LMFDB - Embedded newform 539.2.r.b.144.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(23,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([38, 0]))

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

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

chi := DirichletCharacter("539.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.r (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$276$
Relative dimension:	$23$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			144.15
Character	$\chi$	$=$	539.144
Dual form			539.2.r.b.408.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366692 - 0.934315i) q^{2} +(0.114146 - 1.52317i) q^{3} +(0.727622 + 0.675134i) q^{4} +(-0.0649272 - 0.0442666i) q^{5} +(-1.38126 - 0.665182i) q^{6} +(1.79210 - 1.94638i) q^{7} +(2.70620 - 1.30324i) q^{8} +(0.659474 + 0.0993998i) q^{9} +O(q^{10})$	\(q+(0.366692 - 0.934315i) q^{2} +(0.114146 - 1.52317i) q^{3} +(0.727622 + 0.675134i) q^{4} +(-0.0649272 - 0.0442666i) q^{5} +(-1.38126 - 0.665182i) q^{6} +(1.79210 - 1.94638i) q^{7} +(2.70620 - 1.30324i) q^{8} +(0.659474 + 0.0993998i) q^{9} +(-0.0651672 + 0.0444303i) q^{10} +(-0.988831 + 0.149042i) q^{11} +(1.11140 - 1.03123i) q^{12} +(3.90941 + 4.90225i) q^{13} +(-1.16138 - 2.38810i) q^{14} +(-0.0748368 + 0.0938423i) q^{15} +(-0.0769402 - 1.02670i) q^{16} +(-5.62299 - 1.73446i) q^{17} +(0.334694 - 0.579708i) q^{18} +(1.82662 + 3.16380i) q^{19} +(-0.0173565 - 0.0760440i) q^{20} +(-2.76010 - 2.95184i) q^{21} +(-0.223344 + 0.978532i) q^{22} +(-1.97759 + 0.610006i) q^{23} +(-1.67615 - 4.27076i) q^{24} +(-1.82445 - 4.64862i) q^{25} +(6.01380 - 1.85501i) q^{26} +(1.24634 - 5.46058i) q^{27} +(2.61804 - 0.206320i) q^{28} +(-1.67730 - 7.34875i) q^{29} +(0.0602363 + 0.104332i) q^{30} +(-4.40976 + 7.63792i) q^{31} +(4.75295 + 1.46609i) q^{32} +(0.114146 + 1.52317i) q^{33} +(-3.68244 + 4.61763i) q^{34} +(-0.202515 + 0.0470428i) q^{35} +(0.412740 + 0.517559i) q^{36} +(5.17642 - 4.80302i) q^{37} +(3.62579 - 0.546499i) q^{38} +(7.91321 - 5.39513i) q^{39} +(-0.233396 - 0.0351788i) q^{40} +(-8.34164 + 4.01712i) q^{41} +(-3.77006 + 1.49639i) q^{42} +(-5.59845 - 2.69607i) q^{43} +(-0.820119 - 0.559147i) q^{44} +(-0.0384178 - 0.0356465i) q^{45} +(-0.155228 + 2.07138i) q^{46} +(-0.729756 + 1.85939i) q^{47} -1.57261 q^{48} +(-0.576773 - 6.97620i) q^{49} -5.01229 q^{50} +(-3.28372 + 8.36679i) q^{51} +(-0.465103 + 6.20637i) q^{52} +(6.52200 + 6.05153i) q^{53} +(-4.64488 - 3.16683i) q^{54} +(0.0707996 + 0.0340953i) q^{55} +(2.31318 - 7.60282i) q^{56} +(5.02750 - 2.42112i) q^{57} +(-7.48110 - 1.12759i) q^{58} +(-6.43034 + 4.38413i) q^{59} +(-0.117809 + 0.0177569i) q^{60} +(-0.824525 + 0.765048i) q^{61} +(5.51921 + 6.92087i) q^{62} +(1.37531 - 1.10545i) q^{63} +(4.39652 - 5.51306i) q^{64} +(-0.0368213 - 0.491346i) q^{65} +(1.46498 + 0.451886i) q^{66} +(-2.62309 + 4.54333i) q^{67} +(-2.92042 - 5.05831i) q^{68} +(0.703409 + 3.08184i) q^{69} +(-0.0303080 + 0.206463i) q^{70} +(-2.33063 + 10.2112i) q^{71} +(1.91421 - 0.590456i) q^{72} +(-2.34121 - 5.96531i) q^{73} +(-2.58938 - 6.59764i) q^{74} +(-7.28889 + 2.24833i) q^{75} +(-0.806900 + 3.53526i) q^{76} +(-1.48199 + 2.19174i) q^{77} +(-2.13905 - 9.37178i) q^{78} +(2.74480 + 4.75412i) q^{79} +(-0.0404528 + 0.0700664i) q^{80} +(-6.26325 - 1.93196i) q^{81} +(0.694448 + 9.26676i) q^{82} +(-4.02241 + 5.04394i) q^{83} +(-0.0154229 - 4.01127i) q^{84} +(0.288306 + 0.361525i) q^{85} +(-4.57188 + 4.24209i) q^{86} +(-11.3849 + 1.71599i) q^{87} +(-2.48174 + 1.69202i) q^{88} +(12.9471 + 1.95146i) q^{89} +(-0.0473925 + 0.0228230i) q^{90} +(16.5477 + 1.17611i) q^{91} +(-1.85077 - 0.891286i) q^{92} +(11.1305 + 7.58865i) q^{93} +(1.46966 + 1.36364i) q^{94} +(0.0214533 - 0.286275i) q^{95} +(2.77564 - 7.07221i) q^{96} +7.45992 q^{97} +(-6.72946 - 2.01923i) q^{98} -0.666923 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 276 q + 3 q^{3} + 20 q^{4} + 6 q^{5} - 8 q^{6} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 276 * q + 3 * q^3 + 20 * q^4 + 6 * q^5 - 8 * q^6 + 6 * q^8 + 6 * q^9	\( 276 q + 3 q^{3} + 20 q^{4} + 6 q^{5} - 8 q^{6} + 6 q^{8} + 6 q^{9} + 3 q^{10} + 23 q^{11} - 32 q^{12} - 27 q^{13} - 23 q^{14} + 6 q^{15} + 70 q^{16} - 3 q^{17} - 20 q^{18} - 61 q^{19} - 12 q^{20} - 23 q^{21} - 6 q^{23} + 6 q^{24} - 11 q^{25} + 9 q^{26} - 12 q^{27} - 3 q^{28} - 24 q^{29} - 26 q^{30} - 75 q^{31} + 137 q^{32} + 3 q^{33} - 58 q^{34} + 15 q^{35} - 36 q^{36} - 29 q^{37} - 6 q^{39} - 53 q^{40} - 25 q^{41} + 4 q^{42} + 20 q^{43} + 6 q^{44} + 3 q^{45} + 52 q^{46} + 25 q^{47} + 288 q^{48} + 84 q^{49} - 218 q^{50} - 160 q^{51} + 65 q^{52} + 5 q^{53} + 66 q^{54} - 12 q^{55} - 178 q^{56} + 23 q^{57} + 5 q^{58} + 28 q^{59} - 54 q^{60} - 65 q^{61} - 92 q^{62} + 85 q^{63} - 50 q^{64} + 201 q^{65} - 38 q^{66} - 16 q^{67} - 91 q^{68} - 42 q^{69} - 255 q^{70} - 63 q^{71} - 165 q^{72} + 6 q^{73} - 166 q^{74} - 117 q^{75} - 87 q^{76} + 33 q^{78} + 2 q^{79} - 48 q^{80} + 5 q^{81} + 53 q^{82} + 37 q^{83} - 84 q^{84} + 26 q^{85} + 67 q^{86} - 59 q^{87} - 3 q^{88} - 155 q^{89} + 9 q^{90} + 47 q^{91} - 19 q^{92} + 81 q^{93} + 126 q^{94} - 37 q^{95} + 395 q^{96} + 302 q^{97} + 90 q^{98} + 268 q^{99}+O(q^{100}) \) 276 * q + 3 * q^3 + 20 * q^4 + 6 * q^5 - 8 * q^6 + 6 * q^8 + 6 * q^9 + 3 * q^10 + 23 * q^11 - 32 * q^12 - 27 * q^13 - 23 * q^14 + 6 * q^15 + 70 * q^16 - 3 * q^17 - 20 * q^18 - 61 * q^19 - 12 * q^20 - 23 * q^21 - 6 * q^23 + 6 * q^24 - 11 * q^25 + 9 * q^26 - 12 * q^27 - 3 * q^28 - 24 * q^29 - 26 * q^30 - 75 * q^31 + 137 * q^32 + 3 * q^33 - 58 * q^34 + 15 * q^35 - 36 * q^36 - 29 * q^37 - 6 * q^39 - 53 * q^40 - 25 * q^41 + 4 * q^42 + 20 * q^43 + 6 * q^44 + 3 * q^45 + 52 * q^46 + 25 * q^47 + 288 * q^48 + 84 * q^49 - 218 * q^50 - 160 * q^51 + 65 * q^52 + 5 * q^53 + 66 * q^54 - 12 * q^55 - 178 * q^56 + 23 * q^57 + 5 * q^58 + 28 * q^59 - 54 * q^60 - 65 * q^61 - 92 * q^62 + 85 * q^63 - 50 * q^64 + 201 * q^65 - 38 * q^66 - 16 * q^67 - 91 * q^68 - 42 * q^69 - 255 * q^70 - 63 * q^71 - 165 * q^72 + 6 * q^73 - 166 * q^74 - 117 * q^75 - 87 * q^76 + 33 * q^78 + 2 * q^79 - 48 * q^80 + 5 * q^81 + 53 * q^82 + 37 * q^83 - 84 * q^84 + 26 * q^85 + 67 * q^86 - 59 * q^87 - 3 * q^88 - 155 * q^89 + 9 * q^90 + 47 * q^91 - 19 * q^92 + 81 * q^93 + 126 * q^94 - 37 * q^95 + 395 * q^96 + 302 * q^97 + 90 * q^98 + 268 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{11}{21}\right)$	$1$

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 $

$2$	0.366692	−	0.934315i	0.259290	−	0.660660i	−0.740647	−	0.671895i	$-0.765481\pi$
$2$	0.366692	−	0.934315i	0.259290	−	0.660660i	0.999937	+	0.0112341i	$0.00357601\pi$
$3$	0.114146	−	1.52317i	0.0659021	−	0.879403i	−0.862079	−	0.506775i	$-0.830838\pi$
$3$	0.114146	−	1.52317i	0.0659021	−	0.879403i	0.927981	−	0.372628i	$-0.121543\pi$
$4$	0.727622	+	0.675134i	0.363811	+	0.337567i
$5$	−0.0649272	−	0.0442666i	−0.0290363	−	0.0197966i	0.548715	−	0.836010i	$-0.315117\pi$
$5$	−0.0649272	−	0.0442666i	−0.0290363	−	0.0197966i	−0.577751	+	0.816213i	$0.696070\pi$
$6$	−1.38126	−	0.665182i	−0.563899	−	0.271559i
$7$	1.79210	−	1.94638i	0.677349	−	0.735662i
$7$	1.79210	−	1.94638i	0.677349	−	0.735662i
$8$	2.70620	−	1.30324i	0.956786	−	0.460764i
$9$	0.659474	+	0.0993998i	0.219825	+	0.0331333i
$10$	−0.0651672	+	0.0444303i	−0.0206077	+	0.0140501i
$11$	−0.988831	+	0.149042i	−0.298144	+	0.0449379i
$11$	−0.988831	+	0.149042i	−0.298144	+	0.0449379i
$12$	1.11140	−	1.03123i	0.320833	−	0.297690i
$13$	3.90941	+	4.90225i	1.08428	+	1.35964i	0.928280	+	0.371882i	$0.121287\pi$
$13$	3.90941	+	4.90225i	1.08428	+	1.35964i	0.155997	+	0.987758i	$0.450141\pi$
$14$	−1.16138	−	2.38810i	−0.310393	−	0.638248i
$15$	−0.0748368	+	0.0938423i	−0.0193228	+	0.0242300i
$16$	−0.0769402	−	1.02670i	−0.0192350	−	0.256674i
$17$	−5.62299	−	1.73446i	−1.36378	−	0.420669i	−0.475393	−	0.879773i	$-0.657694\pi$
$17$	−5.62299	−	1.73446i	−1.36378	−	0.420669i	−0.888382	+	0.459104i	$0.848170\pi$
$18$	0.334694	−	0.579708i	0.0788882	−	0.136638i
$19$	1.82662	+	3.16380i	0.419055	+	0.725824i	0.995845	−	0.0910682i	$-0.0290281\pi$
$19$	1.82662	+	3.16380i	0.419055	+	0.725824i	−0.576790	+	0.816893i	$0.695695\pi$
$20$	−0.0173565	−	0.0760440i	−0.00388104	−	0.0170039i
$21$	−2.76010	−	2.95184i	−0.602304	−	0.644144i
$22$	−0.223344	+	0.978532i	−0.0476170	+	0.208624i
$23$	−1.97759	+	0.610006i	−0.412356	+	0.127195i	−0.493991	−	0.869467i	$-0.664462\pi$
$23$	−1.97759	+	0.610006i	−0.412356	+	0.127195i	0.0816342	+	0.996662i	$0.473986\pi$
$24$	−1.67615	−	4.27076i	−0.342143	−	0.871766i
$25$	−1.82445	−	4.64862i	−0.364890	−	0.929724i
$26$	6.01380	−	1.85501i	1.17940	−	0.363797i
$27$	1.24634	−	5.46058i	0.239859	−	1.05089i
$28$	2.61804	−	0.206320i	0.494762	−	0.0389909i
$29$	−1.67730	−	7.34875i	−0.311468	−	1.36463i	−0.852104	−	0.523373i	$-0.824674\pi$
$29$	−1.67730	−	7.34875i	−0.311468	−	1.36463i	0.540636	−	0.841256i	$-0.318184\pi$
$30$	0.0602363	+	0.104332i	0.0109976	+	0.0190484i
$31$	−4.40976	+	7.63792i	−0.792016	+	1.37181i	0.132701	+	0.991156i	$0.457635\pi$
$31$	−4.40976	+	7.63792i	−0.792016	+	1.37181i	−0.924717	+	0.380656i	$0.875698\pi$
$32$	4.75295	+	1.46609i	0.840211	+	0.259171i
$33$	0.114146	+	1.52317i	0.0198702	+	0.265150i
$34$	−3.68244	+	4.61763i	−0.631533	+	0.791917i
$35$	−0.202515	+	0.0470428i	−0.0342314	+	0.00795168i
$36$	0.412740	+	0.517559i	0.0687900	+	0.0862599i
$37$	5.17642	−	4.80302i	0.850999	−	0.789611i	−0.128363	−	0.991727i	$-0.540972\pi$
$37$	5.17642	−	4.80302i	0.850999	−	0.789611i	0.979362	+	0.202116i	$0.0647818\pi$
$38$	3.62579	−	0.546499i	0.588180	−	0.0886539i
$39$	7.91321	−	5.39513i	1.26713	−	0.863913i
$40$	−0.233396	−	0.0351788i	−0.0369031	−	0.00556225i
$41$	−8.34164	+	4.01712i	−1.30275	+	0.627369i	−0.951134	−	0.308777i	$-0.900080\pi$
$41$	−8.34164	+	4.01712i	−1.30275	+	0.627369i	−0.351611	+	0.936146i	$0.614366\pi$
$42$	−3.77006	+	1.49639i	−0.581732	+	0.230898i
$43$	−5.59845	−	2.69607i	−0.853755	−	0.411147i	−0.0447852	−	0.998997i	$-0.514260\pi$
$43$	−5.59845	−	2.69607i	−0.853755	−	0.411147i	−0.808970	+	0.587850i	$0.799975\pi$
$44$	−0.820119	−	0.559147i	−0.123638	−	0.0842946i
