LMFDB - Embedded newform 403.2.bi.b.14.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(14,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 22]))

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

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

chi := DirichletCharacter("403.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.bi (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$17$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			14.4
Character	$\chi$	$=$	403.14
Dual form			403.2.bi.b.144.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.516329 + 1.58910i) q^{2} +(-0.00193962 + 0.00215417i) q^{3} +(-0.640602 - 0.465424i) q^{4} +(-0.479120 + 0.829859i) q^{5} +(-0.00242170 - 0.00419451i) q^{6} +(-0.214858 + 2.04424i) q^{7} +(-1.63317 + 1.18657i) q^{8} +(0.313585 + 2.98356i) q^{9} +O(q^{10})$	\(q+(-0.516329 + 1.58910i) q^{2} +(-0.00193962 + 0.00215417i) q^{3} +(-0.640602 - 0.465424i) q^{4} +(-0.479120 + 0.829859i) q^{5} +(-0.00242170 - 0.00419451i) q^{6} +(-0.214858 + 2.04424i) q^{7} +(-1.63317 + 1.18657i) q^{8} +(0.313585 + 2.98356i) q^{9} +(-1.07134 - 1.18985i) q^{10} +(5.41100 - 2.40913i) q^{11} +(0.00224513 - 0.000477216i) q^{12} +(-0.978148 - 0.207912i) q^{13} +(-3.13755 - 1.39693i) q^{14} +(-0.000858345 - 0.00264172i) q^{15} +(-1.53169 - 4.71407i) q^{16} +(-3.03276 - 1.35027i) q^{17} +(-4.90308 - 1.04218i) q^{18} +(-1.42638 + 0.303185i) q^{19} +(0.693162 - 0.308615i) q^{20} +(-0.00398688 - 0.00442788i) q^{21} +(1.03449 + 9.84251i) q^{22} +(-6.81891 + 4.95423i) q^{23} +(0.000611665 - 0.00581960i) q^{24} +(2.04089 + 3.53492i) q^{25} +(0.835438 - 1.44702i) q^{26} +(-0.0140706 - 0.0102229i) q^{27} +(1.08908 - 1.20954i) q^{28} +(-1.43110 + 4.40448i) q^{29} +0.00464113 q^{30} +(-1.91157 - 5.22933i) q^{31} +4.24456 q^{32} +(-0.00530561 + 0.0163290i) q^{33} +(3.71161 - 4.12217i) q^{34} +(-1.59349 - 1.15773i) q^{35} +(1.18774 - 2.05722i) q^{36} +(-0.666198 - 1.15389i) q^{37} +(0.254688 - 2.42319i) q^{38} +(0.00234511 - 0.00170382i) q^{39} +(-0.202200 - 1.92381i) q^{40} +(-3.36255 - 3.73449i) q^{41} +(0.00909488 - 0.00404930i) q^{42} +(9.08343 - 1.93074i) q^{43} +(-4.58756 - 0.975117i) q^{44} +(-2.62618 - 1.16925i) q^{45} +(-4.35195 - 13.3939i) q^{46} +(1.79484 + 5.52395i) q^{47} +(0.0131258 + 0.00584398i) q^{48} +(2.71430 + 0.576942i) q^{49} +(-6.67111 + 1.41799i) q^{50} +(0.00879111 - 0.00391405i) q^{51} +(0.529836 + 0.588442i) q^{52} +(0.584526 + 5.56139i) q^{53} +(0.0235103 - 0.0170812i) q^{54} +(-0.593274 + 5.64463i) q^{55} +(-2.07472 - 3.59352i) q^{56} +(0.00211351 - 0.00366072i) q^{57} +(-6.26022 - 4.54832i) q^{58} +(2.12517 - 2.36024i) q^{59} +(-0.000679661 + 0.00209178i) q^{60} +7.54705 q^{61} +(9.29692 - 0.337622i) q^{62} -6.16647 q^{63} +(0.871798 - 2.68312i) q^{64} +(0.641187 - 0.712110i) q^{65} +(-0.0232089 - 0.0168623i) q^{66} +(2.68564 - 4.65166i) q^{67} +(1.31434 + 2.27651i) q^{68} +(0.00255386 - 0.0242984i) q^{69} +(2.66252 - 1.93443i) q^{70} +(0.539831 + 5.13614i) q^{71} +(-4.05232 - 4.50056i) q^{72} +(11.5363 - 5.13630i) q^{73} +(2.17762 - 0.462867i) q^{74} +(-0.0115734 - 0.00245999i) q^{75} +(1.05485 + 0.469649i) q^{76} +(3.76224 + 11.5790i) q^{77} +(0.00149669 + 0.00460635i) q^{78} +(11.9700 + 5.32940i) q^{79} +(4.64588 + 0.987512i) q^{80} +(-8.80325 + 1.87119i) q^{81} +(7.67065 - 3.41519i) q^{82} +(3.90718 + 4.33936i) q^{83} +(0.000493160 + 0.00469210i) q^{84} +(2.57359 - 1.86982i) q^{85} +(-1.62190 + 15.4314i) q^{86} +(-0.00671218 - 0.0116258i) q^{87} +(-5.97848 + 10.3550i) q^{88} +(1.89232 + 1.37485i) q^{89} +(3.21402 - 3.56953i) q^{90} +(0.635183 - 1.95489i) q^{91} +6.67403 q^{92} +(0.0149726 + 0.00602507i) q^{93} -9.70482 q^{94} +(0.431803 - 1.32895i) q^{95} +(-0.00823283 + 0.00914349i) q^{96} +(-9.53019 - 6.92409i) q^{97} +(-2.31829 + 4.01539i) q^{98} +(8.88459 + 15.3886i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 6 q^{2} + 2 q^{3} - 34 q^{4} - 15 q^{5} - 10 q^{6} - 8 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) $ 136 * q - 6 * q^2 + 2 * q^3 - 34 * q^4 - 15 * q^5 - 10 * q^6 - 8 * q^7 - 6 * q^8 + 23 * q^9	\( 136 q - 6 q^{2} + 2 q^{3} - 34 q^{4} - 15 q^{5} - 10 q^{6} - 8 q^{7} - 6 q^{8} + 23 q^{9} + 7 q^{10} + 5 q^{11} + 28 q^{12} + 17 q^{13} - 3 q^{14} + 17 q^{15} - 78 q^{16} - 12 q^{17} + 34 q^{18} - 23 q^{19} + 8 q^{20} - 38 q^{21} + 8 q^{22} + 9 q^{23} + 46 q^{24} - 69 q^{25} - 12 q^{26} - 58 q^{27} + 7 q^{28} + 18 q^{29} + 60 q^{30} + 14 q^{31} + 212 q^{32} - 41 q^{33} - 30 q^{35} - 106 q^{36} + 6 q^{37} - 62 q^{38} + 6 q^{39} + 39 q^{40} - 5 q^{41} + 37 q^{42} + q^{43} - 88 q^{44} - 168 q^{45} + 6 q^{46} - 81 q^{47} - 101 q^{48} + 117 q^{49} - 20 q^{50} + 35 q^{51} + 7 q^{52} + 25 q^{53} + 57 q^{54} + 19 q^{55} - 63 q^{56} - 20 q^{57} - 44 q^{58} + 9 q^{59} + 113 q^{60} + 8 q^{61} + 57 q^{62} + 112 q^{63} - 146 q^{64} - 5 q^{65} + 70 q^{66} - 99 q^{67} - 56 q^{68} - 65 q^{69} + 169 q^{70} - q^{71} - 43 q^{72} + 50 q^{73} - 26 q^{74} - 18 q^{75} - 94 q^{76} + 114 q^{77} - 17 q^{79} + 217 q^{80} + 54 q^{81} - 25 q^{82} - 53 q^{83} - 22 q^{84} + 2 q^{85} - 54 q^{86} - 28 q^{87} + 70 q^{88} - 101 q^{89} + 165 q^{90} - 4 q^{91} + 64 q^{92} + 61 q^{93} - 90 q^{94} - 33 q^{95} - 217 q^{96} + 73 q^{97} + 33 q^{98} - 15 q^{99}+O(q^{100}) \) 136 * q - 6 * q^2 + 2 * q^3 - 34 * q^4 - 15 * q^5 - 10 * q^6 - 8 * q^7 - 6 * q^8 + 23 * q^9 + 7 * q^10 + 5 * q^11 + 28 * q^12 + 17 * q^13 - 3 * q^14 + 17 * q^15 - 78 * q^16 - 12 * q^17 + 34 * q^18 - 23 * q^19 + 8 * q^20 - 38 * q^21 + 8 * q^22 + 9 * q^23 + 46 * q^24 - 69 * q^25 - 12 * q^26 - 58 * q^27 + 7 * q^28 + 18 * q^29 + 60 * q^30 + 14 * q^31 + 212 * q^32 - 41 * q^33 - 30 * q^35 - 106 * q^36 + 6 * q^37 - 62 * q^38 + 6 * q^39 + 39 * q^40 - 5 * q^41 + 37 * q^42 + q^43 - 88 * q^44 - 168 * q^45 + 6 * q^46 - 81 * q^47 - 101 * q^48 + 117 * q^49 - 20 * q^50 + 35 * q^51 + 7 * q^52 + 25 * q^53 + 57 * q^54 + 19 * q^55 - 63 * q^56 - 20 * q^57 - 44 * q^58 + 9 * q^59 + 113 * q^60 + 8 * q^61 + 57 * q^62 + 112 * q^63 - 146 * q^64 - 5 * q^65 + 70 * q^66 - 99 * q^67 - 56 * q^68 - 65 * q^69 + 169 * q^70 - q^71 - 43 * q^72 + 50 * q^73 - 26 * q^74 - 18 * q^75 - 94 * q^76 + 114 * q^77 - 17 * q^79 + 217 * q^80 + 54 * q^81 - 25 * q^82 - 53 * q^83 - 22 * q^84 + 2 * q^85 - 54 * q^86 - 28 * q^87 + 70 * q^88 - 101 * q^89 + 165 * q^90 - 4 * q^91 + 64 * q^92 + 61 * q^93 - 90 * q^94 - 33 * q^95 - 217 * q^96 + 73 * q^97 + 33 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{11}{15}\right)$

