LMFDB - Embedded newform 380.2.k.d.343.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(267,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("380.267");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			343.17
Character	$\chi$	$=$	380.343
Dual form			380.2.k.d.267.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.647117 - 1.25747i) q^{2} +(-1.78847 + 1.78847i) q^{3} +(-1.16248 - 1.62746i) q^{4} +(0.0829302 + 2.23453i) q^{5} +(1.09160 + 3.40630i) q^{6} +(-0.904221 - 0.904221i) q^{7} +(-2.79875 + 0.408628i) q^{8} -3.39723i q^{9} +O(q^{10})$	\(q+(0.647117 - 1.25747i) q^{2} +(-1.78847 + 1.78847i) q^{3} +(-1.16248 - 1.62746i) q^{4} +(0.0829302 + 2.23453i) q^{5} +(1.09160 + 3.40630i) q^{6} +(-0.904221 - 0.904221i) q^{7} +(-2.79875 + 0.408628i) q^{8} -3.39723i q^{9} +(2.86353 + 1.34172i) q^{10} -4.92807i q^{11} +(4.98972 + 0.831610i) q^{12} +(-4.64598 - 4.64598i) q^{13} +(-1.72217 + 0.551898i) q^{14} +(-4.14470 - 3.84806i) q^{15} +(-1.29728 + 3.78379i) q^{16} +(-3.50664 + 3.50664i) q^{17} +(-4.27193 - 2.19840i) q^{18} -1.00000 q^{19} +(3.54021 - 2.73256i) q^{20} +3.23434 q^{21} +(-6.19691 - 3.18903i) q^{22} +(2.65546 - 2.65546i) q^{23} +(4.27466 - 5.73630i) q^{24} +(-4.98625 + 0.370620i) q^{25} +(-8.84868 + 2.83570i) q^{26} +(0.710431 + 0.710431i) q^{27} +(-0.420449 + 2.52273i) q^{28} -4.23410i q^{29} +(-7.52094 + 2.72170i) q^{30} +6.52947i q^{31} +(3.91852 + 4.07985i) q^{32} +(8.81369 + 8.81369i) q^{33} +(2.14030 + 6.67871i) q^{34} +(1.94552 - 2.09550i) q^{35} +(-5.52887 + 3.94921i) q^{36} +(-4.68490 + 4.68490i) q^{37} +(-0.647117 + 1.25747i) q^{38} +16.6184 q^{39} +(-1.14519 - 6.22001i) q^{40} +3.99527 q^{41} +(2.09300 - 4.06710i) q^{42} +(-1.41043 + 1.41043i) q^{43} +(-8.02025 + 5.72878i) q^{44} +(7.59121 - 0.281733i) q^{45} +(-1.62078 - 5.05756i) q^{46} +(-0.801371 - 0.801371i) q^{47} +(-4.44704 - 9.08733i) q^{48} -5.36477i q^{49} +(-2.76064 + 6.50991i) q^{50} -12.5430i q^{51} +(-2.16031 + 12.9620i) q^{52} +(-2.72848 - 2.72848i) q^{53} +(1.35308 - 0.433616i) q^{54} +(11.0119 - 0.408686i) q^{55} +(2.90018 + 2.16120i) q^{56} +(1.78847 - 1.78847i) q^{57} +(-5.32427 - 2.73996i) q^{58} -13.9835 q^{59} +(-1.44446 + 11.2187i) q^{60} +6.61259 q^{61} +(8.21063 + 4.22533i) q^{62} +(-3.07185 + 3.07185i) q^{63} +(7.66605 - 2.28730i) q^{64} +(9.99628 - 10.7669i) q^{65} +(16.7865 - 5.37949i) q^{66} +(-1.41268 - 1.41268i) q^{67} +(9.78333 + 1.63053i) q^{68} +9.49840i q^{69} +(-1.37605 - 3.80247i) q^{70} -0.666584i q^{71} +(1.38820 + 9.50801i) q^{72} +(9.09755 + 9.09755i) q^{73} +(2.85946 + 8.92281i) q^{74} +(8.25489 - 9.58058i) q^{75} +(1.16248 + 1.62746i) q^{76} +(-4.45606 + 4.45606i) q^{77} +(10.7540 - 20.8971i) q^{78} -7.09809 q^{79} +(-8.56257 - 2.58502i) q^{80} +7.65052 q^{81} +(2.58541 - 5.02395i) q^{82} +(-6.54308 + 6.54308i) q^{83} +(-3.75985 - 5.26377i) q^{84} +(-8.12650 - 7.54489i) q^{85} +(0.860863 + 2.68628i) q^{86} +(7.57255 + 7.57255i) q^{87} +(2.01375 + 13.7924i) q^{88} +6.08572i q^{89} +(4.55813 - 9.72806i) q^{90} +8.40198i q^{91} +(-7.40858 - 1.23475i) q^{92} +(-11.6777 - 11.6777i) q^{93} +(-1.52628 + 0.489122i) q^{94} +(-0.0829302 - 2.23453i) q^{95} +(-14.3048 - 0.288531i) q^{96} +(1.52334 - 1.52334i) q^{97} +(-6.74605 - 3.47163i) q^{98} -16.7418 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) $ 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8	$ 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) $ 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.647117	−	1.25747i	0.457581	−	0.889168i
$2$	0.647117	−	1.25747i	0.457581	−	0.889168i
$3$	−1.78847	+	1.78847i	−1.03257	+	1.03257i	−0.0331206	+	0.999451i	$0.510545\pi$
$3$	−1.78847	+	1.78847i	−1.03257	+	1.03257i	−0.999451	+	0.0331206i	$0.989455\pi$
$4$	−1.16248	−	1.62746i	−0.581240	−	0.813732i
$5$	0.0829302	+	2.23453i	0.0370875	+	0.999312i
$5$	0.0829302	+	2.23453i	0.0370875	+	0.999312i
$6$	1.09160	+	3.40630i	0.445645	+	1.39061i
$7$	−0.904221	−	0.904221i	−0.341763	−	0.341763i	0.515267	−	0.857030i	$-0.327693\pi$
$7$	−0.904221	−	0.904221i	−0.341763	−	0.341763i	−0.857030	+	0.515267i	$0.827693\pi$
$8$	−2.79875	+	0.408628i	−0.989509	+	0.144472i
$9$		−	3.39723i		−	1.13241i
$10$	2.86353	+	1.34172i	0.905527	+	0.424289i
$11$		−	4.92807i		−	1.48587i	−0.669365	−	0.742934i	$-0.733434\pi$
$11$		−	4.92807i		−	1.48587i	0.669365	−	0.742934i	$-0.266566\pi$
$12$	4.98972	+	0.831610i	1.44041	+	0.240065i
$13$	−4.64598	−	4.64598i	−1.28856	−	1.28856i	−0.935660	−	0.352902i	$-0.885195\pi$
$13$	−4.64598	−	4.64598i	−1.28856	−	1.28856i	−0.352902	−	0.935660i	$-0.614805\pi$
$14$	−1.72217	+	0.551898i	−0.460270	+	0.147501i
$15$	−4.14470	−	3.84806i	−1.07016	−	0.993566i
$16$	−1.29728	+	3.78379i	−0.324320	+	0.945947i
$17$	−3.50664	+	3.50664i	−0.850485	+	0.850485i	−0.990193	−	0.139707i	$-0.955384\pi$
$17$	−3.50664	+	3.50664i	−0.850485	+	0.850485i	0.139707	+	0.990193i	$0.455384\pi$
$18$	−4.27193	−	2.19840i	−1.00690	−	0.518169i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	3.54021	−	2.73256i	0.791616	−	0.611019i
$21$	3.23434			0.705791
$22$	−6.19691	−	3.18903i	−1.32119	−	0.679905i
$23$	2.65546	−	2.65546i	0.553701	−	0.553701i	−0.373806	−	0.927507i	$-0.621947\pi$
$23$	2.65546	−	2.65546i	0.553701	−	0.553701i	0.927507	+	0.373806i	$0.121947\pi$
$24$	4.27466	−	5.73630i	0.872562	−	1.17092i
$25$	−4.98625	+	0.370620i	−0.997249	+	0.0741240i
$26$	−8.84868	+	2.83570i	−1.73537	+	0.556127i
$27$	0.710431	+	0.710431i	0.136722	+	0.136722i
$28$	−0.420449	+	2.52273i	−0.0794574	+	0.476751i
$29$		−	4.23410i		−	0.786253i	−0.919484	−	0.393126i	$-0.871394\pi$
$29$		−	4.23410i		−	0.786253i	0.919484	−	0.393126i	$-0.128606\pi$
$30$	−7.52094	+	2.72170i	−1.37313	+	0.496913i
$31$			6.52947i			1.17273i	0.810048	+	0.586364i	$0.199441\pi$
$31$			6.52947i			1.17273i	−0.810048	+	0.586364i	$0.800559\pi$
$32$	3.91852	+	4.07985i	0.692703	+	0.721223i
$33$	8.81369	+	8.81369i	1.53427	+	1.53427i
$34$	2.14030	+	6.67871i	0.367059	+	1.14539i
$35$	1.94552	−	2.09550i	0.328853	−	0.354204i
$36$	−5.52887	+	3.94921i	−0.921478	+	0.658202i
$37$	−4.68490	+	4.68490i	−0.770193	+	0.770193i	−0.978140	−	0.207947i	$-0.933322\pi$
$37$	−4.68490	+	4.68490i	−0.770193	+	0.770193i	0.207947	+	0.978140i	$0.433322\pi$
$38$	−0.647117	+	1.25747i	−0.104976	+	0.203989i
$39$	16.6184			2.66107
$40$	−1.14519	−	6.22001i	−0.181071	−	0.983470i
$41$	3.99527			0.623956			0.311978	−	0.950089i	$-0.399008\pi$
$41$	3.99527			0.623956			0.311978	+	0.950089i	$0.399008\pi$
$42$	2.09300	−	4.06710i	0.322956	−	0.627567i
$43$	−1.41043	+	1.41043i	−0.215088	+	0.215088i	−0.806425	−	0.591337i	$-0.798600\pi$
$43$	−1.41043	+	1.41043i	−0.215088	+	0.215088i	0.591337	+	0.806425i	$0.298600\pi$
$44$	−8.02025	+	5.72878i	−1.20910	+	0.863646i
$45$	7.59121	−	0.281733i	1.13163	−	0.0419983i
$46$	−1.62078	−	5.05756i	−0.238971	−	0.745697i
$47$	−0.801371	−	0.801371i	−0.116892	−	0.116892i	0.646241	−	0.763133i	$-0.276340\pi$
$47$	−0.801371	−	0.801371i	−0.116892	−	0.116892i	−0.763133	+	0.646241i	$0.776340\pi$
