LMFDB - Embedded newform 504.2.bf.b.115.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(115,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([3, 3, 4, 1]))

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

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

chi := DirichletCharacter("504.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$90$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			115.14
Character	$\chi$	$=$	504.115
Dual form			504.2.bf.b.355.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29841 + 0.560472i) q^{2} +(1.69247 - 0.368153i) q^{3} +(1.37174 - 1.45545i) q^{4} +(0.863157 - 1.49503i) q^{5} +(-1.99119 + 1.42660i) q^{6} +(-2.59622 - 0.509573i) q^{7} +(-0.965350 + 2.65859i) q^{8} +(2.72893 - 1.24618i) q^{9} +O(q^{10})$	\(q+(-1.29841 + 0.560472i) q^{2} +(1.69247 - 0.368153i) q^{3} +(1.37174 - 1.45545i) q^{4} +(0.863157 - 1.49503i) q^{5} +(-1.99119 + 1.42660i) q^{6} +(-2.59622 - 0.509573i) q^{7} +(-0.965350 + 2.65859i) q^{8} +(2.72893 - 1.24618i) q^{9} +(-0.282810 + 2.42494i) q^{10} +(-3.05357 - 5.28895i) q^{11} +(1.78581 - 2.96831i) q^{12} +(0.783302 + 1.35672i) q^{13} +(3.65656 - 0.793470i) q^{14} +(0.910469 - 2.84808i) q^{15} +(-0.236644 - 3.99299i) q^{16} +(2.10649 + 1.21618i) q^{17} +(-2.84482 + 3.14754i) q^{18} +(4.19816 - 2.42381i) q^{19} +(-0.991908 - 3.30708i) q^{20} +(-4.58162 + 0.0933660i) q^{21} +(6.92910 + 5.15578i) q^{22} +(-4.42895 - 2.55705i) q^{23} +(-0.655060 + 4.85499i) q^{24} +(1.00992 + 1.74923i) q^{25} +(-1.77745 - 1.32256i) q^{26} +(4.15985 - 3.11378i) q^{27} +(-4.30300 + 3.07965i) q^{28} +(-9.01172 - 5.20292i) q^{29} +(0.414102 + 4.20826i) q^{30} +1.68378 q^{31} +(2.54522 + 5.05192i) q^{32} +(-7.11523 - 7.82721i) q^{33} +(-3.41672 - 0.398476i) q^{34} +(-3.00277 + 3.44158i) q^{35} +(1.92964 - 5.68124i) q^{36} +(0.795378 - 0.459211i) q^{37} +(-4.09246 + 5.50005i) q^{38} +(1.82520 + 2.00783i) q^{39} +(3.14143 + 3.73801i) q^{40} +(-2.70354 + 1.56089i) q^{41} +(5.89650 - 2.68910i) q^{42} +(-1.27890 + 2.21511i) q^{43} +(-11.8865 - 2.81076i) q^{44} +(0.492416 - 5.15548i) q^{45} +(7.18375 + 0.837807i) q^{46} +7.98068 q^{47} +(-1.87055 - 6.67091i) q^{48} +(6.48067 + 2.64592i) q^{49} +(-2.29168 - 1.70519i) q^{50} +(4.01291 + 1.28284i) q^{51} +(3.04912 + 0.721016i) q^{52} +(8.93809 + 5.16041i) q^{53} +(-3.65601 + 6.37445i) q^{54} -10.5429 q^{55} +(3.86100 - 6.41036i) q^{56} +(6.21294 - 5.64780i) q^{57} +(14.6170 + 1.70471i) q^{58} -5.95284i q^{59} +(-2.89629 - 5.23196i) q^{60} +7.95160 q^{61} +(-2.18624 + 0.943713i) q^{62} +(-7.71990 + 1.84476i) q^{63} +(-6.13620 - 5.13294i) q^{64} +2.70445 q^{65} +(13.6254 + 6.17505i) q^{66} +5.32138 q^{67} +(4.65964 - 1.39759i) q^{68} +(-8.43726 - 2.69721i) q^{69} +(1.96992 - 6.15156i) q^{70} -7.59296i q^{71} +(0.678708 + 8.45809i) q^{72} +(-5.73649 - 3.31196i) q^{73} +(-0.775352 + 1.04203i) q^{74} +(2.35324 + 2.58872i) q^{75} +(2.23107 - 9.43504i) q^{76} +(5.23263 + 15.2873i) q^{77} +(-3.49519 - 1.58402i) q^{78} +7.16154i q^{79} +(-6.17392 - 3.09279i) q^{80} +(5.89408 - 6.80146i) q^{81} +(2.63547 - 3.54193i) q^{82} +(9.57683 + 5.52919i) q^{83} +(-6.14892 + 6.79638i) q^{84} +(3.63646 - 2.09951i) q^{85} +(0.419025 - 3.59291i) q^{86} +(-17.1676 - 5.48811i) q^{87} +(17.0089 - 3.01252i) q^{88} +(-13.0622 + 7.54148i) q^{89} +(2.25014 + 6.96992i) q^{90} +(-1.34227 - 3.92148i) q^{91} +(-9.79703 + 2.93847i) q^{92} +(2.84976 - 0.619890i) q^{93} +(-10.3622 + 4.47295i) q^{94} -8.36852i q^{95} +(6.16760 + 7.61320i) q^{96} +(-2.84277 - 1.64127i) q^{97} +(-9.89754 + 0.196736i) q^{98} +(-14.9240 - 10.6278i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9}+O(q^{10}) $ 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9	$ 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9} - 8 q^{11} + 12 q^{12} + 10 q^{14} + 14 q^{16} - 18 q^{17} + 8 q^{18} - 6 q^{19} + 36 q^{20} - 16 q^{22} - 12 q^{24} - 78 q^{25} - 6 q^{26} + 16 q^{28} + q^{30} - 26 q^{32} - 36 q^{33} - 12 q^{34} - 12 q^{35} + 2 q^{36} - 27 q^{38} + 24 q^{40} - 42 q^{41} + 22 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} - 9 q^{48} + 2 q^{49} + 15 q^{50} + 9 q^{52} - 51 q^{54} + 14 q^{56} - 26 q^{57} + 19 q^{58} + 37 q^{60} - 8 q^{64} + 24 q^{65} + 6 q^{66} + 28 q^{67} + 12 q^{68} + 27 q^{70} - 28 q^{72} + 18 q^{73} + 49 q^{74} - 18 q^{75} - 12 q^{76} - 33 q^{78} - 63 q^{80} - 22 q^{81} - 54 q^{82} + 6 q^{83} + 31 q^{84} - 13 q^{86} + 29 q^{88} - 66 q^{89} - 51 q^{90} + 2 q^{91} - 60 q^{92} - 45 q^{96} - 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) $ 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9 - 8 * q^11 + 12 * q^12 + 10 * q^14 + 14 * q^16 - 18 * q^17 + 8 * q^18 - 6 * q^19 + 36 * q^20 - 16 * q^22 - 12 * q^24 - 78 * q^25 - 6 * q^26 + 16 * q^28 + q^30 - 26 * q^32 - 36 * q^33 - 12 * q^34 - 12 * q^35 + 2 * q^36 - 27 * q^38 + 24 * q^40 - 42 * q^41 + 22 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 - 9 * q^48 + 2 * q^49 + 15 * q^50 + 9 * q^52 - 51 * q^54 + 14 * q^56 - 26 * q^57 + 19 * q^58 + 37 * q^60 - 8 * q^64 + 24 * q^65 + 6 * q^66 + 28 * q^67 + 12 * q^68 + 27 * q^70 - 28 * q^72 + 18 * q^73 + 49 * q^74 - 18 * q^75 - 12 * q^76 - 33 * q^78 - 63 * q^80 - 22 * q^81 - 54 * q^82 + 6 * q^83 + 31 * q^84 - 13 * q^86 + 29 * q^88 - 66 * q^89 - 51 * q^90 + 2 * q^91 - 60 * q^92 - 45 * q^96 - 6 * q^97 + 31 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.29841	+	0.560472i	−0.918115	+	0.396313i
$2$	−1.29841	+	0.560472i	−0.918115	+	0.396313i
$3$	1.69247	−	0.368153i	0.977149	−	0.212553i
$3$	1.69247	−	0.368153i	0.977149	−	0.212553i
$4$	1.37174	−	1.45545i	0.685871	−	0.727723i
$5$	0.863157	−	1.49503i	0.386016	−	0.668599i	−0.605894	−	0.795545i	$-0.707184\pi$
$5$	0.863157	−	1.49503i	0.386016	−	0.668599i	0.991910	+	0.126947i	$0.0405177\pi$
$6$	−1.99119	+	1.42660i	−0.812898	+	0.582406i
$7$	−2.59622	−	0.509573i	−0.981277	−	0.192601i
$7$	−2.59622	−	0.509573i	−0.981277	−	0.192601i
$8$	−0.965350	+	2.65859i	−0.341303	+	0.939953i
$9$	2.72893	−	1.24618i	0.909642	−	0.415393i
$10$	−0.282810	+	2.42494i	−0.0894322	+	0.766834i
$11$	−3.05357	−	5.28895i	−0.920687	−	1.59468i	−0.798354	−	0.602188i	$-0.794296\pi$
$11$	−3.05357	−	5.28895i	−0.920687	−	1.59468i	−0.122333	−	0.992489i	$-0.539038\pi$
$12$	1.78581	−	2.96831i	0.515519	−	0.856878i
$13$	0.783302	+	1.35672i	0.217249	+	0.376286i	0.953966	−	0.299915i	$-0.0969583\pi$
$13$	0.783302	+	1.35672i	0.217249	+	0.376286i	−0.736717	+	0.676201i	$0.763625\pi$
$14$	3.65656	−	0.793470i	0.977256	−	0.212064i
$15$	0.910469	−	2.84808i	0.235082	−	0.735370i
$16$	−0.236644	−	3.99299i	−0.0591610	−	0.998248i
$17$	2.10649	+	1.21618i	0.510898	+	0.294967i	0.733203	−	0.680010i	$-0.238025\pi$
$17$	2.10649	+	1.21618i	0.510898	+	0.294967i	−0.222305	+	0.974977i	$0.571358\pi$
$18$	−2.84482	+	3.14754i	−0.670531	+	0.741882i
$19$	4.19816	−	2.42381i	0.963125	−	0.556060i	0.0659913	−	0.997820i	$-0.478979\pi$
$19$	4.19816	−	2.42381i	0.963125	−	0.556060i	0.897133	+	0.441760i	$0.145646\pi$
$20$	−0.991908	−	3.30708i	−0.221797	−	0.739485i
$21$	−4.58162	+	0.0933660i	−0.999792	+	0.0203741i
$22$	6.92910	+	5.15578i	1.47729	+	1.09922i
$23$	−4.42895	−	2.55705i	−0.923500	−	0.533183i	−0.0387497	−	0.999249i	$-0.512338\pi$
$23$	−4.42895	−	2.55705i	−0.923500	−	0.533183i	−0.884750	+	0.466066i	$0.845671\pi$
$24$	−0.655060	+	4.85499i	−0.133714	+	0.991020i
$25$	1.00992	+	1.74923i	0.201984	+	0.349846i
$26$	−1.77745	−	1.32256i	−0.348587	−	0.259375i
$27$	4.15985	−	3.11378i	0.800563	−	0.599248i
$28$	−4.30300	+	3.07965i	−0.813190	+	0.581999i
$29$	−9.01172	−	5.20292i	−1.67343	−	0.966158i	−0.965693	−	0.259686i	$-0.916381\pi$
$29$	−9.01172	−	5.20292i	−1.67343	−	0.966158i	−0.707742	−	0.706471i	$-0.750286\pi$
$30$	0.414102	+	4.20826i	0.0756044	+	0.768321i
$31$	1.68378			0.302416			0.151208	−	0.988502i	$-0.451684\pi$
$31$	1.68378			0.302416			0.151208	+	0.988502i	$0.451684\pi$
$32$	2.54522	+	5.05192i	0.449936	+	0.893061i
$33$	−7.11523	−	7.82721i	−1.23860	−	1.36254i
$34$	−3.41672	−	0.398476i	−0.585962	−	0.0683380i
$35$	−3.00277	+	3.44158i	−0.507561	+	0.581734i
$36$	1.92964	−	5.68124i	0.321607	−	0.946873i
$37$	0.795378	−	0.459211i	0.130759	−	0.0754939i	−0.433194	−	0.901301i	$-0.642613\pi$
$37$	0.795378	−	0.459211i	0.130759	−	0.0754939i	0.563953	+	0.825807i	$0.309280\pi$
$38$	−4.09246	+	5.50005i	−0.663885	+	0.892227i
$39$	1.82520	+	2.00783i	0.292266	+	0.321511i
$40$	3.14143	+	3.73801i	0.496704	+	0.591031i
$41$	−2.70354	+	1.56089i	−0.422222	+	0.243770i	−0.696027	−	0.718015i	$-0.745051\pi$
$41$	−2.70354	+	1.56089i	−0.422222	+	0.243770i	0.273806	+	0.961785i	$0.411717\pi$
$42$	5.89650	−	2.68910i	0.909850	−	0.414937i
$43$	−1.27890	+	2.21511i	−0.195030	+	0.337802i	−0.946910	−	0.321498i	$-0.895814\pi$
$43$	−1.27890	+	2.21511i	−0.195030	+	0.337802i	0.751880	+	0.659299i	$0.229147\pi$
$44$	−11.8865	−	2.81076i	−1.79196	−	0.423738i
$45$	0.492416	−	5.15548i	0.0734051	−	0.768534i
$46$	7.18375	+	0.837807i	1.05919	+	0.123528i
$47$	7.98068			1.16410			0.582051	−	0.813152i	$-0.302250\pi$
$47$	7.98068			1.16410			0.582051	+	0.813152i	$0.302250\pi$
$48$	−1.87055	−	6.67091i	−0.269990	−	0.962863i
$49$	6.48067	+	2.64592i	0.925810	+	0.377989i
$50$	−2.29168	−	1.70519i	−0.324093	−	0.241150i
$51$	4.01291	+	1.28284i	0.561920	+	0.179634i
$52$	3.04912	+	0.721016i	0.422837	+	0.0999869i
$53$	8.93809	+	5.16041i	1.22774	+	0.708837i	0.966557	−	0.256452i	$-0.0825537\pi$
$53$	8.93809	+	5.16041i	1.22774	+	0.708837i	0.261184	+	0.965289i	$0.415887\pi$
$54$	−3.65601	+	6.37445i	−0.497519	+	0.867453i
