LMFDB - Embedded newform 390.2.bl.a.347.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(107,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 4]))

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

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

chi := DirichletCharacter("390.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bl (of order $12$, degree $4$, 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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			347.3
Character	$\chi$	$=$	390.347
Dual form			390.2.bl.a.263.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-1.39645 + 1.02467i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.994998 - 2.00249i) q^{5} +(1.35118 + 1.08366i) q^{6} +(-0.839078 + 3.13148i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.900122 - 2.86178i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-1.39645 + 1.02467i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.994998 - 2.00249i) q^{5} +(1.35118 + 1.08366i) q^{6} +(-0.839078 + 3.13148i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.900122 - 2.86178i) q^{9} +(-1.67674 + 1.47938i) q^{10} +(2.20287 + 1.27183i) q^{11} +(0.697025 - 1.58561i) q^{12} +(0.482914 - 3.57307i) q^{13} +3.24195 q^{14} +(3.44135 + 1.77683i) q^{15} +(0.500000 - 0.866025i) q^{16} +(5.70384 + 1.52834i) q^{17} +(-2.99724 - 0.128768i) q^{18} +(4.11591 - 2.37632i) q^{19} +(1.86294 + 1.23671i) q^{20} +(-2.03699 - 5.23272i) q^{21} +(0.658346 - 2.45698i) q^{22} +(-2.54524 + 0.681994i) q^{23} +(-1.71198 - 0.262889i) q^{24} +(-3.01996 + 3.98495i) q^{25} +(-3.57630 + 0.458318i) q^{26} +(1.67539 + 4.91864i) q^{27} +(-0.839078 - 3.13148i) q^{28} +(2.90115 - 5.02494i) q^{29} +(0.825604 - 3.78396i) q^{30} +9.58133 q^{31} +(-0.965926 - 0.258819i) q^{32} +(-4.37939 + 0.481166i) q^{33} -5.90505i q^{34} +(7.10565 - 1.43557i) q^{35} +(0.651361 + 2.92843i) q^{36} +(8.08601 - 2.16664i) q^{37} +(-3.36063 - 3.36063i) q^{38} +(2.98683 + 5.48442i) q^{39} +(0.712407 - 2.11955i) q^{40} +(-3.68675 - 2.12855i) q^{41} +(-4.52720 + 3.32191i) q^{42} +(-4.65306 - 1.24678i) q^{43} -2.54366 q^{44} +(-6.62631 + 1.04498i) q^{45} +(1.31751 + 2.28200i) q^{46} +(-2.50195 + 2.50195i) q^{47} +(0.189163 + 1.72169i) q^{48} +(-3.03994 - 1.75511i) q^{49} +(4.63079 + 1.88567i) q^{50} +(-9.53114 + 3.71028i) q^{51} +(1.36832 + 3.33582i) q^{52} +(7.04203 + 7.04203i) q^{53} +(4.31742 - 2.89134i) q^{54} +(0.354975 - 5.67670i) q^{55} +(-2.80761 + 1.62097i) q^{56} +(-3.31271 + 7.53583i) q^{57} +(-5.60459 - 1.50174i) q^{58} +(0.0614633 + 0.106457i) q^{59} +(-3.86871 + 0.181890i) q^{60} +(-1.07943 - 1.86963i) q^{61} +(-2.47983 - 9.25485i) q^{62} +(8.20633 + 5.21997i) q^{63} +1.00000i q^{64} +(-7.63554 + 2.58816i) q^{65} +(1.59824 + 4.10563i) q^{66} +(-4.02597 + 1.07875i) q^{67} +(-5.70384 + 1.52834i) q^{68} +(2.85547 - 3.56038i) q^{69} +(-3.22573 - 6.49198i) q^{70} +(-1.88641 + 1.08912i) q^{71} +(2.66007 - 1.38710i) q^{72} +(-8.15170 + 8.15170i) q^{73} +(-4.18563 - 7.24972i) q^{74} +(0.133965 - 8.65922i) q^{75} +(-2.37632 + 4.11591i) q^{76} +(-5.83108 + 5.83108i) q^{77} +(4.52449 - 4.30453i) q^{78} -13.8606i q^{79} +(-2.23171 - 0.139553i) q^{80} +(-7.37956 - 5.15190i) q^{81} +(-1.10182 + 4.11204i) q^{82} +(6.91640 + 6.91640i) q^{83} +(4.38045 + 3.51317i) q^{84} +(-2.61482 - 12.9426i) q^{85} +4.81720i q^{86} +(1.09758 + 9.98976i) q^{87} +(0.658346 + 2.45698i) q^{88} +(-3.53326 + 6.11979i) q^{89} +(2.72439 + 6.13007i) q^{90} +(10.7838 + 4.51031i) q^{91} +(1.86324 - 1.86324i) q^{92} +(-13.3798 + 9.81765i) q^{93} +(3.06424 + 1.76914i) q^{94} +(-8.85389 - 5.87765i) q^{95} +(1.61407 - 0.628324i) q^{96} +(-1.31674 + 4.91414i) q^{97} +(-0.908512 + 3.39061i) q^{98} +(5.62254 - 5.15933i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q+O(q^{10}) $ 112 * q	$ 112 q + 24 q^{13} + 56 q^{16} - 16 q^{18} - 16 q^{21} + 24 q^{27} + 12 q^{30} - 80 q^{31} + 52 q^{33} - 8 q^{36} - 8 q^{37} - 16 q^{40} + 12 q^{42} - 8 q^{43} + 20 q^{45} - 8 q^{46} - 80 q^{51} + 24 q^{52} + 8 q^{55} - 96 q^{57} + 8 q^{58} - 32 q^{60} - 16 q^{61} - 16 q^{63} - 32 q^{66} + 40 q^{67} - 32 q^{70} - 8 q^{72} - 80 q^{73} - 64 q^{75} + 16 q^{76} - 36 q^{78} + 8 q^{81} - 16 q^{82} + 96 q^{85} - 8 q^{87} + 24 q^{90} - 32 q^{91} - 68 q^{93} - 40 q^{97}+O(q^{100}) $ 112 * q + 24 * q^13 + 56 * q^16 - 16 * q^18 - 16 * q^21 + 24 * q^27 + 12 * q^30 - 80 * q^31 + 52 * q^33 - 8 * q^36 - 8 * q^37 - 16 * q^40 + 12 * q^42 - 8 * q^43 + 20 * q^45 - 8 * q^46 - 80 * q^51 + 24 * q^52 + 8 * q^55 - 96 * q^57 + 8 * q^58 - 32 * q^60 - 16 * q^61 - 16 * q^63 - 32 * q^66 + 40 * q^67 - 32 * q^70 - 8 * q^72 - 80 * q^73 - 64 * q^75 + 16 * q^76 - 36 * q^78 + 8 * q^81 - 16 * q^82 + 96 * q^85 - 8 * q^87 + 24 * q^90 - 32 * q^91 - 68 * q^93 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	−1.39645	+	1.02467i	−0.806238	+	0.591591i
$3$	−1.39645	+	1.02467i	−0.806238	+	0.591591i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−0.994998	−	2.00249i	−0.444977	−	0.895542i
$5$	−0.994998	−	2.00249i	−0.444977	−	0.895542i
$6$	1.35118	+	1.08366i	0.551616	+	0.442402i
$7$	−0.839078	+	3.13148i	−0.317142	+	1.18359i	0.604838	+	0.796349i	$0.293238\pi$
$7$	−0.839078	+	3.13148i	−0.317142	+	1.18359i	−0.921979	+	0.387239i	$0.873429\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.900122	−	2.86178i	0.300041	−	0.953926i
$10$	−1.67674	+	1.47938i	−0.530230	+	0.467820i
$11$	2.20287	+	1.27183i	0.664190	+	0.383470i	0.793872	−	0.608085i	$-0.208062\pi$
$11$	2.20287	+	1.27183i	0.664190	+	0.383470i	−0.129681	+	0.991556i	$0.541395\pi$
$12$	0.697025	−	1.58561i	0.201214	−	0.457726i
$13$	0.482914	−	3.57307i	0.133936	−	0.990990i
$13$	0.482914	−	3.57307i	0.133936	−	0.990990i
$14$	3.24195			0.866447
$15$	3.44135	+	1.77683i	0.888552	+	0.458776i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	5.70384	+	1.52834i	1.38338	+	0.370677i	0.872349	−	0.488883i	$-0.162596\pi$
$17$	5.70384	+	1.52834i	1.38338	+	0.370677i	0.511035	+	0.859560i	$0.329262\pi$
$18$	−2.99724	−	0.128768i	−0.706455	−	0.0303510i
$19$	4.11591	−	2.37632i	0.944254	−	0.545166i	0.0529630	−	0.998596i	$-0.483133\pi$
$19$	4.11591	−	2.37632i	0.944254	−	0.545166i	0.891291	+	0.453431i	$0.149800\pi$
$20$	1.86294	+	1.23671i	0.416566	+	0.276537i
$21$	−2.03699	−	5.23272i	−0.444508	−	1.14187i
$22$	0.658346	−	2.45698i	0.140360	−	0.523830i
$23$	−2.54524	+	0.681994i	−0.530719	+	0.142206i	−0.514220	−	0.857658i	$-0.671919\pi$
$23$	−2.54524	+	0.681994i	−0.530719	+	0.142206i	−0.0164986	+	0.999864i	$0.505252\pi$
$24$	−1.71198	−	0.262889i	−0.349457	−	0.0536619i
$25$	−3.01996	+	3.98495i	−0.603992	+	0.796991i
$26$	−3.57630	+	0.458318i	−0.701371	+	0.0898836i
$27$	1.67539	+	4.91864i	0.322430	+	0.946593i
$28$	−0.839078	−	3.13148i	−0.158571	−	0.591794i
$29$	2.90115	−	5.02494i	0.538730	−	0.933107i	−0.460243	−	0.887793i	$-0.652238\pi$
$29$	2.90115	−	5.02494i	0.538730	−	0.933107i	0.998973	−	0.0453143i	$-0.0144289\pi$
$30$	0.825604	−	3.78396i	0.150734	−	0.690854i
$31$	9.58133			1.72086			0.860428	−	0.509571i	$-0.170196\pi$
$31$	9.58133			1.72086			0.860428	+	0.509571i	$0.170196\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	−4.37939	+	0.481166i	−0.762353	+	0.0837602i
$34$		−	5.90505i		−	1.01271i
$35$	7.10565	−	1.43557i	1.20107	−	0.242655i
$36$	0.651361	+	2.92843i	0.108560	+	0.488072i
$37$	8.08601	−	2.16664i	1.32933	−	0.356193i	0.476866	−	0.878976i	$-0.341773\pi$
$37$	8.08601	−	2.16664i	1.32933	−	0.356193i	0.852466	+	0.522783i	$0.175106\pi$
$38$	−3.36063	−	3.36063i	−0.545166	−	0.545166i
$39$	2.98683	+	5.48442i	0.478276	+	0.878210i
$40$	0.712407	−	2.11955i	0.112641	−	0.335130i
$41$	−3.68675	−	2.12855i	−0.575774	−	0.332423i	0.183678	−	0.982986i	$-0.441200\pi$
$41$	−3.68675	−	2.12855i	−0.575774	−	0.332423i	−0.759452	+	0.650563i	$0.774533\pi$
$42$	−4.52720	+	3.32191i	−0.698563	+	0.512582i
$43$	−4.65306	−	1.24678i	−0.709585	−	0.190133i	−0.114065	−	0.993473i	$-0.536387\pi$
$43$	−4.65306	−	1.24678i	−0.709585	−	0.190133i	−0.595520	+	0.803340i	$0.703054\pi$
$44$	−2.54366			−0.383470
$45$	−6.62631	+	1.04498i	−0.987792	+	0.155776i
$46$	1.31751	+	2.28200i	0.194257	+	0.336462i
$47$	−2.50195	+	2.50195i	−0.364946	+	0.364946i	−0.865630	−	0.500684i	$-0.833082\pi$
$47$	−2.50195	+	2.50195i	−0.364946	+	0.364946i	0.500684	+	0.865630i	$0.333082\pi$
$48$	0.189163	+	1.72169i	0.0273034	+	0.248505i
$49$	−3.03994	−	1.75511i	−0.434277	−	0.250730i
$50$	4.63079	+	1.88567i	0.654893	+	0.266675i
$51$	−9.53114	+	3.71028i	−1.33463	+	0.519544i
$52$	1.36832	+	3.33582i	0.189751	+	0.462595i
$53$	7.04203	+	7.04203i	0.967297	+	0.967297i	0.999482	−	0.0321854i	$-0.0102467\pi$
$53$	7.04203	+	7.04203i	0.967297	+	0.967297i	−0.0321854	+	0.999482i	$0.510247\pi$
$54$	4.31742	−	2.89134i	0.587527	−	0.393462i
$55$	0.354975	−	5.67670i	0.0478648	−	0.765446i
$56$	−2.80761	+	1.62097i	−0.375182	+	0.216612i
$57$	−3.31271	+	7.53583i	−0.438779	+	0.998146i
$58$	−5.60459	−	1.50174i	−0.735918	−	0.197189i
$59$	0.0614633	+	0.106457i	0.00800184	+	0.0138596i	0.869999	−	0.493054i	$-0.164120\pi$
$59$	0.0614633	+	0.106457i	0.00800184	+	0.0138596i	−0.861997	+	0.506914i	$0.830786\pi$
$60$	−3.86871	+	0.181890i	−0.499448	+	0.0234819i
$61$	−1.07943	−	1.86963i	−0.138207	−	0.239382i	0.788611	−	0.614893i	$-0.210801\pi$
$61$	−1.07943	−	1.86963i	−0.138207	−	0.239382i	−0.926818	+	0.375511i	$0.877467\pi$
$62$	−2.47983	−	9.25485i	−0.314939	−	1.17537i
$63$	8.20633	+	5.21997i	1.03390	+	0.657654i
$64$			1.00000i			0.125000i
$65$	−7.63554	+	2.58816i	−0.947072	+	0.321022i
