LMFDB - Embedded newform 130.2.n.a.9.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [130,2,Mod(9,130)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(130, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("130.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	130.n (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:	$1.03805522628$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			9.4
Root			$-0.531325 + 1.98293i$ of defining polynomial
Character	$\chi$	$=$	130.9
Dual form			130.2.n.a.29.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-1.91766 - 1.10716i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.21432 + 0.311108i) q^{5} +(-1.10716 - 1.91766i) q^{6} +(3.38028 - 1.95161i) q^{7} +1.00000i q^{8} +(0.951606 + 1.64823i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-1.91766 - 1.10716i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.21432 + 0.311108i) q^{5} +(-1.10716 - 1.91766i) q^{6} +(3.38028 - 1.95161i) q^{7} +1.00000i q^{8} +(0.951606 + 1.64823i) q^{9} +(1.76210 + 1.37659i) q^{10} +(-0.533338 + 0.923769i) q^{11} -2.21432i q^{12} +(-2.24483 + 2.82148i) q^{13} +3.90321 q^{14} +(-3.90186 - 3.04820i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.13545 + 0.655554i) q^{17} +1.90321i q^{18} +(-3.29605 - 5.70893i) q^{19} +(0.837733 + 2.07321i) q^{20} -8.64296 q^{21} +(-0.923769 + 0.533338i) q^{22} +(-1.85991 - 1.07382i) q^{23} +(1.10716 - 1.91766i) q^{24} +(4.80642 + 1.37778i) q^{25} +(-3.35482 + 1.32106i) q^{26} +2.42864i q^{27} +(3.38028 + 1.95161i) q^{28} +(-4.52543 + 7.83827i) q^{29} +(-1.85501 - 4.59075i) q^{30} -6.92396 q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.04552 - 1.18098i) q^{33} -1.31111 q^{34} +(8.09218 - 3.26985i) q^{35} +(-0.951606 + 1.64823i) q^{36} +(4.34809 + 2.51037i) q^{37} -6.59210i q^{38} +(7.42864 - 2.92525i) q^{39} +(-0.311108 + 2.21432i) q^{40} +(2.97703 - 5.15637i) q^{41} +(-7.48502 - 4.32148i) q^{42} +(1.73205 - 1.00000i) q^{43} -1.06668 q^{44} +(1.59438 + 3.94576i) q^{45} +(-1.07382 - 1.85991i) q^{46} +0.0967881i q^{47} +(1.91766 - 1.10716i) q^{48} +(4.11753 - 7.13177i) q^{49} +(3.47359 + 3.59641i) q^{50} +2.90321 q^{51} +(-3.56589 - 0.533338i) q^{52} -1.49532i q^{53} +(-1.21432 + 2.10326i) q^{54} +(-1.46837 + 1.87959i) q^{55} +(1.95161 + 3.38028i) q^{56} +14.5970i q^{57} +(-7.83827 + 4.52543i) q^{58} +(3.59210 + 6.22171i) q^{59} +(0.688892 - 4.90321i) q^{60} +(-3.94370 - 6.83068i) q^{61} +(-5.99632 - 3.46198i) q^{62} +(6.43339 + 3.71432i) q^{63} -1.00000 q^{64} +(-5.84855 + 5.54927i) q^{65} +2.36196 q^{66} +(-7.29942 - 4.21432i) q^{67} +(-1.13545 - 0.655554i) q^{68} +(2.37778 + 4.11844i) q^{69} +(8.64296 + 1.21432i) q^{70} +(7.73975 + 13.4056i) q^{71} +(-1.64823 + 0.951606i) q^{72} -15.3526i q^{73} +(2.51037 + 4.34809i) q^{74} +(-7.69165 - 7.96360i) q^{75} +(3.29605 - 5.70893i) q^{76} +4.16346i q^{77} +(7.89601 + 1.18098i) q^{78} -4.30174 q^{79} +(-1.37659 + 1.76210i) q^{80} +(5.54371 - 9.60199i) q^{81} +(5.15637 - 2.97703i) q^{82} +9.69381i q^{83} +(-4.32148 - 7.48502i) q^{84} +(-2.71820 + 1.09836i) q^{85} +2.00000 q^{86} +(17.3564 - 10.0207i) q^{87} +(-0.923769 - 0.533338i) q^{88} +(2.26271 - 3.91914i) q^{89} +(-0.592104 + 4.21432i) q^{90} +(-2.08173 + 13.9184i) q^{91} -2.14764i q^{92} +(13.2778 + 7.66593i) q^{93} +(-0.0483940 + 0.0838209i) q^{94} +(-5.52242 - 13.6668i) q^{95} +2.21432 q^{96} +(3.68949 - 2.13013i) q^{97} +(7.13177 - 4.11753i) q^{98} -2.03011 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} - 2 q^{9}+O(q^{10}) $ 12 * q + 6 * q^4 - 2 * q^9	$ 12 q + 6 q^{4} - 2 q^{9} - 2 q^{10} - 6 q^{11} + 20 q^{14} + 4 q^{15} - 6 q^{16} - 26 q^{19} - 24 q^{21} + 4 q^{25} - 28 q^{29} - 16 q^{30} + 24 q^{31} - 16 q^{34} - 6 q^{35} + 2 q^{36} + 36 q^{39} - 4 q^{40} - 4 q^{41} - 12 q^{44} + 12 q^{45} - 4 q^{49} - 8 q^{50} + 8 q^{51} + 12 q^{54} + 12 q^{55} + 10 q^{56} + 16 q^{59} + 8 q^{60} - 8 q^{61} - 12 q^{64} - 10 q^{65} - 24 q^{66} + 28 q^{69} + 24 q^{70} + 40 q^{71} - 10 q^{74} - 8 q^{75} + 26 q^{76} + 56 q^{79} + 26 q^{81} - 12 q^{84} - 16 q^{85} + 24 q^{86} + 14 q^{89} + 20 q^{90} - 38 q^{91} - 14 q^{94} - 8 q^{95} - 52 q^{99}+O(q^{100}) $ 12 * q + 6 * q^4 - 2 * q^9 - 2 * q^10 - 6 * q^11 + 20 * q^14 + 4 * q^15 - 6 * q^16 - 26 * q^19 - 24 * q^21 + 4 * q^25 - 28 * q^29 - 16 * q^30 + 24 * q^31 - 16 * q^34 - 6 * q^35 + 2 * q^36 + 36 * q^39 - 4 * q^40 - 4 * q^41 - 12 * q^44 + 12 * q^45 - 4 * q^49 - 8 * q^50 + 8 * q^51 + 12 * q^54 + 12 * q^55 + 10 * q^56 + 16 * q^59 + 8 * q^60 - 8 * q^61 - 12 * q^64 - 10 * q^65 - 24 * q^66 + 28 * q^69 + 24 * q^70 + 40 * q^71 - 10 * q^74 - 8 * q^75 + 26 * q^76 + 56 * q^79 + 26 * q^81 - 12 * q^84 - 16 * q^85 + 24 * q^86 + 14 * q^89 + 20 * q^90 - 38 * q^91 - 14 * q^94 - 8 * q^95 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/130\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−1.91766	−	1.10716i	−1.10716	−	0.639219i	−0.169068	−	0.985604i	$-0.554076\pi$
$3$	−1.91766	−	1.10716i	−1.10716	−	0.639219i	−0.938092	+	0.346385i	$0.887409\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	2.21432	+	0.311108i	0.990274	+	0.139132i
$5$	2.21432	+	0.311108i	0.990274	+	0.139132i
$6$	−1.10716	−	1.91766i	−0.451996	−	0.782880i
$7$	3.38028	−	1.95161i	1.27763	−	0.737638i	0.301215	−	0.953556i	$-0.402608\pi$
$7$	3.38028	−	1.95161i	1.27763	−	0.737638i	0.976411	+	0.215919i	$0.0692746\pi$
$8$			1.00000i			0.353553i
$9$	0.951606	+	1.64823i	0.317202	+	0.549410i
$10$	1.76210	+	1.37659i	0.557226	+	0.435315i
$11$	−0.533338	+	0.923769i	−0.160808	+	0.278527i	−0.935159	−	0.354229i	$-0.884743\pi$
$11$	−0.533338	+	0.923769i	−0.160808	+	0.278527i	0.774351	+	0.632756i	$0.218077\pi$
$12$		−	2.21432i		−	0.639219i
$13$	−2.24483	+	2.82148i	−0.622603	+	0.782538i
$13$	−2.24483	+	2.82148i	−0.622603	+	0.782538i
$14$	3.90321			1.04318
$15$	−3.90186	−	3.04820i	−1.00746	−	0.787043i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.13545	+	0.655554i	−0.275388	+	0.158995i	−0.631334	−	0.775511i	$-0.717492\pi$
$17$	−1.13545	+	0.655554i	−0.275388	+	0.158995i	0.355946	+	0.934507i	$0.384159\pi$
$18$			1.90321i			0.448591i
$19$	−3.29605	−	5.70893i	−0.756166	−	1.30972i	−0.944792	−	0.327669i	$-0.893737\pi$
$19$	−3.29605	−	5.70893i	−0.756166	−	1.30972i	0.188626	−	0.982049i	$-0.439597\pi$
$20$	0.837733	+	2.07321i	0.187323	+	0.463584i
$21$	−8.64296			−1.88605
$22$	−0.923769	+	0.533338i	−0.196948	+	0.113708i
$23$	−1.85991	−	1.07382i	−0.387819	−	0.223907i	0.293396	−	0.955991i	$-0.405215\pi$
$23$	−1.85991	−	1.07382i	−0.387819	−	0.223907i	−0.681215	+	0.732084i	$0.738548\pi$
$24$	1.10716	−	1.91766i	0.225998	−	0.391440i
$25$	4.80642	+	1.37778i	0.961285	+	0.275557i
$26$	−3.35482	+	1.32106i	−0.657934	+	0.259081i
$27$			2.42864i			0.467392i
$28$	3.38028	+	1.95161i	0.638813	+	0.368819i
$29$	−4.52543	+	7.83827i	−0.840351	+	1.45553i	0.0492475	+	0.998787i	$0.484318\pi$
$29$	−4.52543	+	7.83827i	−0.840351	+	1.45553i	−0.889598	+	0.456744i	$0.849016\pi$
$30$	−1.85501	−	4.59075i	−0.338677	−	0.838153i
$31$	−6.92396			−1.24358			−0.621790	−	0.783184i	$-0.713594\pi$
$31$	−6.92396			−1.24358			−0.621790	+	0.783184i	$0.713594\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	2.04552	−	1.18098i	0.356079	−	0.205582i
$34$	−1.31111			−0.224853
$35$	8.09218	−	3.26985i	1.36783	−	0.552705i
$36$	−0.951606	+	1.64823i	−0.158601	+	0.274705i
$37$	4.34809	+	2.51037i	0.714822	+	0.412703i	0.812844	−	0.582482i	$-0.197918\pi$
$37$	4.34809	+	2.51037i	0.714822	+	0.412703i	−0.0980220	+	0.995184i	$0.531252\pi$
$38$		−	6.59210i		−	1.06938i
$39$	7.42864	−	2.92525i	1.18953	−	0.468414i
$40$	−0.311108	+	2.21432i	−0.0491905	+	0.350115i
$41$	2.97703	−	5.15637i	0.464935	−	0.805290i	−0.534264	−	0.845318i	$-0.679411\pi$
$41$	2.97703	−	5.15637i	0.464935	−	0.805290i	0.999199	+	0.0400274i	$0.0127445\pi$
$42$	−7.48502	−	4.32148i	−1.15496	−	0.666819i
$43$	1.73205	−	1.00000i	0.264135	−	0.152499i	−0.362084	−	0.932145i	$-0.617935\pi$
$43$	1.73205	−	1.00000i	0.264135	−	0.152499i	0.626219	+	0.779647i	$0.284601\pi$
$44$	−1.06668			−0.160808
$45$	1.59438	+	3.94576i	0.237677	+	0.588199i
$46$	−1.07382	−	1.85991i	−0.158326	−	0.274229i
$47$			0.0967881i			0.0141180i	0.999975	+	0.00705900i	$0.00224697\pi$
$47$			0.0967881i			0.0141180i	−0.999975	+	0.00705900i	$0.997753\pi$
$48$	1.91766	−	1.10716i	0.276790	−	0.159805i
$49$	4.11753	−	7.13177i	0.588219	−	1.01882i
$50$	3.47359	+	3.59641i	0.491240	+	0.508609i
$51$	2.90321			0.406531
$52$	−3.56589	−	0.533338i	−0.494500	−	0.0739607i
$53$		−	1.49532i		−	0.205397i	−0.994713	−	0.102699i	$-0.967252\pi$
$53$		−	1.49532i		−	0.205397i	0.994713	−	0.102699i	$-0.0327478\pi$
$54$	−1.21432	+	2.10326i	−0.165248	+	0.286218i
$55$	−1.46837	+	1.87959i	−0.197995	+	0.253444i
$56$	1.95161	+	3.38028i	0.260794	+	0.451709i
$57$			14.5970i			1.93342i
$58$	−7.83827	+	4.52543i	−1.02922	+	0.594218i
$59$	3.59210	+	6.22171i	0.467652	+	0.809997i	0.999317	−	0.0369577i	$-0.0117667\pi$
$59$	3.59210	+	6.22171i	0.467652	+	0.809997i	−0.531665	+	0.846955i	$0.678433\pi$
$60$	0.688892	−	4.90321i	0.0889356	−	0.633002i
$61$	−3.94370	−	6.83068i	−0.504938	−	0.874579i	−0.999984	−	0.00571183i	$-0.998182\pi$
$61$	−3.94370	−	6.83068i	−0.504938	−	0.874579i	0.495045	−	0.868867i	$-0.335151\pi$
