LMFDB - Embedded newform 324.2.p.a.227.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(11,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([27, 13]))

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

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

chi := DirichletCharacter("324.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.p (of order $54$, degree $18$, 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$936$
Relative dimension:	$52$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			227.4
Character	$\chi$	$=$	324.227
Dual form			324.2.p.a.167.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36289 - 0.377544i) q^{2} +(-1.15153 + 1.29382i) q^{3} +(1.71492 + 1.02910i) q^{4} +(-0.216897 - 0.161474i) q^{5} +(2.05788 - 1.32858i) q^{6} +(1.25852 - 1.91349i) q^{7} +(-1.94871 - 2.05001i) q^{8} +(-0.347949 - 2.97975i) q^{9} +O(q^{10})$	\(q+(-1.36289 - 0.377544i) q^{2} +(-1.15153 + 1.29382i) q^{3} +(1.71492 + 1.02910i) q^{4} +(-0.216897 - 0.161474i) q^{5} +(2.05788 - 1.32858i) q^{6} +(1.25852 - 1.91349i) q^{7} +(-1.94871 - 2.05001i) q^{8} +(-0.347949 - 2.97975i) q^{9} +(0.234643 + 0.301959i) q^{10} +(-1.15871 + 0.135434i) q^{11} +(-3.30626 + 1.03376i) q^{12} +(0.114975 - 0.384045i) q^{13} +(-2.43765 + 2.13272i) q^{14} +(0.458683 - 0.0946839i) q^{15} +(1.88191 + 3.52965i) q^{16} +(1.67393 - 0.295159i) q^{17} +(-0.650774 + 4.19243i) q^{18} +(7.02442 + 1.23859i) q^{19} +(-0.205789 - 0.500124i) q^{20} +(1.02649 + 3.83175i) q^{21} +(1.63033 + 0.252884i) q^{22} +(3.41680 - 2.24726i) q^{23} +(4.89635 - 0.160640i) q^{24} +(-1.41305 - 4.71990i) q^{25} +(-0.301692 + 0.480001i) q^{26} +(4.25594 + 2.98110i) q^{27} +(4.12744 - 1.98634i) q^{28} +(0.517300 + 0.488048i) q^{29} +(-0.660880 - 0.0441296i) q^{30} +(3.99744 - 0.232824i) q^{31} +(-1.23223 - 5.52102i) q^{32} +(1.15907 - 1.65513i) q^{33} +(-2.39281 - 0.229714i) q^{34} +(-0.581950 + 0.211812i) q^{35} +(2.46976 - 5.46812i) q^{36} +(1.53801 + 0.559789i) q^{37} +(-9.10586 - 4.34009i) q^{38} +(0.364487 + 0.590997i) q^{39} +(0.0916477 + 0.759307i) q^{40} +(1.65348 + 6.97656i) q^{41} +(0.0476693 - 5.60979i) q^{42} +(0.122368 + 0.0527846i) q^{43} +(-2.12648 - 0.960174i) q^{44} +(-0.405684 + 0.702485i) q^{45} +(-5.50515 + 1.77277i) q^{46} +(0.629879 - 10.8146i) q^{47} +(-6.73381 - 1.62965i) q^{48} +(0.694989 + 1.61116i) q^{49} +(0.143850 + 6.96618i) q^{50} +(-1.54570 + 2.50565i) q^{51} +(0.592394 - 0.540285i) q^{52} +(5.73201 - 3.30938i) q^{53} +(-4.67487 - 5.66970i) q^{54} +(0.273191 + 0.157727i) q^{55} +(-6.37517 + 1.14887i) q^{56} +(-9.69136 + 7.66206i) q^{57} +(-0.520762 - 0.860458i) q^{58} +(7.97639 + 0.932306i) q^{59} +(0.884044 + 0.309655i) q^{60} +(1.74644 - 0.877093i) q^{61} +(-5.53596 - 1.19190i) q^{62} +(-6.13964 - 3.08429i) q^{63} +(-0.405042 + 7.98974i) q^{64} +(-0.0869511 + 0.0647327i) q^{65} +(-2.20456 + 1.81815i) q^{66} +(-7.12272 + 6.71994i) q^{67} +(3.17440 + 1.21647i) q^{68} +(-1.02699 + 7.00852i) q^{69} +(0.873100 - 0.0689645i) q^{70} +(-6.80068 + 5.70645i) q^{71} +(-5.43046 + 6.51998i) q^{72} +(-11.6338 - 9.76192i) q^{73} +(-1.88479 - 1.34360i) q^{74} +(7.73388 + 3.60689i) q^{75} +(10.7717 + 9.35292i) q^{76} +(-1.19912 + 2.38764i) q^{77} +(-0.273628 - 0.943073i) q^{78} +(1.61485 - 6.81360i) q^{79} +(0.161766 - 1.06945i) q^{80} +(-8.75786 + 2.07360i) q^{81} +(0.380461 - 10.1325i) q^{82} +(-11.7828 - 2.79257i) q^{83} +(-2.18291 + 7.62751i) q^{84} +(-0.410731 - 0.206277i) q^{85} +(-0.146846 - 0.118139i) q^{86} +(-1.22713 + 0.107292i) q^{87} +(2.53564 + 2.11145i) q^{88} +(5.88080 - 7.00846i) q^{89} +(0.818120 - 0.804244i) q^{90} +(-0.590167 - 0.703334i) q^{91} +(8.17219 - 0.337652i) q^{92} +(-4.30194 + 5.44008i) q^{93} +(-4.94144 + 14.5013i) q^{94} +(-1.32358 - 1.40291i) q^{95} +(8.56216 + 4.76334i) q^{96} +(-3.86575 - 5.19260i) q^{97} +(-0.338905 - 2.45822i) q^{98} +(0.806735 + 3.40556i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{31}{54}\right)$

Coefficient data

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

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

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

$2$	−1.36289	−	0.377544i	−0.963706	−	0.266964i
$2$	−1.36289	−	0.377544i	−0.963706	−	0.266964i
$3$	−1.15153	+	1.29382i	−0.664837	+	0.746988i
$3$	−1.15153	+	1.29382i	−0.664837	+	0.746988i
$4$	1.71492	+	1.02910i	0.857460	+	0.514550i
$5$	−0.216897	−	0.161474i	−0.0969994	−	0.0722134i	0.547566	−	0.836762i	$-0.315554\pi$
$5$	−0.216897	−	0.161474i	−0.0969994	−	0.0722134i	−0.644566	+	0.764549i	$0.722962\pi$
$6$	2.05788	−	1.32858i	0.840127	−	0.542390i
$7$	1.25852	−	1.91349i	0.475677	−	0.723232i	−0.515337	−	0.856987i	$-0.672333\pi$
$7$	1.25852	−	1.91349i	0.475677	−	0.723232i	0.991014	+	0.133756i	$0.0427037\pi$
$8$	−1.94871	−	2.05001i	−0.688974	−	0.724786i
$9$	−0.347949	−	2.97975i	−0.115983	−	0.993251i
$10$	0.234643	+	0.301959i	0.0742006	+	0.0954879i
$11$	−1.15871	+	0.135434i	−0.349366	+	0.0408350i	−0.288966	−	0.957339i	$-0.593312\pi$
$11$	−1.15871	+	0.135434i	−0.349366	+	0.0408350i	−0.0603995	+	0.998174i	$0.519237\pi$
$12$	−3.30626	+	1.03376i	−0.954434	+	0.298421i
$13$	0.114975	−	0.384045i	0.0318884	−	0.106515i	−0.940564	−	0.339617i	$-0.889703\pi$
$13$	0.114975	−	0.384045i	0.0318884	−	0.106515i	0.972452	+	0.233102i	$0.0748877\pi$
$14$	−2.43765	+	2.13272i	−0.651490	+	0.569995i
$15$	0.458683	−	0.0946839i	0.118431	−	0.0244473i
$16$	1.88191	+	3.52965i	0.470477	+	0.882412i
$17$	1.67393	−	0.295159i	0.405987	−	0.0715865i	0.0330744	−	0.999453i	$-0.489470\pi$
$17$	1.67393	−	0.295159i	0.405987	−	0.0715865i	0.372913	+	0.927866i	$0.378359\pi$
$18$	−0.650774	+	4.19243i	−0.153389	+	0.988166i
$19$	7.02442	+	1.23859i	1.61151	+	0.284153i	0.905595	−	0.424143i	$-0.139424\pi$
$19$	7.02442	+	1.23859i	1.61151	+	0.284153i	0.705916	+	0.708295i	$0.250536\pi$
$20$	−0.205789	−	0.500124i	−0.0460158	−	0.111831i
$21$	1.02649	+	3.83175i	0.223998	+	0.836157i
$22$	1.63033	+	0.252884i	0.347587	+	0.0539151i
$23$	3.41680	−	2.24726i	0.712451	−	0.468587i	−0.140833	−	0.990033i	$-0.544978\pi$
$23$	3.41680	−	2.24726i	0.712451	−	0.468587i	0.853284	+	0.521447i	$0.174608\pi$
$24$	4.89635	−	0.160640i	0.999462	−	0.0327905i
$25$	−1.41305	−	4.71990i	−0.282609	−	0.943980i
$26$	−0.301692	+	0.480001i	−0.0591667	+	0.0941360i
$27$	4.25594	+	2.98110i	0.819057	+	0.573712i
$28$	4.12744	−	1.98634i	0.780013	−	0.375383i
$29$	0.517300	+	0.488048i	0.0960603	+	0.0906282i	0.732774	−	0.680472i	$-0.238225\pi$
$29$	0.517300	+	0.488048i	0.0960603	+	0.0906282i	−0.636714	+	0.771100i	$0.719707\pi$
$30$	−0.660880	−	0.0441296i	−0.120660	−	0.00805692i
$31$	3.99744	−	0.232824i	0.717961	−	0.0418165i	0.304725	−	0.952440i	$-0.401435\pi$
$31$	3.99744	−	0.232824i	0.717961	−	0.0418165i	0.413236	+	0.910624i	$0.364398\pi$
$32$	−1.23223	−	5.52102i	−0.217829	−	0.975987i
$33$	1.15907	−	1.65513i	0.201768	−	0.288121i
$34$	−2.39281	−	0.229714i	−0.410364	−	0.0393956i
$35$	−0.581950	+	0.211812i	−0.0983674	+	0.0358028i
$36$	2.46976	−	5.46812i	0.411627	−	0.911353i
$37$	1.53801	+	0.559789i	0.252847	+	0.0920288i	0.465334	−	0.885135i	$-0.345934\pi$
$37$	1.53801	+	0.559789i	0.252847	+	0.0920288i	−0.212487	+	0.977164i	$0.568156\pi$
$38$	−9.10586	−	4.34009i	−1.47717	−	0.704056i
$39$	0.364487	+	0.590997i	0.0583647	+	0.0946353i
$40$	0.0916477	+	0.759307i	0.0144908	+	0.120057i
$41$	1.65348	+	6.97656i	0.258230	+	1.08956i	0.935361	+	0.353694i	$0.115075\pi$
$41$	1.65348	+	6.97656i	0.258230	+	1.08956i	−0.677132	+	0.735862i	$0.736777\pi$
$42$	0.0476693	−	5.60979i	0.00735553	−	0.865609i
$43$	0.122368	+	0.0527846i	0.0186610	+	0.00804957i	0.405390	−	0.914144i	$-0.367136\pi$
$43$	0.122368	+	0.0527846i	0.0186610	+	0.00804957i	−0.386729	+	0.922193i	$0.626395\pi$
$44$	−2.12648	−	0.960174i	−0.320579	−	0.144752i
$45$	−0.405684	+	0.702485i	−0.0604758	+	0.104720i
$46$	−5.50515	+	1.77277i	−0.811690	+	0.261381i
$47$	0.629879	−	10.8146i	0.0918773	−	1.57747i	−0.566038	−	0.824379i	$-0.691524\pi$
$47$	0.629879	−	10.8146i	0.0918773	−	1.57747i	0.657915	−	0.753092i	$-0.271439\pi$
$48$	−6.73381	−	1.62965i	−0.971942	−	0.235220i
$49$	0.694989	+	1.61116i	0.0992841	+	0.230166i
$50$	0.143850	+	6.96618i	0.0203434	+	0.985166i
$51$	−1.54570	+	2.50565i	−0.216441	+	0.350861i
$52$	0.592394	−	0.540285i	0.0821503	−	0.0749240i
$53$	5.73201	−	3.30938i	0.787353	−	0.454578i	−0.0516771	−	0.998664i	$-0.516457\pi$
$53$	5.73201	−	3.30938i	0.787353	−	0.454578i	0.839030	+	0.544086i	$0.183123\pi$
$54$	−4.67487	−	5.66970i	−0.636170	−	0.771549i
$55$	0.273191	+	0.157727i	0.0368371	+	0.0212679i
$56$	−6.37517	+	1.14887i	−0.851918	+	0.153524i
$57$	−9.69136	+	7.66206i	−1.28365	+	1.01486i
$58$	−0.520762	−	0.860458i	−0.0683794	−	0.112984i
$59$	7.97639	+	0.932306i	1.03844	+	0.121376i	0.618186	−	0.786032i	$-0.287868\pi$
$59$	7.97639	+	0.932306i	1.03844	+	0.121376i	0.420251	+	0.907408i	$0.361942\pi$
$60$	0.884044	+	0.309655i	0.114130	+	0.0399763i
$61$	1.74644	−	0.877093i	0.223608	−	0.112300i	−0.333469	−	0.942761i	$-0.608219\pi$
$61$	1.74644	−	0.877093i	0.223608	−	0.112300i	0.557077	+	0.830461i	$0.311923\pi$
$62$	−5.53596	−	1.19190i	−0.703067	−	0.151371i
$63$	−6.13964	−	3.08429i	−0.773521	−	0.388584i
$64$	−0.405042	+	7.98974i	−0.0506303	+	0.998717i
$65$	−0.0869511	+	0.0647327i	−0.0107850	+	0.00802910i
$66$	−2.20456	+	1.81815i	−0.271363	+	0.223799i
$67$	−7.12272	+	6.71994i	−0.870178	+	0.820971i	−0.985025	−	0.172412i	$-0.944844\pi$
$67$	−7.12272	+	6.71994i	−0.870178	+	0.820971i	0.114846	+	0.993383i	$0.463362\pi$
$68$	3.17440	+	1.21647i	0.384953	+	0.147518i
$69$	−1.02699	+	7.00852i	−0.123635	+	0.843726i