$55$	−10.5429			−1.42160
$56$	3.86100	−	6.41036i	0.515948	−	0.856620i
$57$	6.21294	−	5.64780i	0.822924	−	0.748069i
$58$	14.6170	+	1.70471i	1.91931	+	0.223840i
$59$		−	5.95284i		−	0.774993i	−0.921871	−	0.387497i	$-0.873340\pi$
$59$		−	5.95284i		−	0.774993i	0.921871	−	0.387497i	$-0.126660\pi$
$60$	−2.89629	−	5.23196i	−0.373909	−	0.675444i
$61$	7.95160			1.01810			0.509049	−	0.860738i	$-0.329997\pi$
$61$	7.95160			1.01810			0.509049	+	0.860738i	$0.329997\pi$
$62$	−2.18624	+	0.943713i	−0.277653	+	0.119852i
$63$	−7.71990	+	1.84476i	−0.972616	+	0.232418i
$64$	−6.13620	−	5.13294i	−0.767025	−	0.641617i
$65$	2.70445			0.335446
$66$	13.6254	+	6.17505i	1.67717	+	0.760097i
$67$	5.32138			0.650110			0.325055	−	0.945695i	$-0.394617\pi$
$67$	5.32138			0.650110			0.325055	+	0.945695i	$0.394617\pi$
$68$	4.65964	−	1.39759i	0.565064	−	0.169483i
$69$	−8.43726	−	2.69721i	−1.01573	−	0.324706i
$70$	1.96992	−	6.15156i	0.235450	−	0.735252i
$71$		−	7.59296i		−	0.901119i	−0.892746	−	0.450559i	$-0.851225\pi$
$71$		−	7.59296i		−	0.901119i	0.892746	−	0.450559i	$-0.148775\pi$
$72$	0.678708	+	8.45809i	0.0799865	+	0.996796i
$73$	−5.73649	−	3.31196i	−0.671405	−	0.387636i	0.125204	−	0.992131i	$-0.460042\pi$
$73$	−5.73649	−	3.31196i	−0.671405	−	0.387636i	−0.796609	+	0.604495i	$0.793375\pi$
$74$	−0.775352	+	1.04203i	−0.0901328	+	0.121134i
$75$	2.35324	+	2.58872i	0.271729	+	0.298920i
$76$	2.23107	−	9.43504i	0.255922	−	1.08227i
$77$	5.23263	+	15.2873i	0.596314	+	1.74215i
$78$	−3.49519	−	1.58402i	−0.395753	−	0.179355i
$79$			7.16154i			0.805736i	0.915258	+	0.402868i	$0.131987\pi$
$79$			7.16154i			0.805736i	−0.915258	+	0.402868i	$0.868013\pi$
$80$	−6.17392	−	3.09279i	−0.690265	−	0.345785i
$81$	5.89408	−	6.80146i	0.654898	−	0.755717i
$82$	2.63547	−	3.54193i	0.291039	−	0.391141i
$83$	9.57683	+	5.52919i	1.05119	+	0.606907i	0.922983	−	0.384840i	$-0.125743\pi$
$83$	9.57683	+	5.52919i	1.05119	+	0.606907i	0.128210	+	0.991747i	$0.459077\pi$
$84$	−6.14892	+	6.79638i	−0.670902	+	0.741546i
$85$	3.63646	−	2.09951i	0.394429	−	0.227724i
$86$	0.419025	−	3.59291i	0.0451846	−	0.387434i
$87$	−17.1676	−	5.48811i	−1.84056	−	0.588387i
$88$	17.0089	−	3.01252i	1.81316	−	0.321136i
$89$	−13.0622	+	7.54148i	−1.38459	+	0.799396i	−0.992699	−	0.120615i	$-0.961513\pi$
$89$	−13.0622	+	7.54148i	−1.38459	+	0.799396i	−0.391894	+	0.920010i	$0.628180\pi$
$90$	2.25014	+	6.96992i	0.237186	+	0.734694i
$91$	−1.34227	−	3.92148i	−0.140708	−	0.411083i
$92$	−9.79703	+	2.93847i	−1.02141	+	0.306357i
$93$	2.84976	−	0.619890i	0.295506	−	0.0642796i
$94$	−10.3622	+	4.47295i	−1.06878	+	0.461349i
$95$		−	8.36852i		−	0.858592i
$96$	6.16760	+	7.61320i	0.629478	+	0.777019i
$97$	−2.84277	−	1.64127i	−0.288639	−	0.166646i	0.348689	−	0.937239i	$-0.386627\pi$
$97$	−2.84277	−	1.64127i	−0.288639	−	0.166646i	−0.637328	+	0.770593i	$0.719960\pi$
$98$	−9.89754	+	0.196736i	−0.999803	+	0.0198733i
$99$	−14.9240	−	10.6278i	−1.49991	−	1.06814i
$100$	3.93126	+	0.929613i	0.393126	+	0.0929613i
$101$	7.13816	+	12.3637i	0.710274	+	1.23023i	0.964754	+	0.263152i	$0.0847621\pi$
$101$	7.13816	+	12.3637i	0.710274	+	1.23023i	−0.254481	+	0.967078i	$0.581905\pi$
$102$	−5.92940	+	0.583466i	−0.587098	+	0.0577718i
$103$	−0.609587	+	1.05584i	−0.0600644	+	0.104035i	−0.894494	−	0.447080i	$-0.852464\pi$
$103$	−0.609587	+	1.05584i	−0.0600644	+	0.104035i	0.834430	+	0.551115i	$0.185797\pi$
$104$	−4.36312	+	0.772771i	−0.427839	+	0.0757764i
$105$	−3.81508	+	6.93027i	−0.372313	+	0.676325i
$106$	−14.4976	−	1.69078i	−1.40813	−	0.164223i
$107$	1.06908	+	1.85170i	0.103352	+	0.179010i	0.913064	−	0.407817i	$-0.133710\pi$
$107$	1.06908	+	1.85170i	0.103352	+	0.179010i	−0.809712	+	0.586828i	$0.800377\pi$
$108$	1.17430	−	10.3257i	0.112997	−	0.993595i
$109$	8.91516	+	5.14717i	0.853917	+	0.493009i	0.861971	−	0.506958i	$-0.169230\pi$
$109$	8.91516	+	5.14717i	0.853917	+	0.493009i	−0.00805329	+	0.999968i	$0.502563\pi$
$110$	13.6890	−	5.90898i	1.30519	−	0.563399i
$111$	1.17709	−	1.07002i	0.111725	−	0.101562i
$112$	−1.42034	+	10.4873i	−0.134210	+	0.990953i
$113$	0.560622	+	0.971026i	0.0527389	+	0.0913465i	0.891190	−	0.453631i	$-0.149872\pi$
$113$	0.560622	+	0.971026i	0.0527389	+	0.0913465i	−0.838451	+	0.544977i	$0.816538\pi$
$114$	−4.90152	+	10.8153i	−0.459069	+	1.01295i
$115$	−7.64576	+	4.41428i	−0.712971	+	0.411634i
$116$	−19.9343	+	5.97900i	−1.85086	+	0.555136i
$117$	3.82829	+	2.72625i	0.353925	+	0.252042i
$118$	3.33640	+	7.72923i	0.307140	+	0.711533i
$119$	−4.84916	−	4.23087i	−0.444522	−	0.387844i
$120$	6.69294	+	5.16995i	0.610979	+	0.471950i
$121$	−13.1486	+	22.7741i	−1.19533	+	2.07037i
$122$	−10.3244	+	4.45665i	−0.934731	+	0.403486i
$123$	−4.00102	+	3.63708i	−0.360760	+	0.327944i
$124$	2.30972	−	2.45065i	0.207419	−	0.220075i
$125$	12.1184			1.08391
$126$	8.98967	−	6.72204i	0.800863	−	0.598847i
$127$			2.62046i			0.232529i	0.993218	+	0.116264i	$0.0370920\pi$
$127$			2.62046i			0.232529i	−0.993218	+	0.116264i	$0.962908\pi$
$128$	10.8442	+	3.22550i	0.958499	+	0.285096i
$129$	−1.34900	+	4.21985i	−0.118772	+	0.371537i
$130$	−3.51149	+	1.51577i	−0.307978	+	0.132942i
$131$	8.86241	+	5.11672i	0.774313	+	0.447050i	0.834411	−	0.551143i	$-0.185808\pi$
$131$	8.86241	+	5.11672i	0.774313	+	0.447050i	−0.0600983	+	0.998192i	$0.519141\pi$
$132$	−21.1524	−	0.381088i	−1.84108	−	0.0331695i
$133$	−12.1344	+	4.15346i	−1.05219	+	0.360151i
$134$	−6.90934	+	2.98248i	−0.596876	+	0.257647i
$135$	−1.06461	−	8.90679i	−0.0916266	−	0.766575i
$136$	−5.26682	+	4.42624i	−0.451626	+	0.379547i
$137$	0.247242	+	0.428235i	0.0211233	+	0.0365866i	0.876394	−	0.481595i	$-0.159942\pi$
$137$	0.247242	+	0.428235i	0.0211233	+	0.0365866i	−0.855271	+	0.518182i	$0.826609\pi$
$138$	12.4667	−	1.22676i	1.06124	−	0.104428i
$139$	−18.8282	+	10.8705i	−1.59699	+	0.922020i	−0.604922	+	0.796285i	$0.706796\pi$
$139$	−18.8282	+	10.8705i	−1.59699	+	0.922020i	−0.992064	+	0.125736i	$0.959871\pi$
$140$	0.890010	+	9.09134i	0.0752195	+	0.768358i
$141$	13.5071	−	2.93811i	1.13750	−	0.247434i
$142$	4.25564	+	9.85879i	0.357126	+	0.827331i
$143$	4.78374	−	8.28569i	0.400037	−	0.692884i
$144$	−5.62177	−	10.6017i	−0.468480	−	0.883474i
$145$	−15.5571	+	8.98188i	−1.29194	+	0.745904i
$146$	9.30458	+	1.08515i	0.770053	+	0.0898076i
$147$	11.9425	+	2.09228i	0.984998	+	0.172568i
$148$	0.422696	−	1.78755i	0.0347454	−	0.146936i
$149$	7.54483	+	4.35601i	0.618096	+	0.356858i	0.776127	−	0.630576i	$-0.217181\pi$
$149$	7.54483	+	4.35601i	0.618096	+	0.356858i	−0.158031	+	0.987434i	$0.550515\pi$
$150$	−4.50638	−	2.04230i	−0.367945	−	0.166753i
$151$	0.141191	−	0.0815169i	0.0114900	−	0.00663375i	−0.494244	−	0.869323i	$-0.664555\pi$
$151$	0.141191	−	0.0815169i	0.0114900	−	0.00663375i	0.505734	+	0.862689i	$0.331222\pi$
$152$	2.39122	+	13.5010i	0.193954	+	1.09508i
$153$	7.26402	+	0.693810i	0.587261	+	0.0560912i
$154$	−15.3622	−	16.9164i	−1.23792	−	1.36316i
$155$	1.45337	−	2.51731i	0.116737	−	0.202195i
$156$	5.42600	+	0.0977566i	0.434427	+	0.00782679i
$157$	5.64149			0.450240			0.225120	−	0.974331i	$-0.427723\pi$
$157$	5.64149			0.450240			0.225120	+	0.974331i	$0.427723\pi$
$158$	−4.01384	−	9.29863i	−0.319324	−	0.739759i
$159$	17.0273	+	5.44326i	1.35035	+	0.431679i
$160$	9.74970	+	0.555409i	0.770782	+	0.0439089i
$161$	10.1955	+	8.89554i	0.803518	+	0.701067i
$162$	−3.84091	+	12.1346i	−0.301771	+	0.953381i
$163$	−7.21382	−	12.4947i	−0.565030	−	0.978661i	−0.997047	−	0.0767955i	$-0.975531\pi$
$163$	−7.21382	−	12.4947i	−0.565030	−	0.978661i	0.432017	−	0.901866i	$-0.357802\pi$
$164$	−1.43677	+	6.07599i	−0.112193	+	0.474455i
$165$	−17.8435	+	3.88139i	−1.38911	+	0.302166i
$166$	−15.5336	−	1.81161i	−1.20564	−	0.140608i
$167$	−10.7818	−	18.6746i	−0.834320	−	1.44508i	−0.894583	−	0.446902i	$-0.852527\pi$
$167$	−10.7818	−	18.6746i	−0.834320	−	1.44508i	0.0602628	−	0.998183i	$-0.480806\pi$
$168$	4.17465	−	12.2708i	0.322081	−	0.946712i
$169$	5.27288	−	9.13289i	0.405606	−	0.702530i
$170$	−3.54490	+	4.76416i	−0.271881	+	0.365394i
$171$	8.43598	−	11.8461i	0.645115	−	0.905891i
$172$	1.46966	+	4.89993i	0.112061	+	0.373616i
$173$	−16.5855			−1.26097			−0.630486	−	0.776201i	$-0.717144\pi$
$173$	−16.5855			−1.26097			−0.630486	+	0.776201i	$0.717144\pi$
$174$	25.3665	−	2.49612i	1.92303	−	0.189230i
$175$	−1.73061	−	5.05601i	−0.130822	−	0.382198i
$176$	−20.3961	+	13.4445i	−1.53742	+	1.01342i
$177$	−2.19156	−	10.0750i	−0.164727	−	0.757284i
$178$	12.7334	−	17.1130i	0.954405	−	1.28267i
$179$	−4.01955	+	6.96207i	−0.300435	+	0.520369i	−0.976235	−	0.216716i	$-0.930465\pi$
$179$	−4.01955	+	6.96207i	−0.300435	+	0.520369i	0.675799	+	0.737086i	$0.263799\pi$
$180$	−6.82805	−	7.78868i	−0.508933	−	0.580534i
$181$	6.27825			0.466659			0.233329	−	0.972398i	$-0.425038\pi$
$181$	6.27825			0.466659			0.233329	+	0.972398i	$0.425038\pi$
$182$	3.94070	+	4.33939i	0.292104	+	0.321657i
$183$	13.4579	−	2.92741i	0.994834	−	0.216400i
$184$	11.0736	−	9.30631i	0.816360	−	0.686070i
$185$		−	1.58549i		−	0.116567i
$186$	−3.35272	+	2.40208i	−0.245834	+	0.176129i
$187$		−	14.8548i		−	1.08629i
$188$	10.9474	−	11.6154i	0.798424	−	0.847144i
$189$	−12.3866	+	5.96431i	−0.900990	+	0.433840i
$190$	4.69032	+	10.8658i	0.340271	+	0.788286i
$191$			11.4616i			0.829332i	0.909974	+	0.414666i	$0.136102\pi$
$191$			11.4616i			0.829332i	−0.909974	+	0.414666i	$0.863898\pi$
$192$	−12.2751	−	6.42830i	−0.885876	−	0.463922i
$193$	6.88377			0.495504			0.247752	−	0.968823i	$-0.420308\pi$
$193$	6.88377			0.495504			0.247752	+	0.968823i	$0.420308\pi$
$194$	4.61097	+	0.537755i	0.331048	+	0.0386086i