$62$	−5.99632	−	3.46198i	−0.761534	−	0.439672i
$63$	6.43339	+	3.71432i	0.810531	+	0.467960i
$64$	−1.00000			−0.125000
$65$	−5.84855	+	5.54927i	−0.725424	+	0.688303i
$66$	2.36196			0.290738
$67$	−7.29942	−	4.21432i	−0.891766	−	0.514861i	−0.0172460	−	0.999851i	$-0.505490\pi$
$67$	−7.29942	−	4.21432i	−0.891766	−	0.514861i	−0.874520	+	0.484990i	$0.838823\pi$
$68$	−1.13545	−	0.655554i	−0.137694	−	0.0794976i
$69$	2.37778	+	4.11844i	0.286252	+	0.495802i
$70$	8.64296	+	1.21432i	1.03303	+	0.145139i
$71$	7.73975	+	13.4056i	0.918539	+	1.59096i	0.801636	+	0.597813i	$0.203963\pi$
$71$	7.73975	+	13.4056i	0.918539	+	1.59096i	0.116903	+	0.993143i	$0.462703\pi$
$72$	−1.64823	+	0.951606i	−0.194246	+	0.112148i
$73$		−	15.3526i		−	1.79689i	−0.439091	−	0.898443i	$-0.644699\pi$
$73$		−	15.3526i		−	1.79689i	0.439091	−	0.898443i	$-0.355301\pi$
$74$	2.51037	+	4.34809i	0.291825	+	0.505455i
$75$	−7.69165	−	7.96360i	−0.888155	−	0.919557i
$76$	3.29605	−	5.70893i	0.378083	−	0.654859i
$77$			4.16346i			0.474471i
$78$	7.89601	+	1.18098i	0.894048	+	0.133720i
$79$	−4.30174			−0.483984			−0.241992	−	0.970278i	$-0.577801\pi$
$79$	−4.30174			−0.483984			−0.241992	+	0.970278i	$0.577801\pi$
$80$	−1.37659	+	1.76210i	−0.153907	+	0.197009i
$81$	5.54371	−	9.60199i	0.615968	−	1.06689i
$82$	5.15637	−	2.97703i	0.569426	−	0.328758i
$83$			9.69381i			1.06403i	0.846734	+	0.532017i	$0.178566\pi$
$83$			9.69381i			1.06403i	−0.846734	+	0.532017i	$0.821434\pi$
$84$	−4.32148	−	7.48502i	−0.471512	−	0.816683i
$85$	−2.71820	+	1.09836i	−0.294831	+	0.119134i
$86$	2.00000			0.215666
$87$	17.3564	−	10.0207i	1.86081	−	1.07434i
$88$	−0.923769	−	0.533338i	−0.0984741	−	0.0568541i
$89$	2.26271	−	3.91914i	0.239847	−	0.415428i	−0.720823	−	0.693119i	$-0.756236\pi$
$89$	2.26271	−	3.91914i	0.239847	−	0.415428i	0.960670	+	0.277692i	$0.0895693\pi$
$90$	−0.592104	+	4.21432i	−0.0624133	+	0.444228i
$91$	−2.08173	+	13.9184i	−0.218225	+	1.45905i
$92$		−	2.14764i		−	0.223907i
$93$	13.2778	+	7.66593i	1.37684	+	0.794919i
$94$	−0.0483940	+	0.0838209i	−0.00499146	+	0.00864547i
$95$	−5.52242	−	13.6668i	−0.566588	−	1.40219i
$96$	2.21432			0.225998
$97$	3.68949	−	2.13013i	0.374611	−	0.216282i	−0.300860	−	0.953668i	$-0.597274\pi$
$97$	3.68949	−	2.13013i	0.374611	−	0.216282i	0.675471	+	0.737387i	$0.263940\pi$
$98$	7.13177	−	4.11753i	0.720418	−	0.415934i
$99$	−2.03011			−0.204034
$100$	1.21002	+	4.85138i	0.121002	+	0.485138i
$101$	−0.729376	+	1.26332i	−0.0725756	+	0.125705i	−0.900029	−	0.435829i	$-0.856455\pi$
$101$	−0.729376	+	1.26332i	−0.0725756	+	0.125705i	0.827454	+	0.561534i	$0.189789\pi$
$102$	2.51426	+	1.45161i	0.248948	+	0.143730i
$103$		−	10.2444i		−	1.00941i	−0.863291	−	0.504707i	$-0.831601\pi$
$103$		−	10.2444i		−	1.00941i	0.863291	−	0.504707i	$-0.168399\pi$
$104$	−2.82148	−	2.24483i	−0.276669	−	0.220123i
$105$	−19.1383	−	2.68889i	−1.86770	−	0.262409i
$106$	0.747658	−	1.29498i	0.0726190	−	0.125780i
$107$	−1.91766	−	1.10716i	−0.185387	−	0.107033i	0.404434	−	0.914567i	$-0.367468\pi$
$107$	−1.91766	−	1.10716i	−0.185387	−	0.107033i	−0.589821	+	0.807534i	$0.700802\pi$
$108$	−2.10326	+	1.21432i	−0.202387	+	0.116848i
$109$	−0.133353			−0.0127729			−0.00638645	−	0.999980i	$-0.502033\pi$
$109$	−0.133353			−0.0127729			−0.00638645	+	0.999980i	$0.502033\pi$
$110$	−2.21145	+	0.893590i	−0.210853	+	0.0852004i
$111$	−5.55877	−	9.62806i	−0.527615	−	0.913855i
$112$			3.90321i			0.368819i
$113$	−12.1244	+	7.00000i	−1.14056	+	0.658505i	−0.946570	−	0.322498i	$-0.895477\pi$
$113$	−12.1244	+	7.00000i	−1.14056	+	0.658505i	−0.193993	+	0.981003i	$0.562144\pi$
$114$	−7.29851	+	12.6414i	−0.683568	+	1.18398i
$115$	−3.78437	−	2.95642i	−0.352894	−	0.275687i
$116$	−9.05086			−0.840351
$117$	−6.78664	−	1.01506i	−0.627425	−	0.0938419i
$118$			7.18421i			0.661360i
$119$	−2.55877	+	4.43191i	−0.234562	+	0.406273i
$120$	3.04820	−	3.90186i	0.278262	−	0.356189i
$121$	4.93110	+	8.54092i	0.448282	+	0.776447i
$122$		−	7.88739i		−	0.714091i
$123$	−11.4179	+	6.59210i	−1.02951	+	0.594390i
$124$	−3.46198	−	5.99632i	−0.310895	−	0.538486i
$125$	10.2143	+	4.54617i	0.913597	+	0.406622i
$126$	3.71432	+	6.43339i	0.330898	+	0.573132i
$127$	8.65214	+	4.99532i	0.767753	+	0.443263i	0.832073	−	0.554667i	$-0.187154\pi$
$127$	8.65214	+	4.99532i	0.767753	+	0.443263i	−0.0643192	+	0.997929i	$0.520488\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−4.42864			−0.389920
$130$	−7.83963	+	1.88154i	−0.687581	+	0.165022i
$131$	9.25581			0.808684			0.404342	−	0.914608i	$-0.367501\pi$
$131$	9.25581			0.808684			0.404342	+	0.914608i	$0.367501\pi$
$132$	2.04552	+	1.18098i	0.178040	+	0.102791i
$133$	−22.2832	−	12.8652i	−1.93220	−	1.11555i
$134$	−4.21432	−	7.29942i	−0.364062	−	0.630573i
$135$	−0.755569	+	5.37778i	−0.0650290	+	0.462846i
$136$	−0.655554	−	1.13545i	−0.0562133	−	0.0973643i
$137$	12.8090	−	7.39530i	1.09435	−	0.631823i	0.159619	−	0.987179i	$-0.448974\pi$
$137$	12.8090	−	7.39530i	1.09435	−	0.631823i	0.934731	+	0.355356i	$0.115640\pi$
$138$			4.75557i			0.404821i
$139$	−6.34691	−	10.9932i	−0.538338	−	0.932428i	−0.998994	−	0.0448494i	$-0.985719\pi$
$139$	−6.34691	−	10.9932i	−0.538338	−	0.932428i	0.460656	−	0.887579i	$-0.347614\pi$
$140$	6.87786	+	5.37311i	0.581285	+	0.454111i
$141$	0.107160	−	0.185606i	0.00902449	−	0.0156309i
$142$			15.4795i			1.29901i
$143$	−1.40914	−	3.57851i	−0.117838	−	0.299250i
$144$	−1.90321			−0.158601
$145$	−12.4593	+	15.9485i	−1.03469	+	1.32445i
$146$	7.67630	−	13.2957i	0.635295	−	1.10036i
$147$	−15.7920	+	9.11753i	−1.30250	+	0.752001i
$148$			5.02074i			0.412703i
$149$	3.64296	+	6.30979i	0.298443	+	0.516918i	0.975780	−	0.218755i	$-0.0701994\pi$
$149$	3.64296	+	6.30979i	0.298443	+	0.516918i	−0.677337	+	0.735673i	$0.736866\pi$
$150$	−2.67936	−	10.7425i	−0.218769	−	0.877122i
$151$	20.1082			1.63638			0.818190	−	0.574949i	$-0.194978\pi$
$151$	20.1082			1.63638			0.818190	+	0.574949i	$0.194978\pi$
$152$	5.70893	−	3.29605i	0.463055	−	0.267345i
$153$	−2.16101	−	1.24766i	−0.174707	−	0.100867i
$154$	−2.08173	+	3.60567i	−0.167751	+	0.290553i
$155$	−15.3319	−	2.15410i	−1.23148	−	0.173021i
$156$	6.24766	+	4.97077i	0.500213	+	0.397980i
$157$			1.98418i			0.158355i	0.996861	+	0.0791773i	$0.0252293\pi$
$157$			1.98418i			0.158355i	−0.996861	+	0.0791773i	$0.974771\pi$
$158$	−3.72542	−	2.15087i	−0.296378	−	0.171114i
$159$	−1.65555	+	2.86750i	−0.131294	+	0.227408i
$160$	−2.07321	+	0.837733i	−0.163902	+	0.0662286i
$161$	−8.38271			−0.660650
$162$	9.60199	−	5.54371i	0.754403	−	0.435555i
$163$	−4.07308	+	2.35159i	−0.319028	+	0.184191i	−0.650959	−	0.759113i	$-0.725633\pi$
$163$	−4.07308	+	2.35159i	−0.319028	+	0.184191i	0.331931	+	0.943304i	$0.392300\pi$
$164$	5.95407			0.464935
$165$	4.89685	−	1.97869i	0.381219	−	0.154041i
$166$	−4.84691	+	8.39509i	−0.376193	+	0.651585i
$167$	−8.39642	−	4.84767i	−0.649734	−	0.375124i	0.138620	−	0.990346i	$-0.455733\pi$
$167$	−8.39642	−	4.84767i	−0.649734	−	0.375124i	−0.788354	+	0.615221i	$0.789067\pi$
$168$		−	8.64296i		−	0.666819i
$169$	−2.92149	−	12.6675i	−0.224730	−	0.974421i
$170$	−2.90321	−	0.407896i	−0.222666	−	0.0312842i
$171$	6.27309	−	10.8653i	0.479715	−	0.830890i
$172$	1.73205	+	1.00000i	0.132068	+	0.0762493i
$173$	20.8466	−	12.0358i	1.58494	−	0.915065i	0.590816	−	0.806806i	$-0.298806\pi$
$173$	20.8466	−	12.0358i	1.58494	−	0.915065i	0.994123	−	0.108259i	$-0.0345275\pi$
$174$	20.0415			1.51934
$175$	18.9360	−	4.72295i	1.43142	−	0.357021i
$176$	−0.533338	−	0.923769i	−0.0402019	−	0.0696317i
$177$		−	15.9081i		−	1.19573i
$178$	3.91914	−	2.26271i	0.293752	−	0.169598i
$179$	1.52543	−	2.64212i	0.114016	−	0.197481i	−0.803370	−	0.595480i	$-0.796962\pi$
$179$	1.52543	−	2.64212i	0.114016	−	0.197481i	0.917386	+	0.397999i	$0.130295\pi$
$180$	−2.61994	+	3.35366i	−0.195279	+	0.249967i
$181$	10.6430			0.791085			0.395542	−	0.918448i	$-0.370557\pi$
$181$	10.6430			0.791085			0.395542	+	0.918448i	$0.370557\pi$
$182$	−8.76204	+	11.0128i	−0.649486	+	0.816325i
$183$			17.4652i			1.29107i
$184$	1.07382	−	1.85991i	0.0791632	−	0.137115i
$185$	8.84707	+	6.91149i	0.650449	+	0.508143i
$186$	7.66593	+	13.2778i	0.562093	+	0.973574i
$187$		−	1.39853i		−	0.102270i
$188$	−0.0838209	+	0.0483940i	−0.00611327	+	0.00352950i
$189$	4.73975	+	8.20948i	0.344766	+	0.597152i
$190$	2.05086	−	14.5970i	0.148785	−	1.05898i
$191$	−7.36519	−	12.7569i	−0.532926	−	0.923056i	−0.999261	−	0.0384470i	$-0.987759\pi$
$191$	−7.36519	−	12.7569i	−0.532926	−	0.923056i	0.466334	−	0.884609i	$-0.345574\pi$
$192$	1.91766	+	1.10716i	0.138395	+	0.0799024i
$193$	12.1244	+	7.00000i	0.872730	+	0.503871i	0.868255	−	0.496119i	$-0.165242\pi$
$193$	12.1244	+	7.00000i	0.872730	+	0.503871i	0.00447566	+	0.999990i	$0.498575\pi$
$194$	4.26025			0.305868
$195$	17.3595	−	4.16632i	1.24314	−	0.298357i
$196$	8.23506			0.588219
$197$	−9.01776	−	5.20641i	−0.642489	−	0.370941i	0.143084	−	0.989711i	$-0.454298\pi$
$197$	−9.01776	−	5.20641i	−0.642489	−	0.370941i	−0.785573	+	0.618769i	$0.787632\pi$
$198$	−1.75813	−	1.01506i	−0.124945	−	0.0721369i
$199$	−2.18421	−	3.78316i	−0.154834	−	0.268181i	0.778164	−	0.628061i	$-0.216151\pi$
$199$	−2.18421	−	3.78316i	−0.154834	−	0.268181i	−0.932999	+	0.359880i	$0.882818\pi$
