LMFDB - Embedded newform 819.2.y.a.811.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(307,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("819.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.y (of order $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			811.2
Root			$1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	819.811
Dual form			819.2.y.a.307.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 1.22474i) q^{2} -1.00000i q^{4} +(-2.00000 - 2.00000i) q^{5} +(2.44949 + 1.00000i) q^{7} +(1.22474 + 1.22474i) q^{8} +O(q^{10})$	\(q+(1.22474 - 1.22474i) q^{2} -1.00000i q^{4} +(-2.00000 - 2.00000i) q^{5} +(2.44949 + 1.00000i) q^{7} +(1.22474 + 1.22474i) q^{8} -4.89898 q^{10} +(-4.44949 - 4.44949i) q^{11} +(2.00000 - 3.00000i) q^{13} +(4.22474 - 1.77526i) q^{14} +5.00000 q^{16} +2.00000 q^{17} +(-5.44949 - 5.44949i) q^{19} +(-2.00000 + 2.00000i) q^{20} -10.8990 q^{22} -0.898979i q^{23} +3.00000i q^{25} +(-1.22474 - 6.12372i) q^{26} +(1.00000 - 2.44949i) q^{28} +6.89898 q^{29} +(-0.550510 - 0.550510i) q^{31} +(3.67423 - 3.67423i) q^{32} +(2.44949 - 2.44949i) q^{34} +(-2.89898 - 6.89898i) q^{35} +(-1.89898 - 1.89898i) q^{37} -13.3485 q^{38} -4.89898i q^{40} +(4.00000 + 4.00000i) q^{41} -2.89898i q^{43} +(-4.44949 + 4.44949i) q^{44} +(-1.10102 - 1.10102i) q^{46} +(-6.44949 + 6.44949i) q^{47} +(5.00000 + 4.89898i) q^{49} +(3.67423 + 3.67423i) q^{50} +(-3.00000 - 2.00000i) q^{52} -7.79796 q^{53} +17.7980i q^{55} +(1.77526 + 4.22474i) q^{56} +(8.44949 - 8.44949i) q^{58} +(-0.449490 + 0.449490i) q^{59} +10.0000i q^{61} -1.34847 q^{62} +1.00000i q^{64} +(-10.0000 + 2.00000i) q^{65} +(8.34847 - 8.34847i) q^{67} -2.00000i q^{68} +(-12.0000 - 4.89898i) q^{70} +(2.44949 - 2.44949i) q^{71} +(-1.89898 + 1.89898i) q^{73} -4.65153 q^{74} +(-5.44949 + 5.44949i) q^{76} +(-6.44949 - 15.3485i) q^{77} +6.89898 q^{79} +(-10.0000 - 10.0000i) q^{80} +9.79796 q^{82} +(4.44949 + 4.44949i) q^{83} +(-4.00000 - 4.00000i) q^{85} +(-3.55051 - 3.55051i) q^{86} -10.8990i q^{88} +(-2.00000 + 2.00000i) q^{89} +(7.89898 - 5.34847i) q^{91} -0.898979 q^{92} +15.7980i q^{94} +21.7980i q^{95} +(-1.89898 - 1.89898i) q^{97} +(12.1237 - 0.123724i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{5}+O(q^{10}) $ 4 * q - 8 * q^5	$ 4 q - 8 q^{5} - 8 q^{11} + 8 q^{13} + 12 q^{14} + 20 q^{16} + 8 q^{17} - 12 q^{19} - 8 q^{20} - 24 q^{22} + 4 q^{28} + 8 q^{29} - 12 q^{31} + 8 q^{35} + 12 q^{37} - 24 q^{38} + 16 q^{41} - 8 q^{44} - 24 q^{46} - 16 q^{47} + 20 q^{49} - 12 q^{52} + 8 q^{53} + 12 q^{56} + 24 q^{58} + 8 q^{59} + 24 q^{62} - 40 q^{65} + 4 q^{67} - 48 q^{70} + 12 q^{73} - 48 q^{74} - 12 q^{76} - 16 q^{77} + 8 q^{79} - 40 q^{80} + 8 q^{83} - 16 q^{85} - 24 q^{86} - 8 q^{89} + 12 q^{91} + 16 q^{92} + 12 q^{97} + 24 q^{98}+O(q^{100}) $ 4 * q - 8 * q^5 - 8 * q^11 + 8 * q^13 + 12 * q^14 + 20 * q^16 + 8 * q^17 - 12 * q^19 - 8 * q^20 - 24 * q^22 + 4 * q^28 + 8 * q^29 - 12 * q^31 + 8 * q^35 + 12 * q^37 - 24 * q^38 + 16 * q^41 - 8 * q^44 - 24 * q^46 - 16 * q^47 + 20 * q^49 - 12 * q^52 + 8 * q^53 + 12 * q^56 + 24 * q^58 + 8 * q^59 + 24 * q^62 - 40 * q^65 + 4 * q^67 - 48 * q^70 + 12 * q^73 - 48 * q^74 - 12 * q^76 - 16 * q^77 + 8 * q^79 - 40 * q^80 + 8 * q^83 - 16 * q^85 - 24 * q^86 - 8 * q^89 + 12 * q^91 + 16 * q^92 + 12 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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	−	1.22474i	0.866025	−	0.866025i	−0.126004	−	0.992030i	$-0.540215\pi$
$2$	1.22474	−	1.22474i	0.866025	−	0.866025i	0.992030	+	0.126004i	$0.0402153\pi$
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	−2.00000	−	2.00000i	−0.894427	−	0.894427i	0.100509	−	0.994936i	$-0.467953\pi$
$5$	−2.00000	−	2.00000i	−0.894427	−	0.894427i	−0.994936	+	0.100509i	$0.967953\pi$
$6$		0			0
$7$	2.44949	+	1.00000i	0.925820	+	0.377964i
$7$	2.44949	+	1.00000i	0.925820	+	0.377964i
$8$	1.22474	+	1.22474i	0.433013	+	0.433013i
$9$		0			0
$10$	−4.89898			−1.54919
$11$	−4.44949	−	4.44949i	−1.34157	−	1.34157i	−0.894496	−	0.447075i	$-0.852466\pi$
$11$	−4.44949	−	4.44949i	−1.34157	−	1.34157i	−0.447075	−	0.894496i	$-0.647534\pi$
$12$		0			0
$13$	2.00000	−	3.00000i	0.554700	−	0.832050i
$13$	2.00000	−	3.00000i	0.554700	−	0.832050i
$14$	4.22474	−	1.77526i	1.12911	−	0.474457i
$15$		0			0
$16$	5.00000			1.25000
$17$	2.00000			0.485071			0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000			0.485071			0.242536	+	0.970143i	$0.422021\pi$
$18$		0			0
$19$	−5.44949	−	5.44949i	−1.25020	−	1.25020i	−0.955630	−	0.294568i	$-0.904824\pi$
$19$	−5.44949	−	5.44949i	−1.25020	−	1.25020i	−0.294568	−	0.955630i	$-0.595176\pi$
$20$	−2.00000	+	2.00000i	−0.447214	+	0.447214i
$21$		0			0
$22$	−10.8990			−2.32367
$23$		−	0.898979i		−	0.187450i	−0.995598	−	0.0937251i	$-0.970123\pi$
$23$		−	0.898979i		−	0.187450i	0.995598	−	0.0937251i	$-0.0298775\pi$
$24$		0			0
$25$			3.00000i			0.600000i
$26$	−1.22474	−	6.12372i	−0.240192	−	1.20096i
$27$		0			0
$28$	1.00000	−	2.44949i	0.188982	−	0.462910i
$29$	6.89898			1.28111			0.640554	−	0.767913i	$-0.278705\pi$
$29$	6.89898			1.28111			0.640554	+	0.767913i	$0.278705\pi$
$30$		0			0
$31$	−0.550510	−	0.550510i	−0.0988746	−	0.0988746i	0.655939	−	0.754814i	$-0.272273\pi$
$31$	−0.550510	−	0.550510i	−0.0988746	−	0.0988746i	−0.754814	+	0.655939i	$0.772273\pi$
$32$	3.67423	−	3.67423i	0.649519	−	0.649519i
$33$		0			0
$34$	2.44949	−	2.44949i	0.420084	−	0.420084i
$35$	−2.89898	−	6.89898i	−0.490017	−	1.16614i
$36$		0			0
$37$	−1.89898	−	1.89898i	−0.312190	−	0.312190i	0.533567	−	0.845758i	$-0.320851\pi$
$37$	−1.89898	−	1.89898i	−0.312190	−	0.312190i	−0.845758	+	0.533567i	$0.820851\pi$
$38$	−13.3485			−2.16541
$39$		0			0
$40$		−	4.89898i		−	0.774597i
$41$	4.00000	+	4.00000i	0.624695	+	0.624695i	0.946728	−	0.322033i	$-0.104366\pi$
$41$	4.00000	+	4.00000i	0.624695	+	0.624695i	−0.322033	+	0.946728i	$0.604366\pi$
$42$		0			0
$43$		−	2.89898i		−	0.442090i	−0.975264	−	0.221045i	$-0.929053\pi$
$43$		−	2.89898i		−	0.442090i	0.975264	−	0.221045i	$-0.0709468\pi$
$44$	−4.44949	+	4.44949i	−0.670786	+	0.670786i
$45$		0			0
$46$	−1.10102	−	1.10102i	−0.162337	−	0.162337i
$47$	−6.44949	+	6.44949i	−0.940755	+	0.940755i	−0.998341	−	0.0575858i	$-0.981660\pi$
$47$	−6.44949	+	6.44949i	−0.940755	+	0.940755i	0.0575858	+	0.998341i	$0.481660\pi$
$48$		0			0
$49$	5.00000	+	4.89898i	0.714286	+	0.699854i
$50$	3.67423	+	3.67423i	0.519615	+	0.519615i
$51$		0			0
$52$	−3.00000	−	2.00000i	−0.416025	−	0.277350i
$53$	−7.79796			−1.07113			−0.535566	−	0.844493i	$-0.679902\pi$
$53$	−7.79796			−1.07113			−0.535566	+	0.844493i	$0.679902\pi$
$54$		0			0
$55$			17.7980i			2.39988i
$56$	1.77526	+	4.22474i	0.237228	+	0.564555i
$57$		0			0
$58$	8.44949	−	8.44949i	1.10947	−	1.10947i
$59$	−0.449490	+	0.449490i	−0.0585186	+	0.0585186i	−0.735760	−	0.677242i	$-0.763175\pi$
$59$	−0.449490	+	0.449490i	−0.0585186	+	0.0585186i	0.677242	+	0.735760i	$0.263175\pi$
$60$		0			0
$61$			10.0000i			1.28037i	0.768221	+	0.640184i	$0.221142\pi$
$61$			10.0000i			1.28037i	−0.768221	+	0.640184i	$0.778858\pi$