$66$	1.59824	+	4.10563i	0.196730	+	0.505368i
$67$	−4.02597	+	1.07875i	−0.491850	+	0.131791i	−0.496215	−	0.868200i	$-0.665277\pi$
$67$	−4.02597	+	1.07875i	−0.491850	+	0.131791i	0.00436500	+	0.999990i	$0.498611\pi$
$68$	−5.70384	+	1.52834i	−0.691692	+	0.185338i
$69$	2.85547	−	3.56038i	0.343758	−	0.428620i
$70$	−3.22573	−	6.49198i	−0.385549	−	0.775940i
$71$	−1.88641	+	1.08912i	−0.223876	+	0.129255i	−0.607744	−	0.794133i	$-0.707925\pi$
$71$	−1.88641	+	1.08912i	−0.223876	+	0.129255i	0.383868	+	0.923388i	$0.374592\pi$
$72$	2.66007	−	1.38710i	0.313492	−	0.163471i
$73$	−8.15170	+	8.15170i	−0.954084	+	0.954084i	−0.998991	−	0.0449068i	$-0.985701\pi$
$73$	−8.15170	+	8.15170i	−0.954084	+	0.954084i	0.0449068	+	0.998991i	$0.485701\pi$
$74$	−4.18563	−	7.24972i	−0.486569	−	0.842763i
$75$	0.133965	−	8.65922i	0.0154690	−	0.999880i
$76$	−2.37632	+	4.11591i	−0.272583	+	0.472127i
$77$	−5.83108	+	5.83108i	−0.664513	+	0.664513i
$78$	4.52449	−	4.30453i	0.512298	−	0.487392i
$79$		−	13.8606i		−	1.55944i	−0.626129	−	0.779720i	$-0.715361\pi$
$79$		−	13.8606i		−	1.55944i	0.626129	−	0.779720i	$-0.284639\pi$
$80$	−2.23171	−	0.139553i	−0.249513	−	0.0156025i
$81$	−7.37956	−	5.15190i	−0.819951	−	0.572434i
$82$	−1.10182	+	4.11204i	−0.121675	+	0.454099i
$83$	6.91640	+	6.91640i	0.759174	+	0.759174i	0.976172	−	0.216998i	$-0.0696265\pi$
$83$	6.91640	+	6.91640i	0.759174	+	0.759174i	−0.216998	+	0.976172i	$0.569627\pi$
$84$	4.38045	+	3.51317i	0.477946	+	0.383318i
$85$	−2.61482	−	12.9426i	−0.283617	−	1.40382i
$86$			4.81720i			0.519453i
$87$	1.09758	+	9.98976i	0.117673	+	1.07101i
$88$	0.658346	+	2.45698i	0.0701800	+	0.261915i
$89$	−3.53326	+	6.11979i	−0.374525	+	0.648696i	−0.990256	−	0.139260i	$-0.955528\pi$
$89$	−3.53326	+	6.11979i	−0.374525	+	0.648696i	0.615731	+	0.787957i	$0.288861\pi$
$90$	2.72439	+	6.13007i	0.287175	+	0.646166i
$91$	10.7838	+	4.51031i	1.13045	+	0.472809i
$92$	1.86324	−	1.86324i	0.194257	−	0.194257i
$93$	−13.3798	+	9.81765i	−1.38742	+	1.01804i
$94$	3.06424	+	1.76914i	0.316053	+	0.182473i
$95$	−8.85389	−	5.87765i	−0.908390	−	0.603034i
$96$	1.61407	−	0.628324i	0.164735	−	0.0641280i
$97$	−1.31674	+	4.91414i	−0.133695	+	0.498955i	−1.00000		0.000559756i	$-0.999822\pi$
$97$	−1.31674	+	4.91414i	−0.133695	+	0.498955i	0.866305	+	0.499515i	$0.166488\pi$
$98$	−0.908512	+	3.39061i	−0.0917735	+	0.342503i
$99$	5.62254	−	5.15933i	0.565087	−	0.518532i
$100$	0.622884	−	4.96105i	0.0622884	−	0.496105i
$101$	10.9151	+	6.30184i	1.08609	+	0.627056i	0.932534	−	0.361083i	$-0.117593\pi$
$101$	10.9151	+	6.30184i	1.08609	+	0.627056i	0.153559	+	0.988139i	$0.450926\pi$
$102$	6.05070	+	8.24608i	0.599109	+	0.816484i
$103$	8.21639	−	8.21639i	0.809585	−	0.809585i	−0.174986	−	0.984571i	$-0.555988\pi$
$103$	8.21639	−	8.21639i	0.809585	−	0.809585i	0.984571	+	0.174986i	$0.0559880\pi$
$104$	2.86801	−	2.18507i	0.281232	−	0.214263i
$105$	−8.45168	+	9.28561i	−0.824799	+	0.906182i
$106$	4.97946	−	8.62468i	0.483648	−	0.837703i
$107$	−2.09600	−	7.82239i	−0.202628	−	0.756219i	−0.990159	−	0.139944i	$-0.955308\pi$
$107$	−2.09600	−	7.82239i	−0.202628	−	0.756219i	0.787531	−	0.616275i	$-0.211359\pi$
$108$	−3.91026	−	3.42197i	−0.376265	−	0.329280i
$109$			7.88508i			0.755254i	0.925958	+	0.377627i	$0.123260\pi$
$109$			7.88508i			0.755254i	−0.925958	+	0.377627i	$0.876740\pi$
$110$	−5.57514	+	1.12636i	−0.531569	+	0.107394i
$111$	−9.07160	+	11.3111i	−0.861038	+	1.07360i
$112$	2.29240	+	2.29240i	0.216612	+	0.216612i
$113$	4.12241	−	15.3850i	0.387804	−	1.44730i	−0.445896	−	0.895085i	$-0.647115\pi$
$113$	4.12241	−	15.3850i	0.387804	−	1.44730i	0.833700	−	0.552218i	$-0.186218\pi$
$114$	8.13645	+	1.24942i	0.762048	+	0.117018i
$115$	3.89820	+	4.41824i	0.363509	+	0.412003i
$116$			5.80230i			0.538730i
$117$	−9.79064	−	4.59819i	−0.905145	−	0.425103i
$118$	0.0869222	−	0.0869222i	0.00800184	−	0.00800184i
$119$	−9.57193	+	16.5791i	−0.877457	+	1.51980i
$120$	1.17699	+	3.68981i	0.107444	+	0.336832i
$121$	−2.26491	−	3.92294i	−0.205901	−	0.356631i
$122$	−1.52655	+	1.52655i	−0.138207	+	0.138207i
$123$	7.32940	−	0.805286i	0.660870	−	0.0726102i
$124$	−8.29767	+	4.79066i	−0.745153	+	0.430214i
$125$	10.9847	+	2.08243i	0.982501	+	0.186258i
$126$	2.91815	−	9.27774i	0.259969	−	0.826526i
$127$	−7.12580	+	1.90935i	−0.632313	+	0.169428i	−0.560719	−	0.828006i	$-0.689475\pi$
$127$	−7.12580	+	1.90935i	−0.632313	+	0.169428i	−0.0715938	+	0.997434i	$0.522809\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	7.77529	−	3.02676i	0.684576	−	0.266492i
$130$	4.47619	+	6.70550i	0.392588	+	0.588111i
$131$			9.65905i			0.843915i	0.906616	+	0.421958i	$0.138657\pi$
$131$			9.65905i			0.843915i	−0.906616	+	0.421958i	$0.861343\pi$
$132$	3.55208	−	2.60640i	0.309169	−	0.226858i
$133$	3.98784	+	14.8828i	0.345789	+	1.29050i
$134$	2.08399	+	3.60958i	0.180030	+	0.311820i
$135$	8.18254	−	8.24900i	0.704241	−	0.709961i
$136$	2.95252	+	5.11392i	0.253177	+	0.438515i
$137$	2.94164	+	0.788210i	0.251321	+	0.0673414i	0.382280	−	0.924046i	$-0.375139\pi$
$137$	2.94164	+	0.788210i	0.251321	+	0.0673414i	−0.130959	+	0.991388i	$0.541806\pi$
$138$	−4.17812	−	1.83668i	−0.355665	−	0.156348i
$139$	13.7958	−	7.96502i	1.17015	−	0.675584i	0.216432	−	0.976298i	$-0.430558\pi$
$139$	13.7958	−	7.96502i	1.17015	−	0.675584i	0.953714	+	0.300714i	$0.0972248\pi$
$140$	−5.43589	+	4.79606i	−0.459416	+	0.405341i
$141$	0.930175	−	6.05749i	0.0783348	−	0.510132i
$142$	1.54025	+	1.54025i	0.129255	+	0.129255i
$143$	5.60812	−	7.25681i	0.468975	−	0.606845i
$144$	−2.02831	−	2.21042i	−0.169026	−	0.184202i
$145$	−12.9490	−	0.809729i	−1.07536	−	0.0672443i
$146$	9.98375	+	5.76412i	0.826261	+	0.477042i
$147$	6.04351	−	0.664004i	0.498460	−	0.0547662i
$148$	−5.91937	+	5.91937i	−0.486569	+	0.486569i
$149$	1.58705	+	2.74886i	0.130016	+	0.225195i	0.923683	−	0.383158i	$-0.125164\pi$
$149$	1.58705	+	2.74886i	0.130016	+	0.225195i	−0.793666	+	0.608353i	$0.791830\pi$
$150$	−8.39883	+	2.11177i	−0.685762	+	0.172425i
$151$	7.11861			0.579304			0.289652	−	0.957132i	$-0.406460\pi$
$151$	7.11861			0.579304			0.289652	+	0.957132i	$0.406460\pi$
$152$	4.59070	+	1.23007i	0.372355	+	0.0997722i
$153$	9.50792	−	14.9474i	0.768670	−	1.20843i
$154$	7.14159	+	4.12320i	0.575486	+	0.332257i
$155$	−9.53340	−	19.1865i	−0.765741	−	1.54110i
$156$	−5.32888	−	3.25623i	−0.426652	−	0.260707i
$157$	−11.8373	−	11.8373i	−0.944721	−	0.944721i	0.0538288	−	0.998550i	$-0.482857\pi$
$157$	−11.8373	−	11.8373i	−0.944721	−	0.944721i	−0.998550	+	0.0538288i	$0.982857\pi$
$158$	−13.3883	+	3.58739i	−1.06512	+	0.285397i
$159$	−17.0495	−	2.61809i	−1.35212	−	0.207628i
$160$	0.442811	+	2.19178i	0.0350073	+	0.173276i
$161$		−	8.54261i		−	0.673252i
$162$	−3.06638	+	8.46152i	−0.240918	+	0.664800i
$163$	−9.86992	−	2.64464i	−0.773072	−	0.207144i	−0.149344	−	0.988785i	$-0.547716\pi$
$163$	−9.86992	−	2.64464i	−0.773072	−	0.207144i	−0.623728	+	0.781641i	$0.714383\pi$
$164$	4.25710			0.332423
$165$	5.32101	+	8.29093i	0.414240	+	0.645448i
$166$	4.89064	−	8.47083i	0.379587	−	0.657464i
$167$	−1.62229	−	6.05449i	−0.125537	−	0.468510i	0.874321	−	0.485348i	$-0.161307\pi$
$167$	−1.62229	−	6.05449i	−0.125537	−	0.468510i	−0.999858	+	0.0168373i	$0.994640\pi$
$168$	2.25972	−	5.14046i	0.174341	−	0.396595i
$169$	−12.5336	−	3.45097i	−0.964122	−	0.265459i
$170$	−11.8248	+	5.87551i	−0.906922	+	0.450631i
$171$	−3.09569	−	13.9178i	−0.236733	−	1.06432i
$172$	4.65306	−	1.24678i	0.354793	−	0.0950664i
$173$	6.47563	−	24.1674i	0.492333	−	1.83741i	−0.0521481	−	0.998639i	$-0.516607\pi$
$173$	6.47563	−	24.1674i	0.492333	−	1.83741i	0.544481	−	0.838773i	$-0.316727\pi$
$174$	9.36529	−	3.64572i	0.709981	−	0.276381i
$175$	−9.94482	−	12.8006i	−0.751758	−	0.967636i
$176$	2.20287	−	1.27183i	0.166048	−	0.0958676i
$177$	−0.194913	−	0.0856829i	−0.0146506	−	0.00644032i
$178$	6.82574	+	1.82895i	0.511611	+	0.137086i
$179$	−4.62899	+	8.01764i	−0.345987	+	0.599266i	−0.985533	−	0.169487i	$-0.945789\pi$
$179$	−4.62899	+	8.01764i	−0.345987	+	0.599266i	0.639546	+	0.768753i	$0.279122\pi$
$180$	5.21607	−	4.21813i	0.388783	−	0.314401i
$181$	−1.39290			−0.103534			−0.0517669	−	0.998659i	$-0.516485\pi$
$181$	−1.39290			−0.103534			−0.0517669	+	0.998659i	$0.516485\pi$
$182$	1.56558	−	11.5837i	0.116049	−	0.858640i
$183$	3.42311	+	1.50478i	0.253044	+	0.111237i
$184$	−2.28200	−	1.31751i	−0.168231	−	0.0971283i
$185$	−12.3842	−	14.0364i	−0.910508	−	1.03198i
$186$	12.9461	+	10.3829i	0.949252	+	0.761311i
$187$	10.6210	+	10.6210i	0.776687	+	0.776687i
$188$	0.915776	−	3.41772i	0.0667898	−	0.249263i
$189$	−16.8084	+	1.11934i	−1.22263	+	0.0814199i
$190$	−3.38581	+	10.0734i	−0.245633	+	0.730805i
$191$	18.4894	−	10.6748i	1.33784	−	0.772405i	0.351357	−	0.936242i	$-0.385720\pi$
$191$	18.4894	−	10.6748i	1.33784	−	0.772405i	0.986487	+	0.163837i	$0.0523870\pi$
$192$	−1.02467	−	1.39645i	−0.0739488	−	0.100780i
$193$	1.24444	+	4.64433i	0.0895770	+	0.334306i	0.996142	−	0.0877612i	$-0.0279713\pi$
$193$	1.24444	+	4.64433i	0.0895770	+	0.334306i	−0.906564	+	0.422067i	$0.861305\pi$
$194$	5.08749			0.365261
$195$	8.01062	−	11.4381i	0.573652	−	0.819099i
$196$	3.51022			0.250730
$197$	−4.34909	−	16.2310i	−0.309860	−	1.15641i	−0.928680	−	0.370881i	$-0.879056\pi$
$197$	−4.34909	−	16.2310i	−0.309860	−	1.15641i	0.618820	−	0.785533i	$-0.287611\pi$
$198$	−6.43875	−	4.09563i	−0.457582	−	0.291063i
$199$	−1.35427	+	0.781887i	−0.0960015	+	0.0554265i	−0.547232	−	0.836981i	$-0.684319\pi$
$199$	−1.35427	+	0.781887i	−0.0960015	+	0.0554265i	0.451231	+	0.892407i	$0.350985\pi$