$200$	−1.37778	+	4.80642i	−0.0974241	+	0.339865i
$201$	9.33185	+	16.1632i	0.658218	+	1.14007i
$202$	−1.26332	+	0.729376i	−0.0888866	+	0.0513187i
$203$			35.3274i			2.47950i
$204$	1.45161	+	2.51426i	0.101633	+	0.176033i
$205$	8.19629	−	10.4917i	0.572454	−	0.732771i
$206$	5.12222	−	8.87194i	0.356882	−	0.618137i
$207$		−	4.08742i		−	0.284095i
$208$	−1.32106	−	3.35482i	−0.0915990	−	0.232615i
$209$	7.03164			0.486389
$210$	−15.2298	−	11.8978i	−1.05096	−	0.821025i
$211$	−2.74766	+	4.75908i	−0.189157	+	0.327629i	−0.944969	−	0.327159i	$-0.893909\pi$
$211$	−2.74766	+	4.75908i	−0.189157	+	0.327629i	0.755813	+	0.654788i	$0.227242\pi$
$212$	1.29498	−	0.747658i	0.0889397	−	0.0513494i
$213$		−	34.2766i		−	2.34859i
$214$	−1.10716	−	1.91766i	−0.0756839	−	0.131088i
$215$	4.14642	−	1.67547i	0.282784	−	0.114266i
$216$	−2.42864			−0.165248
$217$	−23.4049	+	13.5128i	−1.58883	+	0.917311i
$218$	−0.115487	−	0.0666765i	−0.00782178	−	0.00451591i
$219$	−16.9978	+	29.4410i	−1.14860	+	1.98944i
$220$	−2.36196	−	0.331851i	−0.159244	−	0.0223734i
$221$	0.699264	−	4.67526i	0.0470376	−	0.314492i
$222$		−	11.1175i		−	0.746160i
$223$	17.4043	+	10.0484i	1.16548	+	0.672890i	0.952611	−	0.304191i	$-0.0983860\pi$
$223$	17.4043	+	10.0484i	1.16548	+	0.672890i	0.212869	+	0.977081i	$0.431719\pi$
$224$	−1.95161	+	3.38028i	−0.130397	+	0.225855i
$225$	2.30292	+	9.23320i	0.153528	+	0.615547i
$226$	−14.0000			−0.931266
$227$	−16.7654	+	9.67952i	−1.11276	+	0.642453i	−0.939543	−	0.342431i	$-0.888750\pi$
$227$	−16.7654	+	9.67952i	−1.11276	+	0.642453i	−0.173218	+	0.984884i	$0.555416\pi$
$228$	−12.6414	+	7.29851i	−0.837197	+	0.483356i
$229$	−15.7255			−1.03917			−0.519584	−	0.854420i	$-0.673913\pi$
$229$	−15.7255			−1.03917			−0.519584	+	0.854420i	$0.673913\pi$
$230$	−1.79915	−	4.45252i	−0.118632	−	0.293590i
$231$	4.60962	−	7.98410i	0.303291	−	0.525315i
$232$	−7.83827	−	4.52543i	−0.514608	−	0.297109i
$233$		−	14.8825i		−	0.974983i	−0.873128	−	0.487491i	$-0.837912\pi$
$233$		−	14.8825i		−	0.974983i	0.873128	−	0.487491i	$-0.162088\pi$
$234$	−5.36987	−	4.27238i	−0.351040	−	0.279294i
$235$	−0.0301115	+	0.214320i	−0.00196426	+	0.0139807i
$236$	−3.59210	+	6.22171i	−0.233826	+	0.404999i
$237$	8.24926	+	4.76271i	0.535847	+	0.309372i
$238$	−4.43191	+	2.55877i	−0.287278	+	0.165860i
$239$	−4.42219			−0.286047			−0.143024	−	0.989719i	$-0.545683\pi$
$239$	−4.42219			−0.286047			−0.143024	+	0.989719i	$0.545683\pi$
$240$	4.59075	−	1.85501i	0.296332	−	0.119740i
$241$	5.64050	+	9.76963i	0.363336	+	0.629317i	0.988508	−	0.151170i	$-0.0483042\pi$
$241$	5.64050	+	9.76963i	0.363336	+	0.629317i	−0.625171	+	0.780488i	$0.714971\pi$
$242$			9.86220i			0.633966i
$243$	−14.9521	+	8.63259i	−0.959176	+	0.553781i
$244$	3.94370	−	6.83068i	0.252469	−	0.437290i
$245$	11.3363	−	14.5110i	0.724249	−	0.927076i
$246$	−13.1842			−0.840594
$247$	23.5067	+	3.51582i	1.49570	+	0.223706i
$248$		−	6.92396i		−	0.439672i
$249$	10.7326	−	18.5894i	0.680151	−	1.17806i
$250$	6.57277	+	9.04426i	0.415699	+	0.572009i
$251$	−1.32616	−	2.29698i	−0.0837067	−	0.144984i	0.821133	−	0.570737i	$-0.193343\pi$
$251$	−1.32616	−	2.29698i	−0.0837067	−	0.144984i	−0.904839	+	0.425753i	$0.860009\pi$
$252$			7.42864i			0.467960i
$253$	1.98393	−	1.14542i	0.124728	−	0.0720120i
$254$	4.99532	+	8.65214i	0.313434	+	0.542884i
$255$	6.42864	+	0.903212i	0.402577	+	0.0565613i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.55219	+	2.05086i	0.221579	+	0.127929i	0.606681	−	0.794945i	$-0.292500\pi$
$257$	3.55219	+	2.05086i	0.221579	+	0.127929i	−0.385102	+	0.922874i	$0.625834\pi$
$258$	−3.83531	−	2.21432i	−0.238776	−	0.137858i
$259$	19.5970			1.21770
$260$	−7.73009	−	2.29036i	−0.479400	−	0.142042i
$261$	−17.2257			−1.06624
$262$	8.01576	+	4.62790i	0.495216	+	0.285913i
$263$	9.35479	+	5.40099i	0.576841	+	0.333039i	0.759877	−	0.650067i	$-0.225259\pi$
$263$	9.35479	+	5.40099i	0.576841	+	0.333039i	−0.183036	+	0.983106i	$0.558593\pi$
$264$	1.18098	+	2.04552i	0.0726844	+	0.125893i
$265$	0.465205	−	3.31111i	0.0285773	−	0.203400i
$266$	−12.8652	−	22.2832i	−0.788815	−	1.36627i
$267$	−8.67822	+	5.01037i	−0.531098	+	0.306630i
$268$		−	8.42864i		−	0.514861i
$269$	−9.29137	−	16.0931i	−0.566505	−	0.981215i	−0.996908	−	0.0785782i	$-0.974962\pi$
$269$	−9.29137	−	16.0931i	−0.566505	−	0.981215i	0.430403	−	0.902637i	$-0.358371\pi$
$270$	−3.34323	+	4.27951i	−0.203463	+	0.260443i
$271$	−9.88739	+	17.1255i	−0.600616	+	1.04030i	0.392112	+	0.919918i	$0.371745\pi$
$271$	−9.88739	+	17.1255i	−0.600616	+	1.04030i	−0.992728	+	0.120380i	$0.961589\pi$
$272$		−	1.31111i		−	0.0794976i
$273$	19.4020	−	24.3859i	1.17426	−	1.47590i
$274$	14.7906			0.893533
$275$	−3.83620	+	3.70520i	−0.231332	+	0.223432i
$276$	−2.37778	+	4.11844i	−0.143126	+	0.247901i
$277$	−0.177493	+	0.102476i	−0.0106645	+	0.00615718i	−0.505323	−	0.862930i	$-0.668627\pi$
$277$	−0.177493	+	0.102476i	−0.0106645	+	0.00615718i	0.494658	+	0.869088i	$0.335293\pi$
$278$		−	12.6938i		−	0.761324i
$279$	−6.58888	−	11.4123i	−0.394466	−	0.683235i
$280$	3.26985	+	8.09218i	0.195411	+	0.483600i
$281$	−20.4558			−1.22029			−0.610146	−	0.792289i	$-0.708889\pi$
$281$	−20.4558			−1.22029			−0.610146	+	0.792289i	$0.708889\pi$
$282$	0.185606	−	0.107160i	0.0110527	−	0.00638128i
$283$	−1.24535	−	0.719004i	−0.0740284	−	0.0427403i	0.462529	−	0.886604i	$-0.346942\pi$
$283$	−1.24535	−	0.719004i	−0.0740284	−	0.0427403i	−0.536557	+	0.843864i	$0.680275\pi$
$284$	−7.73975	+	13.4056i	−0.459270	+	0.795478i
$285$	−4.54125	+	32.3225i	−0.269000	+	1.91462i
$286$	0.568899	−	3.80365i	0.0336397	−	0.224914i
$287$		−	23.2400i		−	1.37181i
$288$	−1.64823	−	0.951606i	−0.0971229	−	0.0560739i
$289$	−7.64050	+	13.2337i	−0.449441	+	0.778455i
$290$	−18.7643	+	7.58220i	−1.10188	+	0.445242i
$291$	−9.43356			−0.553005
$292$	13.2957	−	7.67630i	0.778074	−	0.449221i
$293$	−18.1126	+	10.4573i	−1.05815	+	0.610922i	−0.924919	−	0.380164i	$-0.875868\pi$
$293$	−18.1126	+	10.4573i	−1.05815	+	0.610922i	−0.133228	+	0.991085i	$0.542534\pi$
$294$	−18.2351			−1.06349
$295$	6.01845	+	14.8944i	0.350407	+	0.867184i
$296$	−2.51037	+	4.34809i	−0.145912	+	0.252728i
$297$	−2.24350	−	1.29529i	−0.130181	−	0.0751601i
$298$			7.28592i			0.422062i
$299$	7.20495	−	2.83716i	0.416673	−	0.164077i
$300$	3.05086	−	10.6430i	0.176141	−	0.614472i
$301$	3.90321	−	6.76056i	0.224977	−	0.389672i
$302$	17.4142	+	10.0541i	1.00207	+	0.578547i
$303$	2.79738	−	1.61507i	0.160706	−	0.0927834i
$304$	6.59210			0.378083
$305$	−6.60752	−	16.3522i	−0.378346	−	0.936326i
$306$	−1.24766	−	2.16101i	−0.0713239	−	0.123537i
$307$		−	12.5303i		−	0.715145i	−0.933885	−	0.357572i	$-0.883605\pi$
$307$		−	12.5303i		−	0.715145i	0.933885	−	0.357572i	$-0.116395\pi$
$308$	−3.60567	+	2.08173i	−0.205452	+	0.118618i
$309$	−11.3422	+	19.6453i	−0.645237	+	1.11758i
$310$	−12.2007	−	9.53143i	−0.692955	−	0.541349i
$311$	−9.78123			−0.554643			−0.277321	−	0.960777i	$-0.589447\pi$
$311$	−9.78123			−0.554643			−0.277321	+	0.960777i	$0.589447\pi$
$312$	2.92525	+	7.42864i	0.165610	+	0.420564i
$313$			17.2128i			0.972924i	0.873702	+	0.486462i	$0.161713\pi$
$313$			17.2128i			0.972924i	−0.873702	+	0.486462i	$0.838287\pi$
$314$	−0.992089	+	1.71835i	−0.0559868	+	0.0969720i
$315$	13.0900	+	10.2262i	0.737540	+	0.576179i
$316$	−2.15087	−	3.72542i	−0.120996	−	0.209571i
$317$		−	13.7447i		−	0.771978i	−0.922503	−	0.385989i	$-0.873860\pi$
$317$		−	13.7447i		−	0.771978i	0.922503	−	0.385989i	$-0.126140\pi$
$318$	−2.86750	+	1.65555i	−0.160802	+	0.0928389i
$319$	−4.82717	−	8.36090i	−0.270269	−	0.468120i
$320$	−2.21432	−	0.311108i	−0.123784	−	0.0173915i
$321$	2.45161	+	4.24631i	0.136835	+	0.237006i
$322$	−7.25964	−	4.19135i	−0.404564	−	0.233575i
$323$	7.48502	+	4.32148i	0.416478	+	0.240454i
$324$	11.0874			0.615968
$325$	−14.6770	+	10.4683i	−0.814133	+	0.580679i
$326$	−4.70318			−0.260485
$327$	0.255726	+	0.147643i	0.0141417	+	0.00816469i
$328$	5.15637	+	2.97703i	0.284713	+	0.164379i
$329$	0.188892	+	0.327171i	0.0104140	+	0.0180375i
$330$	5.23014	+	0.734825i	0.287910	+	0.0404508i
$331$	−9.69381	−	16.7902i	−0.532820	−	0.922872i	−0.999265	−	0.0383216i	$-0.987799\pi$
$331$	−9.69381	−	16.7902i	−0.532820	−	0.922872i	0.466445	−	0.884550i	$-0.345534\pi$
$332$	−8.39509	+	4.84691i	−0.460740	+	0.266009i
$333$			9.55554i			0.523640i
$334$	−4.84767	−	8.39642i	−0.265253	−	0.459431i
$335$	−14.8521	−	11.6028i	−0.811459	−	0.633926i
$336$	4.32148	−	7.48502i	0.235756	−	0.408341i
$337$		−	0.555539i		−	0.0302621i	−0.999886	−	0.0151311i	$-0.995183\pi$
$337$		−	0.555539i		−	0.0302621i	0.999886	−	0.0151311i	$-0.00481655\pi$
$338$	3.80365	−	12.4311i	0.206891	−	0.676163i
$339$	31.0005			1.68371
$340$	−2.31031	−	1.80485i	−0.125294	−	0.0978820i
$341$	3.69281	−	6.39614i	0.199977	−	0.346370i
$342$	10.8653	−	6.27309i	0.587528	−	0.339210i
$343$		−	4.82071i		−	0.260294i
$344$	1.00000	+	1.73205i	0.0539164	+	0.0933859i
$345$	3.98389	+	9.85930i	0.214486	+	0.530807i
$346$	24.0716			1.29410
$347$	−5.78890	+	3.34222i	−0.310764	+	0.179420i	−0.647269	−	0.762262i	$-0.724089\pi$
$347$	−5.78890	+	3.34222i	−0.310764	+	0.179420i	0.336504	+	0.941682i	$0.390755\pi$
$348$	17.3564	+	10.0207i	0.930403	+	0.537168i
$349$	5.29137	−	9.16492i	0.283240	−	0.490587i	−0.688941	−	0.724818i	$-0.741924\pi$