$70$	0.873100	−	0.0689645i	0.104355	−	0.00824284i
$71$	−6.80068	+	5.70645i	−0.807093	+	0.677231i	−0.949912	−	0.312518i	$-0.898828\pi$
$71$	−6.80068	+	5.70645i	−0.807093	+	0.677231i	0.142819	+	0.989749i	$0.454383\pi$
$72$	−5.43046	+	6.51998i	−0.639986	+	0.768387i
$73$	−11.6338	−	9.76192i	−1.36163	−	1.14255i	−0.975474	−	0.220115i	$-0.929357\pi$
$73$	−11.6338	−	9.76192i	−1.36163	−	1.14255i	−0.386160	−	0.922432i	$-0.626199\pi$
$74$	−1.88479	−	1.34360i	−0.219102	−	0.156190i
$75$	7.73388	+	3.60689i	0.893031	+	0.416487i
$76$	10.7717	+	9.35292i	1.23560	+	1.07285i
$77$	−1.19912	+	2.38764i	−0.136652	+	0.272097i
$78$	−0.273628	−	0.943073i	−0.0309822	−	0.106782i
$79$	1.61485	−	6.81360i	0.181685	−	0.766589i	−0.803530	−	0.595265i	$-0.797047\pi$
$79$	1.61485	−	6.81360i	0.181685	−	0.766589i	0.985215	−	0.171325i	$-0.0548047\pi$
$80$	0.161766	−	1.06945i	0.0180860	−	0.119568i
$81$	−8.75786	+	2.07360i	−0.973096	+	0.230401i
$82$	0.380461	−	10.1325i	0.0420148	−	1.11895i
$83$	−11.7828	−	2.79257i	−1.29333	−	0.306524i	−0.474343	−	0.880340i	$-0.657314\pi$
$83$	−11.7828	−	2.79257i	−1.29333	−	0.306524i	−0.818984	+	0.573816i	$0.805462\pi$
$84$	−2.18291	+	7.62751i	−0.238175	+	0.832229i
$85$	−0.410731	−	0.206277i	−0.0445500	−	0.0223739i
$86$	−0.146846	−	0.118139i	−0.0158348	−	0.0127392i
$87$	−1.22713	+	0.107292i	−0.131563	+	0.0115029i
$88$	2.53564	+	2.11145i	0.270300	+	0.225081i
$89$	5.88080	−	7.00846i	0.623363	−	0.742895i	−0.358282	−	0.933614i	$-0.616637\pi$
$89$	5.88080	−	7.00846i	0.623363	−	0.742895i	0.981645	+	0.190718i	$0.0610817\pi$
$90$	0.818120	−	0.804244i	0.0862374	−	0.0847748i
$91$	−0.590167	−	0.703334i	−0.0618663	−	0.0737294i
$92$	8.17219	−	0.337652i	0.852010	−	0.0352026i
$93$	−4.30194	+	5.44008i	−0.446091	+	0.564110i
$94$	−4.94144	+	14.5013i	−0.509671	+	1.49569i
$95$	−1.32358	−	1.40291i	−0.135796	−	0.143935i
$96$	8.56216	+	4.76334i	0.873872	+	0.486157i
$97$	−3.86575	−	5.19260i	−0.392507	−	0.527229i	0.561314	−	0.827603i	$-0.310296\pi$
$97$	−3.86575	−	5.19260i	−0.392507	−	0.527229i	−0.953822	+	0.300374i	$0.902889\pi$
$98$	−0.338905	−	2.45822i	−0.0342346	−	0.248318i
$99$	0.806735	+	3.40556i	0.0810799	+	0.342272i
$100$	2.43399	−	9.54842i	0.243399	−	0.954842i
$101$	2.77557	+	5.52661i	0.276179	+	0.549918i	0.988370	−	0.152068i	$-0.0485932\pi$
$101$	2.77557	+	5.52661i	0.276179	+	0.549918i	−0.712191	+	0.701986i	$0.752297\pi$
$102$	3.05261	−	2.83135i	0.302253	−	0.280345i
$103$	−0.906907	+	7.75908i	−0.0893602	+	0.764525i	0.872052	+	0.489413i	$0.162789\pi$
$103$	−0.906907	+	7.75908i	−0.0893602	+	0.764525i	−0.961412	+	0.275112i	$0.911285\pi$
$104$	−1.01135	+	0.512692i	−0.0991708	+	0.0502736i
$105$	0.396086	−	0.996848i	0.0386540	−	0.0972824i
$106$	−9.06152	+	2.34622i	−0.880133	+	0.227885i
$107$	−3.17413	+	5.49776i	−0.306855	+	0.531489i	−0.977673	−	0.210134i	$-0.932610\pi$
$107$	−3.17413	+	5.49776i	−0.306855	+	0.531489i	0.670817	+	0.741622i	$0.265943\pi$
$108$	4.23076	+	9.49214i	0.407105	+	0.913381i
$109$	−7.47920	−	12.9543i	−0.716377	−	1.24080i	−0.962426	−	0.271544i	$-0.912466\pi$
$109$	−7.47920	−	12.9543i	−0.716377	−	1.24080i	0.246049	−	0.969257i	$-0.420868\pi$
$110$	−0.312780	−	0.318106i	−0.0298224	−	0.0303302i
$111$	−2.49533	+	1.34529i	−0.236847	+	0.127690i
$112$	9.12238	+	0.841134i	0.861984	+	0.0794797i
$113$	15.2419	−	6.57473i	1.43384	−	0.618499i	0.469445	−	0.882962i	$-0.344454\pi$
$113$	15.2419	−	6.57473i	1.43384	−	0.618499i	0.964396	+	0.264463i	$0.0851947\pi$
$114$	16.1010	−	6.78361i	1.50800	−	0.635343i
$115$	−1.10397	−	0.0642988i	−0.102946	−	0.00599590i
$116$	0.384879	+	1.36932i	0.0357351	+	0.127138i
$117$	−1.18436	−	0.208970i	−0.109494	−	0.0193193i
$118$	−10.5189	−	4.28207i	−0.968346	−	0.394196i
$119$	1.54189	−	3.57451i	0.141345	−	0.327675i
$120$	−1.08794	−	0.755790i	−0.0993152	−	0.0689939i
$121$	−9.37922	+	2.22291i	−0.852656	+	0.202083i
$122$	−2.71134	+	0.536022i	−0.245473	+	0.0485291i
$123$	−10.9305	−	5.89443i	−0.985566	−	0.531483i
$124$	7.09489	+	3.71449i	0.637140	+	0.333571i
$125$	−0.918074	+	2.52239i	−0.0821150	+	0.225609i
$126$	7.20317	+	6.52152i	0.641710	+	0.580984i
$127$	4.40428	+	12.1007i	0.390817	+	1.07376i	0.966630	+	0.256178i	$0.0824634\pi$
$127$	4.40428	+	12.1007i	0.390817	+	1.07376i	−0.575813	+	0.817581i	$0.695314\pi$
$128$	3.56851	−	10.7362i	0.315414	−	0.948954i
$129$	−0.209205	+	0.0975397i	−0.0184195	+	0.00858790i
$130$	0.142944	−	0.0553955i	0.0125370	−	0.00485850i
$131$	0.269414	+	4.62566i	0.0235388	+	0.404146i	0.989412	+	0.145132i	$0.0463606\pi$
$131$	0.269414	+	4.62566i	0.0235388	+	0.404146i	−0.965874	+	0.259014i	$0.916602\pi$
$132$	3.69100	−	1.64561i	0.321261	−	0.143232i
$133$	11.2104	−	11.8824i	0.972068	−	1.03033i
$134$	12.2445	−	6.46937i	1.05777	−	0.558869i
$135$	−0.441733	−	1.33382i	−0.0380183	−	0.114797i
$136$	−3.86708	−	2.85638i	−0.331599	−	0.244933i
$137$	−10.7965	+	3.23227i	−0.922410	+	0.276151i	−0.712584	−	0.701587i	$-0.752475\pi$
$137$	−10.7965	+	3.23227i	−0.922410	+	0.276151i	−0.209826	+	0.977739i	$0.567290\pi$
$138$	4.04570	−	9.16408i	0.344393	−	0.780098i
$139$	−9.01583	−	13.7079i	−0.764713	−	1.16269i	−0.982422	−	0.186676i	$-0.940229\pi$
$139$	−9.01583	−	13.7079i	−0.764713	−	1.16269i	0.217708	−	0.976014i	$-0.430142\pi$
$140$	−1.21597	−	0.235643i	−0.102769	−	0.0199155i
$141$	13.2668	+	13.2683i	1.11727	+	1.11739i
$142$	11.4230	−	5.20969i	0.958597	−	0.437187i
$143$	−0.0812109	+	0.460570i	−0.00679120	+	0.0385148i
$144$	9.86268	−	6.83576i	0.821890	−	0.569646i
$145$	−0.0333940	−	0.189387i	−0.00277322	−	0.0157277i
$146$	12.1700	+	17.6967i	1.00720	+	1.46459i
$147$	−2.88486	−	0.956116i	−0.237939	−	0.0788591i
$148$	2.06148	+	2.54276i	0.169453	+	0.209013i
$149$	19.4154	+	5.81259i	1.59057	+	0.476186i	0.955185	−	0.296009i	$-0.0956557\pi$
$149$	19.4154	+	5.81259i	1.59057	+	0.476186i	0.635386	+	0.772194i	$0.280841\pi$
$150$	−9.17864	−	7.83566i	−0.749433	−	0.639779i
$151$	−2.39059	−	20.4528i	−0.194543	−	1.66442i	−0.639438	−	0.768842i	$-0.720833\pi$
$151$	−2.39059	−	20.4528i	−0.194543	−	1.66442i	0.444895	−	0.895583i	$-0.353241\pi$
$152$	−11.1494	−	16.8138i	−0.904339	−	1.36378i
$153$	−1.46194	−	4.88519i	−0.118191	−	0.394945i
$154$	2.53570	−	2.80136i	0.204333	−	0.225740i
$155$	−0.904628	−	0.594983i	−0.0726615	−	0.0477902i
$156$	0.0168717	+	1.38861i	0.00135082	+	0.111178i
$157$	1.70813	−	2.29441i	0.136323	−	0.183114i	−0.728719	−	0.684813i	$-0.759884\pi$
$157$	1.70813	−	2.29441i	0.136323	−	0.183114i	0.865042	+	0.501699i	$0.167291\pi$
$158$	−4.77329	+	8.67648i	−0.379743	+	0.690264i
$159$	−2.31885	+	11.2271i	−0.183897	+	0.890364i
$160$	−0.624234	+	1.39647i	−0.0493501	+	0.110400i
$161$		−	9.36624i		−	0.738163i
$162$	12.7189	+	0.480392i	0.999287	+	0.0377432i
$163$		−	5.64195i		−	0.441912i	−0.975284	−	0.220956i	$-0.929082\pi$
$163$		−	5.64195i		−	0.441912i	0.975284	−	0.220956i	$-0.0709177\pi$
$164$	−4.34400	+	13.6658i	−0.339210	+	1.06712i
$165$	−0.518659	+	0.171833i	−0.0403776	+	0.0133772i
$166$	15.0043	+	8.25447i	1.16456	+	0.640671i
$167$	8.79752	−	11.8171i	0.680772	−	0.914436i	−0.318669	−	0.947866i	$-0.603236\pi$
$167$	8.79752	−	11.8171i	0.680772	−	0.914436i	0.999441	+	0.0334302i	$0.0106431\pi$
$168$	5.85478	−	9.57128i	0.451706	−	0.738441i
$169$	10.7271	+	7.05531i	0.825159	+	0.542716i
$170$	0.481901	+	0.436201i	0.0369601	+	0.0334551i
$171$	1.24657	−	21.3620i	0.0953273	−	1.63359i
$172$	0.155531	+	0.216451i	0.0118592	+	0.0165042i
$173$	−0.732937	−	6.27067i	−0.0557241	−	0.476750i	−0.992071	−	0.125675i	$-0.959890\pi$
$173$	−0.732937	−	6.27067i	−0.0557241	−	0.476750i	0.936347	−	0.351075i	$-0.114184\pi$
$174$	1.71295	+	0.317071i	0.129859	+	0.0240371i
$175$	−10.8098	−	3.23625i	−0.817147	−	0.244638i
$176$	−2.65863	−	3.83498i	−0.200402	−	0.289073i
$177$	−10.3913	+	9.24644i	−0.781058	+	0.695005i
$178$	−10.6609	+	7.33148i	−0.799065	+	0.549517i
$179$	3.55768	+	20.1766i	0.265913	+	1.50807i	0.766422	+	0.642337i	$0.222035\pi$
$179$	3.55768	+	20.1766i	0.265913	+	1.50807i	−0.500509	+	0.865731i	$0.666854\pi$
$180$	−1.41864	+	0.787217i	−0.105739	+	0.0586757i
$181$	−2.05151	+	11.6347i	−0.152488	+	0.864802i	0.808559	+	0.588416i	$0.200248\pi$
$181$	−2.05151	+	11.6347i	−0.152488	+	0.864802i	−0.961047	+	0.276386i	$0.910863\pi$
$182$	0.538791	+	1.18138i	0.0399379	+	0.0875696i
$183$	−0.876274	+	3.26958i	−0.0647761	+	0.241694i
$184$	−11.2652	−	2.62518i	−0.830485	−	0.193531i
$185$	−0.243198	−	0.369765i	−0.0178803	−	0.0271857i
$186$	7.91693	−	5.79003i	0.580498	−	0.424546i
$187$	−1.89963	+	0.568712i	−0.138915	+	0.0415884i
$188$	12.2095	−	17.8980i	0.890469	−	1.30534i
$189$	11.0605	−	4.39193i	0.804534	−	0.319466i
$190$	1.27422	+	2.41171i	0.0924419	+	0.174964i
$191$	−9.35554	+	9.91630i	−0.676943	+	0.717518i	−0.971215	−	0.238204i	$-0.923441\pi$
$191$	−9.35554	+	9.91630i	−0.676943	+	0.717518i	0.294272	+	0.955722i	$0.404923\pi$
$192$	−9.87088	−	9.72449i	−0.712369	−	0.701805i
$193$	0.471461	+	8.09467i	0.0339365	+	0.582667i	0.971821	+	0.235720i	$0.0757447\pi$
$193$	0.471461	+	8.09467i	0.0339365	+	0.582667i	−0.937885	+	0.346947i	$0.887218\pi$
$194$	3.30814	+	8.53642i	0.237511	+	0.612879i
$195$	0.0163744	−	0.187041i	0.00117259	−	0.0133943i
$196$	−0.466199	+	3.47823i	−0.0332999	+	0.248445i
$197$	7.08063	+	19.4539i	0.504474	+	1.38603i	0.886864	+	0.462030i	$0.152879\pi$
$197$	7.08063	+	19.4539i	0.504474	+	1.38603i	−0.382390	+	0.924001i	$0.624899\pi$
$198$	0.186262	−	4.94597i	0.0132370	−	0.351495i
$199$	−7.86061	+	21.5968i	−0.557224	+	1.53096i	0.266423	+	0.963856i	$0.414158\pi$
$199$	−7.86061	+	21.5968i	−0.557224	+	1.53096i	−0.823647	+	0.567103i	$0.808064\pi$
$200$	−6.92220	+	12.0945i	−0.489474	+	0.855209i