$45$	−0.0384178	−	0.0356465i	−0.00572698	−	0.00531386i
$46$	−0.155228	+	2.07138i	−0.0228872	+	0.305408i
$47$	−0.729756	+	1.85939i	−0.106446	+	0.271220i	−0.974166	−	0.225834i	$-0.927489\pi$
$47$	−0.729756	+	1.85939i	−0.106446	+	0.271220i	0.867720	+	0.497053i	$0.165585\pi$
$48$	−1.57261			−0.226987
$49$	−0.576773	−	6.97620i	−0.0823961	−	0.996600i
$50$	−5.01229			−0.708844
$51$	−3.28372	+	8.36679i	−0.459813	+	1.17158i
$52$	−0.465103	+	6.20637i	−0.0644982	+	0.860668i
$53$	6.52200	+	6.05153i	0.895866	+	0.831242i	0.986351	−	0.164656i	$-0.0526514\pi$
$53$	6.52200	+	6.05153i	0.895866	+	0.831242i	−0.0904855	+	0.995898i	$0.528842\pi$
$54$	−4.64488	−	3.16683i	−0.632088	−	0.430950i
$55$	0.0707996	+	0.0340953i	0.00954662	+	0.00459741i
$56$	2.31318	−	7.60282i	0.309112	−	1.01597i
$57$	5.02750	−	2.42112i	0.665909	−	0.320685i
$58$	−7.48110	−	1.12759i	−0.982317	−	0.148060i
$59$	−6.43034	+	4.38413i	−0.837159	+	0.570766i	−0.904261	−	0.426981i	$-0.859577\pi$
$59$	−6.43034	+	4.38413i	−0.837159	+	0.570766i	0.0671014	+	0.997746i	$0.478625\pi$
$60$	−0.117809	+	0.0177569i	−0.0152091	+	0.00229240i
$61$	−0.824525	+	0.765048i	−0.105570	+	0.0979543i	−0.731192	−	0.682172i	$-0.761036\pi$
$61$	−0.824525	+	0.765048i	−0.105570	+	0.0979543i	0.625622	+	0.780126i	$0.284845\pi$
$62$	5.51921	+	6.92087i	0.700940	+	0.878951i
$63$	1.37531	−	1.10545i	0.173273	−	0.139274i
$64$	4.39652	−	5.51306i	0.549565	−	0.689132i
$65$	−0.0368213	−	0.491346i	−0.00456712	−	0.0609440i
$66$	1.46498	+	0.451886i	0.180326	+	0.0556233i
$67$	−2.62309	+	4.54333i	−0.320461	+	0.555056i	−0.980583	−	0.196103i	$-0.937171\pi$
$67$	−2.62309	+	4.54333i	−0.320461	+	0.555056i	0.660122	+	0.751159i	$0.270505\pi$
$68$	−2.92042	−	5.05831i	−0.354152	−	0.613410i
$69$	0.703409	+	3.08184i	0.0846805	+	0.371010i
$70$	−0.0303080	+	0.206463i	−0.00362249	+	0.0246771i
$71$	−2.33063	+	10.2112i	−0.276595	+	1.21184i	0.625473	+	0.780246i	$0.284906\pi$
$71$	−2.33063	+	10.2112i	−0.276595	+	1.21184i	−0.902067	+	0.431595i	$0.857951\pi$
$72$	1.91421	−	0.590456i	0.225592	−	0.0695859i
$73$	−2.34121	−	5.96531i	−0.274018	−	0.698187i	−0.999946	−	0.0104156i	$-0.996685\pi$
$73$	−2.34121	−	5.96531i	−0.274018	−	0.698187i	0.725928	−	0.687771i	$-0.241411\pi$
$74$	−2.58938	−	6.59764i	−0.301009	−	0.766960i
$75$	−7.28889	+	2.24833i	−0.841649	+	0.259614i
$76$	−0.806900	+	3.53526i	−0.0925578	+	0.405522i
$77$	−1.48199	+	2.19174i	−0.168888	+	0.249772i
$78$	−2.13905	−	9.37178i	−0.242199	−	1.06114i
$79$	2.74480	+	4.75412i	0.308814	+	0.534881i	0.978103	−	0.208121i	$-0.0667347\pi$
$79$	2.74480	+	4.75412i	0.308814	+	0.534881i	−0.669290	+	0.743002i	$0.733401\pi$
$80$	−0.0404528	+	0.0700664i	−0.00452276	+	0.00783366i
$81$	−6.26325	−	1.93196i	−0.695916	−	0.214662i
$82$	0.694448	+	9.26676i	0.0766889	+	1.02334i
$83$	−4.02241	+	5.04394i	−0.441516	+	0.553644i	−0.951942	−	0.306278i	$-0.900916\pi$
$83$	−4.02241	+	5.04394i	−0.441516	+	0.553644i	0.510426	+	0.859922i	$0.329488\pi$
$84$	−0.0154229	−	4.01127i	−0.00168278	−	0.437665i
$85$	0.288306	+	0.361525i	0.0312712	+	0.0392129i
$86$	−4.57188	+	4.24209i	−0.492999	+	0.457436i
$87$	−11.3849	+	1.71599i	−1.22058	+	0.183974i
$88$	−2.48174	+	1.69202i	−0.264554	+	0.180370i
$89$	12.9471	+	1.95146i	1.37239	+	0.206855i	0.793510	−	0.608557i	$-0.208252\pi$
$89$	12.9471	+	1.95146i	1.37239	+	0.206855i	0.578881	+	0.815412i	$0.303490\pi$
$90$	−0.0473925	+	0.0228230i	−0.00499561	+	0.00240576i
$91$	16.5477	+	1.17611i	1.73467	+	0.123290i
$92$	−1.85077	−	0.891286i	−0.192957	−	0.0929230i
$93$	11.1305	+	7.58865i	1.15418	+	0.786906i
$94$	1.46966	+	1.36364i	0.151584	+	0.140649i
$95$	0.0214533	−	0.286275i	0.00220106	−	0.0293712i
$96$	2.77564	−	7.07221i	0.283287	−	0.721804i
$97$	7.45992			0.757440			0.378720	−	0.925511i	$-0.376364\pi$
$97$	7.45992			0.757440			0.378720	+	0.925511i	$0.376364\pi$
$98$	−6.72946	−	2.01923i	−0.679779	−	0.203973i
$99$	−0.666923			−0.0670283
$100$	1.81093	−	4.61419i	0.181093	−	0.461419i
$101$	0.738070	−	9.84886i	0.0734407	−	0.979998i	−0.831794	−	0.555085i	$-0.812686\pi$
$101$	0.738070	−	9.84886i	0.0734407	−	0.979998i	0.905234	−	0.424913i	$-0.139695\pi$
$102$	6.61310	+	6.13606i	0.654795	+	0.607561i
$103$	11.9463	+	8.14484i	1.17710	+	0.802535i	0.983917	−	0.178627i	$-0.0571657\pi$
$103$	11.9463	+	8.14484i	1.17710	+	0.802535i	0.193186	+	0.981162i	$0.438118\pi$
$104$	16.9685	+	8.17158i	1.66389	+	0.801289i
$105$	0.0485379	+	0.313835i	0.00473681	+	0.0306272i
$106$	8.04560	−	3.87456i	0.781458	−	0.376330i
$107$	5.77401	+	0.870292i	0.558195	+	0.0841343i	0.422080	−	0.906559i	$-0.361300\pi$
$107$	5.77401	+	0.870292i	0.558195	+	0.0841343i	0.136115	+	0.990693i	$0.456538\pi$
$108$	4.59349	−	3.13179i	0.442009	−	0.301357i
$109$	−14.5669	+	2.19561i	−1.39526	+	0.210302i	−0.803256	−	0.595634i	$-0.796901\pi$
$109$	−14.5669	+	2.19561i	−1.39526	+	0.210302i	−0.592004	+	0.805935i	$0.701663\pi$
$110$	0.0578174	−	0.0536467i	0.00551267	−	0.00511501i
$111$	−6.72495	−	8.43282i	−0.638304	−	0.800408i
$112$	−2.13622	−	1.69018i	−0.201854	−	0.159707i
$113$	−0.230341	+	0.288839i	−0.0216687	+	0.0271717i	−0.792548	−	0.609810i	$-0.791246\pi$
$113$	−0.230341	+	0.288839i	−0.0216687	+	0.0271717i	0.770879	+	0.636981i	$0.219817\pi$
$114$	−0.418543	−	5.58507i	−0.0392002	−	0.523090i
$115$	0.155402	+	0.0479353i	0.0144913	+	0.00446999i
$116$	3.74095	−	6.47952i	0.347339	−	0.601608i
$117$	2.09088	+	3.62150i	0.193302	+	0.334808i
$118$	1.73821	+	7.61559i	0.160015	+	0.701072i
$119$	−13.4529	+	7.83614i	−1.23322	+	0.718337i
$120$	−0.0802245	+	0.351486i	−0.00732346	+	0.0320862i
$121$	0.955573	−	0.294755i	0.0868703	−	0.0267959i
$122$	0.412449	+	1.05090i	0.0373414	+	0.0951443i
$123$	5.16660	+	13.1643i	0.465856	+	1.18698i
$124$	−8.36526	+	2.58034i	−0.751223	+	0.231722i
$125$	−0.174753	+	0.765642i	−0.0156304	+	0.0684811i
$126$	−0.528525	−	1.69033i	−0.0470848	−	0.150587i
$127$	1.62294	+	7.11056i	0.144013	+	0.630960i	0.994479	+	0.104932i	$0.0334624\pi$
$127$	1.62294	+	7.11056i	0.144013	+	0.630960i	−0.850467	+	0.526029i	$0.823680\pi$
$128$	1.43516	+	2.48578i	0.126852	+	0.219714i
$129$	−4.74561	+	8.21964i	−0.417828	+	0.723699i
$130$	−0.472574	−	0.145770i	−0.0414475	−	0.0127849i
$131$	−0.906657	−	12.0985i	−0.0792150	−	1.05705i	−0.885229	−	0.465155i	$-0.845999\pi$
$131$	−0.906657	−	12.0985i	−0.0792150	−	1.05705i	0.806014	−	0.591896i	$-0.201620\pi$
$132$	−0.945290	+	1.18536i	−0.0822769	+	0.103172i
$133$	9.43142	+	2.11454i	0.817808	+	0.183354i
$134$	3.28303	+	4.11679i	0.283611	+	0.355637i
$135$	−0.322643	+	0.299369i	−0.0277687	+	0.0257656i
$136$	−17.4774	+	2.63429i	−1.49867	+	0.225888i
$137$	−0.794680	+	0.541804i	−0.0678941	+	0.0462894i	−0.596791	−	0.802396i	$-0.703558\pi$
$137$	−0.794680	+	0.541804i	−0.0678941	+	0.0462894i	0.528897	+	0.848686i	$0.322606\pi$
$138$	3.13734	+	0.472878i	0.267068	+	0.0402541i
$139$	1.23423	−	0.594372i	0.104686	−	0.0504140i	−0.380808	−	0.924654i	$-0.624354\pi$
$139$	1.23423	−	0.594372i	0.104686	−	0.0504140i	0.485494	+	0.874240i	$0.338640\pi$
$140$	−0.179115	−	0.102496i	−0.0151380	−	0.00866248i
$141$	2.74887	+	1.32378i	0.231496	+	0.111483i
$142$	8.68581	+	5.92189i	0.728897	+	0.496954i
$143$	−4.59639	−	4.26483i	−0.384370	−	0.356643i
$144$	0.0513132	−	0.684727i	0.00427610	−	0.0570606i
$145$	−0.216402	+	0.551383i	−0.0179712	+	0.0457898i
$146$	−6.43198			−0.532315
$147$	−10.6918	+	0.0822189i	−0.881842	+	0.00678130i
$148$	7.00916			0.576150
$149$	6.81812	−	17.3723i	0.558562	−	1.42319i	−0.320849	−	0.947130i	$-0.603968\pi$
$149$	6.81812	−	17.3723i	0.558562	−	1.42319i	0.879411	−	0.476063i	$-0.157936\pi$
$150$	−0.572132	+	7.63456i	−0.0467143	+	0.623360i
$151$	6.92387	+	6.42442i	0.563457	+	0.522812i	0.909663	−	0.415347i	$-0.136340\pi$
$151$	6.92387	+	6.42442i	0.563457	+	0.522812i	−0.346206	+	0.938158i	$0.612530\pi$
$152$	9.06637	+	6.18135i	0.735380	+	0.501373i
$153$	−3.53581	−	1.70276i	−0.285854	−	0.137660i
$154$	1.50434	+	2.18834i	0.121223	+	0.176341i
$155$	0.624418	−	0.300704i	0.0501545	−	0.0241531i
$156$	9.40026	+	1.41686i	0.752623	+	0.113440i
$157$	−10.6338	+	7.25001i	−0.848671	+	0.578614i	−0.907689	−	0.419643i	$-0.862155\pi$
$157$	−10.6338	+	7.25001i	−0.848671	+	0.578614i	0.0590187	+	0.998257i	$0.481203\pi$
$158$	5.44834	−	0.821206i	0.433447	−	0.0653316i
$159$	9.96197	−	9.24336i	0.790036	−	0.733046i
$160$	−0.243697	−	0.305586i	−0.0192659	−	0.0241587i
$161$	−2.35673	+	4.94233i	−0.185737	+	0.389510i
$162$	−4.10174	+	5.14341i	−0.322263	+	0.404105i
$163$	1.39424	+	18.6049i	0.109206	+	1.45725i	0.735428	+	0.677603i	$0.236981\pi$
$163$	1.39424	+	18.6049i	0.109206	+	1.45725i	−0.626222	+	0.779645i	$0.715400\pi$
$164$	−8.78166	−	2.70878i	−0.685732	−	0.211520i
$165$	0.0600144	−	0.103948i	0.00467212	−	0.00809234i
$166$	3.23764	+	5.60776i	0.251290	+	0.435247i
$167$	−3.15132	−	13.8069i	−0.243857	−	1.06841i	−0.937472	−	0.348061i	$-0.886840\pi$
$167$	−3.15132	−	13.8069i	−0.243857	−	1.06841i	0.693615	−	0.720346i	$-0.256017\pi$
$168$	−11.3163	−	4.39120i	−0.873075	−	0.338788i
$169$	−5.85577	+	25.6558i	−0.450444	+	1.97352i
$170$	0.443497	−	0.136801i	0.0340147	−	0.0104921i
$171$	0.890127	+	2.26801i	0.0680697	+	0.173439i
$172$	−2.25334	−	5.74143i	−0.171816	−	0.437780i
$173$	−8.08116	+	2.49271i	−0.614399	+	0.189517i	−0.586308	−	0.810088i	$-0.699419\pi$
$173$	−8.08116	+	2.49271i	−0.614399	+	0.189517i	−0.0280913	+	0.999605i	$0.508943\pi$
$174$	−2.57146	+	11.2663i	−0.194942	+	0.854095i
$175$	−12.3176	−	4.77971i	−0.931120	−	0.361312i
$176$	0.229102	+	1.00376i	0.0172692	+	0.0756613i
$177$	5.94378	+	10.2949i	0.446762	+	0.773815i
$178$	6.57088	−	11.3811i	0.492508	−	0.853049i
$179$	−14.7952	−	4.56371i	−1.10584	−	0.341108i	−0.312522	−	0.949910i	$-0.601174\pi$
$179$	−14.7952	−	4.56371i	−1.10584	−	0.341108i	−0.793322	+	0.608803i	$0.791650\pi$
$180$	−0.00388744	−	0.0518743i	−0.000289753	−	0.00386648i
$181$	−11.7844	+	14.7771i	−0.875926	+	1.09838i	0.118502	+	0.992954i	$0.462191\pi$
$181$	−11.7844	+	14.7771i	−0.875926	+	1.09838i	−0.994428	+	0.105423i	$0.966380\pi$
$182$	7.16676	−	15.0295i	0.531235	−	1.11406i
$183$	1.07118	+	1.34322i	0.0791840	+	0.0992936i
$184$	−4.55678	+	4.22807i	−0.335930	+	0.311697i