$349$	5.29137	−	9.16492i	0.283240	−	0.490587i	0.972181	+	0.234231i	$0.0752572\pi$
$350$	18.7605	+	5.37778i	1.00279	+	0.287455i
$351$	−6.85236	−	5.45188i	−0.365752	−	0.291000i
$352$		−	1.06668i		−	0.0568541i
$353$	7.97557	+	4.60470i	0.424497	+	0.245083i	0.696999	−	0.717072i	$-0.254518\pi$
$353$	7.97557	+	4.60470i	0.424497	+	0.245083i	−0.272503	+	0.962155i	$0.587851\pi$
$354$	7.95407	−	13.7768i	0.422754	−	0.732231i
$355$	12.9677	+	32.0923i	0.688253	+	1.70328i
$356$	4.52543			0.239847
$357$	9.81367	−	5.66593i	0.519395	−	0.299873i
$358$	2.64212	−	1.52543i	0.139640	−	0.0806214i
$359$	4.19358			0.221328			0.110664	−	0.993858i	$-0.464702\pi$
$359$	4.19358			0.221328			0.110664	+	0.993858i	$0.464702\pi$
$360$	−3.94576	+	1.59438i	−0.207960	+	0.0840313i
$361$	−12.2279	+	21.1794i	−0.643575	+	1.11470i
$362$	9.21707	+	5.32148i	0.484439	+	0.279691i
$363$		−	21.8381i		−	1.14620i
$364$	−13.0946	+	5.15637i	−0.686342	+	0.270267i
$365$	4.77631	−	33.9956i	0.250004	−	1.77941i
$366$	−8.73260	+	15.1253i	−0.456460	+	0.790613i
$367$	12.0970	+	6.98418i	0.631456	+	0.364571i	0.781316	−	0.624136i	$-0.214549\pi$
$367$	12.0970	+	6.98418i	0.631456	+	0.364571i	−0.149860	+	0.988707i	$0.547882\pi$
$368$	1.85991	−	1.07382i	0.0969547	−	0.0559768i
$369$	11.3319			0.589913
$370$	4.20604	+	10.4091i	0.218662	+	0.541141i
$371$	−2.91827	−	5.05459i	−0.151509	−	0.262421i
$372$			15.3319i			0.794919i
$373$	10.2606	−	5.92396i	0.531273	−	0.306731i	−0.210262	−	0.977645i	$-0.567432\pi$
$373$	10.2606	−	5.92396i	0.531273	−	0.306731i	0.741535	+	0.670914i	$0.234098\pi$
$374$	0.699264	−	1.21116i	0.0361581	−	0.0626276i
$375$	−14.5542	−	20.0269i	−0.751577	−	1.03418i
$376$	−0.0967881			−0.00499146
$377$	−11.9567	−	30.3640i	−0.615802	−	1.56382i
$378$			9.47949i			0.487573i
$379$	0.303197	−	0.525153i	0.0155742	−	0.0269753i	−0.858133	−	0.513427i	$-0.828376\pi$
$379$	0.303197	−	0.525153i	0.0155742	−	0.0269753i	0.873707	+	0.486452i	$0.161709\pi$
$380$	9.07461	−	11.6160i	0.465517	−	0.595887i
$381$	−11.0612	−	19.1586i	−0.566684	−	0.981525i
$382$		−	14.7304i		−	0.753672i
$383$	−30.1201	+	17.3899i	−1.53907	+	0.888580i	−0.540172	+	0.841555i	$0.681641\pi$
$383$	−30.1201	+	17.3899i	−1.53907	+	0.888580i	−0.998894	+	0.0470252i	$0.985026\pi$
$384$	1.10716	+	1.91766i	0.0564995	+	0.0978600i
$385$	−1.29529	+	9.21924i	−0.0660139	+	0.469856i
$386$	7.00000	+	12.1244i	0.356291	+	0.617113i
$387$	3.29646	+	1.90321i	0.167568	+	0.0967457i
$388$	3.68949	+	2.13013i	0.187305	+	0.108141i
$389$	18.6844			0.947339			0.473670	−	0.880703i	$-0.342929\pi$
$389$	18.6844			0.947339			0.473670	+	0.880703i	$0.342929\pi$
$390$	17.1169	+	5.07158i	0.866747	+	0.256810i
$391$	2.81579			0.142401
$392$	7.13177	+	4.11753i	0.360209	+	0.207967i
$393$	−17.7495	−	10.2477i	−0.895342	−	0.516926i
$394$	−5.20641	−	9.01776i	−0.262295	−	0.454308i
$395$	−9.52543	−	1.33830i	−0.479276	−	0.0673374i
$396$	−1.01506	−	1.75813i	−0.0510085	−	0.0883493i
$397$	−19.8968	+	11.4874i	−0.998590	+	0.576536i	−0.907831	−	0.419337i	$-0.862263\pi$
$397$	−19.8968	+	11.4874i	−0.998590	+	0.576536i	−0.0907594	+	0.995873i	$0.528929\pi$
$398$		−	4.36842i		−	0.218969i
$399$	28.4876	+	49.3420i	1.42617	+	2.47019i
$400$	−3.59641	+	3.47359i	−0.179820	+	0.173680i
$401$	2.18667	−	3.78742i	0.109197	−	0.189135i	−0.806248	−	0.591577i	$-0.798505\pi$
$401$	2.18667	−	3.78742i	0.109197	−	0.189135i	0.915445	+	0.402443i	$0.131839\pi$
$402$			18.6637i			0.930861i
$403$	15.5431	−	19.5358i	0.774256	−	0.973147i
$404$	−1.45875			−0.0725756
$405$	15.2628	−	19.5372i	0.758415	−	0.970810i
$406$	−17.6637	+	30.5944i	−0.876635	+	1.51838i
$407$	−4.63801	+	2.67775i	−0.229897	+	0.132731i
$408$			2.90321i			0.143730i
$409$	−1.88493	−	3.26479i	−0.0932038	−	0.161434i	0.815654	−	0.578540i	$-0.196377\pi$
$409$	−1.88493	−	3.26479i	−0.0932038	−	0.161434i	−0.908858	+	0.417107i	$0.863044\pi$
$410$	12.3440	−	4.98792i	0.609629	−	0.246336i
$411$	−32.7511			−1.61549
$412$	8.87194	−	5.12222i	0.437089	−	0.252353i
$413$	24.2846	+	14.0207i	1.19497	+	0.689916i
$414$	2.04371	−	3.53981i	0.100443	−	0.173972i
$415$	−3.01582	+	21.4652i	−0.148041	+	1.05369i
$416$	0.533338	−	3.56589i	0.0261491	−	0.174832i
$417$			28.1082i			1.37646i
$418$	6.08958	+	3.51582i	0.297851	+	0.171964i
$419$	3.72615	−	6.45388i	0.182034	−	0.315293i	−0.760539	−	0.649292i	$-0.775065\pi$
$419$	3.72615	−	6.45388i	0.182034	−	0.315293i	0.942573	+	0.334000i	$0.108398\pi$
$420$	−7.24049	−	17.9187i	−0.353300	−	0.874342i
$421$	27.6751			1.34880			0.674400	−	0.738366i	$-0.264402\pi$
$421$	27.6751			1.34880			0.674400	+	0.738366i	$0.264402\pi$
$422$	−4.75908	+	2.74766i	−0.231669	+	0.133754i
$423$	−0.159529	+	0.0921041i	−0.00775657	+	0.00447825i
$424$	1.49532			0.0726190
$425$	−6.36068	+	1.58646i	−0.308538	+	0.0769547i
$426$	17.1383	−	29.6844i	0.830352	−	1.43821i
$427$	−26.6616	−	15.3931i	−1.29024	−	0.744923i
$428$		−	2.21432i		−	0.107033i
$429$	−1.25973	+	8.42249i	−0.0608201	+	0.406642i
$430$	4.42864	+	0.622216i	0.213568	+	0.0300059i
$431$	−9.84468	+	17.0515i	−0.474202	+	0.821342i	−0.999564	−	0.0295373i	$-0.990597\pi$
$431$	−9.84468	+	17.0515i	−0.474202	+	0.821342i	0.525362	+	0.850879i	$0.323930\pi$
$432$	−2.10326	−	1.21432i	−0.101193	−	0.0584240i
$433$	−11.9046	+	6.87310i	−0.572097	+	0.330300i	−0.757986	−	0.652270i	$-0.773817\pi$
$433$	−11.9046	+	6.87310i	−0.572097	+	0.330300i	0.185890	+	0.982571i	$0.440483\pi$
$434$	−27.0257			−1.29727
$435$	41.5502	−	16.7894i	1.99218	−	0.804990i
$436$	−0.0666765	−	0.115487i	−0.00319323	−	0.00553083i
$437$			14.1575i			0.677244i
$438$	−29.4410	+	16.9978i	−1.40675	+	0.812185i
$439$	20.9114	−	36.2195i	0.998045	−	1.72866i	0.444894	−	0.895583i	$-0.353242\pi$
$439$	20.9114	−	36.2195i	0.998045	−	1.72866i	0.553151	−	0.833081i	$-0.313425\pi$
$440$	−1.87959	−	1.46837i	−0.0896061	−	0.0700019i
$441$	15.6731			0.746337
$442$	2.94321	−	3.69926i	0.139994	−	0.175956i
$443$		−	23.6829i		−	1.12521i	−0.826726	−	0.562605i	$-0.809799\pi$
$443$		−	23.6829i		−	1.12521i	0.826726	−	0.562605i	$-0.190201\pi$
$444$	5.55877	−	9.62806i	0.263807	−	0.456928i
$445$	6.22965	−	7.97427i	0.295314	−	0.378017i
$446$	10.0484	+	17.4043i	0.475805	+	0.824119i
$447$		−	16.1334i		−	0.763081i
$448$	−3.38028	+	1.95161i	−0.159703	+	0.0922047i
$449$	3.52789	+	6.11048i	0.166491	+	0.288371i	0.937184	−	0.348836i	$-0.113423\pi$
$449$	3.52789	+	6.11048i	0.166491	+	0.288371i	−0.770693	+	0.637207i	$0.780090\pi$
$450$	−2.62222	+	9.14764i	−0.123612	+	0.431224i
$451$	3.17553	+	5.50018i	0.149530	+	0.258993i
$452$	−12.1244	−	7.00000i	−0.570282	−	0.329252i
$453$	−38.5606	−	22.2630i	−1.81173	−	1.04600i
$454$	−19.3590			−0.908565
$455$	−8.93975	+	30.1722i	−0.419102	+	1.41449i
$456$	−14.5970			−0.683568
$457$	−30.8994	−	17.8398i	−1.44541	−	0.834509i	−0.447209	−	0.894430i	$-0.647582\pi$
$457$	−30.8994	−	17.8398i	−1.44541	−	0.834509i	−0.998203	+	0.0599208i	$0.980915\pi$
$458$	−13.6186	−	7.86273i	−0.636358	−	0.367401i
$459$	−1.59210	−	2.75761i	−0.0743131	−	0.128714i
$460$	0.668149	−	4.75557i	0.0311526	−	0.221730i
$461$	7.30074	+	12.6452i	0.340029	+	0.588948i	0.984438	−	0.175734i	$-0.0562297\pi$
$461$	7.30074	+	12.6452i	0.340029	+	0.588948i	−0.644409	+	0.764681i	$0.722896\pi$
$462$	7.98410	−	4.60962i	0.371454	−	0.214459i
$463$			30.7511i			1.42913i	0.699571	+	0.714563i	$0.253374\pi$
$463$			30.7511i			1.42913i	−0.699571	+	0.714563i	$0.746626\pi$
$464$	−4.52543	−	7.83827i	−0.210088	−	0.363883i
$465$	27.0163	+	21.1056i	1.25285	+	0.978750i
$466$	7.44123	−	12.8886i	0.344709	−	0.597053i
$467$			20.5620i			0.951496i	0.879582	+	0.475748i	$0.157822\pi$
$467$			20.5620i			0.951496i	−0.879582	+	0.475748i	$0.842178\pi$
$468$	−2.51426	−	6.38493i	−0.116221	−	0.295143i
$469$	−32.8988			−1.51912
$470$	−0.133237	+	0.170551i	−0.00614577	+	0.00786691i
$471$	2.19680	−	3.80497i	0.101223	−	0.175324i
$472$	−6.22171	+	3.59210i	−0.286377	+	0.165340i
$473$			2.13335i			0.0980917i
$474$	4.76271	+	8.24926i	0.218759	+	0.378901i
$475$	−7.97655	−	31.9808i	−0.365989	−	1.46738i
$476$	−5.11753			−0.234562
$477$	2.46462	−	1.42295i	0.112847	−	0.0651525i
$478$	−3.82973	−	2.21109i	−0.175168	−	0.101133i
$479$	5.96666	−	10.3346i	0.272624	−	0.472198i	−0.696909	−	0.717159i	$-0.745442\pi$
$479$	5.96666	−	10.3346i	0.272624	−	0.472198i	0.969533	+	0.244961i	$0.0787753\pi$
$480$	4.90321	+	0.688892i	0.223800	+	0.0314435i
$481$	−16.8437	+	6.63270i	−0.768006	+	0.302425i
$482$			11.2810i			0.513835i
$483$	16.0752	+	9.28100i	0.731445	+	0.422300i
$484$	−4.93110	+	8.54092i	−0.224141	+	0.388223i
$485$	8.83240	−	3.56895i	0.401059	−	0.162058i
$486$	−17.2652			−0.783164
$487$	24.2244	−	13.9859i	1.09771	−	0.633764i	0.162092	−	0.986776i	$-0.448176\pi$
$487$	24.2244	−	13.9859i	1.09771	−	0.633764i	0.935619	+	0.353012i	$0.114842\pi$
$488$	6.83068	−	3.94370i	0.309210	−	0.178523i
$489$	10.4143			0.470953
$490$	17.0730	−	6.89878i	0.771281	−	0.311655i
$491$	10.3906	−	17.9971i	0.468922	−	0.812197i	−0.530447	−	0.847718i	$-0.677976\pi$
$491$	10.3906	−	17.9971i	0.468922	−	0.812197i	0.999369	+	0.0355214i	$0.0113092\pi$
$492$	−11.4179	−	6.59210i	−0.514757	−	0.297195i
$493$		−	11.8666i		−	0.534447i
$494$	18.5995	+	14.7981i	0.836830	+	0.665800i
$495$	−4.49532	−	0.631584i	−0.202049	−	0.0283876i