$201$	−0.492365	−	16.9537i	−0.0347287	−	1.19583i
$202$	−1.69625	−	8.58004i	−0.119347	−	0.603690i
$203$	1.58491	−	0.375631i	0.111239	−	0.0263641i
$204$	−5.22932	+	2.70631i	−0.366125	+	0.189480i
$205$	0.767900	−	1.78019i	0.0536324	−	0.124334i
$206$	4.16541	−	10.2324i	0.290218	−	0.712922i
$207$	−7.88516	−	9.39928i	−0.548056	−	0.653295i
$208$	1.57192	−	0.316913i	0.108993	−	0.0219740i
$209$	−8.30704	−	0.483830i	−0.574610	−	0.0334672i
$210$	−0.916175	+	1.20905i	−0.0632220	+	0.0834324i
$211$	−16.0774	+	6.93511i	−1.10681	+	0.477432i	−0.869466	−	0.493993i	$-0.835537\pi$
$211$	−16.0774	+	6.93511i	−1.10681	+	0.477432i	−0.237347	+	0.971425i	$0.576278\pi$
$212$	13.2356	+	0.223491i	0.909027	+	0.0153495i
$213$	0.448073	−	15.3700i	0.0307015	−	1.05314i
$214$	6.40163	−	6.29445i	0.437607	−	0.430280i
$215$	−0.0180180	−	0.0312081i	−0.00122882	−	0.00212838i
$216$	−2.18235	−	14.5340i	−0.148490	−	0.988914i
$217$	4.58536	−	7.94208i	0.311275	−	0.539143i
$218$	5.30246	+	20.4790i	0.359128	+	1.38702i
$219$	26.0269	−	3.81091i	1.75873	−	0.257517i
$220$	0.306184	+	0.551631i	0.0206430	+	0.0371909i
$221$	0.0791065	−	0.676799i	0.00532128	−	0.0455264i
$222$	3.90876	−	0.891384i	0.262339	−	0.0598258i
$223$	7.07506	+	14.0876i	0.473781	+	0.943376i	0.995896	+	0.0905010i	$0.0288468\pi$
$223$	7.07506	+	14.0876i	0.473781	+	0.943376i	−0.522115	+	0.852875i	$0.674857\pi$
$224$	−12.1152	−	4.59047i	−0.809481	−	0.306714i
$225$	−13.5725	+	5.85281i	−0.904832	+	0.390188i
$226$	−23.2553	+	3.20611i	−1.54692	+	0.213267i
$227$	2.36478	+	3.17644i	0.156956	+	0.210828i	0.873644	−	0.486565i	$-0.161750\pi$
$227$	2.36478	+	3.17644i	0.156956	+	0.210828i	−0.716688	+	0.697393i	$0.754343\pi$
$228$	−24.5049	+	3.16645i	−1.62288	+	0.209703i
$229$	11.3236	+	12.0023i	0.748285	+	0.793136i	0.983902	−	0.178710i	$-0.0571924\pi$
$229$	11.3236	+	12.0023i	0.748285	+	0.793136i	−0.235616	+	0.971846i	$0.575711\pi$
$230$	1.48031	+	0.504429i	0.0976086	+	0.0332611i
$231$	−1.70836	−	4.30089i	−0.112402	−	0.282978i
$232$	−0.00756911	−	2.01153i	−0.000496936	−	0.132064i
$233$	−8.22812	−	9.80589i	−0.539042	−	0.642405i	0.425931	−	0.904756i	$-0.359947\pi$
$233$	−8.22812	−	9.80589i	−0.539042	−	0.642405i	−0.964973	+	0.262350i	$0.915502\pi$
$234$	1.53526	+	0.731953i	0.100363	+	0.0478493i
$235$	−1.88290	+	2.24395i	−0.122827	+	0.146379i
$236$	12.7194	+	9.80733i	0.827965	+	0.638403i
$237$	6.95602	+	9.93540i	0.451842	+	0.645374i
$238$	−3.45096	+	4.28952i	−0.223693	+	0.278048i
$239$	12.4504	+	6.25283i	0.805350	+	0.404462i	0.803329	−	0.595536i	$-0.203060\pi$
$239$	12.4504	+	6.25283i	0.805350	+	0.404462i	0.00202116	+	0.999998i	$0.499357\pi$
$240$	1.19740	+	1.44080i	0.0772918	+	0.0930035i
$241$	12.0282	+	2.85073i	0.774804	+	0.183632i	0.598952	−	0.800785i	$-0.295584\pi$
$241$	12.0282	+	2.85073i	0.774804	+	0.183632i	0.175852	+	0.984417i	$0.443732\pi$
$242$	13.6221	+	0.511487i	0.875659	+	0.0328796i
$243$	7.40208	−	13.7189i	0.474844	−	0.880070i
$244$	3.89762	+	0.293112i	0.249519	+	0.0187646i
$245$	0.109420	−	0.461680i	0.00699060	−	0.0294956i
$246$	12.6716	+	12.1602i	0.807910	+	0.775304i
$247$	1.28331	−	2.55528i	0.0816551	−	0.162589i
$248$	−8.26715	−	7.74106i	−0.524964	−	0.491558i
$249$	17.1813	−	12.0291i	1.08882	−	0.762311i
$250$	2.20354	−	3.09111i	0.139364	−	0.195499i
$251$	−4.16608	−	3.49576i	−0.262961	−	0.220650i	0.501769	−	0.865002i	$-0.332683\pi$
$251$	−4.16608	−	3.49576i	−0.262961	−	0.220650i	−0.764729	+	0.644352i	$0.777127\pi$
$252$	−7.35494	−	11.6076i	−0.463318	−	0.731211i
$253$	−3.65474	+	3.06669i	−0.229771	+	0.192801i
$254$	−1.43400	−	18.1546i	−0.0899772	−	1.13912i
$255$	0.739855	−	0.293878i	0.0463315	−	0.0184034i
$256$	−8.91686	+	13.2849i	−0.557304	+	0.830309i
$257$	−7.25909	+	6.84860i	−0.452809	+	0.427204i	−0.878556	−	0.477639i	$-0.841493\pi$
$257$	−7.25909	+	6.84860i	−0.452809	+	0.427204i	0.425747	+	0.904842i	$0.360011\pi$
$258$	0.321948	−	0.0539515i	0.0200436	−	0.00335888i
$259$	3.00677	−	2.23846i	0.186832	−	0.139091i
$260$	−0.215731	+	0.0215301i	−0.0133790	+	0.00133524i
$261$	1.27427	−	1.71124i	0.0788752	−	0.105923i
$262$	1.37921	−	6.40597i	0.0852079	−	0.395762i
$263$	−0.293714	+	0.147509i	−0.0181112	+	0.00909577i	−0.457832	−	0.889039i	$-0.651374\pi$
$263$	−0.293714	+	0.147509i	−0.0181112	+	0.00909577i	0.439721	+	0.898135i	$0.355077\pi$
$264$	−5.65171	+	0.849269i	−0.347839	+	0.0522689i
$265$	−1.77764	−	0.207776i	−0.109199	−	0.0127636i
$266$	−19.7647	+	11.9619i	−1.21185	+	0.733430i
$267$	2.29577	+	15.6792i	0.140499	+	0.959549i
$268$	−19.1304	+	4.19417i	−1.16857	+	0.256200i
$269$	−13.3867	−	7.72884i	−0.816204	−	0.471236i	0.0329016	−	0.999459i	$-0.489525\pi$
$269$	−13.3867	−	7.72884i	−0.816204	−	0.471236i	−0.849106	+	0.528223i	$0.822859\pi$
$270$	0.0984573	+	1.98461i	0.00599192	+	0.120780i
$271$	−8.71465	+	5.03141i	−0.529378	+	0.305636i	−0.740763	−	0.671767i	$-0.765536\pi$
$271$	−8.71465	+	5.03141i	−0.529378	+	0.305636i	0.211385	+	0.977403i	$0.432202\pi$
$272$	4.19198	+	5.35292i	0.254176	+	0.324568i
$273$	1.58958	+	0.0463402i	0.0962060	+	0.00280464i
$274$	15.9348	−	0.329049i	0.962655	−	0.0198786i
$275$	2.27655	+	5.27765i	0.137281	+	0.318254i
$276$	−8.97368	+	10.9622i	−0.540152	+	0.659845i
$277$	−1.13233	+	19.4413i	−0.0680349	+	1.16811i	0.775610	+	0.631212i	$0.217442\pi$
$277$	−1.13233	+	19.4413i	−0.0680349	+	1.16811i	−0.843645	+	0.536901i	$0.819595\pi$
$278$	7.11222	+	22.0862i	0.426563	+	1.32464i
$279$	−2.08466	−	11.8304i	−0.124806	−	0.708266i
$280$	1.56827	+	0.780238i	0.0937220	+	0.0466282i
$281$	10.5815	+	4.56440i	0.631238	+	0.272289i	0.687565	−	0.726123i	$-0.258680\pi$
$281$	10.5815	+	4.56440i	0.631238	+	0.272289i	−0.0563269	+	0.998412i	$0.517939\pi$
$282$	−13.0718	−	23.0920i	−0.778416	−	1.37511i
$283$	−3.56873	−	15.0577i	−0.212139	−	0.895085i	−0.970085	−	0.242767i	$-0.921945\pi$
$283$	−3.56873	−	15.0577i	−0.212139	−	0.895085i	0.757945	−	0.652318i	$-0.226203\pi$
$284$	−17.5351	+	2.78753i	−1.04052	+	0.165409i
$285$	3.33925	−	0.0969774i	0.197800	−	0.00574445i
$286$	0.284567	−	0.597044i	0.0168268	−	0.0353039i
$287$	15.4305	+	5.61626i	0.910836	+	0.331517i
$288$	−16.0225	+	5.59276i	−0.944136	+	0.329557i
$289$	−13.2599	+	4.82619i	−0.779992	+	0.283894i
$290$	−0.0259897	+	0.270721i	−0.00152616	+	0.0158973i
$291$	11.1698	+	0.977856i	0.654787	+	0.0573230i
$292$	−9.90506	−	28.7133i	−0.579650	−	1.68032i
$293$	−27.2755	+	1.58861i	−1.59345	+	0.0928079i	−0.831760	−	0.555135i	$-0.812667\pi$
$293$	−27.2755	+	1.58861i	−1.59345	+	0.0928079i	−0.761689	+	0.647943i	$0.775630\pi$
$294$	3.57076	+	2.39224i	0.208251	+	0.139518i
$295$	−1.57951	−	1.49019i	−0.0919629	−	0.0867625i
$296$	−1.84956	−	4.24379i	−0.107504	−	0.246665i
$297$	−5.33517	−	2.87784i	−0.309578	−	0.166989i
$298$	−24.2665	−	15.2521i	−1.40572	−	0.883529i
$299$	−0.470201	−	1.57058i	−0.0271924	−	0.0908291i
$300$	9.55114	+	14.1445i	0.551435	+	0.816631i
$301$	0.255006	−	0.167720i	0.0146983	−	0.00966723i
$302$	−4.46373	+	28.7774i	−0.256859	+	1.65595i
$303$	−10.3466	−	2.77298i	−0.594397	−	0.159303i
$304$	8.84749	+	27.1246i	0.507438	+	1.55571i
$305$	−0.520425	−	0.0917650i	−0.0297994	−	0.00525445i
$306$	0.148085	+	7.20991i	0.00846545	+	0.412163i
$307$	4.53362	−	0.799400i	0.258747	−	0.0456242i	−0.0427695	−	0.999085i	$-0.513618\pi$
$307$	4.53362	−	0.799400i	0.258747	−	0.0456242i	0.301517	+	0.953461i	$0.402507\pi$
$308$	−4.51351	+	2.86060i	−0.257181	+	0.162998i
$309$	−8.99454	−	10.1082i	−0.511681	−	0.575036i
$310$	1.00827	+	1.15243i	0.0572661	+	0.0654538i
$311$	6.42612	−	21.4647i	0.364392	−	1.21715i	−0.557654	−	0.830073i	$-0.688298\pi$
$311$	6.42612	−	21.4647i	0.364392	−	1.21715i	0.922046	−	0.387080i	$-0.126516\pi$
$312$	0.501266	−	1.89888i	0.0283786	−	0.107503i
$313$	−30.0445	+	3.51169i	−1.69821	+	0.198493i	−0.909337	−	0.416060i	$-0.863411\pi$
$313$	−30.0445	+	3.51169i	−1.69821	+	0.198493i	−0.788876	+	0.614553i	$0.789337\pi$
$314$	−3.19423	+	2.48213i	−0.180261	+	0.140075i
$315$	0.833637	+	1.66037i	0.0469701	+	0.0935511i
$316$	9.78121	−	10.0229i	0.550236	−	0.563834i
$317$	−9.25988	+	14.0790i	−0.520087	+	0.790753i	−0.996058	−	0.0887075i	$-0.971726\pi$
$317$	−9.25988	+	14.0790i	−0.520087	+	0.790753i	0.475971	+	0.879461i	$0.342097\pi$
$318$	7.39904	−	14.4257i	0.414918	−	0.808955i
$319$	−0.665502	−	0.495448i	−0.0372610	−	0.0277398i
$320$	1.37799	−	1.66755i	0.0770319	−	0.0932188i
$321$	−3.45801	−	10.4376i	−0.193007	−	0.582571i
$322$	−3.53617	+	12.7651i	−0.197063	+	0.711373i
$323$	12.1240			0.674595
$324$	−17.1530	−	5.45665i	−0.952944	−	0.303147i
$325$	−1.97512			−0.109560
$326$	−2.13009	+	7.68934i	−0.117975	+	0.425873i
$327$	25.3731	+	5.24060i	1.40314	+	0.289806i
$328$	11.0798	−	16.9849i	0.611782	−	0.937837i
$329$	−19.9009	−	14.8157i	−1.09717	−	0.816816i
$330$	0.771748	−	0.0383723i	0.0424833	−	0.00211232i
$331$	12.0564	−	18.3309i	0.662681	−	1.00756i	−0.335178	−	0.942155i	$-0.608796\pi$
$331$	12.0564	−	18.3309i	0.662681	−	1.00756i	0.997859	−	0.0654027i	$-0.0208332\pi$
$332$	−17.3327	−	16.9147i	−0.951254	−	0.928313i
$333$	1.13289	−	4.77766i	0.0620818	−	0.261814i
$334$	−16.4515	+	12.7839i	−0.900186	+	0.699506i
$335$	2.62999	−	0.307402i	0.143692	−	0.0167952i
$336$	−11.5930	+	10.8341i	−0.632449	+	0.591051i
$337$	5.93098	−	19.8108i	0.323081	−	1.07917i	−0.630037	−	0.776565i	$-0.716960\pi$
$337$	5.93098	−	19.8108i	0.323081	−	1.07917i	0.953118	−	0.302600i	$-0.0978546\pi$
$338$	−11.9561	−	13.6655i	−0.650326	−	0.743307i
$339$	−9.04505	+	27.2914i	−0.491260	+	1.48226i
$340$	−0.492092	−	0.776432i	−0.0266874	−	0.0421079i
$341$	−4.60036	+	0.811167i	−0.249123	+	0.0439272i
$342$	−9.76403	+	28.6433i	−0.527978	+	1.54885i
$343$	19.7459	+	3.48174i	1.06618	+	0.187996i