$48$	−4.44704	−	9.08733i	−0.641874	−	1.31164i
$49$		−	5.36477i		−	0.766395i
$50$	−2.76064	+	6.50991i	−0.390413	+	0.920640i
$51$		−	12.5430i		−	1.75637i
$52$	−2.16031	+	12.9620i	−0.299581	+	1.79751i
$53$	−2.72848	−	2.72848i	−0.374785	−	0.374785i	0.494431	−	0.869217i	$-0.335376\pi$
$53$	−2.72848	−	2.72848i	−0.374785	−	0.374785i	−0.869217	+	0.494431i	$0.835376\pi$
$54$	1.35308	−	0.433616i	0.184131	−	0.0590077i
$55$	11.0119	−	0.408686i	1.48485	−	0.0551072i
$56$	2.90018	+	2.16120i	0.387553	+	0.288803i
$57$	1.78847	−	1.78847i	0.236888	−	0.236888i
$58$	−5.32427	−	2.73996i	−0.699111	−	0.359774i
$59$	−13.9835			−1.82050			−0.910248	−	0.414063i	$-0.864109\pi$
$59$	−13.9835			−1.82050			−0.910248	+	0.414063i	$0.864109\pi$
$60$	−1.44446	+	11.2187i	−0.186479	+	1.44832i
$61$	6.61259			0.846655			0.423327	−	0.905977i	$-0.360862\pi$
$61$	6.61259			0.846655			0.423327	+	0.905977i	$0.360862\pi$
$62$	8.21063	+	4.22533i	1.04275	+	0.536617i
$63$	−3.07185	+	3.07185i	−0.387016	+	0.387016i
$64$	7.66605	−	2.28730i	0.958256	−	0.285912i
$65$	9.99628	−	10.7669i	1.23989	−	1.33547i
$66$	16.7865	−	5.37949i	2.06627	−	0.662170i
$67$	−1.41268	−	1.41268i	−0.172586	−	0.172586i	0.615528	−	0.788115i	$-0.288943\pi$
$67$	−1.41268	−	1.41268i	−0.172586	−	0.172586i	−0.788115	+	0.615528i	$0.788943\pi$
$68$	9.78333	+	1.63053i	1.18640	+	0.197731i
$69$			9.49840i			1.14347i
$70$	−1.37605	−	3.80247i	−0.164470	−	0.454482i
$71$		−	0.666584i		−	0.0791089i	−0.999217	−	0.0395545i	$-0.987406\pi$
$71$		−	0.666584i		−	0.0791089i	0.999217	−	0.0395545i	$-0.0125939\pi$
$72$	1.38820	+	9.50801i	0.163601	+	1.12053i
$73$	9.09755	+	9.09755i	1.06479	+	1.06479i	0.997750	+	0.0670369i	$0.0213545\pi$
$73$	9.09755	+	9.09755i	1.06479	+	1.06479i	0.0670369	+	0.997750i	$0.478645\pi$
$74$	2.85946	+	8.92281i	0.332406	+	1.03726i
$75$	8.25489	−	9.58058i	0.953193	−	1.10627i
$76$	1.16248	+	1.62746i	0.133346	+	0.186683i
$77$	−4.45606	+	4.45606i	−0.507815	+	0.507815i
$78$	10.7540	−	20.8971i	1.21765	−	2.36614i
$79$	−7.09809			−0.798598			−0.399299	−	0.916821i	$-0.630746\pi$
$79$	−7.09809			−0.798598			−0.399299	+	0.916821i	$0.630746\pi$
$80$	−8.56257	−	2.58502i	−0.957325	−	0.289014i
$81$	7.65052			0.850058
$82$	2.58541	−	5.02395i	0.285510	−	0.554802i
$83$	−6.54308	+	6.54308i	−0.718196	+	0.718196i	−0.968236	−	0.250039i	$-0.919556\pi$
$83$	−6.54308	+	6.54308i	−0.718196	+	0.718196i	0.250039	+	0.968236i	$0.419556\pi$
$84$	−3.75985	−	5.26377i	−0.410234	−	0.574325i
$85$	−8.12650	−	7.54489i	−0.881443	−	0.818358i
$86$	0.860863	+	2.68628i	0.0928293	+	0.289669i
$87$	7.57255	+	7.57255i	0.811862	+	0.811862i
$88$	2.01375	+	13.7924i	0.214666	+	1.47028i
$89$			6.08572i			0.645085i	0.946555	+	0.322542i	$0.104538\pi$
$89$			6.08572i			0.645085i	−0.946555	+	0.322542i	$0.895462\pi$
$90$	4.55813	−	9.72806i	0.480469	−	1.02543i
$91$			8.40198i			0.880767i
$92$	−7.40858	−	1.23475i	−0.772398	−	0.128731i
$93$	−11.6777	−	11.6777i	−1.21092	−	1.21092i
$94$	−1.52628	+	0.489122i	−0.157424	+	0.0504491i
$95$	−0.0829302	−	2.23453i	−0.00850846	−	0.229258i
$96$	−14.3048	−	0.288531i	−1.45998	−	0.0294480i
$97$	1.52334	−	1.52334i	0.154672	−	0.154672i	−0.625529	−	0.780201i	$-0.715117\pi$
$97$	1.52334	−	1.52334i	0.154672	−	0.154672i	0.780201	+	0.625529i	$0.215117\pi$
$98$	−6.74605	−	3.47163i	−0.681454	−	0.350688i
$99$	−16.7418			−1.68261
$100$	6.39958	+	7.68410i	0.639958	+	0.768410i
$101$	−0.349073			−0.0347341			−0.0173670	−	0.999849i	$-0.505528\pi$
$101$	−0.349073			−0.0347341			−0.0173670	+	0.999849i	$0.505528\pi$
$102$	−15.7725	−	8.11680i	−1.56171	−	0.803683i
$103$	6.13616	−	6.13616i	0.604613	−	0.604613i	−0.336920	−	0.941533i	$-0.609385\pi$
$103$	6.13616	−	6.13616i	0.604613	−	0.604613i	0.941533	+	0.336920i	$0.109385\pi$
$104$	14.9014	+	11.1045i	1.46120	+	1.08888i
$105$	0.268225	+	7.22723i	0.0261760	+	0.705305i
$106$	−5.19663	+	1.66535i	−0.504742	+	0.161753i
$107$	7.72854	+	7.72854i	0.747146	+	0.747146i	0.973942	−	0.226796i	$-0.0728252\pi$
$107$	7.72854	+	7.72854i	0.747146	+	0.747146i	−0.226796	+	0.973942i	$0.572825\pi$
$108$	0.330339	−	1.98206i	0.0317869	−	0.190724i
$109$			1.11697i			0.106986i	0.998568	+	0.0534931i	$0.0170355\pi$
$109$			1.11697i			0.106986i	−0.998568	+	0.0534931i	$0.982964\pi$
$110$	6.61208	−	14.1117i	0.630437	−	1.34549i
$111$		−	16.7576i		−	1.59056i
$112$	4.59441	−	2.24835i	0.434131	−	0.212449i
$113$	−7.06685	−	7.06685i	−0.664794	−	0.664794i	0.291712	−	0.956506i	$-0.405775\pi$
$113$	−7.06685	−	7.06685i	−0.664794	−	0.664794i	−0.956506	+	0.291712i	$0.905775\pi$
$114$	−1.09160	−	3.40630i	−0.102238	−	0.319029i
$115$	6.15392	+	5.71348i	0.573856	+	0.532785i
$116$	−6.89085	+	4.92206i	−0.639799	+	0.457001i
$117$	−15.7834	+	15.7834i	−1.45918	+	1.45918i
$118$	−9.04896	+	17.5839i	−0.833024	+	1.61873i
$119$	6.34156			0.581330
$120$	13.1724	+	9.07614i	1.20247	+	0.828535i
$121$	−13.2858			−1.20780
$122$	4.27912	−	8.31515i	0.387413	−	0.752818i
$123$	−7.14541	+	7.14541i	−0.644280	+	0.644280i
$124$	10.6265	−	7.59037i	0.954286	−	0.681636i
$125$	−1.24167	−	11.1112i	−0.111059	−	0.993814i
$126$	1.87492	+	5.85061i	0.167031	+	0.521214i
$127$	−0.443269	−	0.443269i	−0.0393338	−	0.0393338i	0.687166	−	0.726500i	$-0.258854\pi$
$127$	−0.443269	−	0.443269i	−0.0393338	−	0.0393338i	−0.726500	+	0.687166i	$0.758854\pi$
$128$	2.08461	−	11.1200i	0.184255	−	0.982878i
$129$		−	5.04500i		−	0.444188i
$130$	−7.07029	−	19.5375i	−0.620105	−	1.71355i
$131$		−	19.8615i		−	1.73531i	−0.497166	−	0.867655i	$-0.665626\pi$
$131$		−	19.8615i		−	1.73531i	0.497166	−	0.867655i	$-0.334374\pi$
$132$	4.09823	−	24.5897i	0.356705	−	2.14026i
$133$	0.904221	+	0.904221i	0.0784059	+	0.0784059i
$134$	−2.69057	+	0.862238i	−0.232430	+	0.0744860i
$135$	−1.52856	+	1.64639i	−0.131558	+	0.141699i
$136$	8.38131	−	11.2471i	0.718692	−	0.964434i
$137$	−10.4985	+	10.4985i	−0.896951	+	0.896951i	−0.995165	−	0.0982139i	$-0.968687\pi$
$137$	−10.4985	+	10.4985i	−0.896951	+	0.896951i	0.0982139	+	0.995165i	$0.468687\pi$
$138$	11.9440	+	6.14658i	1.01674	+	0.523231i
$139$	18.2723			1.54984			0.774920	−	0.632060i	$-0.217790\pi$
$139$	18.2723			1.54984			0.774920	+	0.632060i	$0.217790\pi$
$140$	−5.67198	−	0.730296i	−0.479369	−	0.0617212i
$141$	2.86645			0.241399
$142$	−0.838212	−	0.431358i	−0.0703411	−	0.0361987i
$143$	−22.8957	+	22.8957i	−1.91463	+	1.91463i
$144$	12.8544	+	4.40716i	1.07120	+	0.367264i
$145$	9.46122	−	0.351135i	0.785712	−	0.0291602i
$146$	17.3271	−	5.55275i	1.43400	−	0.459549i
$147$	9.59471	+	9.59471i	0.791358	+	0.791358i
$148$	13.0706	+	2.17841i	1.07440	+	0.179064i
$149$		−	20.0334i		−	1.64120i	−0.571501	−	0.820601i	$-0.693639\pi$
$149$		−	20.0334i		−	1.64120i	0.571501	−	0.820601i	$-0.306361\pi$
$150$	−6.70544	−	16.5801i	−0.547497	−	1.35376i
$151$			0.536358i			0.0436482i	0.999762	+	0.0218241i	$0.00694738\pi$
$151$			0.536358i			0.0436482i	−0.999762	+	0.0218241i	$0.993053\pi$
$152$	2.79875	−	0.408628i	0.227009	−	0.0331441i
$153$	11.9129	+	11.9129i	0.963098	+	0.963098i