$200$	−4.95322	+	0.682355i	−0.350246	+	0.0482498i
$201$	4.51668	−	5.63169i	0.318582	−	0.397229i
$202$	3.26207	−	12.1742i	0.229518	−	0.856575i
$203$	13.3012	+	13.3012i	0.933561	+	0.933561i
$204$	6.39907	−	7.97877i	0.448024	−	0.558626i
$205$	−0.594091	+	9.50060i	−0.0414931	+	0.663551i
$206$	−10.0630	−	5.80986i	−0.701121	−	0.404792i
$207$	−0.339308	+	7.89779i	−0.0235835	+	0.548934i
$208$	−2.85291	−	2.20475i	−0.197814	−	0.152872i
$209$	12.0891			0.836219
$210$	11.1567	+	5.76040i	0.769883	+	0.397505i
$211$	−13.3927	+	23.1968i	−0.921991	+	1.59694i	−0.125661	+	0.992073i	$0.540105\pi$
$211$	−13.3927	+	23.1968i	−0.921991	+	1.59694i	−0.796330	+	0.604862i	$0.793228\pi$
$212$	−9.61959	−	2.57756i	−0.660676	−	0.177028i
$213$	1.51829	−	3.45384i	0.104032	−	0.236653i
$214$	−7.01336	+	4.04917i	−0.479423	+	0.276795i
$215$	2.13311	+	10.5583i	0.145477	+	0.720068i
$216$	−2.29332	+	4.66269i	−0.156041	+	0.317256i
$217$	−8.03948	+	30.0037i	−0.545755	+	2.03679i
$218$	7.61641	−	2.04081i	0.515848	−	0.138221i
$219$	3.03064	−	19.7362i	0.204792	−	1.33365i
$220$	2.53093	+	5.09365i	0.170635	+	0.343414i
$221$	8.21532	−	19.6421i	0.552622	−	1.32127i
$222$	13.2735	+	5.83497i	0.890862	+	0.391618i
$223$	−0.580270	−	2.16560i	−0.0388578	−	0.145019i	0.943772	−	0.330598i	$-0.107251\pi$
$223$	−0.580270	−	2.16560i	−0.0388578	−	0.145019i	−0.982629	+	0.185579i	$0.940584\pi$
$224$	1.62097	−	2.80761i	0.108306	−	0.187591i
$225$	8.68572	+	12.2294i	0.579048	+	0.815293i
$226$	−15.9278			−1.05950
$227$	10.8288	+	2.90158i	0.718735	+	0.192584i	0.599607	−	0.800295i	$-0.295324\pi$
$227$	10.8288	+	2.90158i	0.718735	+	0.192584i	0.119128	+	0.992879i	$0.461990\pi$
$228$	−0.899025	−	8.18258i	−0.0595394	−	0.541905i
$229$			2.10597i			0.139167i	0.997576	+	0.0695833i	$0.0221670\pi$
$229$			2.10597i			0.139167i	−0.997576	+	0.0695833i	$0.977833\pi$
$230$	3.25876	−	4.90889i	0.214876	−	0.323683i
$231$	2.16788	−	14.1177i	0.142636	−	0.928876i
$232$	5.60459	−	1.50174i	0.367959	−	0.0985944i
$233$	9.31483	+	9.31483i	0.610235	+	0.610235i	0.943007	−	0.332772i	$-0.107984\pi$
$233$	9.31483	+	9.31483i	0.610235	+	0.610235i	−0.332772	+	0.943007i	$0.607984\pi$
$234$	−1.90750	+	10.6471i	−0.124697	+	0.696025i
$235$	7.49956	+	2.52070i	0.489217	+	0.164432i
$236$	−0.106457	−	0.0614633i	−0.00692979	−	0.00400092i
$237$	14.2025	+	19.3556i	0.922550	+	1.25728i
$238$	18.4915	+	4.95479i	1.19863	+	0.321172i
$239$	−8.59190			−0.555764			−0.277882	−	0.960615i	$-0.589632\pi$
$239$	−8.59190			−0.555764			−0.277882	+	0.960615i	$0.589632\pi$
$240$	3.25946	−	2.09188i	0.210397	−	0.135030i
$241$	4.63448	+	8.02715i	0.298533	+	0.517074i	0.975801	−	0.218663i	$-0.0701694\pi$
$241$	4.63448	+	8.02715i	0.298533	+	0.517074i	−0.677268	+	0.735737i	$0.736836\pi$
$242$	−3.20306	+	3.20306i	−0.205901	+	0.205901i
$243$	15.5841	−	0.367227i	0.999722	−	0.0235576i
$244$	1.86963	+	1.07943i	0.119691	+	0.0691036i
$245$	−0.489862	+	7.83379i	−0.0312961	+	0.500482i
$246$	−2.67484	−	6.87124i	−0.170541	−	0.438094i
$247$	−6.50312	−	15.8540i	−0.413784	−	1.00876i
$248$	6.77502	+	6.77502i	0.430214	+	0.430214i
$249$	−16.7454	−	2.57139i	−1.06120	−	0.162955i
$250$	−0.831579	−	11.1494i	−0.0525937	−	0.705148i
$251$	−13.0347	+	7.52561i	−0.822746	+	0.475012i	−0.851362	−	0.524578i	$-0.824223\pi$
$251$	−13.0347	+	7.52561i	−0.822746	+	0.475012i	0.0286168	+	0.999590i	$0.490890\pi$
$252$	−9.71688	−	0.417460i	−0.612106	−	0.0262975i
$253$	−6.47421	−	1.73476i	−0.407030	−	0.109063i
$254$	3.68859	+	6.38882i	0.231443	+	0.400870i
$255$	16.9133	+	15.3943i	1.05915	+	0.964030i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.866280	+	3.23300i	0.0540371	+	0.201669i	0.987667	−	0.156570i	$-0.0500438\pi$
$257$	0.866280	+	3.23300i	0.0540371	+	0.201669i	−0.933630	+	0.358239i	$0.883377\pi$
$258$	−4.93602	−	6.72697i	−0.307303	−	0.418803i
$259$			27.1392i			1.68635i
$260$	5.31849	−	6.05918i	0.329839	−	0.375774i
$261$	−11.7689	−	12.8255i	−0.728475	−	0.793879i
$262$	9.32993	−	2.49995i	0.576405	−	0.154447i
$263$	−23.8965	+	6.40304i	−1.47352	+	0.394829i	−0.904137	−	0.427243i	$-0.859485\pi$
$263$	−23.8965	+	6.40304i	−1.47352	+	0.394829i	−0.569384	+	0.822072i	$0.692818\pi$
$264$	−3.43693	−	2.75646i	−0.211528	−	0.169648i
$265$	7.09481	−	21.1084i	0.435831	−	1.29668i
$266$	13.3436	−	7.70391i	0.818146	−	0.472357i
$267$	−1.33673	−	12.1664i	−0.0818063	−	0.744569i
$268$	2.94721	−	2.94721i	0.180030	−	0.180030i
$269$	−4.24979	−	7.36085i	−0.259114	−	0.448799i	0.706891	−	0.707323i	$-0.250097\pi$
$269$	−4.24979	−	7.36085i	−0.259114	−	0.448799i	−0.966005	+	0.258524i	$0.916764\pi$
$270$	−10.0857	−	5.76872i	−0.613798	−	0.351073i
$271$	−12.1191	+	20.9909i	−0.736184	+	1.27511i	0.218018	+	0.975945i	$0.430041\pi$
$271$	−12.1191	+	20.9909i	−0.736184	+	1.27511i	−0.954202	+	0.299163i	$0.903293\pi$
$272$	4.17550	−	4.17550i	0.253177	−	0.253177i
$273$	−19.6805	+	4.75136i	−1.19112	+	0.287565i
$274$		−	3.04541i		−	0.183980i
$275$	−11.7207	+	4.93747i	−0.706788	+	0.297741i
$276$	−0.692718	+	4.51112i	−0.0416967	+	0.271537i
$277$	6.98152	−	26.0554i	0.419479	−	1.56552i	−0.356213	−	0.934405i	$-0.615932\pi$
$277$	6.98152	−	26.0554i	0.419479	−	1.56552i	0.775692	−	0.631112i	$-0.217401\pi$
$278$	−11.2642	−	11.2642i	−0.675584	−	0.675584i
$279$	8.62436	−	27.4196i	0.516327	−	1.64157i
$280$	6.03955	+	4.00935i	0.360932	+	0.239605i
$281$			23.5790i			1.40661i	0.710891	+	0.703303i	$0.248292\pi$
$281$			23.5790i			1.40661i	−0.710891	+	0.703303i	$0.751708\pi$
$282$	−6.09183	+	0.669313i	−0.362763	+	0.0398570i
$283$	0.226599	+	0.845678i	0.0134699	+	0.0502703i	0.972334	−	0.233596i	$-0.0750494\pi$
$283$	0.226599	+	0.845678i	0.0134699	+	0.0502703i	−0.958864	+	0.283867i	$0.908383\pi$
$284$	1.08912	−	1.88641i	0.0646275	−	0.111938i
$285$	18.3866	−	0.864458i	1.08913	−	0.0512061i
$286$	−8.46103	−	3.53883i	−0.500311	−	0.209255i
$287$	9.75898	−	9.75898i	0.576054	−	0.576054i
$288$	−1.61013	+	2.53130i	−0.0948781	+	0.149158i
$289$	15.4755	+	8.93481i	0.910326	+	0.525577i
$290$	2.56932	+	12.7174i	0.150876	+	0.746790i
$291$	−3.19659	−	8.21155i	−0.187388	−	0.481370i
$292$	2.98373	−	11.1354i	0.174610	−	0.651652i
$293$	−5.53830	+	20.6692i	−0.323551	+	1.20751i	0.592209	+	0.805784i	$0.298256\pi$
$293$	−5.53830	+	20.6692i	−0.323551	+	1.20751i	−0.915760	+	0.401725i	$0.868411\pi$
$294$	−2.20555	−	5.66573i	−0.128631	−	0.330432i
$295$	0.152025	−	0.229005i	0.00885121	−	0.0133332i
$296$	7.24972	+	4.18563i	0.421381	+	0.243285i
$297$	−2.56499	+	12.9659i	−0.148836	+	0.752360i
$298$	2.24443	−	2.24443i	0.130016	−	0.130016i
$299$	1.20768	+	9.42364i	0.0698419	+	0.544983i
$300$	4.21359	+	7.56609i	0.243272	+	0.436828i
$301$	7.80856	−	13.5248i	0.450078	−	0.779558i
$302$	−1.84243	−	6.87605i	−0.106020	−	0.395672i
$303$	−21.6996	+	2.38415i	−1.24661	+	0.136966i
$304$		−	4.75264i		−	0.272583i
$305$	−2.66989	+	4.02183i	−0.152878	+	0.230290i
$306$	−16.8989	−	5.31527i	−0.966049	−	0.303854i
$307$	6.07344	+	6.07344i	0.346630	+	0.346630i	0.858853	−	0.512223i	$-0.171178\pi$
$307$	6.07344	+	6.07344i	0.346630	+	0.346630i	−0.512223	+	0.858853i	$0.671178\pi$
$308$	2.13432	−	7.96541i	0.121614	−	0.453871i
$309$	−3.05469	+	19.8928i	−0.173775	+	1.13166i
$310$	−16.0653	+	14.1744i	−0.912451	+	0.805052i
$311$			14.9724i			0.849008i	0.905426	+	0.424504i	$0.139552\pi$
$311$			14.9724i			0.849008i	−0.905426	+	0.424504i	$0.860448\pi$
$312$	−1.76606	+	5.99008i	−0.0999834	+	0.339121i
$313$	−15.3539	+	15.3539i	−0.867856	+	0.867856i	−0.992235	−	0.124379i	$-0.960306\pi$
$313$	−15.3539	+	15.3539i	−0.867856	+	0.867856i	0.124379	+	0.992235i	$0.460306\pi$
$314$	−8.37025	+	14.4977i	−0.472361	+	0.818153i
$315$	2.28767	−	21.6270i	0.128896	−	1.21854i
$316$	6.93030	+	12.0036i	0.389860	+	0.675257i
$317$	6.76077	−	6.76077i	0.379722	−	0.379722i	−0.491280	−	0.871002i	$-0.663471\pi$
$317$	6.76077	−	6.76077i	0.379722	−	0.379722i	0.871002	+	0.491280i	$0.163471\pi$
$318$	1.88386	+	17.1462i	0.105642	+	0.961511i
$319$	12.7817	−	7.37952i	0.715638	−	0.413174i
$320$	2.00249	−	0.994998i	0.111943	−	0.0556221i
$321$	10.9423	+	8.77584i	0.610739	+	0.489820i
$322$	−8.25153	+	2.21099i	−0.459840	+	0.123214i
$323$	27.1083	−	7.26365i	1.50835	−	0.404160i
$324$	8.96684	+	0.771898i	0.498158	+	0.0428832i
$325$	12.7801	+	12.7149i	0.708913	+	0.705296i
$326$			10.2181i			0.565928i
$327$	−8.07957	−	11.0111i	−0.446801	−	0.608915i
$328$	−1.10182	−	4.11204i	−0.0608377	−	0.227049i
$329$	−5.73547	−	9.93412i	−0.316206	−	0.547686i
$330$	6.63125	−	7.28555i	0.365038	−	0.401057i
$331$	−1.03570	−	1.79389i	−0.0569273	−	0.0986009i	0.836157	−	0.548490i	$-0.184797\pi$
$331$	−1.03570	−	1.79389i	−0.0569273	−	0.0986009i	−0.893085	+	0.449889i	$0.851464\pi$
$332$	−9.44798	−	2.53158i	−0.518526	−	0.138938i
$333$	1.07795	−	25.0906i	0.0590714	−	1.37496i
$334$	−5.42830	+	3.13403i	−0.297024	+	0.171487i
$335$	6.16603	+	6.98861i	0.336886	+	0.381829i
$336$	−5.55016	−	0.852271i	−0.302786	−	0.0464952i
$337$	−17.8662	−	17.8662i	−0.973233	−	0.973233i	0.0264177	−	0.999651i	$-0.491590\pi$
$337$	−17.8662	−	17.8662i	−0.973233	−	0.973233i	−0.999651	+	0.0264177i	$0.991590\pi$
$338$	−0.0894455	+	12.9997i	−0.00486519	+	0.707090i
$339$	10.0078	+	25.7085i	0.543549	+	1.39629i
$340$	8.73580	+	9.90121i	0.473765	+	0.536968i
$341$	21.1064	+	12.1858i	1.14298	+	0.659898i
$342$	−12.6423	+	6.59240i	−0.683620	+	0.356476i
$343$	−7.99998	+	7.99998i	−0.431958	+	0.431958i
$344$	−2.40860	−	4.17182i	−0.129863	−	0.224930i
$345$	−9.97083	−	2.17549i	−0.536812	−	0.117124i
$346$	−25.0199			−1.34508