$344$	−0.130252	−	0.353718i	−0.00702272	−	0.0190712i
$345$	1.35445	−	1.35430i	0.0729209	−	0.0729128i
$346$	−1.36855	+	8.82293i	−0.0735735	+	0.474324i
$347$	−13.9624	+	9.18321i	−0.749541	+	0.492981i	−0.865894	−	0.500227i	$-0.833250\pi$
$347$	−13.9624	+	9.18321i	−0.749541	+	0.492981i	0.116353	+	0.993208i	$0.462879\pi$
$348$	−2.21485	−	1.07885i	−0.118729	−	0.0578323i
$349$	−1.23308	−	4.11876i	−0.0660051	−	0.220472i	0.918623	−	0.395134i	$-0.129302\pi$
$349$	−1.23308	−	4.11876i	−0.0660051	−	0.220472i	−0.984628	+	0.174662i	$0.944117\pi$
$350$	13.5108	+	8.49184i	0.722181	+	0.453908i
$351$	1.63420	−	1.29172i	0.0872273	−	0.0689469i
$352$	2.17553	+	6.23040i	0.115956	+	0.332081i
$353$	−19.7237	−	18.6084i	−1.04979	−	0.990425i	−0.0498238	−	0.998758i	$-0.515866\pi$
$353$	−19.7237	−	18.6084i	−1.04979	−	0.990425i	−0.999965	+	0.00833311i	$0.997347\pi$
$354$	17.6531	−	8.67868i	0.938252	−	0.461267i
$355$	2.39649	−	0.139580i	0.127193	−	0.00740813i
$356$	17.2975	−	5.96703i	0.916766	−	0.316252i
$357$	2.84924	+	6.11110i	0.150798	+	0.323434i
$358$	2.76884	−	28.8416i	0.146338	−	1.52432i
$359$	−18.4511	+	6.71566i	−0.973812	+	0.354439i	−0.779432	−	0.626487i	$-0.784492\pi$
$359$	−18.4511	+	6.71566i	−0.973812	+	0.354439i	−0.194381	+	0.980926i	$0.562270\pi$
$360$	2.23066	−	0.537288i	0.117566	−	0.0283176i
$361$	29.9541	+	10.9024i	1.57653	+	0.573811i
$362$	7.18860	−	15.0823i	0.377825	−	0.792706i
$363$	7.92441	−	14.6948i	0.415924	−	0.771276i
$364$	−0.288289	−	1.81350i	−0.0151104	−	0.0950534i
$365$	0.947044	+	3.99589i	0.0495705	+	0.209155i
$366$	2.42867	−	4.12523i	0.126949	−	0.215629i
$367$	30.8723	+	13.3170i	1.61152	+	0.695142i	0.995691	−	0.0927383i	$-0.0295620\pi$
$367$	30.8723	+	13.3170i	1.61152	+	0.695142i	0.615829	+	0.787880i	$0.288821\pi$
$368$	14.3621	+	7.83096i	0.748678	+	0.408217i
$369$	20.2131	−	7.35444i	1.05225	−	0.382857i
$370$	0.191849	+	0.595766i	0.00997377	+	0.0309724i
$371$	0.881402	−	15.1331i	0.0457601	−	0.785671i
$372$	−12.9759	+	4.90217i	−0.672768	+	0.254166i
$373$	8.99170	+	20.8451i	0.465573	+	1.07932i	0.975678	+	0.219207i	$0.0703470\pi$
$373$	8.99170	+	20.8451i	0.465573	+	1.07932i	−0.510106	+	0.860112i	$0.670394\pi$
$374$	2.80370	−	0.0578957i	0.144976	−	0.00299371i
$375$	−2.20633	−	4.09243i	−0.113934	−	0.211332i
$376$	−23.3974	+	19.7833i	−1.20663	+	1.02025i
$377$	0.246909	−	0.142553i	0.0127165	−	0.00734185i
$378$	−16.7324	+	1.80988i	−0.860620	+	0.0930900i
$379$	4.90191	+	2.83012i	0.251794	+	0.145373i	0.620585	−	0.784139i	$-0.286895\pi$
$379$	4.90191	+	2.83012i	0.251794	+	0.145373i	−0.368791	+	0.929512i	$0.620228\pi$
$380$	−0.826095	−	3.76797i	−0.0423778	−	0.193293i
$381$	−20.7278	−	8.23594i	−1.06192	−	0.421940i
$382$	16.4944	−	9.98266i	0.843926	−	0.510757i
$383$	16.3865	+	1.91531i	0.837310	+	0.0978675i	0.523931	−	0.851761i	$-0.324465\pi$
$383$	16.3865	+	1.91531i	0.837310	+	0.0978675i	0.313379	+	0.949628i	$0.398539\pi$
$384$	9.78146	+	16.9801i	0.499158	+	0.866511i
$385$	0.645627	−	0.324246i	0.0329042	−	0.0165251i
$386$	2.41355	−	11.2101i	0.122846	−	0.570580i
$387$	0.114707	−	0.382994i	0.00583089	−	0.0194687i
$388$	−1.28575	−	12.8831i	−0.0652739	−	0.654042i
$389$	12.5090	−	9.31258i	0.634230	−	0.472167i	−0.231395	−	0.972860i	$-0.574329\pi$
$389$	12.5090	−	9.31258i	0.634230	−	0.472167i	0.865625	+	0.500693i	$0.166922\pi$
$390$	−0.0929327	+	0.248734i	−0.00470583	+	0.0125951i
$391$	5.05617	−	4.77025i	0.255702	−	0.241242i
$392$	1.94856	−	4.56443i	0.0984173	−	0.230538i
$393$	−6.29502	−	4.97802i	−0.317542	−	0.251108i
$394$	−2.30540	−	29.1867i	−0.116144	−	1.47040i
$395$	−1.45048	+	1.21709i	−0.0729814	+	0.0612386i
$396$	−2.12118	+	6.67048i	−0.106593	+	0.335204i
$397$	19.3197	+	16.2111i	0.969627	+	0.813613i	0.982492	−	0.186304i	$-0.0596509\pi$
$397$	19.3197	+	16.2111i	0.969627	+	0.813613i	−0.0128655	+	0.999917i	$0.504095\pi$
$398$	18.8669	−	26.4663i	0.945711	−	1.32664i
$399$	2.46449	+	28.1872i	0.123379	+	1.41113i
$400$	14.0004	−	13.8700i	0.700019	−	0.693498i
$401$	−9.20847	+	18.3356i	−0.459849	+	0.915635i	0.537528	+	0.843246i	$0.319358\pi$
$401$	−9.20847	+	18.3356i	−0.459849	+	0.915635i	−0.997377	+	0.0723884i	$0.976938\pi$
$402$	−5.72975	+	23.2919i	−0.285774	+	1.16170i
$403$	0.370192	−	1.56196i	0.0184406	−	0.0778069i
$404$	−0.927555	+	12.3340i	−0.0461476	+	0.613641i
$405$	2.23439	+	0.964408i	0.111028	+	0.0479218i
$406$	−2.30187	−	0.0864316i	−0.114240	−	0.00428953i
$407$	−1.85793	−	0.440337i	−0.0920941	−	0.0218267i
$408$	8.14872	−	1.71410i	0.403422	−	0.0848605i
$409$	−19.2963	−	9.69095i	−0.954139	−	0.479187i	−0.0975756	−	0.995228i	$-0.531109\pi$
$409$	−19.2963	−	9.69095i	−0.954139	−	0.479187i	−0.856564	+	0.516041i	$0.827405\pi$
$410$	−1.71866	+	2.13628i	−0.0848786	+	0.105504i
$411$	8.25057	−	17.6909i	0.406971	−	0.872625i
$412$	−9.54015	+	12.3729i	−0.470009	+	0.609570i
$413$	11.8224	−	14.0894i	0.581744	−	0.693295i
$414$	7.19793	+	15.7871i	0.353759	+	0.775896i
$415$	2.10472	+	2.50831i	0.103317	+	0.123128i
$416$	−2.26199	−	0.161551i	−0.110903	−	0.00792070i
$417$	28.1176	+	4.12021i	1.37693	+	0.201768i
$418$	11.1389	+	3.79568i	0.544821	+	0.185653i
$419$	−8.89326	−	9.42631i	−0.434464	−	0.460505i	0.472736	−	0.881204i	$-0.343266\pi$
$419$	−8.89326	−	9.42631i	−0.434464	−	0.460505i	−0.907200	+	0.420699i	$0.861785\pi$
$420$	1.70511	−	1.30190i	0.0832010	−	0.0635263i
$421$	−5.07311	−	6.81437i	−0.247248	−	0.332112i	0.661122	−	0.750278i	$-0.270080\pi$
$421$	−5.07311	−	6.81437i	−0.247248	−	0.332112i	−0.908371	+	0.418166i	$0.862673\pi$
$422$	24.5300	−	3.38184i	1.19410	−	0.164625i
$423$	−32.4440	+	1.88605i	−1.57748	+	0.0917027i
$424$	−17.9543	−	5.30163i	−0.871937	−	0.257470i
$425$	−3.75846	−	7.48370i	−0.182312	−	0.363013i
$426$	−6.41354	+	20.7784i	−0.310737	+	1.00672i
$427$	0.519620	−	4.44563i	0.0251462	−	0.215139i
$428$	−11.1011	+	6.16172i	−0.536594	+	0.297838i
$429$	−0.502378	−	0.635433i	−0.0242551	−	0.0306790i
$430$	0.0127741	+	0.0493358i	0.000616021	+	0.00237918i
$431$	13.1377	−	22.7552i	0.632821	−	1.09608i	−0.354151	−	0.935188i	$-0.615230\pi$
$431$	13.1377	−	22.7552i	0.632821	−	1.09608i	0.986972	−	0.160890i	$-0.0514364\pi$
$432$	−2.51294	+	20.6321i	−0.120904	+	0.992664i
$433$	3.08363	+	5.34100i	0.148190	+	0.256672i	0.930558	−	0.366143i	$-0.119322\pi$
$433$	3.08363	+	5.34100i	0.148190	+	0.256672i	−0.782369	+	0.622816i	$0.785989\pi$
$434$	−9.24781	+	9.09298i	−0.443909	+	0.436477i
$435$	0.283487	+	0.174879i	0.0135922	+	0.00838481i
$436$	0.505091	−	29.9125i	0.0241895	−	1.43255i
$437$	26.7844	−	11.5537i	1.28127	−	0.552687i
$438$	−36.9105	−	4.63246i	−1.76365	−	0.221348i
$439$	20.7748	+	1.20999i	0.991527	+	0.0577499i	0.546232	−	0.837634i	$-0.316062\pi$
$439$	20.7748	+	1.20999i	0.991527	+	0.0577499i	0.445295	+	0.895384i	$0.353099\pi$
$440$	−0.209030	−	0.867408i	−0.00996511	−	0.0413521i
$441$	4.55905	−	2.63150i	0.217098	−	0.125309i
$442$	−0.363335	+	0.892535i	−0.0172821	+	0.0424535i
$443$	−1.55783	+	3.61146i	−0.0740148	+	0.171586i	−0.951207	−	0.308554i	$-0.900155\pi$
$443$	−1.55783	+	3.61146i	−0.0740148	+	0.171586i	0.877192	+	0.480140i	$0.159414\pi$
$444$	−5.66374	−	0.260876i	−0.268789	−	0.0123806i
$445$	−2.40721	+	0.570520i	−0.114113	+	0.0270452i
$446$	−4.32382	−	21.8710i	−0.204739	−	1.03562i
$447$	−29.8779	+	18.4267i	−1.41318	+	0.871552i
$448$	14.7785	+	10.8303i	0.698221	+	0.511684i
$449$	−10.7530	+	29.5435i	−0.507464	+	1.39425i	0.376381	+	0.926465i	$0.377168\pi$
$449$	−10.7530	+	29.5435i	−0.507464	+	1.39425i	−0.883845	+	0.467780i	$0.845054\pi$
$450$	20.7074	−	2.85251i	0.976158	−	0.134469i
$451$	−2.86077	−	7.85991i	−0.134709	−	0.370109i
$452$	32.9048	+	4.41034i	1.54771	+	0.207445i
$453$	29.2151	+	20.4590i	1.37265	+	0.961250i
$454$	−2.02367	−	5.22194i	−0.0949757	−	0.245078i
$455$	0.0144355	+	0.247848i	0.000676746	+	0.0116193i
$456$	34.5929	+	4.93618i	1.61996	+	0.231158i
$457$	1.70107	−	1.80303i	0.0795727	−	0.0843422i	−0.686364	−	0.727258i	$-0.740794\pi$
$457$	1.70107	−	1.80303i	0.0795727	−	0.0843422i	0.765936	+	0.642916i	$0.222276\pi$
$458$	−10.9014	−	20.6330i	−0.509389	−	0.964116i
$459$	8.00404	+	3.73396i	0.373597	+	0.174287i
$460$	−1.82705	−	1.24636i	−0.0851866	−	0.0581119i
$461$	22.0987	−	6.61590i	1.02924	−	0.308133i	0.272710	−	0.962096i	$-0.412080\pi$
$461$	22.0987	−	6.61590i	1.02924	−	0.308133i	0.756527	+	0.653963i	$0.226895\pi$
$462$	0.704523	+	6.50660i	0.0327774	+	0.302714i
$463$	15.8809	+	24.1458i	0.738050	+	1.12215i	0.988084	+	0.153914i	$0.0491878\pi$
$463$	15.8809	+	24.1458i	0.738050	+	1.12215i	−0.250034	+	0.968237i	$0.580442\pi$
$464$	−0.749127	+	2.74435i	−0.0347773	+	0.127403i
$465$	1.81151	−	0.485285i	0.0840068	−	0.0225046i
$466$	7.51184	+	16.4708i	0.347979	+	0.762995i
$467$	−5.32065	+	30.1749i	−0.246210	+	1.39633i	0.571454	+	0.820634i	$0.306379\pi$
$467$	−5.32065	+	30.1749i	−0.246210	+	1.39633i	−0.817665	+	0.575695i	$0.804732\pi$
$468$	−1.81604	−	1.57720i	−0.0839464	−	0.0729059i
$469$	3.89444	+	22.0865i	0.179828	+	1.01986i
$470$	3.41336	−	2.34737i	0.157447	−	0.108276i
$471$	1.00160	+	4.85210i	0.0461513	+	0.223573i
$472$	−13.6325	−	18.1684i	−0.627484	−	0.836270i
$473$	−0.148939	−	0.0445894i	−0.00684822	−	0.00205022i
$474$	−5.72922	−	16.1670i	−0.263152	−	0.742576i
$475$	−4.07978	−	34.9047i	−0.187193	−	1.60154i
$476$	6.32276	−	4.54324i	0.289803	−	0.208239i
$477$	−11.8556	−	15.9285i	−0.542830	−	0.729316i
$478$	−14.6078	−	13.2225i	−0.668144	−	0.604782i
$479$	−23.6914	−	15.5821i	−1.08249	−	0.711963i	−0.122630	−	0.992453i	$-0.539133\pi$
$479$	−23.6914	−	15.5821i	−1.08249	−	0.711963i	−0.959857	+	0.280490i	$0.909503\pi$
$480$	−1.08795	−	2.41572i	−0.0496580	−	0.110262i