Coefficient data

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

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

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

$2$	−0.516329	+	1.58910i	−0.365100	+	1.12366i	0.584819	+	0.811164i	$0.301166\pi$
$2$	−0.516329	+	1.58910i	−0.365100	+	1.12366i	−0.949919	+	0.312498i	$0.898834\pi$
$3$	−0.00193962	+	0.00215417i	−0.00111984	+	0.00124371i	−0.743704	−	0.668509i	$-0.766933\pi$
$3$	−0.00193962	+	0.00215417i	−0.00111984	+	0.00124371i	0.742585	+	0.669752i	$0.233600\pi$
$4$	−0.640602	−	0.465424i	−0.320301	−	0.232712i
$5$	−0.479120	+	0.829859i	−0.214269	+	0.371124i	−0.953046	−	0.302825i	$-0.902070\pi$
$5$	−0.479120	+	0.829859i	−0.214269	+	0.371124i	0.738777	+	0.673950i	$0.235404\pi$
$6$	−0.00242170	−	0.00419451i	−0.000988654	−	0.00171240i
$7$	−0.214858	+	2.04424i	−0.0812086	+	0.772648i	0.875817	+	0.482644i	$0.160323\pi$
$7$	−0.214858	+	2.04424i	−0.0812086	+	0.772648i	−0.957025	+	0.290004i	$0.906343\pi$
$8$	−1.63317	+	1.18657i	−0.577412	+	0.419514i
$9$	0.313585	+	2.98356i	0.104528	+	0.994519i
$10$	−1.07134	−	1.18985i	−0.338789	−	0.376263i
$11$	5.41100	−	2.40913i	1.63148	−	0.726381i	0.632633	−	0.774451i	$-0.281974\pi$
$11$	5.41100	−	2.40913i	1.63148	−	0.726381i	0.998844	+	0.0480709i	$0.0153073\pi$
$12$	0.00224513		0.000477216i	0.000648112		0.000137760i
$13$	−0.978148	−	0.207912i	−0.271289	−	0.0576643i
$13$	−0.978148	−	0.207912i	−0.271289	−	0.0576643i
$14$	−3.13755	−	1.39693i	−0.838546	−	0.373345i
$15$	−0.000858345	−	0.00264172i	−0.000221624	−	0.000682088i
$16$	−1.53169	−	4.71407i	−0.382923	−	1.17852i
$17$	−3.03276	−	1.35027i	−0.735552	−	0.327489i	0.00454432	−	0.999990i	$-0.498553\pi$
$17$	−3.03276	−	1.35027i	−0.735552	−	0.327489i	−0.740096	+	0.672501i	$0.765220\pi$
$18$	−4.90308	−	1.04218i	−1.15567	−	0.245644i
$19$	−1.42638	+	0.303185i	−0.327233	+	0.0695555i	−0.368599	−	0.929589i	$-0.620162\pi$
$19$	−1.42638	+	0.303185i	−0.327233	+	0.0695555i	0.0413659	+	0.999144i	$0.486829\pi$
$20$	0.693162	−	0.308615i	0.154996	−	0.0690085i
$21$	−0.00398688	−	0.00442788i	−0.000870009	−	0.000966243i
$22$	1.03449	+	9.84251i	0.220554	+	2.09843i
$23$	−6.81891	+	4.95423i	−1.42184	+	1.03303i	−0.430377	+	0.902649i	$0.641619\pi$
$23$	−6.81891	+	4.95423i	−1.42184	+	1.03303i	−0.991464	+	0.130379i	$0.958381\pi$
$24$	0.000611665	−	0.00581960i	0.000124856	−	0.00118792i
$25$	2.04089	+	3.53492i	0.408178	+	0.706985i
$26$	0.835438	−	1.44702i	0.163843	−	0.283784i
$27$	−0.0140706	−	0.0102229i	−0.00270790	−	0.00196740i
$28$	1.08908	−	1.20954i	0.205816	−	0.228582i
$29$	−1.43110	+	4.40448i	−0.265749	+	0.817891i	0.725771	+	0.687936i	$0.241483\pi$
$29$	−1.43110	+	4.40448i	−0.265749	+	0.817891i	−0.991520	+	0.129954i	$0.958517\pi$
$30$	0.00464113			0.000847351
$31$	−1.91157	−	5.22933i	−0.343329	−	0.939215i
$31$	−1.91157	−	5.22933i	−0.343329	−	0.939215i
$32$	4.24456			0.750339
$33$	−0.00530561	+	0.0163290i	−0.000923588	+	0.00284251i
$34$	3.71161	−	4.12217i	0.636537	−	0.706946i
$35$	−1.59349	−	1.15773i	−0.269348	−	0.195693i
$36$	1.18774	−	2.05722i	0.197956	−	0.342870i
$37$	−0.666198	−	1.15389i	−0.109522	−	0.189698i	0.806055	−	0.591841i	$-0.201599\pi$
$37$	−0.666198	−	1.15389i	−0.109522	−	0.189698i	−0.915577	+	0.402143i	$0.868265\pi$
$38$	0.254688	−	2.42319i	0.0413158	−	0.393094i
$39$	0.00234511	−	0.00170382i	0.000375518	−	0.000272830i
$40$	−0.202200	−	1.92381i	−0.0319707	−	0.304181i
$41$	−3.36255	−	3.73449i	−0.525142	−	0.583229i	0.420968	−	0.907076i	$-0.361690\pi$
$41$	−3.36255	−	3.73449i	−0.525142	−	0.583229i	−0.946110	+	0.323847i	$0.895024\pi$
$42$	0.00909488	−	0.00404930i	0.00140337	−	0.000624821i
$43$	9.08343	−	1.93074i	1.38521	−	0.294436i	0.545792	−	0.837921i	$-0.316229\pi$
$43$	9.08343	−	1.93074i	1.38521	−	0.294436i	0.839419	+	0.543485i	$0.182896\pi$
$44$	−4.58756	−	0.975117i	−0.691601	−	0.147004i
$45$	−2.62618	−	1.16925i	−0.391487	−	0.174301i
$46$	−4.35195	−	13.3939i	−0.641660	−	1.97483i
$47$	1.79484	+	5.52395i	0.261804	+	0.805750i	0.992412	+	0.122953i	$0.0392366\pi$
$47$	1.79484	+	5.52395i	0.261804	+	0.805750i	−0.730608	+	0.682797i	$0.760763\pi$
$48$	0.0131258	+	0.00584398i	0.00189454	+	0.000843506i
$49$	2.71430	+	0.576942i	0.387757	+	0.0824203i
$50$	−6.67111	+	1.41799i	−0.943437	+	0.200534i
$51$	0.00879111	−	0.00391405i	0.00123100	−	0.000548077i
$52$	0.529836	+	0.588442i	0.0734750	+	0.0816023i
$53$	0.584526	+	5.56139i	0.0802908	+	0.763916i	0.958395	+	0.285446i	$0.0921418\pi$
$53$	0.584526	+	5.56139i	0.0802908	+	0.763916i	−0.878104	+	0.478470i	$0.841192\pi$
$54$	0.0235103	−	0.0170812i	0.00319935	−	0.00232446i
$55$	−0.593274	+	5.64463i	−0.0799971	+	0.761122i
$56$	−2.07472	−	3.59352i	−0.277246	−	0.480205i
$57$	0.00211351	−	0.00366072i	0.000279942	−	0.000484874i
$58$	−6.26022	−	4.54832i	−0.822008	−	0.597223i
$59$	2.12517	−	2.36024i	0.276673	−	0.307277i	−0.588753	−	0.808313i	$-0.700381\pi$
$59$	2.12517	−	2.36024i	0.276673	−	0.307277i	0.865426	+	0.501036i	$0.167048\pi$
$60$	−0.000679661		0.00209178i	−8.77439e−5		0.000270048i
$61$	7.54705			0.966300			0.483150	−	0.875538i	$-0.339493\pi$
$61$	7.54705			0.966300			0.483150	+	0.875538i	$0.339493\pi$
$62$	9.29692	−	0.337622i	1.18071	−	0.0428781i
$63$	−6.16647			−0.776902
$64$	0.871798	−	2.68312i	0.108975	−	0.335390i
$65$	0.641187	−	0.712110i	0.0795295	−	0.0883264i
$66$	−0.0232089	−	0.0168623i	−0.00285682	−	0.00207560i
$67$	2.68564	−	4.65166i	0.328103	−	0.568291i	−0.654032	−	0.756467i	$-0.726924\pi$
$67$	2.68564	−	4.65166i	0.328103	−	0.568291i	0.982135	+	0.188175i	$0.0602573\pi$
$68$	1.31434	+	2.27651i	0.159387	+	0.276067i
$69$	0.00255386	−	0.0242984i	0.000307449	−	0.00292518i
$70$	2.66252	−	1.93443i	0.318232	−	0.231209i
$71$	0.539831	+	5.13614i	0.0640661	+	0.609548i	0.978704	+	0.205275i	$0.0658089\pi$
$71$	0.539831	+	5.13614i	0.0640661	+	0.609548i	−0.914638	+	0.404273i	$0.867524\pi$
$72$	−4.05232	−	4.50056i	−0.477571	−	0.530396i
$73$	11.5363	−	5.13630i	1.35022	−	0.601158i	0.401092	−	0.916038i	$-0.368631\pi$
$73$	11.5363	−	5.13630i	1.35022	−	0.601158i	0.949132	+	0.314880i	$0.101964\pi$
$74$	2.17762	−	0.462867i	0.253143	−	0.0538072i
$75$	−0.0115734	−	0.00245999i	−0.00133638	−	0.000284056i
$76$	1.05485	+	0.469649i	0.120999	+	0.0538724i
$77$	3.76224	+	11.5790i	0.428747	+	1.31955i
$78$	0.00149669	+	0.00460635i	0.000169467	+	0.000521566i
$79$	11.9700	+	5.32940i	1.34673	+	0.599604i	0.948236	−	0.317566i	$-0.102865\pi$
