LMFDB - Embedded newform 273.2.p.d.34.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(34,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, 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("273.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.p (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:	$2.17991597518$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			34.1
Root			$-1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	273.34
Dual form			273.2.p.d.265.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 - 1.22474i) q^{2} -1.00000i q^{3} +1.00000i q^{4} +(2.00000 - 2.00000i) q^{5} +(-1.22474 + 1.22474i) q^{6} +(2.44949 - 1.00000i) q^{7} +(-1.22474 + 1.22474i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.22474 - 1.22474i) q^{2} -1.00000i q^{3} +1.00000i q^{4} +(2.00000 - 2.00000i) q^{5} +(-1.22474 + 1.22474i) q^{6} +(2.44949 - 1.00000i) q^{7} +(-1.22474 + 1.22474i) q^{8} -1.00000 q^{9} -4.89898 q^{10} +(4.44949 - 4.44949i) q^{11} +1.00000 q^{12} +(2.00000 + 3.00000i) q^{13} +(-4.22474 - 1.77526i) q^{14} +(-2.00000 - 2.00000i) q^{15} +5.00000 q^{16} -2.00000 q^{17} +(1.22474 + 1.22474i) q^{18} +(-5.44949 + 5.44949i) q^{19} +(2.00000 + 2.00000i) q^{20} +(-1.00000 - 2.44949i) q^{21} -10.8990 q^{22} -0.898979i q^{23} +(1.22474 + 1.22474i) q^{24} -3.00000i q^{25} +(1.22474 - 6.12372i) q^{26} +1.00000i q^{27} +(1.00000 + 2.44949i) q^{28} -6.89898 q^{29} +4.89898i q^{30} +(-0.550510 + 0.550510i) q^{31} +(-3.67423 - 3.67423i) q^{32} +(-4.44949 - 4.44949i) q^{33} +(2.44949 + 2.44949i) q^{34} +(2.89898 - 6.89898i) q^{35} -1.00000i q^{36} +(-1.89898 + 1.89898i) q^{37} +13.3485 q^{38} +(3.00000 - 2.00000i) q^{39} +4.89898i q^{40} +(-4.00000 + 4.00000i) q^{41} +(-1.77526 + 4.22474i) q^{42} +2.89898i q^{43} +(4.44949 + 4.44949i) q^{44} +(-2.00000 + 2.00000i) q^{45} +(-1.10102 + 1.10102i) q^{46} +(6.44949 + 6.44949i) q^{47} -5.00000i q^{48} +(5.00000 - 4.89898i) q^{49} +(-3.67423 + 3.67423i) q^{50} +2.00000i q^{51} +(-3.00000 + 2.00000i) q^{52} +7.79796 q^{53} +(1.22474 - 1.22474i) q^{54} -17.7980i q^{55} +(-1.77526 + 4.22474i) q^{56} +(5.44949 + 5.44949i) q^{57} +(8.44949 + 8.44949i) q^{58} +(0.449490 + 0.449490i) q^{59} +(2.00000 - 2.00000i) q^{60} -10.0000i q^{61} +1.34847 q^{62} +(-2.44949 + 1.00000i) q^{63} -1.00000i q^{64} +(10.0000 + 2.00000i) q^{65} +10.8990i q^{66} +(8.34847 + 8.34847i) q^{67} -2.00000i q^{68} -0.898979 q^{69} +(-12.0000 + 4.89898i) q^{70} +(-2.44949 - 2.44949i) q^{71} +(1.22474 - 1.22474i) q^{72} +(-1.89898 - 1.89898i) q^{73} +4.65153 q^{74} -3.00000 q^{75} +(-5.44949 - 5.44949i) q^{76} +(6.44949 - 15.3485i) q^{77} +(-6.12372 - 1.22474i) q^{78} +6.89898 q^{79} +(10.0000 - 10.0000i) q^{80} +1.00000 q^{81} +9.79796 q^{82} +(-4.44949 + 4.44949i) q^{83} +(2.44949 - 1.00000i) q^{84} +(-4.00000 + 4.00000i) q^{85} +(3.55051 - 3.55051i) q^{86} +6.89898i q^{87} +10.8990i q^{88} +(2.00000 + 2.00000i) q^{89} +4.89898 q^{90} +(7.89898 + 5.34847i) q^{91} +0.898979 q^{92} +(0.550510 + 0.550510i) q^{93} -15.7980i q^{94} +21.7980i q^{95} +(-3.67423 + 3.67423i) q^{96} +(-1.89898 + 1.89898i) q^{97} +(-12.1237 - 0.123724i) q^{98} +(-4.44949 + 4.44949i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{5} - 4 q^{9}+O(q^{10}) $ 4 * q + 8 * q^5 - 4 * q^9	$ 4 q + 8 q^{5} - 4 q^{9} + 8 q^{11} + 4 q^{12} + 8 q^{13} - 12 q^{14} - 8 q^{15} + 20 q^{16} - 8 q^{17} - 12 q^{19} + 8 q^{20} - 4 q^{21} - 24 q^{22} + 4 q^{28} - 8 q^{29} - 12 q^{31} - 8 q^{33} - 8 q^{35} + 12 q^{37} + 24 q^{38} + 12 q^{39} - 16 q^{41} - 12 q^{42} + 8 q^{44} - 8 q^{45} - 24 q^{46} + 16 q^{47} + 20 q^{49} - 12 q^{52} - 8 q^{53} - 12 q^{56} + 12 q^{57} + 24 q^{58} - 8 q^{59} + 8 q^{60} - 24 q^{62} + 40 q^{65} + 4 q^{67} + 16 q^{69} - 48 q^{70} + 12 q^{73} + 48 q^{74} - 12 q^{75} - 12 q^{76} + 16 q^{77} + 8 q^{79} + 40 q^{80} + 4 q^{81} - 8 q^{83} - 16 q^{85} + 24 q^{86} + 8 q^{89} + 12 q^{91} - 16 q^{92} + 12 q^{93} + 12 q^{97} - 24 q^{98} - 8 q^{99}+O(q^{100}) $ 4 * q + 8 * q^5 - 4 * q^9 + 8 * q^11 + 4 * q^12 + 8 * q^13 - 12 * q^14 - 8 * q^15 + 20 * q^16 - 8 * q^17 - 12 * q^19 + 8 * q^20 - 4 * q^21 - 24 * q^22 + 4 * q^28 - 8 * q^29 - 12 * q^31 - 8 * q^33 - 8 * q^35 + 12 * q^37 + 24 * q^38 + 12 * q^39 - 16 * q^41 - 12 * q^42 + 8 * q^44 - 8 * q^45 - 24 * q^46 + 16 * q^47 + 20 * q^49 - 12 * q^52 - 8 * q^53 - 12 * q^56 + 12 * q^57 + 24 * q^58 - 8 * q^59 + 8 * q^60 - 24 * q^62 + 40 * q^65 + 4 * q^67 + 16 * q^69 - 48 * q^70 + 12 * q^73 + 48 * q^74 - 12 * q^75 - 12 * q^76 + 16 * q^77 + 8 * q^79 + 40 * q^80 + 4 * q^81 - 8 * q^83 - 16 * q^85 + 24 * q^86 + 8 * q^89 + 12 * q^91 - 16 * q^92 + 12 * q^93 + 12 * q^97 - 24 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

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	$-0.459785\pi$
$2$	−1.22474	−	1.22474i	−0.866025	−	0.866025i	−0.992030	+	0.126004i	$0.959785\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$			1.00000i			0.500000i
$5$	2.00000	−	2.00000i	0.894427	−	0.894427i	−0.100509	−	0.994936i	$-0.532047\pi$
$5$	2.00000	−	2.00000i	0.894427	−	0.894427i	0.994936	+	0.100509i	$0.0320471\pi$
$6$	−1.22474	+	1.22474i	−0.500000	+	0.500000i
$7$	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
$9$	−1.00000			−0.333333
$10$	−4.89898			−1.54919
$11$	4.44949	−	4.44949i	1.34157	−	1.34157i	0.447075	−	0.894496i	$-0.352466\pi$
$11$	4.44949	−	4.44949i	1.34157	−	1.34157i	0.894496	−	0.447075i	$-0.147534\pi$
$12$	1.00000			0.288675
$13$	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
$15$	−2.00000	−	2.00000i	−0.516398	−	0.516398i
$16$	5.00000			1.25000
$17$	−2.00000			−0.485071			−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$	1.22474	+	1.22474i	0.288675	+	0.288675i
$19$	−5.44949	+	5.44949i	−1.25020	+	1.25020i	−0.294568	+	0.955630i	$0.595176\pi$
$19$	−5.44949	+	5.44949i	−1.25020	+	1.25020i	−0.955630	+	0.294568i	$0.904824\pi$
$20$	2.00000	+	2.00000i	0.447214	+	0.447214i
$21$	−1.00000	−	2.44949i	−0.218218	−	0.534522i
$22$	−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	$-0.0298775\pi$
$24$	1.22474	+	1.22474i	0.250000	+	0.250000i
$25$		−	3.00000i		−	0.600000i
$26$	1.22474	−	6.12372i	0.240192	−	1.20096i
$27$			1.00000i			0.192450i
$28$	1.00000	+	2.44949i	0.188982	+	0.462910i
$29$	−6.89898			−1.28111			−0.640554	−	0.767913i	$-0.721295\pi$
$29$	−6.89898			−1.28111			−0.640554	+	0.767913i	$0.721295\pi$
$30$			4.89898i			0.894427i
$31$	−0.550510	+	0.550510i	−0.0988746	+	0.0988746i	−0.754814	−	0.655939i	$-0.772273\pi$
$31$	−0.550510	+	0.550510i	−0.0988746	+	0.0988746i	0.655939	+	0.754814i	$0.272273\pi$
$32$	−3.67423	−	3.67423i	−0.649519	−	0.649519i
$33$	−4.44949	−	4.44949i	−0.774557	−	0.774557i
$34$	2.44949	+	2.44949i	0.420084	+	0.420084i
$35$	2.89898	−	6.89898i	0.490017	−	1.16614i
$36$		−	1.00000i		−	0.166667i
$37$	−1.89898	+	1.89898i	−0.312190	+	0.312190i	−0.845758	−	0.533567i	$-0.820851\pi$
$37$	−1.89898	+	1.89898i	−0.312190	+	0.312190i	0.533567	+	0.845758i	$0.320851\pi$
$38$	13.3485			2.16541
$39$	3.00000	−	2.00000i	0.480384	−	0.320256i
$40$			4.89898i			0.774597i
$41$	−4.00000	+	4.00000i	−0.624695	+	0.624695i	−0.946728	−	0.322033i	$-0.895634\pi$
$41$	−4.00000	+	4.00000i	−0.624695	+	0.624695i	0.322033	+	0.946728i	$0.395634\pi$
$42$	−1.77526	+	4.22474i	−0.273928	+	0.651892i
$43$			2.89898i			0.442090i	0.975264	+	0.221045i	$0.0709468\pi$
$43$			2.89898i			0.442090i	−0.975264	+	0.221045i	$0.929053\pi$
$44$	4.44949	+	4.44949i	0.670786	+	0.670786i
$45$	−2.00000	+	2.00000i	−0.298142	+	0.298142i
$46$	−1.10102	+	1.10102i	−0.162337	+	0.162337i
$47$	6.44949	+	6.44949i	0.940755	+	0.940755i	0.998341	−	0.0575858i	$-0.0183403\pi$
$47$	6.44949	+	6.44949i	0.940755	+	0.940755i	−0.0575858	+	0.998341i	$0.518340\pi$
$48$		−	5.00000i		−	0.721688i
$49$	5.00000	−	4.89898i	0.714286	−	0.699854i
$50$	−3.67423	+	3.67423i	−0.519615	+	0.519615i
$51$			2.00000i			0.280056i
$52$	−3.00000	+	2.00000i	−0.416025	+	0.277350i
$53$	7.79796			1.07113			0.535566	−	0.844493i	$-0.320098\pi$
$53$	7.79796			1.07113			0.535566	+	0.844493i	$0.320098\pi$