$481$	0.391817	−	0.526302i	0.0178653	−	0.0239973i
$482$	−15.3168	−	8.42640i	−0.697660	−	0.383812i
$483$	12.1182	+	10.7855i	0.551399	+	0.490758i
$484$	−18.3722	−	5.84003i	−0.835101	−	0.265456i
$485$			1.75048i			0.0794852i
$486$	−15.2677	+	15.9027i	−0.692557	+	0.721363i
$487$		−	8.08316i		−	0.366283i	−0.983087	−	0.183142i	$-0.941373\pi$
$487$		−	8.08316i		−	0.366283i	0.983087	−	0.183142i	$-0.0586267\pi$
$488$	−5.20135	−	1.87100i	−0.235454	−	0.0846962i
$489$	7.29968	+	6.49689i	0.330103	+	0.293799i
$490$	−0.323432	+	0.587906i	−0.0146112	+	0.0265589i
$491$	−1.85831	+	2.49615i	−0.0838645	+	0.112650i	−0.842075	−	0.539360i	$-0.818666\pi$
$491$	−1.85831	+	2.49615i	−0.0838645	+	0.112650i	0.758211	+	0.652009i	$0.226074\pi$
$492$	−12.6789	−	21.3570i	−0.571609	−	0.962849i
$493$	1.00998	+	0.664271i	0.0454870	+	0.0299173i
$494$	−2.71374	+	2.99805i	−0.122097	+	0.134889i
$495$	0.374931	−	0.868924i	0.0168519	−	0.0390552i
$496$	8.34459	+	13.6714i	0.374683	+	0.613864i
$497$	2.36043	+	20.1948i	0.105880	+	0.905858i
$498$	−27.9577	+	9.90755i	−1.25281	+	0.443968i
$499$	−30.6381	−	9.17243i	−1.37155	−	0.410614i	−0.485511	−	0.874230i	$-0.661367\pi$
$499$	−30.6381	−	9.17243i	−1.37155	−	0.410614i	−0.886036	+	0.463616i	$0.846552\pi$
$500$	−4.17021	+	3.38090i	−0.186498	+	0.151199i
$501$	5.15862	+	24.9902i	0.230470	+	1.11648i
$502$	4.35810	+	6.33721i	0.194511	+	0.282843i
$503$	−1.24719	−	7.07316i	−0.0556094	−	0.315377i	0.944296	−	0.329096i	$-0.106744\pi$
$503$	−1.24719	−	7.07316i	−0.0556094	−	0.315377i	−0.999906	+	0.0137193i	$0.995633\pi$
$504$	5.64157	+	18.5967i	0.251295	+	0.828362i
$505$	0.290391	−	1.64689i	0.0129222	−	0.0732856i
$506$	6.13880	−	2.79972i	0.272903	−	0.124463i
$507$	−21.4809	+	5.75451i	−0.953999	+	0.255567i
$508$	−4.89980	+	25.2841i	−0.217393	+	1.12180i
$509$	−23.8083	−	36.1988i	−1.05528	−	1.60448i	−0.760986	−	0.648768i	$-0.775285\pi$
$509$	−23.8083	−	36.1988i	−1.05528	−	1.60448i	−0.294298	−	0.955714i	$-0.595086\pi$
$510$	−1.11929	+	0.121195i	−0.0495630	+	0.00536660i
$511$	−33.3208	+	9.97558i	−1.47402	+	0.441294i
$512$	17.1683	−	14.7394i	0.758740	−	0.651394i
$513$	26.2032	+	26.2119i	1.15690	+	1.15728i
$514$	12.4790	−	6.59323i	0.550423	−	0.290815i
$515$	1.44960	−	1.53648i	0.0638768	−	0.0677055i
$516$	−0.459148	−	0.0480198i	−0.0202129	−	0.00211395i
$517$	0.734819	+	12.6163i	0.0323173	+	0.554866i
$518$	−4.94301	+	1.91558i	−0.217183	+	0.0841656i
$519$	8.95713	+	6.27259i	0.393174	+	0.275336i
$520$	0.302145	+	0.0521048i	0.0132499	+	0.00228495i
$521$	−1.86078	−	5.11245i	−0.0815222	−	0.223980i	0.892234	−	0.451573i	$-0.149137\pi$
$521$	−1.86078	−	5.11245i	−0.0815222	−	0.223980i	−0.973756	+	0.227592i	$0.926915\pi$
$522$	−2.38275	+	1.85114i	−0.104290	+	0.0810221i
$523$	−11.1462	+	30.6240i	−0.487390	+	1.33909i	0.415645	+	0.909527i	$0.363556\pi$
$523$	−11.1462	+	30.6240i	−0.487390	+	1.33909i	−0.903035	+	0.429567i	$0.858666\pi$
$524$	−4.29824	+	8.20990i	−0.187770	+	0.358651i
$525$	16.6350	−	10.2594i	0.726012	−	0.447755i
$526$	0.455990	−	0.0901476i	0.0198821	−	0.00393062i
$527$	6.62270	−	1.56961i	0.288490	−	0.0683733i
$528$	8.02328	+	0.976314i	0.349168	+	0.0424886i
$529$	−2.48553	+	5.76210i	−0.108066	+	0.250526i
$530$	2.34427	+	0.954312i	0.101829	+	0.0414527i
$531$	0.00266587	−	24.0921i	0.000115689	−	1.04551i
$532$	31.4531	−	8.84066i	1.36367	−	0.383291i
$533$	2.86942	+	0.167125i	0.124288	+	0.00723898i
$534$	2.79070	−	22.2357i	0.120765	−	0.962232i
$535$	1.57621	−	0.679909i	0.0681454	−	0.0293950i
$536$	27.6560	+	1.50638i	1.19456	+	0.0650659i
$537$	−30.2017	−	18.6310i	−1.30330	−	0.803986i
$538$	15.3266	+	15.5876i	0.660778	+	0.672030i
$539$	−1.02350	−	1.77276i	−0.0440853	−	0.0763580i
$540$	0.615094	−	2.74198i	0.0264694	−	0.117996i
$541$	7.33662	−	12.7074i	0.315426	−	0.546333i	−0.664102	−	0.747642i	$-0.731186\pi$
$541$	7.33662	−	12.7074i	0.315426	−	0.546333i	0.979528	+	0.201308i	$0.0645193\pi$
$542$	13.7767	−	3.56707i	0.591758	−	0.153219i
$543$	−12.6909	−	16.0520i	−0.544617	−	0.688859i
$544$	−3.69223	−	8.87808i	−0.158303	−	0.380645i
$545$	−0.469574	+	4.01746i	−0.0201143	+	0.172089i
$546$	−2.14893	−	0.663295i	−0.0919656	−	0.0283864i
$547$	8.03214	+	15.9933i	0.343429	+	0.683824i	0.997351	−	0.0727380i	$-0.0231737\pi$
$547$	8.03214	+	15.9933i	0.343429	+	0.683824i	−0.653922	+	0.756562i	$0.726877\pi$
$548$	−21.8415	−	5.56763i	−0.933024	−	0.237837i
$549$	−3.22119	−	4.89876i	−0.137477	−	0.209074i
$550$	−1.11014	−	8.05233i	−0.0473366	−	0.343353i
$551$	3.02924	+	4.06898i	0.129050	+	0.173344i
$552$	16.3688	−	11.5522i	0.696703	−	0.491696i
$553$	−11.0054	−	11.6651i	−0.467998	−	0.496049i
$554$	8.88317	−	26.0688i	0.377410	−	1.10756i
$555$	0.758461	+	0.111141i	0.0321949	+	0.00471767i
$556$	−1.35463	−	32.7862i	−0.0574491	−	1.39044i
$557$	16.5073	+	19.6726i	0.699435	+	0.833554i	0.992462	−	0.122550i	$-0.0391072\pi$
$557$	16.5073	+	19.6726i	0.699435	+	0.833554i	−0.293027	+	0.956104i	$0.594663\pi$
$558$	−1.62533	+	16.9105i	−0.0688056	+	0.715879i
$559$	0.0343410	−	0.0409260i	0.00145247	−	0.00173098i
$560$	−1.84280	−	1.65547i	−0.0778724	−	0.0699563i
$561$	1.45167	−	3.11267i	0.0612897	−	0.131417i
$562$	−12.6981	−	10.2157i	−0.535637	−	0.430925i
$563$	−15.7546	−	7.91226i	−0.663977	−	0.333462i	0.0846905	−	0.996407i	$-0.473010\pi$
$563$	−15.7546	−	7.91226i	−0.663977	−	0.333462i	−0.748668	+	0.662945i	$0.769306\pi$
$564$	9.09716	+	36.4070i	0.383060	+	1.53301i
$565$	−4.36758	−	1.03514i	−0.183746	−	0.0435485i
$566$	−0.821156	+	21.8692i	−0.0345158	+	0.919233i
$567$	−7.05415	+	19.3678i	−0.296246	+	0.813370i
$568$	24.9508	+	2.82121i	1.04691	+	0.118375i
$569$	3.38233	−	14.2712i	0.141795	−	0.598279i	−0.855025	−	0.518587i	$-0.826458\pi$
$569$	3.38233	−	14.2712i	0.141795	−	0.598279i	0.996820	−	0.0796922i	$-0.0253937\pi$
$570$	−4.58764	−	1.12855i	−0.192155	−	0.0472696i
$571$	4.05698	−	8.07811i	0.169779	−	0.338058i	−0.792612	−	0.609727i	$-0.791279\pi$
$571$	4.05698	−	8.07811i	0.169779	−	0.338058i	0.962391	+	0.271669i	$0.0875755\pi$
$572$	−0.613243	+	0.706267i	−0.0256410	+	0.0295305i
$573$	−2.05671	−	23.5233i	−0.0859205	−	0.982702i
$574$	−18.9097	−	13.4800i	−0.789275	−	0.562646i
$575$	−15.4349	−	12.9515i	−0.643682	−	0.540113i
$576$	23.9484	−	1.57310i	0.997850	−	0.0655456i
$577$	30.0461	−	25.2117i	1.25084	−	1.04958i	0.254240	−	0.967141i	$-0.418175\pi$
$577$	30.0461	−	25.2117i	1.25084	−	1.04958i	0.996596	−	0.0824347i	$-0.0262696\pi$
$578$	19.8938	−	1.57137i	0.827472	−	0.0653605i
$579$	−11.0160	−	8.71128i	−0.457808	−	0.362029i
$580$	0.137630	−	0.359149i	0.00571477	−	0.0149129i
$581$	−20.1724	+	19.0317i	−0.836894	+	0.789569i
$582$	−14.8540	−	5.54981i	−0.615719	−	0.230047i
$583$	−6.19357	+	4.61094i	−0.256511	+	0.190966i
$584$	2.65895	+	42.8725i	0.110028	+	1.77408i
$585$	0.223142	+	0.236569i	0.00922579	+	0.00978093i
$586$	37.7731	+	8.13259i	1.56039	+	0.335954i
$587$	−10.1576	+	5.10134i	−0.419249	+	0.210555i	−0.645901	−	0.763421i	$-0.723518\pi$
$587$	−10.1576	+	5.10134i	−0.419249	+	0.210555i	0.226652	+	0.973976i	$0.427222\pi$
$588$	−3.96337	−	4.60847i	−0.163447	−	0.190050i
$589$	28.3680	+	3.31575i	1.16888	+	0.136623i
$590$	1.59008	+	2.62730i	0.0654627	+	0.108164i
$591$	−33.3234	−	13.2407i	−1.37074	−	0.544649i
$592$	0.918528	+	6.48210i	0.0377513	+	0.266413i
$593$	−27.0991	−	15.6456i	−1.11282	−	0.642490i	−0.173265	−	0.984875i	$-0.555432\pi$
$593$	−27.0991	−	15.6456i	−1.11282	−	0.642490i	−0.939560	+	0.342386i	$0.888765\pi$
$594$	6.18472	+	5.93643i	0.253762	+	0.243575i
$595$	−0.911624	+	0.526326i	−0.0373729	+	0.0215773i
$596$	27.3141	+	29.9485i	1.11883	+	1.22674i
$597$	−18.8907	−	35.0397i	−0.773146	−	1.43408i
$598$	0.0478671	+	2.31805i	0.00195743	+	0.0947920i
$599$	−3.57972	−	8.29871i	−0.146263	−	0.339076i	0.829297	−	0.558808i	$-0.188741\pi$
$599$	−3.57972	−	8.29871i	−0.146263	−	0.339076i	−0.975560	+	0.219732i	$0.929482\pi$
$600$	−7.67696	−	22.8833i	−0.313411	−	0.934206i
$601$	−1.33245	+	22.8773i	−0.0543519	+	0.933186i	0.855383	+	0.517996i	$0.173322\pi$
$601$	−1.33245	+	22.8773i	−0.0543519	+	0.933186i	−0.909735	+	0.415190i	$0.863715\pi$
$602$	−0.410866	+	0.132308i	−0.0167457	+	0.00539245i
$603$	22.5021	+	18.8857i	0.916356	+	0.769087i
$604$	16.9483	−	37.5351i	0.689617	−	1.52728i
$605$	2.39327	+	1.03236i	0.0973002	+	0.0419712i
$606$	13.0543	+	7.68555i	0.530296	+	0.312204i
$607$	−0.0800392	−	0.337712i	−0.00324869	−	0.0137073i	0.971396	−	0.237464i	$-0.0763161\pi$
$607$	−0.0800392	−	0.337712i	−0.00324869	−	0.0137073i	−0.974645	+	0.223756i	$0.928168\pi$
$608$	−1.81737	−	40.3081i	−0.0737042	−	1.63471i
$609$	−1.33908	+	2.48314i	−0.0542621	+	0.100622i
$610$	0.674635	+	0.321549i	0.0273152	+	0.0130191i
$611$	−4.08087	−	1.48532i	−0.165094	−	0.0600894i
$612$	2.52024	−	9.88220i	0.101875	−	0.399464i
$613$	−36.8304	+	13.4052i	−1.48757	+	0.541429i	−0.952807	−	0.303576i	$-0.901819\pi$
$613$	−36.8304	+	13.4052i	−1.48757	+	0.541429i	−0.534758	+	0.845005i	$0.679597\pi$
$614$	−6.48062	−	0.622151i	−0.261537	−	0.0251080i
$615$	1.41899	+	3.04347i	0.0572192	+	0.122725i
$616$	7.23141	−	2.19462i	0.291362	−	0.0884239i
$617$	13.1938	−	0.768450i	0.531162	−	0.0309366i	0.209531	−	0.977802i	$-0.432806\pi$
$617$	13.1938	−	0.768450i	0.531162	−	0.0309366i	0.321630	+	0.946865i	$0.395769\pi$
$618$	8.44224	+	17.1722i	0.339597	+	0.690766i
$619$	−11.1792	−	10.5470i	−0.449329	−	0.423920i	0.428023	−	0.903768i	$-0.359210\pi$
$619$	−11.1792	−	10.5470i	−0.449329	−	0.423920i	−0.877352	+	0.479848i	$0.840692\pi$
$620$	−0.939069	−	1.95130i	−0.0377139	−	0.0783662i
$621$	21.2410	+	0.621579i	0.852372	+	0.0249431i
$622$	−16.8620	+	26.8279i	−0.676103	+	1.07570i
$623$	−6.00951	−	20.0732i	−0.240766	−	0.804214i