$154$	2.71979	+	8.48697i	0.219167	+	0.683900i
$155$	−14.5903	+	0.541490i	−1.17192	+	0.0434936i
$156$	−19.3185	−	27.0458i	−1.54672	−	2.16540i
$157$	−3.05908	+	3.05908i	−0.244141	+	0.244141i	−0.818561	−	0.574420i	$-0.805228\pi$
$157$	−3.05908	+	3.05908i	−0.244141	+	0.244141i	0.574420	+	0.818561i	$0.305228\pi$
$158$	−4.59330	+	8.92567i	−0.365423	+	0.710088i
$159$	9.75959			0.773985
$160$	−8.79158	+	9.09440i	−0.695036	+	0.718975i
$161$	−4.80224			−0.378470
$162$	4.95078	−	9.62033i	0.388970	−	0.755845i
$163$	−4.16638	+	4.16638i	−0.326336	+	0.326336i	−0.851191	−	0.524856i	$-0.824119\pi$
$163$	−4.16638	+	4.16638i	−0.326336	+	0.326336i	0.524856	+	0.851191i	$0.324119\pi$
$164$	−4.64442	−	6.50216i	−0.362668	−	0.507734i
$165$	−18.9635	+	20.4254i	−1.47631	+	1.59011i
$166$	3.99361	+	12.4619i	0.309965	+	0.967230i
$167$	−1.58055	−	1.58055i	−0.122307	−	0.122307i	0.643304	−	0.765611i	$-0.277563\pi$
$167$	−1.58055	−	1.58055i	−0.122307	−	0.122307i	−0.765611	+	0.643304i	$0.777563\pi$
$168$	−9.05212	+	1.32164i	−0.698386	+	0.101967i
$169$			30.1702i			2.32079i
$170$	−14.7463	+	5.33644i	−1.13099	+	0.409286i
$171$			3.39723i			0.259793i
$172$	3.93501	+	0.655827i	0.300042	+	0.0500063i
$173$	−8.52546	−	8.52546i	−0.648179	−	0.648179i	0.304374	−	0.952553i	$-0.401553\pi$
$173$	−8.52546	−	8.52546i	−0.648179	−	0.648179i	−0.952553	+	0.304374i	$0.901553\pi$
$174$	14.4226	−	4.62196i	1.09337	−	0.350390i
$175$	4.84379	+	4.17355i	0.366156	+	0.315490i
$176$	18.6468	+	6.39309i	1.40555	+	0.481897i
$177$	25.0090	−	25.0090i	1.87979	−	1.87979i
$178$	7.65263	+	3.93817i	0.573589	+	0.295178i
$179$	−15.0799			−1.12713			−0.563564	−	0.826073i	$-0.690570\pi$
$179$	−15.0799			−1.12713			−0.563564	+	0.826073i	$0.690570\pi$
$180$	−9.28314	−	12.0269i	−0.691924	−	0.896433i
$181$	−7.85061			−0.583531			−0.291765	−	0.956490i	$-0.594243\pi$
$181$	−7.85061			−0.583531			−0.291765	+	0.956490i	$0.594243\pi$
$182$	10.5653	+	5.43706i	0.783150	+	0.403022i
$183$	−11.8264	+	11.8264i	−0.874232	+	0.874232i
$184$	−6.34688	+	8.51707i	−0.467898	+	0.627887i
$185$	−10.8571	−	10.0800i	−0.798227	−	0.741098i
$186$	−22.2413	+	7.12759i	−1.63081	+	0.522620i
$187$	17.2810	+	17.2810i	1.26371	+	1.26371i
$188$	−0.372625	+	2.23578i	−0.0271765	+	0.163061i
$189$		−	1.28477i		−	0.0934535i
$190$	−2.86353	−	1.34172i	−0.207742	−	0.0973385i
$191$		−	9.49299i		−	0.686889i	−0.939173	−	0.343444i	$-0.888406\pi$
$191$		−	9.49299i		−	0.686889i	0.939173	−	0.343444i	$-0.111594\pi$
$192$	−9.61971	+	17.8012i	−0.694243	+	1.28469i
$193$	−6.06821	−	6.06821i	−0.436800	−	0.436800i	0.454134	−	0.890933i	$-0.349949\pi$
$193$	−6.06821	−	6.06821i	−0.436800	−	0.436800i	−0.890933	+	0.454134i	$0.849949\pi$
$194$	−0.929783	−	2.90134i	−0.0667545	−	0.208304i
$195$	1.37816	+	37.1342i	0.0986924	+	2.65924i
$196$	−8.73097	+	6.23643i	−0.623641	+	0.445460i
$197$	12.5816	−	12.5816i	0.896402	−	0.896402i	−0.0987143	−	0.995116i	$-0.531473\pi$
$197$	12.5816	−	12.5816i	0.896402	−	0.896402i	0.995116	+	0.0987143i	$0.0314730\pi$
$198$	−10.8339	+	21.0523i	−0.769930	+	1.49612i
$199$	−9.07658			−0.643422			−0.321711	−	0.946838i	$-0.604258\pi$
$199$	−9.07658			−0.643422			−0.321711	+	0.946838i	$0.604258\pi$
$200$	13.8038	−	3.07479i	0.976078	−	0.217421i
$201$	5.05306			0.356415
$202$	−0.225891	+	0.438950i	−0.0158936	+	0.0308844i
$203$	−3.82856	+	3.82856i	−0.268712	+	0.268712i
$204$	−20.4133	+	14.5810i	−1.42922	+	1.02088i
$205$	0.331329	+	8.92755i	0.0231410	+	0.623527i
$206$	−3.74524	−	11.6869i	−0.260944	−	0.814262i
$207$	−9.02120	−	9.02120i	−0.627017	−	0.627017i
$208$	23.6065	−	11.5523i	1.63682	−	0.801005i
$209$			4.92807i			0.340882i
$210$	9.26162	+	4.33957i	0.639113	+	0.299459i
$211$			21.5273i			1.48200i	0.671506	+	0.740999i	$0.265648\pi$
$211$			21.5273i			1.48200i	−0.671506	+	0.740999i	$0.734352\pi$
$212$	−1.26870	+	7.61230i	−0.0871347	+	0.522815i
$213$	1.19216	+	1.19216i	0.0816857	+	0.0816857i
$214$	14.7197	−	4.71717i	1.00622	−	0.322459i
$215$	−3.26861	−	3.03467i	−0.222917	−	0.206963i
$216$	−2.27862	−	1.69802i	−0.155041	−	0.115536i
$217$	5.90408	−	5.90408i	0.400795	−	0.400795i
$218$	1.40456	+	0.722809i	0.0951287	+	0.0489548i
$219$	−32.5413			−2.19894
$220$	−13.4662	−	17.4464i	−0.907894	−	1.17624i
$221$	32.5836			2.19181
$222$	−21.0722	−	10.8441i	−1.41427	−	0.727809i
$223$	11.2136	−	11.2136i	0.750919	−	0.750919i	−0.223732	−	0.974651i	$-0.571824\pi$
$223$	11.2136	−	11.2136i	0.750919	−	0.750919i	0.974651	+	0.223732i	$0.0718239\pi$
$224$	0.145877	−	7.23230i	0.00974679	−	0.483228i
$225$	1.25908	+	16.9394i	0.0839388	+	1.12929i
$226$	−13.4595	+	4.31330i	−0.895310	+	0.286917i
$227$	−10.4346	−	10.4346i	−0.692570	−	0.692570i	0.270227	−	0.962797i	$-0.412901\pi$
$227$	−10.4346	−	10.4346i	−0.692570	−	0.692570i	−0.962797	+	0.270227i	$0.912901\pi$
$228$	−4.98972	−	0.831610i	−0.330453	−	0.0550747i
$229$			3.99464i			0.263973i	0.991252	+	0.131987i	$0.0421356\pi$
$229$			3.99464i			0.263973i	−0.991252	+	0.131987i	$0.957864\pi$
$230$	11.1669	−	4.04110i	0.736321	−	0.266462i
$231$		−	15.9390i		−	1.04871i
$232$	1.73017	+	11.8502i	0.113591	+	0.778004i
$233$	−12.5036	−	12.5036i	−0.819139	−	0.819139i	0.166844	−	0.985983i	$-0.446642\pi$
$233$	−12.5036	−	12.5036i	−0.819139	−	0.819139i	−0.985983	+	0.166844i	$0.946642\pi$
$234$	9.63354	+	30.0610i	0.629764	+	1.96515i
$235$	1.72423	−	1.85715i	0.112476	−	0.121147i
$236$	16.2555	+	22.7576i	1.05814	+	1.48140i
$237$	12.6947	−	12.6947i	0.824610	−	0.824610i
$238$	4.10373	−	7.97434i	0.266005	−	0.516900i
$239$	10.1130			0.654153			0.327077	−	0.944998i	$-0.393936\pi$
$239$	10.1130			0.654153			0.327077	+	0.944998i	$0.393936\pi$
$240$	19.9371	−	10.6906i	1.28693	−	0.690078i
$241$	−21.6620			−1.39537			−0.697687	−	0.716402i	$-0.745787\pi$
$241$	−21.6620			−1.39537			−0.697687	+	0.716402i	$0.745787\pi$
$242$	−8.59749	+	16.7066i	−0.552668	+	1.07394i
$243$	−15.8140	+	15.8140i	−1.01447	+	1.01447i
$244$	−7.68700	−	10.7617i	−0.492110	−	0.688950i
$245$	11.9877	−	0.444902i	0.765868	−	0.0284237i
$246$	4.36125	+	13.6091i	0.278063	+	0.867683i
$247$	4.64598	+	4.64598i	0.295616	+	0.295616i
$248$	−2.66812	−	18.2744i	−0.169426	−	1.16042i
$249$		−	23.4042i		−	1.48318i
$250$	−14.7755	−	5.62886i	−0.934486	−	0.356000i
$251$		−	2.50042i		−	0.157825i	−0.996882	−	0.0789125i	$-0.974855\pi$
$251$		−	2.50042i		−	0.157825i	0.996882	−	0.0789125i	$-0.0251448\pi$
$252$	8.57028	+	1.42836i	0.539877	+	0.0899783i
$253$	−13.0863	−	13.0863i	−0.822727	−	0.822727i
$254$	−0.844246	+	0.270552i	−0.0529727	+	0.0169760i
$255$	28.0278	−	1.04020i	1.75517	−	0.0651396i
$256$	−12.6341	−	9.81728i	−0.789633	−	0.613580i
$257$	3.26731	−	3.26731i	0.203809	−	0.203809i	−0.597821	−	0.801630i	$-0.703966\pi$
$257$	3.26731	−	3.26731i	0.203809	−	0.203809i	0.801630	+	0.597821i	$0.203966\pi$
$258$	−6.34396	−	3.26470i	−0.394957	−	0.203252i
$259$	8.47237			0.526447
$260$	−29.1432	−	3.75233i	−1.80738	−	0.232710i
$261$	−14.3842			−0.890360
$262$	−24.9754	−	12.8527i	−1.54298	−	0.794044i