$496$	3.46198	−	5.99632i	0.155447	−	0.269243i
$497$	52.3250	+	30.2099i	2.34710	+	1.35510i
$498$	18.5894	−	10.7326i	0.833011	−	0.480939i
$499$	−34.2908			−1.53507			−0.767534	−	0.641008i	$-0.778517\pi$
$499$	−34.2908			−1.53507			−0.767534	+	0.641008i	$0.778517\pi$
$500$	1.17006	+	11.1189i	0.0523267	+	0.497254i
$501$	10.7343	+	18.5923i	0.479573	+	0.830645i
$502$		−	2.65233i		−	0.118379i
$503$	−17.5160	+	10.1128i	−0.780998	+	0.450910i	−0.836784	−	0.547533i	$-0.815567\pi$
$503$	−17.5160	+	10.1128i	−0.780998	+	0.450910i	0.0557857	+	0.998443i	$0.482234\pi$
$504$	−3.71432	+	6.43339i	−0.165449	+	0.286566i
$505$	−2.00810	+	2.57047i	−0.0893592	+	0.114384i
$506$	2.29084			0.101840
$507$	−8.42249	+	27.5264i	−0.374056	+	1.22249i
$508$			9.99063i			0.443263i
$509$	−13.6889	+	23.7099i	−0.606749	+	1.05092i	0.385023	+	0.922907i	$0.374194\pi$
$509$	−13.6889	+	23.7099i	−0.606749	+	1.05092i	−0.991772	+	0.128014i	$0.959140\pi$
$510$	5.11576	+	3.99652i	0.226530	+	0.176969i
$511$	−29.9622	−	51.8961i	−1.32545	−	2.29575i
$512$		−	1.00000i		−	0.0441942i
$513$	13.8649	−	8.00492i	0.612152	−	0.353426i
$514$	2.05086	+	3.55219i	0.0904593	+	0.156680i
$515$	3.18712	−	22.6844i	0.140441	−	0.999596i
$516$	−2.21432	−	3.83531i	−0.0974800	−	0.168840i
$517$	−0.0894098	−	0.0516208i	−0.00393224	−	0.00227028i
$518$	16.9715	+	9.79851i	0.745686	+	0.430522i
$519$	−53.3022			−2.33971
$520$	−5.54927	−	5.84855i	−0.243352	−	0.256476i
$521$	−31.2034			−1.36705			−0.683523	−	0.729929i	$-0.739553\pi$
$521$	−31.2034			−1.36705			−0.683523	+	0.729929i	$0.739553\pi$
$522$	−14.9179	−	8.61285i	−0.652938	−	0.376974i
$523$	8.52854	+	4.92396i	0.372927	+	0.215310i	0.674736	−	0.738059i	$-0.264257\pi$
$523$	8.52854	+	4.92396i	0.372927	+	0.215310i	−0.301809	+	0.953368i	$0.597591\pi$
$524$	4.62790	+	8.01576i	0.202171	+	0.350170i
$525$	−41.5417	−	11.9081i	−1.81303	−	0.519714i
$526$	5.40099	+	9.35479i	0.235494	+	0.407888i
$527$	7.86182	−	4.53903i	0.342466	−	0.197723i
$528$			2.36196i			0.102791i
$529$	−9.19381	−	15.9242i	−0.399731	−	0.692355i
$530$	2.05843	−	2.63490i	0.0894126	−	0.114453i
$531$	−6.83654	+	11.8412i	−0.296680	+	0.513865i
$532$		−	25.7304i		−	1.11555i
$533$	7.86567	+	19.9748i	0.340700	+	0.865205i
$534$	−10.0207			−0.433640
$535$	−3.90186	−	3.04820i	−0.168692	−	0.131785i
$536$	4.21432	−	7.29942i	0.182031	−	0.315287i
$537$	−5.85049	+	3.37778i	−0.252467	+	0.145762i
$538$		−	18.5827i		−	0.801159i
$539$	4.39207	+	7.60730i	0.189180	+	0.327669i
$540$	−5.03508	+	2.03455i	−0.216675	+	0.0875531i
$541$	41.6149			1.78916			0.894581	−	0.446905i	$-0.147474\pi$
$541$	41.6149			1.78916			0.894581	+	0.446905i	$0.147474\pi$
$542$	−17.1255	+	9.88739i	−0.735602	+	0.424700i
$543$	−20.4095	−	11.7835i	−0.875857	−	0.505677i
$544$	0.655554	−	1.13545i	0.0281066	−	0.0486821i
$545$	−0.295286	−	0.0414872i	−0.0126487	−	0.00177712i
$546$	28.9956	−	11.4179i	1.24090	−	0.488639i
$547$		−	6.77430i		−	0.289648i	−0.989457	−	0.144824i	$-0.953738\pi$
$547$		−	6.77430i		−	0.289648i	0.989457	−	0.144824i	$-0.0462617\pi$
$548$	12.8090	+	7.39530i	0.547175	+	0.315912i
$549$	7.50569	−	13.0002i	0.320335	−	0.554836i
$550$	−5.17485	+	1.29070i	−0.220656	+	0.0550354i
$551$	59.6642			2.54178
$552$	−4.11844	+	2.37778i	−0.175293	+	0.101205i
$553$	−14.5411	+	8.39530i	−0.618350	+	0.357005i
$554$	−0.204952			−0.00870757
$555$	−9.31352	−	23.0490i	−0.395337	−	0.978375i
$556$	6.34691	−	10.9932i	0.269169	−	0.466214i
$557$	22.0360	+	12.7225i	0.933694	+	0.539068i	0.887978	−	0.459886i	$-0.152110\pi$
$557$	22.0360	+	12.7225i	0.933694	+	0.539068i	0.0457158	+	0.998954i	$0.485443\pi$
$558$		−	13.1778i		−	0.557859i
$559$	−1.06668	+	7.13177i	−0.0451156	+	0.301642i
$560$	−1.21432	+	8.64296i	−0.0513144	+	0.365232i
$561$	−1.54839	+	2.68190i	−0.0653732	+	0.113230i
$562$	−17.7153	−	10.2279i	−0.747274	−	0.431439i
$563$	11.4179	−	6.59210i	0.481205	−	0.277824i	−0.239713	−	0.970844i	$-0.577053\pi$
$563$	11.4179	−	6.59210i	0.481205	−	0.277824i	0.720919	+	0.693020i	$0.243720\pi$
$564$	0.214320			0.00902449
$565$	−29.0250	+	11.7283i	−1.22109	+	0.493411i
$566$	−0.719004	−	1.24535i	−0.0302220	−	0.0523460i
$567$		−	43.2766i		−	1.81744i
$568$	−13.4056	+	7.73975i	−0.562488	+	0.324753i
$569$	−12.2304	+	21.1836i	−0.512724	+	0.888064i	0.487167	+	0.873309i	$0.338030\pi$
$569$	−12.2304	+	21.1836i	−0.512724	+	0.888064i	−0.999891	+	0.0147555i	$0.995303\pi$
$570$	−20.0941	+	25.7215i	−0.841648	+	1.07735i
$571$	24.3526			1.01912			0.509562	−	0.860434i	$-0.329807\pi$
$571$	24.3526			1.01912			0.509562	+	0.860434i	$0.329807\pi$
$572$	2.39451	−	3.00961i	0.100119	−	0.125838i
$573$			32.6178i			1.36263i
$574$	11.6200	−	20.1264i	0.485009	−	0.840060i
$575$	−7.46004	−	7.72380i	−0.311105	−	0.322105i
$576$	−0.951606	−	1.64823i	−0.0396502	−	0.0686762i
$577$			42.0479i			1.75048i	0.483690	+	0.875239i	$0.339296\pi$
$577$			42.0479i			1.75048i	−0.483690	+	0.875239i	$0.660704\pi$
$578$	−13.2337	+	7.64050i	−0.550451	+	0.317803i
$579$	−15.5002	−	26.8472i	−0.644168	−	1.11573i
$580$	−20.0415	−	2.81579i	−0.832177	−	0.116919i
$581$	18.9185	+	32.7678i	0.784872	+	1.35944i
$582$	−8.16970	−	4.71678i	−0.338645	−	0.195517i
$583$	1.38133	+	0.797509i	0.0572087	+	0.0330295i
$584$	15.3526			0.635295
$585$	−14.7120	−	4.35903i	−0.608266	−	0.180224i
$586$	−20.9146			−0.863974
$587$	−6.36195	−	3.67307i	−0.262586	−	0.151604i	0.362928	−	0.931817i	$-0.381777\pi$
$587$	−6.36195	−	3.67307i	−0.262586	−	0.151604i	−0.625513	+	0.780213i	$0.715110\pi$
$588$	−15.7920	−	9.11753i	−0.651252	−	0.376001i
$589$	22.8217	+	39.5284i	0.940353	+	1.62874i
$590$	−2.23506	+	15.9081i	−0.0920161	+	0.654928i
$591$	11.5287	+	19.9682i	0.474225	+	0.821383i
$592$	−4.34809	+	2.51037i	−0.178705	+	0.103176i
$593$			4.19358i			0.172210i	0.996286	+	0.0861048i	$0.0274420\pi$
$593$			4.19358i			0.172210i	−0.996286	+	0.0861048i	$0.972558\pi$
$594$	−1.29529	−	2.24350i	−0.0531462	−	0.0920520i
$595$	−7.04473	+	9.01762i	−0.288806	+	0.369686i
$596$	−3.64296	+	6.30979i	−0.149221	+	0.258459i
$597$			9.67307i			0.395892i
$598$	7.65825	+	1.14542i	0.313169	+	0.0468397i
$599$	−9.33630			−0.381471			−0.190735	−	0.981641i	$-0.561087\pi$
$599$	−9.33630			−0.381471			−0.190735	+	0.981641i	$0.561087\pi$
$600$	7.96360	−	7.69165i	0.325113	−	0.314010i
$601$	1.48571	−	2.57333i	0.0606034	−	0.104968i	−0.834132	−	0.551565i	$-0.814031\pi$
$601$	1.48571	−	2.57333i	0.0606034	−	0.104968i	0.894735	+	0.446597i	$0.147364\pi$
$602$	6.76056	−	3.90321i	0.275540	−	0.159083i
$603$		−	16.0415i		−	0.653260i
$604$	10.0541	+	17.4142i	0.409095	+	0.708573i
$605$	8.26189	+	20.4464i	0.335893	+	0.831265i
$606$	3.23014			0.131216
$607$	14.8464	−	8.57160i	0.602599	−	0.347910i	−0.167465	−	0.985878i	$-0.553558\pi$
$607$	14.8464	−	8.57160i	0.602599	−	0.347910i	0.770063	+	0.637968i	$0.220225\pi$
$608$	5.70893	+	3.29605i	0.231528	+	0.133673i
$609$	39.1131	−	67.7459i	1.58494	−	2.74520i
$610$	2.45383	−	17.4652i	0.0993526	−	0.707145i
$611$	−0.273086	−	0.217273i	−0.0110479	−	0.00878991i
$612$		−	2.49532i		−	0.100867i
$613$	25.3610	+	14.6422i	1.02432	+	0.591393i	0.915353	−	0.402653i	$-0.131912\pi$
$613$	25.3610	+	14.6422i	1.02432	+	0.591393i	0.108969	+	0.994045i	$0.465245\pi$
$614$	6.26517	−	10.8516i	0.252842	−	0.437935i
$615$	−27.3336	+	11.0448i	−1.10220	+	0.445371i
$616$	−4.16346			−0.167751
$617$	11.4453	−	6.60793i	0.460769	−	0.266025i	−0.251599	−	0.967832i	$-0.580956\pi$
$617$	11.4453	−	6.60793i	0.460769	−	0.266025i	0.712368	+	0.701807i	$0.247623\pi$
$618$	−19.6453	+	11.3422i	−0.790250	+	0.456251i
$619$	18.9333			0.760995			0.380497	−	0.924782i	$-0.375753\pi$
$619$	18.9333			0.760995			0.380497	+	0.924782i	$0.375753\pi$
$620$	−5.80042	−	14.3548i	−0.232951	−	0.576503i
$621$	2.60793	−	4.51706i	0.104652	−	0.181263i
$622$	−8.47080	−	4.89062i	−0.339648	−	0.196096i
$623$		−	17.6637i		−	0.707681i
$624$	−1.18098	+	7.89601i	−0.0472771	+	0.316094i
$625$	21.2034	+	13.2444i	0.848137	+	0.529777i
$626$	−8.60639	+	14.9067i	−0.343981	+	0.595792i
$627$	−13.4843	−	7.78515i	−0.538510	−	0.310909i
$628$	−1.71835	+	0.992089i	−0.0685696	+	0.0395887i
$629$	−6.58274			−0.262471
$630$	6.22321	+	15.4011i	0.247939	+	0.613596i
$631$	−1.21432	−	2.10326i	−0.0483413	−	0.0837296i	0.840842	−	0.541280i	$-0.182060\pi$
$631$	−1.21432	−	2.10326i	−0.0483413	−	0.0837296i	−0.889184	+	0.457551i	$0.848727\pi$
$632$		−	4.30174i		−	0.171114i
$633$	10.5381	−	6.08419i	0.418853	−	0.241825i
$634$	6.87233	−	11.9032i	0.272935	−	0.472738i
$635$	17.6045	+	13.7530i	0.698614	+	0.545770i
$636$	−3.31111			−0.131294
$637$	10.8790	+	27.6271i	0.431042	+	1.09463i
$638$		−	9.65433i		−	0.382219i
$639$	−14.7304	+	25.5138i	−0.582725	+	1.00931i
$640$	−1.76210	−	1.37659i	−0.0696532	−	0.0544144i
$641$	−7.54371	−	13.0661i	−0.297959	−	0.516079i	0.677710	−	0.735329i	$-0.262972\pi$
$641$	−7.54371	−	13.0661i	−0.297959	−	0.516079i	−0.975669	+	0.219250i	$0.929639\pi$
$642$			4.90321i			0.193514i
$643$	−5.80513	+	3.35159i	−0.228932	+	0.132174i	−0.610079	−	0.792340i	$-0.708862\pi$
$643$	−5.80513	+	3.35159i	−0.228932	+	0.132174i	0.381147	+	0.924514i	$0.375529\pi$
$644$	−4.19135	−	7.25964i	−0.165162	−	0.286070i
$645$	−9.80642	−	1.37778i	−0.386128	−	0.0542502i
$646$	4.32148	+	7.48502i	0.170026	+	0.294494i