$62$	−1.34847			−0.171256
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−10.0000	+	2.00000i	−1.24035	+	0.248069i
$66$		0			0
$67$	8.34847	−	8.34847i	1.01993	−	1.01993i	0.0201305	−	0.999797i	$-0.493592\pi$
$67$	8.34847	−	8.34847i	1.01993	−	1.01993i	0.999797	−	0.0201305i	$-0.00640817\pi$
$68$		−	2.00000i		−	0.242536i
$69$		0			0
$70$	−12.0000	−	4.89898i	−1.43427	−	0.585540i
$71$	2.44949	−	2.44949i	0.290701	−	0.290701i	−0.546656	−	0.837357i	$-0.684100\pi$
$71$	2.44949	−	2.44949i	0.290701	−	0.290701i	0.837357	+	0.546656i	$0.184100\pi$
$72$		0			0
$73$	−1.89898	+	1.89898i	−0.222259	+	0.222259i	−0.809449	−	0.587190i	$-0.800234\pi$
$73$	−1.89898	+	1.89898i	−0.222259	+	0.222259i	0.587190	+	0.809449i	$0.300234\pi$
$74$	−4.65153			−0.540729
$75$		0			0
$76$	−5.44949	+	5.44949i	−0.625099	+	0.625099i
$77$	−6.44949	−	15.3485i	−0.734988	−	1.74912i
$78$		0			0
$79$	6.89898			0.776196			0.388098	−	0.921618i	$-0.373132\pi$
$79$	6.89898			0.776196			0.388098	+	0.921618i	$0.373132\pi$
$80$	−10.0000	−	10.0000i	−1.11803	−	1.11803i
$81$		0			0
$82$	9.79796			1.08200
$83$	4.44949	+	4.44949i	0.488395	+	0.488395i	0.907799	−	0.419405i	$-0.137761\pi$
$83$	4.44949	+	4.44949i	0.488395	+	0.488395i	−0.419405	+	0.907799i	$0.637761\pi$
$84$		0			0
$85$	−4.00000	−	4.00000i	−0.433861	−	0.433861i
$86$	−3.55051	−	3.55051i	−0.382861	−	0.382861i
$87$		0			0
$88$		−	10.8990i		−	1.16184i
$89$	−2.00000	+	2.00000i	−0.212000	+	0.212000i	−0.805116	−	0.593117i	$-0.797897\pi$
$89$	−2.00000	+	2.00000i	−0.212000	+	0.212000i	0.593117	+	0.805116i	$0.297897\pi$
$90$		0			0
$91$	7.89898	−	5.34847i	0.828038	−	0.560672i
$92$	−0.898979			−0.0937251
$93$		0			0
$94$			15.7980i			1.62944i
$95$			21.7980i			2.23642i
$96$		0			0
$97$	−1.89898	−	1.89898i	−0.192812	−	0.192812i	0.604098	−	0.796910i	$-0.293534\pi$
$97$	−1.89898	−	1.89898i	−0.192812	−	0.192812i	−0.796910	+	0.604098i	$0.793534\pi$
$98$	12.1237	−	0.123724i	1.22468	−	0.0124980i
$99$		0			0
$100$	3.00000			0.300000
$101$	14.8990			1.48250			0.741252	−	0.671227i	$-0.234232\pi$
$101$	14.8990			1.48250			0.741252	+	0.671227i	$0.234232\pi$
$102$		0			0
$103$	17.7980			1.75369			0.876843	−	0.480778i	$-0.159646\pi$
$103$	17.7980			1.75369			0.876843	+	0.480778i	$0.159646\pi$
$104$	6.12372	−	1.22474i	0.600481	−	0.120096i
$105$		0			0
$106$	−9.55051	+	9.55051i	−0.927628	+	0.927628i
$107$	8.89898			0.860297			0.430148	−	0.902758i	$-0.358461\pi$
$107$	8.89898			0.860297			0.430148	+	0.902758i	$0.358461\pi$
$108$		0			0
$109$	−9.89898	+	9.89898i	−0.948150	+	0.948150i	−0.998721	−	0.0505702i	$-0.983896\pi$
$109$	−9.89898	+	9.89898i	−0.948150	+	0.948150i	0.0505702	+	0.998721i	$0.483896\pi$
$110$	21.7980	+	21.7980i	2.07835	+	2.07835i
$111$		0			0
$112$	12.2474	+	5.00000i	1.15728	+	0.472456i
$113$	9.10102			0.856152			0.428076	−	0.903743i	$-0.359192\pi$
$113$	9.10102			0.856152			0.428076	+	0.903743i	$0.359192\pi$
$114$		0			0
$115$	−1.79796	+	1.79796i	−0.167661	+	0.167661i
$116$		−	6.89898i		−	0.640554i
$117$		0			0
$118$			1.10102i			0.101357i
$119$	4.89898	+	2.00000i	0.449089	+	0.183340i
$120$		0			0
$121$			28.5959i			2.59963i
$122$	12.2474	+	12.2474i	1.10883	+	1.10883i
$123$		0			0
$124$	−0.550510	+	0.550510i	−0.0494373	+	0.0494373i
$125$	−4.00000	+	4.00000i	−0.357771	+	0.357771i
$126$		0			0
$127$		−	8.00000i		−	0.709885i	−0.934888	−	0.354943i	$-0.884500\pi$
$127$		−	8.00000i		−	0.709885i	0.934888	−	0.354943i	$-0.115500\pi$
$128$	8.57321	+	8.57321i	0.757772	+	0.757772i
$129$		0			0
$130$	−9.79796	+	14.6969i	−0.859338	+	1.28901i
$131$		−	10.6969i		−	0.934596i	−0.884100	−	0.467298i	$-0.845228\pi$
$131$		−	10.6969i		−	0.934596i	0.884100	−	0.467298i	$-0.154772\pi$
$132$		0			0
$133$	−7.89898	−	18.7980i	−0.684928	−	1.62999i
$134$		−	20.4495i		−	1.76657i
$135$		0			0
$136$	2.44949	+	2.44949i	0.210042	+	0.210042i
$137$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$137$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$138$		0			0
$139$			2.89898i			0.245888i	0.992414	+	0.122944i	$0.0392336\pi$
$139$			2.89898i			0.245888i	−0.992414	+	0.122944i	$0.960766\pi$
$140$	−6.89898	+	2.89898i	−0.583070	+	0.245008i
$141$		0			0
$142$		−	6.00000i		−	0.503509i
$143$	−22.2474	+	4.44949i	−1.86043	+	0.372085i
$144$		0			0
$145$	−13.7980	−	13.7980i	−1.14586	−	1.14586i
$146$			4.65153i			0.384963i
$147$		0			0
$148$	−1.89898	+	1.89898i	−0.156095	+	0.156095i
$149$	−8.89898	+	8.89898i	−0.729033	+	0.729033i	−0.970427	−	0.241394i	$-0.922395\pi$
$149$	−8.89898	+	8.89898i	−0.729033	+	0.729033i	0.241394	+	0.970427i	$0.422395\pi$
$150$		0			0
$151$	2.55051	+	2.55051i	0.207558	+	0.207558i	0.803229	−	0.595671i	$-0.203114\pi$
$151$	2.55051	+	2.55051i	0.207558	+	0.207558i	−0.595671	+	0.803229i	$0.703114\pi$
$152$		−	13.3485i		−	1.08270i
$153$		0			0
$154$	−26.6969	−	10.8990i	−2.15130	−	0.878265i
$155$			2.20204i			0.176872i
$156$		0			0
$157$			12.0000i			0.957704i	0.877896	+	0.478852i	$0.158947\pi$
$157$			12.0000i			0.957704i	−0.877896	+	0.478852i	$0.841053\pi$
$158$	8.44949	−	8.44949i	0.672205	−	0.672205i
$159$		0			0
$160$	−14.6969			−1.16190
$161$	0.898979	−	2.20204i	0.0708495	−	0.173545i
$162$		0			0
$163$	0.550510	+	0.550510i	0.0431193	+	0.0431193i	0.728338	−	0.685218i	$-0.240293\pi$
$163$	0.550510	+	0.550510i	0.0431193	+	0.0431193i	−0.685218	+	0.728338i	$0.740293\pi$
$164$	4.00000	−	4.00000i	0.312348	−	0.312348i
$165$		0			0
$166$	10.8990			0.845925
$167$	−3.34847	+	3.34847i	−0.259112	+	0.259112i	−0.824693	−	0.565581i	$-0.808652\pi$
$167$	−3.34847	+	3.34847i	−0.259112	+	0.259112i	0.565581	+	0.824693i	$0.308652\pi$
$168$		0			0
$169$	−5.00000	−	12.0000i	−0.384615	−	0.923077i
$170$	−9.79796			−0.751469
$171$		0			0
$172$	−2.89898			−0.221045
$173$	16.6969			1.26944			0.634722	−	0.772740i	$-0.281114\pi$
$173$	16.6969			1.26944			0.634722	+	0.772740i	$0.281114\pi$
$174$		0			0
$175$	−3.00000	+	7.34847i	−0.226779	+	0.555492i
$176$	−22.2474	−	22.2474i	−1.67696	−	1.67696i
$177$		0			0
$178$			4.89898i			0.367194i
$179$		−	2.20204i		−	0.164588i	−0.996608	−	0.0822941i	$-0.973775\pi$
$179$		−	2.20204i		−	0.164588i	0.996608	−	0.0822941i	$-0.0262247\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	3.12372	−	16.2247i	0.231546	−	1.20266i
$183$		0			0
$184$	1.10102	−	1.10102i	0.0811683	−	0.0811683i
$185$			7.59592i			0.558463i
$186$		0			0
$187$	−8.89898	−	8.89898i	−0.650758	−	0.650758i
$188$	6.44949	+	6.44949i	0.470377	+	0.470377i
$189$		0			0
$190$	26.6969	+	26.6969i	1.93680	+	1.93680i
$191$	−5.79796			−0.419526			−0.209763	−	0.977752i	$-0.567269\pi$
$191$	−5.79796			−0.419526			−0.209763	+	0.977752i	$0.567269\pi$
$192$		0			0
$193$	−4.79796	−	4.79796i	−0.345365	−	0.345365i	0.513015	−	0.858380i	$-0.328529\pi$
$193$	−4.79796	−	4.79796i	−0.345365	−	0.345365i	−0.858380	+	0.513015i	$0.828529\pi$
$194$	−4.65153			−0.333960
$195$		0			0
$196$	4.89898	−	5.00000i	0.349927	−	0.357143i
$197$	−11.7980	+	11.7980i	−0.840570	+	0.840570i	−0.988933	−	0.148363i	$-0.952600\pi$
$197$	−11.7980	+	11.7980i	−0.840570	+	0.840570i	0.148363	+	0.988933i	$0.452600\pi$