$263$	17.4522	−	17.4522i	1.07615	−	1.07615i	0.0792985	−	0.996851i	$-0.474732\pi$
$263$	17.4522	−	17.4522i	1.07615	−	1.07615i	0.996851	−	0.0792985i	$-0.0252680\pi$
$264$	−28.2689	−	21.0658i	−1.73983	−	1.29651i
$265$	5.87059	−	6.32314i	0.360628	−	0.388427i
$266$	1.72217	−	0.551898i	0.105593	−	0.0338390i
$267$	−10.8841	−	10.8841i	−0.666097	−	0.666097i
$268$	−0.656874	+	3.94129i	−0.0401250	+	0.240753i
$269$			13.8165i			0.842410i	0.906965	+	0.421205i	$0.138393\pi$
$269$			13.8165i			0.842410i	−0.906965	+	0.421205i	$0.861607\pi$
$270$	1.08114	+	2.98754i	0.0657961	+	0.181816i
$271$		−	1.41089i		−	0.0857053i	−0.999081	−	0.0428526i	$-0.986355\pi$
$271$		−	1.41089i		−	0.0857053i	0.999081	−	0.0428526i	$-0.0136446\pi$
$272$	−8.71929	−	17.8175i	−0.528685	−	1.08034i
$273$	−15.0267	−	15.0267i	−0.909455	−	0.909455i
$274$	6.40786	+	19.9954i	0.387113	+	1.20797i
$275$	1.82644	+	24.5726i	0.110139	+	1.48178i
$276$	15.4583	−	11.0417i	0.930481	−	0.664632i
$277$	10.5953	−	10.5953i	0.636609	−	0.636609i	−0.313108	−	0.949717i	$-0.601370\pi$
$277$	10.5953	−	10.5953i	0.636609	−	0.636609i	0.949717	+	0.313108i	$0.101370\pi$
$278$	11.8243	−	22.9770i	0.709176	−	1.37807i
$279$	22.1821			1.32801
$280$	−4.58876	+	6.65977i	−0.274231	+	0.397998i
$281$	3.69749			0.220574			0.110287	−	0.993900i	$-0.464823\pi$
$281$	3.69749			0.220574			0.110287	+	0.993900i	$0.464823\pi$
$282$	1.85493	−	3.60449i	0.110459	−	0.214644i
$283$	10.5387	−	10.5387i	0.626458	−	0.626458i	−0.320717	−	0.947175i	$-0.603924\pi$
$283$	10.5387	−	10.5387i	0.626458	−	0.626458i	0.947175	+	0.320717i	$0.103924\pi$
$284$	−1.08484	+	0.774890i	−0.0643735	+	0.0459813i
$285$	4.14470	+	3.84806i	0.245511	+	0.227940i
$286$	13.9745	+	43.6069i	0.826332	+	2.57853i
$287$	−3.61261	−	3.61261i	−0.213246	−	0.213246i
$288$	13.8602	−	13.3121i	0.816719	−	0.784424i
$289$		−	7.59306i		−	0.446651i
$290$	5.68097	−	12.1245i	0.333598	−	0.711973i
$291$			5.44890i			0.319420i
$292$	4.23022	−	25.3817i	0.247555	−	1.48535i
$293$	0.294186	+	0.294186i	0.0171865	+	0.0171865i	0.715648	−	0.698461i	$-0.246132\pi$
$293$	0.294186	+	0.294186i	0.0171865	+	0.0171865i	−0.698461	+	0.715648i	$0.746132\pi$
$294$	18.2740	−	5.85620i	1.06576	−	0.341540i
$295$	−1.15965	−	31.2465i	−0.0675177	−	1.81924i
$296$	11.1975	−	15.0263i	0.650841	−	0.873384i
$297$	3.50105	−	3.50105i	0.203152	−	0.203152i
$298$	−25.1915	−	12.9640i	−1.45931	−	0.750983i
$299$	−24.6744			−1.42696
$300$	−25.1882	−	2.29732i	−1.45424	−	0.132636i
$301$	2.55067			0.147018
$302$	0.674456	+	0.347086i	0.0388106	+	0.0199726i
$303$	0.624306	−	0.624306i	0.0358654	−	0.0358654i
$304$	1.29728	−	3.78379i	0.0744042	−	0.217015i
$305$	0.548383	+	14.7760i	0.0314003	+	0.846072i
$306$	22.6891	−	7.27110i	1.29705	−	0.415661i
$307$	−0.725482	−	0.725482i	−0.0414055	−	0.0414055i	0.686101	−	0.727506i	$-0.259321\pi$
$307$	−0.725482	−	0.725482i	−0.0414055	−	0.0414055i	−0.727506	+	0.686101i	$0.759321\pi$
$308$	12.4322	+	2.07200i	0.708388	+	0.118063i
$309$			21.9486i			1.24861i
$310$	−8.76071	+	18.6973i	−0.497575	+	1.06194i
$311$		−	13.6716i		−	0.775247i	−0.921818	−	0.387624i	$-0.873296\pi$
$311$		−	13.6716i		−	0.775247i	0.921818	−	0.387624i	$-0.126704\pi$
$312$	−46.5107	+	6.79073i	−2.63315	+	0.384449i
$313$	4.09570	+	4.09570i	0.231502	+	0.231502i	0.813320	−	0.581817i	$-0.197658\pi$
$313$	4.09570	+	4.09570i	0.231502	+	0.231502i	−0.581817	+	0.813320i	$0.697658\pi$
$314$	1.86713	+	5.82629i	0.105368	+	0.328797i
$315$	−7.11888	−	6.60938i	−0.401103	−	0.372397i
$316$	8.25139	+	11.5519i	0.464177	+	0.649845i
$317$	1.42470	−	1.42470i	0.0800191	−	0.0800191i	−0.665964	−	0.745983i	$-0.731980\pi$
$317$	1.42470	−	1.42470i	0.0800191	−	0.0800191i	0.745983	+	0.665964i	$0.231980\pi$
$318$	6.31559	−	12.2724i	0.354161	−	0.688203i
$319$	−20.8659			−1.16827
$320$	5.74678	+	16.9403i	0.321255	+	0.946993i
$321$	−27.6445			−1.54296
$322$	−3.10761	+	6.03870i	−0.173181	+	0.336523i
$323$	3.50664	−	3.50664i	0.195115	−	0.195115i
$324$	−8.89358	−	12.4510i	−0.494088	−	0.691720i
$325$	24.8879	+	21.4441i	1.38053	+	1.18950i
$326$	2.54298	+	7.93524i	0.140842	+	0.439492i
$327$	−1.99766	−	1.99766i	−0.110471	−	0.110471i
$328$	−11.1818	+	1.63258i	−0.617411	+	0.0901441i
$329$			1.44923i			0.0798988i
$330$	13.4127	+	37.0637i	0.738347	+	2.04029i
$331$			7.52474i			0.413597i	0.978384	+	0.206799i	$0.0663045\pi$
$331$			7.52474i			0.413597i	−0.978384	+	0.206799i	$0.933696\pi$
$332$	18.2548	+	3.04243i	1.00186	+	0.166975i
$333$	15.9157	+	15.9157i	0.872174	+	0.872174i
$334$	−3.01030	+	0.964700i	−0.164716	+	0.0527860i
$335$	3.03952	−	3.27383i	0.166067	−	0.178868i
$336$	−4.19585	+	12.2381i	−0.228902	+	0.667641i
$337$	13.7139	−	13.7139i	0.747045	−	0.747045i	−0.226878	−	0.973923i	$-0.572852\pi$
$337$	13.7139	−	13.7139i	0.747045	−	0.747045i	0.973923	+	0.226878i	$0.0728518\pi$
$338$	37.9382	+	19.5237i	2.06357	+	1.06195i
$339$	25.2777			1.37289
$340$	−2.83214	+	21.9964i	−0.153595	+	1.19292i
$341$	32.1777			1.74252
$342$	4.27193	+	2.19840i	0.230999	+	0.118876i
$343$	−11.1805	+	11.1805i	−0.603689	+	0.603689i
$344$	3.37110	−	4.52377i	0.181757	−	0.243906i
$345$	−21.2245	+	0.787705i	−1.14269	+	0.0424086i
$346$	−16.2375	+	5.20357i	−0.872934	+	0.279746i
$347$	−22.6242	−	22.6242i	−1.21453	−	1.21453i	−0.969520	−	0.245012i	$-0.921208\pi$
$347$	−22.6242	−	22.6242i	−1.21453	−	1.21453i	−0.245012	−	0.969520i	$-0.578792\pi$
$348$	3.52112	−	21.1270i	0.188752	−	1.13253i
$349$		−	1.72511i		−	0.0923432i	−0.998934	−	0.0461716i	$-0.985298\pi$
$349$		−	1.72511i		−	0.0923432i	0.998934	−	0.0461716i	$-0.0147021\pi$
$350$	8.38262	−	3.39017i	0.448070	−	0.181212i
$351$		−	6.60129i		−	0.352351i
$352$	20.1058	−	19.3107i	1.07164	−	1.02927i
$353$	10.9581	+	10.9581i	0.583240	+	0.583240i	0.935792	−	0.352552i	$-0.114686\pi$
$353$	10.9581	+	10.9581i	0.583240	+	0.583240i	−0.352552	+	0.935792i	$0.614686\pi$
$354$	−15.2644	−	47.6319i	−0.811295	−	2.53161i
$355$	1.48950	−	0.0552800i	0.0790545	−	0.00293396i
$356$	9.90429	−	7.07453i	0.524926	−	0.374949i
$357$	−11.3417	+	11.3417i	−0.600265	+	0.600265i
$358$	−9.75848	+	18.9626i	−0.515752	+	1.00221i
$359$	26.0612			1.37546			0.687728	−	0.725968i	$-0.258608\pi$
$359$	26.0612			1.37546			0.687728	+	0.725968i	$0.258608\pi$
$360$	−21.1308	+	3.89048i	−1.11369	+	0.205046i
$361$	1.00000			0.0526316
$362$	−5.08026	+	9.87193i	−0.267012	+	0.518857i
$363$	23.7613	−	23.7613i	1.24714	−	1.24714i
$364$	13.6739	−	9.76713i	0.716709	−	0.511937i
$365$	−19.5743	+	21.0832i	−1.02456	+	1.10355i
$366$	7.21832	+	22.5244i	0.377308	+	1.17737i
$367$	2.92099	+	2.92099i	0.152474	+	0.152474i	0.779222	−	0.626748i	$-0.215614\pi$
$367$	2.92099	+	2.92099i	0.152474	+	0.152474i	−0.626748	+	0.779222i	$0.715614\pi$
$368$	6.60282	+	13.4926i	0.344196	+	0.703349i
$369$		−	13.5728i		−	0.706574i
$370$	−19.7012	+	7.12952i	−1.02421	+	0.370646i
$371$			4.93429i			0.256176i
$372$	−5.42997	+	32.5802i	−0.281531	+	1.68921i
$373$	−9.00352	−	9.00352i	−0.466185	−	0.466185i	0.434491	−	0.900676i	$-0.356928\pi$
