			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	$-0.722543\pi$
$541$	−7.03562	+	4.06202i	−0.302485	+	0.174640i	0.341074	+	0.940037i	$0.389209\pi$
$542$	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	−0.920439	−	0.390886i	$-0.872169\pi$
$557$	−2.87228	+	4.97494i	−0.121702	+	0.210795i	0.798737	+	0.601681i	$0.205502\pi$
$558$		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	−0.346034	−	0.938222i	$-0.612472\pi$
$563$	−31.5951	−	18.2414i	−1.33157	−	0.768785i	−0.985541	+	0.169437i	$0.945805\pi$
$564$		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	$-0.560939\pi$
$569$	13.4722	−	7.77817i	0.564784	−	0.326078i	0.755063	+	0.655652i	$0.227606\pi$
$570$		0			0
$571$	21.1069	+	12.1861i	0.883295	+	0.509971i	0.871743	−	0.489963i	$-0.162990\pi$
$571$	21.1069	+	12.1861i	0.883295	+	0.509971i	0.0115516	+	0.999933i	$0.496323\pi$
$572$	−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	0.702376	−	0.711807i	$-0.252123\pi$
$577$	10.5000	+	6.06218i	0.437121	+	0.252372i	−0.265255	+	0.964178i	$0.585456\pi$
$578$	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	$-0.840955\pi$
$587$		−	23.2164i		−	0.958242i	0.877749	−	0.479121i	$-0.159045\pi$
$588$		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	$-0.0521481\pi$
$593$	8.57321	+	14.8492i	0.352060	+	0.609785i	−0.634550	+	0.772881i	$0.718815\pi$
$594$		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	$-0.240039\pi$
$599$	12.2474	+	7.07107i	0.500417	+	0.288916i	−0.228469	+	0.973551i	$0.573372\pi$
$600$		0			0
$601$		−	43.3013i		−	1.76630i	−0.469095	−	0.883148i	$-0.655420\pi$
$601$		−	43.3013i		−	1.76630i	0.469095	−	0.883148i	$-0.344580\pi$
$602$	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	0.405887	−	0.913923i	$-0.366962\pi$
$607$	34.5000	−	19.9186i	1.40031	−	0.808470i	0.994424	+	0.105453i	$0.0336291\pi$
$608$			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	$-0.0271303\pi$
$613$	35.1781	+	20.3101i	1.42083	+	0.820317i	0.424461	+	0.905446i	$0.360464\pi$
$614$	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	$-0.677115\pi$
$619$	11.7260	−	20.3101i	0.471309	−	0.816332i	0.999461	+	0.0328182i	$0.0104482\pi$
$620$	−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	$-0.633835\pi$
$641$	−35.5176	−	20.5061i	−1.40286	−	0.809942i	−0.994685	+	0.102961i	$0.967168\pi$
$642$		0			0
$643$	−37.5233			−1.47978			−0.739888	−	0.672730i	$-0.765121\pi$
$643$	−37.5233			−1.47978			−0.739888	+	0.672730i	$0.765121\pi$
$644$	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	$-0.848666\pi$
$647$	−1.22474	+	2.12132i	−0.0481497	+	0.0833977i	0.840946	+	0.541119i	$0.181999\pi$
$648$		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	0.804337	−	0.594174i	$-0.202521\pi$
$653$	−2.87228	−	4.97494i	−0.112401	−	0.194684i	−0.916738	+	0.399489i	$0.869187\pi$
$654$		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	$-0.682583\pi$
$661$	11.7260	−	20.3101i	0.456090	−	0.789971i	0.998750	+	0.0499812i	$0.0159161\pi$
$662$		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	−0.833849	−	0.551992i	$-0.813868\pi$
$677$	−20.1060	+	11.6082i	−0.772735	+	0.446139i	0.0611143	+	0.998131i	$0.480535\pi$
$678$		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	0.168591	+	0.985686i	$0.446078\pi$
$683$	−20.1060	+	34.8246i	−0.769334	+	1.33252i	−0.937925	+	0.346839i	$0.887255\pi$
$684$		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	−0.837282	−	0.546772i	$-0.815857\pi$
$691$	−23.4521	−	40.6202i	−0.892159	−	1.54526i	−0.0548775	−	0.998493i	$-0.517477\pi$
$692$		−	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	−0.591315	+	0.806441i	$0.701391\pi$