$54$	1.22474	−	1.22474i	0.166667	−	0.166667i
$55$		−	17.7980i		−	2.39988i
$56$	−1.77526	+	4.22474i	−0.237228	+	0.564555i
$57$	5.44949	+	5.44949i	0.721803	+	0.721803i
$58$	8.44949	+	8.44949i	1.10947	+	1.10947i
$59$	0.449490	+	0.449490i	0.0585186	+	0.0585186i	0.735760	−	0.677242i	$-0.236825\pi$
$59$	0.449490	+	0.449490i	0.0585186	+	0.0585186i	−0.677242	+	0.735760i	$0.736825\pi$
$60$	2.00000	−	2.00000i	0.258199	−	0.258199i
$61$		−	10.0000i		−	1.28037i	−0.768221	−	0.640184i	$-0.778858\pi$
$61$		−	10.0000i		−	1.28037i	0.768221	−	0.640184i	$-0.221142\pi$
$62$	1.34847			0.171256
$63$	−2.44949	+	1.00000i	−0.308607	+	0.125988i
$64$		−	1.00000i		−	0.125000i
$65$	10.0000	+	2.00000i	1.24035	+	0.248069i
$66$			10.8990i			1.34157i
$67$	8.34847	+	8.34847i	1.01993	+	1.01993i	0.999797	+	0.0201305i	$0.00640817\pi$
$67$	8.34847	+	8.34847i	1.01993	+	1.01993i	0.0201305	+	0.999797i	$0.493592\pi$
$68$		−	2.00000i		−	0.242536i
$69$	−0.898979			−0.108224
$70$	−12.0000	+	4.89898i	−1.43427	+	0.585540i
$71$	−2.44949	−	2.44949i	−0.290701	−	0.290701i	0.546656	−	0.837357i	$-0.315900\pi$
$71$	−2.44949	−	2.44949i	−0.290701	−	0.290701i	−0.837357	+	0.546656i	$0.815900\pi$
$72$	1.22474	−	1.22474i	0.144338	−	0.144338i
$73$	−1.89898	−	1.89898i	−0.222259	−	0.222259i	0.587190	−	0.809449i	$-0.300234\pi$
$73$	−1.89898	−	1.89898i	−0.222259	−	0.222259i	−0.809449	+	0.587190i	$0.800234\pi$
$74$	4.65153			0.540729
$75$	−3.00000			−0.346410
$76$	−5.44949	−	5.44949i	−0.625099	−	0.625099i
$77$	6.44949	−	15.3485i	0.734988	−	1.74912i
$78$	−6.12372	−	1.22474i	−0.693375	−	0.138675i
$79$	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
$81$	1.00000			0.111111
$82$	9.79796			1.08200
$83$	−4.44949	+	4.44949i	−0.488395	+	0.488395i	−0.907799	−	0.419405i	$-0.862239\pi$
$83$	−4.44949	+	4.44949i	−0.488395	+	0.488395i	0.419405	+	0.907799i	$0.362239\pi$
$84$	2.44949	−	1.00000i	0.267261	−	0.109109i
$85$	−4.00000	+	4.00000i	−0.433861	+	0.433861i
$86$	3.55051	−	3.55051i	0.382861	−	0.382861i
$87$			6.89898i			0.739648i
$88$			10.8990i			1.16184i
$89$	2.00000	+	2.00000i	0.212000	+	0.212000i	0.805116	−	0.593117i	$-0.202103\pi$
$89$	2.00000	+	2.00000i	0.212000	+	0.212000i	−0.593117	+	0.805116i	$0.702103\pi$
$90$	4.89898			0.516398
$91$	7.89898	+	5.34847i	0.828038	+	0.560672i
$92$	0.898979			0.0937251
$93$	0.550510	+	0.550510i	0.0570853	+	0.0570853i
$94$		−	15.7980i		−	1.62944i
$95$			21.7980i			2.23642i
$96$	−3.67423	+	3.67423i	−0.375000	+	0.375000i
$97$	−1.89898	+	1.89898i	−0.192812	+	0.192812i	−0.796910	−	0.604098i	$-0.793534\pi$
$97$	−1.89898	+	1.89898i	−0.192812	+	0.192812i	0.604098	+	0.796910i	$0.293534\pi$
$98$	−12.1237	−	0.123724i	−1.22468	−	0.0124980i
$99$	−4.44949	+	4.44949i	−0.447191	+	0.447191i
$100$	3.00000			0.300000
$101$	−14.8990			−1.48250			−0.741252	−	0.671227i	$-0.765768\pi$
$101$	−14.8990			−1.48250			−0.741252	+	0.671227i	$0.765768\pi$
$102$	2.44949	−	2.44949i	0.242536	−	0.242536i
$103$	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
$105$	−6.89898	−	2.89898i	−0.673271	−	0.282911i
$106$	−9.55051	−	9.55051i	−0.927628	−	0.927628i
$107$	−8.89898			−0.860297			−0.430148	−	0.902758i	$-0.641539\pi$
$107$	−8.89898			−0.860297			−0.430148	+	0.902758i	$0.641539\pi$
$108$	−1.00000			−0.0962250
$109$	−9.89898	−	9.89898i	−0.948150	−	0.948150i	0.0505702	−	0.998721i	$-0.483896\pi$
$109$	−9.89898	−	9.89898i	−0.948150	−	0.948150i	−0.998721	+	0.0505702i	$0.983896\pi$
$110$	−21.7980	+	21.7980i	−2.07835	+	2.07835i
$111$	1.89898	+	1.89898i	0.180243	+	0.180243i
$112$	12.2474	−	5.00000i	1.15728	−	0.472456i
$113$	−9.10102			−0.856152			−0.428076	−	0.903743i	$-0.640808\pi$
$113$	−9.10102			−0.856152			−0.428076	+	0.903743i	$0.640808\pi$
$114$		−	13.3485i		−	1.25020i
$115$	−1.79796	−	1.79796i	−0.167661	−	0.167661i
$116$		−	6.89898i		−	0.640554i
$117$	−2.00000	−	3.00000i	−0.184900	−	0.277350i
$118$		−	1.10102i		−	0.101357i
$119$	−4.89898	+	2.00000i	−0.449089	+	0.183340i
$120$	4.89898			0.447214
$121$		−	28.5959i		−	2.59963i
$122$	−12.2474	+	12.2474i	−1.10883	+	1.10883i
$123$	4.00000	+	4.00000i	0.360668	+	0.360668i
$124$	−0.550510	−	0.550510i	−0.0494373	−	0.0494373i
$125$	4.00000	+	4.00000i	0.357771	+	0.357771i
$126$	4.22474	+	1.77526i	0.376370	+	0.158152i
$127$			8.00000i			0.709885i	0.934888	+	0.354943i	$0.115500\pi$
$127$			8.00000i			0.709885i	−0.934888	+	0.354943i	$0.884500\pi$
$128$	−8.57321	+	8.57321i	−0.757772	+	0.757772i
$129$	2.89898			0.255241
$130$	−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	$-0.154772\pi$
$132$	4.44949	−	4.44949i	0.387278	−	0.387278i
$133$	−7.89898	+	18.7980i	−0.684928	+	1.62999i
$134$		−	20.4495i		−	1.76657i
$135$	2.00000	+	2.00000i	0.172133	+	0.172133i
$136$	2.44949	−	2.44949i	0.210042	−	0.210042i
$137$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$137$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$138$	1.10102	+	1.10102i	0.0937251	+	0.0937251i
$139$		−	2.89898i		−	0.245888i	−0.992414	−	0.122944i	$-0.960766\pi$
$139$		−	2.89898i		−	0.245888i	0.992414	−	0.122944i	$-0.0392336\pi$
$140$	6.89898	+	2.89898i	0.583070	+	0.245008i
$141$	6.44949	−	6.44949i	0.543145	−	0.543145i
$142$			6.00000i			0.503509i
$143$	22.2474	+	4.44949i	1.86043	+	0.372085i
$144$	−5.00000			−0.416667
$145$	−13.7980	+	13.7980i	−1.14586	+	1.14586i
$146$			4.65153i			0.384963i
$147$	−4.89898	−	5.00000i	−0.404061	−	0.412393i
$148$	−1.89898	−	1.89898i	−0.156095	−	0.156095i
$149$	8.89898	+	8.89898i	0.729033	+	0.729033i	0.970427	−	0.241394i	$-0.0776047\pi$
$149$	8.89898	+	8.89898i	0.729033	+	0.729033i	−0.241394	+	0.970427i	$0.577605\pi$
$150$	3.67423	+	3.67423i	0.300000	+	0.300000i
$151$	2.55051	−	2.55051i	0.207558	−	0.207558i	−0.595671	−	0.803229i	$-0.703114\pi$
$151$	2.55051	−	2.55051i	0.207558	−	0.207558i	0.803229	+	0.595671i	$0.203114\pi$
$152$		−	13.3485i		−	1.08270i
$153$	2.00000			0.161690
$154$	−26.6969	+	10.8990i	−2.15130	+	0.878265i
$155$			2.20204i			0.176872i
$156$	2.00000	+	3.00000i	0.160128	+	0.240192i
$157$		−	12.0000i		−	0.957704i	−0.877896	−	0.478852i	$-0.841053\pi$
$157$		−	12.0000i		−	0.957704i	0.877896	−	0.478852i	$-0.158947\pi$
$158$	−8.44949	−	8.44949i	−0.672205	−	0.672205i
$159$		−	7.79796i		−	0.618418i
$160$	−14.6969			−1.16190
$161$	−0.898979	−	2.20204i	−0.0708495	−	0.173545i
$162$	−1.22474	−	1.22474i	−0.0962250	−	0.0962250i
$163$	0.550510	−	0.550510i	0.0431193	−	0.0431193i	−0.685218	−	0.728338i	$-0.740293\pi$
$163$	0.550510	−	0.550510i	0.0431193	−	0.0431193i	0.728338	+	0.685218i	$0.240293\pi$
$164$	−4.00000	−	4.00000i	−0.312348	−	0.312348i
$165$	−17.7980			−1.38557
$166$	10.8990			0.845925
$167$	3.34847	+	3.34847i	0.259112	+	0.259112i	0.824693	−	0.565581i	$-0.191348\pi$
$167$	3.34847	+	3.34847i	0.259112	+	0.259112i	−0.565581	+	0.824693i	$0.691348\pi$
$168$	4.22474	+	1.77526i	0.325946	+	0.136964i
$169$	−5.00000	+	12.0000i	−0.384615	+	0.923077i
$170$	9.79796			0.751469
$171$	5.44949	−	5.44949i	0.416733	−	0.416733i
$172$	−2.89898			−0.221045
$173$	−16.6969			−1.26944			−0.634722	−	0.772740i	$-0.718886\pi$
$173$	−16.6969			−1.26944			−0.634722	+	0.772740i	$0.718886\pi$
$174$	8.44949	−	8.44949i	0.640554	−	0.640554i
$175$	−3.00000	−	7.34847i	−0.226779	−	0.555492i
$176$	22.2474	−	22.2474i	1.67696	−	1.67696i
$177$	0.449490	−	0.449490i	0.0337857	−	0.0337857i
$178$		−	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	$-0.0262247\pi$
$180$	−2.00000	−	2.00000i	−0.149071	−	0.149071i
$181$	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
$183$	−10.0000			−0.739221
$184$	1.10102	+	1.10102i	0.0811683	+	0.0811683i
$185$			7.59592i			0.558463i
$186$		−	1.34847i		−	0.0988746i
$187$	−8.89898	+	8.89898i	−0.650758	+	0.650758i
$188$	−6.44949	+	6.44949i	−0.470377	+	0.470377i
$189$	1.00000	+	2.44949i	0.0727393	+	0.178174i
$190$	26.6969	−	26.6969i	1.93680	−	1.93680i
$191$	5.79796			0.419526			0.209763	−	0.977752i	$-0.432731\pi$
$191$	5.79796			0.419526			0.209763	+	0.977752i	$0.432731\pi$
$192$	−1.00000			−0.0721688