$195$	4.57721	−	0.995652i	0.327781	−	0.0713001i
$196$	12.7408	−	5.80274i	0.910058	−	0.414481i
$197$			5.84996i			0.416792i	0.978045	+	0.208396i	$0.0668243\pi$
$197$			5.84996i			0.416792i	−0.978045	+	0.208396i	$0.933176\pi$
$198$	25.3340	+	5.43486i	1.80041	+	0.386239i
$199$	−3.45810	+	5.98960i	−0.245138	+	0.424592i	−0.962170	−	0.272448i	$-0.912167\pi$
$199$	−3.45810	+	5.98960i	−0.245138	+	0.424592i	0.717032	+	0.697040i	$0.245500\pi$
$200$	−5.62541	+	0.996341i	−0.397777	+	0.0704519i
$201$	9.00629	−	1.95908i	0.635255	−	0.138183i
$202$	−16.1977	−	12.0524i	−1.13967	−	0.848002i
$203$	20.7451	+	18.1000i	1.45602	+	1.27037i
$204$	7.37179	−	4.08084i	0.516128	−	0.285716i
$205$			5.38917i			0.376396i
$206$	0.199728	−	1.71257i	0.0139157	−	0.119320i
$207$	−15.2728	−	1.45876i	−1.06153	−	0.101391i
$208$	5.23201	−	3.44878i	0.362774	−	0.239130i
$209$	−25.6388	−	14.8026i	−1.77347	−	1.02392i
$210$	1.06932	−	11.1366i	0.0737901	−	0.768497i
$211$	2.48848	+	4.31018i	0.171314	+	0.296725i	0.938880	−	0.344246i	$-0.111865\pi$
$211$	2.48848	+	4.31018i	0.171314	+	0.296725i	−0.767565	+	0.640971i	$0.778532\pi$
$212$	19.7715	−	5.93015i	1.35791	−	0.407284i
$213$	−2.79537	−	12.8509i	−0.191536	−	0.880528i
$214$	−2.42592	−	1.80507i	−0.165833	−	0.123392i
$215$	2.20778	+	3.82398i	0.150569	+	0.260793i
$216$	4.26257	+	14.0652i	0.290031	+	0.957017i
$217$	−4.37146	−	0.858011i	−0.296754	−	0.0582456i
$218$	−14.4604	−	1.68645i	−0.979381	−	0.114221i
$219$	−10.9282	−	3.49350i	−0.738457	−	0.236069i
$220$	−14.4621	+	15.3446i	−0.975034	+	1.03453i
$221$			3.81055i			0.256325i
$222$	−0.928635	+	2.04906i	−0.0623259	+	0.137524i
$223$	−11.1469	+	19.3070i	−0.746450	+	1.29289i	0.203064	+	0.979165i	$0.434910\pi$
$223$	−11.1469	+	19.3070i	−0.746450	+	1.29289i	−0.949514	+	0.313724i	$0.898423\pi$
$224$	−4.03362	−	14.4128i	−0.269508	−	0.962998i
$225$	4.93585	+	3.51498i	0.329057	+	0.234332i
$226$	−1.27215	−	0.946578i	−0.0846222	−	0.0629655i
$227$	−8.81520	+	5.08946i	−0.585085	+	0.337799i	−0.763152	−	0.646219i	$-0.776349\pi$
$227$	−8.81520	+	5.08946i	−0.585085	+	0.337799i	0.178067	+	0.984018i	$0.443016\pi$
$228$	0.302493	−	16.7899i	0.0200331	−	1.11194i
$229$	12.7985	−	22.1676i	0.845747	−	1.46488i	−0.0392243	−	0.999230i	$-0.512489\pi$
$229$	12.7985	−	22.1676i	0.845747	−	1.46488i	0.884971	−	0.465646i	$-0.154178\pi$
$230$	7.45326	−	10.0168i	0.491453	−	0.660487i
$231$	14.4841	+	23.9469i	0.952987	+	1.57559i
$232$	22.5319	−	18.9358i	1.47929	−	1.24320i
$233$	14.1018	+	24.4251i	0.923840	+	1.60014i	0.793416	+	0.608680i	$0.208301\pi$
$233$	14.1018	+	24.4251i	0.923840	+	1.60014i	0.130425	+	0.991458i	$0.458366\pi$
$234$	−6.49868	−	1.39415i	−0.424832	−	0.0911384i
$235$	6.88858	−	11.9314i	0.449362	−	0.778317i
$236$	−8.66403	−	8.16576i	−0.563980	−	0.531546i
$237$	2.63654	+	12.1207i	0.171262	+	0.787325i
$238$	8.66749	+	2.77560i	0.561830	+	0.179915i
$239$	−1.36970	+	0.790795i	−0.0885983	+	0.0511523i	−0.543645	−	0.839316i	$-0.682956\pi$
$239$	−1.36970	+	0.790795i	−0.0885983	+	0.0511523i	0.455046	+	0.890468i	$0.349623\pi$
$240$	−11.5878	−	2.96152i	−0.747990	−	0.191165i
$241$	−5.41756	+	3.12783i	−0.348976	+	0.201481i	−0.664234	−	0.747525i	$-0.731242\pi$
$241$	−5.41756	+	3.12783i	−0.348976	+	0.201481i	0.315258	+	0.949006i	$0.397909\pi$
$242$	4.30809	−	36.9396i	0.276935	−	2.37457i
$243$	7.47159	−	13.6812i	0.479303	−	0.877650i
$244$	10.9075	−	11.5731i	0.698284	−	0.740893i
$245$	9.54958	−	7.40496i	0.610100	−	0.473086i
$246$	3.15649	−	6.96488i	0.201250	−	0.444064i
$247$	6.57686	+	3.79715i	0.418476	+	0.241607i
$248$	−1.62544	+	4.47649i	−0.103215	+	0.284257i
$249$	18.2441	+	5.83225i	1.15617	+	0.369604i
$250$	−15.7347	+	6.79205i	−0.995152	+	0.429567i
$251$			6.62587i			0.418222i	0.977892	+	0.209111i	$0.0670569\pi$
$251$			6.62587i			0.418222i	−0.977892	+	0.209111i	$0.932943\pi$
$252$	−7.90477	+	13.7664i	−0.497954	+	0.867204i
$253$			31.2326i			1.96358i
$254$	−1.46870	−	3.40244i	−0.0921542	−	0.213488i
$255$	5.38166	−	4.89214i	0.337013	−	0.306357i
$256$	−15.8880	+	1.88984i	−0.993000	+	0.118115i
$257$	−0.705568	−	0.407360i	−0.0440122	−	0.0254104i	0.477832	−	0.878451i	$-0.341423\pi$
$257$	−0.705568	−	0.407360i	−0.0440122	−	0.0254104i	−0.521845	+	0.853041i	$0.674756\pi$
$258$	−0.613555	−	6.23517i	−0.0381982	−	0.388185i
$259$	−2.29897	+	0.786909i	−0.142851	+	0.0488961i
$260$	3.70981	−	3.93618i	0.230073	−	0.244112i
$261$	−31.0761	−	2.96818i	−1.92356	−	0.183726i
$262$	−14.3748	−	1.67647i	−0.888080	−	0.103573i
$263$	7.51289	−	4.33757i	0.463265	−	0.267466i	−0.250151	−	0.968207i	$-0.580480\pi$
$263$	7.51289	−	4.33757i	0.463265	−	0.267466i	0.713416	+	0.700741i	$0.247147\pi$
$264$	27.6780	−	11.3605i	1.70347	−	0.699190i
$265$	15.4300	−	8.90849i	0.947855	−	0.547244i
$266$	13.4276	−	12.1939i	0.823299	−	0.747657i
$267$	−19.3310	+	17.5727i	−1.18304	+	1.07543i
$268$	7.29957	−	7.74498i	0.445892	−	0.473100i
$269$	12.5848	−	21.7975i	0.767307	−	1.32901i	−0.171712	−	0.985147i	$-0.554930\pi$
$269$	12.5848	−	21.7975i	0.767307	−	1.32901i	0.939018	−	0.343867i	$-0.111737\pi$
$270$	6.37430	+	10.9680i	0.387928	+	0.667491i
$271$	−13.3344	−	23.0958i	−0.810006	−	1.40297i	−0.912859	−	0.408275i	$-0.866130\pi$
$271$	−13.3344	−	23.0958i	−0.810006	−	1.40297i	0.102853	−	0.994697i	$-0.467203\pi$
$272$	4.35771	−	8.69899i	0.264225	−	0.527454i
$273$	−3.71547	−	6.14284i	−0.224870	−	0.371782i
$274$	−0.561035	−	0.417453i	−0.0338933	−	0.0252193i
$275$	6.16773	−	10.6828i	0.371928	−	0.644198i
$276$	−15.4994	+	8.58009i	−0.932954	+	0.516461i
$277$	23.7568	−	13.7160i	1.42741	−	0.824113i	0.430490	−	0.902595i	$-0.358341\pi$
$277$	23.7568	−	13.7160i	1.42741	−	0.824113i	0.996915	+	0.0784825i	$0.0250075\pi$
$278$	18.3541	−	24.6670i	1.10081	−	1.47943i
$279$	4.59492	−	2.09829i	0.275091	−	0.125622i
$280$	−6.25104	−	11.3055i	−0.373571	−	0.675631i
$281$	−0.760849	+	1.31783i	−0.0453885	+	0.0786151i	−0.887827	−	0.460177i	$-0.847786\pi$
$281$	−0.760849	+	1.31783i	−0.0453885	+	0.0786151i	0.842439	+	0.538792i	$0.181119\pi$
$282$	−15.8910	+	11.3852i	−0.946296	+	0.677980i
$283$		−	5.76583i		−	0.342743i	−0.985207	−	0.171371i	$-0.945180\pi$
$283$		−	5.76583i		−	0.342743i	0.985207	−	0.171371i	$-0.0548198\pi$
$284$	−11.0511	−	10.4156i	−0.655765	−	0.618052i
$285$	−3.08090	−	14.1635i	−0.182497	−	0.838973i
$286$	−1.56737	+	13.4394i	−0.0926806	+	0.794687i
$287$	7.81435	−	2.67475i	0.461267	−	0.157886i
$288$	13.2413	+	10.6145i	0.780252	+	0.625466i
$289$	−5.54181	−	9.59870i	−0.325989	−	0.564629i
$290$	15.1654	−	20.3815i	0.890542	−	1.19684i
$291$	−5.41554	−	1.73123i	−0.317465	−	0.101487i
$292$	−12.6894	+	3.80599i	−0.742589	+	0.222729i
$293$	−7.75025	−	13.4238i	−0.452775	−	0.784229i	0.545783	−	0.837927i	$-0.316232\pi$
$293$	−7.75025	−	13.4238i	−0.452775	−	0.784229i	−0.998557	+	0.0536981i	$0.982899\pi$
$294$	−16.6789	+	3.97678i	−0.972732	+	0.231931i
$295$	−8.89968	−	5.13823i	−0.518160	−	0.299160i
$296$	0.453037	+	2.55788i	0.0263323	+	0.148674i
$297$	−29.1711	−	12.4930i	−1.69268	−	0.724920i
$298$	−12.2377	−	1.42723i	−0.708911	−	0.0826770i
$299$		−	8.01178i		−	0.463333i
$300$	6.99579	+	0.126039i	0.403902	+	0.00727684i
$301$	4.44905	−	5.09922i	0.256439	−	0.293914i
$302$	−0.137637	+	0.184976i	−0.00792009	+	0.0106442i
$303$	16.6329	+	18.2972i	0.955533	+	1.05115i
$304$	−10.6717	−	16.1897i	−0.612066	−	0.928541i
$305$	6.86348	−	11.8879i	0.393002	−	0.680699i
$306$	−9.82055	+	3.17043i	−0.561403	+	0.181241i
$307$			14.6360i			0.835319i	0.908604	+	0.417660i	$0.137150\pi$
$307$			14.6360i			0.835319i	−0.908604	+	0.417660i	$0.862850\pi$
$308$	29.4276	+	13.3544i	1.67679	+	0.760937i
$309$	−0.643000	+	2.01139i	−0.0365790	+	0.114424i
$310$	−0.476190	+	4.08308i	−0.0270458	+	0.231903i
$311$	25.5910			1.45113			0.725567	−	0.688151i	$-0.241578\pi$
$311$	25.5910			1.45113			0.725567	+	0.688151i	$0.241578\pi$
$312$	−7.09996	+	2.91419i	−0.401956	+	0.164983i
$313$		−	5.36474i		−	0.303233i	−0.988439	−	0.151617i	$-0.951552\pi$
$313$		−	5.36474i		−	0.303233i	0.988439	−	0.151617i	$-0.0484479\pi$
$314$	−7.32497	+	3.16190i	−0.413372	+	0.178436i
$315$	−3.90551	+	13.1338i	−0.220051	+	0.740007i
$316$	10.4232	+	9.82379i	0.586353	+	0.552632i
$317$			22.1168i			1.24220i	0.783730	+	0.621102i	$0.213315\pi$
$317$			22.1168i			1.24220i	−0.783730	+	0.621102i	$0.786685\pi$
$318$	−25.1592	+	2.47572i	−1.41086	+	0.138832i
$319$			63.5500i			3.55812i
$320$	−12.9704	+	4.74328i	−0.725068	+	0.265158i
$321$	2.49109	+	2.74036i	0.139039	+	0.152952i
$322$	−18.2236	−	5.83578i	−1.01556	−	0.325215i
$323$	11.7912			0.656078
$324$	−1.81399	−	17.9084i	−0.100777	−	0.994909i
$325$	−1.58214	+	2.74035i	−0.0877615	+	0.152007i
$326$	16.3694	+	12.1801i	0.906619	+	0.674595i
$327$	16.9836	+	5.42930i	0.939196	+	0.300241i
$328$	−1.53990	−	8.69440i	−0.0850269	−	0.480068i
$329$	−20.7196	−	4.06674i	−1.14231	−	0.224207i
$330$	20.9928	−	15.0404i	1.15562	−	0.827948i
$331$	9.66929			0.531472			0.265736	−	0.964046i	$-0.414385\pi$
$331$	9.66929			0.531472			0.265736	+	0.964046i	$0.414385\pi$
$332$	21.1844	−	6.35394i	1.16264	−	0.348718i
$333$	1.59827	−	2.24434i	0.0875845	−	0.122989i
$334$	24.4658	+	18.2044i	1.33871	+	0.996102i
$335$	4.59319	−	7.95564i	0.250953	−	0.434663i
$336$	1.45702	+	18.2723i	0.0794871	+	0.996836i
$337$	5.64708	+	9.78103i	0.307616	+	0.532807i	0.977840	−	0.209352i	$-0.0671354\pi$
$337$	5.64708	+	9.78103i	0.307616	+	0.532807i	−0.670224	+	0.742159i	$0.733802\pi$
$338$	−1.72763	+	14.8135i	−0.0939709	+	0.805750i
$339$	1.30632	+	1.43704i	0.0709498	+	0.0780493i
$340$	1.93256	−	8.17265i	0.104808	−	0.443224i
$341$	−5.14156	−	8.90544i	−0.278431	−	0.482256i