$709$	−42.2137	+	24.3721i	−1.58537	+	0.915314i	−0.994056	+	0.108873i	$0.965276\pi$
$710$	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	−0.985553	−	0.169369i	$-0.945827\pi$
$719$	−17.1464	−	29.6985i	−0.639454	−	1.10757i	0.346099	−	0.938198i	$-0.387506\pi$
$720$		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	$-0.927816\pi$
$727$		−	12.1244i		−	0.449667i	0.974397	−	0.224834i	$-0.0721839\pi$
$728$	−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	−0.991836	−	0.127523i	$-0.959297\pi$
$733$	−16.4165	−	28.4341i	−0.606356	−	1.05024i	0.385480	−	0.922716i	$-0.374036\pi$
$734$	−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	$-0.236731\pi$
$739$	14.0712	+	8.12404i	0.517619	+	0.298848i	−0.218341	+	0.975873i	$0.570064\pi$
$740$	−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	0.816801	−	0.576919i	$-0.195745\pi$
$751$	−2.50000	−	4.33013i	−0.0912263	−	0.158009i	−0.908027	+	0.418911i	$0.862412\pi$
$752$	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	$-0.267256\pi$
$761$	−8.57321	−	14.8492i	−0.310779	−	0.538285i	−0.978531	+	0.206099i	$0.933923\pi$
$762$		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	$-0.744929\pi$
$769$		−	39.8372i		−	1.43657i	0.695752	−	0.718283i	$-0.255071\pi$
$770$	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	0.692179	−	0.721726i	$-0.256651\pi$
$773$	11.4891	+	6.63325i	0.413235	+	0.238581i	−0.278944	+	0.960307i	$0.589984\pi$
$774$		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	0.409669	+	0.912234i	$0.365644\pi$
$787$	−16.4165	+	28.4341i	−0.585183	+	1.01357i	−0.994853	+	0.101333i	$0.967689\pi$
$788$		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	$-0.981292\pi$
$797$		−	3.31662i		−	0.117481i	0.998273	−	0.0587404i	$-0.0187084\pi$
$798$		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	$-0.203118\pi$
$809$	19.5959	+	11.3137i	0.688956	+	0.397769i	−0.114265	+	0.993450i	$0.536451\pi$
$810$		0			0
$811$	46.9042			1.64703			0.823514	−	0.567296i	$-0.192011\pi$
$811$	46.9042			1.64703			0.823514	+	0.567296i	$0.192011\pi$
$812$	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	0.675572	−	0.737294i	$-0.263897\pi$
$821$	−8.61684	−	14.9248i	−0.300730	−	0.520880i	−0.976301	+	0.216415i	$0.930564\pi$
$822$		0			0
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	−0.961851	−	0.273573i	$-0.911795\pi$
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	0.717847	+	0.696201i	$0.245128\pi$
$824$	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	$-0.699817\pi$
$829$	11.7260	−	20.3101i	0.407262	−	0.705399i	0.994582	+	0.103956i	$0.0331502\pi$
$830$	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	$-0.203036\pi$
$839$	46.5403			1.60675			0.803375	+	0.595474i	$0.203036\pi$
$840$		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	$-0.395916\pi$
$853$	18.7617			0.642387			0.321194	+	0.947014i	$0.395916\pi$
$854$	−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	$-0.738728\pi$
$857$	8.57321	−	14.8492i	0.292855	−	0.507240i	0.974484	+	0.224458i	$0.0720612\pi$
$858$		0			0
$859$	−2.34521	−	4.06202i	−0.0800175	−	0.138594i	0.823240	−	0.567694i	$-0.192164\pi$
$859$	−2.34521	−	4.06202i	−0.0800175	−	0.138594i	−0.903257	+	0.429100i	$0.858831\pi$
$860$	−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	$-0.557260\pi$
$863$	17.1464	−	9.89949i	0.583671	−	0.336983i	0.762591	+	0.646881i	$0.223927\pi$
$864$		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	$-0.755122\pi$
$877$	−14.0712	+	8.12404i	−0.475152	+	0.274329i	0.243242	+	0.969966i	$0.421789\pi$
$878$	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	$-0.766469\pi$