$79$	11.9700	+	5.32940i	1.34673	+	0.599604i	0.398496	+	0.917170i	$0.369532\pi$
$80$	4.64588	+	0.987512i	0.519425	+	0.110407i
$81$	−8.80325	+	1.87119i	−0.978139	+	0.207910i
$82$	7.67065	−	3.41519i	0.847081	−	0.377145i
$83$	3.90718	+	4.33936i	0.428868	+	0.476307i	0.918385	−	0.395687i	$-0.129494\pi$
$83$	3.90718	+	4.33936i	0.428868	+	0.476307i	−0.489517	+	0.871994i	$0.662827\pi$
$84$	0.000493160		0.00469210i	5.38081e−5		0.000511950i
$85$	2.57359	−	1.86982i	0.279145	−	0.202811i
$86$	−1.62190	+	15.4314i	−0.174894	+	1.66401i
$87$	−0.00671218	−	0.0116258i	−0.000719621	−	0.00124642i
$88$	−5.97848	+	10.3550i	−0.637308	+	1.10385i
$89$	1.89232	+	1.37485i	0.200586	+	0.145734i	0.683544	−	0.729909i	$-0.260438\pi$
$89$	1.89232	+	1.37485i	0.200586	+	0.145734i	−0.482958	+	0.875643i	$0.660438\pi$
$90$	3.21402	−	3.56953i	0.338788	−	0.376262i
$91$	0.635183	−	1.95489i	0.0665853	−	0.204928i
$92$	6.67403			0.695815
$93$	0.0149726	+	0.00602507i	0.00155258	+	0.000624770i
$94$	−9.70482			−1.00098
$95$	0.431803	−	1.32895i	0.0443021	−	0.136348i
$96$	−0.00823283	+	0.00914349i	−0.000840260	+	0.000933203i
$97$	−9.53019	−	6.92409i	−0.967644	−	0.703034i	−0.0127304	−	0.999919i	$-0.504052\pi$
$97$	−9.53019	−	6.92409i	−0.967644	−	0.703034i	−0.954913	+	0.296885i	$0.904052\pi$
$98$	−2.31829	+	4.01539i	−0.234182	+	0.405616i
$99$	8.88459	+	15.3886i	0.892935	+	1.54661i
$100$	0.337843	−	3.21436i	0.0337843	−	0.321436i
$101$	10.3561	−	7.52411i	1.03047	−	0.748677i	0.0620640	−	0.998072i	$-0.480232\pi$
$101$	10.3561	−	7.52411i	1.03047	−	0.748677i	0.968402	+	0.249395i	$0.0802317\pi$
$102$	0.00168071	+	0.0159909i	0.000166415	+	0.00158333i
$103$	4.90622	+	5.44891i	0.483425	+	0.536897i	0.934677	−	0.355499i	$-0.115689\pi$
$103$	4.90622	+	5.44891i	0.483425	+	0.536897i	−0.451252	+	0.892397i	$0.649022\pi$
$104$	1.84418	−	0.821082i	0.180837	−	0.0805137i
$105$	0.00558471	−	0.00118707i	0.000545012	−	0.000115846i
$106$	−9.13940	−	1.94264i	−0.887697	−	0.188686i
$107$	−1.48399	−	0.660715i	−0.143463	−	0.0638738i	0.333749	−	0.942662i	$-0.391686\pi$
$107$	−1.48399	−	0.660715i	−0.143463	−	0.0638738i	−0.477212	+	0.878788i	$0.658353\pi$
$108$	0.00425568	+	0.0130976i	0.000409503	+	0.00126032i
$109$	1.04099	+	3.20383i	0.0997084	+	0.306871i	0.988452	−	0.151533i	$-0.0484211\pi$
$109$	1.04099	+	3.20383i	0.0997084	+	0.306871i	−0.888744	+	0.458404i	$0.848421\pi$
$110$	−8.66354	−	3.85726i	−0.826036	−	0.367775i
$111$	0.00377784		0.000803005i	0.000358577		7.62178e-5i
$112$	9.96576	−	2.11829i	0.941676	−	0.200159i
$113$	−13.1003	+	5.83263i	−1.23237	+	0.548688i	−0.916470	−	0.400103i	$-0.868974\pi$
$113$	−13.1003	+	5.83263i	−1.23237	+	0.548688i	−0.315904	+	0.948791i	$0.602308\pi$
$114$	0.00472596	+	0.00524872i	0.000442627	+	0.000491587i
$115$	−0.844240	−	8.03240i	−0.0787258	−	0.749026i
$116$	2.96672	−	2.15545i	0.275453	−	0.200128i
$117$	0.313585	−	2.98356i	0.0289909	−	0.275830i
$118$	2.65336	+	4.59576i	0.244262	+	0.423074i
$119$	3.41188	−	5.90956i	0.312767	−	0.541728i
$120$	0.00453639	+	0.00329588i	0.000414114	+	0.000300872i
$121$	16.1146	−	17.8970i	1.46496	−	1.62700i
$122$	−3.89676	+	11.9930i	−0.352796	+	1.08579i
$123$	0.0145668			0.00131344
$124$	−1.20930	+	4.23961i	−0.108598	+	0.380728i
$125$	−8.70251			−0.778377
$126$	3.18393	−	9.79912i	0.283647	−	0.872975i
$127$	−6.72953	+	7.47390i	−0.597149	+	0.663201i	−0.963635	−	0.267223i	$-0.913894\pi$
$127$	−6.72953	+	7.47390i	−0.597149	+	0.663201i	0.366486	+	0.930424i	$0.380561\pi$
$128$	10.6814	+	7.76052i	0.944115	+	0.685940i
$129$	−0.0134593	+	0.0233121i	−0.00118502	+	0.00205252i
$130$	0.800549	+	1.38659i	0.0702128	+	0.121612i
$131$	−0.594558	+	5.65684i	−0.0519468	+	0.494240i	0.937357	+	0.348370i	$0.113265\pi$
$131$	−0.594558	+	5.65684i	−0.0519468	+	0.494240i	−0.989304	+	0.145870i	$0.953402\pi$
$132$	0.0109987	−	0.00799102i	0.000957314	−	0.000695529i
$133$	−0.313315	−	2.98099i	−0.0271678	−	0.258485i
$134$	6.00527	+	6.66953i	0.518777	+	0.576160i
$135$	0.0152251	−	0.00677866i	0.00131037	−	0.000583414i
$136$	6.55519	−	1.39335i	0.562103	−	0.119479i
$137$	1.52127	+	0.323356i	0.129971	+	0.0276262i	0.272438	−	0.962173i	$-0.412170\pi$
$137$	1.52127	+	0.323356i	0.129971	+	0.0276262i	−0.142467	+	0.989800i	$0.545503\pi$
$138$	0.0372939	+	0.0166043i	0.00317467	+	0.00141345i
$139$	6.42384	+	19.7705i	0.544863	+	1.67692i	0.721315	+	0.692607i	$0.243538\pi$
$139$	6.42384	+	19.7705i	0.544863	+	1.67692i	−0.176452	+	0.984309i	$0.556462\pi$
$140$	0.481951	+	1.48329i	0.0407323	+	0.125361i
$141$	−0.0153808	−	0.00684798i	−0.00129530	−	0.000576704i
$142$	−8.44057	−	1.79410i	−0.708317	−	0.150557i
$143$	−5.79364	+	1.23148i	−0.484489	+	0.102981i
$144$	13.5844	−	6.04815i	1.13203	−	0.504013i
$145$	−2.96943	−	3.29788i	−0.246597	−	0.273874i
$146$	2.20554	+	20.9844i	0.182532	+	1.73668i
$147$	−0.00650754	+	0.00472800i	−0.000536733	+	0.000389959i
$148$	−0.110280	+	1.04925i	−0.00906500	+	0.0862477i
$149$	−11.8690	−	20.5578i	−0.972350	−	1.68416i	−0.688418	−	0.725315i	$-0.741694\pi$
$149$	−11.8690	−	20.5578i	−0.972350	−	1.68416i	−0.283932	−	0.958844i	$-0.591639\pi$
$150$	0.00988484	−	0.0171210i	0.000807094	−	0.00139793i
$151$	12.5343	+	9.10668i	1.02002	+	0.741091i	0.966288	−	0.257464i	$-0.0828870\pi$
$151$	12.5343	+	9.10668i	1.02002	+	0.741091i	0.0537362	+	0.998555i	$0.482887\pi$
$152$	1.96976	−	2.18764i	0.159769	−	0.177441i
$153$	3.07759	−	9.47183i	0.248808	−	0.765752i
$154$	−20.3427			−1.63926
$155$	5.25548	+	0.919137i	0.422130	+	0.0738268i
$156$	−0.00229528			−0.000183770
$157$	6.98553	−	21.4993i	0.557506	−	1.71583i	−0.131726	−	0.991286i	$-0.542052\pi$
$157$	6.98553	−	21.4993i	0.557506	−	1.71583i	0.689232	−	0.724541i	$-0.257948\pi$
$158$	−14.6494	+	16.2698i	−1.16544	+	1.29436i
$159$	−0.0131139	−	0.00952782i	−0.00104000	−	0.000755606i
$160$	−2.03365	+	3.52239i	−0.160774	+	0.278469i
$161$	−8.66251	−	15.0039i	−0.682702	−	1.18247i
$162$	1.57187	−	14.9554i	0.123498	−	1.17501i
$163$	7.59446	−	5.51770i	0.594844	−	0.432179i	−0.249201	−	0.968452i	$-0.580168\pi$
$163$	7.59446	−	5.51770i	0.594844	−	0.432179i	0.844045	+	0.536272i	$0.180168\pi$
$164$	0.415932	+	3.95733i	0.0324788	+	0.309016i
$165$	−0.0110087	−	0.0122265i	−0.000857030	−	0.000951828i
$166$	−8.91306	+	3.96835i	−0.691787	+	0.308004i
$167$	2.08088	−	0.442305i	0.161023	−	0.0342266i	−0.126694	−	0.991942i	$-0.540437\pi$
$167$	2.08088	−	0.442305i	0.161023	−	0.0342266i	0.287718	+	0.957715i	$0.407103\pi$