$342$	−4.31399	+	20.1092i	−0.233274	+	1.08738i
$343$	−15.4769	−	10.1718i	−0.835675	−	0.549224i
$344$	−4.65450	−	5.53842i	−0.250954	−	0.298612i
$345$	−11.3151	+	10.2859i	−0.609185	+	0.553772i
$346$	21.5348	−	9.29570i	1.15772	−	0.499740i
$347$	16.1150			0.865099			0.432549	−	0.901610i	$-0.357614\pi$
$347$	16.1150			0.865099			0.432549	+	0.901610i	$0.357614\pi$
$348$	−31.5371	+	17.4582i	−1.69057	+	0.935857i
$349$	5.59246	−	9.68643i	0.299358	−	0.518503i	−0.676631	−	0.736322i	$-0.736561\pi$
$349$	5.59246	−	9.68643i	0.299358	−	0.518503i	0.975989	+	0.217819i	$0.0698943\pi$
$350$	5.08079	+	5.59482i	0.271580	+	0.299056i
$351$	7.48295	+	3.20471i	0.399410	+	0.171055i
$352$	18.9473	−	28.8879i	1.00989	−	1.53973i
$353$	8.81289	−	5.08813i	0.469063	−	0.270814i	−0.246784	−	0.969070i	$-0.579374\pi$
$353$	8.81289	−	5.08813i	0.469063	−	0.270814i	0.715847	+	0.698257i	$0.246041\pi$
$354$	8.49230	+	11.8532i	0.451361	+	0.629991i
$355$	−11.3517	−	6.55392i	−0.602487	−	0.347846i
$356$	−6.94180	+	29.3563i	−0.367915	+	1.55588i
$357$	−9.76468	−	5.37541i	−0.516801	−	0.284497i
$358$	1.31699	−	11.2925i	0.0696050	−	0.596826i
$359$	−22.6737	+	13.0907i	−1.19667	+	0.690900i	−0.959812	−	0.280644i	$-0.909452\pi$
$359$	−22.6737	+	13.0907i	−1.19667	+	0.690900i	−0.236861	+	0.971543i	$0.576119\pi$
$360$	13.2310	+	6.28598i	0.697333	+	0.331300i
$361$	2.24971	−	3.89662i	0.118406	−	0.205085i
$362$	−8.15175	+	3.51878i	−0.428446	+	0.184943i
$363$	−13.8693	+	43.3853i	−0.727952	+	2.27714i
$364$	−7.54876	−	3.42566i	−0.395663	−	0.179553i
$365$	−9.90299	+	5.71749i	−0.518346	+	0.299267i
$366$	−15.8331	+	11.3437i	−0.827610	+	0.592946i
$367$	3.59791	+	6.23177i	0.187810	+	0.325296i	0.944520	−	0.328455i	$-0.106528\pi$
$367$	3.59791	+	6.23177i	0.187810	+	0.325296i	−0.756710	+	0.653751i	$0.773195\pi$
$368$	−9.16222	+	18.2899i	−0.477614	+	0.953426i
$369$	−5.43261	+	7.62864i	−0.282810	+	0.397131i
$370$	0.888621	+	2.05861i	0.0461972	+	0.107022i
$371$	−20.5756	−	17.9521i	−1.06823	−	0.932029i
$372$	3.00692	−	4.99799i	0.155901	−	0.259134i
$373$	−23.6219	−	13.6381i	−1.22309	−	0.706153i	−0.257517	−	0.966274i	$-0.582904\pi$
$373$	−23.6219	−	13.6381i	−1.22309	−	0.706153i	−0.965576	+	0.260121i	$0.916238\pi$
$374$	8.32569	+	19.2876i	0.430511	+	0.997339i
$375$	20.5101	−	4.46144i	1.05914	−	0.230388i
$376$	−7.70415	+	21.2174i	−0.397311	+	1.09420i
$377$		−	16.3018i		−	0.839587i
$378$	12.7400	−	14.6864i	0.655276	−	0.755389i
$379$	−32.6422			−1.67672			−0.838359	−	0.545118i	$-0.816485\pi$
$379$	−32.6422			−1.67672			−0.838359	+	0.545118i	$0.816485\pi$
$380$	−12.1799	−	11.4795i	−0.624817	−	0.588884i
$381$	0.964732	+	4.43506i	0.0494247	+	0.227215i
$382$	−6.42390	−	14.8819i	−0.328675	−	0.761422i
$383$	4.18394	−	7.24679i	0.213789	−	0.370294i	−0.739108	−	0.673587i	$-0.764753\pi$
$383$	4.18394	−	7.24679i	0.213789	−	0.370294i	0.952897	+	0.303293i	$0.0980861\pi$
$384$	19.5409	+	1.46675i	0.997195	+	0.0748496i
$385$	27.3715	+	5.37236i	1.39498	+	0.273801i
$386$	−8.93796	+	3.85816i	−0.454930	+	0.196375i
$387$	−0.729588	+	7.63861i	−0.0370871	+	0.388293i
$388$	−6.28833	+	1.88609i	−0.319241	+	0.0957517i
$389$	−20.2865	+	11.7124i	−1.02857	+	0.593845i	−0.916574	−	0.399864i	$-0.869057\pi$
$389$	−20.2865	+	11.7124i	−1.02857	+	0.593845i	−0.111995	+	0.993709i	$0.535724\pi$
$390$	−5.38507	+	3.85816i	−0.272683	+	0.195366i
$391$	−6.21968	−	10.7728i	−0.314543	−	0.544804i
$392$	−13.2905	+	14.6752i	−0.671274	+	0.741210i
$393$	16.8831	+	5.39718i	0.851641	+	0.272252i
$394$	−3.27874	−	7.59565i	−0.165180	−	0.382663i
$395$	10.7067	+	6.18154i	0.538714	+	0.311027i
$396$	−35.9401	+	7.14232i	−1.80606	+	0.358915i
$397$	1.72738	+	2.99192i	0.0866949	+	0.150160i	0.906112	−	0.423037i	$-0.139036\pi$
$397$	1.72738	+	2.99192i	0.0866949	+	0.150160i	−0.819417	+	0.573197i	$0.805703\pi$
$398$	1.13303	−	9.71513i	0.0567937	−	0.486975i
$399$	−19.0081	+	11.4970i	−0.951595	+	0.575568i
$400$	6.74568	−	4.44654i	0.337284	−	0.222327i
$401$	10.8264	−	18.7518i	0.540643	−	0.936422i	−0.458224	−	0.888837i	$-0.651514\pi$
$401$	10.8264	−	18.7518i	0.540643	−	0.936422i	0.998867	−	0.0475850i	$-0.0151525\pi$
$402$	−10.5959	+	7.59147i	−0.528473	+	0.378628i
$403$	1.31891	+	2.28442i	0.0656996	+	0.113795i
$404$	27.7864	+	6.57055i	1.38242	+	0.326897i
$405$	−5.08088	−	14.6826i	−0.252471	−	0.729583i
$406$	−37.0802	−	11.8742i	−1.84026	−	0.589309i
$407$	−4.85749	−	2.80447i	−0.240777	−	0.139013i
$408$	−7.28441	+	9.43029i	−0.360632	+	0.466869i
$409$		−	26.3387i		−	1.30236i	−0.758922	−	0.651182i	$-0.774274\pi$
$409$		−	26.3387i		−	1.30236i	0.758922	−	0.651182i	$-0.225726\pi$
$410$	−3.02048	−	6.99736i	−0.149171	−	0.345575i
$411$	0.576105	+	0.633753i	0.0284172	+	0.0312607i
$412$	0.700515	+	2.33556i	0.0345119	+	0.115065i
$413$	−3.03341	+	15.4548i	−0.149264	+	0.760483i
$414$	20.6480	−	6.66592i	1.01479	−	0.327612i
$415$	16.5326	−	9.54511i	0.811554	−	0.468551i
$416$	−4.86035	+	7.41033i	−0.238298	+	0.363321i
$417$	−27.8642	+	25.3296i	−1.36452	+	1.24040i
$418$	41.5861	+	4.85000i	2.03404	+	0.237221i
$419$	−25.9262	+	14.9685i	−1.26658	+	0.731259i	−0.974339	−	0.225086i	$-0.927734\pi$
$419$	−25.9262	+	14.9685i	−1.26658	+	0.731259i	−0.292239	+	0.956345i	$0.594400\pi$
$420$	4.85332	+	15.0592i	0.236818	+	0.734813i
$421$	−23.1523	−	13.3670i	−1.12837	−	0.651466i	−0.184848	−	0.982767i	$-0.559179\pi$
$421$	−23.1523	−	13.3670i	−1.12837	−	0.651466i	−0.943525	+	0.331301i	$0.892513\pi$
$422$	−5.64680	−	4.20166i	−0.274882	−	0.204533i
$423$	21.7787	−	9.94535i	1.05892	−	0.483559i
$424$	−22.3478	+	18.7811i	−1.08530	+	0.912092i
$425$			4.91297i			0.238314i
$426$	10.8321	+	15.1190i	0.524817	+	0.732518i
$427$	−20.6441	−	4.05192i	−0.999036	−	0.196086i
$428$	4.16154	+	0.984066i	0.201156	+	0.0475666i
$429$	5.04595	−	15.7844i	0.243621	−	0.762080i
$430$	−5.00984	−	3.72770i	−0.241596	−	0.179766i
$431$	−1.21385	−	0.700816i	−0.0584691	−	0.0337571i	0.470480	−	0.882410i	$-0.344081\pi$
$431$	−1.21385	−	0.700816i	−0.0584691	−	0.0337571i	−0.528950	+	0.848653i	$0.677414\pi$
$432$	−13.4177	−	15.8734i	−0.645561	−	0.763709i
$433$			11.2064i			0.538547i	0.963064	+	0.269273i	$0.0867835\pi$
$433$			11.2064i			0.538547i	−0.963064	+	0.269273i	$0.913216\pi$
$434$	6.15685	−	1.33603i	0.295538	−	0.0641315i
$435$	−23.0232	+	20.9290i	−1.10388	+	1.00347i
$436$	19.7207	−	5.91494i	0.944452	−	0.283274i
$437$	−24.7913			−1.18593
$438$	16.1473	−	1.58893i	0.771546	−	0.0759218i
$439$	17.6884			0.844222			0.422111	−	0.906544i	$-0.361289\pi$
$439$	17.6884			0.844222			0.422111	+	0.906544i	$0.361289\pi$
$440$	10.1775	−	28.0291i	0.485196	−	1.33624i
$441$	20.9826	−	0.855536i	0.999170	−	0.0407398i
$442$	−2.13570	−	4.94765i	−0.101585	−	0.235336i
$443$	15.0546			0.715267			0.357634	−	0.933862i	$-0.383584\pi$
$443$	15.0546			0.715267			0.357634	+	0.933862i	$0.383584\pi$
$444$	0.0573099	−	3.18099i	0.00271981	−	0.150963i
$445$			26.0379i			1.23432i
$446$	3.65222	−	31.3159i	0.172938	−	1.48285i
$447$	14.3731	+	4.59477i	0.679824	+	0.217325i
$448$	13.3153	+	16.4531i	0.629088	+	0.777334i
$449$	13.7481			0.648815			0.324407	−	0.945917i	$-0.394835\pi$
$449$	13.7481			0.648815			0.324407	+	0.945917i	$0.394835\pi$
$450$	−8.37881	−	1.79749i	−0.394981	−	0.0847345i
$451$	16.5109	+	9.53258i	0.777468	+	0.448872i
$452$	2.18231	+	0.516043i	0.102647	+	0.0242726i
$453$	0.208952	−	0.189945i	0.00981741	−	0.00892440i
$454$	8.59325	−	11.5489i	0.403301	−	0.542016i
$455$	−7.02134	−	1.37812i	−0.329165	−	0.0646071i
$456$	9.01752	+	21.9698i	0.422284	+	1.02883i
$457$	5.29308			0.247600			0.123800	−	0.992307i	$-0.460492\pi$
$457$	5.29308			0.247600			0.123800	+	0.992307i	$0.460492\pi$
$458$	−4.19336	+	35.9558i	−0.195943	+	1.68011i
$459$	12.5496	−	1.50002i	0.585765	−	0.0700148i
$460$	−4.06327	+	17.1832i	−0.189451	+	0.801173i
$461$	8.40677	−	14.5610i	0.391542	−	0.678171i	−0.601111	−	0.799166i	$-0.705275\pi$
$461$	8.40677	−	14.5610i	0.391542	−	0.678171i	0.992653	+	0.120994i	$0.0386083\pi$
$462$	−32.2279	−	22.9749i	−1.49938	−	1.06889i
$463$	−7.21517	+	4.16568i	−0.335318	+	0.193596i	−0.658199	−	0.752844i	$-0.728682\pi$
$463$	−7.21517	+	4.16568i	−0.335318	+	0.193596i	0.322882	+	0.946439i	$0.395348\pi$
$464$	−18.6427	+	37.2150i	−0.865464	+	1.72766i
$465$	1.53303	−	4.79554i	0.0710927	−	0.222388i
$466$	−31.9995	−	23.8101i	−1.48235	−	1.10298i
$467$	2.21824	−	1.28070i	0.102648	−	0.0592638i	−0.447797	−	0.894135i	$-0.647791\pi$
$467$	2.21824	−	1.28070i	0.102648	−	0.0592638i	0.550445	+	0.834871i	$0.314458\pi$
$468$	9.21934	−	1.83215i	0.426164	−	0.0846910i
$469$	−13.8155	−	2.71163i	−0.637938	−	0.125212i
$470$	−2.25701	+	19.3527i	−0.104108	+	0.892673i
$471$	9.54807	−	2.07693i	0.439952	−	0.0957000i
$472$	15.8262	+	5.74657i	0.728458	+	0.264507i
$473$	15.6208			0.718246
$474$	−10.2166	−	14.2600i	−0.469266	−	0.654982i
$475$	8.47961	+	4.89570i	0.389071	+	0.224630i
$476$	−12.8096	+	1.25401i	−0.587127	+	0.0574777i
$477$	30.8222	+	2.94392i	1.41125	+	0.134793i
$478$	1.33521	−	1.79445i	0.0610712	−	0.0820764i
$479$	3.19952	+	5.54174i	0.146190	+	0.253208i	0.929816	−	0.368024i	$-0.119966\pi$
$479$	3.19952	+	5.54174i	0.146190	+	0.253208i	−0.783626	+	0.621233i	$0.786632\pi$
$480$	16.7056	−	2.64937i	0.762502	−	0.120927i
$481$	1.24604	+	0.719403i	0.0568146	+	0.0328019i
$482$	5.28116	−	7.09759i	0.240550	−	0.323287i
$483$	20.5305	+	11.3019i	0.934171	+	0.514257i
$484$	15.1099	+	50.3773i	0.686815	+	2.28988i
$485$	−4.90751	+	2.83335i	−0.222838	+	0.128656i
$486$	−2.03327	+	21.9514i	−0.0922310	+	0.995738i
$487$	−4.16860	−	2.40674i	−0.188897	−	0.109060i	0.402569	−	0.915390i	$-0.368117\pi$