$185$	−0.548704	+	0.0827038i	−0.0403415	+	0.00608051i
$186$	11.1716	−	7.61670i	0.819145	−	0.558484i
$187$	5.81869	+	0.877027i	0.425505	+	0.0641346i
$188$	−1.78632	+	0.860248i	−0.130281	+	0.0627400i
$189$	−8.39479	−	12.2117i	−0.610631	−	0.888274i
$190$	−0.259604	−	0.125019i	−0.0188337	−	0.00906981i
$191$	−7.82371	−	5.33411i	−0.566103	−	0.385963i	0.246181	−	0.969224i	$-0.420824\pi$
$191$	−7.82371	−	5.33411i	−0.566103	−	0.385963i	−0.812285	+	0.583261i	$0.801777\pi$
$192$	−7.89548	−	7.32594i	−0.569807	−	0.528704i
$193$	1.52671	−	20.3726i	0.109895	−	1.46645i	−0.620920	−	0.783874i	$-0.713241\pi$
$193$	1.52671	−	20.3726i	0.109895	−	1.46645i	0.730816	−	0.682575i	$-0.239140\pi$
$194$	2.73549	−	6.96992i	0.196397	−	0.500411i
$195$	−0.752607			−0.0538953
$196$	4.29020	−	5.46543i	0.306443	−	0.390388i
$197$	22.0960			1.57428			0.787138	−	0.616777i	$-0.211562\pi$
$197$	22.0960			1.57428			0.787138	+	0.616777i	$0.211562\pi$
$198$	−0.244555	+	0.623117i	−0.0173798	+	0.0442830i
$199$	1.52605	−	20.3637i	0.108179	−	1.44355i	−0.633994	−	0.773338i	$-0.718586\pi$
$199$	1.52605	−	20.3637i	0.108179	−	1.44355i	0.742173	−	0.670208i	$-0.233795\pi$
$200$	−10.9956	−	10.2024i	−0.777505	−	0.721419i
$201$	6.62084	+	4.51401i	0.466998	+	0.318394i
$202$	−8.93129	−	4.30108i	−0.628404	−	0.302623i
$203$	−17.3093	−	9.90501i	−1.21488	−	0.695196i
$204$	−8.03802	+	3.87090i	−0.562774	+	0.271018i
$205$	0.719424	+	0.108436i	0.0502467	+	0.00757348i
$206$	11.9904	−	8.17495i	0.835414	−	0.569576i
$207$	−1.36481	+	0.205711i	−0.0948605	+	0.0142979i
$208$	4.73233	−	4.39096i	0.328128	−	0.304458i
$209$	−2.27776	−	2.85622i	−0.157556	−	0.197569i
$210$	0.311019	+	0.0697311i	0.0214624	+	0.00481190i
$211$	17.2181	−	21.5908i	1.18534	−	1.48637i	0.349903	−	0.936786i	$-0.386215\pi$
$211$	17.2181	−	21.5908i	1.18534	−	1.48637i	0.835438	−	0.549585i	$-0.185214\pi$
$212$	0.659952	+	8.80645i	0.0453257	+	0.604830i
$213$	15.2873	+	4.71551i	1.04747	+	0.323101i
$214$	2.93041	−	5.07562i	0.200319	−	0.346962i
$215$	0.244146	+	0.422873i	0.0166506	+	0.0288397i
$216$	−3.74358	−	16.4017i	−0.254719	−	1.11599i
$217$	6.96357	+	22.2710i	0.472718	+	1.51185i
$218$	−3.29018	+	14.4152i	−0.222839	+	0.976322i
$219$	−9.35342	+	2.88515i	−0.632046	+	0.194960i
$220$	0.0284964	+	0.0726078i	0.00192123	+	0.00489521i
$221$	−13.4798	−	34.3460i	−0.906751	−	2.31036i
$222$	−10.3449	+	3.19098i	−0.694303	+	0.214164i
$223$	−1.61749	+	7.08670i	−0.108315	+	0.474560i	0.891455	+	0.453110i	$0.149686\pi$
$223$	−1.61749	+	7.08670i	−0.108315	+	0.474560i	−0.999770	+	0.0214503i	$0.993172\pi$
$224$	11.3713	−	6.62366i	0.759779	−	0.442562i
$225$	−0.741106	−	3.24700i	−0.0494071	−	0.216466i
$226$	0.185402	+	0.321126i	0.0123328	+	0.0213610i
$227$	−7.71999	+	13.3714i	−0.512394	+	0.887492i	0.487503	+	0.873121i	$0.337908\pi$
$227$	−7.71999	+	13.3714i	−0.512394	+	0.887492i	−0.999897	+	0.0143704i	$0.995426\pi$
$228$	5.29270	+	1.63258i	0.350517	+	0.108120i
$229$	−0.447384	−	5.96992i	−0.0295639	−	0.394503i	−0.992282	−	0.123998i	$-0.960428\pi$
$229$	−0.447384	−	5.96992i	−0.0295639	−	0.394503i	0.962719	−	0.270505i	$-0.0871907\pi$
$230$	0.101771	−	0.127617i	0.00671061	−	0.00841484i
$231$	3.16922	+	2.50750i	0.208520	+	0.164981i
$232$	−14.1163	−	17.7013i	−0.926780	−	1.16215i
$233$	−18.1748	+	16.8637i	−1.19067	+	1.10478i	−0.198473	+	0.980106i	$0.563598\pi$
$233$	−18.1748	+	16.8637i	−1.19067	+	1.10478i	−0.992198	+	0.124674i	$0.960211\pi$
$234$	4.15033	−	0.625562i	0.271316	−	0.0408943i
$235$	0.129690	−	0.0884211i	0.00846003	−	0.00576795i
$236$	−7.63874	−	1.15135i	−0.497240	−	0.0749468i
$237$	7.55465	−	3.63813i	0.490727	−	0.236322i
$238$	2.38837	+	15.4427i	0.154815	+	1.00100i
$239$	4.77891	+	2.30140i	0.309122	+	0.148865i	0.582013	−	0.813180i	$-0.302265\pi$
$239$	4.77891	+	2.30140i	0.309122	+	0.148865i	−0.272891	+	0.962045i	$0.587980\pi$
$240$	0.102105	+	0.0696143i	0.00659088	+	0.00449359i
$241$	0.807194	+	0.748967i	0.0519959	+	0.0482452i	0.705743	−	0.708468i	$-0.250613\pi$
$241$	0.807194	+	0.748967i	0.0519959	+	0.0482452i	−0.653747	+	0.756713i	$0.726804\pi$
$242$	0.0750064	−	1.00089i	0.00482159	−	0.0643397i
$243$	2.48122	−	6.32203i	0.159170	−	0.405559i
$244$	−1.11645			−0.0714736
$245$	−0.271365	+	0.478477i	−0.0173368	+	0.0305688i
$246$	14.1941			0.904984
$247$	−8.36871	+	21.3231i	−0.532488	+	1.35676i
$248$	−1.97966	+	26.4167i	−0.125708	+	1.67746i
$249$	7.22363	+	6.70255i	0.457779	+	0.424757i
$250$	0.651270	+	0.444028i	0.0411899	+	0.0280828i
$251$	12.0954	+	5.82484i	0.763455	+	0.367661i	0.774743	−	0.632276i	$-0.217879\pi$
$251$	12.0954	+	5.82484i	0.763455	+	0.367661i	−0.0112885	+	0.999936i	$0.503593\pi$
$252$	1.74704	+	0.124169i	0.110053	+	0.00782193i
$253$	1.86459	−	0.897938i	0.117226	−	0.0564528i
$254$	7.23862	+	1.09105i	0.454191	+	0.0684583i
$255$	0.583573	−	0.397873i	0.0365447	−	0.0249158i
$256$	16.7942	−	2.53131i	1.04964	−	0.158207i
$257$	2.83724	−	2.63258i	0.176982	−	0.164216i	−0.586708	−	0.809799i	$-0.699576\pi$
$257$	2.83724	−	2.63258i	0.176982	−	0.164216i	0.763690	+	0.645583i	$0.223386\pi$
$258$	5.93956	+	7.44797i	0.369781	+	0.463691i
$259$	−0.0718334	−	18.6828i	−0.00446351	−	1.16089i
$260$	0.304933	−	0.382374i	0.0189111	−	0.0237138i
$261$	−0.375675	−	5.01304i	−0.0232537	−	0.310299i
$262$	−11.6363	−	3.58932i	−0.718892	−	0.221749i
$263$	−0.257457	+	0.445928i	−0.0158755	+	0.0274971i	−0.873854	−	0.486188i	$-0.838387\pi$
$263$	−0.257457	+	0.445928i	−0.0158755	+	0.0274971i	0.857979	+	0.513686i	$0.171720\pi$
$264$	2.29395	+	3.97324i	0.141183	+	0.244536i
$265$	−0.155574	−	0.681616i	−0.00955686	−	0.0418713i
$266$	5.43407	−	8.03653i	0.333184	−	0.492751i
$267$	4.45027	−	19.4979i	0.272352	−	1.19325i
$268$	−4.97597	+	1.53488i	−0.303956	+	0.0937580i
$269$	1.21515	+	3.09615i	0.0740890	+	0.188776i	0.963121	−	0.269070i	$-0.0867164\pi$
$269$	1.21515	+	3.09615i	0.0740890	+	0.188776i	−0.889032	+	0.457846i	$0.848621\pi$
$270$	0.161394	+	0.411226i	0.00982215	+	0.0250264i
$271$	4.84553	−	1.49465i	0.294345	−	0.0907935i	−0.144066	−	0.989568i	$-0.546018\pi$
$271$	4.84553	−	1.49465i	0.294345	−	0.0907935i	0.438411	+	0.898775i	$0.355541\pi$
$272$	−1.34813	+	5.90655i	−0.0817425	+	0.358137i
$273$	3.68027	−	25.0707i	0.222740	−	1.51735i
$274$	0.214813	+	0.941157i	0.0129773	+	0.0568573i
$275$	2.49691	+	4.32478i	0.150569	+	0.260794i
$276$	−1.56884	+	2.71731i	−0.0944330	+	0.163563i
$277$	5.95040	+	1.83546i	0.357525	+	0.110282i	0.468314	−	0.883562i	$-0.344862\pi$
$277$	5.95040	+	1.83546i	0.357525	+	0.110282i	−0.110789	+	0.993844i	$0.535338\pi$
$278$	−0.102750	−	1.37111i	−0.00616255	−	0.0822335i
$279$	−3.66733	+	4.59869i	−0.219557	+	0.275316i
$280$	−0.486740	+	0.391233i	−0.0290883	+	0.0233806i
$281$	−3.26834	−	4.09837i	−0.194973	−	0.244488i	0.674729	−	0.738065i	$-0.264260\pi$
$281$	−3.26834	−	4.09837i	−0.194973	−	0.244488i	−0.869702	+	0.493577i	$0.835689\pi$
$282$	2.24482	−	2.08289i	0.133677	−	0.124034i
$283$	−21.9686	+	3.31124i	−1.30590	+	0.196833i	−0.764877	−	0.644176i	$-0.777200\pi$
$283$	−21.9686	+	3.31124i	−1.30590	+	0.196833i	−0.541021	+	0.841009i	$0.681962\pi$
$284$	−8.58972	+	5.85637i	−0.509706	+	0.347512i
$285$	−0.433596	−	0.0653541i	−0.0256840	−	0.00387124i
$286$	−5.67015	+	2.73060i	−0.335283	+	0.161464i
$287$	−7.13019	+	23.4351i	−0.420882	+	1.38333i
$288$	2.98872	+	1.43929i	0.176112	+	0.0848111i
$289$	14.5636	+	9.92929i	0.856682	+	0.584076i
$290$	0.435812	+	0.404375i	0.0255918	+	0.0237457i
$291$	0.851519	−	11.3627i	0.0499169	−	0.666095i
$292$	2.32387	−	5.92112i	0.135994	−	0.346508i
$293$	−11.5572			−0.675177			−0.337588	−	0.941294i	$-0.609611\pi$
$293$	−11.5572			−0.675177			−0.337588	+	0.941294i	$0.609611\pi$
$294$	−3.84376	+	10.0196i	−0.224173	+	0.584357i
$295$	0.611575			0.0356073
$296$	7.74896	−	19.7440i	0.450399	−	1.14760i
$297$	−0.418564	+	5.58535i	−0.0242875	+	0.324095i
$298$	−13.7310	−	12.7405i	−0.795418	−	0.738040i
$299$	−10.7216	−	7.30988i	−0.620048	−	0.422741i
$300$	−6.82148	−	3.28505i	−0.393838	−	0.189663i
$301$	−15.2805	+	6.06507i	−0.880756	+	0.349585i
$302$	8.54135	−	4.11330i	0.491500	−	0.236694i
$303$	−14.9172	−	2.24841i	−0.856973	−	0.129168i
$304$	3.10771	−	2.11880i	0.178240	−	0.121522i
$305$	0.0874002	−	0.0131735i	0.00500452	−	0.000754310i
$306$	−2.88747	+	2.67918i	−0.165065	+	0.153158i
$307$	−11.0781	−	13.8916i	−0.632263	−	0.792833i	0.357748	−	0.933818i	$-0.383545\pi$
$307$	−11.0781	−	13.8916i	−0.632263	−	0.792833i	−0.990012	+	0.140985i	$0.954973\pi$
$308$	−2.55804	+	0.594214i	−0.145758	+	0.0338585i
$309$	13.7696	−	17.2665i	0.783325	−	0.982258i
$310$	−0.0519833	−	0.693669i	−0.00295245	−	0.0393978i
$311$	20.9184	+	6.45248i	1.18617	+	0.365887i	0.824199	−	0.566301i	$-0.191626\pi$
$311$	20.9184	+	6.45248i	1.18617	+	0.365887i	0.361976	+	0.932187i	$0.382102\pi$
$312$	14.3836	−	24.9131i	0.814310	−	1.41043i
$313$	−4.32222	−	7.48631i	−0.244306	−	0.423151i	0.717630	−	0.696425i	$-0.245227\pi$
$313$	−4.32222	−	7.48631i	−0.244306	−	0.423151i	−0.961936	+	0.273274i	$0.911894\pi$
$314$	2.87446	+	12.5938i	0.162215	+	0.710712i
$315$	−0.138230	+	0.0108935i	−0.00778837	+	0.000613780i
$316$	−1.21250	+	5.31231i	−0.0682085	+	0.298841i
$317$	22.4793	−	6.93395i	1.26256	−	0.389450i	0.410007	−	0.912083i	$-0.365526\pi$
$317$	22.4793	−	6.93395i	1.26256	−	0.389450i	0.852558	+	0.522633i	$0.175050\pi$
$318$	−4.98324	−	12.6971i	−0.279446	−	0.712017i
$319$	2.75385	+	7.01668i	0.154186	+	0.392859i
$320$	−0.529498	+	0.163329i	−0.0295999	+	0.00913034i
$321$	1.98468	−	8.69546i	0.110774	−	0.485333i
$322$	3.75350	+	4.01424i	0.209174	+	0.223705i
$323$	−4.78357	−	20.9582i	−0.266165	−	1.16614i
$324$	−3.25295	−	5.63427i	−0.180719	−	0.313015i
$325$	15.6562	−	27.1173i	0.868448	−	1.50420i
$326$	17.8941	+	5.51960i	0.991062	+	0.305702i
$327$	1.68154	+	22.4386i	0.0929892	+	1.24085i
$328$	−17.3389	+	21.7423i	−0.957380	+	1.20052i
$329$	2.31128	+	4.75259i	0.127425	+	0.262019i
$330$	−0.0751134	−	0.0941893i	−0.00413486	−	0.00518495i
$331$	−12.5453	+	11.6403i	−0.689550	+	0.639808i	−0.945022	−	0.327008i	$-0.893960\pi$
$331$	−12.5453	+	11.6403i	−0.689550	+	0.639808i	0.255472	+	0.966816i	$0.417769\pi$