$168$	0.0117652	+	0.00250078i	0.000907707	+	0.000192939i
$169$	0.913545	+	0.406737i	0.0702727	+	0.0312874i
$170$	1.64251	+	5.05513i	0.125975	+	0.387711i
$171$	−1.35186	−	4.16060i	−0.103379	−	0.318169i
$172$	−6.71748	−	2.99081i	−0.512203	−	0.228047i
$173$	−7.35992	−	1.56440i	−0.559565	−	0.118939i	−0.0805572	−	0.996750i	$-0.525670\pi$
$173$	−7.35992	−	1.56440i	−0.559565	−	0.118939i	−0.479007	+	0.877811i	$0.659003\pi$
$174$	0.0219403	−	0.00466355i	0.00166329	−	0.000353543i
$175$	−7.66472	+	3.41255i	−0.579398	+	0.257965i
$176$	−19.6448	−	21.8178i	−1.48078	−	1.64458i
$177$	0.000962327		0.00915593i	7.23330e−5		0.000688202i
$178$	−3.16183	+	2.29721i	−0.236990	+	0.172183i
$179$	0.837299	−	7.96637i	0.0625827	−	0.595434i	−0.917623	−	0.397452i	$-0.869895\pi$
$179$	0.837299	−	7.96637i	0.0625827	−	0.595434i	0.980206	−	0.197982i	$-0.0634388\pi$
$180$	1.13814	+	1.97131i	0.0848317	+	0.146933i
$181$	−12.2548	+	21.2259i	−0.910891	+	1.57771i	−0.0980830	+	0.995178i	$0.531271\pi$
$181$	−12.2548	+	21.2259i	−0.910891	+	1.57771i	−0.812808	+	0.582531i	$0.802062\pi$
$182$	2.77855	+	2.01874i	0.205960	+	0.149639i
$183$	−0.0146384	+	0.0162576i	−0.00108210	+	0.00120180i
$184$	5.25791	−	16.1822i	0.387618	−	1.19297i
$185$	1.27675			0.0938688
$186$	−0.0173052	+	0.0206820i	−0.00126888	+	0.00151648i
$187$	−19.6632			−1.43792
$188$	1.42120	−	4.37401i	0.103652	−	0.319008i
$189$	0.0239213	−	0.0265672i	0.00174002	−	0.00193248i
$190$	1.88888	+	1.37235i	0.137034	+	0.0995611i
$191$	−0.441204	+	0.764187i	−0.0319244	+	0.0552947i	−0.881546	−	0.472098i	$-0.843497\pi$
$191$	−0.441204	+	0.764187i	−0.0319244	+	0.0552947i	0.849622	+	0.527392i	$0.176830\pi$
$192$	0.00408893	+	0.00708223i	0.000295093	+	0.000511116i
$193$	0.719130	−	6.84207i	0.0517641	−	0.492503i	−0.937671	−	0.347525i	$-0.887022\pi$
$193$	0.719130	−	6.84207i	0.0517641	−	0.492503i	0.989435	−	0.144978i	$-0.0463111\pi$
$194$	15.9238	−	11.5693i	1.14326	−	0.830627i
$195$	0.000290345		0.00276245i	2.07920e−5		0.000197823i
$196$	−1.47026	−	1.63289i	−0.105019	−	0.116635i
$197$	16.2954	−	7.25518i	1.16100	−	0.516910i	0.266437	−	0.963852i	$-0.414154\pi$
$197$	16.2954	−	7.25518i	1.16100	−	0.516910i	0.894563	+	0.446942i	$0.147487\pi$
$198$	−29.0413	+	6.17292i	−2.06387	+	0.438690i
$199$	−23.2349	−	4.93873i	−1.64708	−	0.350097i	−0.711354	−	0.702834i	$-0.751918\pi$
$199$	−23.2349	−	4.93873i	−1.64708	−	0.350097i	−0.935723	+	0.352737i	$0.885251\pi$
$200$	−7.52754	−	3.35147i	−0.532277	−	0.236985i
$201$	0.00481134	+	0.0148078i	0.000339366	+	0.00104446i
$202$	6.60942	+	20.3417i	0.465037	+	1.43124i
$203$	−8.69630	−	3.87184i	−0.610361	−	0.271750i
$204$	−0.00745330	−	0.00158425i	−0.000521835	−	0.000110920i
$205$	4.71016	−	1.00118i	0.328972	−	0.0699251i
$206$	−11.1921	+	4.98304i	−0.779789	+	0.347185i
$207$	−16.9195	−	18.7910i	−1.17599	−	1.30607i
$208$	0.518112	+	4.92951i	0.0359246	+	0.341800i
$209$	−6.98770	+	5.07686i	−0.483349	+	0.351174i
$210$	−0.000997184		0.00948757i	−6.88122e−5		0.000654704i
$211$	1.93282	+	3.34775i	0.133061	+	0.230469i	0.924855	−	0.380320i	$-0.124186\pi$
$211$	1.93282	+	3.34775i	0.133061	+	0.230469i	−0.791794	+	0.610788i	$0.790853\pi$
$212$	2.21396	−	3.83469i	0.152055	−	0.263368i
$213$	−0.0121112	−	0.00879929i	−0.000829844	−	0.000602917i
$214$	1.81617	−	2.01706i	0.124151	−	0.137883i
$215$	−2.74980	+	8.46303i	−0.187535	+	0.577174i
$216$	0.0351099			0.00238893
$217$	11.1007	−	2.78414i	0.753564	−	0.189000i
$218$	−5.62869			−0.381223
$219$	−0.0113116	+	0.0348136i	−0.000764369	+	0.00235249i
$220$	3.00720	−	3.33984i	0.202745	−	0.225172i
$221$	2.68575	+	1.95131i	0.180663	+	0.131259i
$222$	−0.00322666	+	0.00558874i	−0.000216559	+	0.000375092i
$223$	−7.84344	−	13.5852i	−0.525235	−	0.909734i	−0.999568	−	0.0293887i	$-0.990644\pi$
$223$	−7.84344	−	13.5852i	−0.525235	−	0.909734i	0.474333	−	0.880346i	$-0.342689\pi$
$224$	−0.911977	+	8.67688i	−0.0609340	+	0.579748i
$225$	−9.90666	+	7.19761i	−0.660444	+	0.479840i
$226$	−2.50455	−	23.8292i	−0.166600	−	1.58510i
$227$	15.3279	+	17.0233i	1.01735	+	1.12988i	0.991486	+	0.130213i	$0.0415660\pi$
$227$	15.3279	+	17.0233i	1.01735	+	1.12988i	0.0258607	+	0.999666i	$0.491767\pi$
$228$	−0.00305771	+	0.00136138i	−0.000202502	+	9.01595e-5i
$229$	5.73860	−	1.21978i	0.379217	−	0.0806051i	−0.0143595	−	0.999897i	$-0.504571\pi$
$229$	5.73860	−	1.21978i	0.379217	−	0.0806051i	0.393577	+	0.919292i	$0.371238\pi$
$230$	13.2002	+	2.80579i	0.870394	+	0.185008i
$231$	−0.0322404	−	0.0143543i	−0.00212126	−	0.000944446i
$232$	−2.88897	−	8.89135i	−0.189670	−	0.583745i
$233$	4.80629	+	14.7922i	0.314870	+	0.969071i	0.975808	+	0.218630i	$0.0701589\pi$
$233$	4.80629	+	14.7922i	0.314870	+	0.969071i	−0.660937	+	0.750441i	$0.729841\pi$
$234$	4.57925	+	2.03881i	0.299355	+	0.133281i
$235$	−5.44404	−	1.15717i	−0.355130	−	0.0754852i
$236$	−2.45990	+	0.522868i	−0.160126	+	0.0340358i
$237$	−0.0346977	+	0.0154484i	−0.00225386	+	0.00100348i
$238$	7.62921	+	8.47309i	0.494528	+	0.549229i
$239$	1.68689	+	16.0496i	0.109116	+	1.03816i	0.902866	+	0.429922i	$0.141459\pi$
$239$	1.68689	+	16.0496i	0.109116	+	1.03816i	−0.793751	+	0.608243i	$0.791875\pi$
$240$	−0.0111385	+	0.00809260i	−0.000718987	+	0.000522375i
$241$	2.19475	−	20.8816i	0.141376	−	1.34510i	−0.661943	−	0.749554i	$-0.730268\pi$
$241$	2.19475	−	20.8816i	0.141376	−	1.34510i	0.803319	−	0.595549i	$-0.203065\pi$
$242$	20.1197	+	34.8483i	1.29334	+	2.24014i
$243$	0.0391325	−	0.0677795i	0.00251035	−	0.00434806i
$244$	−4.83465	−	3.51258i	−0.309507	−	0.224870i
$245$	−1.77925	+	1.97606i	−0.113672	+	0.126246i
$246$	−0.00752125	+	0.0231480i	−0.000479537	+	0.00147586i
$247$	1.45824			0.0927857
$248$	9.32687	+	6.27217i	0.592257	+	0.398283i
$249$	−0.0169261			−0.00107265
$250$	4.49336	−	13.8291i	0.284185	−	0.874632i
$251$	11.0407	−	12.2620i	0.696886	−	0.773970i	−0.285991	−	0.958232i	$-0.592323\pi$
$251$	11.0407	−	12.2620i	0.696886	−	0.773970i	0.982877	+	0.184262i	$0.0589895\pi$
$252$	3.95025	+	2.87003i	0.248842	+	0.180795i
$253$	−24.9617	+	43.2350i	−1.56933	+	2.71816i
$254$	−8.40210	−	14.5529i	−0.527195	−	0.913128i
$255$	−0.000963878		0.00917069i	−6.03604e−5		0.000574291i
$256$	−13.2826	+	9.65035i	−0.830161	+	0.603147i
$257$	−0.0967478	−	0.920494i	−0.00603496	−	0.0574188i	0.991090	−	0.133194i	$-0.0425234\pi$
$257$	−0.0967478	−	0.920494i	−0.00603496	−	0.0574188i	−0.997125	+	0.0757755i	$0.975857\pi$
$258$	−0.0300959	−	0.0334248i	−0.00187369	−	0.00208094i
$259$	2.50196	−	1.11394i	0.155464	−	0.0692171i