$373$	−9.00352	−	9.00352i	−0.466185	−	0.466185i	−0.900676	+	0.434491i	$0.856928\pi$
$374$	32.9132	−	10.5476i	1.70190	−	0.545401i
$375$	22.0927	+	17.6513i	1.14086	+	0.911508i
$376$	2.57030	+	1.91538i	0.132553	+	0.0987781i
$377$	−19.6715	+	19.6715i	−1.01314	+	1.01314i
$378$	−1.61557	−	0.831398i	−0.0830959	−	0.0427625i
$379$	11.5138			0.591425			0.295713	−	0.955277i	$-0.404443\pi$
$379$	11.5138			0.591425			0.295713	+	0.955277i	$0.404443\pi$
$380$	−3.54021	+	2.73256i	−0.181609	+	0.140177i
$381$	1.58554			0.0812299
$382$	−11.9372	−	6.14307i	−0.610760	−	0.314307i
$383$	19.1866	−	19.1866i	0.980387	−	0.980387i	−0.0194239	−	0.999811i	$-0.506183\pi$
$383$	19.1866	−	19.1866i	0.980387	−	0.980387i	0.999811	+	0.0194239i	$0.00618321\pi$
$384$	16.1595	+	23.6160i	0.824636	+	1.20515i
$385$	−10.3267	−	9.58766i	−0.526300	−	0.488632i
$386$	−11.5575	+	3.70378i	−0.588259	+	0.188517i
$387$	4.79154	+	4.79154i	0.243568	+	0.243568i
$388$	−4.25004	−	0.708331i	−0.215763	−	0.0359601i
$389$			19.3955i			0.983390i	0.870767	+	0.491695i	$0.163623\pi$
$389$			19.3955i			0.983390i	−0.870767	+	0.491695i	$0.836377\pi$
$390$	47.5871	+	22.2972i	2.40967	+	1.12906i
$391$			18.6235i			0.941830i
$392$	2.19219	+	15.0147i	0.110723	+	0.758355i
$393$	35.5217	+	35.5217i	1.79183	+	1.79183i
$394$	−7.67926	−	23.9628i	−0.386876	−	1.20723i
$395$	−0.588647	−	15.8609i	−0.0296180	−	0.798049i
$396$	19.4620	+	27.2466i	0.978001	+	1.36920i
$397$	7.98711	−	7.98711i	0.400862	−	0.400862i	−0.477675	−	0.878537i	$-0.658520\pi$
$397$	7.98711	−	7.98711i	0.400862	−	0.400862i	0.878537	+	0.477675i	$0.158520\pi$
$398$	−5.87361	+	11.4136i	−0.294417	+	0.572110i
$399$	−3.23434			−0.161920
$400$	5.06622	−	19.3477i	0.253311	−	0.967385i
$401$	−21.8145			−1.08936			−0.544682	−	0.838643i	$-0.683350\pi$
$401$	−21.8145			−1.08936			−0.544682	+	0.838643i	$0.683350\pi$
$402$	3.26992	−	6.35409i	0.163089	−	0.316913i
$403$	30.3358	−	30.3358i	1.51113	−	1.51113i
$404$	0.405791	+	0.568104i	0.0201888	+	0.0282642i
$405$	0.634460	+	17.0953i	0.0315266	+	0.849473i
$406$	2.33679	+	7.29184i	0.115973	+	0.361888i
$407$	23.0875	+	23.0875i	1.14440	+	1.14440i
$408$	5.12543	+	35.1048i	0.253747	+	1.73795i
$409$			26.8043i			1.32539i	0.748890	+	0.662694i	$0.230587\pi$
$409$			26.8043i			1.32539i	−0.748890	+	0.662694i	$0.769413\pi$
$410$	11.4406	+	5.36053i	0.565009	+	0.264738i
$411$		−	37.5526i		−	1.85233i
$412$	−17.1195	−	2.85322i	−0.843419	−	0.140568i
$413$	12.6442	+	12.6442i	0.622179	+	0.622179i
$414$	−17.1817	+	5.50615i	−0.844434	+	0.270613i
$415$	−15.1633	−	14.0781i	−0.744338	−	0.691066i
$416$	0.749528	−	37.1603i	0.0367487	−	1.82193i
$417$	−32.6795	+	32.6795i	−1.60032	+	1.60032i
$418$	6.19691	+	3.18903i	0.303101	+	0.155981i
$419$	−22.9547			−1.12141			−0.560706	−	0.828015i	$-0.689470\pi$
$419$	−22.9547			−1.12141			−0.560706	+	0.828015i	$0.689470\pi$
$420$	11.4503	−	8.83803i	0.558715	−	0.431252i
$421$	−22.1889			−1.08142			−0.540710	−	0.841209i	$-0.681844\pi$
$421$	−22.1889			−1.08142			−0.540710	+	0.841209i	$0.681844\pi$
$422$	27.0700	+	13.9307i	1.31775	+	0.678134i
$423$	−2.72244	+	2.72244i	−0.132370	+	0.132370i
$424$	8.75127	+	6.52141i	0.424999	+	0.316707i
$425$	16.1853	−	18.7846i	0.785104	−	0.911187i
$426$	2.27058	−	0.727645i	0.110010	−	0.0352545i
$427$	−5.97924	−	5.97924i	−0.289356	−	0.289356i
$428$	3.59365	−	21.5622i	0.173706	−	1.04225i
$429$		−	81.8964i		−	3.95399i
$430$	−5.93119	+	2.14640i	−0.286027	+	0.103509i
$431$		−	3.20599i		−	0.154427i	−0.997015	−	0.0772135i	$-0.975398\pi$
$431$		−	3.20599i		−	0.154427i	0.997015	−	0.0772135i	$-0.0246023\pi$
$432$	−3.60975	+	1.76649i	−0.173674	+	0.0849903i
$433$	−16.1866	−	16.1866i	−0.777880	−	0.777880i	0.201590	−	0.979470i	$-0.435389\pi$
$433$	−16.1866	−	16.1866i	−0.777880	−	0.777880i	−0.979470	+	0.201590i	$0.935389\pi$
$434$	−3.60360	−	11.2449i	−0.172978	−	0.539771i
$435$	−16.2931	+	17.5491i	−0.781194	+	0.841414i
$436$	1.81783	−	1.29845i	0.0870581	−	0.0621847i
$437$	−2.65546	+	2.65546i	−0.127028	+	0.127028i
$438$	−21.0580	+	40.9199i	−1.00619	+	1.95523i
$439$	−33.4711			−1.59749			−0.798745	−	0.601669i	$-0.794502\pi$
$439$	−33.4711			−1.59749			−0.798745	+	0.601669i	$0.794502\pi$
$440$	−30.6526	+	5.64359i	−1.46131	+	0.269047i
$441$	−18.2253			−0.867874
$442$	21.0854	−	40.9730i	1.00293	−	1.94888i
$443$	6.99853	−	6.99853i	0.332510	−	0.332510i	−0.521029	−	0.853539i	$-0.674452\pi$
$443$	6.99853	−	6.99853i	0.332510	−	0.332510i	0.853539	+	0.521029i	$0.174452\pi$
$444$	−27.2724	+	19.4803i	−1.29429	+	0.924496i
$445$	−13.5987	+	0.504690i	−0.644641	+	0.0239246i
$446$	−6.84431	−	21.3573i	−0.324087	−	1.01130i
$447$	35.8291	+	35.8291i	1.69466	+	1.69466i
$448$	−9.00003	−	4.86358i	−0.425211	−	0.229782i
$449$		−	10.8774i		−	0.513334i	−0.966500	−	0.256667i	$-0.917376\pi$
$449$		−	10.8774i		−	0.513334i	0.966500	−	0.256667i	$-0.0826244\pi$
$450$	22.1156	+	9.37852i	1.04254	+	0.442108i
$451$		−	19.6890i		−	0.927117i
$452$	−3.28598	+	19.7161i	−0.154559	+	0.927369i
$453$	−0.959259	−	0.959259i	−0.0450699	−	0.0450699i
$454$	−19.8737	+	6.36884i	−0.932718	+	0.298905i
$455$	−18.7745	+	0.696778i	−0.880161	+	0.0326655i
$456$	−4.27466	+	5.73630i	−0.200179	+	0.268627i
$457$	−2.21461	+	2.21461i	−0.103595	+	0.103595i	−0.757005	−	0.653409i	$-0.773338\pi$
$457$	−2.21461	+	2.21461i	−0.103595	+	0.103595i	0.653409	+	0.757005i	$0.273338\pi$
$458$	5.02315	+	2.58500i	0.234716	+	0.120789i
$459$	−4.98245			−0.232561
$460$	2.14469	−	16.6571i	0.0999965	−	0.776641i
$461$	32.4654			1.51207			0.756033	−	0.654534i	$-0.227135\pi$
$461$	32.4654			1.51207			0.756033	+	0.654534i	$0.227135\pi$
$462$	−20.0429	−	10.3144i	−0.932481	−	0.479870i
$463$	17.6213	−	17.6213i	0.818933	−	0.818933i	−0.167020	−	0.985953i	$-0.553414\pi$
$463$	17.6213	−	17.6213i	0.818933	−	0.818933i	0.985953	+	0.167020i	$0.0534145\pi$
$464$	16.0209	+	5.49282i	0.743754	+	0.254998i
$465$	25.1258	−	27.0627i	1.16518	−	1.25500i
$466$	−23.8143	+	7.63167i	−1.10317	+	0.353530i
$467$	−4.04114	−	4.04114i	−0.187002	−	0.187002i	0.607397	−	0.794399i	$-0.292214\pi$
$467$	−4.04114	−	4.04114i	−0.187002	−	0.187002i	−0.794399	+	0.607397i	$0.792214\pi$
$468$	44.0349	+	7.33906i	2.03552	+	0.339248i
$469$			2.55475i			0.117967i
$470$	−1.21953	−	3.36996i	−0.0562529	−	0.155445i
$471$		−	10.9421i		−	0.504187i
$472$	39.1364	−	5.71405i	1.80140	−	0.263010i
$473$	6.95067	+	6.95067i	0.319592	+	0.319592i
$474$	−7.74830	−	24.1782i	−0.355891	−	1.11054i
$475$	4.98625	−	0.370620i	0.228785	−	0.0170052i
$476$	−7.37193	−	10.3207i	−0.337892	−	0.473047i
$477$	−9.26926	+	9.26926i	−0.424410	+	0.424410i
$478$	6.54427	−	12.7168i	0.299328	−	0.581652i
$479$	−41.6363			−1.90241			−0.951205	−	0.308559i	$-0.900153\pi$
$479$	−41.6363			−1.90241			−0.951205	+	0.308559i	$0.900153\pi$
$480$	−0.541573	−	31.9885i	−0.0247193	−	1.46007i
$481$	43.5319			1.98488
$482$	−14.0179	+	27.2394i	−0.638496	+	1.24072i
$483$	8.58866	−	8.58866i	0.390797	−	0.390797i
$484$	15.4445	+	21.6222i	0.702024	+	0.982829i
$485$	3.53029	+	3.27762i	0.160302	+	0.148829i