$332$	−6.33213	+	0.954414i	−0.347521	+	0.0523803i
$333$	3.89114	−	2.65293i	0.213233	−	0.145380i
$334$	−14.0555	−	2.11853i	−0.769084	−	0.115921i
$335$	0.371428	−	0.178870i	0.0202933	−	0.00977272i
$336$	−2.81828	+	3.06090i	−0.153750	+	0.166986i
$337$	17.1635	+	8.26548i	0.934953	+	0.450250i	0.838386	−	0.545077i	$-0.183500\pi$
$337$	17.1635	+	8.26548i	0.934953	+	0.450250i	0.0965669	+	0.995327i	$0.469214\pi$
$338$	21.8233	+	14.8789i	1.18703	+	0.809305i
$339$	0.413658	+	0.383819i	0.0224668	+	0.0208462i
$340$	−0.0342998	+	0.457699i	−0.00186017	+	0.0248222i
$341$	3.22213	−	8.20986i	0.174488	−	0.444589i
$342$	2.44544			0.132234
$343$	−14.6119	−	11.3794i	−0.788971	−	0.614430i
$344$	−18.6641			−1.00630
$345$	0.0907521	−	0.231233i	0.00488593	−	0.0124491i
$346$	−0.634319	+	8.46440i	−0.0341012	+	0.455049i
$347$	−15.9953	−	14.8415i	−0.858672	−	0.796731i	0.121971	−	0.992534i	$-0.461078\pi$
$347$	−15.9953	−	14.8415i	−0.858672	−	0.796731i	−0.980643	+	0.195802i	$0.937269\pi$
$348$	−9.44240	−	6.43772i	−0.506166	−	0.345098i
$349$	−32.9716	−	15.8783i	−1.76493	−	0.849945i	−0.969948	−	0.243311i	$-0.921766\pi$
$349$	−32.9716	−	15.8783i	−1.76493	−	0.849945i	−0.794981	−	0.606634i	$-0.792519\pi$
$350$	−8.98251	+	9.75580i	−0.480135	+	0.521470i
$351$	31.6416	−	15.2378i	1.68890	−	0.813333i
$352$	−4.91838	−	0.741326i	−0.262150	−	0.0395128i
$353$	18.5899	−	12.6744i	0.989439	−	0.674588i	0.0435406	−	0.999052i	$-0.486136\pi$
$353$	18.5899	−	12.6744i	0.989439	−	0.674588i	0.945898	+	0.324464i	$0.105184\pi$
$354$	11.7983	−	1.77830i	0.627070	−	0.0945156i
$355$	0.603335	−	0.559813i	0.0320217	−	0.0297118i
$356$	8.10310	+	10.1610i	0.429463	+	0.538530i
$357$	10.4002	+	21.3855i	0.550436	+	1.13184i
$358$	−9.68921	+	12.1499i	−0.512091	+	0.642141i
$359$	−0.467900	−	6.24369i	−0.0246948	−	0.329529i	−0.995845	−	0.0910617i	$-0.970974\pi$
$359$	−0.467900	−	6.24369i	−0.0246948	−	0.329529i	0.971150	−	0.238468i	$-0.0766451\pi$
$360$	−0.150422	−	0.0463990i	−0.00792793	−	0.00244544i
$361$	2.82693	−	4.89639i	0.148786	−	0.257705i
$362$	9.48527	+	16.4290i	0.498535	+	0.863488i
$363$	−0.339888	−	1.48915i	−0.0178395	−	0.0781598i
$364$	11.2464	+	12.0277i	0.589473	+	0.630422i
$365$	−0.112056	+	0.490948i	−0.00586527	+	0.0256974i
$366$	1.64778	−	0.508274i	0.0861310	−	0.0265679i
$367$	−5.51867	−	14.0613i	−0.288072	−	0.733996i	−0.999512	−	0.0312485i	$-0.990052\pi$
$367$	−5.51867	−	14.0613i	−0.288072	−	0.733996i	0.711439	−	0.702747i	$-0.248044\pi$
$368$	0.778447	+	1.98345i	0.0405793	+	0.103394i
$369$	−5.90040	+	1.82003i	−0.307162	+	0.0947471i
$370$	−0.123934	+	0.542989i	−0.00644301	+	0.0282287i
$371$	23.4666	−	1.84934i	1.21833	−	0.0960130i
$372$	2.97544	+	13.0363i	0.154269	+	0.675898i
$373$	−10.4725	−	18.1388i	−0.542243	−	0.939193i	−0.998775	−	0.0494859i	$-0.984242\pi$
$373$	−10.4725	−	18.1388i	−0.542243	−	0.939193i	0.456531	−	0.889707i	$-0.349092\pi$
$374$	2.95309	−	5.11490i	0.152700	−	0.264485i
$375$	1.14625	+	0.353573i	0.0591924	+	0.0182584i
$376$	0.448358	+	5.98292i	0.0231223	+	0.308546i
$377$	29.4681	−	36.9519i	1.51769	−	1.90312i
$378$	−14.4879	+	3.36543i	−0.745178	+	0.173099i
$379$	0.872883	+	1.09456i	0.0448370	+	0.0562238i	0.803744	−	0.594975i	$-0.202838\pi$
$379$	0.872883	+	1.09456i	0.0448370	+	0.0562238i	−0.758907	+	0.651199i	$0.774267\pi$
$380$	0.208884	−	0.193816i	0.0107155	−	0.00994254i
$381$	11.0158	−	1.66037i	0.564359	−	0.0850634i
$382$	−7.85263	+	5.35383i	−0.401775	+	0.273926i
$383$	−5.49979	−	0.828960i	−0.281026	−	0.0423579i	0.00701674	−	0.999975i	$-0.497766\pi$
$383$	−5.49979	−	0.828960i	−0.281026	−	0.0423579i	−0.288043	+	0.957618i	$0.593005\pi$
$384$	3.95008	−	1.90226i	0.201577	−	0.0970741i
$385$	0.193242	−	0.0767007i	0.00984853	−	0.00390903i
$386$	−18.4746	−	8.89687i	−0.940330	−	0.452839i
$387$	−3.42404	−	2.33447i	−0.174054	−	0.118668i
$388$	5.42800	+	5.03645i	0.275565	+	0.255687i
$389$	0.518524	−	6.91922i	0.0262902	−	0.350818i	−0.968510	−	0.248974i	$-0.919907\pi$
$389$	0.518524	−	6.91922i	0.0262902	−	0.350818i	0.994800	−	0.101844i	$-0.0324743\pi$
$390$	−0.275975	+	0.703172i	−0.0139745	+	0.0356065i
$391$	12.1780			0.615868
$392$	−10.6525	−	18.1273i	−0.538033	−	0.915568i
$393$	−18.5316			−0.934794
$394$	8.10242	−	20.6446i	0.408194	−	1.04006i
$395$	0.0322372	−	0.430175i	0.00162203	−	0.0216444i
$396$	−0.485268	−	0.450263i	−0.0243856	−	0.0226266i
$397$	13.1425	+	8.96041i	0.659604	+	0.449710i	0.846299	−	0.532708i	$-0.178825\pi$
$397$	13.1425	+	8.96041i	0.659604	+	0.449710i	−0.186696	+	0.982418i	$0.559778\pi$
$398$	−18.4665	−	8.89302i	−0.925644	−	0.445767i
$399$	4.29736	−	14.1243i	0.215137	−	0.707099i
$400$	−4.63234	+	2.23082i	−0.231617	+	0.111541i
$401$	−11.1503	−	1.68063i	−0.556818	−	0.0839269i	−0.135396	−	0.990792i	$-0.543231\pi$
$401$	−11.1503	−	1.68063i	−0.556818	−	0.0839269i	−0.421422	+	0.906865i	$0.638469\pi$
$402$	6.64532	−	4.53070i	0.331438	−	0.225971i
$403$	−54.6826	+	8.24207i	−2.72393	+	0.410567i
$404$	7.18634	−	6.66795i	0.357534	−	0.331743i
$405$	0.321134	+	0.402689i	0.0159573	+	0.0200098i
$406$	−15.6016	+	12.5403i	−0.774294	+	0.622364i
$407$	−4.40275	+	5.52088i	−0.218236	+	0.273660i
$408$	2.01750	+	26.9217i	0.0998812	+	1.33282i
$409$	20.8182	+	6.42157i	1.02939	+	0.317526i	0.763042	−	0.646349i	$-0.223705\pi$
$409$	20.8182	+	6.42157i	1.02939	+	0.317526i	0.266353	+	0.963876i	$0.414181\pi$
$410$	0.365120	−	0.632406i	0.0180320	−	0.0312323i
$411$	0.734550	+	1.27228i	0.0362327	+	0.0627568i
$412$	3.19352	+	13.9917i	0.157333	+	0.689322i
$413$	−2.99062	+	20.3727i	−0.147159	+	1.00247i
$414$	−0.308264	+	1.35059i	−0.0151503	+	0.0663779i
$415$	0.484442	−	0.149430i	0.0237803	−	0.00733525i
$416$	11.3941	+	29.0317i	0.558642	+	1.42340i
$417$	−0.764448	−	1.94778i	−0.0374352	−	0.0953832i
$418$	−3.50384	+	1.08079i	−0.171378	+	0.0528632i
$419$	−5.06980	+	22.2123i	−0.247676	+	1.08514i	0.686163	+	0.727448i	$0.259294\pi$
$419$	−5.06980	+	22.2123i	−0.247676	+	1.08514i	−0.933839	+	0.357693i	$0.883564\pi$
$420$	−0.176564	+	0.261123i	−0.00861543	+	0.0127415i
$421$	8.26343	+	36.2044i	0.402735	+	1.76450i	0.616244	+	0.787555i	$0.288653\pi$
$421$	8.26343	+	36.2044i	0.402735	+	1.76450i	−0.213510	+	0.976941i	$0.568489\pi$
$422$	−13.8589	−	24.0043i	−0.674639	−	1.16851i
$423$	−0.666078	+	1.15368i	−0.0323858	+	0.0560939i
$424$	25.5364	+	7.87694i	1.24016	+	0.382538i
$425$	2.19600	+	29.3036i	0.106522	+	1.42143i
$426$	10.0115	−	12.5540i	0.485058	−	0.608244i
$427$	0.0114420	+	2.97588i	0.000553716	+	0.144013i
$428$	3.61373	+	4.53148i	0.174676	+	0.219037i
$429$	−7.02072	+	6.51427i	−0.338963	+	0.314512i
$430$	0.484623	−	0.0730451i	0.0233706	−	0.00352255i
$431$	−27.0659	+	18.4532i	−1.30372	+	0.888859i	−0.997997	−	0.0632626i	$-0.979849\pi$
$431$	−27.0659	+	18.4532i	−1.30372	+	0.888859i	−0.305720	+	0.952122i	$0.598897\pi$
$432$	−5.70225	−	0.859475i	−0.274349	−	0.0413515i
$433$	15.3047	−	7.37035i	0.735496	−	0.354196i	−0.0283470	−	0.999598i	$-0.509024\pi$
$433$	15.3047	−	7.37035i	0.735496	−	0.354196i	0.763843	+	0.645402i	$0.223310\pi$
$434$	23.3616	+	1.66041i	1.12139	+	0.0797021i
$435$	0.815148	+	0.392555i	0.0390834	+	0.0188216i
$436$	−12.0816	−	8.23707i	−0.578602	−	0.394484i
$437$	−5.54224	−	5.14245i	−0.265121	−	0.245997i
$438$	−0.734184	+	9.79700i	−0.0350807	+	0.468119i
$439$	11.9716	−	30.5030i	0.571372	−	1.45583i	−0.294543	−	0.955638i	$-0.595167\pi$
$439$	11.9716	−	30.5030i	0.571372	−	1.45583i	0.865914	−	0.500193i	$-0.166737\pi$
$440$	0.236032			0.0112524
$441$	0.313066	−	4.65796i	0.0149079	−	0.221807i
$442$	−37.0330			−1.76148
$443$	2.53663	−	6.46323i	0.120519	−	0.307077i	−0.857865	−	0.513876i	$-0.828209\pi$
$443$	2.53663	−	6.46323i	0.120519	−	0.307077i	0.978384	+	0.206798i	$0.0663044\pi$
$444$	0.800067	−	10.6761i	0.0379695	−	0.506667i
$445$	−0.754235	−	0.699828i	−0.0357542	−	0.0331750i
$446$	6.02809	+	4.10988i	0.285438	+	0.194608i
$447$	−25.6827	−	12.3681i	−1.21475	−	0.584992i
$448$	−2.85151	−	18.4372i	−0.134721	−	0.871077i
$449$	28.6841	−	13.8135i	1.35369	−	0.651901i	0.390467	−	0.920617i	$-0.372313\pi$
$449$	28.6841	−	13.8135i	1.35369	−	0.651901i	0.963220	+	0.268715i	$0.0865991\pi$
$450$	−3.30547	−	0.498220i	−0.155822	−	0.0234863i
$451$	7.64975	−	5.21551i	0.360213	−	0.245589i
$452$	−0.362606	+	0.0546541i	−0.0170556	+	0.00257071i
$453$	10.5758	−	9.81292i	0.496895	−	0.461051i
$454$	9.66225	+	12.1161i	0.453472	+	0.568636i
$455$	−1.02233	−	0.808872i	−0.0479277	−	0.0379205i
$456$	10.4501	−	13.1041i	0.489372	−	0.613653i
$457$	0.854053	+	11.3965i	0.0399509	+	0.533108i	0.980894	+	0.194543i	$0.0623224\pi$
$457$	0.854053	+	11.3965i	0.0399509	+	0.533108i	−0.940943	+	0.338565i	$0.890059\pi$
$458$	−5.74184	−	1.77112i	−0.268298	−	0.0827591i
$459$	−16.4793	+	28.5431i	−0.769190	+	1.33228i
$460$	0.0807114	+	0.139796i	0.00376319	+	0.00651804i
$461$	−6.43878	−	28.2101i	−0.299884	−	1.31388i	−0.870301	−	0.492521i	$-0.836076\pi$
$461$	−6.43878	−	28.2101i	−0.299884	−	1.31388i	0.570417	−	0.821355i	$-0.306782\pi$
$462$	3.50492	−	2.04158i	0.163064	−	0.0949827i
$463$	−3.70286	+	16.2233i	−0.172086	+	0.753960i	0.813051	+	0.582192i	$0.197805\pi$
$463$	−3.70286	+	16.2233i	−0.172086	+	0.753960i	−0.985138	+	0.171767i	$0.945052\pi$
$464$	−7.41588	+	2.28750i	−0.344274	+	0.106194i
$465$	−0.386749	−	0.985420i	−0.0179350	−	0.0456977i
$466$	9.09150	+	23.1648i	0.421156	+	1.07309i
$467$	−24.1913	+	7.46202i	−1.11944	+	0.345301i	−0.798618	−	0.601839i	$-0.794435\pi$
$467$	−24.1913	+	7.46202i	−1.11944	+	0.345301i	−0.320821	+	0.947140i	$0.603959\pi$
$468$	−0.923635	+	4.04671i	−0.0426950	+	0.187059i
$469$	4.14219	+	13.2476i	0.191269	+	0.611718i
$470$	−0.0350569	−	0.153594i	−0.00161706	−	0.00708478i
$471$	9.82919	+	17.0247i	0.452905	+	0.784455i
$472$	−11.6882	+	20.2446i	−0.537994	+	0.931834i
$473$	5.93775	+	1.83155i	0.273018	+	0.0842149i
$474$	−0.628930	−	8.39249i	−0.0288877	−	0.385480i
$475$	11.3747	−	14.2634i	0.521908	−	0.654451i
$476$	−15.0790	−	3.38075i	−0.691147	−	0.154956i
$477$	3.69957	+	4.63912i	0.169392	+	0.212411i
$478$	3.90262	−	3.62110i	0.178502	−	0.165625i
$479$	−12.6103	+	1.90069i	−0.576179	+	0.0868449i	−0.430666	−	0.902511i	$-0.641721\pi$