$260$	−0.742179	+	0.157755i	−0.0460280	+	0.00978355i
$261$	−13.5898	−	2.88860i	−0.841186	−	0.178800i
$262$	−8.68228	−	3.86560i	−0.536393	−	0.238818i
$263$	−5.27292	−	16.2284i	−0.325142	−	1.00068i	−0.971376	−	0.237546i	$-0.923657\pi$
$263$	−5.27292	−	16.2284i	−0.325142	−	1.00068i	0.646234	−	0.763139i	$-0.276343\pi$
$264$	−0.0107105	−	0.0329635i	−0.000659184	−	0.00202876i
$265$	−4.89523	−	2.17950i	−0.300712	−	0.133885i
$266$	4.89886	+	1.04128i	0.300368	+	0.0638452i
$267$	−0.00663204	+	0.00140968i	−0.000405875	+	8.62713e-5i
$268$	−3.88542	+	1.72990i	−0.237340	+	0.105671i
$269$	−5.90614	−	6.55943i	−0.360104	−	0.399936i	0.535683	−	0.844419i	$-0.320054\pi$
$269$	−5.90614	−	6.55943i	−0.360104	−	0.399936i	−0.895787	+	0.444483i	$0.853387\pi$
$270$	0.00291078	+	0.0276942i	0.000177144	+	0.00168542i
$271$	−2.08209	+	1.51273i	−0.126478	+	0.0918918i	−0.649226	−	0.760596i	$-0.724907\pi$
$271$	−2.08209	+	1.51273i	−0.126478	+	0.0918918i	0.522748	+	0.852487i	$0.324907\pi$
$272$	−1.72001	+	16.3648i	−0.104291	+	0.992264i
$273$	0.00297915	+	0.00516004i	0.000180306	+	0.000312300i
$274$	−1.29932	+	2.25049i	−0.0784948	+	0.135957i
$275$	19.5593	+	14.2107i	1.17947	+	0.856937i
$276$	−0.0129451	+	0.0143770i	−0.000779202	+	0.000865391i
$277$	−3.20874	+	9.87550i	−0.192795	+	0.593361i	0.807200	+	0.590277i	$0.200982\pi$
$277$	−3.20874	+	9.87550i	−0.192795	+	0.593361i	−0.999995	+	0.00308391i	$0.999018\pi$
$278$	−34.7341			−2.08322
$279$	15.0026	−	7.34313i	0.898180	−	0.439621i
$280$	3.97616			0.237621
$281$	8.47044	−	26.0693i	0.505304	−	1.55517i	−0.294954	−	0.955511i	$-0.595304\pi$
$281$	8.47044	−	26.0693i	0.505304	−	1.55517i	0.800258	−	0.599655i	$-0.204696\pi$
$282$	0.0188237	−	0.0209058i	0.00112093	−	0.00124492i
$283$	−10.7375	−	7.80123i	−0.638276	−	0.463735i	0.220981	−	0.975278i	$-0.429074\pi$
$283$	−10.7375	−	7.80123i	−0.638276	−	0.463735i	−0.859258	+	0.511543i	$0.829074\pi$
$284$	2.04467	−	3.54147i	0.121329	−	0.210148i
$285$	0.00202525	+	0.00350784i	0.000119966	+	0.000207787i
$286$	1.03449	−	9.84251i	0.0611706	−	0.582000i
$287$	8.35664	−	6.07145i	0.493277	−	0.358387i
$288$	1.33103	+	12.6639i	0.0784316	+	0.746226i
$289$	−4.00083	−	4.44337i	−0.235343	−	0.261375i
$290$	6.77386	−	3.01592i	0.397775	−	0.177101i
$291$	0.0334006	−	0.00709951i	0.00195798	−	0.000416181i
$292$	−9.78074	−	2.07896i	−0.572375	−	0.121662i
$293$	4.78012	+	2.12825i	0.279258	+	0.124333i	0.541586	−	0.840645i	$-0.317824\pi$
$293$	4.78012	+	2.12825i	0.279258	+	0.124333i	−0.262329	+	0.964979i	$0.584491\pi$
$294$	−0.00415323	−	0.0127823i	−0.000242221	−	0.000745480i
$295$	0.940456	+	2.89443i	0.0547555	+	0.168520i
$296$	2.45718	+	1.09401i	0.142821	+	0.0635878i
$297$	−0.100765	−	0.0214182i	−0.00584696	−	0.00124281i
$298$	38.7967	−	8.24648i	2.24743	−	0.477706i
$299$	7.69994	−	3.42824i	0.445299	−	0.198260i
$300$	0.00626898	+	0.00696240i	0.000361940	+	0.000401975i
$301$	1.99525	+	18.9835i	0.115004	+	1.09419i
$302$	−20.9432	+	15.2161i	−1.20515	+	0.875590i
$303$	−0.00387862	+	0.0369026i	−0.000222821	+	0.00212000i
$304$	3.61401	+	6.25964i	0.207277	+	0.359015i
$305$	−3.61594	+	6.26299i	−0.207048	+	0.358618i
$306$	13.4626	+	9.78117i	0.769607	+	0.559152i
$307$	−10.5746	+	11.7443i	−0.603525	+	0.670282i	−0.965046	−	0.262082i	$-0.915591\pi$
$307$	−10.5746	+	11.7443i	−0.603525	+	0.670282i	0.361521	+	0.932364i	$0.382258\pi$
$308$	2.97904	−	9.16855i	0.169747	−	0.522427i
$309$	−0.0212541			−0.00120910
$310$	−4.17416	+	7.87689i	−0.237076	+	0.447378i
$311$	30.5460			1.73210			0.866051	−	0.499955i	$-0.166650\pi$
$311$	30.5460			1.73210			0.866051	+	0.499955i	$0.166650\pi$
$312$	−0.00180826	+	0.00556526i	−0.000102373	+	0.000315071i
$313$	12.6966	−	14.1010i	0.717656	−	0.797037i	−0.268426	−	0.963300i	$-0.586503\pi$
$313$	12.6966	−	14.1010i	0.717656	−	0.797037i	0.986081	+	0.166263i	$0.0531701\pi$
$314$	30.5576	+	22.2014i	1.72446	+	1.25290i
$315$	2.95448	−	5.11730i	0.166466	−	0.288327i
$316$	−5.18759	−	8.98516i	−0.291824	−	0.505455i
$317$	0.678140	−	6.45207i	0.0380881	−	0.362384i	−0.958833	−	0.283971i	$-0.908348\pi$
$317$	0.678140	−	6.45207i	0.0380881	−	0.362384i	0.996921	−	0.0784132i	$-0.0249854\pi$
$318$	0.0219117	−	0.0159198i	0.00122875	−	0.000892739i
$319$	2.86728	+	27.2803i	0.160537	+	1.52740i
$320$	1.80891	+	2.00900i	0.101121	+	0.112307i
$321$	0.00430167	−	0.00191523i	0.000240096	−	0.000106898i
$322$	28.3154	−	6.01862i	1.57796	−	0.335405i
$323$	4.73524	+	1.00651i	0.263476	+	0.0560035i
$324$	6.51028	+	2.89856i	0.361682	+	0.161031i
$325$	−1.26134	−	3.88200i	−0.0699665	−	0.215335i
$326$	4.84692	+	14.9173i	0.268446	+	0.826192i
$327$	−0.00892070	−	0.00397175i	−0.000493316	−	0.000219638i
$328$	9.92282	+	2.10916i	0.547896	+	0.116459i
$329$	−11.6779	+	2.48221i	−0.643822	+	0.136849i
$330$	0.0251132	−	0.0111811i	0.00138243	−	0.000615499i
$331$	−19.9429	−	22.1488i	−1.09616	−	1.21741i	−0.974393	−	0.224851i	$-0.927811\pi$
$331$	−19.9429	−	22.1488i	−1.09616	−	1.21741i	−0.121767	−	0.992559i	$-0.538856\pi$
$332$	−0.483301	−	4.59830i	−0.0265246	−	0.252364i
$333$	3.23378	−	2.34948i	0.177210	−	0.128751i
$334$	−0.371554	+	3.53510i	−0.0203305	+	0.193432i
$335$	2.57348	+	4.45741i	0.140604	+	0.243534i
$336$	−0.0147666	+	0.0255766i	−0.000805587	+	0.00139532i
$337$	0.284818	+	0.206932i	0.0155150	+	0.0112723i	0.595516	−	0.803344i	$-0.296948\pi$
$337$	0.284818	+	0.206932i	0.0155150	+	0.0112723i	−0.580001	+	0.814616i	$0.696948\pi$
$338$	−1.11803	+	1.24170i	−0.0608131	+	0.0675397i
$339$	0.0128452	−	0.0395334i	0.000697654	−	0.00214716i
$340$	−2.51891			−0.136607
$341$	−22.9417	−	23.6907i	−1.24236	−	1.28292i
$342$	7.30960			0.395258
$343$	−6.20888	+	19.1090i	−0.335248	+	1.03179i
$344$	−12.5438	+	13.9313i	−0.676317	+	0.751127i
$345$	0.0189406	+	0.0137612i	0.00101973	+	0.000740877i
$346$	6.28613	−	10.8879i	0.337944	−	0.585337i
$347$	8.05894	+	13.9585i	0.432626	+	0.749331i	0.997099	−	0.0761212i	$-0.0242536\pi$
$347$	8.05894	+	13.9585i	0.432626	+	0.749331i	−0.564472	+	0.825452i	$0.690920\pi$
$348$	−0.00111111	+	0.0105715i	−5.95620e−5	+	0.000566694i
$349$	1.06134	−	0.771111i	0.0568124	−	0.0412766i	−0.559017	−	0.829156i	$-0.688821\pi$
$349$	1.06134	−	0.771111i	0.0568124	−	0.0412766i	0.615829	+	0.787880i	$0.288821\pi$
$350$	−1.46536	−	13.9420i	−0.0783269	−	0.745230i
$351$	0.0116377	+	0.0129250i	0.000621175	+	0.000689885i
$352$	22.9673	−	10.2257i	1.22416	−	0.545032i
$353$	−19.8092	+	4.21059i	−1.05434	+	0.224107i	−0.702302	−	0.711879i	$-0.747844\pi$