$198$		0			0
$199$	−13.1010			−0.928707			−0.464353	−	0.885650i	$-0.653713\pi$
$199$	−13.1010			−0.928707			−0.464353	+	0.885650i	$0.653713\pi$
$200$	−3.67423	+	3.67423i	−0.259808	+	0.259808i
$201$		0			0
$202$	18.2474	−	18.2474i	1.28389	−	1.28389i
$203$	16.8990	+	6.89898i	1.18608	+	0.484213i
$204$		0			0
$205$		−	16.0000i		−	1.11749i
$206$	21.7980	−	21.7980i	1.51874	−	1.51874i
$207$		0			0
$208$	10.0000	−	15.0000i	0.693375	−	1.04006i
$209$			48.4949i			3.35446i
$210$		0			0
$211$	18.8990			1.30106			0.650530	−	0.759481i	$-0.274547\pi$
$211$	18.8990			1.30106			0.650530	+	0.759481i	$0.274547\pi$
$212$			7.79796i			0.535566i
$213$		0			0
$214$	10.8990	−	10.8990i	0.745039	−	0.745039i
$215$	−5.79796	+	5.79796i	−0.395418	+	0.395418i
$216$		0			0
$217$	−0.797959	−	1.89898i	−0.0541690	−	0.128911i
$218$			24.2474i			1.64224i
$219$		0			0
$220$	17.7980			1.19994
$221$	4.00000	−	6.00000i	0.269069	−	0.403604i
$222$		0			0
$223$	7.44949	+	7.44949i	0.498855	+	0.498855i	0.911081	−	0.412227i	$-0.135249\pi$
$223$	7.44949	+	7.44949i	0.498855	+	0.498855i	−0.412227	+	0.911081i	$0.635249\pi$
$224$	12.6742	−	5.32577i	0.846833	−	0.355843i
$225$		0			0
$226$	11.1464	−	11.1464i	0.741449	−	0.741449i
$227$	−15.3485	−	15.3485i	−1.01871	−	1.01871i	−0.999822	−	0.0188922i	$-0.993986\pi$
$227$	−15.3485	−	15.3485i	−1.01871	−	1.01871i	−0.0188922	−	0.999822i	$-0.506014\pi$
$228$		0			0
$229$	−13.0000	+	13.0000i	−0.859064	+	0.859064i	−0.991228	−	0.132164i	$-0.957808\pi$
$229$	−13.0000	+	13.0000i	−0.859064	+	0.859064i	0.132164	+	0.991228i	$0.457808\pi$
$230$			4.40408i			0.290397i
$231$		0			0
$232$	8.44949	+	8.44949i	0.554736	+	0.554736i
$233$		−	7.79796i		−	0.510861i	−0.966827	−	0.255431i	$-0.917783\pi$
$233$		−	7.79796i		−	0.510861i	0.966827	−	0.255431i	$-0.0822172\pi$
$234$		0			0
$235$	25.7980			1.68287
$236$	0.449490	+	0.449490i	0.0292593	+	0.0292593i
$237$		0			0
$238$	8.44949	−	3.55051i	0.547699	−	0.230145i
$239$	−7.34847	+	7.34847i	−0.475333	+	0.475333i	−0.903635	−	0.428302i	$-0.859112\pi$
$239$	−7.34847	+	7.34847i	−0.475333	+	0.475333i	0.428302	+	0.903635i	$0.359112\pi$
$240$		0			0
$241$	4.10102	−	4.10102i	0.264170	−	0.264170i	−0.562576	−	0.826746i	$-0.690190\pi$
$241$	4.10102	−	4.10102i	0.264170	−	0.264170i	0.826746	+	0.562576i	$0.190190\pi$
$242$	35.0227	+	35.0227i	2.25134	+	2.25134i
$243$		0			0
$244$	10.0000			0.640184
$245$	−0.202041	−	19.7980i	−0.0129079	−	1.26485i
$246$		0			0
$247$	−27.2474	+	5.44949i	−1.73371	+	0.346743i
$248$		−	1.34847i		−	0.0856279i
$249$		0			0
$250$			9.79796i			0.619677i
$251$	4.89898			0.309221			0.154610	−	0.987976i	$-0.450588\pi$
$251$	4.89898			0.309221			0.154610	+	0.987976i	$0.450588\pi$
$252$		0			0
$253$	−4.00000	+	4.00000i	−0.251478	+	0.251478i
$254$	−9.79796	−	9.79796i	−0.614779	−	0.614779i
$255$		0			0
$256$	19.0000			1.18750
$257$	−8.69694			−0.542500			−0.271250	−	0.962509i	$-0.587437\pi$
$257$	−8.69694			−0.542500			−0.271250	+	0.962509i	$0.587437\pi$
$258$		0			0
$259$	−2.75255	−	6.55051i	−0.171035	−	0.407029i
$260$	2.00000	+	10.0000i	0.124035	+	0.620174i
$261$		0			0
$262$	−13.1010	−	13.1010i	−0.809384	−	0.809384i
$263$	−7.10102			−0.437868			−0.218934	−	0.975740i	$-0.570258\pi$
$263$	−7.10102			−0.437868			−0.218934	+	0.975740i	$0.570258\pi$
$264$		0			0
$265$	15.5959	+	15.5959i	0.958050	+	0.958050i
$266$	−32.6969	−	13.3485i	−2.00478	−	0.818447i
$267$		0			0
$268$	−8.34847	−	8.34847i	−0.509964	−	0.509964i
$269$		−	6.00000i		−	0.365826i	−0.983129	−	0.182913i	$-0.941447\pi$
$269$		−	6.00000i		−	0.365826i	0.983129	−	0.182913i	$-0.0585527\pi$
$270$		0			0
$271$	9.44949	−	9.44949i	0.574016	−	0.574016i	−0.359232	−	0.933248i	$-0.616961\pi$
$271$	9.44949	−	9.44949i	0.574016	−	0.574016i	0.933248	+	0.359232i	$0.116961\pi$
$272$	10.0000			0.606339
$273$		0			0
$274$		0			0
$275$	13.3485	−	13.3485i	0.804943	−	0.804943i
$276$		0			0
$277$		−	1.79796i		−	0.108029i	−0.998540	−	0.0540144i	$-0.982798\pi$
$277$		−	1.79796i		−	0.108029i	0.998540	−	0.0540144i	$-0.0172017\pi$
$278$	3.55051	+	3.55051i	0.212945	+	0.212945i
$279$		0			0
$280$	4.89898	−	12.0000i	0.292770	−	0.717137i
$281$	4.00000	+	4.00000i	0.238620	+	0.238620i	0.816279	−	0.577659i	$-0.196033\pi$
$281$	4.00000	+	4.00000i	0.238620	+	0.238620i	−0.577659	+	0.816279i	$0.696033\pi$
$282$		0			0
$283$	−16.6969			−0.992530			−0.496265	−	0.868171i	$-0.665296\pi$
$283$	−16.6969			−0.992530			−0.496265	+	0.868171i	$0.665296\pi$
$284$	−2.44949	−	2.44949i	−0.145350	−	0.145350i
$285$		0			0
$286$	−21.7980	+	32.6969i	−1.28894	+	1.93341i
$287$	5.79796	+	13.7980i	0.342243	+	0.814468i
$288$		0			0
$289$	−13.0000			−0.764706
$290$	−33.7980			−1.98468
$291$		0			0
$292$	1.89898	+	1.89898i	0.111129	+	0.111129i
$293$	10.6969	−	10.6969i	0.624922	−	0.624922i	−0.321864	−	0.946786i	$-0.604309\pi$
$293$	10.6969	−	10.6969i	0.624922	−	0.624922i	0.946786	+	0.321864i	$0.104309\pi$
$294$		0			0
$295$	1.79796			0.104681
$296$		−	4.65153i		−	0.270365i
$297$		0			0
$298$			21.7980i			1.26272i
$299$	−2.69694	−	1.79796i	−0.155968	−	0.103979i
$300$		0			0
$301$	2.89898	−	7.10102i	0.167094	−	0.409296i
$302$	6.24745			0.359500
$303$		0			0
$304$	−27.2474	−	27.2474i	−1.56275	−	1.56275i
$305$	20.0000	−	20.0000i	1.14520	−	1.14520i
$306$		0			0
$307$	−8.55051	+	8.55051i	−0.488003	+	0.488003i	−0.907676	−	0.419672i	$-0.862145\pi$
$307$	−8.55051	+	8.55051i	−0.488003	+	0.488003i	0.419672	+	0.907676i	$0.362145\pi$
$308$	−15.3485	+	6.44949i	−0.874560	+	0.367494i
$309$		0			0
$310$	2.69694	+	2.69694i	0.153176	+	0.153176i
$311$	24.8990			1.41189			0.705946	−	0.708266i	$-0.250522\pi$
$311$	24.8990			1.41189			0.705946	+	0.708266i	$0.250522\pi$
$312$		0			0
$313$		−	13.5959i		−	0.768487i	−0.923232	−	0.384243i	$-0.874462\pi$
$313$		−	13.5959i		−	0.768487i	0.923232	−	0.384243i	$-0.125538\pi$
$314$	14.6969	+	14.6969i	0.829396	+	0.829396i
$315$		0			0
$316$		−	6.89898i		−	0.388098i
$317$	12.6969	−	12.6969i	0.713131	−	0.713131i	−0.254058	−	0.967189i	$-0.581765\pi$
$317$	12.6969	−	12.6969i	0.713131	−	0.713131i	0.967189	+	0.254058i	$0.0817654\pi$
$318$		0			0
$319$	−30.6969	−	30.6969i	−1.71870	−	1.71870i
$320$	2.00000	−	2.00000i	0.111803	−	0.111803i
$321$		0			0
$322$	−1.59592	−	3.79796i	−0.0889370	−	0.211652i
$323$	−10.8990	−	10.8990i	−0.606435	−	0.606435i
$324$		0			0
$325$	9.00000	+	6.00000i	0.499230	+	0.332820i
$326$	1.34847			0.0746848
$327$		0			0
$328$			9.79796i			0.541002i
$329$	−22.2474	+	9.34847i	−1.22654	+	0.515398i
$330$		0			0
$331$	3.24745	−	3.24745i	0.178496	−	0.178496i	−0.612204	−	0.790700i	$-0.709717\pi$
$331$	3.24745	−	3.24745i	0.178496	−	0.178496i	0.790700	+	0.612204i	$0.209717\pi$
$332$	4.44949	−	4.44949i	0.244197	−	0.244197i
$333$		0			0
$334$			8.20204i			0.448796i
$335$	−33.3939			−1.82450
$336$		0			0
$337$		−	4.20204i		−	0.228900i	−0.993429	−	0.114450i	$-0.963489\pi$
$337$		−	4.20204i		−	0.228900i	0.993429	−	0.114450i	$-0.0365105\pi$
$338$	−20.8207	−	8.57321i	−1.13249	−	0.466321i
$339$		0			0
$340$	−4.00000	+	4.00000i	−0.216930	+	0.216930i