$347$	−15.7825	−	4.22890i	−0.847247	−	0.227019i	−0.191023	−	0.981585i	$-0.561181\pi$
$347$	−15.7825	−	4.22890i	−0.847247	−	0.227019i	−0.656224	+	0.754566i	$0.727847\pi$
$348$	−5.94541	−	8.10259i	−0.318708	−	0.434345i
$349$	6.10030	+	3.52201i	0.326542	+	0.188529i	0.654305	−	0.756231i	$-0.272961\pi$
$349$	6.10030	+	3.52201i	0.326542	+	0.188529i	−0.327763	+	0.944760i	$0.606295\pi$
$350$	−9.79054	+	12.9190i	−0.523327	+	0.690550i
$351$	18.3837	−	3.61101i	0.981250	−	0.192741i
$352$	−1.79864	−	1.79864i	−0.0958676	−	0.0958676i
$353$	26.9750	−	7.22794i	1.43574	−	0.384704i	0.544697	−	0.838633i	$-0.316644\pi$
$353$	26.9750	−	7.22794i	1.43574	−	0.384704i	0.891038	+	0.453928i	$0.149978\pi$
$354$	−0.0323160	+	0.210448i	−0.00171758	+	0.0111852i
$355$	4.05794	+	2.69386i	0.215373	+	0.142975i
$356$		−	7.06652i		−	0.374525i
$357$	−3.62131	−	32.9598i	−0.191660	−	1.74442i
$358$	8.94251	+	2.39614i	0.472627	+	0.126640i
$359$	−24.5551			−1.29597			−0.647983	−	0.761655i	$-0.724387\pi$
$359$	−24.5551			−1.29597			−0.647983	+	0.761655i	$0.724387\pi$
$360$	−5.42442	−	3.94660i	−0.285892	−	0.208004i
$361$	1.79381	−	3.10696i	0.0944109	−	0.163524i
$362$	0.360510	+	1.34544i	0.0189480	+	0.0707149i
$363$	7.18252	+	3.15740i	0.376985	+	0.165720i
$364$	−11.5942	+	1.48584i	−0.607700	+	0.0778794i
$365$	24.4346	+	8.21280i	1.27897	+	0.429878i
$366$	0.567541	−	3.69594i	0.0296658	−	0.193190i
$367$	6.11473	−	1.63844i	0.319186	−	0.0855257i	−0.0956688	−	0.995413i	$-0.530499\pi$
$367$	6.11473	−	1.63844i	0.319186	−	0.0855257i	0.414855	+	0.909888i	$0.363832\pi$
$368$	−0.681994	+	2.54524i	−0.0355514	+	0.132680i
$369$	−9.40997	+	8.63472i	−0.489863	+	0.449506i
$370$	−10.3528	+	15.5951i	−0.538218	+	0.810753i
$371$	−27.9608	+	16.1432i	−1.45165	+	0.838111i
$372$	6.67842	−	15.1922i	0.346260	−	0.787681i
$373$	2.63423	+	0.705839i	0.136395	+	0.0365470i	0.326371	−	0.945242i	$-0.394174\pi$
$373$	2.63423	+	0.705839i	0.136395	+	0.0365470i	−0.189976	+	0.981789i	$0.560841\pi$
$374$	7.51021	−	13.0081i	0.388343	−	0.672631i
$375$	−17.4733	+	8.34764i	−0.902318	+	0.431070i
$376$	−3.53828			−0.182473
$377$	−16.5534	−	12.7926i	−0.852544	−	0.658853i
$378$	5.43154	+	15.9460i	0.279368	+	0.820173i
$379$	1.70971	+	0.987101i	0.0878218	+	0.0507040i	0.543268	−	0.839559i	$-0.317187\pi$
$379$	1.70971	+	0.987101i	0.0878218	+	0.0507040i	−0.455446	+	0.890263i	$0.650520\pi$
$380$	10.6065	+	0.663246i	0.544103	+	0.0340238i
$381$	7.99435	−	9.96787i	0.409563	−	0.510670i
$382$	−15.0965	−	15.0965i	−0.772405	−	0.772405i
$383$	−5.61956	+	20.9725i	−0.287146	+	1.07164i	0.660110	+	0.751169i	$0.270509\pi$
$383$	−5.61956	+	20.9725i	−0.287146	+	1.07164i	−0.947257	+	0.320476i	$0.896157\pi$
$384$	−1.08366	+	1.35118i	−0.0553003	+	0.0689520i
$385$	17.4786	+	5.87479i	0.890793	+	0.299407i
$386$	4.16399	−	2.40408i	0.211942	−	0.122365i
$387$	−7.75635	+	12.1938i	−0.394277	+	0.619845i
$388$	−1.31674	−	4.91414i	−0.0668473	−	0.249478i
$389$	−4.09503			−0.207626			−0.103813	−	0.994597i	$-0.533104\pi$
$389$	−4.09503			−0.207626			−0.103813	+	0.994597i	$0.533104\pi$
$390$	−13.1217	−	4.77726i	−0.664441	−	0.241906i
$391$	−15.5599			−0.786900
$392$	−0.908512	−	3.39061i	−0.0458868	−	0.171252i
$393$	−9.89729	−	13.4883i	−0.499252	−	0.680397i
$394$	−14.5524	+	8.40181i	−0.733137	+	0.423277i
$395$	−27.7558	+	13.7913i	−1.39654	+	0.693914i
$396$	−2.28960	+	7.27938i	−0.115057	+	0.365803i
$397$	−2.00061	+	7.46640i	−0.100408	+	0.374728i	−0.997784	−	0.0665394i	$-0.978804\pi$
$397$	−2.00061	+	7.46640i	−0.100408	+	0.374728i	0.897376	+	0.441267i	$0.145471\pi$
$398$	1.10575	+	1.10575i	0.0554265	+	0.0554265i
$399$	−20.8187	−	16.6968i	−1.04224	−	0.835887i
$400$	1.94109	+	4.60784i	0.0970546	+	0.230392i
$401$	−17.4404	−	10.0692i	−0.870930	−	0.502831i	−0.00327255	−	0.999995i	$-0.501042\pi$
$401$	−17.4404	−	10.0692i	−0.870930	−	0.502831i	−0.867657	+	0.497163i	$0.834375\pi$
$402$	−6.60880	−	2.90519i	−0.329617	−	0.144898i
$403$	4.62696	−	34.2347i	0.230485	−	1.70535i
$404$	−12.6037			−0.627056
$405$	−2.97400	+	19.9037i	−0.147779	+	0.989020i
$406$	9.40537	−	16.2906i	0.466781	−	0.808488i
$407$	20.5680	+	5.51119i	1.01952	+	0.273179i
$408$	−9.36310	−	4.11597i	−0.463543	−	0.203771i
$409$	−31.6178	+	18.2545i	−1.56340	+	0.902629i	−0.566490	+	0.824069i	$0.691699\pi$
$409$	−31.6178	+	18.2545i	−1.56340	+	0.902629i	−0.996909	+	0.0785600i	$0.974968\pi$
$410$	9.33064	−	1.88509i	0.460807	−	0.0930979i
$411$	−4.91550	+	1.91350i	−0.242463	+	0.0943862i
$412$	−3.00741	+	11.2238i	−0.148164	+	0.552957i
$413$	−0.384942	+	0.103145i	−0.0189418	+	0.00507543i
$414$	7.71650	−	1.71635i	0.379245	−	0.0843541i
$415$	6.96825	−	20.7319i	0.342058	−	1.01769i
$416$	−1.39124	+	3.32633i	−0.0682110	+	0.163087i
$417$	−11.1036	+	25.2588i	−0.543747	+	1.23693i
$418$	−3.12889	−	11.6772i	−0.153039	−	0.571149i
$419$	1.13380	−	1.96380i	0.0553898	−	0.0959380i	−0.837001	−	0.547201i	$-0.815693\pi$
$419$	1.13380	−	1.96380i	0.0553898	−	0.0959380i	0.892391	+	0.451263i	$0.149027\pi$
$420$	2.67656	−	12.2674i	0.130603	−	0.598588i
$421$	7.13266			0.347624			0.173812	−	0.984779i	$-0.444391\pi$
$421$	7.13266			0.347624			0.173812	+	0.984779i	$0.444391\pi$
$422$	25.8727	+	6.93257i	1.25946	+	0.337472i
$423$	4.90796	+	9.41207i	0.238633	+	0.457631i
$424$			9.95893i			0.483648i
$425$	−23.3157	+	18.1140i	−1.13098	+	0.878659i
$426$	−3.72912	−	0.572635i	−0.180676	−	0.0277443i
$427$	6.76044	−	1.81145i	0.327161	−	0.0876624i
$428$	5.72638	+	5.72638i	0.276795	+	0.276795i
$429$	−0.395629	+	15.8802i	−0.0191012	+	0.766703i
$430$	9.64642	−	4.79311i	0.465192	−	0.231144i
$431$	−17.6769	−	10.2058i	−0.851466	−	0.491594i	0.00967910	−	0.999953i	$-0.496919\pi$
$431$	−17.6769	−	10.2058i	−0.851466	−	0.491594i	−0.861145	+	0.508359i	$0.830252\pi$
$432$	5.09737	+	1.00839i	0.245247	+	0.0485161i
$433$	18.6719	+	5.00312i	0.897314	+	0.240434i	0.677862	−	0.735189i	$-0.262907\pi$
$433$	18.6719	+	5.00312i	0.897314	+	0.240434i	0.219451	+	0.975623i	$0.429573\pi$
$434$	31.0621			1.49103
$435$	18.9123	−	12.1377i	0.906777	−	0.581957i
$436$	−3.94254	−	6.82868i	−0.188814	−	0.327035i
$437$	−8.85533	+	8.85533i	−0.423608	+	0.423608i
$438$	−19.8481	+	2.18072i	−0.948377	+	0.104199i
$439$	20.9830	+	12.1145i	1.00146	+	0.578195i	0.908681	−	0.417492i	$-0.137091\pi$
$439$	20.9830	+	12.1145i	1.00146	+	0.578195i	0.0927818	+	0.995686i	$0.470424\pi$
$440$	4.26504	−	3.76303i	0.203328	−	0.179395i
$441$	−7.75905	+	7.11982i	−0.369479	+	0.339039i
$442$	−21.0991	−	2.85163i	−1.00358	−	0.135638i
$443$	−13.3047	−	13.3047i	−0.632124	−	0.632124i	0.316477	−	0.948600i	$-0.397500\pi$
$443$	−13.3047	−	13.3047i	−0.632124	−	0.632124i	−0.948600	+	0.316477i	$0.897500\pi$
$444$	2.20071	−	14.3315i	0.104441	−	0.680141i
$445$	15.7704	+	0.986155i	0.747590	+	0.0467482i
$446$	−1.94162	+	1.12100i	−0.0919384	+	0.0530807i
$447$	−5.03289	−	2.21243i	−0.238048	−	0.104644i
$448$	−3.13148	−	0.839078i	−0.147949	−	0.0396427i
$449$	−10.6789	−	18.4965i	−0.503971	−	0.872903i	−0.999989	−	0.00459112i	$-0.998539\pi$
$449$	−10.6789	−	18.4965i	−0.503971	−	0.872903i	0.496019	−	0.868312i	$-0.334795\pi$
$450$	9.56466	−	11.5550i	0.450882	−	0.544706i
$451$	−5.41429	−	9.37783i	−0.254949	−	0.441585i
$452$	4.12241	+	15.3850i	0.193902	+	0.723651i
$453$	−9.94075	+	7.29419i	−0.467057	+	0.342711i
$454$		−	11.2108i		−	0.526150i
$455$	−1.69797	−	26.0822i	−0.0796019	−	1.22275i
$456$	−7.67108	+	2.98620i	−0.359231	+	0.139842i
$457$	−3.44410	+	0.922843i	−0.161108	+	0.0431688i	−0.338472	−	0.940977i	$-0.609910\pi$
$457$	−3.44410	+	0.922843i	−0.161108	+	0.0431688i	0.177363	+	0.984145i	$0.443243\pi$
$458$	2.03421	−	0.545066i	0.0950526	−	0.0254693i
$459$	2.03882	+	30.6157i	0.0951640	+	1.42902i
$460$	−5.58506	−	1.87721i	−0.260405	−	0.0875253i
$461$	7.91843	−	4.57171i	0.368798	−	0.212926i	−0.304135	−	0.952629i	$-0.598367\pi$
$461$	7.91843	−	4.57171i	0.368798	−	0.212926i	0.672933	+	0.739703i	$0.265034\pi$
$462$	−14.1977	+	1.55991i	−0.660539	+	0.0725738i
$463$	−26.6012	+	26.6012i	−1.23626	+	1.23626i	−0.274748	+	0.961516i	$0.588594\pi$
$463$	−26.6012	+	26.6012i	−1.23626	+	1.23626i	−0.961516	+	0.274748i	$0.911406\pi$
$464$	−2.90115	−	5.02494i	−0.134682	−	0.233277i
$465$	32.9727	+	17.0244i	1.52907	+	0.789489i
$466$	6.58658	−	11.4083i	0.305117	−	0.528479i
$467$	−0.0850788	+	0.0850788i	−0.00393698	+	0.00393698i	−0.709073	−	0.705136i	$-0.750886\pi$
$467$	−0.0850788	+	0.0850788i	−0.00393698	+	0.00393698i	0.705136	+	0.709073i	$0.250886\pi$
$468$	10.7780	−	0.913173i	0.498215	−	0.0422114i
$469$		−	13.5124i		−	0.623944i
$470$	0.493779	−	7.89642i	0.0227763	−	0.364235i
$471$	28.6595	+	4.40089i	1.32056	+	0.202782i
$472$	−0.0318157	+	0.118738i	−0.00146444	+	0.00546536i
$473$	−8.66440	−	8.66440i	−0.398389	−	0.398389i
$474$	15.0202	−	18.7281i	0.689900	−	0.860212i
$475$	−2.96034	+	23.5781i	−0.135830	+	1.08184i
$476$		−	19.1439i		−	0.877457i
$477$	26.4914	−	13.8140i	1.21296	−	0.632501i
$478$	2.22375	+	8.29914i	0.101712	+	0.379594i
$479$	6.96353	−	12.0612i	0.318172	−	0.551089i	−0.661935	−	0.749561i	$-0.730265\pi$
$479$	6.96353	−	12.0612i	0.318172	−	0.551089i	0.980107	+	0.198472i	$0.0635979\pi$
$480$	−2.86421	−	2.60698i	−0.130733	−	0.118992i
$481$	−3.83670	−	29.9381i	−0.174938	−	1.36506i
$482$	6.55414	−	6.55414i	0.298533	−	0.298533i
$483$	8.75331	+	11.9293i	0.398290	+	0.542801i
$484$	3.92294	+	2.26491i	0.178315	+	0.102950i
$485$	11.1507	−	2.25280i	0.506327	−	0.102294i
$486$	−4.38818	−	14.9581i	−0.199052	−	0.678512i
$487$	−0.263042	+	0.981687i	−0.0119196	+	0.0444845i	−0.971629	−	0.236508i	$-0.923997\pi$