$353$	−19.8092	+	4.21059i	−1.05434	+	0.224107i	−0.352038	+	0.935986i	$0.614511\pi$
$354$	−0.0150466	−	0.00319824i	−0.000799715	−	0.000169985i
$355$	−4.52092	−	2.01284i	−0.239946	−	0.106831i
$356$	−0.572335	−	1.76146i	−0.0303337	−	0.0933575i
$357$	0.00611241	+	0.0188121i	0.000323503	+	0.000995640i
$358$	12.2270	+	5.44382i	0.646218	+	0.287715i
$359$	0.171454	+	0.0364437i	0.00904899	+	0.00192342i	0.212434	−	0.977175i	$-0.431861\pi$
$359$	0.171454	+	0.0364437i	0.00904899	+	0.00192342i	−0.203385	+	0.979099i	$0.565194\pi$
$360$	5.67638	−	1.20655i	0.299172	−	0.0635909i
$361$	−15.4147	+	6.86308i	−0.811302	+	0.361215i
$362$	−27.4025	−	30.4336i	−1.44025	−	1.59956i
$363$	0.00729706	+	0.0694269i	0.000382996	+	0.00364397i
$364$	−1.31675	+	0.956678i	−0.0690167	+	0.0501435i
$365$	−1.26487	+	12.0344i	−0.0662062	+	0.629910i
$366$	−0.0182767	−	0.0316561i	−0.000955337	−	0.00165469i
$367$	14.7094	−	25.4774i	0.767823	−	1.32991i	−0.170918	−	0.985285i	$-0.554673\pi$
$367$	14.7094	−	25.4774i	0.767823	−	1.32991i	0.938741	−	0.344624i	$-0.111993\pi$
$368$	33.7990	+	24.5564i	1.76190	+	1.28009i
$369$	10.0876	−	11.2034i	0.525140	−	0.583227i
$370$	−0.659225	+	2.02889i	−0.0342715	+	0.105477i
$371$	−11.4944			−0.596759
$372$	−0.00678725	−	0.0108283i	−0.000351902	−	0.000561420i
$373$	−17.5532			−0.908872			−0.454436	−	0.890779i	$-0.650159\pi$
$373$	−17.5532			−0.908872			−0.454436	+	0.890779i	$0.650159\pi$
$374$	10.1527	−	31.2468i	0.524984	−	1.61573i
$375$	0.0168796	−	0.0187467i	0.000871658	−	0.000968074i
$376$	−9.48580	−	6.89184i	−0.489193	−	0.355419i
$377$	2.31557	−	4.01068i	0.119258	−	0.206561i
$378$	0.0298667	+	0.0517307i	0.00153618	+	0.00266074i
$379$	−1.04102	+	9.90466i	−0.0534737	+	0.508768i	0.934701	+	0.355435i	$0.115667\pi$
$379$	−1.04102	+	9.90466i	−0.0534737	+	0.508768i	−0.988175	+	0.153333i	$0.950999\pi$
$380$	−0.895141	+	0.650358i	−0.0459198	+	0.0333627i
$381$	−0.00304729	−	0.0289930i	−0.000156117	−	0.00148536i
$382$	−0.986562	−	1.09569i	−0.0504769	−	0.0560603i
$383$	−7.22673	+	3.21755i	−0.369268	+	0.164409i	−0.582977	−	0.812489i	$-0.698112\pi$
$383$	−7.22673	+	3.21755i	−0.369268	+	0.164409i	0.213709	+	0.976897i	$0.431446\pi$
$384$	−0.0374354	+	0.00795714i	−0.00191037	+	0.000406061i
$385$	−11.4115	−	2.42559i	−0.581583	−	0.123619i
$386$	10.5014	+	4.67553i	0.534507	+	0.237978i
$387$	8.60891	+	26.4955i	0.437615	+	1.34684i
$388$	2.88242	+	8.87116i	0.146332	+	0.450365i
$389$	8.40771	+	3.74335i	0.426288	+	0.189796i	0.608655	−	0.793435i	$-0.291709\pi$
$389$	8.40771	+	3.74335i	0.426288	+	0.189796i	−0.182367	+	0.983230i	$0.558376\pi$
$390$	−0.00453971		0.000964946i	−0.000229877		4.88619e-5i
$391$	27.3697	−	5.81760i	1.38414	−	0.294209i
$392$	−5.11749	+	2.27845i	−0.258472	+	0.115079i
$393$	−0.0110326	−	0.0122529i	−0.000556519	−	0.000618077i
$394$	3.11540	+	29.6411i	0.156952	+	1.49329i
$395$	−10.1577	+	7.38002i	−0.511090	+	0.371329i
$396$	1.47073	−	13.9930i	0.0739069	−	0.703177i
$397$	3.81082	+	6.60054i	0.191260	+	0.331271i	0.945668	−	0.325134i	$-0.105409\pi$
$397$	3.81082	+	6.60054i	0.191260	+	0.331271i	−0.754408	+	0.656405i	$0.772076\pi$
$398$	19.8450	−	34.3725i	0.994738	−	1.72294i
$399$	0.00702926	+	0.00510706i	0.000351903	+	0.000255673i
$400$	13.5379	−	15.0353i	0.676893	−	0.751765i
$401$	−1.93688	+	5.96111i	−0.0967232	+	0.297683i	−0.987699	−	0.156367i	$-0.950022\pi$
$401$	−1.93688	+	5.96111i	−0.0967232	+	0.297683i	0.890976	+	0.454051i	$0.150022\pi$
$402$	−0.0260152			−0.00129752
$403$	0.782562	+	5.51249i	0.0389822	+	0.274597i
$404$	−10.1360			−0.504285
$405$	2.66499	−	8.20199i	0.132424	−	0.407560i
$406$	10.6429	−	11.8201i	0.528198	−	0.586623i
$407$	−6.38467	−	4.63873i	−0.316476	−	0.229933i
$408$	−0.00971308	+	0.0168235i	−0.000480869	+	0.000832890i
$409$	4.18389	+	7.24671i	0.206880	+	0.358327i	0.950730	−	0.310020i	$-0.100336\pi$
$409$	4.18389	+	7.24671i	0.206880	+	0.358327i	−0.743850	+	0.668346i	$0.767002\pi$
$410$	−0.841028	+	8.00184i	−0.0415354	+	0.395183i
$411$	−0.00364725	+	0.00264988i	−0.000179906	+	0.000130709i
$412$	−0.606878	−	5.77406i	−0.0298987	−	0.284468i
$413$	4.36827	+	4.85146i	0.214949	+	0.238725i
$414$	38.5968	−	17.1844i	1.89693	−	0.844568i
$415$	−5.47306	+	1.16334i	−0.268662	+	0.0571059i
$416$	−4.15180	−	0.882493i	−0.203559	−	0.0432678i
$417$	−0.0550489	−	0.0245093i	−0.00269575	−	0.00120023i
$418$	−4.45968	−	13.7255i	−0.218130	−	0.671335i
$419$	−2.65477	−	8.17055i	−0.129694	−	0.399158i	0.865033	−	0.501715i	$-0.167297\pi$
$419$	−2.65477	−	8.17055i	−0.129694	−	0.399158i	−0.994727	+	0.102557i	$0.967297\pi$
$420$	−0.00413007	−	0.00183882i	−0.000201527	−	8.97254e-5i
$421$	−12.4538	−	2.64714i	−0.606961	−	0.129014i	−0.105829	−	0.994384i	$-0.533750\pi$
$421$	−12.4538	−	2.64714i	−0.606961	−	0.129014i	−0.501132	+	0.865371i	$0.667083\pi$
$422$	−6.31787	+	1.34291i	−0.307549	+	0.0653716i
$423$	−15.9182	+	7.08723i	−0.773968	+	0.344593i
$424$	−7.55359	−	8.38911i	−0.366835	−	0.407411i
$425$	−1.41642	−	13.4763i	−0.0687064	−	0.653698i
$426$	0.0202363	−	0.0147025i	0.000980451	−	0.000712339i
$427$	−1.62154	+	15.4279i	−0.0784719	+	0.746610i
$428$	0.643134	+	1.11394i	0.0310871	+	0.0538444i
$429$	0.00858466	−	0.0148691i	0.000414471	−	0.000717885i
$430$	−12.0288	−	8.73942i	−0.580079	−	0.421452i
$431$	21.7630	−	24.1703i	1.04829	−	1.16424i	0.0621932	−	0.998064i	$-0.480191\pi$
$431$	21.7630	−	24.1703i	1.04829	−	1.16424i	0.986096	−	0.166179i	$-0.0531428\pi$
$432$	−0.0266396	+	0.0819884i	−0.00128170	+	0.00394467i
$433$	30.0223			1.44278			0.721390	−	0.692529i	$-0.243504\pi$
$433$	30.0223			1.44278			0.721390	+	0.692529i	$0.243504\pi$
$434$	−1.30734	+	19.0776i	−0.0627541	+	0.915755i
$435$	0.0128638			0.000616770
$436$	0.824282	−	2.53688i	0.0394759	−	0.121494i
$437$	8.22428	−	9.13398i	0.393420	−	0.436938i
$438$	−0.0494817	−	0.0359506i	−0.00236433	−	0.00171778i
$439$	−20.2202	+	35.0224i	−0.965058	+	1.67153i	−0.255599	+	0.966783i	$0.582273\pi$
$439$	−20.2202	+	35.0224i	−0.965058	+	1.67153i	−0.709459	+	0.704747i	$0.751061\pi$
$440$	−5.72881	−	9.92259i	−0.273110	−	0.473041i
$441$	−0.870177	+	8.27918i	−0.0414370	+	0.394247i
$442$	−4.48755	+	3.26040i	−0.213451	+	0.155081i
$443$	1.29172	+	12.2899i	0.0613714	+	0.583910i	0.981389	+	0.192032i	$0.0615078\pi$
$443$	1.29172	+	12.2899i	0.0613714	+	0.583910i	−0.920017	+	0.391878i	$0.871826\pi$
$444$	−0.00204635	−	0.00227271i	−9.71156e−5	−	0.000107858i
$445$	−2.04758	+	0.911642i	−0.0970647	+	0.0432160i