$341$			4.89898i			0.265295i
$342$		0			0
$343$	7.34847	+	17.0000i	0.396780	+	0.917914i
$344$	3.55051	−	3.55051i	0.191431	−	0.191431i
$345$		0			0
$346$	20.4495	−	20.4495i	1.09937	−	1.09937i
$347$	−21.7980			−1.17018			−0.585088	−	0.810970i	$-0.698940\pi$
$347$	−21.7980			−1.17018			−0.585088	+	0.810970i	$0.698940\pi$
$348$		0			0
$349$	10.7980	−	10.7980i	0.578001	−	0.578001i	−0.356351	−	0.934352i	$-0.615979\pi$
$349$	10.7980	−	10.7980i	0.578001	−	0.578001i	0.934352	+	0.356351i	$0.115979\pi$
$350$	5.32577	+	12.6742i	0.284674	+	0.677466i
$351$		0			0
$352$	−32.6969			−1.74275
$353$	9.79796	+	9.79796i	0.521493	+	0.521493i	0.918022	−	0.396529i	$-0.129785\pi$
$353$	9.79796	+	9.79796i	0.521493	+	0.521493i	−0.396529	+	0.918022i	$0.629785\pi$
$354$		0			0
$355$	−9.79796			−0.520022
$356$	2.00000	+	2.00000i	0.106000	+	0.106000i
$357$		0			0
$358$	−2.69694	−	2.69694i	−0.142538	−	0.142538i
$359$	0.449490	+	0.449490i	0.0237232	+	0.0237232i	0.718869	−	0.695146i	$-0.244660\pi$
$359$	0.449490	+	0.449490i	0.0237232	+	0.0237232i	−0.695146	+	0.718869i	$0.744660\pi$
$360$		0			0
$361$			40.3939i			2.12599i
$362$	2.44949	−	2.44949i	0.128742	−	0.128742i
$363$		0			0
$364$	−5.34847	−	7.89898i	−0.280336	−	0.414019i
$365$	7.59592			0.397589
$366$		0			0
$367$		−	22.4949i		−	1.17422i	−0.809506	−	0.587112i	$-0.800265\pi$
$367$		−	22.4949i		−	1.17422i	0.809506	−	0.587112i	$-0.199735\pi$
$368$		−	4.49490i		−	0.234313i
$369$		0			0
$370$	9.30306	+	9.30306i	0.483643	+	0.483643i
$371$	−19.1010	−	7.79796i	−0.991676	−	0.404850i
$372$		0			0
$373$	−9.79796			−0.507319			−0.253660	−	0.967294i	$-0.581634\pi$
$373$	−9.79796			−0.507319			−0.253660	+	0.967294i	$0.581634\pi$
$374$	−21.7980			−1.12715
$375$		0			0
$376$	−15.7980			−0.814718
$377$	13.7980	−	20.6969i	0.710631	−	1.06595i
$378$		0			0
$379$	8.55051	−	8.55051i	0.439210	−	0.439210i	−0.452536	−	0.891746i	$-0.649481\pi$
$379$	8.55051	−	8.55051i	0.439210	−	0.439210i	0.891746	+	0.452536i	$0.149481\pi$
$380$	21.7980			1.11821
$381$		0			0
$382$	−7.10102	+	7.10102i	−0.363320	+	0.363320i
$383$	8.24745	+	8.24745i	0.421425	+	0.421425i	0.885694	−	0.464269i	$-0.153683\pi$
$383$	8.24745	+	8.24745i	0.421425	+	0.421425i	−0.464269	+	0.885694i	$0.653683\pi$
$384$		0			0
$385$	−17.7980	+	43.5959i	−0.907068	+	2.22185i
$386$	−11.7526			−0.598189
$387$		0			0
$388$	−1.89898	+	1.89898i	−0.0964061	+	0.0964061i
$389$			10.8990i			0.552600i	0.961071	+	0.276300i	$0.0891084\pi$
$389$			10.8990i			0.552600i	−0.961071	+	0.276300i	$0.910892\pi$
$390$		0			0
$391$		−	1.79796i		−	0.0909267i
$392$	0.123724	+	12.1237i	0.00624902	+	0.612341i
$393$		0			0
$394$			28.8990i			1.45591i
$395$	−13.7980	−	13.7980i	−0.694251	−	0.694251i
$396$		0			0
$397$	−10.7980	+	10.7980i	−0.541934	+	0.541934i	−0.924096	−	0.382162i	$-0.875180\pi$
$397$	−10.7980	+	10.7980i	−0.541934	+	0.541934i	0.382162	+	0.924096i	$0.375180\pi$
$398$	−16.0454	+	16.0454i	−0.804284	+	0.804284i
$399$		0			0
$400$			15.0000i			0.750000i
$401$	14.0000	+	14.0000i	0.699127	+	0.699127i	0.964222	−	0.265096i	$-0.0854035\pi$
$401$	14.0000	+	14.0000i	0.699127	+	0.699127i	−0.265096	+	0.964222i	$0.585403\pi$
$402$		0			0
$403$	−2.75255	+	0.550510i	−0.137114	+	0.0274229i
$404$		−	14.8990i		−	0.741252i
$405$		0			0
$406$	29.1464	−	12.2474i	1.44651	−	0.607831i
$407$			16.8990i			0.837651i
$408$		0			0
$409$	23.6969	+	23.6969i	1.17174	+	1.17174i	0.981795	+	0.189943i	$0.0608304\pi$
$409$	23.6969	+	23.6969i	1.17174	+	1.17174i	0.189943	+	0.981795i	$0.439170\pi$
$410$	−19.5959	−	19.5959i	−0.967773	−	0.967773i
$411$		0			0
$412$		−	17.7980i		−	0.876843i
$413$	−1.55051	+	0.651531i	−0.0762956	+	0.0320597i
$414$		0			0
$415$		−	17.7980i		−	0.873667i
$416$	−3.67423	−	18.3712i	−0.180144	−	0.900721i
$417$		0			0
$418$	59.3939	+	59.3939i	2.90505	+	2.90505i
$419$		−	34.2929i		−	1.67532i	−0.546195	−	0.837658i	$-0.683924\pi$
$419$		−	34.2929i		−	1.67532i	0.546195	−	0.837658i	$-0.316076\pi$
$420$		0			0
$421$	4.10102	−	4.10102i	0.199872	−	0.199872i	−0.600073	−	0.799945i	$-0.704862\pi$
$421$	4.10102	−	4.10102i	0.199872	−	0.199872i	0.799945	+	0.600073i	$0.204862\pi$
$422$	23.1464	−	23.1464i	1.12675	−	1.12675i
$423$		0			0
$424$	−9.55051	−	9.55051i	−0.463814	−	0.463814i
$425$			6.00000i			0.291043i
$426$		0			0
$427$	−10.0000	+	24.4949i	−0.483934	+	1.18539i
$428$		−	8.89898i		−	0.430148i
$429$		0			0
$430$			14.2020i			0.684883i
$431$	20.0454	−	20.0454i	0.965553	−	0.965553i	−0.0338728	−	0.999426i	$-0.510784\pi$
$431$	20.0454	−	20.0454i	0.965553	−	0.965553i	0.999426	+	0.0338728i	$0.0107841\pi$
$432$		0			0
$433$	−29.7980			−1.43200			−0.715999	−	0.698101i	$-0.754029\pi$
$433$	−29.7980			−1.43200			−0.715999	+	0.698101i	$0.754029\pi$
$434$	−3.30306	−	1.34847i	−0.158552	−	0.0647286i
$435$		0			0
$436$	9.89898	+	9.89898i	0.474075	+	0.474075i
$437$	−4.89898	+	4.89898i	−0.234350	+	0.234350i
$438$		0			0
$439$	−27.5959			−1.31708			−0.658541	−	0.752545i	$-0.728826\pi$
$439$	−27.5959			−1.31708			−0.658541	+	0.752545i	$0.728826\pi$
$440$	−21.7980	+	21.7980i	−1.03918	+	1.03918i
$441$		0			0
$442$	−2.44949	−	12.2474i	−0.116510	−	0.582552i
$443$	5.30306			0.251956			0.125978	−	0.992033i	$-0.459793\pi$
$443$	5.30306			0.251956			0.125978	+	0.992033i	$0.459793\pi$
$444$		0			0
$445$	8.00000			0.379236
$446$	18.2474			0.864042
$447$		0			0
$448$	−1.00000	+	2.44949i	−0.0472456	+	0.115728i
$449$	−14.8990	−	14.8990i	−0.703126	−	0.703126i	0.261954	−	0.965080i	$-0.415633\pi$
$449$	−14.8990	−	14.8990i	−0.703126	−	0.703126i	−0.965080	+	0.261954i	$0.915633\pi$
$450$		0			0
$451$		−	35.5959i		−	1.67615i
$452$		−	9.10102i		−	0.428076i
$453$		0			0
$454$	−37.5959			−1.76446
$455$	−26.4949	−	5.10102i	−1.24210	−	0.239140i
$456$		0			0
$457$	6.79796	−	6.79796i	0.317995	−	0.317995i	−0.530002	−	0.847997i	$-0.677809\pi$
$457$	6.79796	−	6.79796i	0.317995	−	0.317995i	0.847997	+	0.530002i	$0.177809\pi$
$458$			31.8434i			1.48794i
$459$		0			0
$460$	1.79796	+	1.79796i	0.0838303	+	0.0838303i
$461$	4.69694	+	4.69694i	0.218758	+	0.218758i	0.807975	−	0.589217i	$-0.200564\pi$
$461$	4.69694	+	4.69694i	0.218758	+	0.218758i	−0.589217	+	0.807975i	$0.700564\pi$
$462$		0			0
$463$	−20.1464	−	20.1464i	−0.936284	−	0.936284i	0.0618044	−	0.998088i	$-0.480315\pi$
$463$	−20.1464	−	20.1464i	−0.936284	−	0.936284i	−0.998088	+	0.0618044i	$0.980315\pi$
$464$	34.4949			1.60139
$465$		0			0
$466$	−9.55051	−	9.55051i	−0.442419	−	0.442419i
$467$	−31.1010			−1.43918			−0.719592	−	0.694397i	$-0.755671\pi$
$467$	−31.1010			−1.43918			−0.719592	+	0.694397i	$0.755671\pi$
$468$		0			0
$469$	28.7980	−	12.1010i	1.32977	−	0.558773i
$470$	31.5959	−	31.5959i	1.45741	−	1.45741i
$471$		0			0
$472$	−1.10102			−0.0506786
$473$	−12.8990	+	12.8990i	−0.593096	+	0.593096i
$474$		0			0
$475$	16.3485	−	16.3485i	0.750119	−	0.750119i
$476$	2.00000	−	4.89898i	0.0916698	−	0.224544i
$477$		0			0
$478$			18.0000i			0.823301i
$479$	10.2474	−	10.2474i	0.468218	−	0.468218i	−0.433119	−	0.901337i	$-0.642587\pi$
$479$	10.2474	−	10.2474i	0.468218	−	0.468218i	0.901337	+	0.433119i	$0.142587\pi$