$193$	−4.79796	+	4.79796i	−0.345365	+	0.345365i	−0.858380	−	0.513015i	$-0.828529\pi$
$193$	−4.79796	+	4.79796i	−0.345365	+	0.345365i	0.513015	+	0.858380i	$0.328529\pi$
$194$	4.65153			0.333960
$195$	2.00000	−	10.0000i	0.143223	−	0.716115i
$196$	4.89898	+	5.00000i	0.349927	+	0.357143i
$197$	11.7980	+	11.7980i	0.840570	+	0.840570i	0.988933	−	0.148363i	$-0.0474005\pi$
$197$	11.7980	+	11.7980i	0.840570	+	0.840570i	−0.148363	+	0.988933i	$0.547400\pi$
$198$	10.8990			0.774557
$199$	−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
$201$	8.34847	−	8.34847i	0.588856	−	0.588856i
$202$	18.2474	+	18.2474i	1.28389	+	1.28389i
$203$	−16.8990	+	6.89898i	−1.18608	+	0.484213i
$204$	−2.00000			−0.140028
$205$			16.0000i			1.11749i
$206$	−21.7980	−	21.7980i	−1.51874	−	1.51874i
$207$			0.898979i			0.0624834i
$208$	10.0000	+	15.0000i	0.693375	+	1.04006i
$209$			48.4949i			3.35446i
$210$	4.89898	+	12.0000i	0.338062	+	0.828079i
$211$	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
$213$	−2.44949	+	2.44949i	−0.167836	+	0.167836i
$214$	10.8990	+	10.8990i	0.745039	+	0.745039i
$215$	5.79796	+	5.79796i	0.395418	+	0.395418i
$216$	−1.22474	−	1.22474i	−0.0833333	−	0.0833333i
$217$	−0.797959	+	1.89898i	−0.0541690	+	0.128911i
$218$			24.2474i			1.64224i
$219$	−1.89898	+	1.89898i	−0.128321	+	0.128321i
$220$	17.7980			1.19994
$221$	−4.00000	−	6.00000i	−0.269069	−	0.403604i
$222$		−	4.65153i		−	0.312190i
$223$	7.44949	−	7.44949i	0.498855	−	0.498855i	−0.412227	−	0.911081i	$-0.635249\pi$
$223$	7.44949	−	7.44949i	0.498855	−	0.498855i	0.911081	+	0.412227i	$0.135249\pi$
$224$	−12.6742	−	5.32577i	−0.846833	−	0.355843i
$225$			3.00000i			0.200000i
$226$	11.1464	+	11.1464i	0.741449	+	0.741449i
$227$	15.3485	−	15.3485i	1.01871	−	1.01871i	0.0188922	−	0.999822i	$-0.493986\pi$
$227$	15.3485	−	15.3485i	1.01871	−	1.01871i	0.999822	−	0.0188922i	$-0.00601392\pi$
$228$	−5.44949	+	5.44949i	−0.360901	+	0.360901i
$229$	−13.0000	−	13.0000i	−0.859064	−	0.859064i	0.132164	−	0.991228i	$-0.457808\pi$
$229$	−13.0000	−	13.0000i	−0.859064	−	0.859064i	−0.991228	+	0.132164i	$0.957808\pi$
$230$			4.40408i			0.290397i
$231$	−15.3485	−	6.44949i	−1.00986	−	0.424345i
$232$	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	$-0.0822172\pi$
$234$	−1.22474	+	6.12372i	−0.0800641	+	0.400320i
$235$	25.7980			1.68287
$236$	−0.449490	+	0.449490i	−0.0292593	+	0.0292593i
$237$		−	6.89898i		−	0.448137i
$238$	8.44949	+	3.55051i	0.547699	+	0.230145i
$239$	7.34847	+	7.34847i	0.475333	+	0.475333i	0.903635	−	0.428302i	$-0.140888\pi$
$239$	7.34847	+	7.34847i	0.475333	+	0.475333i	−0.428302	+	0.903635i	$0.640888\pi$
$240$	−10.0000	−	10.0000i	−0.645497	−	0.645497i
$241$	4.10102	+	4.10102i	0.264170	+	0.264170i	0.826746	−	0.562576i	$-0.190190\pi$
$241$	4.10102	+	4.10102i	0.264170	+	0.264170i	−0.562576	+	0.826746i	$0.690190\pi$
$242$	−35.0227	+	35.0227i	−2.25134	+	2.25134i
$243$		−	1.00000i		−	0.0641500i
$244$	10.0000			0.640184
$245$	0.202041	−	19.7980i	0.0129079	−	1.26485i
$246$		−	9.79796i		−	0.624695i
$247$	−27.2474	−	5.44949i	−1.73371	−	0.346743i
$248$		−	1.34847i		−	0.0856279i
$249$	4.44949	+	4.44949i	0.281975	+	0.281975i
$250$		−	9.79796i		−	0.619677i
$251$	−4.89898			−0.309221			−0.154610	−	0.987976i	$-0.549412\pi$
$251$	−4.89898			−0.309221			−0.154610	+	0.987976i	$0.549412\pi$
$252$	−1.00000	−	2.44949i	−0.0629941	−	0.154303i
$253$	−4.00000	−	4.00000i	−0.251478	−	0.251478i
$254$	9.79796	−	9.79796i	0.614779	−	0.614779i
$255$	4.00000	+	4.00000i	0.250490	+	0.250490i
$256$	19.0000			1.18750
$257$	8.69694			0.542500			0.271250	−	0.962509i	$-0.412563\pi$
$257$	8.69694			0.542500			0.271250	+	0.962509i	$0.412563\pi$
$258$	−3.55051	−	3.55051i	−0.221045	−	0.221045i
$259$	−2.75255	+	6.55051i	−0.171035	+	0.407029i
$260$	−2.00000	+	10.0000i	−0.124035	+	0.620174i
$261$	6.89898			0.427036
$262$	−13.1010	+	13.1010i	−0.809384	+	0.809384i
$263$	7.10102			0.437868			0.218934	−	0.975740i	$-0.429742\pi$
$263$	7.10102			0.437868			0.218934	+	0.975740i	$0.429742\pi$
$264$	10.8990			0.670786
$265$	15.5959	−	15.5959i	0.958050	−	0.958050i
$266$	32.6969	−	13.3485i	2.00478	−	0.818447i
$267$	2.00000	−	2.00000i	0.122398	−	0.122398i
$268$	−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	$-0.0585527\pi$
$270$		−	4.89898i		−	0.298142i
$271$	9.44949	+	9.44949i	0.574016	+	0.574016i	0.933248	−	0.359232i	$-0.116961\pi$
$271$	9.44949	+	9.44949i	0.574016	+	0.574016i	−0.359232	+	0.933248i	$0.616961\pi$
$272$	−10.0000			−0.606339
$273$	5.34847	−	7.89898i	0.323704	−	0.478068i
$274$		0			0
$275$	−13.3485	−	13.3485i	−0.804943	−	0.804943i
$276$		−	0.898979i		−	0.0541122i
$277$			1.79796i			0.108029i	0.998540	+	0.0540144i	$0.0172017\pi$
$277$			1.79796i			0.108029i	−0.998540	+	0.0540144i	$0.982798\pi$
$278$	−3.55051	+	3.55051i	−0.212945	+	0.212945i
$279$	0.550510	−	0.550510i	0.0329582	−	0.0329582i
$280$	4.89898	+	12.0000i	0.292770	+	0.717137i
$281$	−4.00000	+	4.00000i	−0.238620	+	0.238620i	−0.816279	−	0.577659i	$-0.803967\pi$
$281$	−4.00000	+	4.00000i	−0.238620	+	0.238620i	0.577659	+	0.816279i	$0.303967\pi$
$282$	−15.7980			−0.940755
$283$	−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
$285$	21.7980			1.29120
$286$	−21.7980	−	32.6969i	−1.28894	−	1.93341i
$287$	−5.79796	+	13.7980i	−0.342243	+	0.814468i
$288$	3.67423	+	3.67423i	0.216506	+	0.216506i
$289$	−13.0000			−0.764706
$290$	33.7980			1.98468
$291$	1.89898	+	1.89898i	0.111320	+	0.111320i
$292$	1.89898	−	1.89898i	0.111129	−	0.111129i
$293$	−10.6969	−	10.6969i	−0.624922	−	0.624922i	0.321864	−	0.946786i	$-0.395691\pi$
$293$	−10.6969	−	10.6969i	−0.624922	−	0.624922i	−0.946786	+	0.321864i	$0.895691\pi$
$294$	−0.123724	+	12.1237i	−0.00721575	+	0.707070i
$295$	1.79796			0.104681
$296$		−	4.65153i		−	0.270365i
$297$	4.44949	+	4.44949i	0.258186	+	0.258186i
$298$		−	21.7980i		−	1.26272i
$299$	2.69694	−	1.79796i	0.155968	−	0.103979i
$300$		−	3.00000i		−	0.173205i
$301$	2.89898	+	7.10102i	0.167094	+	0.409296i
$302$	−6.24745			−0.359500
$303$			14.8990i			0.855924i
$304$	−27.2474	+	27.2474i	−1.56275	+	1.56275i
$305$	−20.0000	−	20.0000i	−1.14520	−	1.14520i
$306$	−2.44949	−	2.44949i	−0.140028	−	0.140028i
$307$	−8.55051	−	8.55051i	−0.488003	−	0.488003i	0.419672	−	0.907676i	$-0.362145\pi$
$307$	−8.55051	−	8.55051i	−0.488003	−	0.488003i	−0.907676	+	0.419672i	$0.862145\pi$
$308$	15.3485	+	6.44949i	0.874560	+	0.367494i
$309$		−	17.7980i		−	1.01249i
$310$	2.69694	−	2.69694i	0.153176	−	0.153176i
$311$	−24.8990			−1.41189			−0.705946	−	0.708266i	$-0.749478\pi$
$311$	−24.8990			−1.41189			−0.705946	+	0.708266i	$0.749478\pi$
$312$	−1.22474	+	6.12372i	−0.0693375	+	0.346688i
$313$			13.5959i			0.768487i	0.923232	+	0.384243i	$0.125538\pi$
$313$			13.5959i			0.768487i	−0.923232	+	0.384243i	$0.874462\pi$
$314$	−14.6969	+	14.6969i	−0.829396	+	0.829396i
$315$	−2.89898	+	6.89898i	−0.163339	+	0.388713i
$316$			6.89898i			0.388098i
$317$	−12.6969	−	12.6969i	−0.713131	−	0.713131i	0.254058	−	0.967189i	$-0.418235\pi$
$317$	−12.6969	−	12.6969i	−0.713131	−	0.713131i	−0.967189	+	0.254058i	$0.918235\pi$
$318$	−9.55051	+	9.55051i	−0.535566	+	0.535566i
$319$	−30.6969	+	30.6969i	−1.71870	+	1.71870i
$320$	−2.00000	−	2.00000i	−0.111803	−	0.111803i
$321$			8.89898i			0.496693i
$322$	−1.59592	+	3.79796i	−0.0889370	+	0.211652i
$323$	10.8990	−	10.8990i	0.606435	−	0.606435i
$324$			1.00000i			0.0555556i
$325$	9.00000	−	6.00000i	0.499230	−	0.332820i
$326$	−1.34847			−0.0746848
$327$	−9.89898	+	9.89898i	−0.547415	+	0.547415i
$328$		−	9.79796i		−	0.541002i
$329$	22.2474	+	9.34847i	1.22654	+	0.515398i
$330$	21.7980	+	21.7980i	1.19994	+	1.19994i
$331$	3.24745	+	3.24745i	0.178496	+	0.178496i	0.790700	−	0.612204i	$-0.209717\pi$
$331$	3.24745	+	3.24745i	0.178496	+	0.178496i	−0.612204	+	0.790700i	$0.709717\pi$
$332$	−4.44949	−	4.44949i	−0.244197	−	0.244197i
$333$	1.89898	−	1.89898i	0.104063	−	0.104063i
$334$		−	8.20204i		−	0.448796i
$335$	33.3939			1.82450
$336$	−5.00000	−	12.2474i	−0.272772	−	0.668153i
$337$			4.20204i			0.228900i	0.993429	+	0.114450i	$0.0365105\pi$