$486$	9.65218	+	30.1192i	0.437832	+	1.36623i
$487$	20.9898	+	20.9898i	0.951140	+	0.951140i	0.998861	−	0.0477211i	$-0.0151959\pi$
$487$	20.9898	+	20.9898i	0.951140	+	0.951140i	−0.0477211	+	0.998861i	$0.515196\pi$
$488$	−18.5070	+	2.70209i	−0.837772	+	0.122318i
$489$		−	14.9029i		−	0.673930i
$490$	7.19801	−	15.3622i	0.325173	−	0.693992i
$491$			26.4536i			1.19384i	0.802302	+	0.596918i	$0.203608\pi$
$491$			26.4536i			1.19384i	−0.802302	+	0.596918i	$0.796392\pi$
$492$	19.9353	+	3.32251i	0.898753	+	0.149790i
$493$	14.8475	+	14.8475i	0.668696	+	0.668696i
$494$	8.84868	−	2.83570i	0.398121	−	0.127584i
$495$	−1.38840	−	37.4100i	−0.0624039	−	1.68145i
$496$	−24.7061	−	8.47056i	−1.10934	−	0.380339i
$497$	−0.602739	+	0.602739i	−0.0270365	+	0.0270365i
$498$	−29.4301	−	15.1452i	−1.31880	−	0.678674i
$499$	−15.2356			−0.682041			−0.341021	−	0.940056i	$-0.610773\pi$
$499$	−15.2356			−0.682041			−0.341021	+	0.940056i	$0.610773\pi$
$500$	−16.6396	+	14.9373i	−0.744147	+	0.668016i
$501$	5.65353			0.252581
$502$	−3.14421	−	1.61806i	−0.140333	−	0.0722176i
$503$	−12.4917	+	12.4917i	−0.556977	+	0.556977i	−0.928445	−	0.371469i	$-0.878854\pi$
$503$	−12.4917	+	12.4917i	−0.556977	+	0.556977i	0.371469	+	0.928445i	$0.378854\pi$
$504$	7.34210	−	9.85258i	0.327043	−	0.438869i
$505$	−0.0289487	−	0.780014i	−0.00128820	−	0.0347102i
$506$	−24.9240	+	7.98730i	−1.10801	+	0.355079i
$507$	−53.9584	−	53.9584i	−2.39638	−	2.39638i
$508$	−0.206113	+	1.23670i	−0.00914480	+	0.0548695i
$509$		−	17.6173i		−	0.780873i	−0.920630	−	0.390437i	$-0.872324\pi$
$509$		−	17.6173i		−	0.780873i	0.920630	−	0.390437i	$-0.127676\pi$
$510$	16.8292	−	35.9173i	0.745210	−	1.59044i
$511$		−	16.4524i		−	0.727811i
$512$	−20.5207	+	9.53415i	−0.906896	+	0.421354i
$513$	−0.710431	−	0.710431i	−0.0313663	−	0.0313663i
$514$	−1.99423	−	6.22289i	−0.0879616	−	0.274480i
$515$	14.2203	+	13.2025i	0.626621	+	0.581774i
$516$	−8.21056	+	5.86471i	−0.361450	+	0.258180i
$517$	−3.94921	+	3.94921i	−0.173686	+	0.173686i
$518$	5.48261	−	10.6538i	0.240892	−	0.468100i
$519$	30.4950			1.33858
$520$	−23.5775	+	34.2186i	−1.03394	+	1.50058i
$521$	11.6663			0.511111			0.255555	−	0.966794i	$-0.417742\pi$
$521$	11.6663			0.511111			0.255555	+	0.966794i	$0.417742\pi$
$522$	−9.30826	+	18.0878i	−0.407412	+	0.791680i
$523$	−11.2249	+	11.2249i	−0.490833	+	0.490833i	−0.908569	−	0.417736i	$-0.862824\pi$
$523$	−11.2249	+	11.2249i	−0.490833	+	0.490833i	0.417736	+	0.908569i	$0.362824\pi$
$524$	−32.3239	+	23.0886i	−1.41208	+	1.00863i
$525$	−16.1272	+	1.19871i	−0.703849	+	0.0523161i
$526$	−10.6521	−	33.2393i	−0.464453	−	1.44930i
$527$	−22.8965	−	22.8965i	−0.997387	−	0.997387i
$528$	−44.7830	+	21.9153i	−1.94893	+	0.953741i
$529$			8.89707i			0.386829i
$530$	−4.15222	−	11.4739i	−0.180361	−	0.498395i
$531$			47.5051i			2.06155i
$532$	0.420449	−	2.52273i	0.0182288	−	0.109374i
$533$	−18.5619	−	18.5619i	−0.804007	−	0.804007i
$534$	−20.7298	+	6.64319i	−0.897065	+	0.287479i
$535$	−16.6287	+	17.9106i	−0.718922	+	0.774342i
$536$	4.53100	+	3.37648i	0.195709	+	0.145842i
$537$	26.9700	−	26.9700i	1.16384	−	1.16384i
$538$	17.3739	+	8.94092i	0.749044	+	0.385470i
$539$	−26.4379			−1.13876
$540$	4.45637	+	0.573780i	0.191772	+	0.0246916i
$541$	11.7416			0.504811			0.252405	−	0.967622i	$-0.418778\pi$
$541$	11.7416			0.504811			0.252405	+	0.967622i	$0.418778\pi$
$542$	−1.77415	−	0.913008i	−0.0762064	−	0.0392171i
$543$	14.0405	−	14.0405i	0.602538	−	0.602538i
$544$	−28.0474	−	0.565721i	−1.20252	−	0.0242551i
$545$	−2.49590	+	0.0926305i	−0.106913	+	0.00396786i
$546$	−28.6196	+	9.17163i	−1.22481	+	0.392510i
$547$	4.80032	+	4.80032i	0.205247	+	0.205247i	0.802244	−	0.596997i	$-0.203639\pi$
$547$	4.80032	+	4.80032i	0.205247	+	0.205247i	−0.596997	+	0.802244i	$0.703639\pi$
$548$	29.2904	+	4.88166i	1.25122	+	0.208534i
$549$		−	22.4645i		−	0.958760i
$550$	32.0813	+	13.6046i	1.36795	+	0.580102i
$551$			4.23410i			0.180379i
$552$	−3.88131	−	26.5837i	−0.165200	−	1.13148i
$553$	6.41825	+	6.41825i	0.272932	+	0.272932i
$554$	−6.46691	−	20.1797i	−0.274753	−	0.857353i
$555$	37.4453	−	1.38971i	1.58946	−	0.0589899i
$556$	−21.2412	−	29.7376i	−0.900828	−	1.26115i
$557$	23.5262	−	23.5262i	0.996839	−	0.996839i	−0.00315589	−	0.999995i	$-0.501005\pi$
$557$	23.5262	−	23.5262i	0.996839	−	0.996839i	0.999995	+	0.00315589i	$0.00100455\pi$
$558$	14.3544	−	27.8934i	0.607670	−	1.18082i
$559$	13.1056			0.554308
$560$	5.40503	+	10.0799i	0.228404	+	0.425953i
$561$	−61.8129			−2.60974
$562$	2.39271	−	4.64950i	0.100930	−	0.196127i
$563$	−16.6377	+	16.6377i	−0.701194	+	0.701194i	−0.964667	−	0.263473i	$-0.915132\pi$
$563$	−16.6377	+	16.6377i	−0.701194	+	0.701194i	0.263473	+	0.964667i	$0.415132\pi$
$564$	−3.33219	−	4.66505i	−0.140311	−	0.196434i
$565$	15.2050	−	16.3771i	0.639681	−	0.688992i
$566$	−6.43234	−	20.0718i	−0.270371	−	0.843682i
$567$	−6.91776	−	6.91776i	−0.290519	−	0.290519i
$568$	0.272385	+	1.86560i	0.0114290	+	0.0782790i
$569$			34.4084i			1.44247i	0.692689	+	0.721237i	$0.256426\pi$
$569$			34.4084i			1.44247i	−0.692689	+	0.721237i	$0.743574\pi$
$570$	7.52094	−	2.72170i	0.315018	−	0.114000i
$571$			46.0355i			1.92652i	0.268563	+	0.963262i	$0.413451\pi$
$571$			46.0355i			1.92652i	−0.268563	+	0.963262i	$0.586549\pi$
$572$	63.8777	+	10.6461i	2.67086	+	0.445138i
$573$	16.9779	+	16.9779i	0.709262	+	0.709262i
$574$	−6.88054	+	2.20498i	−0.287188	+	0.0920341i
$575$	−12.2566	+	14.2249i	−0.511136	+	0.593221i
$576$	−7.77048	−	26.0433i	−0.323770	−	1.08514i
$577$	−20.6188	+	20.6188i	−0.858372	+	0.858372i	−0.991146	−	0.132775i	$-0.957611\pi$
$577$	−20.6188	+	20.6188i	−0.858372	+	0.858372i	0.132775	+	0.991146i	$0.457611\pi$
$578$	−9.54808	−	4.91360i	−0.397148	−	0.204379i
$579$	21.7056			0.902054
$580$	−11.5699	−	14.9896i	−0.480416	−	0.622410i
$581$	11.8328			0.490907
$582$	6.85185	+	3.52607i	0.284018	+	0.146160i
$583$	−13.4461	+	13.4461i	−0.556881	+	0.556881i
$584$	−29.1793	−	21.7443i	−1.20745	−	0.899785i
$585$	−36.5775	−	33.9597i	−1.51229	−	1.40406i
$586$	0.560303	−	0.179558i	0.0231459	−	0.00741749i
$587$	10.5267	+	10.5267i	0.434482	+	0.434482i	0.890150	−	0.455668i	$-0.150599\pi$
$587$	10.5267	+	10.5267i	0.434482	+	0.434482i	−0.455668	+	0.890150i	$0.650599\pi$
$588$	4.46139	−	26.7687i	0.183985	−	1.10392i
$589$		−	6.52947i		−	0.269042i
$590$	−40.0421	−	18.7619i	−1.64851	−	0.772416i
$591$			45.0035i			1.85120i
$592$	−11.6490	−	23.8043i	−0.478773	−	0.978351i
$593$	1.48897	+	1.48897i	0.0611445	+	0.0611445i	0.737018	−	0.675873i	$-0.236233\pi$
$593$	1.48897	+	1.48897i	0.0611445	+	0.0611445i	−0.675873	+	0.737018i	$0.736233\pi$
$594$	−2.13689	−	6.66807i	−0.0876777	−	0.273594i
$595$	0.525907	+	14.1704i	0.0215601	+	0.580930i
$596$	−32.6037	+	23.2885i	−1.33550	+	0.953933i
$597$	16.2332	−	16.2332i	0.664379	−	0.664379i
$598$	−15.9672	+	31.0274i	−0.652948	+	1.26881i
$599$	40.1937			1.64227			0.821134	−	0.570735i	$-0.193342\pi$
$599$	40.1937			1.64227			0.821134	+	0.570735i	$0.193342\pi$