$647$	19.3759	+	11.1867i	0.761744	+	0.439793i	0.829922	−	0.557880i	$-0.188385\pi$
$647$	19.3759	+	11.1867i	0.761744	+	0.439793i	−0.0681773	+	0.997673i	$0.521718\pi$
$648$	9.60199	+	5.54371i	0.377202	+	0.217777i
$649$	−7.66323			−0.300808
$650$	−17.9448	+	1.72735i	−0.703853	+	0.0677524i
$651$	59.8435			2.34545
$652$	−4.07308	−	2.35159i	−0.159514	−	0.0920954i
$653$	−14.2139	−	8.20641i	−0.556234	−	0.321142i	0.195399	−	0.980724i	$-0.437400\pi$
$653$	−14.2139	−	8.20641i	−0.556234	−	0.321142i	−0.751632	+	0.659582i	$0.770733\pi$
$654$	0.147643	+	0.255726i	0.00577331	+	0.00999966i
$655$	20.4953	+	2.87955i	0.800818	+	0.112513i
$656$	2.97703	+	5.15637i	0.116234	+	0.201323i
$657$	25.3046	−	14.6096i	0.987227	−	0.569976i
$658$			0.377784i			0.0147276i
$659$	4.33407	+	7.50684i	0.168832	+	0.292425i	0.938009	−	0.346610i	$-0.112667\pi$
$659$	4.33407	+	7.50684i	0.168832	+	0.292425i	−0.769178	+	0.639035i	$0.779334\pi$
$660$	4.16202	+	3.25145i	0.162007	+	0.126562i
$661$	−8.71509	+	15.0950i	−0.338978	+	0.587126i	−0.984241	−	0.176834i	$-0.943414\pi$
$661$	−8.71509	+	15.0950i	−0.338978	+	0.587126i	0.645263	+	0.763960i	$0.276748\pi$
$662$		−	19.3876i		−	0.753522i
$663$	−6.51721	+	8.19135i	−0.253108	+	0.318126i
$664$	−9.69381			−0.376193
$665$	−45.3396	−	35.4201i	−1.75819	−	1.37353i
$666$	−4.77777	+	8.27534i	−0.185135	+	0.320663i
$667$	16.8338	−	9.71900i	0.651808	−	0.376321i
$668$		−	9.69535i		−	0.375124i
$669$	−22.2504	−	38.5387i	−0.860249	−	1.48999i
$670$	−7.06095	−	17.4743i	−0.272788	−	0.675093i
$671$	8.41329			0.324792
$672$	7.48502	−	4.32148i	0.288741	−	0.166705i
$673$	−35.0593	−	20.2415i	−1.35144	−	0.780253i	−0.362987	−	0.931794i	$-0.618243\pi$
$673$	−35.0593	−	20.2415i	−1.35144	−	0.780253i	−0.988451	+	0.151541i	$0.951576\pi$
$674$	0.277770	−	0.481111i	0.0106993	−	0.0185317i
$675$	−3.34614	+	11.6731i	−0.128793	+	0.449297i
$676$	9.50961	−	8.86382i	0.365754	−	0.340916i
$677$		−	40.0228i		−	1.53820i	−0.639129	−	0.769100i	$-0.720705\pi$
$677$		−	40.0228i		−	1.53820i	0.639129	−	0.769100i	$-0.279295\pi$
$678$	26.8472	+	15.5002i	1.03106	+	0.595283i
$679$	8.31433	−	14.4008i	0.319075	−	0.552654i
$680$	−1.09836	−	2.71820i	−0.0421201	−	0.104238i
$681$	42.8671			1.64267
$682$	6.39614	−	3.69281i	0.244921	−	0.141405i
$683$	37.5064	−	21.6543i	1.43514	−	0.828580i	0.437636	−	0.899152i	$-0.355816\pi$
$683$	37.5064	−	21.6543i	1.43514	−	0.828580i	0.997507	+	0.0705721i	$0.0224825\pi$
$684$	12.5462			0.479715
$685$	30.6640	−	12.3906i	1.17161	−	0.473419i
$686$	2.41036	−	4.17486i	0.0920279	−	0.159397i
$687$	30.1560	+	17.4106i	1.15052	+	0.664256i
$688$			2.00000i			0.0762493i
$689$	4.21900	+	3.35673i	0.160731	+	0.127881i
$690$	−1.47949	+	10.5303i	−0.0563234	+	0.400884i
$691$	−14.1741	+	24.5502i	−0.539207	+	0.933934i	0.459740	+	0.888054i	$0.347943\pi$
$691$	−14.1741	+	24.5502i	−0.539207	+	0.933934i	−0.998947	+	0.0458806i	$0.985391\pi$
$692$	20.8466	+	12.0358i	0.792469	+	0.457532i
$693$	−6.86235	+	3.96198i	−0.260679	+	0.150503i
$694$	−6.68445			−0.253738
$695$	−10.6340	−	26.3170i	−0.403371	−	0.998259i
$696$	10.0207	+	17.3564i	0.379835	+	0.657894i
$697$			7.80642i			0.295689i
$698$	9.16492	−	5.29137i	0.346897	−	0.200281i
$699$	−16.4773	+	28.5395i	−0.623228	+	1.07946i
$700$	13.5582	+	14.0375i	0.512451	+	0.530569i
$701$	12.8080			0.483750			0.241875	−	0.970307i	$-0.422238\pi$
$701$	12.8080			0.483750			0.241875	+	0.970307i	$0.422238\pi$
$702$	−3.20838	−	8.14764i	−0.121092	−	0.307513i
$703$		−	33.0973i		−	1.24829i
$704$	0.533338	−	0.923769i	0.0201009	−	0.0348159i
$705$	0.295030	−	0.377654i	0.0111115	−	0.0142233i
$706$	4.60470	+	7.97557i	0.173300	+	0.300165i
$707$			5.69381i			0.214138i
$708$	13.7768	−	7.95407i	0.517766	−	0.298932i
$709$	1.26126	+	2.18456i	0.0473675	+	0.0820429i	0.888737	−	0.458417i	$-0.151583\pi$
$709$	1.26126	+	2.18456i	0.0473675	+	0.0820429i	−0.841370	+	0.540460i	$0.818250\pi$
$710$	−4.81579	+	34.2766i	−0.180733	+	1.28638i
$711$	−4.09356	−	7.09026i	−0.153521	−	0.265905i
$712$	3.91914	+	2.26271i	0.146876	+	0.0847988i
$713$	12.8780	+	7.43509i	0.482283	+	0.278446i
$714$	11.3319			0.424084
$715$	−2.00699	−	8.36235i	−0.0750572	−	0.312734i
$716$	3.05086			0.114016
$717$	8.48024	+	4.89607i	0.316700	+	0.182847i
$718$	3.63174	+	2.09679i	0.135535	+	0.0782514i
$719$	8.51114	+	14.7417i	0.317412	+	0.549773i	0.979947	−	0.199257i	$-0.0638529\pi$
$719$	8.51114	+	14.7417i	0.317412	+	0.549773i	−0.662535	+	0.749031i	$0.730520\pi$
$720$	−4.21432	−	0.592104i	−0.157058	−	0.0220664i
$721$	−19.9931	−	34.6291i	−0.744582	−	1.28965i
$722$	−21.1794	+	12.2279i	−0.788215	+	0.455076i
$723$		−	24.9797i		−	0.929006i
$724$	5.32148	+	9.21707i	0.197771	+	0.342550i
$725$	−32.5506	+	31.4390i	−1.20890	+	1.16761i
$726$	10.9190	−	18.9123i	0.405243	−	0.701902i
$727$			30.5353i			1.13249i	0.824237	+	0.566245i	$0.191605\pi$
$727$			30.5353i			1.13249i	−0.824237	+	0.566245i	$0.808395\pi$
$728$	−13.9184	−	2.08173i	−0.515851	−	0.0771541i
$729$	4.96836			0.184013
$730$	21.1342	−	27.0529i	0.782211	−	1.00127i
$731$	−1.31111	+	2.27091i	−0.0484931	+	0.0839925i
$732$	−15.1253	+	8.73260i	−0.559048	+	0.322766i
$733$			24.4499i			0.903076i	0.892252	+	0.451538i	$0.149124\pi$
$733$			24.4499i			0.903076i	−0.892252	+	0.451538i	$0.850876\pi$
$734$	6.98418	+	12.0970i	0.257791	+	0.446507i
$735$	−37.8051	+	15.2761i	−1.39446	+	0.563468i
$736$	2.14764			0.0791632
$737$	7.78612	−	4.49532i	0.286805	−	0.165587i
$738$	9.81367	+	5.66593i	0.361246	+	0.208566i
$739$	−5.39776	+	9.34920i	−0.198560	+	0.343916i	−0.948062	−	0.318086i	$-0.896960\pi$
$739$	−5.39776	+	9.34920i	−0.198560	+	0.343916i	0.749502	+	0.662002i	$0.230293\pi$
$740$	−1.56199	+	11.1175i	−0.0574200	+	0.408689i
$741$	−41.1852	−	32.7678i	−1.51298	−	1.20376i
$742$		−	5.83654i		−	0.214266i
$743$	−25.9248	−	14.9677i	−0.951087	−	0.549110i	−0.0576686	−	0.998336i	$-0.518367\pi$
$743$	−25.9248	−	14.9677i	−0.951087	−	0.549110i	−0.893418	+	0.449225i	$0.851700\pi$
$744$	−7.66593	+	13.2778i	−0.281046	+	0.486787i
$745$	6.10365	+	15.1052i	0.223620	+	0.553413i
$746$	11.8479			0.433783
$747$	−15.9776	+	9.22469i	−0.584591	+	0.337514i
$748$	1.21116	−	0.699264i	0.0442844	−	0.0255676i
$749$	−8.64296			−0.315807
$750$	−2.59089	−	24.6209i	−0.0946058	−	0.899028i
$751$	−13.4588	+	23.3112i	−0.491117	+	0.850639i	−0.999948	−	0.0102272i	$-0.996745\pi$
$751$	−13.4588	+	23.3112i	−0.491117	+	0.850639i	0.508831	+	0.860866i	$0.330078\pi$
$752$	−0.0838209	−	0.0483940i	−0.00305663	−	0.00176475i
$753$			5.87310i			0.214028i
$754$	4.82717	−	32.2743i	0.175795	−	1.17536i
$755$	44.5259	+	6.25581i	1.62046	+	0.227672i
$756$	−4.73975	+	8.20948i	−0.172383	+	0.298576i
$757$	−31.0960	−	17.9533i	−1.13020	−	0.652524i	−0.186218	−	0.982508i	$-0.559623\pi$
$757$	−31.0960	−	17.9533i	−1.13020	−	0.652524i	−0.943986	+	0.329985i	$0.892956\pi$
$758$	0.525153	−	0.303197i	0.0190744	−	0.0110126i
$759$	−5.07265			−0.184126
$760$	13.6668	−	5.52242i	0.495748	−	0.200319i
$761$	−11.2699	−	19.5200i	−0.408532	−	0.707598i	0.586193	−	0.810171i	$-0.300626\pi$
$761$	−11.2699	−	19.5200i	−0.408532	−	0.707598i	−0.994725	+	0.102573i	$0.967293\pi$
$762$		−	22.1225i		−	0.801412i
$763$	−0.450771	+	0.260253i	−0.0163190	+	0.00942178i
$764$	7.36519	−	12.7569i	0.266463	−	0.461528i
$765$	−4.39700	−	3.43502i	−0.158974	−	0.124193i
$766$	−34.7797			−1.25664
$767$	−25.6181	−	3.83161i	−0.925015	−	0.138352i
$768$			2.21432i			0.0799024i
$769$	1.23729	−	2.14304i	0.0446177	−	0.0772801i	−0.842854	−	0.538142i	$-0.819126\pi$
$769$	1.23729	−	2.14304i	0.0446177	−	0.0772801i	0.887472	+	0.460862i	$0.152460\pi$
$770$	−5.73137	+	7.33645i	−0.206544	+	0.264387i
$771$	−4.54125	−	7.86567i	−0.163549	−	0.283275i
$772$			14.0000i			0.503871i
$773$	−38.2788	+	22.1003i	−1.37679	+	0.794891i	−0.991772	−	0.128018i	$-0.959139\pi$
$773$	−38.2788	+	22.1003i	−1.37679	+	0.794891i	−0.385019	+	0.922908i	$0.625805\pi$
$774$	1.90321	+	3.29646i	0.0684095	+	0.118489i
$775$	−33.2795	−	9.53972i	−1.19543	−	0.342677i
$776$	2.13013	+	3.68949i	0.0764671	+	0.132445i
$777$	−37.5804	−	21.6970i	−1.34819	−	0.778377i
$778$	16.1812	+	9.34222i	0.580124	+	0.334935i
$779$	−39.2498			−1.40627
$780$	12.2879	+	12.9506i	0.439976	+	0.463705i
$781$	−16.5116			−0.590832
$782$	2.43855	+	1.40790i	0.0872023	+	0.0503463i
$783$	−19.0363	−	10.9906i	−0.680303	−	0.392773i
$784$	4.11753	+	7.13177i	0.147055	+	0.254706i
$785$	−0.617293	+	4.39361i	−0.0220321	+	0.156815i
$786$	−10.2477	−	17.7495i	−0.365522	−	0.633102i
$787$	−29.4714	+	17.0153i	−1.05054	+	0.606530i	−0.922801	−	0.385278i	$-0.874106\pi$
$787$	−29.4714	+	17.0153i	−1.05054	+	0.606530i	−0.127740	+	0.991808i	$0.540772\pi$
$788$		−	10.4128i		−	0.370941i
$789$	−11.9595	−	20.7145i	−0.425770	−	0.737455i
$790$	−7.58011	−	5.92172i	−0.269688	−	0.210685i
$791$	−27.3225	+	47.3239i	−0.971476	+	1.68265i
$792$		−	2.03011i		−	0.0721369i
$793$	28.1255	+	4.20665i	0.998767	+	0.149382i
$794$	−22.9748			−0.815346
$795$	−4.55803	+	5.83451i	−0.161657	+	0.206929i
$796$	2.18421	−	3.78316i	0.0774172	−	0.134091i
$797$	−7.04754	+	4.06890i	−0.249637	+	0.144128i	−0.619598	−	0.784919i	$-0.712704\pi$
$797$	−7.04754	+	4.06890i	−0.249637	+	0.144128i	0.369961	+	0.929047i	$0.379371\pi$
$798$			56.9753i			2.01690i
$799$	−0.0634498	−	0.109898i	−0.00224469	−	0.00388792i