$337$			4.20204i			0.228900i	−0.993429	+	0.114450i	$0.963489\pi$
$338$	20.8207	−	8.57321i	1.13249	−	0.466321i
$339$			9.10102i			0.494300i
$340$	−4.00000	−	4.00000i	−0.216930	−	0.216930i
$341$			4.89898i			0.265295i
$342$	−13.3485			−0.721803
$343$	7.34847	−	17.0000i	0.396780	−	0.917914i
$344$	−3.55051	−	3.55051i	−0.191431	−	0.191431i
$345$	−1.79796	+	1.79796i	−0.0967989	+	0.0967989i
$346$	20.4495	+	20.4495i	1.09937	+	1.09937i
$347$	21.7980			1.17018			0.585088	−	0.810970i	$-0.301060\pi$
$347$	21.7980			1.17018			0.585088	+	0.810970i	$0.301060\pi$
$348$	−6.89898			−0.369824
$349$	10.7980	+	10.7980i	0.578001	+	0.578001i	0.934352	−	0.356351i	$-0.115979\pi$
$349$	10.7980	+	10.7980i	0.578001	+	0.578001i	−0.356351	+	0.934352i	$0.615979\pi$
$350$	−5.32577	+	12.6742i	−0.284674	+	0.677466i
$351$	−3.00000	+	2.00000i	−0.160128	+	0.106752i
$352$	−32.6969			−1.74275
$353$	−9.79796	+	9.79796i	−0.521493	+	0.521493i	−0.918022	−	0.396529i	$-0.870215\pi$
$353$	−9.79796	+	9.79796i	−0.521493	+	0.521493i	0.396529	+	0.918022i	$0.370215\pi$
$354$	−1.10102			−0.0585186
$355$	−9.79796			−0.520022
$356$	−2.00000	+	2.00000i	−0.106000	+	0.106000i
$357$	2.00000	+	4.89898i	0.105851	+	0.259281i
$358$	−2.69694	+	2.69694i	−0.142538	+	0.142538i
$359$	−0.449490	+	0.449490i	−0.0237232	+	0.0237232i	−0.718869	−	0.695146i	$-0.755340\pi$
$359$	−0.449490	+	0.449490i	−0.0237232	+	0.0237232i	0.695146	+	0.718869i	$0.255340\pi$
$360$		−	4.89898i		−	0.258199i
$361$		−	40.3939i		−	2.12599i
$362$	−2.44949	−	2.44949i	−0.128742	−	0.128742i
$363$	−28.5959			−1.50090
$364$	−5.34847	+	7.89898i	−0.280336	+	0.414019i
$365$	−7.59592			−0.397589
$366$	12.2474	+	12.2474i	0.640184	+	0.640184i
$367$			22.4949i			1.17422i	0.809506	+	0.587112i	$0.199735\pi$
$367$			22.4949i			1.17422i	−0.809506	+	0.587112i	$0.800265\pi$
$368$		−	4.49490i		−	0.234313i
$369$	4.00000	−	4.00000i	0.208232	−	0.208232i
$370$	9.30306	−	9.30306i	0.483643	−	0.483643i
$371$	19.1010	−	7.79796i	0.991676	−	0.404850i
$372$	−0.550510	+	0.550510i	−0.0285426	+	0.0285426i
$373$	−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
$375$	4.00000	−	4.00000i	0.206559	−	0.206559i
$376$	−15.7980			−0.814718
$377$	−13.7980	−	20.6969i	−0.710631	−	1.06595i
$378$	1.77526	−	4.22474i	0.0913093	−	0.217297i
$379$	8.55051	+	8.55051i	0.439210	+	0.439210i	0.891746	−	0.452536i	$-0.149481\pi$
$379$	8.55051	+	8.55051i	0.439210	+	0.439210i	−0.452536	+	0.891746i	$0.649481\pi$
$380$	−21.7980			−1.11821
$381$	8.00000			0.409852
$382$	−7.10102	−	7.10102i	−0.363320	−	0.363320i
$383$	−8.24745	+	8.24745i	−0.421425	+	0.421425i	−0.885694	−	0.464269i	$-0.846317\pi$
$383$	−8.24745	+	8.24745i	−0.421425	+	0.421425i	0.464269	+	0.885694i	$0.346317\pi$
$384$	8.57321	+	8.57321i	0.437500	+	0.437500i
$385$	−17.7980	−	43.5959i	−0.907068	−	2.22185i
$386$	11.7526			0.598189
$387$		−	2.89898i		−	0.147363i
$388$	−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	$0.910892\pi$
$390$	−14.6969	+	9.79796i	−0.744208	+	0.496139i
$391$			1.79796i			0.0909267i
$392$	−0.123724	+	12.1237i	−0.00624902	+	0.612341i
$393$	−10.6969			−0.539589
$394$		−	28.8990i		−	1.45591i
$395$	13.7980	−	13.7980i	0.694251	−	0.694251i
$396$	−4.44949	−	4.44949i	−0.223595	−	0.223595i
$397$	−10.7980	−	10.7980i	−0.541934	−	0.541934i	0.382162	−	0.924096i	$-0.375180\pi$
$397$	−10.7980	−	10.7980i	−0.541934	−	0.541934i	−0.924096	+	0.382162i	$0.875180\pi$
$398$	16.0454	+	16.0454i	0.804284	+	0.804284i
$399$	18.7980	+	7.89898i	0.941075	+	0.395444i
$400$		−	15.0000i		−	0.750000i
$401$	−14.0000	+	14.0000i	−0.699127	+	0.699127i	−0.964222	−	0.265096i	$-0.914597\pi$
$401$	−14.0000	+	14.0000i	−0.699127	+	0.699127i	0.265096	+	0.964222i	$0.414597\pi$
$402$	−20.4495			−1.01993
$403$	−2.75255	−	0.550510i	−0.137114	−	0.0274229i
$404$		−	14.8990i		−	0.741252i
$405$	2.00000	−	2.00000i	0.0993808	−	0.0993808i
$406$	29.1464	+	12.2474i	1.44651	+	0.607831i
$407$			16.8990i			0.837651i
$408$	−2.44949	−	2.44949i	−0.121268	−	0.121268i
$409$	23.6969	−	23.6969i	1.17174	−	1.17174i	0.189943	−	0.981795i	$-0.439170\pi$
$409$	23.6969	−	23.6969i	1.17174	−	1.17174i	0.981795	−	0.189943i	$-0.0608304\pi$
$410$	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
$414$	1.10102	−	1.10102i	0.0541122	−	0.0541122i
$415$			17.7980i			0.873667i
$416$	3.67423	−	18.3712i	0.180144	−	0.900721i
$417$	−2.89898			−0.141964
$418$	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	$-0.316076\pi$
$420$	2.89898	−	6.89898i	0.141456	−	0.336636i
$421$	4.10102	+	4.10102i	0.199872	+	0.199872i	0.799945	−	0.600073i	$-0.204862\pi$
$421$	4.10102	+	4.10102i	0.199872	+	0.199872i	−0.600073	+	0.799945i	$0.704862\pi$
$422$	−23.1464	−	23.1464i	−1.12675	−	1.12675i
$423$	−6.44949	−	6.44949i	−0.313585	−	0.313585i
$424$	−9.55051	+	9.55051i	−0.463814	+	0.463814i
$425$			6.00000i			0.291043i
$426$	6.00000			0.290701
$427$	−10.0000	−	24.4949i	−0.483934	−	1.18539i
$428$		−	8.89898i		−	0.430148i
$429$	4.44949	−	22.2474i	0.214823	−	1.07412i
$430$		−	14.2020i		−	0.684883i
$431$	−20.0454	−	20.0454i	−0.965553	−	0.965553i	0.0338728	−	0.999426i	$-0.489216\pi$
$431$	−20.0454	−	20.0454i	−0.965553	−	0.965553i	−0.999426	+	0.0338728i	$0.989216\pi$
$432$			5.00000i			0.240563i
$433$	−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
$435$	13.7980	+	13.7980i	0.661561	+	0.661561i
$436$	9.89898	−	9.89898i	0.474075	−	0.474075i
$437$	4.89898	+	4.89898i	0.234350	+	0.234350i
$438$	4.65153			0.222259
$439$	−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
$441$	−5.00000	+	4.89898i	−0.238095	+	0.233285i
$442$	−2.44949	+	12.2474i	−0.116510	+	0.582552i
$443$	−5.30306			−0.251956			−0.125978	−	0.992033i	$-0.540207\pi$
$443$	−5.30306			−0.251956			−0.125978	+	0.992033i	$0.540207\pi$
$444$	−1.89898	+	1.89898i	−0.0901216	+	0.0901216i
$445$	8.00000			0.379236
$446$	−18.2474			−0.864042
$447$	8.89898	−	8.89898i	0.420907	−	0.420907i
$448$	−1.00000	−	2.44949i	−0.0472456	−	0.115728i
$449$	14.8990	−	14.8990i	0.703126	−	0.703126i	−0.261954	−	0.965080i	$-0.584367\pi$
$449$	14.8990	−	14.8990i	0.703126	−	0.703126i	0.965080	+	0.261954i	$0.0843669\pi$
$450$	3.67423	−	3.67423i	0.173205	−	0.173205i
$451$			35.5959i			1.67615i
$452$		−	9.10102i		−	0.428076i
$453$	−2.55051	−	2.55051i	−0.119833	−	0.119833i
$454$	−37.5959			−1.76446
$455$	26.4949	−	5.10102i	1.24210	−	0.239140i
$456$	−13.3485			−0.625099
$457$	6.79796	+	6.79796i	0.317995	+	0.317995i	0.847997	−	0.530002i	$-0.177809\pi$
$457$	6.79796	+	6.79796i	0.317995	+	0.317995i	−0.530002	+	0.847997i	$0.677809\pi$
$458$			31.8434i			1.48794i
$459$		−	2.00000i		−	0.0933520i
$460$	1.79796	−	1.79796i	0.0838303	−	0.0838303i
$461$	−4.69694	+	4.69694i	−0.218758	+	0.218758i	−0.807975	−	0.589217i	$-0.799436\pi$
$461$	−4.69694	+	4.69694i	−0.218758	+	0.218758i	0.589217	+	0.807975i	$0.299436\pi$
$462$	10.8990	+	26.6969i	0.507066	+	1.24205i
$463$	−20.1464	+	20.1464i	−0.936284	+	0.936284i	−0.998088	−	0.0618044i	$-0.980315\pi$
$463$	−20.1464	+	20.1464i	−0.936284	+	0.936284i	0.0618044	+	0.998088i	$0.480315\pi$
$464$	−34.4949			−1.60139
$465$	2.20204			0.102117
$466$	−9.55051	+	9.55051i	−0.442419	+	0.442419i
$467$	31.1010			1.43918			0.719592	−	0.694397i	$-0.244329\pi$
$467$	31.1010			1.43918			0.719592	+	0.694397i	$0.244329\pi$
$468$	3.00000	−	2.00000i	0.138675	−	0.0924500i
$469$	28.7980	+	12.1010i	1.32977	+	0.558773i
$470$	−31.5959	−	31.5959i	−1.45741	−	1.45741i
$471$	−12.0000			−0.552931
$472$	−1.10102			−0.0506786
$473$	12.8990	+	12.8990i	0.593096	+	0.593096i
$474$	−8.44949	+	8.44949i	−0.388098	+	0.388098i
$475$	16.3485	+	16.3485i	0.750119	+	0.750119i
$476$	−2.00000	−	4.89898i	−0.0916698	−	0.224544i
$477$	−7.79796			−0.357044
$478$		−	18.0000i		−	0.823301i
$479$	−10.2474	−	10.2474i	−0.468218	−	0.468218i	0.433119	−	0.901337i	$-0.357413\pi$
$479$	−10.2474	−	10.2474i	−0.468218	−	0.468218i	−0.901337	+	0.433119i	$0.857413\pi$
$480$			14.6969i			0.670820i
$481$	−9.49490	−	1.89898i	−0.432930	−	0.0865860i
$482$		−	10.0454i		−	0.457556i
$483$	−2.20204	+	0.898979i	−0.100196	+	0.0409050i