$446$	25.6381	−	5.44954i	1.21400	−	0.258043i
$447$	0.0673063	+	0.0143064i	0.00318348	+	0.000676669i
$448$	5.29761	+	2.35865i	0.250289	+	0.111436i
$449$	−8.06475	−	24.8207i	−0.380599	−	1.17136i	−0.939623	−	0.342212i	$-0.888824\pi$
$449$	−8.06475	−	24.8207i	−0.380599	−	1.17136i	0.559024	−	0.829152i	$-0.311176\pi$
$450$	−6.32261	−	19.4590i	−0.298050	−	0.917305i
$451$	−27.1916	−	12.1065i	−1.28040	−	0.570072i
$452$	11.1067	+	2.36081i	0.522417	+	0.111043i
$453$	−0.0439290	+	0.00933740i	−0.00206397	+	0.000438709i
$454$	−34.9660	+	15.5678i	−1.64103	+	0.730635i
$455$	1.31796	+	1.46374i	0.0617868	+	0.0686212i
$456$	0.000891955		0.00848639i	4.17696e−5		0.000397412i
$457$	12.5511	−	9.11893i	0.587117	−	0.426566i	−0.254166	−	0.967161i	$-0.581801\pi$
$457$	12.5511	−	9.11893i	0.587117	−	0.426566i	0.841283	+	0.540595i	$0.181801\pi$
$458$	−1.02466	+	9.74900i	−0.0478793	+	0.455541i
$459$	0.0288692	+	0.0500029i	0.00134750	+	0.00233393i
$460$	−3.19766	+	5.53850i	−0.149091	+	0.258234i
$461$	−20.9487	−	15.2201i	−0.975678	−	0.708871i	−0.0189391	−	0.999821i	$-0.506029\pi$
$461$	−20.9487	−	15.2201i	−0.975678	−	0.708871i	−0.956738	+	0.290949i	$0.906029\pi$
$462$	0.0394571	−	0.0438215i	0.00183571	−	0.00203876i
$463$	8.67602	−	26.7020i	0.403209	−	1.24095i	−0.519173	−	0.854669i	$-0.673760\pi$
$463$	8.67602	−	26.7020i	0.403209	−	1.24095i	0.922382	−	0.386280i	$-0.126240\pi$
$464$	22.9550			1.06566
$465$	−0.0121736	+	0.00953840i	−0.000564538	+	0.000442333i
$466$	−25.9879			−1.20387
$467$	−4.20756	+	12.9495i	−0.194702	+	0.599233i	0.805277	+	0.592898i	$0.202016\pi$
$467$	−4.20756	+	12.9495i	−0.194702	+	0.599233i	−0.999980	+	0.00633444i	$0.997984\pi$
$468$	−1.58950	+	1.76532i	−0.0734748	+	0.0816020i
$469$	8.93207	+	6.48953i	0.412444	+	0.299658i
$470$	4.64977	−	8.05363i	0.214478	−	0.371486i
$471$	0.0327637	+	0.0567484i	0.00150967	+	0.00261483i
$472$	−0.670178	+	6.37632i	−0.0308474	+	0.293494i
$473$	44.4990	−	32.3304i	2.04607	−	1.48656i
$474$	−0.00663360	−	0.0631145i	−0.000304691	−	0.00289895i
$475$	−3.98281	−	4.42336i	−0.182744	−	0.202958i
$476$	−4.93611	+	2.19770i	−0.226246	+	0.100731i
$477$	−16.4094	+	3.48793i	−0.751336	+	0.159701i
$478$	−26.3754	−	5.60627i	−1.20638	−	0.256425i
$479$	13.4697	+	5.99712i	0.615448	+	0.274015i	0.690691	−	0.723150i	$-0.257306\pi$
$479$	13.4697	+	5.99712i	0.615448	+	0.274015i	−0.0752426	+	0.997165i	$0.523973\pi$
$480$	−0.00364330	−	0.0112129i	−0.000166293	−	0.000511797i
$481$	0.411733	+	1.26718i	0.0187734	+	0.0577786i
$482$	32.0497	+	14.2694i	1.45982	+	0.649956i
$483$	0.0491229	+	0.0104414i	0.00223517	+	0.000475100i
$484$	−18.6527	+	3.96476i	−0.847851	+	0.180216i
$485$	10.3121	−	4.59125i	0.468249	−	0.208478i
$486$	0.0875030	+	0.0971820i	0.00396922	+	0.00440826i
$487$	3.11893	+	29.6746i	0.141332	+	1.34468i	0.803489	+	0.595319i	$0.202974\pi$
$487$	3.11893	+	29.6746i	0.141332	+	1.34468i	−0.662157	+	0.749365i	$0.730359\pi$
$488$	−12.3256	+	8.95507i	−0.557954	+	0.405377i
$489$	−0.00284433	+	0.0270620i	−0.000128625	+	0.00122378i
$490$	−2.22147	−	3.84771i	−0.100356	−	0.173822i
$491$	−8.00048	+	13.8572i	−0.361057	+	0.625369i	−0.988135	−	0.153588i	$-0.950917\pi$
$491$	−8.00048	+	13.8572i	−0.361057	+	0.625369i	0.627078	+	0.778956i	$0.284251\pi$
$492$	−0.00933150	−	0.00677973i	−0.000420697	−	0.000305654i
$493$	10.2874	−	11.4253i	0.463322	−	0.514571i
$494$	−0.752933	+	2.31729i	−0.0338760	+	0.104260i
$495$	−17.0271			−0.765312
$496$	−21.7235	+	17.0210i	−0.975413	+	0.764266i
$497$	−10.6155			−0.476169
$498$	0.00873946	−	0.0268973i	0.000391625	−	0.00120530i
$499$	−5.15746	+	5.72794i	−0.230880	+	0.256418i	−0.847442	−	0.530888i	$-0.821858\pi$
$499$	−5.15746	+	5.72794i	−0.230880	+	0.256418i	0.616562	+	0.787306i	$0.288525\pi$
$500$	5.57485	+	4.05036i	0.249315	+	0.181138i
$501$	−0.00308332	+	0.00534047i	−0.000137753	+	0.000238595i
$502$	13.7848	+	23.8761i	0.615248	+	1.06564i
$503$	4.20675	−	40.0246i	0.187570	−	1.78461i	−0.345381	−	0.938462i	$-0.612250\pi$
$503$	4.20675	−	40.0246i	0.187570	−	1.78461i	0.532951	−	0.846146i	$-0.321083\pi$
$504$	10.0709	−	7.31692i	0.448593	−	0.325922i
$505$	1.28217	+	12.1990i	0.0570557	+	0.542849i
$506$	−55.8161	−	61.9901i	−2.48133	−	2.75580i
$507$	−0.00264811	+	0.00117901i	−0.000117607	+	5.23619e-5i
$508$	7.78948	−	1.65571i	0.345602	−	0.0734600i
$509$	−32.1657	−	6.83704i	−1.42572	−	0.303047i	−0.570495	−	0.821301i	$-0.693249\pi$
$509$	−32.1657	−	6.83704i	−1.42572	−	0.303047i	−0.855227	+	0.518254i	$0.826582\pi$
$510$	−0.0140754	−	0.00626679i	−0.000623271	−	0.000277498i
$511$	8.02114	+	24.6865i	0.354834	+	1.09207i
$512$	−0.317282	−	0.976493i	−0.0140220	−	0.0431553i
$513$	0.0231695	+	0.0103157i	0.00102296	+	0.000455450i
$514$	1.51271	+	0.321536i	0.0667227	+	0.0141823i
$515$	−6.87250	+	1.46079i	−0.302838	+	0.0643703i
$516$	0.0194721	−	0.00866953i	0.000857210	−	0.000381655i
$517$	23.0198	+	25.5661i	1.01241	+	1.12439i
$518$	0.478331	+	4.55102i	0.0210167	+	0.199960i
$519$	0.0176454	−	0.0128202i	0.000774549	−	0.000562743i
$520$	−0.202200	+	1.92381i	−0.00886707	+	0.0843645i
$521$	−15.3495	−	26.5862i	−0.672475	−	1.16476i	−0.977200	−	0.212321i	$-0.931898\pi$
$521$	−15.3495	−	26.5862i	−0.672475	−	1.16476i	0.304725	−	0.952440i	$-0.401436\pi$
$522$	11.6071	−	20.1040i	0.508027	−	0.879929i
$523$	−18.9223	−	13.7479i	−0.827415	−	0.601152i	0.0914115	−	0.995813i	$-0.470862\pi$
$523$	−18.9223	−	13.7479i	−0.827415	−	0.601152i	−0.918827	+	0.394661i	$0.870862\pi$
$524$	3.01371	−	3.34706i	0.131654	−	0.146217i
$525$	0.00751544	−	0.0231301i	0.000328001	−	0.00100948i
$526$	28.5110			1.24314
$527$	−1.26367	+	18.4404i	−0.0550464	+	0.803278i
$528$	0.0851026			0.00370361
$529$	14.8458	−	45.6906i	0.645468	−	1.98655i
$530$	5.99099	−	6.65366i	0.260232	−	0.289017i
$531$	7.70833	+	5.60043i	0.334513	+	0.243038i
$532$	−1.18672	+	2.05545i	−0.0514506	+	0.0891151i
$533$	2.51262	+	4.35199i	0.108834	+	0.188506i
$534$	0.00118419	−	0.0112668i	5.12450e−5	−	0.000487563i
$535$	1.25931	−	0.914942i	0.0544447	−	0.0395564i
$536$	1.13341	+	10.7836i	0.0489557	+	0.465782i
$537$	0.0155368	+	0.0172554i	0.000670464	+	0.000744626i
$538$	13.4731	−	5.99861i	0.580866	−	0.258618i
$539$	16.0770	−	3.41727i	0.692485	−	0.147192i
$540$	−0.0129082	−	0.00274372i	−0.000555480	−	0.000118071i
$541$	−15.3885	−	6.85142i	−0.661605	−	0.294565i	0.0483316	−	0.998831i	$-0.484610\pi$
$541$	−15.3885	−	6.85142i	−0.661605	−	0.294565i	−0.709936	+	0.704266i	$0.751276\pi$
$542$	−1.32883	−	4.08972i	−0.0570781	−	0.175668i