$881$	−44.0908			−1.48546			−0.742729	+	0.669593i	$0.766469\pi$
$882$		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	$-0.100747\pi$
$887$	6.12372	+	10.6066i	0.205615	+	0.356135i	−0.744714	+	0.667384i	$0.767414\pi$
$888$		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	$-0.568925\pi$
$907$	−35.1781	−	20.3101i	−1.16807	−	0.674386i	−0.953225	+	0.302262i	$0.902258\pi$
$908$	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	0.997429	+	0.0716652i	$0.0228313\pi$
$919$	17.0000	+	29.4449i	0.560778	+	0.971296i	−0.436650	+	0.899631i	$0.643835\pi$
$920$	−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	$-0.205132\pi$
$929$	−3.67423	−	6.36396i	−0.120548	−	0.208795i	−0.919984	+	0.391956i	$0.871798\pi$
$930$		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	$-0.797497\pi$
$937$		−	36.3731i		−	1.18826i	0.804370	−	0.594128i	$-0.202503\pi$
$938$		0			0
$939$		0			0
$940$	−42.2137	+	24.3721i	−1.37686	+	0.794931i
$941$	−31.5951	−	18.2414i	−1.02997	−	0.594654i	−0.112994	−	0.993596i	$-0.536044\pi$
$941$	−31.5951	−	18.2414i	−1.02997	−	0.594654i	−0.916976	+	0.398942i	$0.869378\pi$
$942$		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	−0.997494	−	0.0707515i	$-0.977460\pi$
$947$	−17.2337	−	29.8496i	−0.560020	−	0.969982i	0.437474	−	0.899231i	$-0.355873\pi$
$948$		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	−0.960173	−	0.279406i	$-0.909862\pi$
$971$	−37.3397	+	21.5581i	−1.19829	+	0.691831i	−0.238114	+	0.971237i	$0.576529\pi$
$972$		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	$-0.458987\pi$
$977$	−20.8207	−	12.0208i	−0.666112	−	0.384580i	−0.794602	+	0.607131i	$0.792320\pi$
$978$		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	$-0.783392\pi$
$983$	4.89898	−	8.48528i	0.156253	−	0.270638i	0.933515	+	0.358539i	$0.116725\pi$
$984$		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	0.441927	+	0.897051i	$0.354295\pi$
$991$	−17.5000	+	30.3109i	−0.555906	+	0.962857i	−0.997832	+	0.0658059i	$0.979038\pi$
$992$	−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	$-0.929351\pi$
$997$	−9.38083	+	16.2481i	−0.297094	+	0.514582i	0.678376	+	0.734715i	$0.262684\pi$
$998$	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.269.3	yes	8
3.2	odd	2	inner	504.2.ch.a.269.2	yes	8
4.3	odd	2		2016.2.cp.a.17.2		8
7.5	odd	6	inner	504.2.ch.a.341.1	yes	8
8.3	odd	2		2016.2.cp.a.17.3		8
8.5	even	2	inner	504.2.ch.a.269.4	yes	8
12.11	even	2		2016.2.cp.a.17.4		8
21.5	even	6	inner	504.2.ch.a.341.4	yes	8
24.5	odd	2	inner	504.2.ch.a.269.1	✓	8
24.11	even	2		2016.2.cp.a.17.1		8
28.19	even	6		2016.2.cp.a.593.1		8
56.5	odd	6	inner	504.2.ch.a.341.2	yes	8
56.19	even	6		2016.2.cp.a.593.4		8
84.47	odd	6		2016.2.cp.a.593.3		8
168.5	even	6	inner	504.2.ch.a.341.3	yes	8
168.131	odd	6		2016.2.cp.a.593.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.ch.a.269.1	✓	8	24.5	odd	2	inner
504.2.ch.a.269.2	yes	8	3.2	odd	2	inner
504.2.ch.a.269.3	yes	8	1.1	even	1	trivial
504.2.ch.a.269.4	yes	8	8.5	even	2	inner
504.2.ch.a.341.1	yes	8	7.5	odd	6	inner
504.2.ch.a.341.2	yes	8	56.5	odd	6	inner
504.2.ch.a.341.3	yes	8	168.5	even	6	inner
504.2.ch.a.341.4	yes	8	21.5	even	6	inner
2016.2.cp.a.17.1		8	24.11	even	2
2016.2.cp.a.17.2		8	4.3	odd	2
2016.2.cp.a.17.3		8	8.3	odd	2
2016.2.cp.a.17.4		8	12.11	even	2
2016.2.cp.a.593.1		8	28.19	even	6
2016.2.cp.a.593.2		8	168.131	odd	6
2016.2.cp.a.593.3		8	84.47	odd	6
2016.2.cp.a.593.4		8	56.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
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

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Representations

Groups

Database

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