$484$	28.5959			1.29981
$485$			7.59592i			0.344913i
$486$	−1.22474	+	1.22474i	−0.0555556	+	0.0555556i
$487$	15.2474	+	15.2474i	0.690928	+	0.690928i	0.962436	−	0.271508i	$-0.0875224\pi$
$487$	15.2474	+	15.2474i	0.690928	+	0.690928i	−0.271508	+	0.962436i	$0.587522\pi$
$488$	12.2474	+	12.2474i	0.554416	+	0.554416i
$489$	−0.550510	−	0.550510i	−0.0248949	−	0.0248949i
$490$	−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	$0.686843\pi$
$492$	−4.00000	+	4.00000i	−0.180334	+	0.180334i
$493$	13.7980			0.621429
$494$	26.6969	+	40.0454i	1.20115	+	1.80173i
$495$			17.7980i			0.799959i
$496$	−2.75255	+	2.75255i	−0.123593	+	0.123593i
$497$	−8.44949	−	3.55051i	−0.379011	−	0.159262i
$498$		−	10.8990i		−	0.488395i
$499$	−15.2474	−	15.2474i	−0.682570	−	0.682570i	0.278009	−	0.960578i	$-0.410326\pi$
$499$	−15.2474	−	15.2474i	−0.682570	−	0.682570i	−0.960578	+	0.278009i	$0.910326\pi$
$500$	−4.00000	+	4.00000i	−0.178885	+	0.178885i
$501$	3.34847	−	3.34847i	0.149599	−	0.149599i
$502$	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	$0.797081\pi$
$504$	1.77526	−	4.22474i	0.0790761	−	0.188185i
$505$	−29.7980	+	29.7980i	−1.32599	+	1.32599i
$506$			9.79796i			0.435572i
$507$	12.0000	+	5.00000i	0.532939	+	0.222058i
$508$	−8.00000			−0.354943
$509$	−5.10102	+	5.10102i	−0.226099	+	0.226099i	−0.811061	−	0.584962i	$-0.801109\pi$
$509$	−5.10102	+	5.10102i	−0.226099	+	0.226099i	0.584962	+	0.811061i	$0.301109\pi$
$510$		−	9.79796i		−	0.433861i
$511$	−6.55051	−	2.75255i	−0.289778	−	0.121766i
$512$	−6.12372	−	6.12372i	−0.270633	−	0.270633i
$513$	−5.44949	−	5.44949i	−0.240601	−	0.240601i
$514$	−10.6515	−	10.6515i	−0.469819	−	0.469819i
$515$	35.5959	−	35.5959i	1.56854	−	1.56854i
$516$			2.89898i			0.127620i
$517$	57.3939			2.52418
$518$	11.3939	−	4.65153i	0.500618	−	0.204377i
$519$			16.6969i			0.732914i
$520$	−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	$-0.241378\pi$
$522$	−8.44949	−	8.44949i	−0.369824	−	0.369824i
$523$		−	18.4949i		−	0.808725i	−0.914599	−	0.404363i	$-0.867493\pi$
$523$		−	18.4949i		−	0.808725i	0.914599	−	0.404363i	$-0.132507\pi$
$524$	10.6969			0.467298
$525$	−7.34847	+	3.00000i	−0.320713	+	0.130931i
$526$	−8.69694	−	8.69694i	−0.379205	−	0.379205i
$527$	1.10102	−	1.10102i	0.0479612	−	0.0479612i
$528$	−22.2474	−	22.2474i	−0.968196	−	0.968196i
$529$	22.1918			0.964862
$530$	−38.2020			−1.65939
$531$	−0.449490	−	0.449490i	−0.0195062	−	0.0195062i
$532$	−18.7980	−	7.89898i	−0.814995	−	0.342464i
$533$	−20.0000	−	4.00000i	−0.866296	−	0.173259i
$534$	−4.89898			−0.212000
$535$	−17.7980	+	17.7980i	−0.769473	+	0.769473i
$536$	−20.4495			−0.883283
$537$	−2.20204			−0.0950251
$538$	−7.34847	+	7.34847i	−0.316815	+	0.316815i
$539$	0.449490	−	44.0454i	0.0193609	−	1.89717i
$540$	−2.00000	+	2.00000i	−0.0860663	+	0.0860663i
$541$	−2.10102	+	2.10102i	−0.0903299	+	0.0903299i	−0.750828	−	0.660498i	$-0.770345\pi$
$541$	−2.10102	+	2.10102i	−0.0903299	+	0.0903299i	0.660498	+	0.750828i	$0.270345\pi$
$542$		−	23.1464i		−	0.994224i
$543$		−	2.00000i		−	0.0858282i
$544$	7.34847	+	7.34847i	0.315063	+	0.315063i
$545$	−39.5959			−1.69610
$546$	−16.2247	+	3.12372i	−0.694355	+	0.133683i
$547$	−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
$549$			10.0000i			0.426790i
$550$			32.6969i			1.39420i
$551$	37.5959	−	37.5959i	1.60164	−	1.60164i
$552$	1.10102	−	1.10102i	0.0468625	−	0.0468625i
$553$	16.8990	−	6.89898i	0.718618	−	0.293374i
$554$	2.20204	−	2.20204i	0.0935558	−	0.0935558i
$555$	7.59592			0.322429
$556$	2.89898			0.122944
$557$	−10.6969	+	10.6969i	−0.453244	+	0.453244i	−0.896430	−	0.443186i	$-0.853848\pi$
$557$	−10.6969	+	10.6969i	−0.453244	+	0.453244i	0.443186	+	0.896430i	$0.353848\pi$
$558$	−1.34847			−0.0570853
$559$	−8.69694	+	5.79796i	−0.367841	+	0.245228i
$560$	14.4949	−	34.4949i	0.612521	−	1.45768i
$561$	8.89898	+	8.89898i	0.375715	+	0.375715i
$562$	9.79796			0.413302
$563$	−2.20204			−0.0928050			−0.0464025	−	0.998923i	$-0.514776\pi$
$563$	−2.20204			−0.0928050			−0.0464025	+	0.998923i	$0.514776\pi$
$564$	6.44949	+	6.44949i	0.271573	+	0.271573i
$565$	−18.2020	+	18.2020i	−0.765766	+	0.765766i
$566$	20.4495	+	20.4495i	0.859556	+	0.859556i
$567$	2.44949	−	1.00000i	0.102869	−	0.0419961i
$568$	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	$0.733928\pi$
$570$	−26.6969	−	26.6969i	−1.11821	−	1.11821i
$571$		−	35.1918i		−	1.47273i	−0.676583	−	0.736366i	$-0.736540\pi$
$571$		−	35.1918i		−	1.47273i	0.676583	−	0.736366i	$-0.263460\pi$
$572$	−4.44949	+	22.2474i	−0.186043	+	0.930213i
$573$		−	5.79796i		−	0.242213i
$574$	24.0000	−	9.79796i	1.00174	−	0.408959i
$575$	−2.69694			−0.112470
$576$			1.00000i			0.0416667i
$577$	8.10102	−	8.10102i	0.337250	−	0.337250i	−0.518081	−	0.855331i	$-0.673354\pi$
$577$	8.10102	−	8.10102i	0.337250	−	0.337250i	0.855331	+	0.518081i	$0.173354\pi$
$578$	15.9217	+	15.9217i	0.662255	+	0.662255i
$579$	4.79796	+	4.79796i	0.199396	+	0.199396i
$580$	−13.7980	−	13.7980i	−0.572929	−	0.572929i
$581$	−6.44949	+	15.3485i	−0.267570	+	0.636762i
$582$		−	4.65153i		−	0.192812i
$583$	34.6969	−	34.6969i	1.43700	−	1.43700i
$584$	4.65153			0.192482
$585$	−10.0000	−	2.00000i	−0.413449	−	0.0826898i
$586$			26.2020i			1.08240i
$587$	−8.44949	+	8.44949i	−0.348748	+	0.348748i	−0.859643	−	0.510895i	$-0.829314\pi$
$587$	−8.44949	+	8.44949i	−0.348748	+	0.348748i	0.510895	+	0.859643i	$0.329314\pi$
$588$	5.00000	−	4.89898i	0.206197	−	0.202031i
$589$		−	6.00000i		−	0.247226i
$590$	−2.20204	−	2.20204i	−0.0906566	−	0.0906566i
$591$	11.7980	−	11.7980i	0.485303	−	0.485303i
$592$	−9.49490	+	9.49490i	−0.390238	+	0.390238i
$593$	26.8990	+	26.8990i	1.10461	+	1.10461i	0.993847	+	0.110762i	$0.0353290\pi$
$593$	26.8990	+	26.8990i	1.10461	+	1.10461i	0.110762	+	0.993847i	$0.464671\pi$
$594$		−	10.8990i		−	0.447191i
$595$	−5.79796	+	13.7980i	−0.237693	+	0.565661i
$596$	−8.89898	+	8.89898i	−0.364516	+	0.364516i
$597$			13.1010i			0.536189i
$598$	−5.50510	−	1.10102i	−0.225120	−	0.0450241i
$599$	−44.4949			−1.81801			−0.909006	−	0.416783i	$-0.863158\pi$
$599$	−44.4949			−1.81801			−0.909006	+	0.416783i	$0.863158\pi$
$600$	3.67423	−	3.67423i	0.150000	−	0.150000i
$601$			2.40408i			0.0980646i	0.998797	+	0.0490323i	$0.0156137\pi$
$601$			2.40408i			0.0980646i	−0.998797	+	0.0490323i	$0.984386\pi$
$602$	5.14643	−	12.2474i	0.209753	−	0.499169i
$603$	−8.34847	−	8.34847i	−0.339976	−	0.339976i
$604$	2.55051	+	2.55051i	0.103779	+	0.103779i
$605$	−57.1918	−	57.1918i	−2.32518	−	2.32518i
$606$	18.2474	−	18.2474i	0.741252	−	0.741252i
$607$		−	5.10102i		−	0.207044i	−0.994627	−	0.103522i	$-0.966989\pi$
$607$		−	5.10102i		−	0.207044i	0.994627	−	0.103522i	$-0.0330112\pi$
$608$	40.0454			1.62406
$609$	6.89898	+	16.8990i	0.279561	+	0.684781i
$610$			48.9898i			1.98354i
$611$	−6.44949	+	32.2474i	−0.260918	+	1.30459i
$612$			2.00000i			0.0808452i
$613$	1.89898	+	1.89898i	0.0766991	+	0.0766991i	0.744416	−	0.667717i	$-0.232728\pi$
$613$	1.89898	+	1.89898i	0.0766991	+	0.0766991i	−0.667717	+	0.744416i	$0.732728\pi$
$614$			20.9444i			0.845247i
$615$	16.0000			0.645182
$616$	10.8990	+	26.6969i	0.439132	+	1.07565i
$617$	21.7980	+	21.7980i	0.877553	+	0.877553i	0.993281	−	0.115728i	$-0.0369201\pi$
$617$	21.7980	+	21.7980i	0.877553	+	0.877553i	−0.115728	+	0.993281i	$0.536920\pi$
$618$	−21.7980	+	21.7980i	−0.876843	+	0.876843i
$619$	15.4495	+	15.4495i	0.620967	+	0.620967i	0.945779	−	0.324811i	$-0.105301\pi$
$619$	15.4495	+	15.4495i	0.620967	+	0.620967i	−0.324811	+	0.945779i	$0.605301\pi$
$620$	−2.20204			−0.0884361
$621$	0.898979			0.0360748
$622$	30.4949	+	30.4949i	1.22273	+	1.22273i
$623$	6.89898	+	2.89898i	0.276402	+	0.116145i
$624$	15.0000	−	10.0000i	0.600481	−	0.400320i
$625$	31.0000			1.24000
$626$	16.6515	−	16.6515i	0.665529	−	0.665529i
$627$	48.4949			1.93670
$628$	12.0000			0.478852
$629$	3.79796	−	3.79796i	0.151435	−	0.151435i
$630$	12.0000	−	4.89898i	0.478091	−	0.195180i
$631$	−11.2474	+	11.2474i	−0.447754	+	0.447754i	−0.894607	−	0.446853i	$-0.852545\pi$
$631$	−11.2474	+	11.2474i	−0.447754	+	0.447754i	0.446853	+	0.894607i	$0.352545\pi$