$479$	−12.6103	+	1.90069i	−0.576179	+	0.0868449i	−0.145513	+	0.989356i	$0.546483\pi$
$480$	−0.493277	+	0.336311i	−0.0225149	+	0.0153504i
$481$	43.7824	+	6.59913i	1.99630	+	0.300895i
$482$	0.995762	−	0.479534i	0.0453557	−	0.0218422i
$483$	7.25900	+	4.15385i	0.330296	+	0.189007i
$484$	0.894295	+	0.430670i	0.0406498	+	0.0195759i
$485$	−0.484352	−	0.330226i	−0.0219933	−	0.0149948i
$486$	−4.99693	−	4.63647i	−0.226665	−	0.210315i
$487$	1.42014	−	18.9505i	0.0643528	−	0.858728i	−0.867858	−	0.496812i	$-0.834504\pi$
$487$	1.42014	−	18.9505i	0.0643528	−	0.858728i	0.932211	−	0.361916i	$-0.117877\pi$
$488$	−1.23429	+	3.14492i	−0.0558738	+	0.142364i
$489$	28.4976			1.28870
$490$	0.347541	+	0.428993i	0.0157003	+	0.0193799i
$491$	−18.1405			−0.818671			−0.409335	−	0.912384i	$-0.634239\pi$
$491$	−18.1405			−0.818671			−0.409335	+	0.912384i	$0.634239\pi$
$492$	−5.12833	+	13.0668i	−0.231203	+	0.589095i
$493$	−3.31467	+	44.2312i	−0.149285	+	1.99207i
$494$	16.8538	+	15.6380i	0.758288	+	0.703588i
$495$	0.0433015	+	0.0295225i	0.00194626	+	0.00132694i
$496$	8.18111	+	3.93981i	0.367343	+	0.176903i
$497$	15.6981	+	22.8357i	0.704154	+	1.02432i
$498$	8.91114	−	4.29138i	0.399318	−	0.192301i
$499$	−19.2191	−	2.89682i	−0.860367	−	0.129679i	−0.295984	−	0.955193i	$-0.595648\pi$
$499$	−19.2191	−	2.89682i	−0.860367	−	0.129679i	−0.564382	+	0.825513i	$0.690886\pi$
$500$	−0.644065	+	0.439116i	−0.0288035	+	0.0196379i
$501$	−21.3899	+	3.22401i	−0.955630	+	0.144038i
$502$	9.87752	−	9.16500i	0.440855	−	0.409054i
$503$	3.01173	+	3.77659i	0.134286	+	0.168390i	0.844428	−	0.535669i	$-0.179941\pi$
$503$	3.01173	+	3.77659i	0.134286	+	0.168390i	−0.710142	+	0.704059i	$0.751369\pi$
$504$	2.28120	−	4.78393i	0.101613	−	0.213093i
$505$	−0.483897	+	0.606787i	−0.0215331	+	0.0270017i
$506$	−0.155228	−	2.07138i	−0.00690074	−	0.0920840i
$507$	38.4097	+	11.8478i	1.70584	+	0.526181i
$508$	−3.61970	+	6.26950i	−0.160598	+	0.278164i
$509$	12.7859	+	22.1459i	0.566726	+	0.981599i	0.996887	+	0.0788462i	$0.0251236\pi$
$509$	12.7859	+	22.1459i	0.566726	+	0.981599i	−0.430161	+	0.902752i	$0.641543\pi$
$510$	−0.157748	−	0.691137i	−0.00698518	−	0.0306041i
$511$	−15.8064	−	6.13353i	−0.699235	−	0.271332i
$512$	2.51582	−	11.0225i	0.111185	−	0.487132i
$513$	19.5528	−	6.03122i	0.863275	−	0.266285i
$514$	−1.41926	−	3.61622i	−0.0626010	−	0.159505i
$515$	−0.415094	−	1.05764i	−0.0182912	−	0.0466053i
$516$	−9.00238	+	2.77687i	−0.396308	+	0.122245i
$517$	0.444478	−	1.94738i	0.0195481	−	0.0856459i
$518$	−17.4819	−	6.78369i	−0.768111	−	0.298058i
$519$	2.87439	+	12.5935i	0.126172	+	0.552794i
$520$	−0.739986	−	1.28169i	−0.0324506	−	0.0562060i
$521$	4.68429	−	8.11343i	0.205223	−	0.355456i	−0.744981	−	0.667086i	$-0.767542\pi$
$521$	4.68429	−	8.11343i	0.205223	−	0.355456i	0.950204	+	0.311630i	$0.100875\pi$
$522$	−4.82151	−	1.48724i	−0.211032	−	0.0650947i
$523$	2.18247	+	29.1230i	0.0954327	+	1.27346i	0.815173	+	0.579218i	$0.196642\pi$
$523$	2.18247	+	29.1230i	0.0954327	+	1.27346i	−0.719740	+	0.694244i	$0.755739\pi$
$524$	7.50841	−	9.41525i	0.328007	−	0.411307i
$525$	−8.68632	+	18.2162i	−0.379102	+	0.795018i
$526$	0.322230	+	0.404064i	0.0140499	+	0.0176180i
$527$	38.0437	−	35.2994i	1.65721	−	1.53767i
$528$	1.55505	−	0.234386i	0.0676748	−	0.0102003i
$529$	−15.4647	+	10.5437i	−0.672380	+	0.458421i
$530$	−0.693892	−	0.104587i	−0.0301407	−	0.00454299i
$531$	−4.67643	+	2.25205i	−0.202940	+	0.0977306i
$532$	5.43491	+	7.90606i	0.235633	+	0.342771i
$533$	−52.3039	−	25.1882i	−2.26553	−	1.09102i
$534$	−16.5853	−	11.3077i	−0.717716	−	0.489331i
$535$	−0.336366	−	0.312102i	−0.0145424	−	0.0134933i
$536$	−1.17758	+	15.7137i	−0.0508635	+	0.678727i
$537$	−8.64011	+	22.0146i	−0.372848	+	0.950002i
$538$	3.33836			0.143927
$539$	1.61008	+	6.81232i	0.0693510	+	0.293427i
$540$	−0.436876			−0.0188002
$541$	1.09024	−	2.77789i	0.0468732	−	0.119431i	−0.905520	−	0.424304i	$-0.860519\pi$
$541$	1.09024	−	2.77789i	0.0468732	−	0.119431i	0.952393	+	0.304873i	$0.0986141\pi$
$542$	0.380343	−	5.07533i	0.0163371	−	0.218004i
$543$	21.1630	+	19.6364i	0.908190	+	0.842677i
$544$	−24.1829	−	16.4876i	−1.03683	−	0.706902i
$545$	1.04298	+	0.502274i	0.0446765	+	0.0215151i
$546$	−22.0744	−	12.6317i	−0.944697	−	0.540589i
$547$	3.15762	−	1.52063i	0.135010	−	0.0650175i	−0.365159	−	0.930945i	$-0.618985\pi$
$547$	3.15762	−	1.52063i	0.135010	−	0.0650175i	0.500169	+	0.865928i	$0.333271\pi$
$548$	−0.944017	−	0.142288i	−0.0403264	−	0.00607823i
$549$	−0.619799	+	0.422572i	−0.0264524	+	0.0180349i
$550$	4.95630	−	0.747042i	0.211337	−	0.0318540i
$551$	20.1862	−	18.7300i	0.859959	−	0.797925i
$552$	5.91993	+	7.42336i	0.251969	+	0.315959i
$553$	14.1723	+	3.17745i	0.602666	+	0.135119i
$554$	3.89686	−	4.88650i	0.165562	−	0.207608i
$555$	0.0633397	+	0.845210i	0.00268862	+	0.0358772i
$556$	1.29933	+	0.400790i	0.0551039	+	0.0169973i
$557$	11.8609	−	20.5437i	0.502562	−	0.870463i	−0.497434	−	0.867502i	$-0.665724\pi$
$557$	11.8609	−	20.5437i	0.502562	−	0.870463i	0.999996	−	0.00296063i	$-0.000942398\pi$
$558$	2.95184	+	5.11274i	0.124961	+	0.216440i
$559$	−8.66984	−	37.9851i	−0.366695	−	1.60660i
$560$	0.0638802	+	0.204302i	0.00269943	+	0.00863335i
$561$	2.00004	−	8.76275i	0.0844418	−	0.369964i
$562$	−5.02764	+	1.55082i	−0.212078	+	0.0654175i
$563$	15.1248	+	38.5375i	0.637436	+	1.62416i	0.773747	+	0.633495i	$0.218380\pi$
$563$	15.1248	+	38.5375i	0.637436	+	1.62416i	−0.136310	+	0.990666i	$0.543524\pi$
$564$	1.10640	+	2.81907i	0.0465880	+	0.118704i
$565$	0.0277413	−	0.00855707i	0.00116709	−	0.000359999i
$566$	−4.96197	+	21.7398i	−0.208567	+	0.913792i
$567$	−14.9847	+	8.72839i	−0.629297	+	0.366558i
$568$	7.00041	+	30.6708i	0.293731	+	1.28692i
$569$	0.853430	+	1.47818i	0.0357776	+	0.0619687i	0.883360	−	0.468696i	$-0.155276\pi$
$569$	0.853430	+	1.47818i	0.0357776	+	0.0619687i	−0.847582	+	0.530664i	$0.821943\pi$
$570$	−0.220057	+	0.381151i	−0.00921719	+	0.0159646i
$571$	6.82636	+	2.10565i	0.285674	+	0.0881189i	0.434281	−	0.900778i	$-0.357003\pi$
$571$	6.82636	+	2.10565i	0.285674	+	0.0881189i	−0.148606	+	0.988896i	$0.547479\pi$
$572$	−0.465103	−	6.20637i	−0.0194469	−	0.259501i
$573$	−9.01780	+	11.3080i	−0.376724	+	0.472397i
$574$	19.2811	+	15.2553i	0.804779	+	0.636743i
$575$	6.44370	+	8.08015i	0.268721	+	0.336965i
$576$	3.44739	−	3.19871i	0.143641	−	0.133280i
$577$	18.2848	−	2.75599i	0.761206	−	0.114733i	0.243043	−	0.970015i	$-0.421854\pi$
$577$	18.2848	−	2.75599i	0.761206	−	0.114733i	0.518163	+	0.855282i	$0.326616\pi$
$578$	14.6174	−	9.96600i	0.608005	−	0.414531i
$579$	−30.8566	−	4.65088i	−1.28236	−	0.193284i
$580$	−0.529716	+	0.255098i	−0.0219953	+	0.0105924i
$581$	2.60886	+	16.8683i	0.108234	+	0.699817i
$582$	−10.3041	−	4.96220i	−0.427120	−	0.205690i
$583$	−7.35109	−	5.01189i	−0.304451	−	0.207571i
$584$	−14.1100	−	13.0922i	−0.583876	−	0.541758i
$585$	0.0245570	−	0.327690i	0.00101531	−	0.0135483i
$586$	−4.23792	+	10.7980i	−0.175067	+	0.446063i
$587$	30.9287			1.27656			0.638282	−	0.769803i	$-0.279645\pi$
$587$	30.9287			1.27656			0.638282	+	0.769803i	$0.279645\pi$
$588$	−7.83508	−	7.15856i	−0.323113	−	0.295214i
$589$	−32.2198			−1.32759
$590$	0.224259	−	0.571404i	0.00923262	−	0.0235243i
$591$	2.52217	−	33.6560i	0.103748	−	1.38442i
$592$	−5.32951	−	4.94506i	−0.219042	−	0.203241i
$593$	17.1991	+	11.7261i	0.706281	+	0.481534i	0.862415	−	0.506202i	$-0.168951\pi$
$593$	17.1991	+	11.7261i	0.706281	+	0.481534i	−0.156134	+	0.987736i	$0.549903\pi$
$594$	5.06499	+	2.43917i	0.207819	+	0.100080i
$595$	1.22034	+	0.0867345i	0.0500289	+	0.00355577i
$596$	16.6896	−	8.03731i	0.683634	−	0.329221i
$597$	−30.8432	−	4.64887i	−1.26233	−	0.190265i
$598$	−10.7613	+	7.33690i	−0.440061	+	0.300028i
$599$	−2.62877	+	0.396224i	−0.107409	+	0.0161893i	−0.202527	−	0.979277i	$-0.564915\pi$
$599$	−2.62877	+	0.396224i	−0.107409	+	0.0161893i	0.0951179	+	0.995466i	$0.469677\pi$
$600$	−16.7951	+	15.5836i	−0.685657	+	0.636197i
$601$	6.29948	+	7.89929i	0.256961	+	0.322219i	0.893532	−	0.448999i	$-0.148219\pi$
$601$	6.29948	+	7.89929i	0.256961	+	0.322219i	−0.636571	+	0.771218i	$0.719648\pi$
$602$	0.0634442	+	16.5008i	0.00258579	+	0.672524i
$603$	−2.18147	+	2.73547i	−0.0888362	+	0.111397i
$604$	0.700618	+	9.34909i	0.0285077	+	0.380409i
$605$	−0.0750905	−	0.0231624i	−0.00305286	−	0.000941684i
$606$	−7.57075	+	13.1129i	−0.307541	+	0.532676i
$607$	−8.24645	−	14.2833i	−0.334713	−	0.579740i	0.648717	−	0.761030i	$-0.275306\pi$
$607$	−8.24645	−	14.2833i	−0.334713	−	0.579740i	−0.983430	+	0.181290i	$0.941973\pi$
$608$	4.04342	+	17.7154i	0.163982	+	0.718453i
$609$	−17.0628	+	25.2345i	−0.691420	+	1.02255i
$610$	0.0197408	−	0.0864899i	0.000799280	−	0.00350187i
$611$	−11.9681	+	3.69167i	−0.484178	+	0.149349i
$612$	−1.42314	−	3.62611i	−0.0575272	−	0.146577i
$613$	−1.27165	−	3.24010i	−0.0513613	−	0.130866i	0.902891	−	0.429871i	$-0.141441\pi$
$613$	−1.27165	−	3.24010i	−0.0513613	−	0.130866i	−0.954252	+	0.299004i	$0.903346\pi$
$614$	−17.0414	+	5.25656i	−0.687733	+	0.212138i
$615$	0.247285	−	1.08343i	0.00997150	−	0.0436880i
$616$	−1.15421	+	7.86266i	−0.0465043	+	0.316796i
$617$	−4.18574	−	18.3389i	−0.168512	−	0.738298i	−0.986594	−	0.163196i	$-0.947820\pi$
$617$	−4.18574	−	18.3389i	−0.168512	−	0.738298i	0.818082	−	0.575102i	$-0.195038\pi$
$618$	−11.0832	−	19.1966i	−0.445831	−	0.772202i
$619$	17.4890	−	30.2919i	0.702943	−	1.21753i	−0.264486	−	0.964390i	$-0.585202\pi$
$619$	17.4890	−	30.2919i	0.702943	−	1.21753i	0.967429	−	0.253143i	$-0.0814643\pi$
$620$	0.657356	+	0.202768i	0.0264001	+	0.00814334i
$621$	0.866233	+	11.5591i	0.0347607	+	0.463850i
$622$	13.6993	−	17.1783i	0.549290	−	0.688788i
$623$	27.0008	−	21.7028i	1.08176	−	0.869502i
$624$	−6.14800	−	7.70935i	−0.246117	−	0.308621i
$625$	−18.2584	+	16.9413i	−0.730337	+	0.677654i
$626$	−8.57949	+	1.29315i	−0.342905	+	0.0516847i
$627$	−4.61050	+	3.14338i	−0.184126	+	0.125535i
$628$	−12.6321	−	1.90399i	−0.504077	−	0.0759773i
$629$	−37.4376	+	18.0290i	−1.49274	+	0.718864i
$630$	−0.0405098	+	0.133145i	−0.00161395	+	0.00530461i
$631$	37.9651	+	18.2830i	1.51137	+	0.727835i	0.991943	−	0.126683i	$-0.0404330\pi$
$631$	37.9651	+	18.2830i	1.51137	+	0.727835i	0.519422	+	0.854518i	$0.326147\pi$