$487$	−0.263042	+	0.981687i	−0.0119196	+	0.0444845i	0.959710	+	0.280993i	$0.0906637\pi$
$488$	0.558755	−	2.08530i	0.0252937	−	0.0943972i
$489$	16.4927	−	6.42027i	0.745824	−	0.290335i
$490$	7.69364	−	1.55436i	0.347563	−	0.0702190i
$491$	7.95569	+	4.59322i	0.359035	+	0.207289i	0.668658	−	0.743571i	$-0.266869\pi$
$491$	7.95569	+	4.59322i	0.359035	+	0.207289i	−0.309622	+	0.950860i	$0.600203\pi$
$492$	−5.94481	+	4.36210i	−0.268013	+	0.196659i
$493$	24.2275	−	24.2275i	1.09115	−	1.09115i
$494$	−13.6306	+	10.3848i	−0.613271	+	0.467236i
$495$	−15.9259	−	6.12558i	−0.715818	−	0.275324i
$496$	4.79066	−	8.29767i	0.215107	−	0.372576i
$497$	−1.82772	−	6.82113i	−0.0819842	−	0.305969i
$498$	1.85026	+	16.8403i	0.0829120	+	0.754633i
$499$		−	23.5299i		−	1.05334i	−0.850069	−	0.526671i	$-0.823440\pi$
$499$		−	23.5299i		−	1.05334i	0.850069	−	0.526671i	$-0.176560\pi$
$500$	−10.5542	+	3.68891i	−0.472000	+	0.164973i
$501$	8.46927	+	6.79245i	0.378379	+	0.303464i
$502$	10.6428	+	10.6428i	0.475012	+	0.475012i
$503$	−1.18181	+	4.41059i	−0.0526945	+	0.196659i	−0.987255	−	0.159145i	$-0.949126\pi$
$503$	−1.18181	+	4.41059i	−0.0526945	+	0.196659i	0.934561	+	0.355804i	$0.115793\pi$
$504$	2.11168	+	9.49383i	0.0940616	+	0.422889i
$505$	1.75888	−	28.1277i	0.0782692	−	1.25167i
$506$			6.70259i			0.297967i
$507$	21.0386	−	8.02365i	0.934355	−	0.356343i
$508$	5.21645	−	5.21645i	0.231443	−	0.231443i
$509$	−18.5495	+	32.1288i	−0.822194	+	1.42408i	0.0818510	+	0.996645i	$0.473917\pi$
$509$	−18.5495	+	32.1288i	−0.822194	+	1.42408i	−0.904045	+	0.427437i	$0.859416\pi$
$510$	10.4923	−	20.3213i	0.464606	−	0.899843i
$511$	−18.6870	−	32.3668i	−0.826663	−	1.43182i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	18.5840	+	16.2634i	0.820506	+	0.718047i
$514$	2.89863	−	1.67352i	0.127853	−	0.0738160i
$515$	−24.6286	−	8.27797i	−1.08526	−	0.364771i
$516$	−5.22021	+	6.50890i	−0.229807	+	0.286538i
$517$	−8.69350	+	2.32942i	−0.382340	+	0.102448i
$518$	26.2144	−	7.02413i	1.15180	−	0.308623i
$519$	15.7206	+	40.3838i	0.690058	+	1.77265i
$520$	−7.22925	−	3.56903i	−0.317023	−	0.156512i
$521$		−	10.1420i		−	0.444330i	−0.975009	−	0.222165i	$-0.928688\pi$
$521$		−	10.1420i		−	0.444330i	0.975009	−	0.222165i	$-0.0713124\pi$
$522$	−9.34248	+	14.6873i	−0.408909	+	0.642847i
$523$	−5.76087	−	21.4998i	−0.251905	−	0.940123i	−0.969786	−	0.243957i	$-0.921554\pi$
$523$	−5.76087	−	21.4998i	−0.251905	−	0.940123i	0.717881	−	0.696166i	$-0.245112\pi$
$524$	−4.82953	−	8.36498i	−0.210979	−	0.365426i
$525$	27.0038	+	7.68526i	1.17854	+	0.335412i
$526$	12.3697	+	21.4250i	0.539346	+	0.934174i
$527$	54.6504	+	14.6435i	2.38061	+	0.637882i
$528$	−1.77299	+	4.03324i	−0.0771595	+	0.175524i
$529$	−13.9055	+	8.02832i	−0.604585	+	0.349058i
$530$	−22.2254	−	1.38980i	−0.965411	−	0.0603690i
$531$	0.359982	−	0.0800695i	0.0156219	−	0.00347472i
$532$	−10.8950	−	10.8950i	−0.472357	−	0.472357i
$533$	−9.38583	+	12.1451i	−0.406545	+	0.526063i
$534$	−11.4058	+	4.44006i	−0.493579	+	0.192140i
$535$	−13.5788	+	11.9805i	−0.587061	+	0.517962i
$536$	−3.60958	−	2.08399i	−0.155910	−	0.0900148i
$537$	−1.75127	−	15.9394i	−0.0755728	−	0.687834i
$538$	−6.01011	+	6.01011i	−0.259114	+	0.259114i
$539$	−4.46439	−	7.73256i	−0.192295	−	0.333065i
$540$	−2.96178	+	11.2351i	−0.127455	+	0.483482i
$541$	12.6124			0.542251			0.271126	−	0.962544i	$-0.412604\pi$
$541$	12.6124			0.542251			0.271126	+	0.962544i	$0.412604\pi$
$542$	23.4123	+	6.27331i	1.00565	+	0.269462i
$543$	1.94512	−	1.42726i	0.0834729	−	0.0612496i
$544$	−5.11392	−	2.95252i	−0.219258	−	0.126588i
$545$	15.7898	−	7.84564i	0.676362	−	0.336070i
$546$	9.68315	+	17.7802i	0.414401	+	0.760922i
$547$	10.8843	+	10.8843i	0.465379	+	0.465379i	0.900414	−	0.435035i	$-0.143264\pi$
$547$	10.8843	+	10.8843i	0.465379	+	0.465379i	−0.435035	+	0.900414i	$0.643264\pi$
$548$	−2.94164	+	0.788210i	−0.125661	+	0.0336707i
$549$	−6.32209	+	1.40620i	−0.269820	+	0.0600151i
$550$	7.80278	+	10.0435i	0.332712	+	0.428255i
$551$		−	27.5762i		−	1.17479i
$552$	4.53669	−	0.498450i	0.193095	−	0.0212154i
$553$	43.4042	+	11.6301i	1.84573	+	0.494563i
$554$	−26.9745			−1.14604
$555$	31.6765	+	6.91134i	1.34459	+	0.293370i
$556$	−7.96502	+	13.7958i	−0.337792	+	0.585073i
$557$	−2.86382	−	10.6879i	−0.121344	−	0.452862i	0.878339	−	0.478038i	$-0.158652\pi$
$557$	−2.86382	−	10.6879i	−0.121344	−	0.452862i	−0.999683	+	0.0251762i	$0.991985\pi$
$558$	−28.7175	−	1.23377i	−1.21571	−	0.0522297i
$559$	−6.70187	+	16.0236i	−0.283459	+	0.677726i
$560$	2.30958	−	6.87146i	0.0975978	−	0.290372i
$561$	−25.7147	−	3.94869i	−1.08568	−	0.166714i
$562$	22.7756	−	6.10270i	0.960729	−	0.257427i
$563$	3.94338	−	14.7169i	0.166194	−	0.620244i	−0.831691	−	0.555239i	$-0.812627\pi$
$563$	3.94338	−	14.7169i	0.166194	−	0.620244i	0.997885	−	0.0650052i	$-0.0207064\pi$
$564$	2.22319	+	5.71103i	0.0936131	+	0.240478i
$565$	−34.9102	+	7.05299i	−1.46868	+	0.296721i
$566$	0.758214	−	0.437755i	0.0318701	−	0.0184002i
$567$	22.3251	−	18.7861i	0.937566	−	0.788942i
$568$	−2.10402	−	0.563771i	−0.0882828	−	0.0236553i
$569$	11.6091	−	20.1075i	0.486677	−	0.842949i	−0.513206	−	0.858266i	$-0.671542\pi$
$569$	11.6091	−	20.1075i	0.486677	−	0.842949i	0.999883	+	0.0153166i	$0.00487561\pi$
$570$	−5.59380	−	17.5363i	−0.234299	−	0.734517i
$571$	−7.32536			−0.306557			−0.153278	−	0.988183i	$-0.548983\pi$
$571$	−7.32536			−0.306557			−0.153278	+	0.988183i	$0.548983\pi$
$572$	−1.22837	+	9.08865i	−0.0513606	+	0.380015i
$573$	−14.8813	+	33.8523i	−0.621674	+	1.41420i
$574$	−11.9523	−	6.90064i	−0.498878	−	0.288027i
$575$	4.96880	−	12.2022i	0.207213	−	0.508869i
$576$	2.86178	+	0.900122i	0.119241	+	0.0375051i
$577$	25.4083	+	25.4083i	1.05776	+	1.05776i	0.998226	+	0.0595345i	$0.0189616\pi$
$577$	25.4083	+	25.4083i	1.05776	+	1.05776i	0.0595345	+	0.998226i	$0.481038\pi$
$578$	4.62500	−	17.2607i	0.192374	−	0.717951i
$579$	−6.49668	−	5.21041i	−0.269993	−	0.216537i
$580$	11.6191	−	5.77327i	0.482455	−	0.239722i
$581$	−27.4620	+	15.8552i	−1.13932	+	0.657784i
$582$	−7.10441	+	5.21298i	−0.294487	+	0.216085i
$583$	6.55642	+	24.4689i	0.271539	+	1.01340i
$584$	−11.5282			−0.477042
$585$	0.533828	+	24.1809i	0.0220711	+	0.999756i
$586$	21.3984			0.883958
$587$	−1.75805	−	6.56112i	−0.0725624	−	0.270807i	0.920107	−	0.391667i	$-0.128101\pi$
$587$	−1.75805	−	6.56112i	−0.0725624	−	0.270807i	−0.992670	+	0.120860i	$0.961435\pi$
$588$	−4.90183	+	3.59680i	−0.202148	+	0.148330i
$589$	39.4359	−	22.7683i	1.62493	−	0.938152i
$590$	−0.260548	−	0.0875737i	−0.0107266	−	0.00360535i
$591$	22.7047	+	18.2094i	0.933945	+	0.749035i
$592$	2.16664	−	8.08601i	0.0890484	−	0.332333i
$593$	−0.942761	−	0.942761i	−0.0387146	−	0.0387146i	0.687484	−	0.726199i	$-0.258715\pi$
$593$	−0.942761	−	0.942761i	−0.0387146	−	0.0387146i	−0.726199	+	0.687484i	$0.758715\pi$
$594$	13.1880	−	0.878241i	0.541111	−	0.0360347i
$595$	42.7235	+	2.67159i	1.75149	+	0.109524i
$596$	−2.74886	−	1.58705i	−0.112598	−	0.0650082i
$597$	1.08999	−	2.47953i	0.0446103	−	0.101481i
$598$	8.78997	−	3.60555i	0.359449	−	0.147442i
$599$	−10.1561			−0.414967			−0.207484	−	0.978238i	$-0.566527\pi$
$599$	−10.1561			−0.414967			−0.207484	+	0.978238i	$0.566527\pi$
$600$	6.21772	−	6.02826i	0.253837	−	0.246103i
$601$	−18.8319	+	32.6178i	−0.768170	+	1.33051i	0.170384	+	0.985378i	$0.445499\pi$
$601$	−18.8319	+	32.6178i	−0.768170	+	1.33051i	−0.938554	+	0.345132i	$0.887834\pi$
$602$	−15.0850	−	4.04201i	−0.614818	−	0.164740i
$603$	−0.536705	+	12.4924i	−0.0218563	+	0.508731i
$604$	−6.16489	+	3.55930i	−0.250846	+	0.144826i
$605$	−5.60208	+	8.43878i	−0.227757	+	0.343085i
$606$	7.91919	+	20.3432i	0.321695	+	0.826384i
$607$	−8.99110	+	33.5552i	−0.364937	+	1.36197i	0.502568	+	0.864538i	$0.332389\pi$
$607$	−8.99110	+	33.5552i	−0.364937	+	1.36197i	−0.867506	+	0.497428i	$0.834278\pi$
$608$	−4.59070	+	1.23007i	−0.186177	+	0.0498861i
$609$	−32.2037	−	4.94513i	−1.30496	−	0.200387i
$610$	4.57581	+	1.53799i	0.185269	+	0.0622714i
$611$	7.73139	+	10.1478i	0.312779	+	0.410538i
$612$	−0.760383	+	17.6988i	−0.0307367	+	0.715433i
$613$	−9.64392	−	35.9916i	−0.389514	−	1.45369i	−0.830926	−	0.556383i	$-0.812189\pi$
$613$	−9.64392	−	35.9916i	−0.389514	−	1.45369i	0.441412	−	0.897305i	$-0.354478\pi$
$614$	4.29457	−	7.43842i	0.173315	−	0.300190i
$615$	−8.90532	−	13.8758i	−0.359097	−	0.559527i
$616$	−8.24640			−0.332257
$617$	−4.32364	−	1.15852i	−0.174063	−	0.0466401i	0.170735	−	0.985317i	$-0.445386\pi$
$617$	−4.32364	−	1.15852i	−0.174063	−	0.0466401i	−0.344798	+	0.938677i	$0.612053\pi$
$618$	20.0056	−	2.19802i	0.804742	−	0.0884175i
$619$			6.76786i			0.272023i	0.990707	+	0.136012i	$0.0434284\pi$
$619$			6.76786i			0.272023i	−0.990707	+	0.136012i	$0.956572\pi$
$620$	17.8494	+	11.8493i	0.716851	+	0.475881i
$621$	−7.61876	−	11.3765i	−0.305730	−	0.456524i
$622$	14.4623	−	3.87515i	0.579883	−	0.155379i
$623$	−16.1993	−	16.1993i	−0.649012	−	0.649012i
$624$	6.24306	+	0.155536i	0.249922	+	0.00622641i
$625$	−6.75970	−	24.0688i	−0.270388	−	0.962751i
$626$	18.8047	+	10.8569i	0.751585	+	0.433928i
$627$	−16.8818	+	12.3873i	−0.674192	+	0.494700i
$628$	16.1701	+	4.33276i	0.645257	+	0.172896i
$629$	49.4327			1.97101
$630$	−21.4822	+	3.38776i	−0.855870	+	0.134971i
$631$	−5.32142	−	9.21696i	−0.211842	−	0.366922i	0.740449	−	0.672113i	$-0.234613\pi$
$631$	−5.32142	−	9.21696i	−0.211842	−	0.366922i	−0.952291	+	0.305191i	$0.901280\pi$
$632$	9.80093	−	9.80093i	0.389860	−	0.389860i
$633$	−5.06681	−	46.1161i	−0.201388	−	1.83295i
$634$	−8.28021	−	4.78058i	−0.328849	−	0.189861i