$624$	−1.40008	+	2.39871i	−0.0560482	+	0.0960254i
$625$	−19.9753	+	13.1380i	−0.799013	+	0.525519i
$626$	42.2730	+	6.55707i	1.68957	+	0.262073i
$627$	10.1918	−	10.1907i	0.407022	−	0.406977i
$628$	5.29049	−	2.17690i	0.211113	−	0.0868679i
$629$	2.73974	+	0.483091i	0.109241	+	0.0192621i
$630$	−0.509292	−	2.57763i	−0.0202907	−	0.102695i
$631$	35.1768	−	6.20263i	1.40037	−	0.246923i	0.578073	−	0.815985i	$-0.303805\pi$
$631$	35.1768	−	6.20263i	1.40037	−	0.246923i	0.822295	+	0.569062i	$0.192694\pi$
$632$	−17.1148	+	9.96728i	−0.680790	+	0.396477i
$633$	9.54083	−	28.7873i	0.379214	−	1.14419i
$634$	17.9356	−	15.6920i	0.712314	−	0.623210i
$635$	0.998666	−	3.33578i	0.0396309	−	0.132376i
$636$	−15.5304	+	16.8672i	−0.615821	+	0.668828i
$637$	0.698666	−	0.0816623i	0.0276821	−	0.00323558i
$638$	0.719951	+	0.926496i	0.0285031	+	0.0366803i
$639$	19.3701	+	18.2788i	0.766270	+	0.723098i
$640$	−2.50762	+	1.75243i	−0.0991222	+	0.0692708i
$641$	−11.0370	+	16.7810i	−0.435936	+	0.662809i	−0.984917	−	0.173026i	$-0.944646\pi$
$641$	−11.0370	+	16.7810i	−0.435936	+	0.662809i	0.548981	+	0.835835i	$0.315016\pi$
$642$	0.772212	+	15.5308i	0.0304768	+	0.612953i
$643$	12.0327	+	8.95804i	0.474525	+	0.353270i	0.807699	−	0.589595i	$-0.200713\pi$
$643$	12.0327	+	8.95804i	0.474525	+	0.353270i	−0.333175	+	0.942865i	$0.608120\pi$
$644$	9.63880	−	16.0624i	0.379822	−	0.632946i
$645$	0.0611261	+	0.0126251i	0.00240684	+	0.000497111i
$646$	−16.5236	−	4.57733i	−0.650111	−	0.180093i
$647$	1.54048			0.0605626			0.0302813	−	0.999541i	$-0.490360\pi$
$647$	1.54048			0.0605626			0.0302813	+	0.999541i	$0.490360\pi$
$648$	21.3175	+	13.9128i	0.837429	+	0.546547i
$649$	−9.36863			−0.367751
$650$	2.69186	+	0.745694i	0.105584	+	0.0292485i
$651$	4.99544	+	15.0782i	0.195787	+	0.590961i
$652$	5.80613	−	9.67550i	0.227386	−	0.378922i
$653$	−38.1178	−	28.3777i	−1.49167	−	1.11050i	−0.965591	−	0.260066i	$-0.916256\pi$
$653$	−38.1178	−	28.3777i	−1.49167	−	1.11050i	−0.526075	−	0.850438i	$-0.676337\pi$
$654$	−32.6022	−	16.7218i	−1.27485	−	0.653875i
$655$	0.688489	−	1.04680i	0.0269015	−	0.0409017i
$656$	−21.5131	+	18.9654i	−0.839947	+	0.740476i
$657$	−25.0401	+	38.0625i	−0.976909	+	1.48496i
$658$	21.5291	+	27.7056i	0.839293	+	1.08008i
$659$	0.750282	−	0.0876954i	0.0292268	−	0.00341613i	−0.101467	−	0.994839i	$-0.532354\pi$
$659$	0.750282	−	0.0876954i	0.0292268	−	0.00341613i	0.130694	+	0.991423i	$0.458280\pi$
$660$	−1.06629	−	0.239072i	−0.0415054	−	0.00930587i
$661$	13.0432	−	43.5672i	0.507320	−	1.69457i	−0.193390	−	0.981122i	$-0.561948\pi$
$661$	13.0432	−	43.5672i	0.507320	−	1.69457i	0.700710	−	0.713446i	$-0.252867\pi$
$662$	−23.3523	+	20.4311i	−0.907612	+	0.794078i
$663$	0.784564	+	0.881706i	0.0304699	+	0.0342426i
$664$	17.2364	+	29.5966i	0.668904	+	1.14857i
$665$	−4.35021	+	0.767059i	−0.168694	+	0.0297453i
$666$	−3.34777	+	6.08370i	−0.129724	+	0.235739i
$667$	2.86428	+	0.505050i	0.110905	+	0.0195556i
$668$	27.2480	−	11.2119i	1.05426	−	0.433801i
$669$	−26.3740	−	7.06846i	−1.01968	−	0.273282i
$670$	−3.70044	−	0.573984i	−0.142961	−	0.0221750i
$671$	−1.90483	+	1.25283i	−0.0735352	+	0.0483649i
$672$	19.8903	−	10.3888i	0.767285	−	0.400758i
$673$	6.25236	+	20.8843i	0.241011	+	0.805032i	0.989830	+	0.142257i	$0.0454361\pi$
$673$	6.25236	+	20.8843i	0.241011	+	0.805032i	−0.748819	+	0.662775i	$0.769379\pi$
$674$	−15.5627	+	24.7607i	−0.599454	+	0.953748i
$675$	8.05664	−	24.3001i	0.310100	−	0.935310i
$676$	11.1355	+	23.1385i	0.428287	+	0.889943i
$677$	6.19480	+	5.84449i	0.238086	+	0.224622i	0.796032	−	0.605255i	$-0.206929\pi$
$677$	6.19480	+	5.84449i	0.238086	+	0.224622i	−0.557946	+	0.829877i	$0.688410\pi$
$678$	22.6311	−	33.7801i	0.869141	−	1.29732i
$679$	−14.8011	+	0.862068i	−0.568015	+	0.0330831i
$680$	0.377528	+	1.24397i	0.0144775	+	0.0477043i
$681$	−6.83287	−	0.598179i	−0.261836	−	0.0229223i
$682$	6.57602	+	0.631309i	0.251809	+	0.0241741i
$683$	−16.0221	+	5.83156i	−0.613068	+	0.223139i	−0.629845	−	0.776721i	$-0.716882\pi$
$683$	−16.0221	+	5.83156i	−0.613068	+	0.223139i	0.0167770	+	0.999859i	$0.494659\pi$
$684$	24.1214	−	35.3513i	0.922305	−	1.35169i
$685$	2.86367	+	1.04229i	0.109415	+	0.0398238i
$686$	−25.5970	−	12.2002i	−0.977296	−	0.465805i
$687$	−28.5684	+	0.829673i	−1.08995	+	0.0316540i
$688$	0.0439748	+	0.531253i	0.00167652	+	0.0202538i
$689$	−0.611909	−	2.58185i	−0.0233119	−	0.0983605i
$690$	−2.35726	+	1.33439i	−0.0897395	+	0.0507993i
$691$	4.38418	+	1.89115i	0.166782	+	0.0719428i	0.477834	−	0.878450i	$-0.341422\pi$
$691$	4.38418	+	1.89115i	0.166782	+	0.0719428i	−0.311052	+	0.950393i	$0.600681\pi$
$692$	5.19622	−	11.5080i	0.197531	−	0.437467i
$693$	7.53181	+	2.74230i	0.286110	+	0.104171i
$694$	22.4962	−	7.24426i	0.853946	−	0.274988i
$695$	−0.257962	+	4.42903i	−0.00978505	+	0.168003i
$696$	2.61128	+	2.30655i	0.0989804	+	0.0874296i
$697$	4.82699	+	11.1902i	0.182835	+	0.423860i
$698$	0.125529	+	6.07895i	0.00475134	+	0.230092i
$699$	22.1620	+	0.646076i	0.838245	+	0.0244368i
$700$	−15.2076	−	16.6743i	−0.574793	−	0.630230i
$701$	−37.8322	+	21.8424i	−1.42890	+	0.824976i	−0.997034	−	0.0769612i	$-0.975478\pi$
$701$	−37.8322	+	21.8424i	−1.42890	+	0.824976i	−0.431867	+	0.901937i	$0.642145\pi$
$702$	−2.71492	+	1.14348i	−0.102468	+	0.0431580i
$703$	10.1103	+	5.83716i	0.381316	+	0.220153i
$704$	−0.612756	−	9.31269i	−0.0230941	−	0.350985i
$705$	−0.735054	−	5.02011i	−0.0276837	−	0.189068i
$706$	19.8557	+	32.8077i	0.747281	+	1.23473i
$707$	14.0682	+	1.64434i	0.529091	+	0.0618418i
$708$	−27.3358	+	5.16323i	−1.02734	+	0.194046i
$709$	−30.5735	+	15.3546i	−1.14821	+	0.576654i	−0.918037	−	0.396496i	$-0.870226\pi$
$709$	−30.5735	+	15.3546i	−1.14821	+	0.576654i	−0.230175	+	0.973149i	$0.573930\pi$
$710$	−3.31885	−	0.714551i	−0.124554	−	0.0268166i
$711$	−20.8647	−	2.44108i	−0.782488	−	0.0915475i
$712$	−25.8274	+	1.60181i	−0.967921	+	0.0600303i
$713$	13.1352	−	9.77880i	0.491917	−	0.366219i
$714$	−1.57598	−	9.40445i	−0.0589797	−	0.351953i
$715$	0.0919845	−	0.0867829i	0.00344003	−	0.00324550i
$716$	−14.6626	+	38.2624i	−0.547967	+	1.42993i
$717$	−22.4271	+	8.90827i	−0.837555	+	0.332686i
$718$	27.6822	−	2.18657i	1.03309	−	0.0816020i
$719$	−6.51635	+	5.46786i	−0.243019	+	0.203917i	−0.756159	−	0.654388i	$-0.772926\pi$
$719$	−6.51635	+	5.46786i	−0.243019	+	0.203917i	0.513140	+	0.858305i	$0.328482\pi$
$720$	−3.24299	−	0.109910i	−0.120859	−	0.00409610i
$721$	13.7056	+	11.5003i	0.510422	+	0.428295i
$722$	−36.7080	−	26.1678i	−1.36613	−	0.973864i
$723$	−17.5392	+	12.2796i	−0.652289	+	0.456684i
$724$	−15.4915	+	17.8414i	−0.575736	+	0.663071i
$725$	1.57257	−	3.13124i	0.0584037	−	0.116291i
$726$	−16.3480	+	17.0355i	−0.606731	+	0.632247i
$727$	−1.99951	+	8.43659i	−0.0741577	+	0.312896i	−0.997464	−	0.0711676i	$-0.977327\pi$
$727$	−1.99951	+	8.43659i	−0.0741577	+	0.312896i	0.923307	+	0.384064i	$0.125476\pi$
$728$	−0.291772	+	2.58044i	−0.0108138	+	0.0956375i
$729$	9.22612	+	25.3748i	0.341708	+	0.939806i
$730$	0.217912	−	5.80350i	0.00806530	−	0.214797i
$731$	0.220416	+	0.0522395i	0.00815237	+	0.00193215i
$732$	−4.86746	+	4.70529i	−0.179907	+	0.173913i
$733$	−17.3289	−	8.70292i	−0.640059	−	0.321450i	0.0990030	−	0.995087i	$-0.468435\pi$
$733$	−17.3289	−	8.70292i	−0.640059	−	0.321450i	−0.739062	+	0.673637i	$0.764731\pi$
$734$	−37.0477	−	29.8052i	−1.36745	−	1.10013i
$735$	0.471331	+	0.673209i	0.0173853	+	0.0248317i
$736$	−16.6174	−	16.0950i	−0.612527	−	0.593271i
$737$	7.34309	−	8.75115i	0.270486	−	0.322353i
$738$	−30.3248	+	2.39192i	−1.11627	+	0.0880479i
$739$	−24.5265	−	29.2295i	−0.902220	−	1.07522i	−0.996818	−	0.0797085i	$-0.974601\pi$
$739$	−24.5265	−	29.2295i	−0.902220	−	1.07522i	0.0945982	−	0.995516i	$-0.469843\pi$
$740$	−0.0365406	−	0.884394i	−0.00134326	−	0.0325110i
$741$	1.82831	+	4.60286i	0.0671645	+	0.169090i
$742$	−6.91466	+	20.2919i	−0.253845	+	0.744940i
$743$	0.231105	+	0.244957i	0.00847842	+	0.00898660i	0.731599	−	0.681735i	$-0.238774\pi$
$743$	0.231105	+	0.244957i	0.00847842	+	0.00898660i	−0.723121	+	0.690722i	$0.757293\pi$
$744$	19.5354	−	1.78214i	0.716204	−	0.0653362i
$745$	−3.27257	−	4.39582i	−0.119898	−	0.161050i
$746$	−4.38472	−	31.8043i	−0.160536	−	1.16444i
$747$	−4.22136	+	36.0814i	−0.154451	+	1.32015i
$748$	−3.84298	−	0.979614i	−0.140513	−	0.0358182i
$749$	6.52520	+	12.9927i	0.238426	+	0.474744i
$750$	1.46190	+	6.41051i	0.0533811	+	0.234079i
$751$	−3.81464	+	32.6364i	−0.139198	+	1.19092i	0.725354	+	0.688376i	$0.241676\pi$
$751$	−3.81464	+	32.6364i	−0.139198	+	1.19092i	−0.864553	+	0.502542i	$0.832398\pi$
$752$	39.3571	−	18.1288i	1.43521	−	0.661090i
$753$	9.32027	−	1.36469i	0.339649	−	0.0497321i
$754$	−0.390329	+	0.101064i	−0.0142149	+	0.00368055i
$755$	−2.78408	+	4.82217i	−0.101323	+	0.175497i
$756$	23.4876	+	3.85055i	0.854237	+	0.140043i
$757$	−6.88494	−	11.9251i	−0.250237	−	0.433424i	0.713354	−	0.700804i	$-0.247175\pi$
$757$	−6.88494	−	11.9251i	−0.250237	−	0.433424i	−0.963591	+	0.267380i	$0.913842\pi$
$758$	−5.61225	−	5.70782i	−0.203846	−	0.207317i
$759$	0.240798	−	8.25997i	0.00874041	−	0.299818i
$760$	−0.296701	+	5.44720i	−0.0107625	+	0.197591i
$761$	43.5356	−	18.7794i	1.57816	−	0.680753i	0.586540	−	0.809920i	$-0.300490\pi$
$761$	43.5356	−	18.7794i	1.57816	−	0.680753i	0.991623	+	0.129167i	$0.0412303\pi$
$762$	25.1402	+	19.0503i	0.910732	+	0.690120i
$763$	−34.2008	−	1.99197i	−1.23815	−	0.0721141i
$764$	−26.2489	+	7.37787i	−0.949651	+	0.266922i
$765$	−0.471741	+	1.29565i	−0.0170558	+	0.0468444i
$766$	−21.6098	−	8.79697i	−0.780794	−	0.317847i
$767$	1.27514	−	2.95610i	0.0460425	−	0.106738i
$768$	−6.92030	−	26.8349i	−0.249715	−	0.968319i