$632$	−8.44949	+	8.44949i	−0.336103	+	0.336103i
$633$		−	18.8990i		−	0.751167i
$634$			31.1010i			1.23518i
$635$	16.0000	+	16.0000i	0.634941	+	0.634941i
$636$	7.79796			0.309209
$637$	24.6969	+	5.20204i	0.978528	+	0.206112i
$638$	75.1918			2.97687
$639$	2.44949	+	2.44949i	0.0969003	+	0.0969003i
$640$			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	$-0.134032\pi$
$642$	10.8990	−	10.8990i	0.430148	−	0.430148i
$643$	−20.1464	+	20.1464i	−0.794498	+	0.794498i	−0.982222	−	0.187724i	$-0.939889\pi$
$643$	−20.1464	+	20.1464i	−0.794498	+	0.794498i	0.187724	+	0.982222i	$0.439889\pi$
$644$	2.20204	−	0.898979i	0.0867726	−	0.0354248i
$645$	5.79796	−	5.79796i	0.228294	−	0.228294i
$646$	−26.6969			−1.05038
$647$	−12.0000			−0.471769			−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000			−0.471769			−0.235884	+	0.971781i	$0.575799\pi$
$648$	−1.22474	+	1.22474i	−0.0481125	+	0.0481125i
$649$	4.00000			0.157014
$650$	−18.3712	−	3.67423i	−0.720577	−	0.144115i
$651$	1.89898	+	0.797959i	0.0744269	+	0.0312745i
$652$	0.550510	+	0.550510i	0.0215596	+	0.0215596i
$653$	10.8990			0.426510			0.213255	−	0.976997i	$-0.431593\pi$
$653$	10.8990			0.426510			0.213255	+	0.976997i	$0.431593\pi$
$654$	24.2474			0.948150
$655$	−21.3939	−	21.3939i	−0.835928	−	0.835928i
$656$	−20.0000	+	20.0000i	−0.780869	+	0.780869i
$657$	1.89898	+	1.89898i	0.0740862	+	0.0740862i
$658$	−15.7980	−	38.6969i	−0.615869	−	1.50856i
$659$	7.59592			0.295895			0.147947	−	0.988995i	$-0.452733\pi$
$659$	7.59592			0.295895			0.147947	+	0.988995i	$0.452733\pi$
$660$		−	17.7980i		−	0.692785i
$661$	32.3939	+	32.3939i	1.25998	+	1.25998i	0.951104	+	0.308872i	$0.0999516\pi$
$661$	32.3939	+	32.3939i	1.25998	+	1.25998i	0.308872	+	0.951104i	$0.400048\pi$
$662$		−	7.95459i		−	0.309164i
$663$	−6.00000	+	4.00000i	−0.233021	+	0.155347i
$664$		−	10.8990i		−	0.422962i
$665$	21.7980	+	53.3939i	0.845289	+	2.07053i
$666$	−4.65153			−0.180243
$667$			6.20204i			0.240144i
$668$	−3.34847	+	3.34847i	−0.129556	+	0.129556i
$669$	−7.44949	−	7.44949i	−0.288014	−	0.288014i
$670$	−40.8990	−	40.8990i	−1.58007	−	1.58007i
$671$	−44.4949	−	44.4949i	−1.71771	−	1.71771i
$672$	−5.32577	+	12.6742i	−0.205446	+	0.488919i
$673$		−	45.3939i		−	1.74981i	−0.484299	−	0.874903i	$-0.660925\pi$
$673$		−	45.3939i		−	1.74981i	0.484299	−	0.874903i	$-0.339075\pi$
$674$	5.14643	−	5.14643i	0.198233	−	0.198233i
$675$	3.00000			0.115470
$676$	−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	$-0.160219\pi$
$678$	11.1464	−	11.1464i	0.428076	−	0.428076i
$679$	−2.75255	+	6.55051i	−0.105633	+	0.251386i
$680$		−	9.79796i		−	0.375735i
$681$	−15.3485	−	15.3485i	−0.588155	−	0.588155i
$682$	6.00000	−	6.00000i	0.229752	−	0.229752i
$683$	26.2474	−	26.2474i	1.00433	−	1.00433i	0.00434013	−	0.999991i	$-0.498618\pi$
$683$	26.2474	−	26.2474i	1.00433	−	1.00433i	0.999991	−	0.00434013i	$-0.00138151\pi$
$684$	5.44949	+	5.44949i	0.208366	+	0.208366i
$685$		0			0
$686$	−29.8207	+	11.8207i	−1.13856	+	0.451315i
$687$	−13.0000	+	13.0000i	−0.495981	+	0.495981i
$688$			14.4949i			0.552613i
$689$	15.5959	+	23.3939i	0.594157	+	0.891236i
$690$	4.40408			0.167661
$691$	−8.14643	+	8.14643i	−0.309905	+	0.309905i	−0.844872	−	0.534968i	$-0.820324\pi$
$691$	−8.14643	+	8.14643i	−0.309905	+	0.309905i	0.534968	+	0.844872i	$0.320324\pi$
$692$		−	16.6969i		−	0.634722i
$693$	−6.44949	+	15.3485i	−0.244996	+	0.583040i
$694$	−26.6969	−	26.6969i	−1.01340	−	1.01340i
$695$	−5.79796	−	5.79796i	−0.219929	−	0.219929i
$696$	−8.44949	−	8.44949i	−0.320277	−	0.320277i
$697$	8.00000	−	8.00000i	0.303022	−	0.303022i
$698$		−	26.4495i		−	1.00113i
$699$	−7.79796			−0.294946
$700$	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	$0.995810\pi$
$702$	6.12372	+	1.22474i	0.231125	+	0.0462250i
$703$		−	20.6969i		−	0.780600i
$704$	−4.44949	−	4.44949i	−0.167696	−	0.167696i
$705$		−	25.7980i		−	0.971607i
$706$	24.0000			0.903252
$707$	−36.4949	+	14.8990i	−1.37253	+	0.560334i
$708$	0.449490	+	0.449490i	0.0168929	+	0.0168929i
$709$	−10.1010	+	10.1010i	−0.379352	+	0.379352i	−0.870868	−	0.491516i	$-0.836443\pi$
$709$	−10.1010	+	10.1010i	−0.379352	+	0.379352i	0.491516	+	0.870868i	$0.336443\pi$
$710$	12.0000	+	12.0000i	0.450352	+	0.450352i
$711$	−6.89898			−0.258732
$712$	−4.89898			−0.183597
$713$	0.494897	+	0.494897i	0.0185341	+	0.0185341i
$714$	3.55051	−	8.44949i	0.132875	−	0.316214i
$715$	53.3939	−	35.5959i	1.99682	−	1.33121i
$716$	2.20204			0.0822941
$717$	7.34847	−	7.34847i	0.274434	−	0.274434i
$718$	1.10102			0.0410897
$719$	16.8990			0.630226			0.315113	−	0.949054i	$-0.397958\pi$
$719$	16.8990			0.630226			0.315113	+	0.949054i	$0.397958\pi$
$720$	−10.0000	+	10.0000i	−0.372678	+	0.372678i
$721$	43.5959	−	17.7980i	1.62360	−	0.662831i
$722$	−49.4722	+	49.4722i	−1.84116	+	1.84116i
$723$	4.10102	−	4.10102i	0.152519	−	0.152519i
$724$			2.00000i			0.0743294i
$725$			20.6969i			0.768665i
$726$	35.0227	+	35.0227i	1.29981	+	1.29981i
$727$	−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
$729$	−1.00000			−0.0370370
$730$	9.30306	+	9.30306i	0.344322	+	0.344322i
$731$		−	5.79796i		−	0.214445i
$732$		−	10.0000i		−	0.369611i
$733$	9.00000	−	9.00000i	0.332423	−	0.332423i	−0.521083	−	0.853506i	$-0.674472\pi$
$733$	9.00000	−	9.00000i	0.332423	−	0.332423i	0.853506	+	0.521083i	$0.174472\pi$
$734$	27.5505	−	27.5505i	1.01691	−	1.01691i
$735$	−19.7980	−	0.202041i	−0.730259	−	0.00745240i
$736$	−3.30306	+	3.30306i	−0.121752	+	0.121752i
$737$	74.2929			2.73661
$738$	−9.79796			−0.360668
$739$	7.65153	−	7.65153i	0.281466	−	0.281466i	−0.552227	−	0.833694i	$-0.686222\pi$
$739$	7.65153	−	7.65153i	0.281466	−	0.281466i	0.833694	+	0.552227i	$0.186222\pi$
$740$	−7.59592			−0.279231
$741$	−5.44949	+	27.2474i	−0.200192	+	1.00096i
$742$	−32.9444	−	13.8434i	−1.20943	−	0.508206i
$743$	−26.0454	−	26.0454i	−0.955513	−	0.955513i	0.0435384	−	0.999052i	$-0.486137\pi$
$743$	−26.0454	−	26.0454i	−0.955513	−	0.955513i	−0.999052	+	0.0435384i	$0.986137\pi$
$744$	−1.34847			−0.0494373
$745$	35.5959			1.30413
$746$	12.0000	+	12.0000i	0.439351	+	0.439351i
$747$	4.44949	−	4.44949i	0.162798	−	0.162798i
$748$	−8.89898	−	8.89898i	−0.325379	−	0.325379i
$749$	−21.7980	+	8.89898i	−0.796480	+	0.325162i
$750$	−9.79796			−0.357771
$751$			48.2929i			1.76223i	0.472901	+	0.881116i	$0.343207\pi$
$751$			48.2929i			1.76223i	−0.472901	+	0.881116i	$0.656793\pi$
$752$	32.2474	+	32.2474i	1.17594	+	1.17594i
$753$			4.89898i			0.178529i
$754$	−8.44949	+	42.2474i	−0.307712	+	1.53856i
$755$		−	10.2020i		−	0.371290i
$756$	−2.44949	+	1.00000i	−0.0890871	+	0.0363696i
$757$	−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
$759$	−4.00000	+	4.00000i	−0.145191	+	0.145191i
$760$	−26.6969	−	26.6969i	−0.968400	−	0.968400i
$761$	−14.6969	−	14.6969i	−0.532764	−	0.532764i	0.388630	−	0.921394i	$-0.372948\pi$
$761$	−14.6969	−	14.6969i	−0.532764	−	0.532764i	−0.921394	+	0.388630i	$0.872948\pi$
$762$	−9.79796	−	9.79796i	−0.354943	−	0.354943i
$763$	−34.1464	−	14.3485i	−1.23618	−	0.519449i
$764$			5.79796i			0.209763i
$765$	4.00000	−	4.00000i	0.144620	−	0.144620i
$766$	20.2020			0.729929
$767$	−0.449490	+	2.24745i	−0.0162301	+	0.0811507i
$768$		−	19.0000i		−	0.685603i
$769$	−13.8990	+	13.8990i	−0.501210	+	0.501210i	−0.911814	−	0.410604i	$-0.865318\pi$
$769$	−13.8990	+	13.8990i	−0.501210	+	0.501210i	0.410604	+	0.911814i	$0.365318\pi$
$770$	−31.5959	+	75.1918i	−1.13864	+	2.70973i
$771$		−	8.69694i		−	0.313213i
$772$	−4.79796	−	4.79796i	−0.172682	−	0.172682i
$773$	−36.0000	+	36.0000i	−1.29483	+	1.29483i	−0.363067	+	0.931763i	$0.618270\pi$
$773$	−36.0000	+	36.0000i	−1.29483	+	1.29483i	−0.931763	+	0.363067i	$0.881730\pi$
$774$	−3.55051	+	3.55051i	−0.127620	+	0.127620i
$775$	1.65153	+	1.65153i	0.0593247	+	0.0593247i
$776$		−	4.65153i		−	0.166980i
$777$	6.55051	+	2.75255i	0.234998	+	0.0987472i
$778$	13.3485	−	13.3485i	0.478566	−	0.478566i
$779$		−	43.5959i		−	1.56199i
$780$	10.0000	+	2.00000i	0.358057	+	0.0716115i
$781$	−21.7980			−0.779992