$635$	10.9136	+	12.3696i	0.433094	+	0.490871i
$636$	16.0744	−	6.25743i	0.637390	−	0.248123i
$637$	−7.73915	+	10.0143i	−0.306636	+	0.396782i
$638$	−10.4362	−	10.4362i	−0.413174	−	0.413174i
$639$	1.41882	+	6.37884i	0.0561278	+	0.252343i
$640$	−1.47938	−	1.67674i	−0.0584775	−	0.0662788i
$641$	7.13092	−	4.11704i	0.281654	−	0.162613i	−0.352518	−	0.935805i	$-0.614674\pi$
$641$	7.13092	−	4.11704i	0.281654	−	0.162613i	0.634172	+	0.773192i	$0.281341\pi$
$642$	5.64474	−	12.8408i	0.222780	−	0.506785i
$643$	10.9513	+	2.93440i	0.431878	+	0.115721i	0.468208	−	0.883618i	$-0.344900\pi$
$643$	10.9513	+	2.93440i	0.431878	+	0.115721i	−0.0363295	+	0.999340i	$0.511567\pi$
$644$	4.27130	+	7.39811i	0.168313	+	0.291527i
$645$	−13.7975	−	12.5583i	−0.543275	−	0.494484i
$646$	−14.0323	−	24.3046i	−0.552093	−	0.956254i
$647$	−10.2584	−	38.2848i	−0.403298	−	1.50513i	−0.807173	−	0.590316i	$-0.799003\pi$
$647$	−10.2584	−	38.2848i	−0.403298	−	1.50513i	0.403874	−	0.914815i	$-0.367663\pi$
$648$	−1.57519	−	8.86108i	−0.0618794	−	0.348096i
$649$			0.312683i			0.0122739i
$650$	8.97391	−	15.6355i	0.351986	−	0.613275i
$651$	−19.5171	−	50.1364i	−0.764935	−	1.96500i
$652$	9.86992	−	2.64464i	0.386536	−	0.103572i
$653$	−13.2114	+	3.53997i	−0.517001	+	0.138530i	−0.507879	−	0.861429i	$-0.669570\pi$
$653$	−13.2114	+	3.53997i	−0.517001	+	0.138530i	−0.00912169	+	0.999958i	$0.502904\pi$
$654$	−8.54475	+	10.6541i	−0.334126	+	0.416610i
$655$	19.3422	−	9.61074i	0.755762	−	0.375523i
$656$	−3.68675	+	2.12855i	−0.143944	+	0.0831059i
$657$	15.9908	+	30.6659i	0.623862	+	1.19639i
$658$	−8.11117	+	8.11117i	−0.316206	+	0.316206i
$659$	14.4718	+	25.0658i	0.563740	+	0.976426i	0.997166	+	0.0752366i	$0.0239712\pi$
$659$	14.4718	+	25.0658i	0.563740	+	0.976426i	−0.433426	+	0.901189i	$0.642695\pi$
$660$	−8.75360	−	4.51965i	−0.340733	−	0.175927i
$661$	8.52390	−	14.7638i	0.331541	−	0.574246i	−0.651273	−	0.758843i	$-0.725765\pi$
$661$	8.52390	−	14.7638i	0.331541	−	0.574246i	0.982814	+	0.184597i	$0.0590981\pi$
$662$	−1.46470	+	1.46470i	−0.0569273	+	0.0569273i
$663$	8.65436	+	35.8471i	0.336108	+	1.39219i
$664$			9.78127i			0.379587i
$665$	25.8348	−	22.7940i	1.00183	−	0.883912i
$666$	−24.5147	+	5.45271i	−0.949924	+	0.211288i
$667$	−3.95713	+	14.7682i	−0.153221	+	0.571828i
$668$	4.43219	+	4.43219i	0.171487	+	0.171487i
$669$	3.02933	+	2.42956i	0.117121	+	0.0939321i
$670$	5.15460	−	7.76471i	0.199139	−	0.299977i
$671$		−	5.49141i		−	0.211993i
$672$	0.613257	+	5.58163i	0.0236569	+	0.215316i
$673$	−10.7003	−	39.9340i	−0.412465	−	1.53934i	−0.789859	−	0.613289i	$-0.789846\pi$
$673$	−10.7003	−	39.9340i	−0.412465	−	1.53934i	0.377394	−	0.926053i	$-0.376820\pi$
$674$	−12.6333	+	21.8815i	−0.486617	+	0.842845i
$675$	−24.6602	−	8.17773i	−0.949171	−	0.314761i
$676$	12.5799	−	3.27817i	0.483842	−	0.126083i
$677$	−22.6992	+	22.6992i	−0.872403	+	0.872403i	−0.992734	−	0.120331i	$-0.961604\pi$
$677$	−22.6992	+	22.6992i	−0.872403	+	0.872403i	0.120331	+	0.992734i	$0.461604\pi$
$678$	22.2423	−	16.3206i	0.854209	−	0.626790i
$679$	−14.2837	−	8.24669i	−0.548158	−	0.316479i
$680$	7.30284	−	11.0008i	0.280051	−	0.421860i
$681$	−18.0950	+	7.04403i	−0.693403	+	0.269928i
$682$	6.30783	−	23.5411i	0.241539	−	0.901437i
$683$	−4.04544	+	15.0978i	−0.154794	+	0.577701i	0.844328	+	0.535826i	$0.180000\pi$
$683$	−4.04544	+	15.0978i	−0.154794	+	0.577701i	−0.999123	+	0.0418747i	$0.986667\pi$
$684$	9.63984	+	10.5053i	0.368589	+	0.401681i
$685$	−1.34854	−	6.67489i	−0.0515251	−	0.255034i
$686$	9.79794	+	5.65684i	0.374087	+	0.215979i
$687$	−2.15792	−	2.94088i	−0.0823297	−	0.112201i
$688$	−3.40628	+	3.40628i	−0.129863	+	0.129863i
$689$	28.5623	−	21.7609i	1.08814	−	0.829025i
$690$	0.479284	+	10.1941i	0.0182460	+	0.388084i
$691$	−21.0379	+	36.4387i	−0.800319	+	1.38619i	0.119087	+	0.992884i	$0.462003\pi$
$691$	−21.0379	+	36.4387i	−0.800319	+	1.38619i	−0.919406	+	0.393310i	$0.871330\pi$
$692$	6.47563	+	24.1674i	0.246167	+	0.918706i
$693$	11.4386	+	21.9360i	0.434516	+	0.833278i
$694$			16.3392i			0.620228i
$695$	−29.6767	−	19.7009i	−1.12570	−	0.747296i
$696$	−6.28772	+	7.83993i	−0.238335	+	0.297172i
$697$	−17.7755	−	17.7755i	−0.673296	−	0.673296i
$698$	1.82313	−	6.80400i	0.0690064	−	0.257535i
$699$	−22.5522	−	3.46307i	−0.853004	−	0.130985i
$700$	15.0128	+	6.11325i	0.567430	+	0.231059i
$701$			3.71040i			0.140140i	0.997542	+	0.0700699i	$0.0223222\pi$
$701$			3.71040i			0.140140i	−0.997542	+	0.0700699i	$0.977678\pi$
$702$	−8.24602	−	16.8227i	−0.311226	−	0.634932i
$703$	28.1327	−	28.1327i	1.06104	−	1.06104i
$704$	−1.27183	+	2.20287i	−0.0479338	+	0.0830238i
$705$	−13.0556	+	4.16452i	−0.491702	+	0.156845i
$706$	−13.9633	−	24.1851i	−0.525516	−	0.910220i
$707$	−28.8927	+	28.8927i	−1.08662	+	1.08662i
$708$	0.211641	−	0.0232532i	0.00795397	−	0.000873908i
$709$	31.3277	−	18.0870i	1.17653	−	0.679273i	0.221324	−	0.975200i	$-0.428962\pi$
$709$	31.3277	−	18.0870i	1.17653	−	0.679273i	0.955210	+	0.295928i	$0.0956287\pi$
$710$	1.55180	−	4.61689i	0.0582378	−	0.173269i
$711$	−39.6660	−	12.4762i	−1.48759	−	0.467895i
$712$	−6.82574	+	1.82895i	−0.255805	+	0.0685428i
$713$	−24.3868	+	6.53441i	−0.913291	+	0.244716i
$714$	−30.8994	+	12.0285i	−1.15638	+	0.450157i
$715$	−20.1118	−	4.00971i	−0.752138	−	0.149954i
$716$		−	9.25797i		−	0.345987i
$717$	11.9981	−	8.80383i	0.448078	−	0.328785i
$718$	6.35532	+	23.7184i	0.237178	+	0.885161i
$719$	−1.78995	−	3.10029i	−0.0667539	−	0.115621i	0.830717	−	0.556695i	$-0.187931\pi$
$719$	−1.78995	−	3.10029i	−0.0667539	−	0.115621i	−0.897471	+	0.441074i	$0.854598\pi$
$720$	−2.40818	+	6.26104i	−0.0897476	+	0.233335i
$721$	18.8353	+	32.6236i	0.701462	+	1.21497i
$722$	−3.46537	−	0.928543i	−0.128968	−	0.0345568i
$723$	−14.6969	−	6.46069i	−0.546585	−	0.240276i
$724$	1.20629	−	0.696452i	0.0448315	−	0.0258835i
$725$	11.2628	+	26.7360i	0.418289	+	0.992951i
$726$	1.19084	−	7.75498i	0.0441961	−	0.287814i
$727$	−24.1251	−	24.1251i	−0.894750	−	0.894750i	0.100216	−	0.994966i	$-0.468047\pi$
$727$	−24.1251	−	24.1251i	−0.894750	−	0.894750i	−0.994966	+	0.100216i	$0.968047\pi$
$728$	4.43601	+	10.8146i	0.164409	+	0.400814i
$729$	−21.3861	+	16.4813i	−0.792078	+	0.610420i
$730$	1.60880	−	25.7277i	0.0595445	−	0.952224i
$731$	−24.6348	−	14.2229i	−0.911152	−	0.526054i
$732$	−3.71690	+	0.408378i	−0.137380	+	0.0150941i
$733$	18.2864	−	18.2864i	0.675422	−	0.675422i	−0.283539	−	0.958961i	$-0.591509\pi$
$733$	18.2864	−	18.2864i	0.675422	−	0.675422i	0.958961	+	0.283539i	$0.0915085\pi$
$734$	−3.16522	−	5.48232i	−0.116830	−	0.202356i
$735$	−7.34294	−	11.4414i	−0.270849	−	0.422023i
$736$	2.63502			0.0971283
$737$	−10.2407	−	2.74398i	−0.377220	−	0.101076i
$738$	10.7760	+	6.85450i	0.396669	+	0.252318i
$739$	−23.4643	−	13.5471i	−0.863146	−	0.498338i	0.00191827	−	0.999998i	$-0.499389\pi$
$739$	−23.4643	−	13.5471i	−0.863146	−	0.498338i	−0.865065	+	0.501660i	$0.832723\pi$
$740$	17.7433	+	5.96374i	0.652255	+	0.219231i
$741$	25.3263	+	15.4757i	0.930384	+	0.568514i
$742$	22.8299	+	22.8299i	0.838111	+	0.838111i
$743$	14.2643	−	3.82210i	0.523305	−	0.140219i	0.0125100	−	0.999922i	$-0.496018\pi$
$743$	14.2643	−	3.82210i	0.523305	−	0.140219i	0.510795	+	0.859703i	$0.329351\pi$
$744$	−16.4031	−	2.51882i	−0.601366	−	0.0923445i
$745$	3.92545	−	5.91317i	0.143817	−	0.216642i
$746$		−	2.72715i		−	0.0998482i
$747$	26.0188	−	13.5676i	0.951979	−	0.496413i
$748$	−14.5086	−	3.88757i	−0.530487	−	0.142144i
$749$	26.2544			0.959313
$750$	12.5856	+	14.7174i	0.459562	+	0.537404i
$751$	17.5962	−	30.4775i	0.642094	−	1.11214i	−0.342870	−	0.939383i	$-0.611399\pi$
$751$	17.5962	−	30.4775i	0.642094	−	1.11214i	0.984964	−	0.172757i	$-0.0552676\pi$
$752$	0.915776	+	3.41772i	0.0333949	+	0.124631i
$753$	10.4911	−	23.8654i	0.382316	−	0.869702i
$754$	−8.07237	+	19.3003i	−0.293978	+	0.702877i
$755$	−7.08300	−	14.2550i	−0.257777	−	0.518791i
$756$	13.9968	−	9.37359i	0.509061	−	0.340914i
$757$	−1.82125	+	0.488003i	−0.0661945	+	0.0177368i	−0.291764	−	0.956490i	$-0.594242\pi$
$757$	−1.82125	+	0.488003i	−0.0661945	+	0.0177368i	0.225570	+	0.974227i	$0.427576\pi$
$758$	0.510961	−	1.90693i	0.0185589	−	0.0692629i
$759$	10.8184	−	4.21140i	0.392684	−	0.152864i
$760$	−2.10452	−	10.4168i	−0.0763390	−	0.377856i
$761$	41.9798	−	24.2370i	1.52177	−	0.878592i	0.522096	−	0.852887i	$-0.325150\pi$
$761$	41.9798	−	24.2370i	1.52177	−	0.878592i	0.999670	−	0.0257053i	$-0.00818316\pi$
$762$	−11.6973	−	5.14208i	−0.423749	−	0.186278i
$763$	−24.6920	−	6.61620i	−0.893910	−	0.239522i
$764$	−10.6748	+	18.4894i	−0.386202	+	0.668922i
$765$	−39.3925	−	4.16688i	−1.42424	−	0.150654i
$766$	21.7123			0.784498
$767$	0.410061	−	0.168202i	0.0148064	−	0.00607344i
$768$	1.58561	+	0.697025i	0.0572157	+	0.0251517i
$769$	−0.388615	−	0.224367i	−0.0140138	−	0.00809087i	0.492977	−	0.870042i	$-0.335909\pi$
$769$	−0.388615	−	0.224367i	−0.0140138	−	0.00809087i	−0.506991	+	0.861952i	$0.669242\pi$
$770$	1.15081	−	18.4036i	0.0414723	−	0.663218i
$771$	−4.52246	−	3.62706i	−0.162872	−	0.130626i
$772$	−3.39988	−	3.39988i	−0.122365	−	0.122365i
$773$	−2.08641	+	7.78660i	−0.0750431	+	0.280065i	−0.993243	−	0.116053i	$-0.962976\pi$
$773$	−2.08641	+	7.78660i	−0.0750431	+	0.280065i	0.918200	+	0.396117i	$0.129643\pi$
$774$	13.7858	+	4.33607i	0.495519	+	0.155857i
$775$	−28.9352	+	38.1811i	−1.03938	+	1.37151i
$776$	−4.40590	+	2.54375i	−0.158163	+	0.0913152i
$777$	−27.8086	−	37.8984i	−0.997627	−	1.35960i
$778$	1.05987	+	3.95549i	0.0379982	+	0.141811i
$779$	−20.2325			−0.724903
$780$	−1.21835	+	13.9110i	−0.0436239	+	0.498093i