$800$	−4.85138	+	1.21002i	−0.171522	+	0.0427805i
$801$	8.61285			0.304320
$802$	3.78742	−	2.18667i	0.133739	−	0.0772140i
$803$	14.1823	+	8.18813i	0.500481	+	0.288953i
$804$	−9.33185	+	16.1632i	−0.329109	+	0.570034i
$805$	−18.5620	−	2.60793i	−0.654224	−	0.0919173i
$806$	23.2286	−	9.14695i	0.818193	−	0.322188i
$807$			41.1481i			1.44848i
$808$	−1.26332	−	0.729376i	−0.0444433	−	0.0256593i
$809$	−3.92618	+	6.80034i	−0.138037	+	0.239087i	−0.926754	−	0.375670i	$-0.877413\pi$
$809$	−3.92618	+	6.80034i	−0.138037	+	0.239087i	0.788716	+	0.614757i	$0.210746\pi$
$810$	22.9866	−	9.28829i	0.807665	−	0.326357i
$811$	9.33477			0.327788			0.163894	−	0.986478i	$-0.447595\pi$
$811$	9.33477			0.327788			0.163894	+	0.986478i	$0.447595\pi$
$812$	−30.5944	+	17.6637i	−1.07365	+	0.619874i
$813$	37.9213	−	21.8938i	1.32996	−	0.767851i
$814$	−5.35551			−0.187711
$815$	−9.75069	+	3.94001i	−0.341552	+	0.138012i
$816$	−1.45161	+	2.51426i	−0.0508164	+	0.0880165i
$817$	−11.4179	−	6.59210i	−0.399460	−	0.230629i
$818$		−	3.76986i		−	0.131810i
$819$	−24.9217	+	9.81367i	−0.870836	+	0.342917i
$820$	13.1842	+	1.85236i	0.460413	+	0.0646871i
$821$	23.7659	−	41.1638i	0.829437	−	1.43663i	−0.0690434	−	0.997614i	$-0.521995\pi$
$821$	23.7659	−	41.1638i	0.829437	−	1.43663i	0.898480	−	0.439013i	$-0.144672\pi$
$822$	−28.3633	−	16.3756i	−0.989284	−	0.571163i
$823$	−1.20131	+	0.693576i	−0.0418750	+	0.0241765i	−0.520791	−	0.853684i	$-0.674363\pi$
$823$	−1.20131	+	0.693576i	−0.0418750	+	0.0241765i	0.478916	+	0.877861i	$0.341030\pi$
$824$	10.2444			0.356882
$825$	11.4588	−	2.85801i	0.398943	−	0.0995032i
$826$	14.0207	+	24.2846i	0.487844	+	0.844971i
$827$			31.5131i			1.09582i	0.836537	+	0.547910i	$0.184576\pi$
$827$			31.5131i			1.09582i	−0.836537	+	0.547910i	$0.815424\pi$
$828$	3.53981	−	2.04371i	0.123017	−	0.0710238i
$829$	−14.4128	+	24.9637i	−0.500578	+	0.867026i	0.499422	+	0.866359i	$0.333546\pi$
$829$	−14.4128	+	24.9637i	−0.500578	+	0.867026i	−1.00000		0.000667386i	$0.999788\pi$
$830$	−13.3444	+	17.0815i	−0.463190	+	0.592908i
$831$	0.453829			0.0157431
$832$	2.24483	−	2.82148i	0.0778254	−	0.0978172i
$833$			10.7971i			0.374096i
$834$	−14.0541	+	24.3424i	−0.486653	+	0.842908i
$835$	−17.0842	−	13.3465i	−0.591223	−	0.461874i
$836$	3.51582	+	6.08958i	0.121597	+	0.210613i
$837$		−	16.8158i		−	0.581239i
$838$	6.45388	−	3.72615i	0.222946	−	0.128718i
$839$	4.21755	+	7.30500i	0.145606	+	0.252197i	0.929599	−	0.368573i	$-0.120154\pi$
$839$	4.21755	+	7.30500i	0.145606	+	0.252197i	−0.783993	+	0.620770i	$0.786820\pi$
$840$	2.68889	−	19.1383i	0.0927756	−	0.660333i
$841$	−26.4590	−	45.8283i	−0.912379	−	1.58029i
$842$	23.9673	+	13.8375i	0.825968	+	0.476873i
$843$	39.2273	+	22.6479i	1.35106	+	0.780034i
$844$	−5.49532			−0.189157
$845$	−2.52817	−	28.9587i	−0.0869718	−	0.996211i
$846$	−0.184208			−0.00633321
$847$	33.3370	+	19.2471i	1.14547	+	0.661339i
$848$	1.29498	+	0.747658i	0.0444699	+	0.0256747i
$849$	1.59210	+	2.75761i	0.0546409	+	0.0946408i
$850$	−6.30174	−	1.80642i	−0.216148	−	0.0619598i
$851$	−5.39138	−	9.33815i	−0.184814	−	0.320108i
$852$	29.6844	−	17.1383i	1.01697	−	0.587148i
$853$		−	40.0656i		−	1.37182i	−0.727686	−	0.685910i	$-0.759404\pi$
$853$		−	40.0656i		−	1.37182i	0.727686	−	0.685910i	$-0.240596\pi$
$854$	−15.3931	−	26.6616i	−0.526740	−	0.912341i
$855$	17.2709	−	22.1076i	0.590652	−	0.756066i
$856$	1.10716	−	1.91766i	0.0378419	−	0.0655442i
$857$		−	32.0479i		−	1.09474i	−0.836892	−	0.547368i	$-0.815630\pi$
$857$		−	32.0479i		−	1.09474i	0.836892	−	0.547368i	$-0.184370\pi$
$858$	−5.30220	+	6.66423i	−0.181014	+	0.227513i
$859$	26.6894			0.910630			0.455315	−	0.890331i	$-0.349527\pi$
$859$	26.6894			0.910630			0.455315	+	0.890331i	$0.349527\pi$
$860$	3.52421	+	2.75317i	0.120174	+	0.0938825i
$861$	−25.7304	+	44.5663i	−0.876889	+	1.51882i
$862$	−17.0515	+	9.84468i	−0.580776	+	0.335311i
$863$			30.6593i			1.04365i	0.853052	+	0.521827i	$0.174749\pi$
$863$			30.6593i			1.04365i	−0.853052	+	0.521827i	$0.825251\pi$
$864$	−1.21432	−	2.10326i	−0.0413120	−	0.0715545i
$865$	49.9055	−	20.1656i	1.69684	−	0.685650i
$866$	−13.7462			−0.467115
$867$	29.3037	−	16.9185i	0.995206	−	0.574583i
$868$	−23.4049	−	13.5128i	−0.794415	−	0.458655i
$869$	2.29428	−	3.97381i	0.0778282	−	0.134802i
$870$	44.3783	+	6.23506i	1.50456	+	0.211388i
$871$	28.2766	−	11.1347i	0.958114	−	0.377286i
$872$		−	0.133353i		−	0.00451591i
$873$	7.02188	+	4.05408i	0.237654	+	0.137210i
$874$	−7.07874	+	12.2607i	−0.239442	+	0.414726i
$875$	43.3996	−	4.56699i	1.46717	−	0.154393i
$876$	−33.9956			−1.14860
$877$	−18.1263	+	10.4652i	−0.612081	+	0.353385i	−0.773779	−	0.633455i	$-0.781636\pi$
$877$	−18.1263	+	10.4652i	−0.612081	+	0.353385i	0.161699	+	0.986840i	$0.448303\pi$
$878$	36.2195	−	20.9114i	1.22235	−	0.705724i
$879$	46.3116			1.56205
$880$	−0.893590	−	2.21145i	−0.0301229	−	0.0745478i
$881$	−10.7351	+	18.5937i	−0.361673	+	0.626437i	−0.988236	−	0.152934i	$-0.951128\pi$
$881$	−10.7351	+	18.5937i	−0.361673	+	0.626437i	0.626563	+	0.779371i	$0.284461\pi$
$882$	13.5733	+	7.83654i	0.457036	+	0.263870i
$883$		−	7.73530i		−	0.260314i	−0.991493	−	0.130157i	$-0.958452\pi$
$883$		−	7.73530i		−	0.260314i	0.991493	−	0.130157i	$-0.0415481\pi$
$884$	4.39853	−	1.73205i	0.147939	−	0.0582552i
$885$	4.94914	−	35.2257i	0.166364	−	1.18410i
$886$	11.8415	−	20.5100i	0.397822	−	0.689047i
$887$	−41.9559	−	24.2232i	−1.40874	−	0.813337i	−0.413473	−	0.910516i	$-0.635685\pi$
$887$	−41.9559	−	24.2232i	−1.40874	−	0.813337i	−0.995267	+	0.0971796i	$0.969018\pi$
$888$	9.62806	−	5.55877i	0.323097	−	0.186540i
$889$	38.9956			1.30787
$890$	9.38217	−	3.79110i	0.314491	−	0.127078i
$891$	5.91335	+	10.2422i	0.198105	+	0.343127i
$892$			20.0968i			0.672890i
$893$	0.552556	−	0.319019i	0.0184906	−	0.0106755i
$894$	8.06668	−	13.9719i	0.269790	−	0.467290i
$895$	4.19977	−	5.37592i	0.140383	−	0.179697i
$896$	−3.90321			−0.130397
$897$	−16.9578	−	2.53633i	−0.566205	−	0.0846855i
$898$			7.05578i			0.235454i
$899$	31.3339	−	54.2718i	1.04504	−	1.81007i
$900$	−6.84473	+	6.61098i	−0.228158	+	0.220366i
$901$	0.980260	+	1.69786i	0.0326572	+	0.0565639i
$902$			6.35106i			0.211467i
$903$	−14.9700	+	8.64296i	−0.498172	+	0.287620i
$904$	−7.00000	−	12.1244i	−0.232817	−	0.403250i
$905$	23.5669	+	3.31111i	0.783391	+	0.110065i
$906$	−22.2630	−	38.5606i	−0.739637	−	1.28109i
$907$	10.4017	+	6.00545i	0.345384	+	0.199408i	0.662650	−	0.748929i	$-0.269432\pi$
$907$	10.4017	+	6.00545i	0.345384	+	0.199408i	−0.317266	+	0.948337i	$0.602765\pi$
$908$	−16.7654	−	9.67952i	−0.556380	−	0.321226i
$909$	−2.77631			−0.0920845
$910$	−22.8281	+	21.6600i	−0.756745	+	0.718022i
$911$	−8.10171			−0.268422			−0.134211	−	0.990953i	$-0.542850\pi$
$911$	−8.10171			−0.268422			−0.134211	+	0.990953i	$0.542850\pi$
$912$	−12.6414	−	7.29851i	−0.418598	−	0.241678i
$913$	−8.95485	−	5.17008i	−0.296362	−	0.171105i
$914$	−17.8398	−	30.8994i	−0.590087	−	1.02206i
$915$	−5.43356	+	38.6735i	−0.179628	+	1.27851i
$916$	−7.86273	−	13.6186i	−0.259792	−	0.449973i
$917$	31.2872	−	18.0637i	1.03320	−	0.596516i
$918$		−	3.18421i		−	0.105095i
$919$	8.29682	+	14.3705i	0.273687	+	0.474039i	0.969803	−	0.243890i	$-0.0784235\pi$
$919$	8.29682	+	14.3705i	0.273687	+	0.474039i	−0.696116	+	0.717929i	$0.745090\pi$
$920$	2.95642	−	3.78437i	0.0974702	−	0.124767i
$921$	−13.8731	+	24.0289i	−0.457134	+	0.791780i
$922$			14.6015i			0.480874i
$923$	−55.1981	−	8.25581i	−1.81687	−	0.271743i
$924$	9.21924			0.303291
$925$	17.4400	+	18.0566i	0.573424	+	0.593699i
$926$	−15.3756	+	26.6313i	−0.505272	+	0.875157i
$927$	16.8852	−	9.74866i	0.554582	−	0.320188i
$928$		−	9.05086i		−	0.297109i
$929$	28.5605	+	49.4682i	0.937038	+	1.62300i	0.770958	+	0.636886i	$0.219778\pi$
$929$	28.5605	+	49.4682i	0.937038	+	1.62300i	0.166080	+	0.986112i	$0.446889\pi$
$930$	12.8440	+	31.7862i	0.421171	+	1.04231i
$931$	−54.2864			−1.77916
$932$	12.8886	−	7.44123i	0.422180	−	0.243746i
$933$	18.7571	+	10.8294i	0.614078	+	0.354538i
$934$	−10.2810	+	17.8072i	−0.336404	+	0.582670i
$935$	0.435093	−	3.09679i	0.0142291	−	0.101276i
$936$	1.01506	−	6.78664i	0.0331781	−	0.221828i
$937$			11.1842i			0.365372i	0.983171	+	0.182686i	$0.0584792\pi$
$937$			11.1842i			0.365372i	−0.983171	+	0.182686i	$0.941521\pi$
$938$	−28.4912	−	16.4494i	−0.930270	−	0.537091i
$939$	19.0573	−	33.0082i	0.621912	−	1.07718i
$940$	−0.200662	+	0.0810825i	−0.00654488	+	0.00264462i
$941$	−7.68598			−0.250556			−0.125278	−	0.992122i	$-0.539982\pi$
$941$	−7.68598			−0.250556			−0.125278	+	0.992122i	$0.539982\pi$
$942$	3.80497	−	2.19680i	0.123973	−	0.0715757i
$943$	−11.0741	+	6.39361i	−0.360621	+	0.208204i
$944$	−7.18421			−0.233826
$945$	7.94128	+	19.6530i	0.258330	+	0.639312i
$946$	−1.06668	+	1.84754i	−0.0346806	+	0.0600686i
$947$	17.9047	+	10.3373i	0.581826	+	0.335917i	0.761859	−	0.647743i	$-0.224287\pi$
$947$	17.9047	+	10.3373i	0.581826	+	0.335917i	−0.180033	+	0.983661i	$0.557620\pi$
$948$			9.52543i			0.309372i
$949$	43.3170	+	34.4639i	1.40613	+	1.11875i
$950$	9.08250	−	31.6844i	0.294675	−	1.02798i
$951$	−15.2175	+	26.3576i	−0.493463	+	0.854703i
$952$	−4.43191	−	2.55877i	−0.143639	−	0.0829301i
$953$	−26.8254	+	15.4876i	−0.868959	+	0.501694i	−0.867002	−	0.498304i	$-0.833956\pi$