$782$	2.20204	−	2.20204i	0.0787448	−	0.0787448i
$783$		−	6.89898i		−	0.246549i
$784$	25.0000	−	24.4949i	0.892857	−	0.874818i
$785$	−24.0000	−	24.0000i	−0.856597	−	0.856597i
$786$	13.1010	+	13.1010i	0.467298	+	0.467298i
$787$	−9.24745	−	9.24745i	−0.329636	−	0.329636i	0.522812	−	0.852448i	$-0.324883\pi$
$787$	−9.24745	−	9.24745i	−0.329636	−	0.329636i	−0.852448	+	0.522812i	$0.824883\pi$
$788$	−11.7980	+	11.7980i	−0.420285	+	0.420285i
$789$		−	7.10102i		−	0.252803i
$790$	−33.7980			−1.20248
$791$	−22.2929	+	9.10102i	−0.792643	+	0.323595i
$792$		−	10.8990i		−	0.387278i
$793$	30.0000	−	20.0000i	1.06533	−	0.710221i
$794$			26.4495i			0.938657i
$795$	−15.5959	−	15.5959i	−0.553130	−	0.553130i
$796$		−	13.1010i		−	0.464353i
$797$	−37.1918			−1.31740			−0.658701	−	0.752405i	$-0.728894\pi$
$797$	−37.1918			−1.31740			−0.658701	+	0.752405i	$0.728894\pi$
$798$	−13.3485	−	32.6969i	−0.472531	−	1.15746i
$799$	−12.8990	−	12.8990i	−0.456333	−	0.456333i
$800$	−11.0227	+	11.0227i	−0.389711	+	0.389711i
$801$	−2.00000	−	2.00000i	−0.0706665	−	0.0706665i
$802$	34.2929			1.21092
$803$	−16.8990			−0.596352
$804$	8.34847	+	8.34847i	0.294428	+	0.294428i
$805$	−6.20204	−	2.60612i	−0.218593	−	0.0918538i
$806$	2.69694	+	4.04541i	0.0949956	+	0.142493i
$807$	−6.00000			−0.211210
$808$	18.2474	−	18.2474i	0.641943	−	0.641943i
$809$	−13.1010			−0.460607			−0.230304	−	0.973119i	$-0.573972\pi$
$809$	−13.1010			−0.460607			−0.230304	+	0.973119i	$0.573972\pi$
$810$	−4.89898			−0.172133
$811$	37.0454	−	37.0454i	1.30084	−	1.30084i	0.373015	−	0.927825i	$-0.378324\pi$
$811$	37.0454	−	37.0454i	1.30084	−	1.30084i	0.927825	−	0.373015i	$-0.121676\pi$
$812$	−6.89898	−	16.8990i	−0.242107	−	0.593038i
$813$	9.44949	−	9.44949i	0.331408	−	0.331408i
$814$	20.6969	−	20.6969i	0.725427	−	0.725427i
$815$		−	2.20204i		−	0.0771341i
$816$			10.0000i			0.350070i
$817$	−15.7980	−	15.7980i	−0.552701	−	0.552701i
$818$	−58.0454			−2.02951
$819$	−7.89898	−	5.34847i	−0.276013	−	0.186891i
$820$	−16.0000			−0.558744
$821$	3.59592	+	3.59592i	0.125498	+	0.125498i	0.767066	−	0.641568i	$-0.221716\pi$
$821$	3.59592	+	3.59592i	0.125498	+	0.125498i	−0.641568	+	0.767066i	$0.721716\pi$
$822$		0			0
$823$			16.6969i			0.582019i	0.956720	+	0.291009i	$0.0939911\pi$
$823$			16.6969i			0.582019i	−0.956720	+	0.291009i	$0.906009\pi$
$824$	−21.7980	+	21.7980i	−0.759368	+	0.759368i
$825$	−13.3485	+	13.3485i	−0.464734	+	0.464734i
$826$	−1.10102	−	2.69694i	−0.0383094	−	0.0938385i
$827$	−5.34847	+	5.34847i	−0.185984	+	0.185984i	−0.793958	−	0.607973i	$-0.791983\pi$
$827$	−5.34847	+	5.34847i	−0.185984	+	0.185984i	0.607973	+	0.793958i	$0.291983\pi$
$828$	−0.898979			−0.0312417
$829$	−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
$831$	1.79796			0.0623705
$832$	3.00000	−	2.00000i	0.104006	−	0.0693375i
$833$	−10.0000	+	9.79796i	−0.346479	+	0.339479i
$834$	3.55051	+	3.55051i	0.122944	+	0.122944i
$835$	13.3939			0.463514
$836$	−48.4949			−1.67723
$837$	−0.550510	−	0.550510i	−0.0190284	−	0.0190284i
$838$	−42.0000	+	42.0000i	−1.45087	+	1.45087i
$839$	3.55051	+	3.55051i	0.122577	+	0.122577i	0.765734	−	0.643157i	$-0.222376\pi$
$839$	3.55051	+	3.55051i	0.122577	+	0.122577i	−0.643157	+	0.765734i	$0.722376\pi$
$840$	12.0000	−	4.89898i	0.414039	−	0.169031i
$841$	18.5959			0.641239
$842$		−	10.0454i		−	0.346188i
$843$	4.00000	+	4.00000i	0.137767	+	0.137767i
$844$			18.8990i			0.650530i
$845$	14.0000	+	34.0000i	0.481615	+	1.16964i
$846$			15.7980i			0.543145i
$847$	−28.5959	−	70.0454i	−0.982567	−	2.40679i
$848$	38.9898			1.33892
$849$			16.6969i			0.573037i
$850$	7.34847	−	7.34847i	0.252050	−	0.252050i
$851$	1.70714	+	1.70714i	0.0585201	+	0.0585201i
$852$	−2.44949	−	2.44949i	−0.0839181	−	0.0839181i
$853$	38.7980	+	38.7980i	1.32842	+	1.32842i	0.906752	+	0.421665i	$0.138554\pi$
$853$	38.7980	+	38.7980i	1.32842	+	1.32842i	0.421665	+	0.906752i	$0.361446\pi$
$854$	−17.7526	+	42.2474i	−0.607480	+	1.44568i
$855$		−	21.7980i		−	0.745474i
$856$	10.8990	−	10.8990i	0.372519	−	0.372519i
$857$	−26.4949			−0.905048			−0.452524	−	0.891752i	$-0.649476\pi$
$857$	−26.4949			−0.905048			−0.452524	+	0.891752i	$0.649476\pi$
$858$	−32.6969	+	21.7980i	−1.11626	+	0.744170i
$859$		−	29.7980i		−	1.01669i	−0.861153	−	0.508347i	$-0.830257\pi$
$859$		−	29.7980i		−	1.01669i	0.861153	−	0.508347i	$-0.169743\pi$
$860$	−5.79796	+	5.79796i	−0.197709	+	0.197709i
$861$	13.7980	+	5.79796i	0.470233	+	0.197594i
$862$			49.1010i			1.67239i
$863$	−19.1464	−	19.1464i	−0.651752	−	0.651752i	0.301663	−	0.953415i	$-0.402458\pi$
$863$	−19.1464	−	19.1464i	−0.651752	−	0.651752i	−0.953415	+	0.301663i	$0.902458\pi$
$864$	3.67423	−	3.67423i	0.125000	−	0.125000i
$865$	−33.3939	+	33.3939i	−1.13543	+	1.13543i
$866$	36.4949	+	36.4949i	1.24015	+	1.24015i
$867$			13.0000i			0.441503i
$868$	−1.89898	−	0.797959i	−0.0644556	−	0.0270845i
$869$	30.6969	−	30.6969i	1.04132	−	1.04132i
$870$		−	33.7980i		−	1.14586i
$871$	−8.34847	+	41.7423i	−0.282877	+	1.41439i
$872$	24.2474			0.821122
$873$	1.89898	−	1.89898i	0.0642707	−	0.0642707i
$874$		−	12.0000i		−	0.405906i
$875$	13.7980	+	5.79796i	0.466456	+	0.196007i
$876$	−1.89898	−	1.89898i	−0.0641606	−	0.0641606i
$877$	−17.6969	−	17.6969i	−0.597583	−	0.597583i	0.342086	−	0.939669i	$-0.388867\pi$
$877$	−17.6969	−	17.6969i	−0.597583	−	0.597583i	−0.939669	+	0.342086i	$0.888867\pi$
$878$	33.7980	+	33.7980i	1.14063	+	1.14063i
$879$	−10.6969	+	10.6969i	−0.360799	+	0.360799i
$880$		−	88.9898i		−	2.99985i
$881$	12.6969			0.427771			0.213885	−	0.976859i	$-0.431388\pi$
$881$	12.6969			0.427771			0.213885	+	0.976859i	$0.431388\pi$
$882$	12.1237	+	0.123724i	0.408227	+	0.00416602i
$883$		−	37.7980i		−	1.27200i	−0.771688	−	0.636001i	$-0.780587\pi$
$883$		−	37.7980i		−	1.27200i	0.771688	−	0.636001i	$-0.219413\pi$
$884$	6.00000	−	4.00000i	0.201802	−	0.134535i
$885$		−	1.79796i		−	0.0604377i
$886$	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	$-0.0645687\pi$
$888$	−4.65153			−0.156095
$889$	8.00000	+	19.5959i	0.268311	+	0.657226i
$890$	−9.79796	−	9.79796i	−0.328428	−	0.328428i
$891$	4.44949	−	4.44949i	0.149064	−	0.149064i
$892$	7.44949	+	7.44949i	0.249427	+	0.249427i
$893$	−70.2929			−2.35226
$894$	−21.7980			−0.729033
$895$	−4.40408	−	4.40408i	−0.147212	−	0.147212i
$896$	−12.4268	+	29.5732i	−0.415150	+	0.987972i
$897$	−1.79796	−	2.69694i	−0.0600321	−	0.0900482i
$898$	−36.4949			−1.21785
$899$	3.79796	−	3.79796i	0.126669	−	0.126669i
$900$	−3.00000			−0.100000
$901$	−15.5959			−0.519575
$902$	43.5959	−	43.5959i	1.45159	−	1.45159i
$903$	7.10102	−	2.89898i	0.236307	−	0.0964720i
$904$	11.1464	−	11.1464i	0.370725	−	0.370725i
$905$	4.00000	−	4.00000i	0.132964	−	0.132964i
$906$			6.24745i			0.207558i
$907$		−	39.5959i		−	1.31476i	−0.753559	−	0.657380i	$-0.771664\pi$
$907$		−	39.5959i		−	1.31476i	0.753559	−	0.657380i	$-0.228336\pi$
$908$	15.3485	+	15.3485i	0.509357	+	0.509357i
$909$	14.8990			0.494168
$910$	−38.6969	−	26.2020i	−1.28279	−	0.868589i
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	27.2474	+	27.2474i	0.902253	+	0.902253i
$913$			39.5959i			1.31043i
$914$		−	16.6515i		−	0.550784i
$915$	−20.0000	+	20.0000i	−0.661180	+	0.661180i
$916$	13.0000	−	13.0000i	0.429532	−	0.429532i
$917$	−10.6969	−	26.2020i	−0.353244	−	0.865268i
$918$	−2.44949	+	2.44949i	−0.0808452	+	0.0808452i
$919$	−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
$921$	−8.55051	+	8.55051i	−0.281749	+	0.281749i
$922$	11.5051			0.378900
$923$	2.44949	−	12.2474i	0.0806259	−	0.403130i
$924$	6.44949	−	15.3485i	0.212173	−	0.504928i
$925$	5.69694	+	5.69694i	0.187314	+	0.187314i
$926$	49.3485			1.62169
$927$	−17.7980			−0.584562
$928$	25.3485	+	25.3485i	0.832104	+	0.832104i
$929$	4.89898	−	4.89898i	0.160730	−	0.160730i	−0.622160	−	0.782890i	$-0.713745\pi$
$929$	4.89898	−	4.89898i	0.160730	−	0.160730i	0.782890	+	0.622160i	$0.213745\pi$
$930$	−2.69694	−	2.69694i	−0.0884361	−	0.0884361i
$931$	−0.550510	+	53.9444i	−0.0180422	+	1.76796i
$932$	7.79796			0.255431
$933$			24.8990i			0.815156i
$934$	−38.0908	−	38.0908i	−1.24637	−	1.24637i