$480$		0			0
$481$	−9.49490	+	1.89898i	−0.432930	+	0.0865860i
$482$		−	10.0454i		−	0.457556i
$483$		0			0
$484$	28.5959			1.29981
$485$			7.59592i			0.344913i
$486$		0			0
$487$	15.2474	−	15.2474i	0.690928	−	0.690928i	−0.271508	−	0.962436i	$-0.587522\pi$
$487$	15.2474	−	15.2474i	0.690928	−	0.690928i	0.962436	+	0.271508i	$0.0875224\pi$
$488$	−12.2474	+	12.2474i	−0.554416	+	0.554416i
$489$		0			0
$490$	−24.4949	−	24.0000i	−1.10657	−	1.08421i
$491$			36.8990i			1.66523i	0.553854	+	0.832614i	$0.313157\pi$
$491$			36.8990i			1.66523i	−0.553854	+	0.832614i	$0.686843\pi$
$492$		0			0
$493$	13.7980			0.621429
$494$	−26.6969	+	40.0454i	−1.20115	+	1.80173i
$495$		0			0
$496$	−2.75255	−	2.75255i	−0.123593	−	0.123593i
$497$	8.44949	−	3.55051i	0.379011	−	0.159262i
$498$		0			0
$499$	−15.2474	+	15.2474i	−0.682570	+	0.682570i	−0.960578	−	0.278009i	$-0.910326\pi$
$499$	−15.2474	+	15.2474i	−0.682570	+	0.682570i	0.278009	+	0.960578i	$0.410326\pi$
$500$	4.00000	+	4.00000i	0.178885	+	0.178885i
$501$		0			0
$502$	6.00000	−	6.00000i	0.267793	−	0.267793i
$503$			26.6969i			1.19036i	0.803593	+	0.595179i	$0.202919\pi$
$503$			26.6969i			1.19036i	−0.803593	+	0.595179i	$0.797081\pi$
$504$		0			0
$505$	−29.7980	−	29.7980i	−1.32599	−	1.32599i
$506$			9.79796i			0.435572i
$507$		0			0
$508$	−8.00000			−0.354943
$509$	5.10102	+	5.10102i	0.226099	+	0.226099i	0.811061	−	0.584962i	$-0.198891\pi$
$509$	5.10102	+	5.10102i	0.226099	+	0.226099i	−0.584962	+	0.811061i	$0.698891\pi$
$510$		0			0
$511$	−6.55051	+	2.75255i	−0.289778	+	0.121766i
$512$	6.12372	−	6.12372i	0.270633	−	0.270633i
$513$		0			0
$514$	−10.6515	+	10.6515i	−0.469819	+	0.469819i
$515$	−35.5959	−	35.5959i	−1.56854	−	1.56854i
$516$		0			0
$517$	57.3939			2.52418
$518$	−11.3939	−	4.65153i	−0.500618	−	0.204377i
$519$		0			0
$520$	−14.6969	−	9.79796i	−0.644503	−	0.429669i
$521$		−	31.3939i		−	1.37539i	−0.725999	−	0.687695i	$-0.758622\pi$
$521$		−	31.3939i		−	1.37539i	0.725999	−	0.687695i	$-0.241378\pi$
$522$		0			0
$523$			18.4949i			0.808725i	0.914599	+	0.404363i	$0.132507\pi$
$523$			18.4949i			0.808725i	−0.914599	+	0.404363i	$0.867493\pi$
$524$	−10.6969			−0.467298
$525$		0			0
$526$	−8.69694	+	8.69694i	−0.379205	+	0.379205i
$527$	−1.10102	−	1.10102i	−0.0479612	−	0.0479612i
$528$		0			0
$529$	22.1918			0.964862
$530$	38.2020			1.65939
$531$		0			0
$532$	−18.7980	+	7.89898i	−0.814995	+	0.342464i
$533$	20.0000	−	4.00000i	0.866296	−	0.173259i
$534$		0			0
$535$	−17.7980	−	17.7980i	−0.769473	−	0.769473i
$536$	20.4495			0.883283
$537$		0			0
$538$	−7.34847	−	7.34847i	−0.316815	−	0.316815i
$539$	−0.449490	−	44.0454i	−0.0193609	−	1.89717i
$540$		0			0
$541$	−2.10102	−	2.10102i	−0.0903299	−	0.0903299i	0.660498	−	0.750828i	$-0.270345\pi$
$541$	−2.10102	−	2.10102i	−0.0903299	−	0.0903299i	−0.750828	+	0.660498i	$0.770345\pi$
$542$		−	23.1464i		−	0.994224i
$543$		0			0
$544$	7.34847	−	7.34847i	0.315063	−	0.315063i
$545$	39.5959			1.69610
$546$		0			0
$547$	−5.79796			−0.247903			−0.123951	−	0.992288i	$-0.539557\pi$
$547$	−5.79796			−0.247903			−0.123951	+	0.992288i	$0.539557\pi$
$548$		0			0
$549$		0			0
$550$		−	32.6969i		−	1.39420i
$551$	−37.5959	−	37.5959i	−1.60164	−	1.60164i
$552$		0			0
$553$	16.8990	+	6.89898i	0.718618	+	0.293374i
$554$	−2.20204	−	2.20204i	−0.0935558	−	0.0935558i
$555$		0			0
$556$	2.89898			0.122944
$557$	10.6969	+	10.6969i	0.453244	+	0.453244i	0.896430	−	0.443186i	$-0.146152\pi$
$557$	10.6969	+	10.6969i	0.453244	+	0.453244i	−0.443186	+	0.896430i	$0.646152\pi$
$558$		0			0
$559$	−8.69694	−	5.79796i	−0.367841	−	0.245228i
$560$	−14.4949	−	34.4949i	−0.612521	−	1.45768i
$561$		0			0
$562$	9.79796			0.413302
$563$	2.20204			0.0928050			0.0464025	−	0.998923i	$-0.485224\pi$
$563$	2.20204			0.0928050			0.0464025	+	0.998923i	$0.485224\pi$
$564$		0			0
$565$	−18.2020	−	18.2020i	−0.765766	−	0.765766i
$566$	−20.4495	+	20.4495i	−0.859556	+	0.859556i
$567$		0			0
$568$	6.00000			0.251754
$569$			35.3939i			1.48379i	0.670517	+	0.741894i	$0.266072\pi$
$569$			35.3939i			1.48379i	−0.670517	+	0.741894i	$0.733928\pi$
$570$		0			0
$571$			35.1918i			1.47273i	0.676583	+	0.736366i	$0.263460\pi$
$571$			35.1918i			1.47273i	−0.676583	+	0.736366i	$0.736540\pi$
$572$	4.44949	+	22.2474i	0.186043	+	0.930213i
$573$		0			0
$574$	24.0000	+	9.79796i	1.00174	+	0.408959i
$575$	2.69694			0.112470
$576$		0			0
$577$	8.10102	+	8.10102i	0.337250	+	0.337250i	0.855331	−	0.518081i	$-0.173354\pi$
$577$	8.10102	+	8.10102i	0.337250	+	0.337250i	−0.518081	+	0.855331i	$0.673354\pi$
$578$	−15.9217	+	15.9217i	−0.662255	+	0.662255i
$579$		0			0
$580$	−13.7980	+	13.7980i	−0.572929	+	0.572929i
$581$	6.44949	+	15.3485i	0.267570	+	0.636762i
$582$		0			0
$583$	34.6969	+	34.6969i	1.43700	+	1.43700i
$584$	−4.65153			−0.192482
$585$		0			0
$586$		−	26.2020i		−	1.08240i
$587$	8.44949	+	8.44949i	0.348748	+	0.348748i	0.859643	−	0.510895i	$-0.170686\pi$
$587$	8.44949	+	8.44949i	0.348748	+	0.348748i	−0.510895	+	0.859643i	$0.670686\pi$
$588$		0			0
$589$			6.00000i			0.247226i
$590$	2.20204	−	2.20204i	0.0906566	−	0.0906566i
$591$		0			0
$592$	−9.49490	−	9.49490i	−0.390238	−	0.390238i
$593$	−26.8990	+	26.8990i	−1.10461	+	1.10461i	−0.110762	+	0.993847i	$0.535329\pi$
$593$	−26.8990	+	26.8990i	−1.10461	+	1.10461i	−0.993847	+	0.110762i	$0.964671\pi$
$594$		0			0
$595$	−5.79796	−	13.7980i	−0.237693	−	0.565661i
$596$	8.89898	+	8.89898i	0.364516	+	0.364516i
$597$		0			0
$598$	−5.50510	+	1.10102i	−0.225120	+	0.0450241i
$599$	44.4949			1.81801			0.909006	−	0.416783i	$-0.136842\pi$
$599$	44.4949			1.81801			0.909006	+	0.416783i	$0.136842\pi$
$600$		0			0
$601$		−	2.40408i		−	0.0980646i	−0.998797	−	0.0490323i	$-0.984386\pi$
$601$		−	2.40408i		−	0.0980646i	0.998797	−	0.0490323i	$-0.0156137\pi$
$602$	−5.14643	−	12.2474i	−0.209753	−	0.499169i
$603$		0			0
$604$	2.55051	−	2.55051i	0.103779	−	0.103779i
$605$	57.1918	−	57.1918i	2.32518	−	2.32518i
$606$		0			0
$607$			5.10102i			0.207044i	0.994627	+	0.103522i	$0.0330112\pi$
$607$			5.10102i			0.207044i	−0.994627	+	0.103522i	$0.966989\pi$
$608$	−40.0454			−1.62406
$609$		0			0
$610$		−	48.9898i		−	1.98354i
$611$	6.44949	+	32.2474i	0.260918	+	1.30459i
$612$		0			0
$613$	1.89898	−	1.89898i	0.0766991	−	0.0766991i	−0.667717	−	0.744416i	$-0.732728\pi$
$613$	1.89898	−	1.89898i	0.0766991	−	0.0766991i	0.744416	+	0.667717i	$0.232728\pi$
$614$			20.9444i			0.845247i
$615$		0			0
$616$	10.8990	−	26.6969i	0.439132	−	1.07565i
$617$	−21.7980	+	21.7980i	−0.877553	+	0.877553i	−0.993281	−	0.115728i	$-0.963080\pi$
$617$	−21.7980	+	21.7980i	−0.877553	+	0.877553i	0.115728	+	0.993281i	$0.463080\pi$
$618$		0			0
$619$	15.4495	−	15.4495i	0.620967	−	0.620967i	−0.324811	−	0.945779i	$-0.605301\pi$
$619$	15.4495	−	15.4495i	0.620967	−	0.620967i	0.945779	+	0.324811i	$0.105301\pi$
$620$	2.20204			0.0884361
$621$		0			0
$622$	30.4949	−	30.4949i	1.22273	−	1.22273i
$623$	−6.89898	+	2.89898i	−0.276402	+	0.116145i
$624$		0			0
$625$	31.0000			1.24000
$626$	−16.6515	−	16.6515i	−0.665529	−	0.665529i