$487$	−4.16860	−	2.40674i	−0.188897	−	0.109060i	−0.591466	+	0.806330i	$0.701451\pi$
$488$	−7.67607	+	21.1400i	−0.347479	+	0.956964i
$489$	−16.8092	−	18.4912i	−0.760137	−	0.836199i
$490$	−8.24901	+	14.9670i	−0.372652	+	0.676138i
$491$	−7.68148	−	13.3047i	−0.346660	−	0.600433i	0.638994	−	0.769212i	$-0.279351\pi$
$491$	−7.68148	−	13.3047i	−0.346660	−	0.600433i	−0.985654	+	0.168779i	$0.946018\pi$
$492$	−0.194800	+	10.8124i	−0.00878226	+	0.487461i
$493$	−12.6554	−	21.9198i	−0.569969	−	0.987216i
$494$	−10.6677	−	1.24412i	−0.479961	−	0.0559756i
$495$	−28.7707	+	13.1383i	−1.29315	+	0.590522i
$496$	−0.398457	−	6.72333i	−0.0178912	−	0.301887i
$497$	−3.86917	+	19.7130i	−0.173556	+	0.884248i
$498$	−26.9572	+	2.65264i	−1.20798	+	0.118868i
$499$	−3.60856	+	6.25021i	−0.161541	+	0.279798i	−0.935422	−	0.353534i	$-0.884980\pi$
$499$	−3.60856	+	6.25021i	−0.161541	+	0.279798i	0.773880	+	0.633332i	$0.218313\pi$
$500$	16.6234	−	17.6377i	0.743421	−	0.788784i
$501$	−25.1230	−	27.6369i	−1.12241	−	1.23473i
$502$	−3.71362	−	8.60311i	−0.165747	−	0.383976i
$503$	19.2536			0.858476			0.429238	−	0.903191i	$-0.358782\pi$
$503$	19.2536			0.858476			0.429238	+	0.903191i	$0.358782\pi$
$504$	2.54795	−	22.3049i	0.113495	−	0.993539i
$505$	24.6454			1.09671
$506$	−17.5050	−	40.5528i	−0.778193	−	1.80279i
$507$	5.56190	−	17.3984i	0.247012	−	0.772690i
$508$	3.81394	+	3.59460i	0.169216	+	0.159485i
$509$	−2.91012	+	5.04048i	−0.128989	+	0.223415i	−0.923285	−	0.384115i	$-0.874506\pi$
$509$	−2.91012	+	5.04048i	−0.128989	+	0.223415i	0.794296	+	0.607531i	$0.207840\pi$
$510$	−4.24571	+	9.36827i	−0.188003	+	0.414834i
$511$	13.2055	+	11.5217i	0.584176	+	0.509691i
$512$	19.5700	−	11.3586i	0.864878	−	0.501982i
$513$	9.91650	−	23.1549i	0.437824	−	1.02231i
$514$	1.14443	+	0.133470i	0.0504787	+	0.00588710i
$515$	1.05234	+	1.82270i	0.0463716	+	0.0803180i
$516$	4.29128	+	7.75194i	0.188913	+	0.341260i
$517$	−24.3696	−	42.2094i	−1.07177	−	1.85637i
$518$	2.54397	−	2.31024i	0.111776	−	0.101506i
$519$	−28.0705	+	6.10600i	−1.23216	+	0.268024i
$520$	−2.61074	+	7.19003i	−0.114489	+	0.315304i
$521$	−13.8959	−	8.02279i	−0.608789	−	0.351485i	0.163702	−	0.986510i	$-0.447656\pi$
$521$	−13.8959	−	8.02279i	−0.608789	−	0.351485i	−0.772492	+	0.635025i	$0.780990\pi$
$522$	42.0131	−	13.5634i	1.83886	−	0.593652i
$523$	15.3603	−	8.86827i	0.671659	−	0.387782i	−0.125046	−	0.992151i	$-0.539908\pi$
$523$	15.3603	−	8.86827i	0.671659	−	0.387782i	0.796705	+	0.604369i	$0.206575\pi$
$524$	19.6041	−	5.87994i	0.856407	−	0.256866i
$525$	−4.79039	−	7.92003i	−0.209070	−	0.345658i
$526$	−7.32374	+	9.84272i	−0.319330	+	0.429163i
$527$	3.54686	+	2.04778i	0.154504	+	0.0892028i
$528$	−29.5702	+	30.2633i	−1.28688	+	1.31704i
$529$	1.57705	+	2.73154i	0.0685676	+	0.118763i
$530$	−15.0415	+	20.2149i	−0.653360	+	0.878081i
$531$	−7.41829	−	16.2449i	−0.321927	−	0.704967i
$532$	−10.6002	+	23.3585i	−0.459577	+	1.01272i
$533$	−4.23537	−	2.44529i	−0.183454	−	0.105917i
$534$	15.2507	−	33.6510i	0.659961	−	1.45622i
$535$	3.69113			0.159581
$536$	−5.13699	+	14.1474i	−0.221884	+	0.611073i
$537$	−4.23987	+	13.2629i	−0.182964	+	0.572337i
$538$	−4.12334	+	35.3555i	−0.177770	+	1.52428i
$539$	−5.79506	−	42.3554i	−0.249611	−	1.82438i
$540$	−14.4237	−	10.6684i	−0.620698	−	0.459093i
$541$	29.8156	−	17.2140i	1.28187	−	0.740090i	0.304682	−	0.952454i	$-0.401450\pi$
$541$	29.8156	−	17.2140i	1.28187	−	0.740090i	0.977191	+	0.212364i	$0.0681164\pi$
$542$	30.2581	+	22.5143i	1.29970	+	0.967073i
$543$	10.6258	−	2.31136i	0.455995	−	0.0991898i
$544$	−0.782566	+	13.7372i	−0.0335522	+	0.588979i
$545$	15.3904	−	8.88563i	0.659251	−	0.380619i
$546$	8.26709	+	5.89352i	0.353799	+	0.252219i
$547$	12.3656	−	21.4178i	0.528715	−	0.915761i	−0.470725	−	0.882280i	$-0.656008\pi$
$547$	12.3656	−	21.4178i	0.528715	−	0.915761i	0.999439	−	0.0334805i	$-0.0106592\pi$
$548$	0.962424	+	0.227581i	0.0411127	+	0.00972180i
$549$	21.6993	−	9.90911i	0.926105	−	0.422910i
$550$	−2.02083	+	17.3275i	−0.0861684	+	0.738848i
$551$	−50.4436			−2.14897
$552$	15.3157	−	19.8275i	0.651879	−	0.843913i
$553$	3.64933	−	18.5929i	0.155185	−	0.790651i
$554$	−23.1586	+	31.1240i	−0.983916	+	1.32233i
$555$	−0.583702	−	2.68339i	−0.0247768	−	0.113904i
$556$	−10.0061	+	42.3149i	−0.424352	+	1.79455i
$557$	11.4325	+	6.60054i	0.484409	+	0.279674i	0.722252	−	0.691630i	$-0.243107\pi$
$557$	11.4325	+	6.60054i	0.484409	+	0.279674i	−0.237843	+	0.971304i	$0.576440\pi$
$558$	−4.79006	+	5.29977i	−0.202779	+	0.224357i
$559$	−4.00705			−0.169480
$560$	14.4528	+	11.1756i	0.610743	+	0.472256i
$561$	−5.46884	−	25.1413i	−0.230894	−	1.06147i
$562$	0.249289	−	2.13752i	0.0105156	−	0.0901658i
$563$		−	42.3959i		−	1.78678i	−0.449286	−	0.893388i	$-0.648322\pi$
$563$		−	42.3959i		−	1.78678i	0.449286	−	0.893388i	$-0.351678\pi$
$564$	14.2520	−	23.6892i	0.600117	−	0.997494i
$565$	1.93562			0.0814322
$566$	3.23158	+	7.48641i	0.135834	+	0.314677i
$567$	−18.7681	+	14.6546i	−0.788188	+	0.615435i
$568$	20.1866	+	7.32987i	0.847010	+	0.307554i
$569$	−10.4218			−0.436904			−0.218452	−	0.975848i	$-0.570101\pi$
$569$	−10.4218			−0.436904			−0.218452	+	0.975848i	$0.570101\pi$
$570$	11.9385	+	16.6633i	0.500049	+	0.697948i
$571$	38.1473			1.59641			0.798207	−	0.602384i	$-0.205782\pi$
$571$	38.1473			1.59641			0.798207	+	0.602384i	$0.205782\pi$
$572$	−5.49730	−	18.3283i	−0.229854	−	0.766345i
$573$	4.21962	+	19.3984i	0.176277	+	0.810381i
$574$	−8.64712	+	7.85265i	−0.360924	+	0.327763i
$575$		−	10.3297i		−	0.430777i
$576$	−23.1418	−	6.36061i	−0.964241	−	0.265026i
$577$	15.3019	+	8.83453i	0.637025	+	0.367786i	0.783468	−	0.621433i	$-0.213449\pi$
$577$	15.3019	+	8.83453i	0.637025	+	0.367786i	−0.146443	+	0.989219i	$0.546782\pi$
$578$	12.5754	+	9.35703i	0.523066	+	0.389201i
$579$	11.6506	−	2.53428i	0.484182	−	0.105321i
$580$	−8.26766	+	34.9633i	−0.343296	+	1.45177i
$581$	−22.0460	−	19.2351i	−0.914622	−	0.798004i
$582$	8.00191	−	0.787405i	0.331690	−	0.0326390i
$583$		−	63.0308i		−	2.61047i
$584$	14.3429	−	12.0538i	0.593512	−	0.498789i
$585$	7.38025	−	3.37023i	0.305136	−	0.139342i
$586$	17.5867	+	13.0859i	0.726500	+	0.540572i
$587$	0.376606	+	0.217434i	0.0155442	+	0.00897445i	0.507752	−	0.861503i	$-0.330477\pi$
$587$	0.376606	+	0.217434i	0.0155442	+	0.00897445i	−0.492208	+	0.870478i	$0.663810\pi$
$588$	19.4272	−	14.5115i	0.801163	−	0.598446i
$589$	7.06879	−	4.08117i	0.291265	−	0.168162i
$590$	14.4353	+	1.68352i	0.594291	+	0.0693094i
$591$	2.15368	+	9.90089i	0.0885906	+	0.407268i
$592$	−2.02185	−	3.06727i	−0.0830975	−	0.126064i
$593$	−32.4341	+	18.7258i	−1.33191	+	0.768978i	−0.985592	−	0.169140i	$-0.945901\pi$
$593$	−32.4341	+	18.7258i	−1.33191	+	0.768978i	−0.346317	+	0.938118i	$0.612568\pi$
$594$	44.8780	−	0.128445i	1.84137	−	0.00527017i
$595$	−10.5109	+	3.59774i	−0.430904	+	0.147493i
$596$	16.6895	−	5.00576i	0.683628	−	0.205044i
$597$	−3.64765	+	11.4103i	−0.149288	+	0.466994i
$598$	4.49038	+	10.4026i	0.183625	+	0.425394i
$599$		−	0.990145i		−	0.0404562i	−0.999795	−	0.0202281i	$-0.993561\pi$
$599$		−	0.990145i		−	0.0404562i	0.999795	−	0.0202281i	$-0.00643924\pi$
$600$	−9.15405	+	3.75729i	−0.373713	+	0.153391i
$601$	−17.4142	−	10.0541i	−0.710342	−	0.410116i	0.100846	−	0.994902i	$-0.467845\pi$
$601$	−17.4142	−	10.0541i	−0.710342	−	0.410116i	−0.811188	+	0.584786i	$0.801179\pi$
$602$	−2.91873	+	9.11445i	−0.118959	+	0.371477i
$603$	14.5217	−	6.63139i	0.591368	−	0.270051i
$604$	0.0750349	−	0.317317i	0.00305313	−	0.0129114i
$605$	22.6987	+	39.3153i	0.922833	+	1.59839i
$606$	−31.8514	−	14.4351i	−1.29387	−	0.586384i
$607$	−13.1872	+	22.8408i	−0.535251	+	0.927081i	0.463900	+	0.885887i	$0.346450\pi$
$607$	−13.1872	+	22.8408i	−0.535251	+	0.927081i	−0.999151	+	0.0411941i	$0.986884\pi$
$608$	22.9301	+	15.0396i	0.929940	+	0.609937i
$609$	41.7741	+	22.9964i	1.69277	+	0.931863i
$610$	−2.24879	+	19.2822i	−0.0910508	+	0.780712i
$611$	6.25128	+	10.8275i	0.252900	+	0.438035i
$612$	10.9742	−	9.62066i	0.443605	−	0.388892i
$613$	6.38950	+	3.68898i	0.258069	+	0.148996i	0.623454	−	0.781860i	$-0.285729\pi$
$613$	6.38950	+	3.68898i	0.258069	+	0.148996i	−0.365384	+	0.930857i	$0.619062\pi$
$614$	−8.20305	−	19.0035i	−0.331048	−	0.766919i
$615$	1.98404	+	9.12102i	0.0800042	+	0.367795i
$616$	−45.6939	−	0.846134i	−1.84106	−	0.0340917i
$617$	−7.63909	−	13.2313i	−0.307538	−	0.532672i	0.670285	−	0.742104i	$-0.266172\pi$
$617$	−7.63909	−	13.2313i	−0.307538	−	0.532672i	−0.977823	+	0.209432i	$0.932839\pi$
$618$	−0.292451	−	2.97200i	−0.0117641	−	0.119551i
$619$	−0.975903	+	0.563438i	−0.0392248	+	0.0226465i	−0.519484	−	0.854480i	$-0.673876\pi$
$619$	−0.975903	+	0.563438i	−0.0392248	+	0.0226465i	0.480259	+	0.877127i	$0.340543\pi$
$620$	−1.67016	−	5.56840i	−0.0670752	−	0.223632i
$621$	−26.3859	+	3.15383i	−1.05883	+	0.126559i
$622$	−33.2277	+	14.3430i	−1.33231	+	0.575104i
$623$	37.7553	−	12.9232i	1.51263	−	0.517755i
$624$	7.58535	−	7.76314i	0.303657	−	0.310775i
$625$	5.41053	−	9.37132i	0.216421	−	0.374853i
$626$	3.00679	+	6.96564i	0.120175	+	0.278403i
$627$	−48.8426	−	15.6139i	−1.95059	−	0.623561i
$628$	7.73867	−	8.21088i	0.308807	−	0.327650i
$629$	2.23394			0.0890728
$630$	−2.29017	−	19.2420i	−0.0912426	−	0.766621i
$631$		−	9.15820i		−	0.364582i	−0.983245	−	0.182291i	$-0.941649\pi$
$631$		−	9.15820i		−	0.364582i	0.983245	−	0.182291i	$-0.0583513\pi$
$632$	−19.0396	−	6.91339i	−0.757355	−	0.275000i
$633$	5.79849	+	6.37871i	0.230469	+	0.253531i
$634$	−12.3958	−	28.7167i	−0.492302	−	1.14049i
$635$	3.91768	+	2.26187i	0.155468	+	0.0897597i