$632$	13.6237	+	9.28849i	0.541922	+	0.369476i
$633$	−30.9211	−	28.6906i	−1.22900	−	1.14035i
$634$	1.76448	−	23.5454i	0.0700766	−	0.935107i
$635$	0.209388	−	0.533511i	0.00830929	−	0.0211717i
$636$	13.4891			0.534876
$637$	31.9442	−	30.1003i	1.26568	−	1.19262i
$638$	7.56561			0.299525
$639$	−2.55198	+	6.50233i	−0.100955	+	0.257228i
$640$	0.0168558	−	0.224924i	0.000666282	−	0.00889092i
$641$	8.19779	+	7.60643i	0.323793	+	0.300436i	0.825274	−	0.564733i	$-0.191021\pi$
$641$	8.19779	+	7.60643i	0.323793	+	0.300436i	−0.501481	+	0.865169i	$0.667211\pi$
$642$	−7.39653	−	5.04287i	−0.291918	−	0.199026i
$643$	0.675916	+	0.325504i	0.0266555	+	0.0128366i	0.447164	−	0.894452i	$-0.352434\pi$
$643$	0.675916	+	0.325504i	0.0266555	+	0.0128366i	−0.420508	+	0.907289i	$0.638148\pi$
$644$	−5.05155	+	2.00504i	−0.199059	+	0.0790095i
$645$	0.671975	−	0.323606i	0.0264590	−	0.0127420i
$646$	−21.3356	−	3.21583i	−0.839440	−	0.126525i
$647$	15.8630	−	10.8152i	0.623640	−	0.425191i	−0.209843	−	0.977735i	$-0.567295\pi$
$647$	15.8630	−	10.8152i	0.623640	−	0.425191i	0.833484	+	0.552544i	$0.186343\pi$
$648$	−19.4674	+	2.93424i	−0.764752	+	0.115268i
$649$	5.70510	−	5.29356i	0.223945	−	0.207790i
$650$	−19.5951	−	24.5715i	−0.768583	−	0.963773i
$651$	34.7173	−	8.06456i	1.36068	−	0.316075i
$652$	−11.5463	+	14.4786i	−0.452189	+	0.567027i
$653$	−1.26786	−	16.9184i	−0.0496151	−	0.662067i	−0.965463	−	0.260541i	$-0.916099\pi$
$653$	−1.26786	−	16.9184i	−0.0496151	−	0.662067i	0.915848	−	0.401526i	$-0.131520\pi$
$654$	21.5813	+	6.65694i	0.843895	+	0.260307i
$655$	−0.476693	+	0.825657i	−0.0186259	+	0.0322611i
$656$	4.76617	+	8.25524i	0.186088	+	0.322313i
$657$	−0.951019	−	4.16669i	−0.0371028	−	0.162558i
$658$	5.28794	−	0.416728i	0.206145	−	0.0162457i
$659$	−1.49337	+	6.54288i	−0.0581734	+	0.254875i	−0.995650	−	0.0931745i	$-0.970299\pi$
$659$	−1.49337	+	6.54288i	−0.0581734	+	0.254875i	0.937476	+	0.348049i	$0.113156\pi$
$660$	0.113847	−	0.0351171i	0.00443148	−	0.00136693i
$661$	−10.1090	−	25.7574i	−0.393195	−	1.00185i	−0.981201	−	0.192989i	$-0.938182\pi$
$661$	−10.1090	−	25.7574i	−0.393195	−	1.00185i	0.588006	−	0.808857i	$-0.299913\pi$
$662$	6.27546	+	15.9896i	0.243903	+	0.621454i
$663$	−53.8535	+	16.6116i	−2.09150	+	0.645142i
$664$	−4.31199	+	18.8921i	−0.167338	+	0.733154i
$665$	−0.518752	−	0.554788i	−0.0201163	−	0.0215138i
$666$	−1.05183	−	4.60836i	−0.0407575	−	0.178570i
$667$	7.79981	+	13.5097i	0.302010	+	0.523096i
$668$	7.02851	−	12.1737i	0.271941	−	0.471016i
$669$	10.6096	+	3.27263i	0.410191	+	0.126527i
$670$	−0.0309216	−	0.412621i	−0.00119461	−	0.0159409i
$671$	0.701292	−	0.879392i	0.0270731	−	0.0339485i
$672$	−8.79098	−	18.0765i	−0.339119	−	0.697317i
$673$	−9.58150	−	12.0148i	−0.369340	−	0.463137i	0.562081	−	0.827082i	$-0.310001\pi$
$673$	−9.58150	−	12.0148i	−0.369340	−	0.463137i	−0.931420	+	0.363945i	$0.881430\pi$
$674$	14.0163	−	13.0052i	0.539886	−	0.500941i
$675$	−27.6581	+	4.16878i	−1.06456	+	0.160456i
$676$	−21.5819	+	14.7143i	−0.830073	+	0.565934i
$677$	−3.08265	−	0.464635i	−0.118476	−	0.0178574i	0.0895366	−	0.995984i	$-0.471461\pi$
$677$	−3.08265	−	0.464635i	−0.118476	−	0.0178574i	−0.208013	+	0.978126i	$0.566700\pi$
$678$	0.510292	−	0.245744i	0.0195977	−	0.00943774i
$679$	13.3689	−	14.5198i	0.513051	−	0.557220i
$680$	1.25137	+	0.602627i	0.0479877	+	0.0231097i
$681$	19.4857	+	13.2851i	0.746695	+	0.509088i
$682$	−6.48906	−	6.02097i	−0.248479	−	0.230555i
$683$	−1.34051	+	17.8879i	−0.0512932	+	0.684461i	0.910993	+	0.412422i	$0.135317\pi$
$683$	−1.34051	+	17.8879i	−0.0512932	+	0.684461i	−0.962286	+	0.272039i	$0.912302\pi$
$684$	−0.883534	+	2.25121i	−0.0337828	+	0.0860771i
$685$	0.0755802			0.00288777
$686$	−15.9900	+	9.47943i	−0.610502	+	0.361926i
$687$	−9.14427			−0.348876
$688$	−2.33730	+	5.95534i	−0.0891086	+	0.227045i
$689$	−4.16892	+	55.6304i	−0.158823	+	2.11935i
$690$	−0.182766	−	0.169582i	−0.00695779	−	0.00645588i
$691$	10.2737	+	7.00452i	0.390832	+	0.266465i	0.742754	−	0.669565i	$-0.233519\pi$
$691$	10.2737	+	7.00452i	0.390832	+	0.266465i	−0.351922	+	0.936029i	$0.614472\pi$
$692$	−7.56294	−	3.64212i	−0.287500	−	0.138453i
$693$	−1.19519	+	1.29808i	−0.0454016	+	0.0493102i
$694$	−19.7319	+	9.50240i	−0.749014	+	0.360706i
$695$	−0.106446	−	0.0160441i	−0.00403771	−	0.000608588i
$696$	−28.5734	+	19.4810i	−1.08307	+	0.738425i
$697$	53.8725	−	8.11997i	2.04057	−	0.307566i
$698$	−26.9257	+	24.9834i	−1.01915	+	0.945637i
$699$	23.6118	+	29.6082i	0.893079	+	1.11989i
$700$	−5.73558	−	11.7938i	−0.216784	−	0.445765i
$701$	18.2530	−	22.8885i	0.689405	−	0.864486i	−0.306778	−	0.951781i	$-0.599251\pi$
$701$	18.2530	−	22.8885i	0.689405	−	0.864486i	0.996183	+	0.0872949i	$0.0278223\pi$
$702$	−2.63419	−	35.1508i	−0.0994210	−	1.32668i
$703$	24.6511	+	7.60386i	0.929734	+	0.286785i
$704$	−3.52573	+	6.10675i	−0.132881	+	0.230157i
$705$	−0.119877	−	0.207633i	−0.00451482	−	0.00781990i
$706$	−5.02509	−	22.0164i	−0.189122	−	0.828597i
$707$	−17.8469	−	19.0867i	−0.671202	−	0.717828i
$708$	−2.62564	+	11.5037i	−0.0986776	+	0.432335i
$709$	−46.9064	+	14.4687i	−1.76161	+	0.543383i	−0.995102	−	0.0988561i	$-0.968482\pi$
$709$	−46.9064	+	14.4687i	−1.76161	+	0.543383i	−0.766504	+	0.642239i	$0.778005\pi$
$710$	−0.301804	−	0.768983i	−0.0113265	−	0.0288594i
$711$	1.33756	+	3.40806i	0.0501625	+	0.127812i
$712$	37.5807	−	11.5921i	1.40840	−	0.434433i
$713$	4.06152	−	17.7947i	0.152105	−	0.666416i
$714$	23.7944	−	1.87517i	0.890484	−	0.0701766i
$715$	0.109641	+	0.480370i	0.00410035	+	0.0179648i
$716$	−7.68418	−	13.3094i	−0.287171	−	0.497395i
$717$	4.05092	−	7.01640i	0.151284	−	0.262032i
$718$	−6.00515	−	1.85234i	−0.224110	−	0.0691288i
$719$	−2.99793	−	40.0045i	−0.111804	−	1.49192i	−0.717688	−	0.696365i	$-0.754800\pi$
$719$	−2.99793	−	40.0045i	−0.111804	−	1.49192i	0.605884	−	0.795553i	$-0.292819\pi$
$720$	−0.0336422	+	0.0421860i	−0.00125377	+	0.00157218i
$721$	37.2618	−	8.65564i	1.38770	−	0.322353i
$722$	−3.53816	−	4.43671i	−0.131677	−	0.165117i
$723$	1.23294	−	1.14400i	0.0458536	−	0.0425459i
$724$	−18.5511	+	2.79613i	−0.689447	+	0.103917i
$725$	−31.1014	+	21.2046i	−1.15508	+	0.787518i
$726$	−1.51596	−	0.228495i	−0.0562627	−	0.00848024i
$727$	22.9159	−	11.0357i	0.849902	−	0.409291i	0.0423607	−	0.999102i	$-0.486512\pi$
$727$	22.9159	−	11.0357i	0.849902	−	0.409291i	0.807541	+	0.589811i	$0.200798\pi$
$728$	46.3141	−	18.3828i	1.71651	−	0.681310i
$729$	−27.0624	−	13.0325i	−1.00231	−	0.482687i
$730$	0.417611	+	0.284722i	0.0154565	+	0.0105380i
$731$	26.8038	+	24.8703i	0.991374	+	0.919860i
$732$	−0.127438	+	1.70055i	−0.00471026	+	0.0628540i
$733$	−5.80514	+	14.7913i	−0.214418	+	0.546327i	−0.997101	−	0.0760931i	$-0.975755\pi$
$733$	−5.80514	+	14.7913i	−0.214418	+	0.546327i	0.782683	+	0.622421i	$0.213851\pi$
$734$	−15.1614			−0.559616
$735$	0.697827	+	0.467950i	0.0257397	+	0.0172606i
$736$	−10.2937			−0.379432
$737$	1.91664	−	4.88353i	0.0706005	−	0.179887i
$738$	−0.463144	+	6.18022i	−0.0170486	+	0.227497i
$739$	−18.9923	−	17.6223i	−0.698644	−	0.648247i	0.248657	−	0.968592i	$-0.420011\pi$
$739$	−18.9923	−	17.6223i	−0.698644	−	0.648247i	−0.947301	+	0.320345i	$0.896201\pi$
$740$	−0.455085	−	0.310272i	−0.0167293	−	0.0114058i
$741$	31.5235	+	15.1809i	1.15804	+	0.557685i
$742$	6.87715	−	22.6034i	0.252468	−	0.829795i
$743$	21.7532	−	10.4758i	0.798047	−	0.384319i	0.0100125	−	0.999950i	$-0.496813\pi$
$743$	21.7532	−	10.4758i	0.798047	−	0.384319i	0.788035	+	0.615630i	$0.211099\pi$
$744$	40.0112	+	6.03071i	1.46688	+	0.221097i
$745$	−1.21169	+	0.826119i	−0.0443930	+	0.0302667i
$746$	−20.7875	+	3.13322i	−0.761086	+	0.114715i
$747$	−3.15404	+	2.92652i	−0.115400	+	0.107076i
$748$	3.64170	+	4.56655i	0.133154	+	0.166969i
$749$	12.0415	−	9.67876i	0.439987	−	0.353654i
$750$	0.750671	−	0.941311i	0.0274106	−	0.0343718i
$751$	−2.92412	−	39.0197i	−0.106703	−	1.42385i	−0.751620	−	0.659597i	$-0.770727\pi$
$751$	−2.92412	−	39.0197i	−0.106703	−	1.42385i	0.644917	−	0.764253i	$-0.276892\pi$
$752$	1.96517	+	0.606175i	0.0716625	+	0.0221049i
$753$	10.2529	−	17.7585i	0.373635	−	0.647155i
$754$	−23.7190	−	41.0825i	−0.863794	−	1.49614i
$755$	−0.165161	−	0.723616i	−0.00601081	−	0.0263351i
$756$	2.13634	−	14.5531i	0.0776979	−	0.529293i
$757$	0.710879	−	3.11456i	0.0258373	−	0.113201i	−0.960365	−	0.278746i	$-0.910081\pi$
$757$	0.710879	−	3.11456i	0.0258373	−	0.113201i	0.986202	+	0.165545i	$0.0529384\pi$
$758$	1.34274	−	0.414181i	0.0487706	−	0.0150437i
$759$	−1.15488	−	2.94258i	−0.0419194	−	0.106809i
$760$	−0.315027	−	0.802675i	−0.0114272	−	0.0291161i
$761$	−9.88412	+	3.04885i	−0.358299	+	0.110521i	−0.468678	−	0.883369i	$-0.655270\pi$
$761$	−9.88412	+	3.04885i	−0.358299	+	0.110521i	0.110379	+	0.993890i	$0.464793\pi$
$762$	2.48811	−	10.9011i	0.0901346	−	0.394906i
$763$	−21.8319	+	32.2875i	−0.790367	+	1.16889i
$764$	−2.09146	−	9.16327i	−0.0756662	−	0.331516i
$765$	0.154195	+	0.267074i	0.00557494	+	0.00965608i
$766$	−2.79124	+	4.83456i	−0.100851	+	0.174680i
$767$	−46.6310	−	14.3838i	−1.68375	−	0.519367i
$768$	−1.93864	−	25.8693i	−0.0699546	−	0.933479i
$769$	11.6532	−	14.6127i	0.420225	−	0.526946i	−0.525987	−	0.850493i	$-0.676304\pi$
$769$	11.6532	−	14.6127i	0.420225	−	0.526946i	0.946212	+	0.323547i	$0.104875\pi$
$770$	−0.000802334	−	0.208675i	−2.89141e−5	−	0.00752011i
$771$	−3.68600	−	4.62210i	−0.132748	−	0.166461i
$772$	14.8651	−	13.7928i	0.535006	−	0.496413i
$773$	−22.7833	+	3.43403i	−0.819458	+	0.123513i	−0.545375	−	0.838192i	$-0.683613\pi$
$773$	−22.7833	+	3.43403i	−0.819458	+	0.123513i	−0.274084	+	0.961706i	$0.588375\pi$
$774$	−3.43670	+	2.34310i	−0.123530	+	0.0842211i
$775$	43.5512	+	6.56429i	1.56440	+	0.235796i
$776$	20.1880	−	9.72205i	0.724708	−	0.349001i
$777$	−28.4652	−	2.02314i	−1.02118	−	0.0725799i
$778$	−6.27459	−	3.02168i	−0.224955	−	0.108333i
$779$	−27.9463	−	19.0535i	−1.00128	−	0.682662i
$780$	−0.547613	−	0.508111i	−0.0196077	−	0.0181933i
$781$	0.782705	−	10.4445i	0.0280074	−	0.373732i
$782$	4.46557	−	11.3781i	0.159689	−	0.406880i
$783$	−42.2190			−1.50878
$784$	−7.11805	+	1.12892i	−0.254216	+	0.0403186i
$785$	1.01136			0.0360969