$627$		0			0
$628$	12.0000			0.478852
$629$	−3.79796	−	3.79796i	−0.151435	−	0.151435i
$630$		0			0
$631$	−11.2474	−	11.2474i	−0.447754	−	0.447754i	0.446853	−	0.894607i	$-0.352545\pi$
$631$	−11.2474	−	11.2474i	−0.447754	−	0.447754i	−0.894607	+	0.446853i	$0.852545\pi$
$632$	8.44949	+	8.44949i	0.336103	+	0.336103i
$633$		0			0
$634$		−	31.1010i		−	1.23518i
$635$	−16.0000	+	16.0000i	−0.634941	+	0.634941i
$636$		0			0
$637$	24.6969	−	5.20204i	0.978528	−	0.206112i
$638$	−75.1918			−2.97687
$639$		0			0
$640$		−	34.2929i		−	1.35554i
$641$		−	20.6969i		−	0.817480i	−0.912651	−	0.408740i	$-0.865968\pi$
$641$		−	20.6969i		−	0.817480i	0.912651	−	0.408740i	$-0.134032\pi$
$642$		0			0
$643$	−20.1464	−	20.1464i	−0.794498	−	0.794498i	0.187724	−	0.982222i	$-0.439889\pi$
$643$	−20.1464	−	20.1464i	−0.794498	−	0.794498i	−0.982222	+	0.187724i	$0.939889\pi$
$644$	−2.20204	−	0.898979i	−0.0867726	−	0.0354248i
$645$		0			0
$646$	−26.6969			−1.05038
$647$	12.0000			0.471769			0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000			0.471769			0.235884	+	0.971781i	$0.424201\pi$
$648$		0			0
$649$	4.00000			0.157014
$650$	18.3712	−	3.67423i	0.720577	−	0.144115i
$651$		0			0
$652$	0.550510	−	0.550510i	0.0215596	−	0.0215596i
$653$	−10.8990			−0.426510			−0.213255	−	0.976997i	$-0.568407\pi$
$653$	−10.8990			−0.426510			−0.213255	+	0.976997i	$0.568407\pi$
$654$		0			0
$655$	−21.3939	+	21.3939i	−0.835928	+	0.835928i
$656$	20.0000	+	20.0000i	0.780869	+	0.780869i
$657$		0			0
$658$	−15.7980	+	38.6969i	−0.615869	+	1.50856i
$659$	−7.59592			−0.295895			−0.147947	−	0.988995i	$-0.547267\pi$
$659$	−7.59592			−0.295895			−0.147947	+	0.988995i	$0.547267\pi$
$660$		0			0
$661$	32.3939	−	32.3939i	1.25998	−	1.25998i	0.308872	−	0.951104i	$-0.400048\pi$
$661$	32.3939	−	32.3939i	1.25998	−	1.25998i	0.951104	−	0.308872i	$-0.0999516\pi$
$662$		−	7.95459i		−	0.309164i
$663$		0			0
$664$			10.8990i			0.422962i
$665$	−21.7980	+	53.3939i	−0.845289	+	2.07053i
$666$		0			0
$667$		−	6.20204i		−	0.240144i
$668$	3.34847	+	3.34847i	0.129556	+	0.129556i
$669$		0			0
$670$	−40.8990	+	40.8990i	−1.58007	+	1.58007i
$671$	44.4949	−	44.4949i	1.71771	−	1.71771i
$672$		0			0
$673$			45.3939i			1.74981i	0.484299	+	0.874903i	$0.339075\pi$
$673$			45.3939i			1.74981i	−0.484299	+	0.874903i	$0.660925\pi$
$674$	−5.14643	−	5.14643i	−0.198233	−	0.198233i
$675$		0			0
$676$	−12.0000	+	5.00000i	−0.461538	+	0.192308i
$677$		−	25.1010i		−	0.964711i	−0.875976	−	0.482355i	$-0.839781\pi$
$677$		−	25.1010i		−	0.964711i	0.875976	−	0.482355i	$-0.160219\pi$
$678$		0			0
$679$	−2.75255	−	6.55051i	−0.105633	−	0.251386i
$680$		−	9.79796i		−	0.375735i
$681$		0			0
$682$	6.00000	+	6.00000i	0.229752	+	0.229752i
$683$	−26.2474	−	26.2474i	−1.00433	−	1.00433i	−0.999991	−	0.00434013i	$-0.998618\pi$
$683$	−26.2474	−	26.2474i	−1.00433	−	1.00433i	−0.00434013	−	0.999991i	$-0.501382\pi$
$684$		0			0
$685$		0			0
$686$	29.8207	+	11.8207i	1.13856	+	0.451315i
$687$		0			0
$688$		−	14.4949i		−	0.552613i
$689$	−15.5959	+	23.3939i	−0.594157	+	0.891236i
$690$		0			0
$691$	−8.14643	−	8.14643i	−0.309905	−	0.309905i	0.534968	−	0.844872i	$-0.320324\pi$
$691$	−8.14643	−	8.14643i	−0.309905	−	0.309905i	−0.844872	+	0.534968i	$0.820324\pi$
$692$		−	16.6969i		−	0.634722i
$693$		0			0
$694$	−26.6969	+	26.6969i	−1.01340	+	1.01340i
$695$	5.79796	−	5.79796i	0.219929	−	0.219929i
$696$		0			0
$697$	8.00000	+	8.00000i	0.303022	+	0.303022i
$698$		−	26.4495i		−	1.00113i
$699$		0			0
$700$	7.34847	+	3.00000i	0.277746	+	0.113389i
$701$			0.696938i			0.0263230i	0.999913	+	0.0131615i	$0.00418956\pi$
$701$			0.696938i			0.0263230i	−0.999913	+	0.0131615i	$0.995810\pi$
$702$		0			0
$703$			20.6969i			0.780600i
$704$	4.44949	−	4.44949i	0.167696	−	0.167696i
$705$		0			0
$706$	24.0000			0.903252
$707$	36.4949	+	14.8990i	1.37253	+	0.560334i
$708$		0			0
$709$	−10.1010	−	10.1010i	−0.379352	−	0.379352i	0.491516	−	0.870868i	$-0.336443\pi$
$709$	−10.1010	−	10.1010i	−0.379352	−	0.379352i	−0.870868	+	0.491516i	$0.836443\pi$
$710$	−12.0000	+	12.0000i	−0.450352	+	0.450352i
$711$		0			0
$712$	−4.89898			−0.183597
$713$	−0.494897	+	0.494897i	−0.0185341	+	0.0185341i
$714$		0			0
$715$	53.3939	+	35.5959i	1.99682	+	1.33121i
$716$	−2.20204			−0.0822941
$717$		0			0
$718$	1.10102			0.0410897
$719$	−16.8990			−0.630226			−0.315113	−	0.949054i	$-0.602042\pi$
$719$	−16.8990			−0.630226			−0.315113	+	0.949054i	$0.602042\pi$
$720$		0			0
$721$	43.5959	+	17.7980i	1.62360	+	0.662831i
$722$	49.4722	+	49.4722i	1.84116	+	1.84116i
$723$		0			0
$724$		−	2.00000i		−	0.0743294i
$725$			20.6969i			0.768665i
$726$		0			0
$727$	−5.10102			−0.189186			−0.0945932	−	0.995516i	$-0.530155\pi$
$727$	−5.10102			−0.189186			−0.0945932	+	0.995516i	$0.530155\pi$
$728$	16.2247	+	3.12372i	0.601329	+	0.115773i
$729$		0			0
$730$	9.30306	−	9.30306i	0.344322	−	0.344322i
$731$		−	5.79796i		−	0.214445i
$732$		0			0
$733$	9.00000	+	9.00000i	0.332423	+	0.332423i	0.853506	−	0.521083i	$-0.174472\pi$
$733$	9.00000	+	9.00000i	0.332423	+	0.332423i	−0.521083	+	0.853506i	$0.674472\pi$
$734$	−27.5505	−	27.5505i	−1.01691	−	1.01691i
$735$		0			0
$736$	−3.30306	−	3.30306i	−0.121752	−	0.121752i
$737$	−74.2929			−2.73661
$738$		0			0
$739$	7.65153	+	7.65153i	0.281466	+	0.281466i	0.833694	−	0.552227i	$-0.186222\pi$
$739$	7.65153	+	7.65153i	0.281466	+	0.281466i	−0.552227	+	0.833694i	$0.686222\pi$
$740$	7.59592			0.279231
$741$		0			0
$742$	−32.9444	+	13.8434i	−1.20943	+	0.508206i
$743$	26.0454	−	26.0454i	0.955513	−	0.955513i	−0.0435384	−	0.999052i	$-0.513863\pi$
$743$	26.0454	−	26.0454i	0.955513	−	0.955513i	0.999052	+	0.0435384i	$0.0138631\pi$
$744$		0			0
$745$	35.5959			1.30413
$746$	−12.0000	+	12.0000i	−0.439351	+	0.439351i
$747$		0			0
$748$	−8.89898	+	8.89898i	−0.325379	+	0.325379i
$749$	21.7980	+	8.89898i	0.796480	+	0.325162i
$750$		0			0
$751$		−	48.2929i		−	1.76223i	−0.472901	−	0.881116i	$-0.656793\pi$
$751$		−	48.2929i		−	1.76223i	0.472901	−	0.881116i	$-0.343207\pi$
$752$	−32.2474	+	32.2474i	−1.17594	+	1.17594i
$753$		0			0
$754$	−8.44949	−	42.2474i	−0.307712	−	1.53856i
$755$		−	10.2020i		−	0.371290i
$756$		0			0
$757$	−18.2020			−0.661564			−0.330782	−	0.943707i	$-0.607313\pi$
$757$	−18.2020			−0.661564			−0.330782	+	0.943707i	$0.607313\pi$
$758$		−	20.9444i		−	0.760734i
$759$		0			0
$760$	−26.6969	+	26.6969i	−0.968400	+	0.968400i
$761$	14.6969	−	14.6969i	0.532764	−	0.532764i	−0.388630	−	0.921394i	$-0.627052\pi$
$761$	14.6969	−	14.6969i	0.532764	−	0.532764i	0.921394	+	0.388630i	$0.127052\pi$
$762$		0			0
$763$	−34.1464	+	14.3485i	−1.23618	+	0.519449i
$764$			5.79796i			0.209763i
$765$		0			0
$766$	20.2020			0.729929
$767$	0.449490	+	2.24745i	0.0162301	+	0.0811507i
$768$		0			0
$769$	−13.8990	−	13.8990i	−0.501210	−	0.501210i	0.410604	−	0.911814i	$-0.365318\pi$
$769$	−13.8990	−	13.8990i	−0.501210	−	0.501210i	−0.911814	+	0.410604i	$0.865318\pi$
$770$	31.5959	+	75.1918i	1.13864	+	2.70973i
$771$		0			0
$772$	−4.79796	+	4.79796i	−0.172682	+	0.172682i
$773$	36.0000	+	36.0000i	1.29483	+	1.29483i	0.931763	+	0.363067i	$0.118270\pi$