$636$	31.2794	−	17.3155i	1.24031	−	0.686606i
$637$	1.48655	+	10.8650i	0.0588991	+	0.430487i
$638$	−35.6180	−	82.5140i	−1.41013	−	3.26676i
$639$	−9.46218	−	20.7206i	−0.374318	−	0.819696i
$640$	14.1825	−	13.4283i	0.560611	−	0.530800i
$641$	−6.22751	−	10.7864i	−0.245972	−	0.426036i	0.716433	−	0.697656i	$-0.245774\pi$
$641$	−6.22751	−	10.7864i	−0.245972	−	0.426036i	−0.962404	+	0.271621i	$0.912440\pi$
$642$	−4.77035	−	2.16193i	−0.188271	−	0.0853245i
$643$	24.3449	−	14.0555i	0.960069	−	0.554296i	0.0638745	−	0.997958i	$-0.479654\pi$
$643$	24.3449	−	14.0555i	0.960069	−	0.554296i	0.896194	+	0.443662i	$0.146321\pi$
$644$	26.9326	−	2.63660i	1.06129	−	0.103897i
$645$	5.14441	+	5.65919i	0.202561	+	0.222830i
$646$	−15.3098	+	6.60861i	−0.602355	+	0.260012i
$647$	1.11934	−	1.93876i	0.0440059	−	0.0762204i	−0.843184	−	0.537626i	$-0.819321\pi$
$647$	1.11934	−	1.93876i	0.0440059	−	0.0762204i	0.887189	+	0.461405i	$0.152655\pi$
$648$	12.3924	+	22.2357i	0.486821	+	0.873502i
$649$	−31.4842	+	18.1774i	−1.23586	+	0.713527i
$650$	0.518382	−	4.44485i	0.0203326	−	0.174341i
$651$	−7.71446	+	0.157208i	−0.302354	+	0.00616147i
$652$	−28.0809	−	6.64020i	−1.09973	−	0.260050i
$653$	16.3224	+	9.42377i	0.638747	+	0.368781i	0.784132	−	0.620595i	$-0.213109\pi$
$653$	16.3224	+	9.42377i	0.638747	+	0.368781i	−0.145385	+	0.989375i	$0.546442\pi$
$654$	−25.0947	+	2.46937i	−0.981279	+	0.0965600i
$655$	15.2993	−	8.83306i	0.597794	−	0.345136i
$656$	6.87239	+	10.4258i	0.268322	+	0.407061i
$657$	−19.7818	−	1.88942i	−0.771760	−	0.0737132i
$658$	29.1818	−	6.33243i	1.13763	−	0.246864i
$659$	−20.7475	+	35.9357i	−0.808207	+	1.39986i	0.105897	+	0.994377i	$0.466229\pi$
$659$	−20.7475	+	35.9357i	−0.808207	+	1.39986i	−0.914104	+	0.405479i	$0.867105\pi$
$660$	−18.8275	+	31.2945i	−0.732861	+	1.21814i
$661$	19.3522			0.752713			0.376357	−	0.926475i	$-0.377177\pi$
$661$	19.3522			0.752713			0.376357	+	0.926475i	$0.377177\pi$
$662$	−12.5547	+	5.41936i	−0.487953	+	0.210630i
$663$	1.40286	+	6.44924i	0.0544827	+	0.250468i
$664$	−23.9448	+	20.1233i	−0.929239	+	0.780934i
$665$	−4.26437	+	21.7265i	−0.165365	+	0.842517i
$666$	−0.817321	+	3.80986i	−0.0316706	+	0.147629i
$667$	26.6083	+	46.0869i	1.03028	+	1.78449i
$668$	−41.9697	−	9.92445i	−1.62386	−	0.383988i
$669$	−11.7579	+	36.7803i	−0.454585	+	1.42201i
$670$	−1.50494	+	12.9040i	−0.0581408	+	0.498527i
$671$	−24.2808	−	42.0556i	−0.937350	−	1.62354i
$672$	−12.1329	−	22.9083i	−0.468038	−	0.883708i
$673$	−7.71659	+	13.3655i	−0.297453	+	0.515203i	−0.975552	−	0.219767i	$-0.929470\pi$
$673$	−7.71659	+	13.3655i	−0.297453	+	0.515203i	0.678100	+	0.734970i	$0.262804\pi$
$674$	−12.8142	−	9.53477i	−0.493585	−	0.367266i
$675$	9.64784	+	4.13187i	0.371345	+	0.159036i
$676$	−6.05939	−	20.2024i	−0.233054	−	0.777014i
$677$	−41.8589			−1.60877			−0.804383	−	0.594110i	$-0.797504\pi$
$677$	−41.8589			−1.60877			−0.804383	+	0.594110i	$0.797504\pi$
$678$	−2.50157	−	1.13371i	−0.0960721	−	0.0435399i
$679$	6.54409	+	5.70969i	0.251139	+	0.219118i
$680$	2.07128	+	11.6946i	0.0794300	+	0.448468i
$681$	−13.0458	+	11.8591i	−0.499915	+	0.454442i
$682$	11.6671	+	8.68122i	0.446756	+	0.332421i
$683$	−10.1849	+	17.6408i	−0.389715	+	0.675006i	−0.992411	−	0.122965i	$-0.960760\pi$
$683$	−10.1849	+	17.6408i	−0.389715	+	0.675006i	0.602696	+	0.797971i	$0.294093\pi$
$684$	−5.66930	−	28.5279i	−0.216771	−	1.09079i
$685$	0.853633			0.0326157
$686$	25.7964	+	4.53275i	0.984911	+	0.173061i
$687$	13.5000	−	42.2299i	0.515057	−	1.61117i
$688$	9.14758	+	4.58243i	0.348748	+	0.174704i
$689$			16.1686i			0.615976i
$690$	8.92672	−	19.6971i	0.339835	−	0.749855i
$691$			7.19958i			0.273885i	0.990579	+	0.136942i	$0.0437275\pi$
$691$			7.19958i			0.273885i	−0.990579	+	0.136942i	$0.956272\pi$
$692$	−22.7510	+	24.1393i	−0.864865	+	0.917638i
$693$	33.3301	+	35.1970i	1.26611	+	1.33702i
$694$	−20.9239	+	9.03200i	−0.794260	+	0.342850i
$695$			37.5317i			1.42366i
$696$	31.1633	−	40.3436i	1.18124	−	1.52922i
$697$	−7.59329			−0.287616
$698$	−1.83235	+	15.7114i	−0.0693553	+	0.594685i
$699$	32.8591	+	36.1471i	1.24284	+	1.36721i
$700$	−9.73269	−	4.41674i	−0.367861	−	0.166937i
$701$			12.2219i			0.461615i	0.972999	+	0.230808i	$0.0741368\pi$
$701$			12.2219i			0.461615i	−0.972999	+	0.230808i	$0.925863\pi$
$702$	−11.5121	+	0.0329487i	−0.434496	+	0.00124357i
$703$	2.22608	−	3.85569i	0.0839583	−	0.145420i
$704$	−8.41049	+	48.1278i	−0.316982	+	1.81389i
$705$	7.26617	−	22.7296i	0.273660	−	0.856046i
$706$	−8.59101	+	11.5459i	−0.323327	+	0.434534i
$707$	−12.2320	−	35.7361i	−0.460032	−	1.34400i
$708$	−17.6699	−	10.6306i	−0.664075	−	0.399524i
$709$		−	19.3141i		−	0.725358i	−0.931914	−	0.362679i	$-0.881862\pi$
$709$		−	19.3141i		−	0.725358i	0.931914	−	0.362679i	$-0.118138\pi$
$710$	18.4125	+	2.14736i	0.691009	+	0.0805891i
$711$	8.92456	+	19.5433i	0.334697	+	0.732932i
$712$	−7.44009	−	42.0073i	−0.278829	−	1.57429i
$713$	−7.45739	−	4.30552i	−0.279281	−	0.161243i
$714$	15.6913	+	1.50666i	0.587233	+	0.0563854i
$715$	−8.25825	−	14.3037i	−0.308841	−	0.534928i
$716$	4.61912	+	15.4004i	0.172625	+	0.575540i
$717$	−2.02704	+	1.84266i	−0.0757012	+	0.0688153i
$718$	22.1029	−	29.7051i	0.824871	−	1.10858i
$719$	15.6572	+	27.1190i	0.583914	+	1.01137i	0.995010	+	0.0997770i	$0.0318129\pi$
$719$	15.6572	+	27.1190i	0.583914	+	1.01137i	−0.411096	+	0.911592i	$0.634854\pi$
$720$	−20.7023	−	0.746203i	−0.771530	−	0.0278093i
$721$	2.12064	−	2.43055i	0.0789769	−	0.0905183i
$722$	−0.737108	+	6.32031i	−0.0274323	+	0.235218i
$723$	−8.01755	+	7.28825i	−0.298176	+	0.271053i
$724$	8.61214	−	9.13765i	0.320068	−	0.339598i
$725$		−	21.0181i		−	0.780593i
$726$	−6.30810	−	64.1053i	−0.234116	−	2.37917i
$727$	−6.40005	+	11.0852i	−0.237365	+	0.411128i	−0.959957	−	0.280146i	$-0.909617\pi$
$727$	−6.40005	+	11.0852i	−0.237365	+	0.411128i	0.722593	+	0.691274i	$0.242950\pi$
$728$	11.7214	+	0.217050i	0.434423	+	0.00804441i
$729$	7.60869	−	25.9057i	0.281803	−	0.959472i
$730$	9.65365	−	12.9740i	0.357298	−	0.480189i
$731$	−5.38795	+	3.11074i	−0.199281	+	0.115055i
$732$	14.2000	−	23.6028i	0.524849	−	0.872386i
$733$	14.6106	−	25.3062i	0.539653	−	0.934707i	−0.459269	−	0.888297i	$-0.651889\pi$
$733$	14.6106	−	25.3062i	0.539653	−	0.934707i	0.998922	−	0.0464098i	$-0.0147780\pi$
$734$	−8.16430	−	6.07487i	−0.301350	−	0.224228i
$735$	13.4362	−	16.0484i	0.495603	−	0.591954i
$736$	1.64537	−	28.8829i	0.0606491	−	1.06464i
$737$	−16.2492	−	28.1445i	−0.598548	−	1.03672i
$738$	2.77813	−	12.9499i	0.102264	−	0.476694i
$739$	17.9006	−	31.0047i	0.658483	−	1.14053i	−0.322526	−	0.946561i	$-0.604532\pi$
$739$	17.9006	−	31.0047i	0.658483	−	1.14053i	0.981009	−	0.193965i	$-0.0621347\pi$
$740$	−2.30759	−	2.17488i	−0.0848287	−	0.0799502i
$741$	12.5291	+	4.00528i	0.460267	+	0.147138i
$742$	36.7773	+	11.7772i	1.35014	+	0.432355i
$743$	−15.9329	+	9.19887i	−0.584522	+	0.337474i	−0.762928	−	0.646483i	$-0.776239\pi$
$743$	−15.9329	+	9.19887i	−0.584522	+	0.337474i	0.178407	+	0.983957i	$0.442906\pi$
$744$	−1.10298	+	8.17474i	−0.0404371	+	0.299701i
$745$	13.0247	−	7.51984i	0.477190	−	0.275506i
$746$	38.3146	+	4.46846i	1.40280	+	0.163602i
$747$	33.0248	+	3.15431i	1.20831	+	0.115410i
$748$	−21.6203	−	20.3769i	−0.790518	−	0.745055i
$749$	−1.83198	−	5.35217i	−0.0669391	−	0.195564i
$750$	−24.1301	+	17.2881i	−0.881106	+	0.631274i
$751$	−35.9657	−	20.7648i	−1.31241	−	0.757718i	−0.329912	−	0.944012i	$-0.607019\pi$
$751$	−35.9657	−	20.7648i	−1.31241	−	0.757718i	−0.982494	+	0.186294i	$0.940352\pi$
$752$	−1.88858	−	31.8668i	−0.0688694	−	1.16206i
$753$	2.43934	+	11.2141i	0.0888944	+	0.408665i
$754$	9.13672	+	21.1665i	0.332740	+	0.770838i
$755$		−	0.281448i		−	0.0102429i
$756$	−8.31045	+	26.2095i	−0.302248	+	0.953229i
$757$			37.8816i			1.37683i	0.725318	+	0.688414i	$0.241693\pi$
$757$			37.8816i			1.37683i	−0.725318	+	0.688414i	$0.758307\pi$
$758$	42.3830	−	18.2950i	1.53942	−	0.664506i
$759$	11.4984	+	52.8604i	0.417365	+	1.91871i
$760$	22.2485	+	8.07855i	0.807036	+	0.293040i
$761$	21.9321	+	12.6625i	0.795039	+	0.459016i	0.841734	−	0.539893i	$-0.181535\pi$
$761$	21.9321	+	12.6625i	0.795039	+	0.459016i	−0.0466942	+	0.998909i	$0.514869\pi$
$762$	−3.73835	−	5.21783i	−0.135426	−	0.189022i
$763$	−20.5228	−	17.9061i	−0.742976	−	0.648244i
$764$	16.6817	+	15.7224i	0.603524	+	0.568815i
$765$	7.30726	−	10.2611i	0.264195	−	0.370990i
$766$	−1.37085	+	11.7543i	−0.0495307	+	0.424700i
$767$	8.07633	−	4.66287i	0.291619	−	0.168366i
$768$	−26.1943	+	9.04771i	−0.945204	+	0.326481i
$769$	−29.2455	+	16.8849i	−1.05462	+	0.608885i	−0.923939	−	0.382539i	$-0.875050\pi$
$769$	−29.2455	+	16.8849i	−1.05462	+	0.608885i	−0.130681	+	0.991424i	$0.541716\pi$
$770$	−38.5506	+	8.36544i	−1.38927	+	0.301470i
$771$	−1.34413	−	0.429689i	−0.0484075	−	0.0154749i
$772$	9.44276	−	10.0189i	0.339852	−	0.360590i
$773$	−18.3019	+	31.6998i	−0.658274	+	1.14016i	0.322788	+	0.946471i	$0.395380\pi$
$773$	−18.3019	+	31.6998i	−0.658274	+	1.14016i	−0.981062	+	0.193693i	$0.937953\pi$
$774$	−3.33392	−	10.3270i	−0.119835	−	0.371195i
$775$	1.70048	+	2.94532i	0.0610832	+	0.105799i
$776$	7.10773	−	5.97335i	0.255153	−	0.214431i
$777$	−3.60125	+	2.17820i	−0.129194	+	0.0781423i
$778$	19.7758	−	26.5776i	0.708996	−	0.952853i
$779$	−7.56660	+	13.1057i	−0.271101	+	0.469561i
$780$	4.82964	−	8.02766i	0.172929	−	0.287436i
$781$	−40.1588	+	23.1857i	−1.43699	+	0.829649i
$782$	14.1135	+	10.5016i	0.504699	+	0.375535i
$783$	−53.6882	+	6.41720i	−1.91866	+	0.229332i
$784$	9.03155	−	26.5034i	0.322555	−	0.946551i
$785$	4.86949	−	8.43421i	0.173800	−	0.301030i