$786$	−6.79537	+	17.3143i	−0.242383	+	0.617581i
$787$	1.04373	−	13.9275i	0.0372048	−	0.496463i	−0.947211	−	0.320609i	$-0.896112\pi$
$787$	1.04373	−	13.9275i	0.0372048	−	0.496463i	0.984416	−	0.175854i	$-0.0562686\pi$
$788$	16.0775	+	14.9178i	0.572739	+	0.531424i
$789$	0.649837	+	0.443051i	0.0231348	+	0.0157730i
$790$	−0.390098	−	0.187861i	−0.0138791	−	0.00668380i
$791$	0.149395	+	0.965958i	0.00531189	+	0.0343455i
$792$	−1.80483	+	0.869160i	−0.0641318	+	0.0308842i
$793$	−6.97387	−	1.05114i	−0.247649	−	0.0373271i
$794$	13.1911	−	8.99354i	0.468134	−	0.319169i
$795$	−1.05598	+	0.159163i	−0.0374516	+	0.00564492i
$796$	14.8586	−	13.7868i	0.526650	−	0.488660i
$797$	3.62863	+	4.55016i	0.128533	+	0.161175i	0.841934	−	0.539581i	$-0.181417\pi$
$797$	3.62863	+	4.55016i	0.128533	+	0.161175i	−0.713401	+	0.700756i	$0.752846\pi$
$798$	−11.6207	−	9.19435i	−0.411369	−	0.325476i
$799$	7.32845	−	9.18959i	0.259262	−	0.325104i
$800$	−1.85622	−	24.7695i	−0.0656272	−	0.875734i
$801$	8.34431	+	2.57388i	0.294832	+	0.0909436i
$802$	−5.65896	+	9.80160i	−0.199825	+	0.346107i
$803$	3.20415	+	5.54974i	0.113072	+	0.195846i
$804$	1.76990	+	7.75445i	0.0624197	+	0.273479i
$805$	0.371796	−	0.216567i	0.0131041	−	0.00763299i
$806$	−12.3510	+	54.1131i	−0.435044	+	1.90605i
$807$	4.85467	−	1.49747i	0.170892	−	0.0527133i
$808$	−10.8380	−	27.6149i	−0.381281	−	0.971488i
$809$	17.8763	+	45.5480i	0.628496	+	1.60138i	0.789033	+	0.614351i	$0.210582\pi$
$809$	17.8763	+	45.5480i	0.628496	+	1.60138i	−0.160537	+	0.987030i	$0.551323\pi$
$810$	0.493996	−	0.152378i	0.0173572	−	0.00535400i
$811$	8.49520	−	37.2199i	0.298307	−	1.30697i	−0.574340	−	0.818617i	$-0.694741\pi$
$811$	8.49520	−	37.2199i	0.298307	−	1.30697i	0.872647	−	0.488351i	$-0.162402\pi$
$812$	−5.90744	−	18.8932i	−0.207311	−	0.663023i
$813$	−1.72351	−	7.55118i	−0.0604460	−	0.264831i
$814$	3.54379	+	6.13802i	0.124210	+	0.215137i
$815$	0.733052	−	1.26968i	0.0256777	−	0.0444750i
$816$	8.84279	+	2.72764i	0.309560	+	0.0954865i
$817$	−1.69641	−	22.6370i	−0.0593499	−	0.791970i
$818$	13.6336	−	17.0960i	0.476689	−	0.597749i
$819$	10.7959	+	2.42045i	0.377238	+	0.0845775i
$820$	0.450260	+	0.564608i	0.0157238	+	0.0197170i
$821$	17.5234	−	16.2593i	0.611570	−	0.567454i	−0.312385	−	0.949956i	$-0.601128\pi$
$821$	17.5234	−	16.2593i	0.611570	−	0.567454i	0.923955	+	0.382502i	$0.124937\pi$
$822$	1.45806	−	0.219767i	0.0508557	−	0.00766527i
$823$	43.4532	−	29.6259i	1.51468	−	1.03269i	0.532141	−	0.846656i	$-0.321388\pi$
$823$	43.4532	−	29.6259i	1.51468	−	1.03269i	0.982543	−	0.186037i	$-0.0595646\pi$
$824$	42.9437	+	6.47272i	1.49601	+	0.225488i
$825$	6.87239	−	3.30957i	0.239266	−	0.115224i
$826$	17.9379	+	10.2647i	0.624138	+	0.357154i
$827$	10.4243	+	5.02010i	0.362490	+	0.174566i	0.606259	−	0.795267i	$-0.292670\pi$
$827$	10.4243	+	5.02010i	0.362490	+	0.174566i	−0.243769	+	0.969833i	$0.578384\pi$
$828$	−1.13195	−	0.771747i	−0.0393378	−	0.0268201i
$829$	−18.8812	−	17.5192i	−0.655770	−	0.608466i	0.280455	−	0.959867i	$-0.409515\pi$
$829$	−18.8812	−	17.5192i	−0.655770	−	0.608466i	−0.936225	+	0.351401i	$0.885705\pi$
$830$	0.0380256	−	0.507416i	0.00131989	−	0.0176127i
$831$	3.47493	−	8.85397i	0.120544	−	0.307141i
$832$	44.2142			1.53285
$833$	−8.85677	+	40.2275i	−0.306869	+	1.39380i
$834$	−2.10016			−0.0727225
$835$	−0.406576	+	1.03594i	−0.0140702	+	0.0358502i
$836$	0.270984	−	3.61604i	0.00937219	−	0.125063i
$837$	36.2114	+	33.5993i	1.25165	+	1.16136i
$838$	18.8942	+	12.8818i	0.652689	+	0.444996i
$839$	−11.7859	−	5.67578i	−0.406894	−	0.195950i	0.219230	−	0.975673i	$-0.429645\pi$
$839$	−11.7859	−	5.67578i	−0.406894	−	0.195950i	−0.626124	+	0.779723i	$0.715360\pi$
$840$	0.540355	+	0.786045i	0.0186440	+	0.0271211i
$841$	−25.0627	+	12.0696i	−0.864232	+	0.416192i
$842$	36.8565	+	5.55522i	1.27016	+	0.191446i
$843$	−6.61558	+	4.51043i	−0.227853	+	0.155347i
$844$	27.1049	−	4.08541i	0.932990	−	0.140626i
$845$	1.51589	−	1.40654i	0.0521484	−	0.0483866i
$846$	0.833656	+	1.04537i	0.0286617	+	0.0359406i
$847$	1.13877	−	2.38814i	0.0391288	−	0.0820573i
$848$	5.71128	−	7.16171i	0.196126	−	0.245934i
$849$	2.53595	+	33.8399i	0.0870336	+	1.16138i
$850$	28.1840	+	8.69362i	0.966704	+	0.298189i
$851$	−7.30698	+	12.6561i	−0.250480	+	0.433844i
$852$	7.93977	+	13.7521i	0.272012	+	0.471139i
$853$	−3.19517	−	13.9989i	−0.109400	−	0.479315i	−0.999713	−	0.0239645i	$-0.992371\pi$
$853$	−3.19517	−	13.9989i	−0.109400	−	0.479315i	0.890312	−	0.455350i	$-0.150486\pi$
$854$	2.78460	+	1.08054i	0.0952871	+	0.0369753i
$855$	0.0426036	−	0.186658i	0.00145701	−	0.00638358i
$856$	16.7598	−	5.16972i	0.572839	−	0.176697i
$857$	5.70725	+	14.5418i	0.194956	+	0.496740i	0.994606	−	0.103727i	$-0.0330768\pi$
$857$	5.70725	+	14.5418i	0.194956	+	0.496740i	−0.799650	+	0.600467i	$0.794982\pi$
$858$	3.51195	+	8.94829i	0.119896	+	0.305490i
$859$	−10.7373	+	3.31200i	−0.366350	+	0.113004i	−0.472464	−	0.881350i	$-0.656635\pi$
$859$	−10.7373	+	3.31200i	−0.366350	+	0.113004i	0.106114	+	0.994354i	$0.466159\pi$
$860$	−0.107850	+	0.472523i	−0.00367766	+	0.0161129i
$861$	34.8817	+	13.5355i	1.18876	+	0.461289i
$862$	7.31627	+	32.0547i	0.249193	+	1.09179i
$863$	0.121471	+	0.210395i	0.00413493	+	0.00716192i	0.868085	−	0.496415i	$-0.165350\pi$
$863$	0.121471	+	0.210395i	0.00413493	+	0.00716192i	−0.863951	+	0.503577i	$0.832017\pi$
$864$	13.9295	−	24.1266i	0.473892	−	0.820805i
$865$	0.635031	+	0.195881i	0.0215917	+	0.00666016i
$866$	−1.27413	−	17.0020i	−0.0432966	−	0.577753i
$867$	16.7864	−	21.0495i	0.570095	−	0.714877i
$868$	−9.96905	+	20.9062i	−0.338371	+	0.709602i
$869$	−3.42270	−	4.29193i	−0.116107	−	0.145594i
$870$	0.665678	−	0.617659i	0.0225686	−	0.0209406i
$871$	−32.5273	+	4.90270i	−1.10214	+	0.166122i
$872$	−36.5597	+	24.9260i	−1.23807	+	0.844099i
$873$	4.91963	+	0.741514i	0.166504	+	0.0250965i
$874$	−6.83696	+	3.29250i	−0.231264	+	0.111371i
$875$	1.17705	+	1.71224i	0.0397917	+	0.0578842i
$876$	−8.75362	−	4.21552i	−0.295757	−	0.142429i
$877$	−3.89900	−	2.65829i	−0.131660	−	0.0897642i	0.495699	−	0.868494i	$-0.334912\pi$
$877$	−3.89900	−	2.65829i	−0.131660	−	0.0897642i	−0.627359	+	0.778730i	$0.715864\pi$
$878$	−24.1096	−	22.3704i	−0.813659	−	0.754965i
$879$	−1.31920	+	17.6035i	−0.0444956	+	0.593752i
$880$	0.0295582	−	0.0753130i	0.000996405	−	0.00253880i
$881$	11.8283			0.398506			0.199253	−	0.979948i	$-0.436148\pi$
$881$	11.8283			0.398506			0.199253	+	0.979948i	$0.436148\pi$
$882$	−4.23720	−	2.00054i	−0.142674	−	0.0673615i
$883$	20.4665			0.688752			0.344376	−	0.938832i	$-0.388090\pi$
$883$	20.4665			0.688752			0.344376	+	0.938832i	$0.388090\pi$
$884$	13.3800	−	34.0916i	0.450017	−	1.14663i
$885$	0.0698087	−	0.931533i	0.00234660	−	0.0313131i
$886$	−5.10853	−	4.74003i	−0.171625	−	0.159244i
$887$	−35.7000	−	24.3398i	−1.19869	−	0.817252i	−0.211588	−	0.977359i	$-0.567864\pi$
$887$	−35.7000	−	24.3398i	−1.19869	−	0.817252i	−0.987100	+	0.160107i	$0.948816\pi$
$888$	−29.1890	−	14.0567i	−0.979519	−	0.471712i
$889$	16.7483	+	9.58396i	0.561720	+	0.321436i
$890$	−0.930431	+	0.448072i	−0.0311881	+	0.0150194i
$891$	6.48123	+	0.976889i	0.217130	+	0.0327270i
$892$	−5.96140	+	4.06441i	−0.199602	+	0.136087i
$893$	−7.21571	+	1.08759i	−0.241464	+	0.0363949i
$894$	−20.9734	+	19.4604i	−0.701454	+	0.650854i
$895$	0.758590	+	0.951242i	0.0253569	+	0.0317965i
$896$	7.41021	+	1.66138i	0.247558	+	0.0555029i
$897$	−12.3580	+	15.4965i	−0.412622	+	0.517412i
$898$	−2.38797	−	31.8653i	−0.0796878	−	1.06336i
$899$	63.5257	+	19.5951i	2.11870	+	0.653533i
$900$	1.65291	−	2.86293i	0.0550972	−	0.0954311i
$901$	−26.1770	−	45.3399i	−0.872082	−	1.51049i
$902$	−2.06783	−	9.05976i	−0.0688512	−	0.301657i
$903$	7.49393	+	23.9672i	0.249382	+	0.797577i
$904$	−0.246924	+	1.08184i	−0.00821257	+	0.0359816i
$905$	1.41926	−	0.437784i	0.0471778	−	0.0145524i
$906$	−5.29029	−	13.4795i	−0.175758	−	0.447825i
$907$	−10.1811	−	25.9410i	−0.338057	−	0.861355i	−0.994282	−	0.106790i	$-0.965943\pi$
$907$	−10.1811	−	25.9410i	−0.338057	−	0.861355i	0.656225	−	0.754566i	$-0.272152\pi$
$908$	−14.6447	+	4.51730i	−0.486002	+	0.149912i
$909$	1.46571	−	6.42171i	0.0486146	−	0.212995i
$910$	−1.13062	+	0.658574i	−0.0374798	+	0.0218315i
$911$	2.10757	+	9.23388i	0.0698270	+	0.305932i	0.997766	−	0.0667989i	$-0.0212786\pi$
$911$	2.10757	+	9.23388i	0.0698270	+	0.305932i	−0.927939	+	0.372731i	$0.878421\pi$
$912$	−2.87257	−	4.97543i	−0.0951202	−	0.164753i
$913$	3.22572	−	5.58711i	0.106756	−	0.184906i
$914$	10.9611	+	3.38106i	0.362562	+	0.111836i
$915$	−0.0100891	−	0.134629i	−0.000333534	−	0.00445070i
$916$	3.70497	−	4.64589i	0.122416	−	0.153504i
$917$	−25.1731	−	19.9170i	−0.831288	−	0.657717i
$918$	20.6254	+	25.8634i	0.680739	+	0.853619i
$919$	−40.2958	+	37.3891i	−1.32924	+	1.23335i	−0.377659	+	0.925945i	$0.623271\pi$
$919$	−40.2958	+	37.3891i	−1.32924	+	1.23335i	−0.951578	+	0.307407i	$0.900539\pi$
$920$	0.483021	−	0.0728037i	0.0159247	−	0.00240027i
$921$	−22.4237	+	15.2882i	−0.738887	+	0.503765i
$922$	−28.7182	−	4.32857i	−0.945783	−	0.142554i
$923$	−59.1690	+	28.4943i	−1.94757	+	0.937902i
$924$	0.613099	+	3.96416i	0.0201695	+	0.130411i
$925$	−31.7715	−	15.3004i	−1.04464	−	0.503073i
$926$	13.7998	+	9.40857i	0.453491	+	0.309185i
$927$	7.06867	+	6.55877i	0.232166	+	0.215418i
$928$	2.80180	−	37.3874i	0.0919734	−	1.22730i
$929$	10.0311	−	25.5587i	0.329108	−	0.838554i	−0.666549	−	0.745461i	$-0.732229\pi$
$929$	10.0311	−	25.5587i	0.329108	−	0.838554i	0.995657	−	0.0930931i	$-0.0296754\pi$
$930$	−1.06251			−0.0348411
$931$	21.0177	−	14.5676i	0.688828	−	0.477435i
$932$	−24.6097			−0.806117
$933$	12.2160	−	31.1258i	0.399933	−	1.01901i
$934$	−1.89886	+	25.3385i	−0.0621326	+	0.829102i
$935$	−0.338969	−	0.314517i	−0.0110855	−	0.0102858i
$936$	10.3780	+	7.07561i	0.339216	+	0.231273i
$937$	−4.30113	−	2.07132i	−0.140512	−	0.0676670i	0.362307	−	0.932059i	$-0.381989\pi$
$937$	−4.30113	−	2.07132i	−0.140512	−	0.0676670i	−0.502819	+	0.864392i	$0.667704\pi$
$938$	13.8963	+	0.987672i	0.453732	+	0.0322486i
$939$	−11.8963	+	5.72895i	−0.388220	+	0.186957i
$940$	0.154061	+	0.0232210i	0.00502493	+	0.000757386i