$781$	−5.54070			−0.198262
$782$	4.02721	+	15.0298i	0.144013	+	0.537463i
$783$	29.5764	+	5.85097i	1.05698	+	0.209097i
$784$	−3.03994	+	1.75511i	−0.108569	+	0.0626825i
$785$	−11.9260	+	35.4823i	−0.425659	+	1.26642i
$786$	−10.4671	+	13.0511i	−0.373350	+	0.465517i
$787$	6.38922	−	23.8449i	0.227751	−	0.849978i	−0.753533	−	0.657411i	$-0.771652\pi$
$787$	6.38922	−	23.8449i	0.227751	−	0.849978i	0.981284	−	0.192568i	$-0.0616816\pi$
$788$	11.8819	+	11.8819i	0.423277	+	0.423277i
$789$	26.8092	−	33.4274i	0.954432	−	1.19005i
$790$	20.5051	+	23.2406i	0.729538	+	0.826862i
$791$	44.7189	+	25.8185i	1.59002	+	0.918000i
$792$	7.62393	+	0.327542i	0.270905	+	0.0116387i
$793$	−7.20159	+	2.95401i	−0.255736	+	0.104900i
$794$	7.72978			0.274320
$795$	11.7215	+	36.7466i	0.415720	+	1.30327i
$796$	0.781887	−	1.35427i	0.0277132	−	0.0480007i
$797$	−9.74904	−	2.61225i	−0.345329	−	0.0925306i	0.0819860	−	0.996633i	$-0.473874\pi$
$797$	−9.74904	−	2.61225i	−0.345329	−	0.0925306i	−0.427315	+	0.904103i	$0.640540\pi$
$798$	−10.7396	+	24.4308i	−0.380179	+	0.864840i
$799$	−18.0945	+	10.4469i	−0.640138	+	0.369584i
$800$	3.94844	−	3.06755i	0.139598	−	0.108454i
$801$	14.3331	+	15.6200i	0.506436	+	0.551905i
$802$	−5.21220	+	19.4522i	−0.184049	+	0.686881i
$803$	−28.3247	+	7.58958i	−0.999557	+	0.267830i
$804$	−1.09572	+	7.13553i	−0.0386429	+	0.251651i
$805$	−17.1065	+	8.49988i	−0.602925	+	0.299581i
$806$	−34.2657	+	4.39130i	−1.20696	+	0.154677i
$807$	13.4770	+	5.92442i	0.474413	+	0.208549i
$808$	3.26207	+	12.1742i	0.114759	+	0.428287i
$809$	−19.9772	+	34.6016i	−0.702362	+	1.21653i	0.265273	+	0.964173i	$0.414538\pi$
$809$	−19.9772	+	34.6016i	−0.702362	+	1.21653i	−0.967635	+	0.252354i	$0.918795\pi$
$810$	19.9952	−	2.27878i	0.702559	−	0.0800681i
$811$	−29.6547			−1.04132			−0.520658	−	0.853765i	$-0.674313\pi$
$811$	−29.6547			−1.04132			−0.520658	+	0.853765i	$0.674313\pi$
$812$	−18.1698	−	4.86858i	−0.637634	−	0.170854i
$813$	−4.58498	−	41.7307i	−0.160802	−	1.46356i
$814$		−	21.2936i		−	0.746340i
$815$	4.52468	+	22.3958i	0.158493	+	0.784492i
$816$	−1.55237	+	10.1094i	−0.0543438	+	0.353898i
$817$	−22.1143	+	5.92552i	−0.773683	+	0.207308i
$818$	25.8158	+	25.8158i	0.902629	+	0.902629i
$819$	22.6142	−	26.8010i	0.790206	−	0.936501i
$820$	−4.23580	−	8.52481i	−0.147921	−	0.297699i
$821$	15.8715	+	9.16340i	0.553919	+	0.319805i	0.750701	−	0.660642i	$-0.229716\pi$
$821$	15.8715	+	9.16340i	0.553919	+	0.319805i	−0.196782	+	0.980447i	$0.563049\pi$
$822$	3.12053	+	4.25275i	0.108841	+	0.148332i
$823$	−40.3612	−	10.8148i	−1.40690	−	0.376979i	−0.526085	−	0.850432i	$-0.676340\pi$
$823$	−40.3612	−	10.8148i	−1.40690	−	0.376979i	−0.880819	+	0.473454i	$0.843007\pi$
$824$	11.6197			0.404792
$825$	11.3081	−	18.9048i	0.393699	−	0.658179i
$826$	0.199261	+	0.345130i	0.00693316	+	0.0120086i
$827$	9.95363	−	9.95363i	0.346122	−	0.346122i	−0.512541	−	0.858663i	$-0.671296\pi$
$827$	9.95363	−	9.95363i	0.346122	−	0.346122i	0.858663	+	0.512541i	$0.171296\pi$
$828$	−3.65504	−	7.00934i	−0.127022	−	0.243591i
$829$	19.8519	+	11.4615i	0.689484	+	0.398074i	0.803419	−	0.595415i	$-0.203012\pi$
$829$	19.8519	+	11.4615i	0.689484	+	0.398074i	−0.113935	+	0.993488i	$0.536346\pi$
$830$	−21.8290	−	1.36501i	−0.757694	−	0.0473801i
$831$	16.9487	+	43.5387i	0.587945	+	1.51034i
$832$	3.57307	+	0.482914i	0.123874	+	0.0167420i
$833$	−14.6569	−	14.6569i	−0.507832	−	0.507832i
$834$	27.2720	+	4.18783i	0.944351	+	0.145013i
$835$	−10.5099	+	9.27284i	−0.363710	+	0.320900i
$836$	−10.4695	+	6.04454i	−0.362094	+	0.209055i
$837$	16.0525	+	47.1271i	0.554855	+	1.62895i
$838$	−2.19034	−	0.586899i	−0.0756639	−	0.0202741i
$839$	−6.43259	−	11.1416i	−0.222078	−	0.384650i	0.733361	−	0.679839i	$-0.237951\pi$
$839$	−6.43259	−	11.1416i	−0.222078	−	0.384650i	−0.955439	+	0.295190i	$0.904617\pi$
$840$	−12.5422	+	0.589678i	−0.432745	+	0.0203458i
$841$	−2.33332	−	4.04143i	−0.0804593	−	0.139360i
$842$	−1.84607	−	6.88962i	−0.0636197	−	0.237432i
$843$	−24.1606	−	32.9268i	−0.832135	−	1.13406i
$844$		−	26.7854i		−	0.921991i
$845$	5.56036	+	28.5321i	0.191282	+	0.981535i
$846$	7.82109	−	7.17675i	0.268895	−	0.246742i
$847$	14.1850	−	3.80087i	0.487404	−	0.130599i
$848$	9.61959	−	2.57756i	0.330338	−	0.0885138i
$849$	−1.18297	−	0.948756i	−0.0405994	−	0.0325612i
$850$	23.5313	+	17.8330i	0.807119	+	0.611667i
$851$	−19.1032	+	11.0292i	−0.654849	+	0.378077i
$852$	0.412043	+	3.75026i	0.0141164	+	0.128482i
$853$	2.71534	−	2.71534i	0.0929716	−	0.0929716i	−0.659091	−	0.752063i	$-0.729059\pi$
$853$	2.71534	−	2.71534i	0.0929716	−	0.0929716i	0.752063	+	0.659091i	$0.229059\pi$
$854$	−3.49946	−	6.06124i	−0.119749	−	0.207412i
$855$	−24.7901	+	20.0473i	−0.847804	+	0.685602i
$856$	4.04917	−	7.01336i	0.138398	−	0.239712i
$857$	2.16954	−	2.16954i	0.0741102	−	0.0741102i	−0.669080	−	0.743190i	$-0.733312\pi$
$857$	2.16954	−	2.16954i	0.0741102	−	0.0741102i	0.743190	+	0.669080i	$0.233312\pi$
$858$	15.4415	−	3.72795i	0.527164	−	0.127270i
$859$		−	54.4901i		−	1.85918i	−0.368597	−	0.929589i	$-0.620162\pi$
$859$		−	54.4901i		−	1.85918i	0.368597	−	0.929589i	$-0.379838\pi$
$860$	−7.12646	−	8.07718i	−0.243010	−	0.275429i
$861$	−3.62820	+	23.6276i	−0.123649	+	0.805226i
$862$	−5.28289	+	19.7160i	−0.179936	+	0.671530i
$863$	39.3788	+	39.3788i	1.34047	+	1.34047i	0.895591	+	0.444878i	$0.146753\pi$
$863$	39.3788	+	39.3788i	1.34047	+	1.34047i	0.444878	+	0.895591i	$0.353247\pi$
$864$	−0.345267	−	5.18467i	−0.0117462	−	0.176386i
$865$	−54.8383	+	11.0791i	−1.86456	+	0.376700i
$866$		−	19.3306i		−	0.656879i
$867$	−30.7659	+	3.38027i	−1.04487	+	0.114800i
$868$	−8.03948	−	30.0037i	−0.272878	−	1.01839i
$869$	17.6283	−	30.5331i	0.597999	−	1.03576i
$870$	−16.6190	−	15.1264i	−0.563436	−	0.512834i
$871$	1.91026	+	14.9060i	0.0647268	+	0.505070i
$872$	−5.57560	+	5.57560i	−0.188814	+	0.188814i
$873$	12.8780	+	8.19155i	0.435853	+	0.277242i
$874$	10.8455	+	6.26166i	0.366855	+	0.211804i
$875$	−15.7381	+	32.6510i	−0.532044	+	1.10381i
$876$	7.24347	+	18.6073i	0.244734	+	0.628684i
$877$	7.73848	−	28.8804i	0.261310	−	0.975222i	−0.703160	−	0.711031i	$-0.748228\pi$
$877$	7.73848	−	28.8804i	0.261310	−	0.975222i	0.964470	−	0.264191i	$-0.0851049\pi$
$878$	6.27094	−	23.4035i	0.211634	−	0.789828i
$879$	−13.4451	−	34.5384i	−0.453492	−	1.16495i
$880$	−4.73868	−	3.14577i	−0.159741	−	0.106044i
$881$	−4.51696	−	2.60787i	−0.152180	−	0.0878613i	0.421976	−	0.906607i	$-0.361337\pi$
$881$	−4.51696	−	2.60787i	−0.152180	−	0.0878613i	−0.574156	+	0.818746i	$0.694670\pi$
$882$	8.88541	+	5.65192i	0.299187	+	0.190310i
$883$	−15.2152	+	15.2152i	−0.512032	+	0.512032i	−0.915148	−	0.403117i	$-0.867927\pi$
$883$	−15.2152	+	15.2152i	−0.512032	+	0.512032i	0.403117	+	0.915148i	$0.367927\pi$
$884$	2.70639	+	21.1182i	0.0910258	+	0.710284i
$885$	0.0223591	+	0.475567i	0.000751593	+	0.0159860i
$886$	−9.40782	+	16.2948i	−0.316062	+	0.547435i
$887$	−7.31866	−	27.3136i	−0.245736	−	0.917101i	−0.973012	−	0.230755i	$-0.925880\pi$
$887$	−7.31866	−	27.3136i	−0.245736	−	0.917101i	0.727275	−	0.686346i	$-0.240786\pi$
$888$	−14.4127	+	1.58353i	−0.483659	+	0.0531399i
$889$		−	23.9164i		−	0.802131i
$890$	−3.12913	−	15.4883i	−0.104889	−	0.519169i
$891$	−9.70388	−	20.7345i	−0.325092	−	0.694632i
$892$	1.58533	+	1.58533i	0.0530807	+	0.0530807i
$893$	−4.35235	+	16.2432i	−0.145646	+	0.543558i
$894$	−0.834436	+	5.43402i	−0.0279077	+	0.181741i
$895$	20.6611	+	1.29198i	0.690624	+	0.0431861i
$896$			3.24195i			0.108306i
$897$	−11.3425	−	11.9221i	−0.378716	−	0.398069i
$898$	−15.1023	+	15.1023i	−0.503971	+	0.503971i
$899$	27.7968	−	48.1455i	0.927077	−	1.60574i
$900$	−13.6368	−	6.24811i	−0.454559	−	0.208270i
$901$	29.4040	+	50.9292i	0.979589	+	1.69670i
$902$	−7.65697	+	7.65697i	−0.254949	+	0.254949i
$903$	2.95418	+	26.8878i	0.0983091	+	0.894771i
$904$	13.7938	−	7.96388i	0.458777	−	0.264875i
$905$	1.38594	+	2.78928i	0.0460701	+	0.0927189i
$906$	9.61850	+	7.71415i	0.319553	+	0.256285i
$907$	2.42335	−	0.649333i	0.0804659	−	0.0215608i	−0.218362	−	0.975868i	$-0.570071\pi$
$907$	2.42335	−	0.649333i	0.0804659	−	0.0215608i	0.298827	+	0.954307i	$0.403405\pi$
$908$	−10.8288	+	2.90158i	−0.359367	+	0.0962922i
$909$	27.8594	−	25.5642i	0.924037	−	0.847910i
$910$	−24.7540	+	8.39068i	−0.820587	+	0.278148i
$911$			27.9986i			0.927635i	0.885931	+	0.463818i	$0.153521\pi$
$911$			27.9986i			0.927635i	−0.885931	+	0.463818i	$0.846479\pi$
$912$	4.86987	+	6.63681i	0.161257	+	0.219767i
$913$	6.43947	+	24.0324i	0.213115	+	0.795357i
$914$	1.78280	+	3.08789i	0.0589697	+	0.102138i
$915$	−0.392676	−	8.35202i	−0.0129815	−	0.276109i
$916$	−1.05299	−	1.82383i	−0.0347917	−	0.0602609i
$917$	−30.2471	−	8.10469i	−0.998848	−	0.267641i
$918$	29.0448	−	9.89328i	0.958622	−	0.326527i
$919$	25.2405	−	14.5726i	0.832608	−	0.480707i	−0.0221367	−	0.999755i	$-0.507047\pi$
$919$	25.2405	−	14.5726i	0.832608	−	0.480707i	0.854745	+	0.519048i	$0.173714\pi$
$920$	−0.367726	+	5.88061i	−0.0121236	+	0.193878i
$921$	−14.7045	−	2.25799i	−0.484529	−	0.0744033i
$922$	−6.46537	−	6.46537i	−0.212926	−	0.212926i
$923$	2.98053	+	7.26623i	0.0981052	+	0.239171i
$924$	5.18141	+	13.3102i	0.170456	+	0.437874i
$925$	−15.7855	+	38.7655i	−0.519023	+	1.27460i
$926$	32.5797	+	18.8099i	1.07064	+	0.618132i
$927$	−16.1177	−	30.9092i	−0.529376	−	1.01519i
$928$	−4.10284	+	4.10284i	−0.134682	+	0.134682i
$929$	10.1264	+	17.5395i	0.332237	+	0.575452i	0.982950	−	0.183872i	$-0.0588631\pi$
$929$	10.1264	+	17.5395i	0.332237	+	0.575452i	−0.650713	+	0.759324i	$0.725530\pi$
$930$	7.91038	−	36.2554i	0.259391	−	1.18886i