$786$	−24.9462	+	2.45476i	−0.889802	+	0.0875584i
$787$			40.5878i			1.44680i	0.690429	+	0.723400i	$0.257422\pi$
$787$			40.5878i			1.44680i	−0.690429	+	0.723400i	$0.742578\pi$
$788$	8.51429	+	8.02464i	0.303309	+	0.285866i
$789$	11.1185	−	10.1071i	0.395828	−	0.359823i
$790$	−17.3663	−	2.02535i	−0.617866	−	0.0720588i
$791$	−0.960687	−	2.80667i	−0.0341581	−	0.0997938i
$792$	42.6619	−	29.4171i	1.51593	−	1.04529i
$793$	6.22850	+	10.7881i	0.221181	+	0.383096i
$794$	−3.91974	−	2.91659i	−0.139106	−	0.103506i
$795$	22.8351	−	20.7580i	0.809877	−	0.736209i
$796$	3.97392	+	13.2493i	0.140852	+	0.469608i
$797$	4.73280	+	8.19746i	0.167644	+	0.290369i	0.937591	−	0.347739i	$-0.113051\pi$
$797$	4.73280	+	8.19746i	0.167644	+	0.290369i	−0.769947	+	0.638108i	$0.779717\pi$
$798$	18.2366	−	25.5813i	0.645569	−	0.905567i
$799$	16.8112	+	9.70595i	0.594737	+	0.343372i
$800$	−6.26650	+	9.55420i	−0.221554	+	0.337792i
$801$	−26.2478	+	36.8580i	−0.927422	+	1.30231i
$802$	−3.54721	+	30.4155i	−0.125256	+	1.07401i
$803$			40.4533i			1.42757i
$804$	9.50298	−	15.7955i	0.335144	−	0.557065i
$805$	22.0994	−	7.56435i	0.778903	−	0.266608i
$806$	−2.99284	−	2.22690i	−0.105418	−	0.0784394i
$807$	13.2746	−	41.5247i	0.467287	−	1.46174i
$808$	−39.7607	+	7.04219i	−1.39878	+	0.247743i
$809$	21.9972	−	38.1002i	0.773379	−	1.33953i	−0.162322	−	0.986738i	$-0.551898\pi$
$809$	21.9972	−	38.1002i	0.773379	−	1.33953i	0.935701	−	0.352794i	$-0.114768\pi$
$810$	14.8262	+	16.2163i	0.520941	+	0.569783i
$811$		−	19.1340i		−	0.671884i	−0.941883	−	0.335942i	$-0.890945\pi$
$811$		−	19.1340i		−	0.671884i	0.941883	−	0.335942i	$-0.109055\pi$
$812$	54.8006	−	5.36478i	1.92312	−	0.188267i
$813$	−31.0709	−	34.1800i	−1.08970	−	1.19874i
$814$	7.87885	+	0.918873i	0.276153	+	0.0322065i
$815$	−24.9067			−0.872442
$816$	4.17275	−	16.3271i	0.146075	−	0.571563i
$817$			12.3992i			0.433793i
$818$	14.7621	+	34.1984i	0.516144	+	1.19572i
$819$	−8.54983	−	9.02873i	−0.298755	−	0.315489i
$820$	7.84364	+	7.39255i	0.273912	+	0.258159i
$821$		−	3.92792i		−	0.137085i	−0.997648	−	0.0685427i	$-0.978165\pi$
$821$		−	3.92792i		−	0.137085i	0.997648	−	0.0685427i	$-0.0218349\pi$
$822$	−1.10322	−	0.499981i	−0.0384793	−	0.0174388i
$823$		−	10.4001i		−	0.362526i	−0.983435	−	0.181263i	$-0.941981\pi$
$823$		−	10.4001i		−	0.362526i	0.983435	−	0.181263i	$-0.0580186\pi$
$824$	−2.21857	−	2.63989i	−0.0772875	−	0.0919650i
$825$	6.50580	−	20.3510i	0.226503	−	0.708532i
$826$	−4.72340	−	21.7669i	−0.164348	−	0.757367i
$827$	−16.0448			−0.557932			−0.278966	−	0.960301i	$-0.589992\pi$
$827$	−16.0448			−0.557932			−0.278966	+	0.960301i	$0.589992\pi$
$828$	−23.0735	+	20.2277i	−0.801860	+	0.702962i
$829$	7.50457	−	12.9983i	0.260644	−	0.451449i	−0.705769	−	0.708442i	$-0.749398\pi$
$829$	7.50457	−	12.9983i	0.260644	−	0.451449i	0.966413	+	0.256993i	$0.0827317\pi$
$830$	−16.1164	+	21.6595i	−0.559407	+	0.751814i
$831$	35.1581	−	31.9600i	1.21962	−	1.10868i
$832$	2.15746	−	12.3457i	0.0747963	−	0.428012i
$833$	10.4335	+	13.4553i	0.361500	+	0.466197i
$834$	21.9827	−	48.5053i	0.761197	−	1.67960i
$835$	−37.2255			−1.28824
$836$	−56.7142	+	17.0106i	−1.96150	+	0.588323i
$837$	7.00428	−	5.24294i	0.242103	−	0.181222i
$838$	25.2734	−	33.9662i	0.873057	−	1.17334i
$839$	−24.6028	+	42.6133i	−0.849382	+	1.47117i	0.0323785	+	0.999476i	$0.489692\pi$
$839$	−24.6028	+	42.6133i	−0.849382	+	1.47117i	−0.881761	+	0.471697i	$0.843642\pi$
$840$	−14.7419	−	16.8329i	−0.508642	−	0.580789i
$841$	39.6407	+	68.6598i	1.36692	+	2.36758i
$842$	37.5530	+	4.37963i	1.29416	+	0.150932i
$843$	−0.802553	+	2.51050i	−0.0276414	+	0.0864662i
$844$	9.68678	+	2.29060i	0.333433	+	0.0788458i
$845$	−9.10264	−	15.7662i	−0.313140	−	0.542375i
$846$	−22.7036	+	25.1195i	−0.780566	+	0.863626i
$847$	45.7418	−	52.4263i	1.57171	−	1.80139i
$848$	18.4903	−	36.9109i	0.634961	−	1.26753i
$849$	−2.12271	−	9.75850i	−0.0728511	−	0.334911i
$850$	−2.75358	−	6.37906i	−0.0944471	−	0.218800i
$851$	−4.69691			−0.161008
$852$	−22.5383	−	13.5596i	−0.772149	−	0.464544i
$853$	−25.3892	+	43.9754i	−0.869309	+	1.50569i	−0.00660589	+	0.999978i	$0.502103\pi$
$853$	−25.3892	+	43.9754i	−0.869309	+	1.50569i	−0.862704	+	0.505710i	$0.831231\pi$
$854$	29.0755	−	6.30935i	0.994942	−	0.215902i
$855$	−10.4287	−	22.8371i	−0.356653	−	0.781011i
$856$	−5.95493	+	1.05470i	−0.203535	+	0.0360490i
$857$	27.8210	−	16.0624i	0.950346	−	0.548682i	0.0571573	−	0.998365i	$-0.481796\pi$
$857$	27.8210	−	16.0624i	0.950346	−	0.548682i	0.893188	+	0.449683i	$0.148463\pi$
$858$	2.29502	+	23.3228i	0.0783506	+	0.796228i
$859$	−46.2600	−	26.7082i	−1.57837	−	0.911272i	−0.995087	−	0.0990034i	$-0.968435\pi$
$859$	−46.2600	−	26.7082i	−1.57837	−	0.911272i	−0.583283	−	0.812269i	$-0.698232\pi$
$860$	8.59410	+	2.03222i	0.293056	+	0.0692981i
$861$	12.2409	−	7.40382i	0.417167	−	0.252322i
$862$	1.96886	+	0.229619i	0.0670598	+	0.00782087i
$863$	−30.0193	+	17.3316i	−1.02187	+	0.589976i	−0.914645	−	0.404259i	$-0.867530\pi$
$863$	−30.0193	+	17.3316i	−1.02187	+	0.589976i	−0.107224	+	0.994235i	$0.534196\pi$
$864$	26.3183	+	13.0899i	0.895367	+	0.445329i
$865$	−14.3159	+	24.7959i	−0.486755	+	0.843084i
$866$	−6.28089	−	14.5506i	−0.213433	−	0.494448i
$867$	−12.9132	−	14.2053i	−0.438554	−	0.482437i
$868$	−7.24531	+	5.18546i	−0.245922	+	0.176006i
$869$	37.8770	−	21.8683i	1.28489	−	0.741831i
$870$	18.1635	−	40.0782i	0.615800	−	1.35878i
$871$	4.16825	+	7.21962i	0.141236	+	0.244627i
$872$	−22.2905	+	18.7329i	−0.754850	+	0.634377i
$873$	−9.80302	−	0.936317i	−0.331782	−	0.0316895i
$874$	32.1892	−	13.8948i	1.08882	−	0.469999i
$875$	−31.4621	−	6.17524i	−1.06361	−	0.208761i
$876$	−20.0752	+	11.1132i	−0.678279	+	0.375479i
$877$	−2.73401	−	1.57848i	−0.0923210	−	0.0533016i	0.453129	−	0.891445i	$-0.350308\pi$
$877$	−2.73401	−	1.57848i	−0.0923210	−	0.0533016i	−0.545450	+	0.838144i	$0.683641\pi$
$878$	−22.9668	+	9.91386i	−0.775093	+	0.334577i
$879$	−18.0591	−	19.8662i	−0.609119	−	0.670070i
$880$	2.49490	+	42.0976i	0.0841032	+	1.41911i
$881$			5.24089i			0.176570i	0.996095	+	0.0882850i	$0.0281386\pi$
$881$			5.24089i			0.176570i	−0.996095	+	0.0882850i	$0.971861\pi$
$882$	−26.7645	+	12.8710i	−0.901207	+	0.433388i
$883$	26.9883			0.908229			0.454115	−	0.890943i	$-0.349956\pi$
$883$	26.9883			0.908229			0.454115	+	0.890943i	$0.349956\pi$
$884$	5.54604	+	5.22709i	0.186534	+	0.175806i
$885$	−16.9541	−	5.41987i	−0.569907	−	0.182187i
$886$	−19.5471	+	8.43770i	−0.656698	+	0.283470i
$887$	−13.6962	+	23.7224i	−0.459872	+	0.796522i	−0.998954	−	0.0457318i	$-0.985438\pi$
$887$	−13.6962	+	23.7224i	−0.459872	+	0.796522i	0.539082	+	0.842253i	$0.318771\pi$
$888$	1.70845	+	4.16236i	0.0573317	+	0.139680i
$889$	1.33532	−	6.80329i	0.0447852	−	0.228175i
$890$	−14.5935	−	33.8080i	−0.489176	−	1.13325i
$891$	−53.9706	−	10.4047i	−1.80808	−	0.348571i
$892$	12.8096	+	42.7079i	0.428897	+	1.42996i
$893$	33.5042	−	19.3437i	1.12118	−	0.647311i
$894$	−21.2374	+	2.08981i	−0.710286	+	0.0698937i
$895$	6.93901	+	12.0187i	0.231946	+	0.401742i
$896$	−26.5102	−	13.9000i	−0.885643	−	0.464366i
$897$	−2.94956	−	13.5597i	−0.0984831	−	0.452746i
$898$	−17.8507	+	7.70545i	−0.595687	+	0.257134i
$899$	−15.1738	−	8.76059i	−0.506074	−	0.292182i
$900$	11.8866	−	2.36220i	0.396219	−	0.0787401i
$901$	12.5520	+	21.7407i	0.418167	+	0.724286i
$902$	−26.7807	−	3.12331i	−0.891700	−	0.103995i
$903$	5.65261	−	10.2682i	0.188107	−	0.341705i
$904$	−3.12276	+	0.553085i	−0.103861	+	0.0183953i
$905$	5.41912	−	9.38619i	0.180138	−	0.312007i
$906$	−0.164846	+	0.363738i	−0.00547666	+	0.0120844i
$907$	21.7463	+	37.6657i	0.722074	+	1.25067i	0.960167	+	0.279426i	$0.0901443\pi$
$907$	21.7463	+	37.6657i	0.722074	+	1.25067i	−0.238093	+	0.971242i	$0.576522\pi$
$908$	−4.68476	+	19.8115i	−0.155469	+	0.657467i
$909$	34.8868	+	24.8441i	1.15712	+	0.824027i
$910$	9.88898	−	2.14590i	0.327817	−	0.0711359i
$911$	2.50635	+	1.44704i	0.0830390	+	0.0479426i	0.540945	−	0.841058i	$-0.318067\pi$
$911$	2.50635	+	1.44704i	0.0830390	+	0.0479426i	−0.457906	+	0.889001i	$0.651400\pi$
$912$	−24.0219	−	23.4717i	−0.795444	−	0.777226i
$913$		−	67.5351i		−	2.23509i
$914$	−6.87259	+	2.96662i	−0.227325	+	0.0981271i
$915$	7.23968	−	22.6467i	0.239337	−	0.748678i
$916$	−14.7075	−	49.0357i	−0.485950	−	1.62019i
$917$	−20.4014	−	17.8001i	−0.673713	−	0.587813i
$918$	−15.4538	+	8.98133i	−0.510052	+	0.296428i
$919$	−39.8479	+	23.0062i	−1.31446	+	0.758905i	−0.982832	−	0.184505i	$-0.940932\pi$
$919$	−39.8479	+	23.0062i	−1.31446	+	0.758905i	−0.331630	+	0.943410i	$0.607599\pi$
$920$	−4.35493	−	24.5883i	−0.143578	−	0.810651i
$921$	5.38828	+	24.7710i	0.177550	+	0.816232i
$922$	−2.75444	+	23.6179i	−0.0907127	+	0.777813i
$923$	10.3015	−	5.94758i	0.339079	−	0.195767i
$924$	54.7219	+	11.7681i	1.80022	+	0.387141i
$925$	1.60653	+	0.927533i	0.0528225	+	0.0304971i
$926$	7.03351	−	9.45267i	0.231136	−	0.310634i
$927$	−0.347759	+	3.64095i	−0.0114219	+	0.119585i
$928$	3.34788	−	58.7690i	0.109900	−	1.92919i
$929$			12.9477i			0.424801i	0.977183	+	0.212400i	$0.0681281\pi$
$929$			12.9477i			0.424801i	−0.977183	+	0.212400i	$0.931872\pi$
$930$	0.697259	+	7.08580i	0.0228640	+	0.232353i
$931$	33.6201	−	4.59990i	1.10186	−	0.150755i
$932$	54.8934	+	12.9805i	1.79809	+	0.425189i
$933$	43.3121	−	9.42142i	1.41797	−	0.308443i
$934$	−2.16239	+	2.90614i	−0.0707556	+	0.0950918i
$935$	−22.2084	−	12.8220i	−0.726292	−	0.419325i
$936$	−10.9436	+	7.54606i	−0.357704	+	0.246651i
$937$		−	12.5249i		−	0.409172i	−0.978849	−	0.204586i	$-0.934415\pi$
$937$		−	12.5249i		−	0.409172i	0.978849	−	0.204586i	$-0.0655848\pi$