$600$	−19.1885	+	30.1869i	−0.783368	+	1.23237i
$601$	−36.4888			−1.48841			−0.744204	−	0.667953i	$-0.767171\pi$
$601$	−36.4888			−1.48841			−0.744204	+	0.667953i	$0.767171\pi$
$602$	1.65058	−	3.20741i	0.0672728	−	0.130724i
$603$	−4.79919	+	4.79919i	−0.195438	+	0.195438i
$604$	0.872904	−	0.623505i	0.0355179	−	0.0253701i
$605$	−1.10180	−	29.6876i	−0.0447945	−	1.20697i
$606$	−0.381049	−	1.18905i	−0.0154791	−	0.0483017i
$607$	−1.97147	−	1.97147i	−0.0800195	−	0.0800195i	0.665964	−	0.745984i	$-0.268020\pi$
$607$	−1.97147	−	1.97147i	−0.0800195	−	0.0800195i	−0.745984	+	0.665964i	$0.768020\pi$
$608$	−3.91852	−	4.07985i	−0.158917	−	0.165460i
$609$		−	13.6945i		−	0.554930i
$610$	18.9353	+	8.87223i	0.766669	+	0.359226i
$611$			7.44631i			0.301245i
$612$	5.53930	−	33.2362i	0.223913	−	1.34349i
$613$	28.7912	+	28.7912i	1.16286	+	1.16286i	0.983846	+	0.179019i	$0.0572924\pi$
$613$	28.7912	+	28.7912i	1.16286	+	1.16286i	0.179019	+	0.983846i	$0.442708\pi$
$614$	−1.38175	+	0.442803i	−0.0557627	+	0.0178701i
$615$	−16.5592	−	15.3741i	−0.667731	−	0.619942i
$616$	10.6506	−	14.2923i	0.429123	−	0.575853i
$617$	−0.750563	+	0.750563i	−0.0302165	+	0.0302165i	−0.722054	−	0.691837i	$-0.756802\pi$
$617$	−0.750563	+	0.750563i	−0.0302165	+	0.0302165i	0.691837	+	0.722054i	$0.256802\pi$
$618$	27.5998	+	14.2033i	1.11023	+	0.571341i
$619$	26.8459			1.07903			0.539514	−	0.841977i	$-0.318608\pi$
$619$	26.8459			1.07903			0.539514	+	0.841977i	$0.318608\pi$
$620$	17.8422	+	23.1157i	0.716559	+	0.928349i
$621$	3.77304			0.151407
$622$	−17.1917	−	8.84715i	−0.689325	−	0.354738i
$623$	5.50284	−	5.50284i	0.220466	−	0.220466i
$624$	−21.5587	+	62.8804i	−0.863038	+	2.51723i
$625$	24.7253	−	3.69601i	0.989011	−	0.147840i
$626$	7.80063	−	2.49984i	0.311776	−	0.0999136i
$627$	−8.81369	−	8.81369i	−0.351985	−	0.351985i
$628$	8.53466	+	1.42243i	0.340570	+	0.0567610i
$629$		−	32.8565i		−	1.31008i
$630$	−12.9179	+	4.67476i	−0.514660	+	0.186247i
$631$		−	0.106404i		−	0.00423588i	−0.999998	−	0.00211794i	$-0.999326\pi$
$631$		−	0.106404i		−	0.00423588i	0.999998	−	0.00211794i	$-0.000674162\pi$
$632$	19.8658	−	2.90048i	0.790220	−	0.115375i
$633$	−38.5008	−	38.5008i	−1.53027	−	1.53027i
$634$	−0.869575	−	2.71347i	−0.0345352	−	0.107766i
$635$	0.953738	−	1.02726i	0.0378479	−	0.0407655i
$636$	−11.3453	−	15.8834i	−0.449871	−	0.629817i
$637$	−24.9246	+	24.9246i	−0.987548	+	0.987548i
$638$	−13.5027	+	26.2384i	−0.534577	+	1.03879i
$639$	−2.26454			−0.0895837
$640$	25.0208	+	3.73594i	0.989036	+	0.147676i
$641$	−13.7498			−0.543084			−0.271542	−	0.962427i	$-0.587534\pi$
$641$	−13.7498			−0.543084			−0.271542	+	0.962427i	$0.587534\pi$
$642$	−17.8892	+	34.7622i	−0.706030	+	1.37195i
$643$	−23.5125	+	23.5125i	−0.927244	+	0.927244i	−0.997527	−	0.0702828i	$-0.977610\pi$
$643$	−23.5125	+	23.5125i	−0.927244	+	0.927244i	0.0702828	+	0.997527i	$0.477610\pi$
$644$	5.58251	+	7.81548i	0.219982	+	0.307973i
$645$	11.2732	−	0.418383i	0.443882	−	0.0164738i
$646$	−2.14030	−	6.67871i	−0.0842091	−	0.262771i
$647$	−14.0408	−	14.0408i	−0.552002	−	0.552002i	0.375016	−	0.927018i	$-0.377637\pi$
$647$	−14.0408	−	14.0408i	−0.552002	−	0.552002i	−0.927018	+	0.375016i	$0.877637\pi$
$648$	−21.4119	+	3.12622i	−0.841140	+	0.122809i
$649$			68.9116i			2.70502i
$650$	43.0707	−	17.4190i	1.68937	−	0.683230i
$651$			21.1185i			0.827700i
$652$	11.6240	+	1.93730i	0.455229	+	0.0758706i
$653$	−5.12437	−	5.12437i	−0.200532	−	0.200532i	0.599696	−	0.800228i	$-0.295288\pi$
$653$	−5.12437	−	5.12437i	−0.200532	−	0.200532i	−0.800228	+	0.599696i	$0.795288\pi$
$654$	−3.80473	+	1.21929i	−0.148777	+	0.0476779i
$655$	44.3812	−	1.64712i	1.73412	−	0.0643584i
$656$	−5.18299	+	15.1173i	−0.202362	+	0.590230i
$657$	30.9064	−	30.9064i	1.20578	−	1.20578i
$658$	1.82237	+	0.937823i	0.0710435	+	0.0365602i
$659$	−3.86388			−0.150515			−0.0752576	−	0.997164i	$-0.523978\pi$
$659$	−3.86388			−0.150515			−0.0752576	+	0.997164i	$0.523978\pi$
$660$	55.2863	+	7.11839i	2.15201	+	0.277083i
$661$	15.1842			0.590596			0.295298	−	0.955405i	$-0.404581\pi$
$661$	15.1842			0.590596			0.295298	+	0.955405i	$0.404581\pi$
$662$	9.46216	+	4.86939i	0.367757	+	0.189254i
$663$	−58.2746	+	58.2746i	−2.26320	+	2.26320i
$664$	15.6388	−	20.9862i	0.606903	−	0.814421i
$665$	−1.94552	+	2.09550i	−0.0754441	+	0.0812599i
$666$	30.3128	−	9.71424i	1.17460	−	0.376419i
$667$	−11.2435	−	11.2435i	−0.435349	−	0.435349i
$668$	−0.734932	+	4.40965i	−0.0284354	+	0.170614i
$669$			40.1104i			1.55076i
$670$	−2.14983	−	5.94066i	−0.0830550	−	0.229508i
$671$		−	32.5873i		−	1.25802i
$672$	12.6738	+	13.1956i	0.488904	+	0.509032i
$673$	16.4676	+	16.4676i	0.634778	+	0.634778i	0.949262	−	0.314485i	$-0.101832\pi$
$673$	16.4676	+	16.4676i	0.634778	+	0.634778i	−0.314485	+	0.949262i	$0.601832\pi$
$674$	−8.37039	−	26.1194i	−0.322415	−	1.00608i
$675$	−3.80568	−	3.27908i	−0.146481	−	0.126212i
$676$	49.1010	−	35.0723i	1.88850	−	1.34893i
$677$	−13.1053	+	13.1053i	−0.503676	+	0.503676i	−0.912578	−	0.408902i	$-0.865912\pi$
$677$	−13.1053	+	13.1053i	−0.503676	+	0.503676i	0.408902	+	0.912578i	$0.365912\pi$
$678$	16.3576	−	31.7860i	0.628210	−	1.22073i
$679$	−2.75488			−0.105723
$680$	25.8271	+	17.7956i	0.990425	+	0.682429i
$681$	37.3240			1.43026
$682$	20.8227	−	40.4626i	0.797342	−	1.54939i
$683$	−10.6014	+	10.6014i	−0.405652	+	0.405652i	−0.880219	−	0.474567i	$-0.842605\pi$
$683$	−10.6014	+	10.6014i	−0.405652	+	0.405652i	0.474567	+	0.880219i	$0.342605\pi$
$684$	5.52887	−	3.94921i	0.211402	−	0.151002i
$685$	−24.3300	−	22.5887i	−0.929600	−	0.863069i
$686$	6.82409	+	21.2942i	0.260545	+	0.813018i
$687$	−7.14428	−	7.14428i	−0.272571	−	0.272571i
$688$	−3.50703	−	7.16647i	−0.133704	−	0.273219i
$689$			25.3529i			0.965868i
$690$	−12.7442	+	27.1989i	−0.485163	+	1.03545i
$691$			16.8100i			0.639483i	0.947505	+	0.319742i	$0.103596\pi$
$691$			16.8100i			0.639483i	−0.947505	+	0.319742i	$0.896404\pi$
$692$	−3.96421	+	23.7856i	−0.150697	+	0.904192i
$693$	15.1383	+	15.1383i	0.575055	+	0.575055i
$694$	−43.0899	+	13.8088i	−1.63567	+	0.524177i
$695$	1.51533	+	40.8301i	0.0574797	+	1.54877i
$696$	−24.2881	−	18.0993i	−0.920636	−	0.686054i
$697$	−14.0100	+	14.0100i	−0.530666	+	0.530666i
$698$	−2.16928	−	1.11635i	−0.0821086	−	0.0422545i
$699$	44.7246			1.69164
$700$	1.16149	−	12.7348i	0.0439001	−	0.481329i
$701$	−19.1823			−0.724505			−0.362253	−	0.932080i	$-0.617992\pi$
$701$	−19.1823			−0.724505			−0.362253	+	0.932080i	$0.617992\pi$
$702$	−8.30095	−	4.27181i	−0.313299	−	0.161229i
$703$	4.68490	−	4.68490i	0.176694	−	0.176694i
$704$	−11.2720	−	37.7788i	−0.424828	−	1.42384i
$705$	0.237716	+	6.40517i	0.00895289	+	0.241233i
$706$	20.8707	−	6.68835i	0.785478	−	0.251719i
$707$	0.315639	+	0.315639i	0.0118708	+	0.0118708i
$708$	−69.7738	−	11.6288i	−2.62226	−	0.437038i
$709$		−	22.4644i		−	0.843668i	−0.906673	−	0.421834i	$-0.861387\pi$
$709$		−	22.4644i		−	0.843668i	0.906673	−	0.421834i	$-0.138613\pi$
$710$	0.894368	−	1.90878i	0.0335650	−	0.0716353i