$773$	36.0000	+	36.0000i	1.29483	+	1.29483i	0.363067	+	0.931763i	$0.381730\pi$
$774$		0			0
$775$	1.65153	−	1.65153i	0.0593247	−	0.0593247i
$776$		−	4.65153i		−	0.166980i
$777$		0			0
$778$	13.3485	+	13.3485i	0.478566	+	0.478566i
$779$		−	43.5959i		−	1.56199i
$780$		0			0
$781$	−21.7980			−0.779992
$782$	−2.20204	−	2.20204i	−0.0787448	−	0.0787448i
$783$		0			0
$784$	25.0000	+	24.4949i	0.892857	+	0.874818i
$785$	24.0000	−	24.0000i	0.856597	−	0.856597i
$786$		0			0
$787$	−9.24745	+	9.24745i	−0.329636	+	0.329636i	−0.852448	−	0.522812i	$-0.824883\pi$
$787$	−9.24745	+	9.24745i	−0.329636	+	0.329636i	0.522812	+	0.852448i	$0.324883\pi$
$788$	11.7980	+	11.7980i	0.420285	+	0.420285i
$789$		0			0
$790$	−33.7980			−1.20248
$791$	22.2929	+	9.10102i	0.792643	+	0.323595i
$792$		0			0
$793$	30.0000	+	20.0000i	1.06533	+	0.710221i
$794$			26.4495i			0.938657i
$795$		0			0
$796$			13.1010i			0.464353i
$797$	37.1918			1.31740			0.658701	−	0.752405i	$-0.271106\pi$
$797$	37.1918			1.31740			0.658701	+	0.752405i	$0.271106\pi$
$798$		0			0
$799$	−12.8990	+	12.8990i	−0.456333	+	0.456333i
$800$	11.0227	+	11.0227i	0.389711	+	0.389711i
$801$		0			0
$802$	34.2929			1.21092
$803$	16.8990			0.596352
$804$		0			0
$805$	−6.20204	+	2.60612i	−0.218593	+	0.0918538i
$806$	−2.69694	+	4.04541i	−0.0949956	+	0.142493i
$807$		0			0
$808$	18.2474	+	18.2474i	0.641943	+	0.641943i
$809$	13.1010			0.460607			0.230304	−	0.973119i	$-0.426028\pi$
$809$	13.1010			0.460607			0.230304	+	0.973119i	$0.426028\pi$
$810$		0			0
$811$	37.0454	+	37.0454i	1.30084	+	1.30084i	0.927825	+	0.373015i	$0.121676\pi$
$811$	37.0454	+	37.0454i	1.30084	+	1.30084i	0.373015	+	0.927825i	$0.378324\pi$
$812$	6.89898	−	16.8990i	0.242107	−	0.593038i
$813$		0			0
$814$	20.6969	+	20.6969i	0.725427	+	0.725427i
$815$		−	2.20204i		−	0.0771341i
$816$		0			0
$817$	−15.7980	+	15.7980i	−0.552701	+	0.552701i
$818$	58.0454			2.02951
$819$		0			0
$820$	−16.0000			−0.558744
$821$	−3.59592	+	3.59592i	−0.125498	+	0.125498i	−0.767066	−	0.641568i	$-0.778284\pi$
$821$	−3.59592	+	3.59592i	−0.125498	+	0.125498i	0.641568	+	0.767066i	$0.278284\pi$
$822$		0			0
$823$		−	16.6969i		−	0.582019i	−0.956720	−	0.291009i	$-0.906009\pi$
$823$		−	16.6969i		−	0.582019i	0.956720	−	0.291009i	$-0.0939911\pi$
$824$	21.7980	+	21.7980i	0.759368	+	0.759368i
$825$		0			0
$826$	−1.10102	+	2.69694i	−0.0383094	+	0.0938385i
$827$	5.34847	+	5.34847i	0.185984	+	0.185984i	0.793958	−	0.607973i	$-0.208017\pi$
$827$	5.34847	+	5.34847i	0.185984	+	0.185984i	−0.607973	+	0.793958i	$0.708017\pi$
$828$		0			0
$829$	−53.7980			−1.86848			−0.934240	−	0.356644i	$-0.883921\pi$
$829$	−53.7980			−1.86848			−0.934240	+	0.356644i	$0.883921\pi$
$830$	−21.7980	−	21.7980i	−0.756618	−	0.756618i
$831$		0			0
$832$	3.00000	+	2.00000i	0.104006	+	0.0693375i
$833$	10.0000	+	9.79796i	0.346479	+	0.339479i
$834$		0			0
$835$	13.3939			0.463514
$836$	48.4949			1.67723
$837$		0			0
$838$	−42.0000	−	42.0000i	−1.45087	−	1.45087i
$839$	−3.55051	+	3.55051i	−0.122577	+	0.122577i	−0.765734	−	0.643157i	$-0.777624\pi$
$839$	−3.55051	+	3.55051i	−0.122577	+	0.122577i	0.643157	+	0.765734i	$0.277624\pi$
$840$		0			0
$841$	18.5959			0.641239
$842$		−	10.0454i		−	0.346188i
$843$		0			0
$844$		−	18.8990i		−	0.650530i
$845$	−14.0000	+	34.0000i	−0.481615	+	1.16964i
$846$		0			0
$847$	−28.5959	+	70.0454i	−0.982567	+	2.40679i
$848$	−38.9898			−1.33892
$849$		0			0
$850$	7.34847	+	7.34847i	0.252050	+	0.252050i
$851$	−1.70714	+	1.70714i	−0.0585201	+	0.0585201i
$852$		0			0
$853$	38.7980	−	38.7980i	1.32842	−	1.32842i	0.421665	−	0.906752i	$-0.361446\pi$
$853$	38.7980	−	38.7980i	1.32842	−	1.32842i	0.906752	−	0.421665i	$-0.138554\pi$
$854$	17.7526	+	42.2474i	0.607480	+	1.44568i
$855$		0			0
$856$	10.8990	+	10.8990i	0.372519	+	0.372519i
$857$	26.4949			0.905048			0.452524	−	0.891752i	$-0.350524\pi$
$857$	26.4949			0.905048			0.452524	+	0.891752i	$0.350524\pi$
$858$		0			0
$859$			29.7980i			1.01669i	0.861153	+	0.508347i	$0.169743\pi$
$859$			29.7980i			1.01669i	−0.861153	+	0.508347i	$0.830257\pi$
$860$	5.79796	+	5.79796i	0.197709	+	0.197709i
$861$		0			0
$862$		−	49.1010i		−	1.67239i
$863$	19.1464	−	19.1464i	0.651752	−	0.651752i	−0.301663	−	0.953415i	$-0.597542\pi$
$863$	19.1464	−	19.1464i	0.651752	−	0.651752i	0.953415	+	0.301663i	$0.0975416\pi$
$864$		0			0
$865$	−33.3939	−	33.3939i	−1.13543	−	1.13543i
$866$	−36.4949	+	36.4949i	−1.24015	+	1.24015i
$867$		0			0
$868$	−1.89898	+	0.797959i	−0.0644556	+	0.0270845i
$869$	−30.6969	−	30.6969i	−1.04132	−	1.04132i
$870$		0			0
$871$	−8.34847	−	41.7423i	−0.282877	−	1.41439i
$872$	−24.2474			−0.821122
$873$		0			0
$874$			12.0000i			0.405906i
$875$	−13.7980	+	5.79796i	−0.466456	+	0.196007i
$876$		0			0
$877$	−17.6969	+	17.6969i	−0.597583	+	0.597583i	−0.939669	−	0.342086i	$-0.888867\pi$
$877$	−17.6969	+	17.6969i	−0.597583	+	0.597583i	0.342086	+	0.939669i	$0.388867\pi$
$878$	−33.7980	+	33.7980i	−1.14063	+	1.14063i
$879$		0			0
$880$			88.9898i			2.99985i
$881$	−12.6969			−0.427771			−0.213885	−	0.976859i	$-0.568612\pi$
$881$	−12.6969			−0.427771			−0.213885	+	0.976859i	$0.568612\pi$
$882$		0			0
$883$			37.7980i			1.27200i	0.771688	+	0.636001i	$0.219413\pi$
$883$			37.7980i			1.27200i	−0.771688	+	0.636001i	$0.780587\pi$
$884$	−6.00000	−	4.00000i	−0.201802	−	0.134535i
$885$		0			0
$886$	6.49490	−	6.49490i	0.218200	−	0.218200i
$887$		−	12.0000i		−	0.402921i	−0.979497	−	0.201460i	$-0.935431\pi$
$887$		−	12.0000i		−	0.402921i	0.979497	−	0.201460i	$-0.0645687\pi$
$888$		0			0
$889$	8.00000	−	19.5959i	0.268311	−	0.657226i
$890$	9.79796	−	9.79796i	0.328428	−	0.328428i
$891$		0			0
$892$	7.44949	−	7.44949i	0.249427	−	0.249427i
$893$	70.2929			2.35226
$894$		0			0
$895$	−4.40408	+	4.40408i	−0.147212	+	0.147212i
$896$	12.4268	+	29.5732i	0.415150	+	0.987972i
$897$		0			0
$898$	−36.4949			−1.21785
$899$	−3.79796	−	3.79796i	−0.126669	−	0.126669i
$900$		0			0
$901$	−15.5959			−0.519575
$902$	−43.5959	−	43.5959i	−1.45159	−	1.45159i
$903$		0			0
$904$	11.1464	+	11.1464i	0.370725	+	0.370725i
$905$	−4.00000	−	4.00000i	−0.132964	−	0.132964i
$906$		0			0
$907$			39.5959i			1.31476i	0.753559	+	0.657380i	$0.228336\pi$
$907$			39.5959i			1.31476i	−0.753559	+	0.657380i	$0.771664\pi$
$908$	−15.3485	+	15.3485i	−0.509357	+	0.509357i
$909$		0			0
$910$	−38.6969	+	26.2020i	−1.28279	+	0.868589i
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$		0			0
$913$		−	39.5959i		−	1.31043i
$914$		−	16.6515i		−	0.550784i
$915$		0			0
$916$	13.0000	+	13.0000i	0.429532	+	0.429532i
$917$	10.6969	−	26.2020i	0.353244	−	0.865268i
$918$		0			0
$919$	−34.4949			−1.13788			−0.568941	−	0.822378i	$-0.692647\pi$
$919$	−34.4949			−1.13788			−0.568941	+	0.822378i	$0.692647\pi$
$920$	−4.40408			−0.145198
$921$		0			0
$922$	11.5051			0.378900
$923$	−2.44949	−	12.2474i	−0.0806259	−	0.403130i
$924$		0			0
$925$	5.69694	−	5.69694i	0.187314	−	0.187314i
$926$	−49.3485			−1.62169
$927$		0			0
$928$	25.3485	−	25.3485i	0.832104	−	0.832104i