$941$	43.3122	−	29.5297i	1.41194	−	0.962642i	0.413291	−	0.910599i	$-0.364379\pi$
$941$	43.3122	−	29.5297i	1.41194	−	0.962642i	0.998645	−	0.0520427i	$-0.0165732\pi$
$942$	19.5107	−	2.94076i	0.635692	−	0.0958152i
$943$	14.0459	−	13.0327i	0.457397	−	0.424402i
$944$	4.99592	+	6.26469i	0.162603	+	0.203898i
$945$	0.00447733	+	1.16448i	0.000145648	+	0.0378807i
$946$	3.88857	−	4.87611i	0.126428	−	0.158536i
$947$	2.14182	+	28.5806i	0.0695999	+	0.928746i	0.917281	+	0.398240i	$0.130379\pi$
$947$	2.14182	+	28.5806i	0.0695999	+	0.928746i	−0.847681	+	0.530506i	$0.822002\pi$
$948$	7.95315	+	2.45322i	0.258306	+	0.0796770i
$949$	20.0907	−	34.7981i	0.652171	−	1.12959i
$950$	−9.15553	−	15.8578i	−0.297045	−	0.514497i
$951$	−7.99567	−	35.0313i	−0.259277	−	1.13597i
$952$	−26.1938	+	38.7384i	−0.848946	+	1.25552i
$953$	−2.53025	+	11.0857i	−0.0819627	+	0.359102i	−0.999233	−	0.0391635i	$-0.987531\pi$
$953$	−2.53025	+	11.0857i	−0.0819627	+	0.359102i	0.917270	+	0.398266i	$0.130388\pi$
$954$	5.69100	−	1.75544i	0.184253	−	0.0568345i
$955$	0.271848	+	0.692658i	0.00879680	+	0.0224139i
$956$	1.92348	+	4.90096i	0.0622099	+	0.158508i
$957$	11.0019	−	3.39365i	0.355642	−	0.109701i
$958$	−2.84824	+	12.4789i	−0.0920224	+	0.403176i
$959$	−0.369590	+	2.51771i	−0.0119347	+	0.0813012i
$960$	0.188337	+	0.825159i	0.00607856	+	0.0266319i
$961$	−23.3919	−	40.5160i	−0.754578	−	1.30697i
$962$	22.2203	−	38.4867i	0.716411	−	1.24086i
$963$	3.72131	+	1.14787i	0.119917	+	0.0369896i
$964$	0.0816789	+	1.08993i	0.00263070	+	0.0351043i
$965$	−1.00095	+	1.25515i	−0.0322217	+	0.0404047i
$966$	6.54282	−	5.25901i	0.210512	−	0.169206i
$967$	7.87641	+	9.87670i	0.253288	+	0.317613i	0.892177	−	0.451686i	$-0.149177\pi$
$967$	7.87641	+	9.87670i	0.253288	+	0.317613i	−0.638889	+	0.769299i	$0.720606\pi$
$968$	2.20184	−	2.04300i	0.0707697	−	0.0656647i
$969$	−32.4689	+	4.89390i	−1.04305	+	0.157215i
$970$	−0.486142	+	0.331446i	−0.0156091	+	0.0106421i
$971$	−38.6366	−	5.82354i	−1.23991	−	0.186886i	−0.503842	−	0.863796i	$-0.668081\pi$
$971$	−38.6366	−	5.82354i	−1.23991	−	0.186886i	−0.736066	+	0.676910i	$0.763319\pi$
$972$	6.07361	−	2.92490i	0.194811	−	0.0938161i
$973$	1.05498	−	3.46744i	0.0338211	−	0.111161i
$974$	−17.1850	−	8.27584i	−0.550642	−	0.265175i
$975$	−39.5172	−	26.9423i	−1.26556	−	0.862846i
$976$	0.848910	+	0.787673i	0.0271729	+	0.0252128i
$977$	−3.10296	+	41.4061i	−0.0992724	+	1.32470i	0.695823	+	0.718213i	$0.255040\pi$
$977$	−3.10296	+	41.4061i	−0.0992724	+	1.32470i	−0.795095	+	0.606484i	$0.792579\pi$
$978$	10.4498	−	26.6257i	0.334148	−	0.851396i
$979$	−13.0934			−0.418465
$980$	−0.520487	+	0.164943i	−0.0166263	+	0.00526890i
$981$	−9.82477			−0.313681
$982$	−6.65198	+	16.9490i	−0.212273	+	0.540863i
$983$	−2.32233	+	30.9893i	−0.0740708	+	0.988406i	0.829093	+	0.559110i	$0.188857\pi$
$983$	−2.32233	+	30.9893i	−0.0740708	+	0.988406i	−0.903164	+	0.429296i	$0.858762\pi$
$984$	31.1380	+	28.8919i	0.992644	+	0.921039i
$985$	−1.43463	−	0.978116i	−0.0457112	−	0.0311654i
$986$	40.1104	+	19.3162i	1.27738	+	0.615152i
$987$	7.50282	−	2.97798i	0.238817	−	0.0947902i
$988$	−20.4852	+	9.86517i	−0.651722	+	0.313853i
$989$	12.7161	+	1.91664i	0.404347	+	0.0609455i
$990$	0.0434616	−	0.0296316i	0.00138130	−	0.000941754i
$991$	−13.4314	+	2.02446i	−0.426664	+	0.0643092i	−0.358864	−	0.933390i	$-0.616836\pi$
$991$	−13.4314	+	2.02446i	−0.426664	+	0.0643092i	−0.0677994	+	0.997699i	$0.521598\pi$
$992$	−32.1573	+	29.8376i	−1.02099	+	0.947344i
$993$	16.2982	+	20.4372i	0.517206	+	0.648556i
$994$	27.0921	−	6.29327i	0.859308	−	0.199611i
$995$	−1.00052	+	1.25461i	−0.0317185	+	0.0397737i
$996$	0.730950	+	9.75385i	0.0231610	+	0.309062i
$997$	−12.7707	−	3.93924i	−0.404452	−	0.124757i	0.0858531	−	0.996308i	$-0.472638\pi$
$997$	−12.7707	−	3.93924i	−0.404452	−	0.124757i	−0.490305	+	0.871551i	$0.663115\pi$
$998$	−9.75404	+	16.8945i	−0.308759	+	0.534786i
$999$	−19.7757	−	34.2525i	−0.625675	−	1.08370i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.r.b.144.15	✓	276
49.16	even	21	inner	539.2.r.b.408.15	yes	276

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
539.2.r.b.144.15	✓	276	1.1	even	1	trivial
539.2.r.b.408.15	yes	276	49.16	even	21	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.r (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366692 - 0.934315i) q^{2} +(0.114146 - 1.52317i) q^{3} +(0.727622 + 0.675134i) q^{4} +(-0.0649272 - 0.0442666i) q^{5} +(-1.38126 - 0.665182i) q^{6} +(1.79210 - 1.94638i) q^{7} +(2.70620 - 1.30324i) q^{8} +(0.659474 + 0.0993998i) q^{9} +O(q^{10})\)	\(q+(0.366692 - 0.934315i) q^{2} +(0.114146 - 1.52317i) q^{3} +(0.727622 + 0.675134i) q^{4} +(-0.0649272 - 0.0442666i) q^{5} +(-1.38126 - 0.665182i) q^{6} +(1.79210 - 1.94638i) q^{7} +(2.70620 - 1.30324i) q^{8} +(0.659474 + 0.0993998i) q^{9} +(-0.0651672 + 0.0444303i) q^{10} +(-0.988831 + 0.149042i) q^{11} +(1.11140 - 1.03123i) q^{12} +(3.90941 + 4.90225i) q^{13} +(-1.16138 - 2.38810i) q^{14} +(-0.0748368 + 0.0938423i) q^{15} +(-0.0769402 - 1.02670i) q^{16} +(-5.62299 - 1.73446i) q^{17} +(0.334694 - 0.579708i) q^{18} +(1.82662 + 3.16380i) q^{19} +(-0.0173565 - 0.0760440i) q^{20} +(-2.76010 - 2.95184i) q^{21} +(-0.223344 + 0.978532i) q^{22} +(-1.97759 + 0.610006i) q^{23} +(-1.67615 - 4.27076i) q^{24} +(-1.82445 - 4.64862i) q^{25} +(6.01380 - 1.85501i) q^{26} +(1.24634 - 5.46058i) q^{27} +(2.61804 - 0.206320i) q^{28} +(-1.67730 - 7.34875i) q^{29} +(0.0602363 + 0.104332i) q^{30} +(-4.40976 + 7.63792i) q^{31} +(4.75295 + 1.46609i) q^{32} +(0.114146 + 1.52317i) q^{33} +(-3.68244 + 4.61763i) q^{34} +(-0.202515 + 0.0470428i) q^{35} +(0.412740 + 0.517559i) q^{36} +(5.17642 - 4.80302i) q^{37} +(3.62579 - 0.546499i) q^{38} +(7.91321 - 5.39513i) q^{39} +(-0.233396 - 0.0351788i) q^{40} +(-8.34164 + 4.01712i) q^{41} +(-3.77006 + 1.49639i) q^{42} +(-5.59845 - 2.69607i) q^{43} +(-0.820119 - 0.559147i) q^{44} +(-0.0384178 - 0.0356465i) q^{45} +(-0.155228 + 2.07138i) q^{46} +(-0.729756 + 1.85939i) q^{47} -1.57261 q^{48} +(-0.576773 - 6.97620i) q^{49} -5.01229 q^{50} +(-3.28372 + 8.36679i) q^{51} +(-0.465103 + 6.20637i) q^{52} +(6.52200 + 6.05153i) q^{53} +(-4.64488 - 3.16683i) q^{54} +(0.0707996 + 0.0340953i) q^{55} +(2.31318 - 7.60282i) q^{56} +(5.02750 - 2.42112i) q^{57} +(-7.48110 - 1.12759i) q^{58} +(-6.43034 + 4.38413i) q^{59} +(-0.117809 + 0.0177569i) q^{60} +(-0.824525 + 0.765048i) q^{61} +(5.51921 + 6.92087i) q^{62} +(1.37531 - 1.10545i) q^{63} +(4.39652 - 5.51306i) q^{64} +(-0.0368213 - 0.491346i) q^{65} +(1.46498 + 0.451886i) q^{66} +(-2.62309 + 4.54333i) q^{67} +(-2.92042 - 5.05831i) q^{68} +(0.703409 + 3.08184i) q^{69} +(-0.0303080 + 0.206463i) q^{70} +(-2.33063 + 10.2112i) q^{71} +(1.91421 - 0.590456i) q^{72} +(-2.34121 - 5.96531i) q^{73} +(-2.58938 - 6.59764i) q^{74} +(-7.28889 + 2.24833i) q^{75} +(-0.806900 + 3.53526i) q^{76} +(-1.48199 + 2.19174i) q^{77} +(-2.13905 - 9.37178i) q^{78} +(2.74480 + 4.75412i) q^{79} +(-0.0404528 + 0.0700664i) q^{80} +(-6.26325 - 1.93196i) q^{81} +(0.694448 + 9.26676i) q^{82} +(-4.02241 + 5.04394i) q^{83} +(-0.0154229 - 4.01127i) q^{84} +(0.288306 + 0.361525i) q^{85} +(-4.57188 + 4.24209i) q^{86} +(-11.3849 + 1.71599i) q^{87} +(-2.48174 + 1.69202i) q^{88} +(12.9471 + 1.95146i) q^{89} +(-0.0473925 + 0.0228230i) q^{90} +(16.5477 + 1.17611i) q^{91} +(-1.85077 - 0.891286i) q^{92} +(11.1305 + 7.58865i) q^{93} +(1.46966 + 1.36364i) q^{94} +(0.0214533 - 0.286275i) q^{95} +(2.77564 - 7.07221i) q^{96} +7.45992 q^{97} +(-6.72946 - 2.01923i) q^{98} -0.666923 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 276 q + 3 q^{3} + 20 q^{4} + 6 q^{5} - 8 q^{6} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 276 * q + 3 * q^3 + 20 * q^4 + 6 * q^5 - 8 * q^6 + 6 * q^8 + 6 * q^9	\( 276 q + 3 q^{3} + 20 q^{4} + 6 q^{5} - 8 q^{6} + 6 q^{8} + 6 q^{9} + 3 q^{10} + 23 q^{11} - 32 q^{12} - 27 q^{13} - 23 q^{14} + 6 q^{15} + 70 q^{16} - 3 q^{17} - 20 q^{18} - 61 q^{19} - 12 q^{20} - 23 q^{21} - 6 q^{23} + 6 q^{24} - 11 q^{25} + 9 q^{26} - 12 q^{27} - 3 q^{28} - 24 q^{29} - 26 q^{30} - 75 q^{31} + 137 q^{32} + 3 q^{33} - 58 q^{34} + 15 q^{35} - 36 q^{36} - 29 q^{37} - 6 q^{39} - 53 q^{40} - 25 q^{41} + 4 q^{42} + 20 q^{43} + 6 q^{44} + 3 q^{45} + 52 q^{46} + 25 q^{47} + 288 q^{48} + 84 q^{49} - 218 q^{50} - 160 q^{51} + 65 q^{52} + 5 q^{53} + 66 q^{54} - 12 q^{55} - 178 q^{56} + 23 q^{57} + 5 q^{58} + 28 q^{59} - 54 q^{60} - 65 q^{61} - 92 q^{62} + 85 q^{63} - 50 q^{64} + 201 q^{65} - 38 q^{66} - 16 q^{67} - 91 q^{68} - 42 q^{69} - 255 q^{70} - 63 q^{71} - 165 q^{72} + 6 q^{73} - 166 q^{74} - 117 q^{75} - 87 q^{76} + 33 q^{78} + 2 q^{79} - 48 q^{80} + 5 q^{81} + 53 q^{82} + 37 q^{83} - 84 q^{84} + 26 q^{85} + 67 q^{86} - 59 q^{87} - 3 q^{88} - 155 q^{89} + 9 q^{90} + 47 q^{91} - 19 q^{92} + 81 q^{93} + 126 q^{94} - 37 q^{95} + 395 q^{96} + 302 q^{97} + 90 q^{98} + 268 q^{99}+O(q^{100}) \) 276 * q + 3 * q^3 + 20 * q^4 + 6 * q^5 - 8 * q^6 + 6 * q^8 + 6 * q^9 + 3 * q^10 + 23 * q^11 - 32 * q^12 - 27 * q^13 - 23 * q^14 + 6 * q^15 + 70 * q^16 - 3 * q^17 - 20 * q^18 - 61 * q^19 - 12 * q^20 - 23 * q^21 - 6 * q^23 + 6 * q^24 - 11 * q^25 + 9 * q^26 - 12 * q^27 - 3 * q^28 - 24 * q^29 - 26 * q^30 - 75 * q^31 + 137 * q^32 + 3 * q^33 - 58 * q^34 + 15 * q^35 - 36 * q^36 - 29 * q^37 - 6 * q^39 - 53 * q^40 - 25 * q^41 + 4 * q^42 + 20 * q^43 + 6 * q^44 + 3 * q^45 + 52 * q^46 + 25 * q^47 + 288 * q^48 + 84 * q^49 - 218 * q^50 - 160 * q^51 + 65 * q^52 + 5 * q^53 + 66 * q^54 - 12 * q^55 - 178 * q^56 + 23 * q^57 + 5 * q^58 + 28 * q^59 - 54 * q^60 - 65 * q^61 - 92 * q^62 + 85 * q^63 - 50 * q^64 + 201 * q^65 - 38 * q^66 - 16 * q^67 - 91 * q^68 - 42 * q^69 - 255 * q^70 - 63 * q^71 - 165 * q^72 + 6 * q^73 - 166 * q^74 - 117 * q^75 - 87 * q^76 + 33 * q^78 + 2 * q^79 - 48 * q^80 + 5 * q^81 + 53 * q^82 + 37 * q^83 - 84 * q^84 + 26 * q^85 + 67 * q^86 - 59 * q^87 - 3 * q^88 - 155 * q^89 + 9 * q^90 + 47 * q^91 - 19 * q^92 + 81 * q^93 + 126 * q^94 - 37 * q^95 + 395 * q^96 + 302 * q^97 + 90 * q^98 + 268 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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