$953$	−26.8254	+	15.4876i	−0.868959	+	0.501694i	−0.00195715	+	0.999998i	$0.500623\pi$
$954$	2.84590			0.0921395
$955$	−12.3401	−	30.5392i	−0.399317	−	0.988225i
$956$	−2.21109	−	3.82973i	−0.0715119	−	0.123862i
$957$			21.3778i			0.691046i
$958$	10.3346	−	5.96666i	0.333895	−	0.192774i
$959$	28.8654	−	49.9964i	0.932113	−	1.61447i
$960$	3.90186	+	3.04820i	0.125932	+	0.0983804i
$961$	16.9412			0.546489
$962$	−17.9034	−	2.67775i	−0.577229	−	0.0863343i
$963$		−	4.21432i		−	0.135805i
$964$	−5.64050	+	9.76963i	−0.181668	+	0.314659i
$965$	24.6694	+	19.2722i	0.794138	+	0.620395i
$966$	9.28100	+	16.0752i	0.298611	+	0.517210i
$967$			0.529873i			0.0170396i	0.999964	+	0.00851979i	$0.00271197\pi$
$967$			0.529873i			0.0170396i	−0.999964	+	0.00851979i	$0.997288\pi$
$968$	−8.54092	+	4.93110i	−0.274515	+	0.158492i
$969$	−9.56914	−	16.5742i	−0.307405	−	0.532441i
$970$	9.43356	+	1.32540i	0.302893	+	0.0425560i
$971$	17.1620	+	29.7255i	0.550755	+	0.953936i	0.998220	+	0.0596344i	$0.0189935\pi$
$971$	17.1620	+	29.7255i	0.550755	+	0.953936i	−0.447465	+	0.894301i	$0.647673\pi$
$972$	−14.9521	−	8.63259i	−0.479588	−	0.276890i
$973$	−42.9087	−	24.7733i	−1.37559	−	0.794196i
$974$	27.9719			0.896277
$975$	39.7355	−	3.82491i	1.27256	−	0.122495i
$976$	7.88739			0.252469
$977$	17.2931	+	9.98418i	0.553255	+	0.319422i	0.750434	−	0.660945i	$-0.229845\pi$
$977$	17.2931	+	9.98418i	0.553255	+	0.319422i	−0.197179	+	0.980368i	$0.563178\pi$
$978$	9.01909	+	5.20717i	0.288399	+	0.166507i
$979$	2.41358	+	4.18045i	0.0771385	+	0.133608i
$980$	18.2351	+	2.56199i	0.582498	+	0.0818399i
$981$	−0.126900	−	0.219797i	−0.00405159	−	0.00701756i
$982$	17.9971	−	10.3906i	0.574310	−	0.331578i
$983$		−	20.8524i		−	0.665087i	−0.943088	−	0.332543i	$-0.892093\pi$
$983$		−	20.8524i		−	0.665087i	0.943088	−	0.332543i	$-0.107907\pi$
$984$	−6.59210	−	11.4179i	−0.210149	−	0.363988i
$985$	−18.3485	−	14.3342i	−0.584631	−	0.456724i
$986$	5.93332	−	10.2768i	0.188956	−	0.327281i
$987$		−	0.836535i		−	0.0266272i
$988$	8.70856	+	22.1153i	0.277056	+	0.703582i
$989$	−4.29529			−0.136582
$990$	−3.57727	−	2.79463i	−0.113693	−	0.0888190i
$991$	1.47949	−	2.56256i	0.0469977	−	0.0814024i	−0.841570	−	0.540149i	$-0.818368\pi$
$991$	1.47949	−	2.56256i	0.0469977	−	0.0814024i	0.888567	+	0.458746i	$0.151701\pi$
$992$	5.99632	−	3.46198i	0.190383	−	0.109918i
$993$			42.9304i			1.36236i
$994$	30.2099	+	52.3250i	0.958199	+	1.65965i
$995$	−3.65956	−	9.05665i	−0.116016	−	0.287115i
$996$	21.4652			0.680151
$997$	18.2281	−	10.5240i	0.577288	−	0.333297i	−0.182767	−	0.983156i	$-0.558505\pi$
$997$	18.2281	−	10.5240i	0.577288	−	0.333297i	0.760055	+	0.649859i	$0.225172\pi$
$998$	−29.6967	−	17.1454i	−0.940034	−	0.542729i
$999$	−6.09679	+	10.5599i	−0.192894	+	0.334102i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.2.n.a.9.4	yes	12
3.2	odd	2		1170.2.bp.h.919.1		12
4.3	odd	2		1040.2.dh.b.529.6		12
5.2	odd	4		650.2.e.j.451.1		6
5.3	odd	4		650.2.e.k.451.3		6
5.4	even	2	inner	130.2.n.a.9.3	✓	12
13.3	even	3	inner	130.2.n.a.29.3	yes	12
13.4	even	6		1690.2.b.b.339.6		6
13.6	odd	12		1690.2.c.b.1689.6		6
13.7	odd	12		1690.2.c.c.1689.6		6
13.9	even	3		1690.2.b.c.339.3		6
15.14	odd	2		1170.2.bp.h.919.4		12
20.19	odd	2		1040.2.dh.b.529.1		12
39.29	odd	6		1170.2.bp.h.289.4		12
52.3	odd	6		1040.2.dh.b.289.1		12
65.3	odd	12		650.2.e.k.601.3		6
65.4	even	6		1690.2.b.b.339.1		6
65.9	even	6		1690.2.b.c.339.4		6
65.17	odd	12		8450.2.a.bt.1.3		3
65.19	odd	12		1690.2.c.c.1689.1		6
65.22	odd	12		8450.2.a.cb.1.3		3
65.29	even	6	inner	130.2.n.a.29.4	yes	12
65.42	odd	12		650.2.e.j.601.1		6
65.43	odd	12		8450.2.a.ca.1.1		3
65.48	odd	12		8450.2.a.bu.1.1		3
65.59	odd	12		1690.2.c.b.1689.1		6
195.29	odd	6		1170.2.bp.h.289.1		12
260.159	odd	6		1040.2.dh.b.289.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.n.a.9.3	✓	12	5.4	even	2	inner
130.2.n.a.9.4	yes	12	1.1	even	1	trivial
130.2.n.a.29.3	yes	12	13.3	even	3	inner
130.2.n.a.29.4	yes	12	65.29	even	6	inner
650.2.e.j.451.1		6	5.2	odd	4
650.2.e.j.601.1		6	65.42	odd	12
650.2.e.k.451.3		6	5.3	odd	4
650.2.e.k.601.3		6	65.3	odd	12
1040.2.dh.b.289.1		12	52.3	odd	6
1040.2.dh.b.289.6		12	260.159	odd	6
1040.2.dh.b.529.1		12	20.19	odd	2
1040.2.dh.b.529.6		12	4.3	odd	2
1170.2.bp.h.289.1		12	195.29	odd	6
1170.2.bp.h.289.4		12	39.29	odd	6
1170.2.bp.h.919.1		12	3.2	odd	2
1170.2.bp.h.919.4		12	15.14	odd	2
1690.2.b.b.339.1		6	65.4	even	6
1690.2.b.b.339.6		6	13.4	even	6
1690.2.b.c.339.3		6	13.9	even	3
1690.2.b.c.339.4		6	65.9	even	6
1690.2.c.b.1689.1		6	65.59	odd	12
1690.2.c.b.1689.6		6	13.6	odd	12
1690.2.c.c.1689.1		6	65.19	odd	12
1690.2.c.c.1689.6		6	13.7	odd	12
8450.2.a.bt.1.3		3	65.17	odd	12
8450.2.a.bu.1.1		3	65.48	odd	12
8450.2.a.ca.1.1		3	65.43	odd	12
8450.2.a.cb.1.3		3	65.22	odd	12

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:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	130.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.91766 - 1.10716i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.21432 + 0.311108i) q^{5} +(-1.10716 - 1.91766i) q^{6} +(3.38028 - 1.95161i) q^{7} +1.00000i q^{8} +(0.951606 + 1.64823i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.91766 - 1.10716i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.21432 + 0.311108i) q^{5} +(-1.10716 - 1.91766i) q^{6} +(3.38028 - 1.95161i) q^{7} +1.00000i q^{8} +(0.951606 + 1.64823i) q^{9} +(1.76210 + 1.37659i) q^{10} +(-0.533338 + 0.923769i) q^{11} -2.21432i q^{12} +(-2.24483 + 2.82148i) q^{13} +3.90321 q^{14} +(-3.90186 - 3.04820i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.13545 + 0.655554i) q^{17} +1.90321i q^{18} +(-3.29605 - 5.70893i) q^{19} +(0.837733 + 2.07321i) q^{20} -8.64296 q^{21} +(-0.923769 + 0.533338i) q^{22} +(-1.85991 - 1.07382i) q^{23} +(1.10716 - 1.91766i) q^{24} +(4.80642 + 1.37778i) q^{25} +(-3.35482 + 1.32106i) q^{26} +2.42864i q^{27} +(3.38028 + 1.95161i) q^{28} +(-4.52543 + 7.83827i) q^{29} +(-1.85501 - 4.59075i) q^{30} -6.92396 q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.04552 - 1.18098i) q^{33} -1.31111 q^{34} +(8.09218 - 3.26985i) q^{35} +(-0.951606 + 1.64823i) q^{36} +(4.34809 + 2.51037i) q^{37} -6.59210i q^{38} +(7.42864 - 2.92525i) q^{39} +(-0.311108 + 2.21432i) q^{40} +(2.97703 - 5.15637i) q^{41} +(-7.48502 - 4.32148i) q^{42} +(1.73205 - 1.00000i) q^{43} -1.06668 q^{44} +(1.59438 + 3.94576i) q^{45} +(-1.07382 - 1.85991i) q^{46} +0.0967881i q^{47} +(1.91766 - 1.10716i) q^{48} +(4.11753 - 7.13177i) q^{49} +(3.47359 + 3.59641i) q^{50} +2.90321 q^{51} +(-3.56589 - 0.533338i) q^{52} -1.49532i q^{53} +(-1.21432 + 2.10326i) q^{54} +(-1.46837 + 1.87959i) q^{55} +(1.95161 + 3.38028i) q^{56} +14.5970i q^{57} +(-7.83827 + 4.52543i) q^{58} +(3.59210 + 6.22171i) q^{59} +(0.688892 - 4.90321i) q^{60} +(-3.94370 - 6.83068i) q^{61} +(-5.99632 - 3.46198i) q^{62} +(6.43339 + 3.71432i) q^{63} -1.00000 q^{64} +(-5.84855 + 5.54927i) q^{65} +2.36196 q^{66} +(-7.29942 - 4.21432i) q^{67} +(-1.13545 - 0.655554i) q^{68} +(2.37778 + 4.11844i) q^{69} +(8.64296 + 1.21432i) q^{70} +(7.73975 + 13.4056i) q^{71} +(-1.64823 + 0.951606i) q^{72} -15.3526i q^{73} +(2.51037 + 4.34809i) q^{74} +(-7.69165 - 7.96360i) q^{75} +(3.29605 - 5.70893i) q^{76} +4.16346i q^{77} +(7.89601 + 1.18098i) q^{78} -4.30174 q^{79} +(-1.37659 + 1.76210i) q^{80} +(5.54371 - 9.60199i) q^{81} +(5.15637 - 2.97703i) q^{82} +9.69381i q^{83} +(-4.32148 - 7.48502i) q^{84} +(-2.71820 + 1.09836i) q^{85} +2.00000 q^{86} +(17.3564 - 10.0207i) q^{87} +(-0.923769 - 0.533338i) q^{88} +(2.26271 - 3.91914i) q^{89} +(-0.592104 + 4.21432i) q^{90} +(-2.08173 + 13.9184i) q^{91} -2.14764i q^{92} +(13.2778 + 7.66593i) q^{93} +(-0.0483940 + 0.0838209i) q^{94} +(-5.52242 - 13.6668i) q^{95} +2.21432 q^{96} +(3.68949 - 2.13013i) q^{97} +(7.13177 - 4.11753i) q^{98} -2.03011 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} - 2 q^{9}+O(q^{10}) \) 12 * q + 6 * q^4 - 2 * q^9	\( 12 q + 6 q^{4} - 2 q^{9} - 2 q^{10} - 6 q^{11} + 20 q^{14} + 4 q^{15} - 6 q^{16} - 26 q^{19} - 24 q^{21} + 4 q^{25} - 28 q^{29} - 16 q^{30} + 24 q^{31} - 16 q^{34} - 6 q^{35} + 2 q^{36} + 36 q^{39} - 4 q^{40} - 4 q^{41} - 12 q^{44} + 12 q^{45} - 4 q^{49} - 8 q^{50} + 8 q^{51} + 12 q^{54} + 12 q^{55} + 10 q^{56} + 16 q^{59} + 8 q^{60} - 8 q^{61} - 12 q^{64} - 10 q^{65} - 24 q^{66} + 28 q^{69} + 24 q^{70} + 40 q^{71} - 10 q^{74} - 8 q^{75} + 26 q^{76} + 56 q^{79} + 26 q^{81} - 12 q^{84} - 16 q^{85} + 24 q^{86} + 14 q^{89} + 20 q^{90} - 38 q^{91} - 14 q^{94} - 8 q^{95} - 52 q^{99}+O(q^{100}) \) 12 * q + 6 * q^4 - 2 * q^9 - 2 * q^10 - 6 * q^11 + 20 * q^14 + 4 * q^15 - 6 * q^16 - 26 * q^19 - 24 * q^21 + 4 * q^25 - 28 * q^29 - 16 * q^30 + 24 * q^31 - 16 * q^34 - 6 * q^35 + 2 * q^36 + 36 * q^39 - 4 * q^40 - 4 * q^41 - 12 * q^44 + 12 * q^45 - 4 * q^49 - 8 * q^50 + 8 * q^51 + 12 * q^54 + 12 * q^55 + 10 * q^56 + 16 * q^59 + 8 * q^60 - 8 * q^61 - 12 * q^64 - 10 * q^65 - 24 * q^66 + 28 * q^69 + 24 * q^70 + 40 * q^71 - 10 * q^74 - 8 * q^75 + 26 * q^76 + 56 * q^79 + 26 * q^81 - 12 * q^84 - 16 * q^85 + 24 * q^86 + 14 * q^89 + 20 * q^90 - 38 * q^91 - 14 * q^94 - 8 * q^95 - 52 * q^99

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