$931$	−16.6828			−0.546757
$932$	−12.7243	−	3.40946i	−0.416798	−	0.111681i
$933$	−15.3417	−	20.9082i	−0.502265	−	0.684503i
$934$	0.104200	+	0.0601598i	0.00340952	+	0.00196849i
$935$	10.7006	−	31.8365i	0.349948	−	1.04116i
$936$	−3.67162	−	10.1744i	−0.120011	−	0.332562i
$937$	19.1842	+	19.1842i	0.626722	+	0.626722i	0.947242	−	0.320520i	$-0.103858\pi$
$937$	19.1842	+	19.1842i	0.626722	+	0.626722i	−0.320520	+	0.947242i	$0.603858\pi$
$938$	−13.0520	+	3.49726i	−0.426162	+	0.114190i
$939$	5.70830	−	37.1736i	0.186283	−	1.21311i
$940$	−7.75516	+	1.56679i	−0.252945	+	0.0511031i
$941$		−	36.7745i		−	1.19882i	−0.800444	−	0.599408i	$-0.795403\pi$
$941$		−	36.7745i		−	1.19882i	0.800444	−	0.599408i	$-0.204597\pi$
$942$	−3.16669	−	28.8220i	−0.103176	−	0.939070i
$943$	10.8353	+	2.90332i	0.352847	+	0.0945450i
$944$	0.122927			0.00400092
$945$	18.9658	+	32.5450i	0.616958	+	1.05869i
$946$	−6.12665	+	10.6117i	−0.199195	+	0.345015i
$947$	1.20771	+	4.50722i	0.0392451	+	0.146465i	0.982768	−	0.184842i	$-0.0591772\pi$
$947$	1.20771	+	4.50722i	0.0392451	+	0.146465i	−0.943523	+	0.331307i	$0.892511\pi$
$948$	−21.9775	−	9.66119i	−0.713796	−	0.313781i
$949$	25.1900	+	33.0631i	0.817702	+	1.07327i
$950$	23.5409	−	3.24299i	0.763767	−	0.105216i
$951$	−2.51352	+	16.3686i	−0.0815065	+	0.530787i
$952$	−18.4915	+	4.95479i	−0.599314	+	0.160586i
$953$	−4.82619	+	18.0116i	−0.156336	+	0.583452i	0.842652	+	0.538459i	$0.180993\pi$
$953$	−4.82619	+	18.0116i	−0.156336	+	0.583452i	−0.998987	+	0.0449933i	$0.985673\pi$
$954$	−20.1998	−	22.0134i	−0.653993	−	0.712710i
$955$	−39.7732	−	26.4034i	−1.28703	−	0.854394i
$956$	7.44081	−	4.29595i	0.240653	−	0.138941i
$957$	−10.2874	+	23.4021i	−0.332545	+	0.756482i
$958$	−13.4525	−	3.60459i	−0.434630	−	0.116459i
$959$	−4.93653	+	8.55032i	−0.159409	+	0.276104i
$960$	−1.77683	+	3.44135i	−0.0573471	+	0.111069i
$961$	60.8018			1.96135
$962$	−27.9250	+	11.4545i	−0.900339	+	0.369309i
$963$	−24.2726	−	1.04281i	−0.782174	−	0.0336040i
$964$	−8.02715	−	4.63448i	−0.258537	−	0.149266i
$965$	8.06202	−	7.11309i	0.259525	−	0.228978i
$966$	9.25728	−	11.5426i	0.297848	−	0.371376i
$967$	40.0577	+	40.0577i	1.28817	+	1.28817i	0.935898	+	0.352272i	$0.114591\pi$
$967$	40.0577	+	40.0577i	1.28817	+	1.28817i	0.352272	+	0.935898i	$0.385409\pi$
$968$	1.17240	−	4.37547i	0.0376825	−	0.140633i
$969$	−30.4125	+	37.9202i	−0.976990	+	1.21817i
$970$	−5.06204	−	10.1877i	−0.162532	−	0.327106i
$971$	−5.40657	+	3.12148i	−0.173505	+	0.100173i	−0.584237	−	0.811583i	$-0.698606\pi$
$971$	−5.40657	+	3.12148i	−0.173505	+	0.100173i	0.410733	+	0.911756i	$0.365273\pi$
$972$	−13.3126	+	8.11009i	−0.427003	+	0.260131i
$973$	13.3665	+	49.8846i	0.428512	+	1.59923i
$974$	1.01632			0.0325649
$975$	−30.8753	−	4.66032i	−0.988800	−	0.149250i
$976$	−2.15886			−0.0691036
$977$	3.02594	+	11.2930i	0.0968083	+	0.361294i	0.997287	−	0.0736058i	$-0.0234506\pi$
$977$	3.02594	+	11.2930i	0.0968083	+	0.361294i	−0.900479	+	0.434899i	$0.856784\pi$
$978$	−10.4701	−	14.2690i	−0.334798	−	0.456273i
$979$	−15.5666	+	8.98740i	−0.497512	+	0.287239i
$980$	−3.49266	−	7.02919i	−0.111569	−	0.224539i
$981$	22.5654	+	7.09754i	0.720457	+	0.226607i
$982$	2.37763	−	8.87342i	0.0758731	−	0.283162i
$983$	−33.7535	−	33.7535i	−1.07657	−	1.07657i	−0.996815	−	0.0797537i	$-0.974587\pi$
$983$	−33.7535	−	33.7535i	−1.07657	−	1.07657i	−0.0797537	−	0.996815i	$-0.525413\pi$
$984$	5.75209	+	4.61325i	0.183370	+	0.147065i
$985$	−28.1752	+	24.8589i	−0.897737	+	0.792070i
$986$	−29.6725	−	17.1314i	−0.944965	−	0.545576i
$987$	18.1884	+	7.99553i	0.578944	+	0.254500i
$988$	13.5589	+	10.4784i	0.431365	+	0.333362i
$989$	12.6934			0.403628
$990$	−1.79492	+	16.9687i	−0.0570464	+	0.539300i
$991$	−12.5441	+	21.7270i	−0.398477	+	0.690182i	−0.993538	−	0.113498i	$-0.963794\pi$
$991$	−12.5441	+	21.7270i	−0.398477	+	0.690182i	0.595062	+	0.803680i	$0.297128\pi$
$992$	−9.25485	−	2.47983i	−0.293842	−	0.0787347i
$993$	3.28443	+	1.44382i	0.104228	+	0.0458182i
$994$	−6.11565	+	3.53087i	−0.193977	+	0.111993i
$995$	2.91322	+	1.93394i	0.0923552	+	0.0613099i
$996$	15.7876	−	6.14581i	0.500250	−	0.194737i
$997$	9.47265	−	35.3524i	0.300002	−	1.11962i	−0.637161	−	0.770730i	$-0.719892\pi$
$997$	9.47265	−	35.3524i	0.300002	−	1.11962i	0.937163	−	0.348891i	$-0.113442\pi$
$998$	−22.7281	+	6.08998i	−0.719446	+	0.192775i
$999$	24.2042	+	36.1422i	0.765787	+	1.14349i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bl.a.347.3	yes	112
3.2	odd	2	inner	390.2.bl.a.347.28	yes	112
5.3	odd	4	inner	390.2.bl.a.113.5	yes	112
13.3	even	3	inner	390.2.bl.a.107.21	yes	112
15.8	even	4	inner	390.2.bl.a.113.21	yes	112
39.29	odd	6	inner	390.2.bl.a.107.5	✓	112
65.3	odd	12	inner	390.2.bl.a.263.28	yes	112
195.68	even	12	inner	390.2.bl.a.263.3	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bl.a.107.5	✓	112	39.29	odd	6	inner
390.2.bl.a.107.21	yes	112	13.3	even	3	inner
390.2.bl.a.113.5	yes	112	5.3	odd	4	inner
390.2.bl.a.113.21	yes	112	15.8	even	4	inner
390.2.bl.a.263.3	yes	112	195.68	even	12	inner
390.2.bl.a.263.28	yes	112	65.3	odd	12	inner
390.2.bl.a.347.3	yes	112	1.1	even	1	trivial
390.2.bl.a.347.28	yes	112	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bl (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-1.39645 + 1.02467i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.994998 - 2.00249i) q^{5} +(1.35118 + 1.08366i) q^{6} +(-0.839078 + 3.13148i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.900122 - 2.86178i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-1.39645 + 1.02467i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.994998 - 2.00249i) q^{5} +(1.35118 + 1.08366i) q^{6} +(-0.839078 + 3.13148i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.900122 - 2.86178i) q^{9} +(-1.67674 + 1.47938i) q^{10} +(2.20287 + 1.27183i) q^{11} +(0.697025 - 1.58561i) q^{12} +(0.482914 - 3.57307i) q^{13} +3.24195 q^{14} +(3.44135 + 1.77683i) q^{15} +(0.500000 - 0.866025i) q^{16} +(5.70384 + 1.52834i) q^{17} +(-2.99724 - 0.128768i) q^{18} +(4.11591 - 2.37632i) q^{19} +(1.86294 + 1.23671i) q^{20} +(-2.03699 - 5.23272i) q^{21} +(0.658346 - 2.45698i) q^{22} +(-2.54524 + 0.681994i) q^{23} +(-1.71198 - 0.262889i) q^{24} +(-3.01996 + 3.98495i) q^{25} +(-3.57630 + 0.458318i) q^{26} +(1.67539 + 4.91864i) q^{27} +(-0.839078 - 3.13148i) q^{28} +(2.90115 - 5.02494i) q^{29} +(0.825604 - 3.78396i) q^{30} +9.58133 q^{31} +(-0.965926 - 0.258819i) q^{32} +(-4.37939 + 0.481166i) q^{33} -5.90505i q^{34} +(7.10565 - 1.43557i) q^{35} +(0.651361 + 2.92843i) q^{36} +(8.08601 - 2.16664i) q^{37} +(-3.36063 - 3.36063i) q^{38} +(2.98683 + 5.48442i) q^{39} +(0.712407 - 2.11955i) q^{40} +(-3.68675 - 2.12855i) q^{41} +(-4.52720 + 3.32191i) q^{42} +(-4.65306 - 1.24678i) q^{43} -2.54366 q^{44} +(-6.62631 + 1.04498i) q^{45} +(1.31751 + 2.28200i) q^{46} +(-2.50195 + 2.50195i) q^{47} +(0.189163 + 1.72169i) q^{48} +(-3.03994 - 1.75511i) q^{49} +(4.63079 + 1.88567i) q^{50} +(-9.53114 + 3.71028i) q^{51} +(1.36832 + 3.33582i) q^{52} +(7.04203 + 7.04203i) q^{53} +(4.31742 - 2.89134i) q^{54} +(0.354975 - 5.67670i) q^{55} +(-2.80761 + 1.62097i) q^{56} +(-3.31271 + 7.53583i) q^{57} +(-5.60459 - 1.50174i) q^{58} +(0.0614633 + 0.106457i) q^{59} +(-3.86871 + 0.181890i) q^{60} +(-1.07943 - 1.86963i) q^{61} +(-2.47983 - 9.25485i) q^{62} +(8.20633 + 5.21997i) q^{63} +1.00000i q^{64} +(-7.63554 + 2.58816i) q^{65} +(1.59824 + 4.10563i) q^{66} +(-4.02597 + 1.07875i) q^{67} +(-5.70384 + 1.52834i) q^{68} +(2.85547 - 3.56038i) q^{69} +(-3.22573 - 6.49198i) q^{70} +(-1.88641 + 1.08912i) q^{71} +(2.66007 - 1.38710i) q^{72} +(-8.15170 + 8.15170i) q^{73} +(-4.18563 - 7.24972i) q^{74} +(0.133965 - 8.65922i) q^{75} +(-2.37632 + 4.11591i) q^{76} +(-5.83108 + 5.83108i) q^{77} +(4.52449 - 4.30453i) q^{78} -13.8606i q^{79} +(-2.23171 - 0.139553i) q^{80} +(-7.37956 - 5.15190i) q^{81} +(-1.10182 + 4.11204i) q^{82} +(6.91640 + 6.91640i) q^{83} +(4.38045 + 3.51317i) q^{84} +(-2.61482 - 12.9426i) q^{85} +4.81720i q^{86} +(1.09758 + 9.98976i) q^{87} +(0.658346 + 2.45698i) q^{88} +(-3.53326 + 6.11979i) q^{89} +(2.72439 + 6.13007i) q^{90} +(10.7838 + 4.51031i) q^{91} +(1.86324 - 1.86324i) q^{92} +(-13.3798 + 9.81765i) q^{93} +(3.06424 + 1.76914i) q^{94} +(-8.85389 - 5.87765i) q^{95} +(1.61407 - 0.628324i) q^{96} +(-1.31674 + 4.91414i) q^{97} +(-0.908512 + 3.39061i) q^{98} +(5.62254 - 5.15933i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q+O(q^{10}) \) 112 * q	\( 112 q + 24 q^{13} + 56 q^{16} - 16 q^{18} - 16 q^{21} + 24 q^{27} + 12 q^{30} - 80 q^{31} + 52 q^{33} - 8 q^{36} - 8 q^{37} - 16 q^{40} + 12 q^{42} - 8 q^{43} + 20 q^{45} - 8 q^{46} - 80 q^{51} + 24 q^{52} + 8 q^{55} - 96 q^{57} + 8 q^{58} - 32 q^{60} - 16 q^{61} - 16 q^{63} - 32 q^{66} + 40 q^{67} - 32 q^{70} - 8 q^{72} - 80 q^{73} - 64 q^{75} + 16 q^{76} - 36 q^{78} + 8 q^{81} - 16 q^{82} + 96 q^{85} - 8 q^{87} + 24 q^{90} - 32 q^{91} - 68 q^{93} - 40 q^{97}+O(q^{100}) \) 112 * q + 24 * q^13 + 56 * q^16 - 16 * q^18 - 16 * q^21 + 24 * q^27 + 12 * q^30 - 80 * q^31 + 52 * q^33 - 8 * q^36 - 8 * q^37 - 16 * q^40 + 12 * q^42 - 8 * q^43 + 20 * q^45 - 8 * q^46 - 80 * q^51 + 24 * q^52 + 8 * q^55 - 96 * q^57 + 8 * q^58 - 32 * q^60 - 16 * q^61 - 16 * q^63 - 32 * q^66 + 40 * q^67 - 32 * q^70 - 8 * q^72 - 80 * q^73 - 64 * q^75 + 16 * q^76 - 36 * q^78 + 8 * q^81 - 16 * q^82 + 96 * q^85 - 8 * q^87 + 24 * q^90 - 32 * q^91 - 68 * q^93 - 40 * q^97

Introduction

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