$711$			24.1139i			0.904340i
$712$	−2.48680	−	17.0324i	−0.0931966	−	0.638317i
$713$	17.3387	+	17.3387i	0.649341	+	0.649341i
$714$	6.92246	+	21.6012i	0.259067	+	0.808406i
$715$	−53.0598	−	49.2624i	−1.98433	−	1.84231i
$716$	17.5301	+	24.5421i	0.655131	+	0.917180i
$717$	−18.0867	+	18.0867i	−0.675460	+	0.675460i
$718$	16.8646	−	32.7712i	0.629382	−	1.22301i
$719$	−45.9737			−1.71453			−0.857265	−	0.514876i	$-0.827838\pi$
$719$	−45.9737			−1.71453			−0.857265	+	0.514876i	$0.827838\pi$
$720$	−8.78192	+	29.0890i	−0.327283	+	1.08408i
$721$	−11.0969			−0.413270
$722$	0.647117	−	1.25747i	0.0240832	−	0.0467983i
$723$	38.7418	−	38.7418i	1.44082	−	1.44082i
$724$	9.12617	+	12.7766i	0.339171	+	0.474838i
$725$	1.56924	+	21.1123i	0.0582802	+	0.784090i
$726$	−14.5029	−	45.2555i	−0.538252	−	1.67959i
$727$	−19.6989	−	19.6989i	−0.730592	−	0.730592i	0.240145	−	0.970737i	$-0.422805\pi$
$727$	−19.6989	−	19.6989i	−0.730592	−	0.730592i	−0.970737	+	0.240145i	$0.922805\pi$
$728$	−3.43329	−	23.5151i	−0.127246	−	0.871527i
$729$		−	33.6141i		−	1.24497i
$730$	13.8447	+	38.2574i	0.512416	+	1.41597i
$731$		−	9.89172i		−	0.365858i
$732$	32.9950	+	5.49909i	1.21953	+	0.203252i
$733$	−26.8457	−	26.8457i	−0.991567	−	0.991567i	0.00839797	−	0.999965i	$-0.497327\pi$
$733$	−26.8457	−	26.8457i	−0.991567	−	0.991567i	−0.999965	+	0.00839797i	$0.997327\pi$
$734$	5.56328	−	1.78284i	0.205345	−	0.0658060i
$735$	−20.6440	+	22.2354i	−0.761464	+	0.820164i
$736$	21.2394	+	0.428401i	0.782893	+	0.0157911i
$737$	−6.96178	+	6.96178i	−0.256440	+	0.256440i
$738$	−17.0675	−	8.78322i	−0.628263	−	0.323315i
$739$	−40.4662			−1.48857			−0.744286	−	0.667861i	$-0.767210\pi$
$739$	−40.4662			−1.48857			−0.744286	+	0.667861i	$0.767210\pi$
$740$	−3.78377	+	29.3873i	−0.139094	+	1.08030i
$741$	−16.6184			−0.610491
$742$	6.20475	+	3.19307i	0.227783	+	0.117221i
$743$	22.3693	−	22.3693i	0.820650	−	0.820650i	−0.165551	−	0.986201i	$-0.552940\pi$
$743$	22.3693	−	22.3693i	0.820650	−	0.820650i	0.986201	+	0.165551i	$0.0529403\pi$
$744$	37.4550	+	27.9113i	1.37317	+	1.02328i
$745$	44.7653	−	1.66138i	1.64007	−	0.0608682i
$746$	−17.1480	+	5.49536i	−0.627834	+	0.201199i
$747$	22.2283	+	22.2283i	0.813292	+	0.813292i
$748$	8.03538	−	48.2129i	0.293803	−	1.76284i
$749$		−	13.9766i		−	0.510694i
$750$	36.4926	−	16.3585i	1.33252	−	0.597328i
$751$		−	51.1851i		−	1.86777i	−0.357573	−	0.933885i	$-0.616396\pi$
$751$		−	51.1851i		−	1.86777i	0.357573	−	0.933885i	$-0.383604\pi$
$752$	4.07182	−	1.99262i	0.148484	−	0.0726632i
$753$	4.47191	+	4.47191i	0.162966	+	0.162966i
$754$	12.0067	+	37.4662i	0.437257	+	1.36444i
$755$	−1.19851	+	0.0444803i	−0.0436182	+	0.00161880i
$756$	−2.09092	+	1.49352i	−0.0760461	+	0.0543189i
$757$	−4.56094	+	4.56094i	−0.165770	+	0.165770i	−0.785117	−	0.619347i	$-0.787397\pi$
$757$	−4.56094	+	4.56094i	−0.165770	+	0.165770i	0.619347	+	0.785117i	$0.287397\pi$
$758$	7.45078	−	14.4783i	0.270625	−	0.525876i
$759$	46.8088			1.69905
$760$	1.14519	+	6.22001i	0.0415405	+	0.225624i
$761$	−16.9886			−0.615835			−0.307918	−	0.951413i	$-0.599632\pi$
$761$	−16.9886			−0.615835			−0.307918	+	0.951413i	$0.599632\pi$
$762$	1.02603	−	1.99378i	0.0371692	−	0.0722270i
$763$	1.00999	−	1.00999i	0.0365640	−	0.0365640i
$764$	−15.4495	+	11.0354i	−0.558944	+	0.399247i
$765$	−25.6317	+	27.6076i	−0.926716	+	0.998154i
$766$	−11.7106	−	36.5425i	−0.423123	−	1.32034i
$767$	64.9670	+	64.9670i	2.34582	+	2.34582i
$768$	40.1536	−	5.03783i	1.44892	−	0.181787i
$769$		−	34.8444i		−	1.25652i	−0.778004	−	0.628260i	$-0.783767\pi$
$769$		−	34.8444i		−	1.25652i	0.778004	−	0.628260i	$-0.216233\pi$
$770$	−18.7388	+	6.78127i	−0.675301	+	0.244380i
$771$			11.6870i			0.420896i

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.647117 - 1.25747i) q^{2} +(-1.78847 + 1.78847i) q^{3} +(-1.16248 - 1.62746i) q^{4} +(0.0829302 + 2.23453i) q^{5} +(1.09160 + 3.40630i) q^{6} +(-0.904221 - 0.904221i) q^{7} +(-2.79875 + 0.408628i) q^{8} -3.39723i q^{9} +O(q^{10})\)	\(q+(0.647117 - 1.25747i) q^{2} +(-1.78847 + 1.78847i) q^{3} +(-1.16248 - 1.62746i) q^{4} +(0.0829302 + 2.23453i) q^{5} +(1.09160 + 3.40630i) q^{6} +(-0.904221 - 0.904221i) q^{7} +(-2.79875 + 0.408628i) q^{8} -3.39723i q^{9} +(2.86353 + 1.34172i) q^{10} -4.92807i q^{11} +(4.98972 + 0.831610i) q^{12} +(-4.64598 - 4.64598i) q^{13} +(-1.72217 + 0.551898i) q^{14} +(-4.14470 - 3.84806i) q^{15} +(-1.29728 + 3.78379i) q^{16} +(-3.50664 + 3.50664i) q^{17} +(-4.27193 - 2.19840i) q^{18} -1.00000 q^{19} +(3.54021 - 2.73256i) q^{20} +3.23434 q^{21} +(-6.19691 - 3.18903i) q^{22} +(2.65546 - 2.65546i) q^{23} +(4.27466 - 5.73630i) q^{24} +(-4.98625 + 0.370620i) q^{25} +(-8.84868 + 2.83570i) q^{26} +(0.710431 + 0.710431i) q^{27} +(-0.420449 + 2.52273i) q^{28} -4.23410i q^{29} +(-7.52094 + 2.72170i) q^{30} +6.52947i q^{31} +(3.91852 + 4.07985i) q^{32} +(8.81369 + 8.81369i) q^{33} +(2.14030 + 6.67871i) q^{34} +(1.94552 - 2.09550i) q^{35} +(-5.52887 + 3.94921i) q^{36} +(-4.68490 + 4.68490i) q^{37} +(-0.647117 + 1.25747i) q^{38} +16.6184 q^{39} +(-1.14519 - 6.22001i) q^{40} +3.99527 q^{41} +(2.09300 - 4.06710i) q^{42} +(-1.41043 + 1.41043i) q^{43} +(-8.02025 + 5.72878i) q^{44} +(7.59121 - 0.281733i) q^{45} +(-1.62078 - 5.05756i) q^{46} +(-0.801371 - 0.801371i) q^{47} +(-4.44704 - 9.08733i) q^{48} -5.36477i q^{49} +(-2.76064 + 6.50991i) q^{50} -12.5430i q^{51} +(-2.16031 + 12.9620i) q^{52} +(-2.72848 - 2.72848i) q^{53} +(1.35308 - 0.433616i) q^{54} +(11.0119 - 0.408686i) q^{55} +(2.90018 + 2.16120i) q^{56} +(1.78847 - 1.78847i) q^{57} +(-5.32427 - 2.73996i) q^{58} -13.9835 q^{59} +(-1.44446 + 11.2187i) q^{60} +6.61259 q^{61} +(8.21063 + 4.22533i) q^{62} +(-3.07185 + 3.07185i) q^{63} +(7.66605 - 2.28730i) q^{64} +(9.99628 - 10.7669i) q^{65} +(16.7865 - 5.37949i) q^{66} +(-1.41268 - 1.41268i) q^{67} +(9.78333 + 1.63053i) q^{68} +9.49840i q^{69} +(-1.37605 - 3.80247i) q^{70} -0.666584i q^{71} +(1.38820 + 9.50801i) q^{72} +(9.09755 + 9.09755i) q^{73} +(2.85946 + 8.92281i) q^{74} +(8.25489 - 9.58058i) q^{75} +(1.16248 + 1.62746i) q^{76} +(-4.45606 + 4.45606i) q^{77} +(10.7540 - 20.8971i) q^{78} -7.09809 q^{79} +(-8.56257 - 2.58502i) q^{80} +7.65052 q^{81} +(2.58541 - 5.02395i) q^{82} +(-6.54308 + 6.54308i) q^{83} +(-3.75985 - 5.26377i) q^{84} +(-8.12650 - 7.54489i) q^{85} +(0.860863 + 2.68628i) q^{86} +(7.57255 + 7.57255i) q^{87} +(2.01375 + 13.7924i) q^{88} +6.08572i q^{89} +(4.55813 - 9.72806i) q^{90} +8.40198i q^{91} +(-7.40858 - 1.23475i) q^{92} +(-11.6777 - 11.6777i) q^{93} +(-1.52628 + 0.489122i) q^{94} +(-0.0829302 - 2.23453i) q^{95} +(-14.3048 - 0.288531i) q^{96} +(1.52334 - 1.52334i) q^{97} +(-6.74605 - 3.47163i) q^{98} -16.7418 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) \) 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8	\( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) \) 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

Introduction

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