$938$	19.4579	−	4.22236i	0.635324	−	0.137865i
$939$	−1.97505	−	9.07968i	−0.0644532	−	0.296304i
$940$	−7.91611	−	26.3927i	−0.258195	−	0.860836i
$941$	1.57395			0.0513095			0.0256547	−	0.999671i	$-0.491833\pi$
$941$	1.57395			0.0513095			0.0256547	+	0.999671i	$0.491833\pi$
$942$	−11.2333	+	8.04813i	−0.365999	+	0.262222i
$943$	15.9651			0.519895
$944$	−23.7696	+	1.40870i	−0.773636	+	0.0458494i
$945$	−1.77472	+	23.6665i	−0.0577317	+	0.769870i
$946$	−20.2822	+	8.75503i	−0.659433	+	0.284651i
$947$	48.4946			1.57586			0.787932	−	0.615762i	$-0.211152\pi$
$947$	48.4946			1.57586			0.787932	+	0.615762i	$0.211152\pi$
$948$	21.2577	+	12.7892i	0.690418	+	0.415372i
$949$		−	10.3771i		−	0.336854i
$950$	−13.7539	−	1.60405i	−0.446236	−	0.0520424i
$951$	8.14237	+	37.4321i	0.264034	+	1.21382i
$952$	15.9293	−	8.80765i	0.516271	−	0.285458i
$953$	−33.2618			−1.07745			−0.538727	−	0.842480i	$-0.681095\pi$
$953$	−33.2618			−1.07745			−0.538727	+	0.842480i	$0.681095\pi$
$954$	−41.6698	+	13.4525i	−1.34911	+	0.435542i
$955$	17.1355	+	9.89316i	0.554490	+	0.320135i
$956$	−0.727913	+	3.07829i	−0.0235424	+	0.0995589i
$957$	23.3961	+	107.557i	0.756290	+	3.47681i
$958$	−7.26029	−	5.40221i	−0.234569	−	0.174538i
$959$	−0.423675	−	1.23778i	−0.0136812	−	0.0399699i
$960$	−20.2058	+	12.8030i	−0.652140	+	0.413214i
$961$	−28.1649			−0.908544
$962$	−2.02108	−	0.235709i	−0.0651622	−	0.00759956i
$963$	5.22497	+	3.72088i	0.168372	+	0.119904i
$964$	−2.87911	+	12.1755i	−0.0927299	+	0.392148i
$965$	5.94177	−	10.2915i	0.191272	−	0.331294i
$966$	−32.9915	−	3.16780i	−1.06148	−	0.101922i
$967$	0.0642262	−	0.0370810i	0.00206537	−	0.00119244i	−0.498967	−	0.866621i	$-0.666287\pi$
$967$	0.0642262	−	0.0370810i	0.00206537	−	0.00119244i	0.501032	+	0.865429i	$0.332954\pi$
$968$	−47.8540	−	56.9418i	−1.53809	−	1.83018i
$969$	19.9562	−	4.34095i	0.641086	−	0.139451i
$970$	4.78395	−	6.42938i	0.153603	−	0.206435i
$971$	0.741537	−	0.428127i	0.0237971	−	0.0137392i	−0.488054	−	0.872813i	$-0.662293\pi$
$971$	0.741537	−	0.428127i	0.0237971	−	0.0137392i	0.511851	+	0.859074i	$0.328960\pi$
$972$	−9.66314	−	29.6416i	−0.309946	−	0.950754i
$973$	54.4213	−	18.6277i	1.74467	−	0.597177i
$974$	6.76147	+	0.788559i	0.216652	+	0.0252670i
$975$	−1.66886	+	5.22044i	−0.0534464	+	0.167188i
$976$	−1.88170	−	31.7507i	−0.0602317	−	1.01631i
$977$	−42.4077			−1.35674			−0.678372	−	0.734719i	$-0.737314\pi$
$977$	−42.4077			−1.35674			−0.678372	+	0.734719i	$0.737314\pi$
$978$	32.1890	+	14.5881i	1.02929	+	0.466475i
$979$	79.7730	+	46.0570i	2.54956	+	1.47199i
$980$	2.32205	−	24.0566i	0.0741750	−	0.768460i
$981$	30.7431	+	2.93637i	0.981552	+	0.0937511i
$982$	17.4306	+	12.9697i	0.556234	+	0.413881i
$983$	17.4980	+	30.3074i	0.558099	+	0.966656i	0.997655	+	0.0684405i	$0.0218023\pi$
$983$	17.4980	+	30.3074i	0.558099	+	0.966656i	−0.439556	+	0.898215i	$0.644864\pi$
$984$	−5.80711	−	14.1481i	−0.185124	−	0.451026i
$985$	8.74587	+	5.04943i	0.278667	+	0.160888i
$986$	28.7173	+	21.3679i	0.914545	+	0.680492i
$987$	−36.5645	+	0.745124i	−1.16386	+	0.0237176i
$988$	14.5483	−	4.36355i	0.462843	−	0.138823i
$989$	11.3283	−	6.54041i	0.360220	−	0.207973i
$990$	29.9926	−	33.1841i	0.953226	−	1.05466i
$991$	−20.7110	−	11.9575i	−0.657907	−	0.379843i	0.133572	−	0.991039i	$-0.457355\pi$
$991$	−20.7110	−	11.9575i	−0.657907	−	0.379843i	−0.791479	+	0.611196i	$0.790689\pi$
$992$	4.28560	+	8.50633i	0.136068	+	0.270076i
$993$	16.3650	−	3.55978i	0.519328	−	0.112966i
$994$	−6.02479	−	27.7641i	−0.191095	−	0.880624i
$995$	5.96976	+	10.3399i	0.189254	+	0.327798i
$996$	33.5148	−	18.5530i	1.06196	−	0.587873i
$997$	−8.11546	−	14.0564i	−0.257019	−	0.445170i	0.708423	−	0.705788i	$-0.249407\pi$
$997$	−8.11546	−	14.0564i	−0.257019	−	0.445170i	−0.965442	+	0.260618i	$0.916074\pi$
$998$	1.18233	−	10.1378i	0.0374259	−	0.320908i
$999$	1.87876	−	4.38688i	0.0594415	−	0.138795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bf.b.115.14	yes	180
7.5	odd	6		504.2.cz.b.187.72	yes	180
8.3	odd	2	inner	504.2.bf.b.115.13	✓	180
9.4	even	3		504.2.cz.b.283.48	yes	180
56.19	even	6		504.2.cz.b.187.48	yes	180
63.40	odd	6	inner	504.2.bf.b.355.14	yes	180
72.67	odd	6		504.2.cz.b.283.72	yes	180
504.355	even	6	inner	504.2.bf.b.355.13	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bf.b.115.13	✓	180	8.3	odd	2	inner
504.2.bf.b.115.14	yes	180	1.1	even	1	trivial
504.2.bf.b.355.13	yes	180	504.355	even	6	inner
504.2.bf.b.355.14	yes	180	63.40	odd	6	inner
504.2.cz.b.187.48	yes	180	56.19	even	6
504.2.cz.b.187.72	yes	180	7.5	odd	6
504.2.cz.b.283.48	yes	180	9.4	even	3
504.2.cz.b.283.72	yes	180	72.67	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.29841 + 0.560472i) q^{2} +(1.69247 - 0.368153i) q^{3} +(1.37174 - 1.45545i) q^{4} +(0.863157 - 1.49503i) q^{5} +(-1.99119 + 1.42660i) q^{6} +(-2.59622 - 0.509573i) q^{7} +(-0.965350 + 2.65859i) q^{8} +(2.72893 - 1.24618i) q^{9} +O(q^{10})\)	\(q+(-1.29841 + 0.560472i) q^{2} +(1.69247 - 0.368153i) q^{3} +(1.37174 - 1.45545i) q^{4} +(0.863157 - 1.49503i) q^{5} +(-1.99119 + 1.42660i) q^{6} +(-2.59622 - 0.509573i) q^{7} +(-0.965350 + 2.65859i) q^{8} +(2.72893 - 1.24618i) q^{9} +(-0.282810 + 2.42494i) q^{10} +(-3.05357 - 5.28895i) q^{11} +(1.78581 - 2.96831i) q^{12} +(0.783302 + 1.35672i) q^{13} +(3.65656 - 0.793470i) q^{14} +(0.910469 - 2.84808i) q^{15} +(-0.236644 - 3.99299i) q^{16} +(2.10649 + 1.21618i) q^{17} +(-2.84482 + 3.14754i) q^{18} +(4.19816 - 2.42381i) q^{19} +(-0.991908 - 3.30708i) q^{20} +(-4.58162 + 0.0933660i) q^{21} +(6.92910 + 5.15578i) q^{22} +(-4.42895 - 2.55705i) q^{23} +(-0.655060 + 4.85499i) q^{24} +(1.00992 + 1.74923i) q^{25} +(-1.77745 - 1.32256i) q^{26} +(4.15985 - 3.11378i) q^{27} +(-4.30300 + 3.07965i) q^{28} +(-9.01172 - 5.20292i) q^{29} +(0.414102 + 4.20826i) q^{30} +1.68378 q^{31} +(2.54522 + 5.05192i) q^{32} +(-7.11523 - 7.82721i) q^{33} +(-3.41672 - 0.398476i) q^{34} +(-3.00277 + 3.44158i) q^{35} +(1.92964 - 5.68124i) q^{36} +(0.795378 - 0.459211i) q^{37} +(-4.09246 + 5.50005i) q^{38} +(1.82520 + 2.00783i) q^{39} +(3.14143 + 3.73801i) q^{40} +(-2.70354 + 1.56089i) q^{41} +(5.89650 - 2.68910i) q^{42} +(-1.27890 + 2.21511i) q^{43} +(-11.8865 - 2.81076i) q^{44} +(0.492416 - 5.15548i) q^{45} +(7.18375 + 0.837807i) q^{46} +7.98068 q^{47} +(-1.87055 - 6.67091i) q^{48} +(6.48067 + 2.64592i) q^{49} +(-2.29168 - 1.70519i) q^{50} +(4.01291 + 1.28284i) q^{51} +(3.04912 + 0.721016i) q^{52} +(8.93809 + 5.16041i) q^{53} +(-3.65601 + 6.37445i) q^{54} -10.5429 q^{55} +(3.86100 - 6.41036i) q^{56} +(6.21294 - 5.64780i) q^{57} +(14.6170 + 1.70471i) q^{58} -5.95284i q^{59} +(-2.89629 - 5.23196i) q^{60} +7.95160 q^{61} +(-2.18624 + 0.943713i) q^{62} +(-7.71990 + 1.84476i) q^{63} +(-6.13620 - 5.13294i) q^{64} +2.70445 q^{65} +(13.6254 + 6.17505i) q^{66} +5.32138 q^{67} +(4.65964 - 1.39759i) q^{68} +(-8.43726 - 2.69721i) q^{69} +(1.96992 - 6.15156i) q^{70} -7.59296i q^{71} +(0.678708 + 8.45809i) q^{72} +(-5.73649 - 3.31196i) q^{73} +(-0.775352 + 1.04203i) q^{74} +(2.35324 + 2.58872i) q^{75} +(2.23107 - 9.43504i) q^{76} +(5.23263 + 15.2873i) q^{77} +(-3.49519 - 1.58402i) q^{78} +7.16154i q^{79} +(-6.17392 - 3.09279i) q^{80} +(5.89408 - 6.80146i) q^{81} +(2.63547 - 3.54193i) q^{82} +(9.57683 + 5.52919i) q^{83} +(-6.14892 + 6.79638i) q^{84} +(3.63646 - 2.09951i) q^{85} +(0.419025 - 3.59291i) q^{86} +(-17.1676 - 5.48811i) q^{87} +(17.0089 - 3.01252i) q^{88} +(-13.0622 + 7.54148i) q^{89} +(2.25014 + 6.96992i) q^{90} +(-1.34227 - 3.92148i) q^{91} +(-9.79703 + 2.93847i) q^{92} +(2.84976 - 0.619890i) q^{93} +(-10.3622 + 4.47295i) q^{94} -8.36852i q^{95} +(6.16760 + 7.61320i) q^{96} +(-2.84277 - 1.64127i) q^{97} +(-9.89754 + 0.196736i) q^{98} +(-14.9240 - 10.6278i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9}+O(q^{10}) \) 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9	\( 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9} - 8 q^{11} + 12 q^{12} + 10 q^{14} + 14 q^{16} - 18 q^{17} + 8 q^{18} - 6 q^{19} + 36 q^{20} - 16 q^{22} - 12 q^{24} - 78 q^{25} - 6 q^{26} + 16 q^{28} + q^{30} - 26 q^{32} - 36 q^{33} - 12 q^{34} - 12 q^{35} + 2 q^{36} - 27 q^{38} + 24 q^{40} - 42 q^{41} + 22 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} - 9 q^{48} + 2 q^{49} + 15 q^{50} + 9 q^{52} - 51 q^{54} + 14 q^{56} - 26 q^{57} + 19 q^{58} + 37 q^{60} - 8 q^{64} + 24 q^{65} + 6 q^{66} + 28 q^{67} + 12 q^{68} + 27 q^{70} - 28 q^{72} + 18 q^{73} + 49 q^{74} - 18 q^{75} - 12 q^{76} - 33 q^{78} - 63 q^{80} - 22 q^{81} - 54 q^{82} + 6 q^{83} + 31 q^{84} - 13 q^{86} + 29 q^{88} - 66 q^{89} - 51 q^{90} + 2 q^{91} - 60 q^{92} - 45 q^{96} - 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) \) 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9 - 8 * q^11 + 12 * q^12 + 10 * q^14 + 14 * q^16 - 18 * q^17 + 8 * q^18 - 6 * q^19 + 36 * q^20 - 16 * q^22 - 12 * q^24 - 78 * q^25 - 6 * q^26 + 16 * q^28 + q^30 - 26 * q^32 - 36 * q^33 - 12 * q^34 - 12 * q^35 + 2 * q^36 - 27 * q^38 + 24 * q^40 - 42 * q^41 + 22 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 - 9 * q^48 + 2 * q^49 + 15 * q^50 + 9 * q^52 - 51 * q^54 + 14 * q^56 - 26 * q^57 + 19 * q^58 + 37 * q^60 - 8 * q^64 + 24 * q^65 + 6 * q^66 + 28 * q^67 + 12 * q^68 + 27 * q^70 - 28 * q^72 + 18 * q^73 + 49 * q^74 - 18 * q^75 - 12 * q^76 - 33 * q^78 - 63 * q^80 - 22 * q^81 - 54 * q^82 + 6 * q^83 + 31 * q^84 - 13 * q^86 + 29 * q^88 - 66 * q^89 - 51 * q^90 + 2 * q^91 - 60 * q^92 - 45 * q^96 - 6 * q^97 + 31 * q^98 + 4 * q^99

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