$769$	22.6880	−	5.37715i	0.818149	−	0.193905i	0.199829	−	0.979831i	$-0.435961\pi$
$769$	22.6880	−	5.37715i	0.818149	−	0.193905i	0.618321	+	0.785926i	$0.287813\pi$
$770$	−1.00233	+	0.198158i	−0.0361216	+	0.00714112i
$771$	−0.501792	−	17.2783i	−0.0180716	−	0.622264i
$772$	−7.52171	+	14.3669i	−0.270712	+	0.517076i
$773$	−12.8772	+	35.3798i	−0.463161	+	1.27252i	0.459935	+	0.887953i	$0.347873\pi$
$773$	−12.8772	+	35.3798i	−0.463161	+	1.27252i	−0.923096	+	0.384571i	$0.874350\pi$
$774$	−0.300930	+	0.478670i	−0.0108167	+	0.0172055i
$775$	−6.74747	−	18.5385i	−0.242376	−	0.665923i
$776$	−3.11163	+	18.0437i	−0.111701	+	0.647731i
$777$	−0.566227	+	6.46788i	−0.0203133	+	0.232034i
$778$	−20.5642	+	7.96931i	−0.737263	+	0.285713i
$779$	2.97357	+	51.0543i	0.106539	+	1.82921i
$780$	0.220565	−	0.303910i	0.00789748	−	0.0108817i
$781$	7.10720	−	7.53320i	0.254316	−	0.269559i
$782$	−8.69197	+	4.59239i	−0.310824	+	0.164223i
$783$	0.746684	+	3.61923i	0.0266843	+	0.129341i
$784$	−4.37894	+	5.48513i	−0.156391	+	0.195897i
$785$	−0.740977	+	0.221834i	−0.0264466	+	0.00791759i
$786$	6.69998	+	9.16113i	0.238980	+	0.326767i
$787$	1.30350	+	1.98188i	0.0464649	+	0.0706464i	0.857973	−	0.513694i	$-0.171723\pi$
$787$	1.30350	+	1.98188i	0.0464649	+	0.0706464i	−0.811508	+	0.584341i	$0.801353\pi$
$788$	−7.87726	+	40.6485i	−0.280616	+	1.44804i
$789$	0.147371	−	0.549874i	0.00524655	−	0.0195760i
$790$	2.43634	−	1.11114i	0.0866811	−	0.0395327i
$791$	6.60164	−	37.4398i	0.234727	−	1.33121i
$792$	5.40932	−	8.29027i	0.192212	−	0.294582i
$793$	−0.136046	−	0.771553i	−0.00483112	−	0.0273987i
$794$	−20.2101	−	29.3880i	−0.717230	−	1.04294i
$795$	2.31583	−	2.06068i	0.0821341	−	0.0730850i
$796$	−35.7056	+	28.9475i	−1.26555	+	1.02602i
$797$	20.8891	+	6.25380i	0.739931	+	0.221521i	0.634518	−	0.772908i	$-0.281198\pi$
$797$	20.8891	+	6.25380i	0.739931	+	0.221521i	0.105413	+	0.994429i	$0.466384\pi$
$798$	7.28310	−	39.3464i	0.257819	−	1.39285i
$799$	−2.13765	−	18.2888i	−0.0756247	−	0.647011i
$800$	−24.3175	+	13.6174i	−0.859752	+	0.481449i
$801$	−22.9297	−	15.0847i	−0.810181	−	0.532993i
$802$	19.4726	−	21.5127i	0.687601	−	0.759640i
$803$	14.8024	+	9.73567i	0.522364	+	0.343564i
$804$	16.6027	−	29.5810i	0.585533	−	1.04324i
$805$	−1.51241	+	2.03151i	−0.0533053	+	0.0716014i
$806$	−1.09424	+	1.98902i	−0.0385430	+	0.0700601i
$807$	25.4150	−	8.42005i	0.894650	−	0.296400i
$808$	5.92080	−	16.4597i	0.208293	−	0.579050i
$809$		−	6.08317i		−	0.213873i	−0.994266	−	0.106936i	$-0.965896\pi$
$809$		−	6.08317i		−	0.213873i	0.994266	−	0.106936i	$-0.0341041\pi$
$810$	−2.68111	−	2.15796i	−0.0942047	−	0.0758230i
$811$		−	48.8953i		−	1.71694i	−0.512860	−	0.858472i	$-0.671414\pi$
$811$		−	48.8953i		−	1.71694i	0.512860	−	0.858472i	$-0.328586\pi$
$812$	3.10456	+	0.986854i	0.108949	+	0.0346318i
$813$	3.52546	−	17.0690i	0.123643	−	0.598637i
$814$	2.36590	+	1.30158i	0.0829247	+	0.0456203i
$815$	−0.911029	+	1.22372i	−0.0319119	+	0.0428652i
$816$	−11.7529	−	0.740379i	−0.411435	−	0.0259184i
$817$	0.794188	+	0.522345i	0.0277851	+	0.0182746i
$818$	22.6399	+	20.4929i	0.791585	+	0.716516i
$819$	−1.89041	+	2.00328i	−0.0660564	+	0.0700002i
$820$	3.14888	−	2.26264i	0.109964	−	0.0790149i
$821$	2.48656	+	21.2739i	0.0867816	+	0.742464i	0.964645	+	0.263553i	$0.0848943\pi$
$821$	2.48656	+	21.2739i	0.0867816	+	0.742464i	−0.877863	+	0.478911i	$0.841032\pi$
$822$	−17.9237	+	20.9957i	−0.625160	+	0.732308i
$823$	21.8171	+	6.53160i	0.760496	+	0.227677i	0.643491	−	0.765454i	$-0.277486\pi$
$823$	21.8171	+	6.53160i	0.760496	+	0.227677i	0.117005	+	0.993131i	$0.462671\pi$
$824$	17.6735	−	13.2611i	0.615684	−	0.461971i
$825$	−9.44986	−	3.13192i	−0.329002	−	0.109040i
$826$	−21.4320	+	14.7388i	−0.745715	+	0.512828i
$827$	5.61315	+	31.8337i	0.195188	+	1.10697i	0.912150	+	0.409856i	$0.134421\pi$
$827$	5.61315	+	31.8337i	0.195188	+	1.10697i	−0.716962	+	0.697112i	$0.754468\pi$
$828$	−3.84962	−	24.2336i	−0.133784	−	0.842177i
$829$	−1.83368	+	10.3993i	−0.0636862	+	0.361182i	0.936265	+	0.351295i	$0.114258\pi$
$829$	−1.83368	+	10.3993i	−0.0636862	+	0.361182i	−0.999951	+	0.00988757i	$0.996853\pi$
$830$	−1.92150	−	4.21317i	−0.0666963	−	0.146241i
$831$	−23.8496	−	23.8523i	−0.827335	−	0.827426i
$832$	3.02185	+	1.07418i	0.104764	+	0.0372404i
$833$	1.63891	+	2.49184i	0.0567849	+	0.0863372i
$834$	−36.7656	−	16.2310i	−1.27309	−	0.562034i
$835$	−3.81632	+	1.14253i	−0.132069	+	0.0395389i
$836$	−13.7480	−	9.37851i	−0.475485	−	0.324363i
$837$	17.7069	+	10.9259i	0.612041	+	0.377653i
$838$	8.56166	+	16.2046i	0.295758	+	0.559778i
$839$	−2.58854	+	2.74370i	−0.0893665	+	0.0947229i	−0.770513	−	0.637424i	$-0.780000\pi$
$839$	−2.58854	+	2.74370i	−0.0893665	+	0.0947229i	0.681147	+	0.732147i	$0.261482\pi$
$840$	−2.81540	+	1.13059i	−0.0971405	+	0.0390091i
$841$	−1.65679	−	28.4460i	−0.0571307	−	0.980897i
$842$	4.34135	+	11.2025i	0.149613	+	0.386065i
$843$	−18.0904	+	8.43449i	−0.623068	+	0.290499i
$844$	−34.7084	−	4.65208i	−1.19471	−	0.160131i
$845$	−1.18742	−	3.26242i	−0.0408486	−	0.112231i
$846$	44.9296	+	9.67858i	1.54471	+	0.332756i
$847$	−7.55043	+	20.7446i	−0.259436	+	0.712794i
$848$	22.4681	+	14.0041i	0.771556	+	0.480901i
$849$	23.5914	+	12.7221i	0.809656	+	0.436620i
$850$	2.29692	+	11.6184i	0.0787838	+	0.398509i
$851$	6.51305	−	1.54362i	0.223265	−	0.0529147i
$852$	16.5857	−	25.8973i	0.568217	−	0.887226i
$853$	4.56894	−	10.5920i	0.156438	−	0.362663i	−0.821914	−	0.569611i	$-0.807094\pi$
$853$	4.56894	−	10.5920i	0.156438	−	0.362663i	0.978352	+	0.206948i	$0.0663531\pi$
$854$	−2.38661	+	5.86271i	−0.0816680	+	0.200618i
$855$	−3.71979	+	4.43207i	−0.127214	+	0.151574i
$856$	17.4559	−	4.20656i	0.596631	−	0.143777i
$857$	−34.2796	−	1.99656i	−1.17097	−	0.0682012i	−0.538389	−	0.842696i	$-0.680967\pi$
$857$	−34.2796	−	1.99656i	−1.17097	−	0.0682012i	−0.632580	+	0.774495i	$0.718004\pi$
$858$	0.444781	+	1.05569i	0.0151846	+	0.0360408i
$859$	19.5720	−	8.44254i	0.667788	−	0.288056i	−0.0350707	−	0.999385i	$-0.511166\pi$
$859$	19.5720	−	8.44254i	0.667788	−	0.288056i	0.702859	+	0.711329i	$0.251906\pi$
$860$	0.00121681	−	0.0720619i	4.14928e−5	−	0.00245729i
$861$	−25.0352	+	13.4971i	−0.853197	+	0.459979i
$862$	−26.4963	+	26.0527i	−0.902467	+	0.887357i
$863$	12.5608	+	21.7560i	0.427576	+	0.740584i	0.996657	−	0.0816978i	$-0.0260342\pi$
$863$	12.5608	+	21.7560i	0.427576	+	0.740584i	−0.569081	+	0.822281i	$0.692701\pi$
$864$	11.2144	−	27.1705i	0.381522	−	0.924360i
$865$	−0.853579	+	1.47844i	−0.0290226	+	0.0502685i
$866$	−2.18617	−	8.44339i	−0.0742892	−	0.286918i
$867$	9.02491	−	22.7134i	0.306502	−	0.771388i
$868$	16.0367	−	8.90124i	0.544322	−	0.302128i
$869$	−0.948358	+	8.11372i	−0.0321708	+	0.275239i
$870$	−0.320336	−	0.345369i	−0.0108604	−	0.0117091i
$871$	1.76182	+	3.50807i	0.0596969	+	0.118866i
$872$	−11.9817	+	40.5767i	−0.405751	+	1.37410i
$873$	−14.1276	+	13.3257i	−0.478146	+	0.451008i
$874$	−40.8662	+	5.63405i	−1.38232	+	0.190574i
$875$	3.67115	+	4.93121i	0.124108	+	0.166705i
$876$	48.5558	+	20.2489i	1.64055	+	0.684146i
$877$	−25.3707	−	26.8914i	−0.856707	−	0.908057i	0.139916	−	0.990163i	$-0.455317\pi$
$877$	−25.3707	−	26.8914i	−0.856707	−	0.908057i	−0.996624	+	0.0821066i	$0.973835\pi$
$878$	−27.8569	−	9.49249i	−0.940124	−	0.320356i
$879$	29.3532	−	37.1189i	0.990058	−	1.25199i
$880$	−0.0426009	+	1.26110i	−0.00143608	+	0.0425116i
$881$	27.4357	+	32.6965i	0.924331	+	1.10157i	0.994573	+	0.104045i	$0.0331785\pi$
$881$	27.4357	+	32.6965i	0.924331	+	1.10157i	−0.0702418	+	0.997530i	$0.522377\pi$
$882$	−7.20698	+	1.86519i	−0.242672	+	0.0628042i
$883$	−1.27235	+	1.51632i	−0.0428179	+	0.0510284i	−0.787028	−	0.616917i	$-0.788382\pi$
$883$	−1.27235	+	1.51632i	−0.0428179	+	0.0510284i	0.744210	+	0.667945i	$0.232826\pi$
$884$	0.832155	−	1.07925i	0.0279884	−	0.0362991i
$885$	3.74691	−	0.327603i	0.125951	−	0.0110123i
$886$	3.48663	−	4.33386i	0.117136	−	0.145599i
$887$	10.7600	+	5.40387i	0.361285	+	0.181444i	0.620177	−	0.784462i	$-0.287061\pi$
$887$	10.7600	+	5.40387i	0.361285	+	0.181444i	−0.258892	+	0.965906i	$0.583357\pi$
$888$	7.62054	+	2.49386i	0.255729	+	0.0836883i
$889$	28.6974	+	6.80141i	0.962480	+	0.228112i
$890$	3.49616	+	0.131275i	0.117191	+	0.00440036i
$891$	9.86703	−	3.58883i	0.330558	−	0.120230i
$892$	−2.36439	+	31.4401i	−0.0791655	+	1.05269i
$893$	17.8194	−	75.1861i	0.596305	−	2.51601i
$894$	47.6771	−	13.8333i	1.59456	−	0.462653i
$895$	2.48634	−	4.95072i	0.0831093	−	0.165484i
$896$	−16.0526	−	20.3401i	−0.536278	−	0.679513i
$897$	2.57350	+	1.20022i	0.0859268	+	0.0400741i
$898$	25.8091	−	36.2048i	0.861260	−	1.20817i
$899$	2.18151	+	1.83050i	0.0727573	+	0.0610506i
$900$	−29.2988	−	3.93032i	−0.976628	−	0.131011i
$901$	8.61819	−	7.23152i	0.287113	−	0.240917i
$902$	0.931447	+	11.7922i	0.0310138	+	0.392639i
$903$	−0.0766477	+	0.523068i	−0.00255068	+	0.0174066i
$904$	−43.1804	−	18.4338i	−1.43616	−	0.613099i
$905$	2.32367	−	2.19227i	0.0772415	−	0.0728736i
$906$	−32.0927	−	38.9134i	−1.06621	−	1.29281i
$907$	−33.4643	+	24.9132i	−1.11116	+	0.827230i	−0.986303	−	0.164944i	$-0.947256\pi$
$907$	−33.4643	+	24.9132i	−1.11116	+	0.827230i	−0.124860	+	0.992174i	$0.539848\pi$
$908$	0.786523	+	7.88094i	0.0261017	+	0.261538i
$909$	15.5022	−	10.1935i	0.514175	−	0.338097i
$910$	0.0738996	−	0.343239i	0.00244975	−	0.0113782i
$911$	44.4984	−	22.3480i	1.47430	−	0.740421i	0.483447	−	0.875374i	$-0.339385\pi$
$911$	44.4984	−	22.3480i	1.47430	−	0.740421i	0.990852	+	0.134953i	$0.0430882\pi$
$912$	−45.2826	−	19.7878i	−1.49946	−	0.655240i
$913$	14.0311	+	1.64000i	0.464361	+	0.0542760i
$914$	−2.99909	+	1.81510i	−0.0992011	+	0.0600380i
$915$	0.718013	−	0.567667i	0.0237368	−	0.0187665i