$935$			35.5959i			1.16411i
$936$	6.12372	+	1.22474i	0.200160	+	0.0400320i
$937$		−	29.5959i		−	0.966856i	−0.875384	−	0.483428i	$-0.839391\pi$
$937$		−	29.5959i		−	0.966856i	0.875384	−	0.483428i	$-0.160609\pi$
$938$	−20.4495	−	50.0908i	−0.667700	−	1.63552i
$939$	13.5959			0.443686
$940$			25.7980i			0.841437i
$941$	−7.10102	+	7.10102i	−0.231487	+	0.231487i	−0.813313	−	0.581826i	$-0.802338\pi$
$941$	−7.10102	+	7.10102i	−0.231487	+	0.231487i	0.581826	+	0.813313i	$0.302338\pi$
$942$	14.6969	+	14.6969i	0.478852	+	0.478852i
$943$	3.59592	+	3.59592i	0.117099	+	0.117099i
$944$	2.24745	+	2.24745i	0.0731482	+	0.0731482i
$945$	6.89898	+	2.89898i	0.224424	+	0.0943038i
$946$		−	31.5959i		−	1.02727i
$947$	−18.4495	+	18.4495i	−0.599528	+	0.599528i	−0.940187	−	0.340659i	$-0.889350\pi$
$947$	−18.4495	+	18.4495i	−0.599528	+	0.599528i	0.340659	+	0.940187i	$0.389350\pi$
$948$	6.89898			0.224068
$949$	1.89898	−	9.49490i	0.0616435	−	0.308217i
$950$		−	40.0454i		−	1.29924i
$951$	−12.6969	+	12.6969i	−0.411726	+	0.411726i
$952$	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	$0.969018\pi$
$954$	9.55051	+	9.55051i	0.309209	+	0.309209i
$955$	11.5959	−	11.5959i	0.375235	−	0.375235i
$956$	−7.34847	+	7.34847i	−0.237666	+	0.237666i
$957$	30.6969	+	30.6969i	0.992291	+	0.992291i
$958$			25.1010i			0.810977i
$959$		0			0
$960$	−2.00000	+	2.00000i	−0.0645497	+	0.0645497i
$961$			30.3939i			0.980448i
$962$	9.30306	+	13.9546i	0.299943	+	0.449914i
$963$	8.89898			0.286766
$964$	−4.10102	+	4.10102i	−0.132085	+	0.132085i
$965$			19.1918i			0.617807i
$966$	3.79796	+	1.59592i	0.122197	+	0.0513478i
$967$	35.2474	+	35.2474i	1.13348	+	1.13348i	0.989594	+	0.143887i	$0.0459603\pi$
$967$	35.2474	+	35.2474i	1.13348	+	1.13348i	0.143887	+	0.989594i	$0.454040\pi$
$968$	35.0227	+	35.0227i	1.12567	+	1.12567i
$969$	−10.8990	−	10.8990i	−0.350126	−	0.350126i
$970$	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	$-0.138121\pi$
$972$	1.00000			0.0320750
$973$	−2.89898	−	7.10102i	−0.0929370	−	0.227648i
$974$		−	37.3485i		−	1.19672i
$975$	−6.00000	−	9.00000i	−0.192154	−	0.288231i
$976$		−	50.0000i		−	1.60046i
$977$	5.59592	+	5.59592i	0.179029	+	0.179029i	0.790933	−	0.611903i	$-0.209596\pi$
$977$	5.59592	+	5.59592i	0.179029	+	0.179029i	−0.611903	+	0.790933i	$0.709596\pi$
$978$			1.34847i			0.0431193i
$979$	17.7980			0.568825
$980$	19.7980	+	0.202041i	0.632423	+	0.00645396i
$981$	9.89898	+	9.89898i	0.316050	+	0.316050i
$982$	45.1918	−	45.1918i	1.44213	−	1.44213i
$983$	−42.2474	−	42.2474i	−1.34748	−	1.34748i	−0.888385	−	0.459099i	$-0.848172\pi$
$983$	−42.2474	−	42.2474i	−1.34748	−	1.34748i	−0.459099	−	0.888385i	$-0.651828\pi$
$984$	−9.79796			−0.312348
$985$	47.1918			1.50366
$986$	−16.8990	−	16.8990i	−0.538173	−	0.538173i
$987$	9.34847	−	22.2474i	0.297565	−	0.708144i
$988$	5.44949	−	27.2474i	0.173371	−	0.866857i
$989$	2.60612			0.0828699
$990$	21.7980	−	21.7980i	0.692785	−	0.692785i
$991$	−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
$993$	3.24745	−	3.24745i	0.103055	−	0.103055i
$994$	6.00000	+	14.6969i	0.190308	+	0.466159i
$995$	−26.2020	+	26.2020i	−0.830661	+	0.830661i
$996$	−4.44949	+	4.44949i	−0.140987	+	0.140987i
$997$			9.39388i			0.297507i	0.988874	+	0.148754i	$0.0475261\pi$
$997$			9.39388i			0.297507i	−0.988874	+	0.148754i	$0.952474\pi$
$998$			37.3485i			1.18225i
$999$	−1.89898	−	1.89898i	−0.0600811	−	0.0600811i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.p.a.34.1	✓	4	7.6	odd	2
273.2.p.a.265.1	yes	4	13.5	odd	4
273.2.p.d.34.1	yes	4	1.1	even	1	trivial
273.2.p.d.265.1	yes	4	91.83	even	4	inner
819.2.y.a.307.2		4	3.2	odd	2
819.2.y.a.811.2		4	273.83	odd	4
819.2.y.d.307.2		4	21.20	even	2
819.2.y.d.811.2		4	39.5	even	4

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 1.22474i) q^{2} -1.00000i q^{3} +1.00000i q^{4} +(2.00000 - 2.00000i) q^{5} +(-1.22474 + 1.22474i) q^{6} +(2.44949 - 1.00000i) q^{7} +(-1.22474 + 1.22474i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.22474 - 1.22474i) q^{2} -1.00000i q^{3} +1.00000i q^{4} +(2.00000 - 2.00000i) q^{5} +(-1.22474 + 1.22474i) q^{6} +(2.44949 - 1.00000i) q^{7} +(-1.22474 + 1.22474i) q^{8} -1.00000 q^{9} -4.89898 q^{10} +(4.44949 - 4.44949i) q^{11} +1.00000 q^{12} +(2.00000 + 3.00000i) q^{13} +(-4.22474 - 1.77526i) q^{14} +(-2.00000 - 2.00000i) q^{15} +5.00000 q^{16} -2.00000 q^{17} +(1.22474 + 1.22474i) q^{18} +(-5.44949 + 5.44949i) q^{19} +(2.00000 + 2.00000i) q^{20} +(-1.00000 - 2.44949i) q^{21} -10.8990 q^{22} -0.898979i q^{23} +(1.22474 + 1.22474i) q^{24} -3.00000i q^{25} +(1.22474 - 6.12372i) q^{26} +1.00000i q^{27} +(1.00000 + 2.44949i) q^{28} -6.89898 q^{29} +4.89898i q^{30} +(-0.550510 + 0.550510i) q^{31} +(-3.67423 - 3.67423i) q^{32} +(-4.44949 - 4.44949i) q^{33} +(2.44949 + 2.44949i) q^{34} +(2.89898 - 6.89898i) q^{35} -1.00000i q^{36} +(-1.89898 + 1.89898i) q^{37} +13.3485 q^{38} +(3.00000 - 2.00000i) q^{39} +4.89898i q^{40} +(-4.00000 + 4.00000i) q^{41} +(-1.77526 + 4.22474i) q^{42} +2.89898i q^{43} +(4.44949 + 4.44949i) q^{44} +(-2.00000 + 2.00000i) q^{45} +(-1.10102 + 1.10102i) q^{46} +(6.44949 + 6.44949i) q^{47} -5.00000i q^{48} +(5.00000 - 4.89898i) q^{49} +(-3.67423 + 3.67423i) q^{50} +2.00000i q^{51} +(-3.00000 + 2.00000i) q^{52} +7.79796 q^{53} +(1.22474 - 1.22474i) q^{54} -17.7980i q^{55} +(-1.77526 + 4.22474i) q^{56} +(5.44949 + 5.44949i) q^{57} +(8.44949 + 8.44949i) q^{58} +(0.449490 + 0.449490i) q^{59} +(2.00000 - 2.00000i) q^{60} -10.0000i q^{61} +1.34847 q^{62} +(-2.44949 + 1.00000i) q^{63} -1.00000i q^{64} +(10.0000 + 2.00000i) q^{65} +10.8990i q^{66} +(8.34847 + 8.34847i) q^{67} -2.00000i q^{68} -0.898979 q^{69} +(-12.0000 + 4.89898i) q^{70} +(-2.44949 - 2.44949i) q^{71} +(1.22474 - 1.22474i) q^{72} +(-1.89898 - 1.89898i) q^{73} +4.65153 q^{74} -3.00000 q^{75} +(-5.44949 - 5.44949i) q^{76} +(6.44949 - 15.3485i) q^{77} +(-6.12372 - 1.22474i) q^{78} +6.89898 q^{79} +(10.0000 - 10.0000i) q^{80} +1.00000 q^{81} +9.79796 q^{82} +(-4.44949 + 4.44949i) q^{83} +(2.44949 - 1.00000i) q^{84} +(-4.00000 + 4.00000i) q^{85} +(3.55051 - 3.55051i) q^{86} +6.89898i q^{87} +10.8990i q^{88} +(2.00000 + 2.00000i) q^{89} +4.89898 q^{90} +(7.89898 + 5.34847i) q^{91} +0.898979 q^{92} +(0.550510 + 0.550510i) q^{93} -15.7980i q^{94} +21.7980i q^{95} +(-3.67423 + 3.67423i) q^{96} +(-1.89898 + 1.89898i) q^{97} +(-12.1237 - 0.123724i) q^{98} +(-4.44949 + 4.44949i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{5} - 4 q^{9}+O(q^{10}) \) 4 * q + 8 * q^5 - 4 * q^9	\( 4 q + 8 q^{5} - 4 q^{9} + 8 q^{11} + 4 q^{12} + 8 q^{13} - 12 q^{14} - 8 q^{15} + 20 q^{16} - 8 q^{17} - 12 q^{19} + 8 q^{20} - 4 q^{21} - 24 q^{22} + 4 q^{28} - 8 q^{29} - 12 q^{31} - 8 q^{33} - 8 q^{35} + 12 q^{37} + 24 q^{38} + 12 q^{39} - 16 q^{41} - 12 q^{42} + 8 q^{44} - 8 q^{45} - 24 q^{46} + 16 q^{47} + 20 q^{49} - 12 q^{52} - 8 q^{53} - 12 q^{56} + 12 q^{57} + 24 q^{58} - 8 q^{59} + 8 q^{60} - 24 q^{62} + 40 q^{65} + 4 q^{67} + 16 q^{69} - 48 q^{70} + 12 q^{73} + 48 q^{74} - 12 q^{75} - 12 q^{76} + 16 q^{77} + 8 q^{79} + 40 q^{80} + 4 q^{81} - 8 q^{83} - 16 q^{85} + 24 q^{86} + 8 q^{89} + 12 q^{91} - 16 q^{92} + 12 q^{93} + 12 q^{97} - 24 q^{98} - 8 q^{99}+O(q^{100}) \) 4 * q + 8 * q^5 - 4 * q^9 + 8 * q^11 + 4 * q^12 + 8 * q^13 - 12 * q^14 - 8 * q^15 + 20 * q^16 - 8 * q^17 - 12 * q^19 + 8 * q^20 - 4 * q^21 - 24 * q^22 + 4 * q^28 - 8 * q^29 - 12 * q^31 - 8 * q^33 - 8 * q^35 + 12 * q^37 + 24 * q^38 + 12 * q^39 - 16 * q^41 - 12 * q^42 + 8 * q^44 - 8 * q^45 - 24 * q^46 + 16 * q^47 + 20 * q^49 - 12 * q^52 - 8 * q^53 - 12 * q^56 + 12 * q^57 + 24 * q^58 - 8 * q^59 + 8 * q^60 - 24 * q^62 + 40 * q^65 + 4 * q^67 + 16 * q^69 - 48 * q^70 + 12 * q^73 + 48 * q^74 - 12 * q^75 - 12 * q^76 + 16 * q^77 + 8 * q^79 + 40 * q^80 + 4 * q^81 - 8 * q^83 - 16 * q^85 + 24 * q^86 + 8 * q^89 + 12 * q^91 - 16 * q^92 + 12 * q^93 + 12 * q^97 - 24 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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