$929$	−4.89898	−	4.89898i	−0.160730	−	0.160730i	0.622160	−	0.782890i	$-0.286255\pi$
$929$	−4.89898	−	4.89898i	−0.160730	−	0.160730i	−0.782890	+	0.622160i	$0.786255\pi$
$930$		0			0
$931$	−0.550510	−	53.9444i	−0.0180422	−	1.76796i
$932$	−7.79796			−0.255431
$933$		0			0
$934$	−38.0908	+	38.0908i	−1.24637	+	1.24637i
$935$			35.5959i			1.16411i
$936$		0			0
$937$			29.5959i			0.966856i	0.875384	+	0.483428i	$0.160609\pi$
$937$			29.5959i			0.966856i	−0.875384	+	0.483428i	$0.839391\pi$
$938$	20.4495	−	50.0908i	0.667700	−	1.63552i
$939$		0			0
$940$		−	25.7980i		−	0.841437i
$941$	7.10102	+	7.10102i	0.231487	+	0.231487i	0.813313	−	0.581826i	$-0.197662\pi$
$941$	7.10102	+	7.10102i	0.231487	+	0.231487i	−0.581826	+	0.813313i	$0.697662\pi$
$942$		0			0
$943$	3.59592	−	3.59592i	0.117099	−	0.117099i
$944$	−2.24745	+	2.24745i	−0.0731482	+	0.0731482i
$945$		0			0
$946$			31.5959i			1.02727i
$947$	18.4495	+	18.4495i	0.599528	+	0.599528i	0.940187	−	0.340659i	$-0.110650\pi$
$947$	18.4495	+	18.4495i	0.599528	+	0.599528i	−0.340659	+	0.940187i	$0.610650\pi$
$948$		0			0
$949$	1.89898	+	9.49490i	0.0616435	+	0.308217i
$950$		−	40.0454i		−	1.29924i
$951$		0			0
$952$	3.55051	+	8.44949i	0.115073	+	0.273850i
$953$			6.00000i			0.194359i	0.995267	+	0.0971795i	$0.0309821\pi$
$953$			6.00000i			0.194359i	−0.995267	+	0.0971795i	$0.969018\pi$
$954$		0			0
$955$	11.5959	+	11.5959i	0.375235	+	0.375235i
$956$	7.34847	+	7.34847i	0.237666	+	0.237666i
$957$		0			0
$958$		−	25.1010i		−	0.810977i
$959$		0			0
$960$		0			0
$961$		−	30.3939i		−	0.980448i
$962$	−9.30306	+	13.9546i	−0.299943	+	0.449914i
$963$		0			0
$964$	−4.10102	−	4.10102i	−0.132085	−	0.132085i
$965$			19.1918i			0.617807i
$966$		0			0
$967$	35.2474	−	35.2474i	1.13348	−	1.13348i	0.143887	−	0.989594i	$-0.454040\pi$
$967$	35.2474	−	35.2474i	1.13348	−	1.13348i	0.989594	−	0.143887i	$-0.0459603\pi$
$968$	−35.0227	+	35.0227i	−1.12567	+	1.12567i
$969$		0			0
$970$	9.30306	+	9.30306i	0.298703	+	0.298703i
$971$		−	26.2020i		−	0.840864i	−0.907324	−	0.420432i	$-0.861879\pi$
$971$		−	26.2020i		−	0.840864i	0.907324	−	0.420432i	$-0.138121\pi$
$972$		0			0
$973$	−2.89898	+	7.10102i	−0.0929370	+	0.227648i
$974$		−	37.3485i		−	1.19672i
$975$		0			0
$976$			50.0000i			1.60046i
$977$	−5.59592	+	5.59592i	−0.179029	+	0.179029i	−0.790933	−	0.611903i	$-0.790404\pi$
$977$	−5.59592	+	5.59592i	−0.179029	+	0.179029i	0.611903	+	0.790933i	$0.290404\pi$
$978$		0			0
$979$	17.7980			0.568825
$980$	−19.7980	+	0.202041i	−0.632423	+	0.00645396i
$981$		0			0
$982$	45.1918	+	45.1918i	1.44213	+	1.44213i
$983$	42.2474	−	42.2474i	1.34748	−	1.34748i	0.459099	−	0.888385i	$-0.348172\pi$
$983$	42.2474	−	42.2474i	1.34748	−	1.34748i	0.888385	−	0.459099i	$-0.151828\pi$
$984$		0			0
$985$	47.1918			1.50366
$986$	16.8990	−	16.8990i	0.538173	−	0.538173i
$987$		0			0
$988$	5.44949	+	27.2474i	0.173371	+	0.866857i
$989$	−2.60612			−0.0828699
$990$		0			0
$991$	−23.1918			−0.736713			−0.368356	−	0.929685i	$-0.620079\pi$
$991$	−23.1918			−0.736713			−0.368356	+	0.929685i	$0.620079\pi$
$992$	−4.04541			−0.128442
$993$		0			0
$994$	6.00000	−	14.6969i	0.190308	−	0.466159i
$995$	26.2020	+	26.2020i	0.830661	+	0.830661i
$996$		0			0
$997$		−	9.39388i		−	0.297507i	−0.988874	−	0.148754i	$-0.952474\pi$
$997$		−	9.39388i		−	0.297507i	0.988874	−	0.148754i	$-0.0475261\pi$
$998$			37.3485i			1.18225i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.y.a.811.2		4
3.2	odd	2		273.2.p.d.265.1	yes	4
7.6	odd	2		819.2.y.d.811.2		4
13.8	odd	4		819.2.y.d.307.2		4
21.20	even	2		273.2.p.a.265.1	yes	4
39.8	even	4		273.2.p.a.34.1	✓	4
91.34	even	4	inner	819.2.y.a.307.2		4
273.125	odd	4		273.2.p.d.34.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.p.a.34.1	✓	4	39.8	even	4
273.2.p.a.265.1	yes	4	21.20	even	2
273.2.p.d.34.1	yes	4	273.125	odd	4
273.2.p.d.265.1	yes	4	3.2	odd	2
819.2.y.a.307.2		4	91.34	even	4	inner
819.2.y.a.811.2		4	1.1	even	1	trivial
819.2.y.d.307.2		4	13.8	odd	4
819.2.y.d.811.2		4	7.6	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.y (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 1.22474i) q^{2} -1.00000i q^{4} +(-2.00000 - 2.00000i) q^{5} +(2.44949 + 1.00000i) q^{7} +(1.22474 + 1.22474i) q^{8} +O(q^{10})\)	\(q+(1.22474 - 1.22474i) q^{2} -1.00000i q^{4} +(-2.00000 - 2.00000i) q^{5} +(2.44949 + 1.00000i) q^{7} +(1.22474 + 1.22474i) q^{8} -4.89898 q^{10} +(-4.44949 - 4.44949i) q^{11} +(2.00000 - 3.00000i) q^{13} +(4.22474 - 1.77526i) q^{14} +5.00000 q^{16} +2.00000 q^{17} +(-5.44949 - 5.44949i) q^{19} +(-2.00000 + 2.00000i) q^{20} -10.8990 q^{22} -0.898979i q^{23} +3.00000i q^{25} +(-1.22474 - 6.12372i) q^{26} +(1.00000 - 2.44949i) q^{28} +6.89898 q^{29} +(-0.550510 - 0.550510i) q^{31} +(3.67423 - 3.67423i) q^{32} +(2.44949 - 2.44949i) q^{34} +(-2.89898 - 6.89898i) q^{35} +(-1.89898 - 1.89898i) q^{37} -13.3485 q^{38} -4.89898i q^{40} +(4.00000 + 4.00000i) q^{41} -2.89898i q^{43} +(-4.44949 + 4.44949i) q^{44} +(-1.10102 - 1.10102i) q^{46} +(-6.44949 + 6.44949i) q^{47} +(5.00000 + 4.89898i) q^{49} +(3.67423 + 3.67423i) q^{50} +(-3.00000 - 2.00000i) q^{52} -7.79796 q^{53} +17.7980i q^{55} +(1.77526 + 4.22474i) q^{56} +(8.44949 - 8.44949i) q^{58} +(-0.449490 + 0.449490i) q^{59} +10.0000i q^{61} -1.34847 q^{62} +1.00000i q^{64} +(-10.0000 + 2.00000i) q^{65} +(8.34847 - 8.34847i) q^{67} -2.00000i q^{68} +(-12.0000 - 4.89898i) q^{70} +(2.44949 - 2.44949i) q^{71} +(-1.89898 + 1.89898i) q^{73} -4.65153 q^{74} +(-5.44949 + 5.44949i) q^{76} +(-6.44949 - 15.3485i) q^{77} +6.89898 q^{79} +(-10.0000 - 10.0000i) q^{80} +9.79796 q^{82} +(4.44949 + 4.44949i) q^{83} +(-4.00000 - 4.00000i) q^{85} +(-3.55051 - 3.55051i) q^{86} -10.8990i q^{88} +(-2.00000 + 2.00000i) q^{89} +(7.89898 - 5.34847i) q^{91} -0.898979 q^{92} +15.7980i q^{94} +21.7980i q^{95} +(-1.89898 - 1.89898i) q^{97} +(12.1237 - 0.123724i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{5}+O(q^{10}) \) 4 * q - 8 * q^5	\( 4 q - 8 q^{5} - 8 q^{11} + 8 q^{13} + 12 q^{14} + 20 q^{16} + 8 q^{17} - 12 q^{19} - 8 q^{20} - 24 q^{22} + 4 q^{28} + 8 q^{29} - 12 q^{31} + 8 q^{35} + 12 q^{37} - 24 q^{38} + 16 q^{41} - 8 q^{44} - 24 q^{46} - 16 q^{47} + 20 q^{49} - 12 q^{52} + 8 q^{53} + 12 q^{56} + 24 q^{58} + 8 q^{59} + 24 q^{62} - 40 q^{65} + 4 q^{67} - 48 q^{70} + 12 q^{73} - 48 q^{74} - 12 q^{76} - 16 q^{77} + 8 q^{79} - 40 q^{80} + 8 q^{83} - 16 q^{85} - 24 q^{86} - 8 q^{89} + 12 q^{91} + 16 q^{92} + 12 q^{97} + 24 q^{98}+O(q^{100}) \) 4 * q - 8 * q^5 - 8 * q^11 + 8 * q^13 + 12 * q^14 + 20 * q^16 + 8 * q^17 - 12 * q^19 - 8 * q^20 - 24 * q^22 + 4 * q^28 + 8 * q^29 - 12 * q^31 + 8 * q^35 + 12 * q^37 - 24 * q^38 + 16 * q^41 - 8 * q^44 - 24 * q^46 - 16 * q^47 + 20 * q^49 - 12 * q^52 + 8 * q^53 + 12 * q^56 + 24 * q^58 + 8 * q^59 + 24 * q^62 - 40 * q^65 + 4 * q^67 - 48 * q^70 + 12 * q^73 - 48 * q^74 - 12 * q^76 - 16 * q^77 + 8 * q^79 - 40 * q^80 + 8 * q^83 - 16 * q^85 - 24 * q^86 - 8 * q^89 + 12 * q^91 + 16 * q^92 + 12 * q^97 + 24 * q^98

Introduction

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