$916$	7.06750	+	32.2362i	0.233517	+	1.06511i
$917$	9.19023	+	5.30598i	0.303488	+	0.175219i
$918$	−9.49887	−	8.11085i	−0.313509	−	0.267698i
$919$	−15.3885	+	8.88454i	−0.507619	+	0.293074i	−0.731854	−	0.681461i	$-0.761345\pi$
$919$	−15.3885	+	8.88454i	−0.507619	+	0.293074i	0.224235	+	0.974535i	$0.428012\pi$
$920$	2.01950	+	2.38844i	0.0665811	+	0.0787446i
$921$	−4.18633	+	6.78623i	−0.137944	+	0.223614i
$922$	−32.6158	+	0.673508i	−1.07414	+	0.0221808i
$923$	1.40962	+	3.26787i	0.0463982	+	0.107563i
$924$	1.49634	−	9.13375i	0.0492261	−	0.300478i
$925$	0.468874	−	8.05026i	0.0154165	−	0.264691i
$926$	−12.5278	−	38.9038i	−0.411690	−	1.27846i
$927$	23.4357	+	0.00259324i	0.769730	+	8.51732e-5i
$928$	2.05709	−	3.45741i	0.0675272	−	0.113495i
$929$	52.7826	+	22.7682i	1.73174	+	0.747000i	0.997692	+	0.0679025i	$0.0216307\pi$
$929$	52.7826	+	22.7682i	1.73174	+	0.747000i	0.734048	+	0.679097i	$0.237629\pi$
$930$	−2.65210	−	0.0225363i	−0.0869658	−	0.000738994i
$931$	2.88631	+	12.1783i	0.0945950	+	0.399128i
$932$	−4.01933	−	25.2839i	−0.131658	−	0.828201i
$933$	20.3717	+	33.0316i	0.666938	+	1.08141i
$934$	18.6438	−	39.1162i	0.610044	−	1.27992i
$935$	0.503857	+	0.183389i	0.0164779	+	0.00599746i
$936$	1.87959	+	2.83518i	0.0614364	+	0.0926706i
$937$	33.4828	−	12.1867i	1.09383	−	0.398123i	0.268795	−	0.963197i	$-0.413375\pi$
$937$	33.4828	−	12.1867i	1.09383	−	0.398123i	0.825040	+	0.565074i	$0.191152\pi$
$938$	3.03094	−	31.5717i	0.0989636	−	1.03085i
$939$	30.0536	−	42.9160i	0.980763	−	1.40051i
$940$	−5.53827	+	1.91051i	−0.180638	+	0.0623138i
$941$	13.5715	−	0.790447i	0.442417	−	0.0257678i	0.164509	−	0.986376i	$-0.447396\pi$
$941$	13.5715	−	0.790447i	0.442417	−	0.0257678i	0.277908	+	0.960608i	$0.410359\pi$
$942$	0.466818	−	6.99102i	0.0152097	−	0.227780i
$943$	21.3278	+	20.1217i	0.694527	+	0.655253i
$944$	11.7201	+	29.9084i	0.381457	+	0.973435i
$945$	−3.10818	−	0.833387i	−0.101109	−	0.0271101i
$946$	0.186152	+	0.117001i	0.00605234	+	0.00380404i
$947$	4.00764	+	13.3864i	0.130231	+	0.435001i	0.998088	−	0.0618132i	$-0.0196883\pi$
$947$	4.00764	+	13.3864i	0.130231	+	0.435001i	−0.867857	+	0.496814i	$0.834503\pi$
$948$	1.70451	+	24.1969i	0.0553598	+	0.785878i
$949$	−5.08662	+	3.34552i	−0.165119	+	0.108600i
$950$	−7.61780	+	49.1115i	−0.247154	+	1.59339i
$951$	−7.55262	−	28.1930i	−0.244911	−	0.914221i
$952$	−10.3325	+	3.80480i	−0.334877	+	0.123314i
$953$	46.0939	+	8.12759i	1.49313	+	0.263279i	0.859810	−	0.510614i	$-0.170582\pi$
$953$	46.0939	+	8.12759i	1.49313	+	0.263279i	0.633317	+	0.773893i	$0.281693\pi$
$954$	10.1441	+	26.1847i	0.328428	+	0.847762i
$955$	3.63042	−	0.640140i	0.117478	−	0.0207145i
$956$	14.9167	+	23.5358i	0.482440	+	0.761203i
$957$	1.40737	−	0.290517i	0.0454938	−	0.00939108i
$958$	26.4057	+	30.1811i	0.853131	+	0.975108i
$959$	−7.40277	+	24.7270i	−0.239048	+	0.798475i
$960$	0.570714	+	3.70311i	0.0184197	+	0.119517i
$961$	−14.8651	+	1.73748i	−0.479519	+	0.0560477i
$962$	−0.732705	+	0.569362i	−0.0236234	+	0.0183570i
$963$	17.4864	+	7.54520i	0.563492	+	0.243141i
$964$	17.6937	+	17.2670i	0.569876	+	0.556132i
$965$	1.20482	−	1.83184i	0.0387845	−	0.0589690i
$966$	−12.4438	−	19.2746i	−0.400372	−	0.620151i
$967$	−5.03305	−	3.74697i	−0.161852	−	0.120494i	0.513186	−	0.858278i	$-0.328465\pi$
$967$	−5.03305	−	3.74697i	−0.161852	−	0.120494i	−0.675038	+	0.737783i	$0.735873\pi$
$968$	22.8344	+	14.8956i	0.733925	+	0.478763i
$969$	−13.9611	+	15.6862i	−0.448496	+	0.503914i
$970$	0.660883	−	2.38570i	0.0212197	−	0.0766004i
$971$	−9.53371			−0.305951			−0.152976	−	0.988230i	$-0.548886\pi$
$971$	−9.53371			−0.305951			−0.152976	+	0.988230i	$0.548886\pi$
$972$	26.8121	−	15.9094i	0.860000	−	0.510294i
$973$	−37.5766			−1.20465
$974$	−3.05175	+	11.0164i	−0.0977844	+	0.352989i
$975$	2.27441	−	2.55545i	0.0728395	−	0.0818399i
$976$	6.38246	+	4.51370i	0.204298	+	0.144480i
$977$	13.7665	+	10.2488i	0.440429	+	0.327888i	0.794428	−	0.607358i	$-0.207771\pi$
$977$	13.7665	+	10.2488i	0.440429	+	0.327888i	−0.353999	+	0.935246i	$0.615178\pi$
$978$	−7.49577	−	11.6105i	−0.239688	−	0.371262i
$979$	−5.86498	+	8.91727i	−0.187446	+	0.284997i
$980$	0.662762	−	0.679140i	0.0211711	−	0.0216943i
$981$	−35.9984	+	26.7936i	−1.14934	+	0.855454i
$982$	3.47508	−	2.70037i	0.110894	−	0.0861723i
$983$	43.2670	−	5.05719i	1.38000	−	0.161299i	0.606496	−	0.795086i	$-0.292575\pi$
$983$	43.2670	−	5.05719i	1.38000	−	0.161299i	0.773508	+	0.633787i	$0.218500\pi$
$984$	9.21670	+	33.8940i	0.293818	+	1.08050i
$985$	1.60553	−	5.36283i	0.0511563	−	0.170874i
$986$	−1.12569	−	1.28664i	−0.0358493	−	0.0409749i
$987$	42.0854	−	8.68751i	1.33959	−	0.276527i
$988$	4.83042	−	3.06145i	0.153676	−	0.0973977i
$989$	0.536728	−	0.0946397i	0.0170670	−	0.00300937i
$990$	−0.839046	+	1.04269i	−0.0266666	+	0.0331389i
$991$	13.7712	+	2.42823i	0.437455	+	0.0771352i	0.388039	−	0.921643i	$-0.373153\pi$
$991$	13.7712	+	2.42823i	0.437455	+	0.0771352i	0.0494166	+	0.998778i	$0.484264\pi$
$992$	−6.21117	−	21.7830i	−0.197205	−	0.691612i
$993$	9.83356	+	36.7075i	0.312059	+	1.16488i
$994$	4.40742	−	28.4143i	0.139795	−	0.901248i
$995$	5.19227	−	3.41501i	0.164606	−	0.108263i
$996$	41.8437	−	2.94761i	1.32587	−	0.0933986i
$997$	−9.34384	−	31.2106i	−0.295922	−	0.988449i	−0.968623	−	0.248535i	$-0.920051\pi$
$997$	−9.34384	−	31.2106i	−0.295922	−	0.988449i	0.672701	−	0.739915i	$-0.265134\pi$
$998$	38.2932	+	24.0682i	1.21215	+	0.761866i
$999$	4.87689	+	6.96738i	0.154298	+	0.220438i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.p.a.227.4	yes	936
3.2	odd	2		972.2.p.a.35.49		936
4.3	odd	2	inner	324.2.p.a.227.48	yes	936
12.11	even	2		972.2.p.a.35.5		936
81.5	odd	54	inner	324.2.p.a.167.48	yes	936
81.76	even	27		972.2.p.a.611.5		936
324.167	even	54	inner	324.2.p.a.167.4	✓	936
324.319	odd	54		972.2.p.a.611.49		936

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.p.a.167.4	✓	936	324.167	even	54	inner
324.2.p.a.167.48	yes	936	81.5	odd	54	inner
324.2.p.a.227.4	yes	936	1.1	even	1	trivial
324.2.p.a.227.48	yes	936	4.3	odd	2	inner
972.2.p.a.35.5		936	12.11	even	2
972.2.p.a.35.49		936	3.2	odd	2
972.2.p.a.611.5		936	81.76	even	27
972.2.p.a.611.49		936	324.319	odd	54

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.p (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36289 - 0.377544i) q^{2} +(-1.15153 + 1.29382i) q^{3} +(1.71492 + 1.02910i) q^{4} +(-0.216897 - 0.161474i) q^{5} +(2.05788 - 1.32858i) q^{6} +(1.25852 - 1.91349i) q^{7} +(-1.94871 - 2.05001i) q^{8} +(-0.347949 - 2.97975i) q^{9} +O(q^{10})\)	\(q+(-1.36289 - 0.377544i) q^{2} +(-1.15153 + 1.29382i) q^{3} +(1.71492 + 1.02910i) q^{4} +(-0.216897 - 0.161474i) q^{5} +(2.05788 - 1.32858i) q^{6} +(1.25852 - 1.91349i) q^{7} +(-1.94871 - 2.05001i) q^{8} +(-0.347949 - 2.97975i) q^{9} +(0.234643 + 0.301959i) q^{10} +(-1.15871 + 0.135434i) q^{11} +(-3.30626 + 1.03376i) q^{12} +(0.114975 - 0.384045i) q^{13} +(-2.43765 + 2.13272i) q^{14} +(0.458683 - 0.0946839i) q^{15} +(1.88191 + 3.52965i) q^{16} +(1.67393 - 0.295159i) q^{17} +(-0.650774 + 4.19243i) q^{18} +(7.02442 + 1.23859i) q^{19} +(-0.205789 - 0.500124i) q^{20} +(1.02649 + 3.83175i) q^{21} +(1.63033 + 0.252884i) q^{22} +(3.41680 - 2.24726i) q^{23} +(4.89635 - 0.160640i) q^{24} +(-1.41305 - 4.71990i) q^{25} +(-0.301692 + 0.480001i) q^{26} +(4.25594 + 2.98110i) q^{27} +(4.12744 - 1.98634i) q^{28} +(0.517300 + 0.488048i) q^{29} +(-0.660880 - 0.0441296i) q^{30} +(3.99744 - 0.232824i) q^{31} +(-1.23223 - 5.52102i) q^{32} +(1.15907 - 1.65513i) q^{33} +(-2.39281 - 0.229714i) q^{34} +(-0.581950 + 0.211812i) q^{35} +(2.46976 - 5.46812i) q^{36} +(1.53801 + 0.559789i) q^{37} +(-9.10586 - 4.34009i) q^{38} +(0.364487 + 0.590997i) q^{39} +(0.0916477 + 0.759307i) q^{40} +(1.65348 + 6.97656i) q^{41} +(0.0476693 - 5.60979i) q^{42} +(0.122368 + 0.0527846i) q^{43} +(-2.12648 - 0.960174i) q^{44} +(-0.405684 + 0.702485i) q^{45} +(-5.50515 + 1.77277i) q^{46} +(0.629879 - 10.8146i) q^{47} +(-6.73381 - 1.62965i) q^{48} +(0.694989 + 1.61116i) q^{49} +(0.143850 + 6.96618i) q^{50} +(-1.54570 + 2.50565i) q^{51} +(0.592394 - 0.540285i) q^{52} +(5.73201 - 3.30938i) q^{53} +(-4.67487 - 5.66970i) q^{54} +(0.273191 + 0.157727i) q^{55} +(-6.37517 + 1.14887i) q^{56} +(-9.69136 + 7.66206i) q^{57} +(-0.520762 - 0.860458i) q^{58} +(7.97639 + 0.932306i) q^{59} +(0.884044 + 0.309655i) q^{60} +(1.74644 - 0.877093i) q^{61} +(-5.53596 - 1.19190i) q^{62} +(-6.13964 - 3.08429i) q^{63} +(-0.405042 + 7.98974i) q^{64} +(-0.0869511 + 0.0647327i) q^{65} +(-2.20456 + 1.81815i) q^{66} +(-7.12272 + 6.71994i) q^{67} +(3.17440 + 1.21647i) q^{68} +(-1.02699 + 7.00852i) q^{69} +(0.873100 - 0.0689645i) q^{70} +(-6.80068 + 5.70645i) q^{71} +(-5.43046 + 6.51998i) q^{72} +(-11.6338 - 9.76192i) q^{73} +(-1.88479 - 1.34360i) q^{74} +(7.73388 + 3.60689i) q^{75} +(10.7717 + 9.35292i) q^{76} +(-1.19912 + 2.38764i) q^{77} +(-0.273628 - 0.943073i) q^{78} +(1.61485 - 6.81360i) q^{79} +(0.161766 - 1.06945i) q^{80} +(-8.75786 + 2.07360i) q^{81} +(0.380461 - 10.1325i) q^{82} +(-11.7828 - 2.79257i) q^{83} +(-2.18291 + 7.62751i) q^{84} +(-0.410731 - 0.206277i) q^{85} +(-0.146846 - 0.118139i) q^{86} +(-1.22713 + 0.107292i) q^{87} +(2.53564 + 2.11145i) q^{88} +(5.88080 - 7.00846i) q^{89} +(0.818120 - 0.804244i) q^{90} +(-0.590167 - 0.703334i) q^{91} +(8.17219 - 0.337652i) q^{92} +(-4.30194 + 5.44008i) q^{93} +(-4.94144 + 14.5013i) q^{94} +(-1.32358 - 1.40291i) q^{95} +(8.56216 + 4.76334i) q^{96} +(-3.86575 - 5.19260i) q^{97} +(-0.338905 - 2.45822i) q^{98} +(0.806735 + 3.40556i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more