$543$	−0.0219545	−	0.0675691i	−0.000942159	−	0.00289967i
$544$	−12.8727	−	5.73131i	−0.551913	−	0.245728i
$545$	−3.15748	−	0.671144i	−0.135252	−	0.0287486i
$546$	−0.00973803	+	0.00206988i	−0.000416749	+	8.85828e-5i
$547$	−16.8007	+	7.48017i	−0.718348	+	0.319829i	−0.733155	−	0.680061i	$-0.761953\pi$
$547$	−16.8007	+	7.48017i	−0.718348	+	0.319829i	0.0148074	+	0.999890i	$0.495286\pi$
$548$	−0.824031	−	0.915179i	−0.0352008	−	0.0390945i
$549$	2.36664	+	22.5170i	0.101006	+	0.961004i
$550$	−32.6812	+	23.7443i	−1.39353	+	1.01246i
$551$	0.705914	−	6.71632i	0.0300730	−	0.286125i
$552$	0.0246608	+	0.0427137i	0.00104963	+	0.00181802i
$553$	−13.4664	+	23.3245i	−0.572649	+	0.991858i
$554$	−14.0364	−	10.1980i	−0.596348	−	0.433272i
$555$	−0.00247642	+	0.00275034i	−0.000105118	+	0.000116745i
$556$	5.08657	−	15.6549i	0.215719	−	0.663914i
$557$	−7.17791			−0.304138			−0.152069	−	0.988370i	$-0.548594\pi$
$557$	−7.17791			−0.304138			−0.152069	+	0.988370i	$0.548594\pi$
$558$	3.92268	+	27.6320i	0.166060	+	1.16976i
$559$	−9.28636			−0.392771
$560$	−3.01691	+	9.28509i	−0.127488	+	0.392367i
$561$	0.0381392	−	0.0423579i	0.00161024	−	0.00178835i
$562$	37.0532	+	26.9207i	1.56299	+	1.13558i
$563$	−4.86644	+	8.42893i	−0.205096	+	0.355237i	−0.950163	−	0.311752i	$-0.899084\pi$
$563$	−4.86644	+	8.42893i	−0.205096	+	0.355237i	0.745067	+	0.666989i	$0.232417\pi$
$564$	0.00666576	+	0.0115454i	0.000280679	+	0.000486150i
$565$	1.43635	−	13.6659i	0.0604276	−	0.574931i
$566$	17.9410	−	13.0349i	0.754116	−	0.547897i
$567$	−1.93370	−	18.3980i	−0.0812079	−	0.772642i
$568$	−6.97601	−	7.74764i	−0.292707	−	0.325084i
$569$	−25.7882	+	11.4816i	−1.08110	+	0.481336i	−0.868442	−	0.495791i	$-0.834878\pi$
$569$	−25.7882	+	11.4816i	−1.08110	+	0.481336i	−0.212656	+	0.977127i	$0.568211\pi$
$570$	−0.00662000	+	0.00140712i	−0.000277281	+	5.89379e-5i
$571$	24.8479	+	5.28159i	1.03985	+	0.221028i	0.696035	−	0.718008i	$-0.254946\pi$
$571$	24.8479	+	5.28159i	1.03985	+	0.221028i	0.343819	+	0.939036i	$0.388279\pi$
$572$	4.28458	+	1.90762i	0.179147	+	0.0797614i
$573$	−0.000790419	−	0.00243266i	−3.30202e−5	−	0.000101626i
$574$	5.33336	+	16.4144i	0.222610	+	0.685123i
$575$	−31.4295	−	13.9933i	−1.31070	−	0.583561i
$576$	8.27862	+	1.75967i	0.344942	+	0.0733198i
$577$	11.5416	−	2.45324i	0.480482	−	0.102130i	0.0386976	−	0.999251i	$-0.487679\pi$
$577$	11.5416	−	2.45324i	0.480482	−	0.102130i	0.441784	+	0.897121i	$0.354346\pi$
$578$	9.12669	−	4.06346i	0.379620	−	0.169018i
$579$	0.0133441	+	0.0148201i	0.000554562	+	0.000615904i
$580$	0.367305	+	3.49467i	0.0152515	+	0.145108i
$581$	−9.71016	+	7.05484i	−0.402845	+	0.292684i
$582$	−0.00596387	+	0.0567425i	−0.000247211	+	0.00235205i
$583$	16.5610	+	28.6845i	0.685886	+	1.18799i
$584$	−12.7462	+	22.0770i	−0.527441	+	0.913554i
$585$	2.32569	+	1.68971i	0.0961554	+	0.0698610i
$586$	−5.85011	+	6.49720i	−0.241666	+	0.268397i
$587$	−0.908687	+	2.79665i	−0.0375055	+	0.115430i	−0.968056	−	0.250732i	$-0.919329\pi$
$587$	−0.908687	+	2.79665i	−0.0375055	+	0.115430i	0.930551	+	0.366163i	$0.119329\pi$
$588$	0.00636927			0.000262664
$589$	4.31208	+	6.87943i	0.177676	+	0.283462i
$590$	−5.08511			−0.209351
$591$	−0.0159780	+	0.0491753i	−0.000657248	+	0.00202280i
$592$	−4.41910	+	4.90791i	−0.181624	+	0.201714i
$593$	−9.61915	−	6.98872i	−0.395011	−	0.286992i	0.372495	−	0.928034i	$-0.378502\pi$
$593$	−9.61915	−	6.98872i	−0.395011	−	0.286992i	−0.767506	+	0.641042i	$0.778502\pi$
$594$	0.0860633	−	0.149066i	0.00353122	−	0.00611625i
$595$	3.26940	+	5.66277i	0.134032	+	0.232151i
$596$	−1.96477	+	18.6935i	−0.0804799	+	0.765715i
$597$	0.0557057	−	0.0404725i	0.00227988	−	0.00165643i
$598$	1.47210	+	14.0061i	0.0601985	+	0.572750i
$599$	26.3809	+	29.2990i	1.07790	+	1.19712i	0.979388	+	0.201988i	$0.0647403\pi$
$599$	26.3809	+	29.2990i	1.07790	+	1.19712i	0.0985080	+	0.995136i	$0.468593\pi$
$600$	0.0218202	−	0.00971498i	0.000890806	−	0.000396612i
$601$	46.0005	−	9.77771i	1.87640	−	0.398841i	0.879389	−	0.476103i	$-0.157951\pi$
$601$	46.0005	−	9.77771i	1.87640	−	0.398841i	0.997011	+	0.0772623i	$0.0246179\pi$
$602$	−31.1969	−	6.63110i	−1.27149	−	0.270263i
$603$	14.7207	+	6.55407i	0.599472	+	0.266902i
$604$	−3.79100	−	11.6675i	−0.154254	−	0.474744i
$605$	7.13121	+	21.9476i	0.289925	+	0.892298i
$606$	−0.0566392	−	0.0252174i	−0.00230081	−	0.00102439i
$607$	3.20062	+	0.680314i	0.129909	+	0.0276131i	0.272407	−	0.962182i	$-0.412180\pi$
$607$	3.20062	+	0.680314i	0.129909	+	0.0276131i	−0.142498	+	0.989795i	$0.545513\pi$
$608$	−6.05433	+	1.28689i	−0.245536	+	0.0521902i
$609$	0.0252081	−	0.0112234i	0.00102148	−	0.000454794i
$610$	−8.08548	−	8.97984i	−0.327372	−	0.363583i
$611$	−0.607124	−	5.77640i	−0.0245616	−	0.233688i
$612$	−6.37993	+	4.63529i	−0.257893	+	0.187371i
$613$	−4.31663	+	41.0700i	−0.174347	+	1.65880i	0.461614	+	0.887081i	$0.347271\pi$
$613$	−4.31663	+	41.0700i	−0.174347	+	1.65880i	−0.635961	+	0.771721i	$0.719396\pi$
$614$	−13.2029	−	22.8680i	−0.532824	−	0.922878i
$615$	−0.00697923	+	0.0120884i	−0.000281430	+	0.000487450i
$616$	−19.8836	−	14.4463i	−0.801133	−	0.582057i
$617$	−11.8885	+	13.2035i	−0.478613	+	0.531553i	−0.933300	−	0.359098i	$-0.883084\pi$
$617$	−11.8885	+	13.2035i	−0.478613	+	0.531553i	0.454687	+	0.890651i	$0.349751\pi$
$618$	0.0109741	−	0.0337748i	0.000441443	−	0.00135862i
$619$	−13.0804			−0.525746			−0.262873	−	0.964830i	$-0.584670\pi$
$619$	−13.0804			−0.525746			−0.262873	+	0.964830i	$0.584670\pi$
$620$	−2.93888	−	3.03483i	−0.118028	−	0.121882i
$621$	0.146593			0.00588258
$622$	−15.7718	+	48.5405i	−0.632390	+	1.94630i
$623$	−3.21710	+	3.57295i	−0.128890	+	0.143147i
$624$	−0.0116239	−	0.00844528i	−0.000465330	−	0.000338082i
$625$	−6.03490	+	10.4528i	−0.241396	+	0.418110i
$626$	15.8523	+	27.4569i	0.633584	+	1.09740i
$627$	0.00261708	−	0.0248999i	0.000104516	−	0.000994405i
$628$	−14.4812	+	10.5212i	−0.577864	+	0.419843i
$629$	0.462355	+	4.39902i	0.0184353	+	0.175400i
$630$	6.60641	+	7.33716i	0.263206	+	0.292320i
$631$	13.6615	−	6.08250i	0.543856	−	0.242140i	−0.116372	−	0.993206i	$-0.537126\pi$
$631$	13.6615	−	6.08250i	0.543856	−	0.242140i	0.660228	+	0.751065i	$0.270460\pi$
$632$	−25.8727	+	5.49942i	−1.02916	+	0.218755i
$633$	−0.0109606	−	0.00232974i	−0.000435643	−	9.25987e-5i
$634$	9.90283	+	4.40902i	0.393292	+	0.175105i
$635$	−2.97804	−	9.16545i	−0.118180	−	0.363720i
$636$	0.00396632	+	0.0122071i	0.000157275	+	0.000484042i
$637$	−2.53503	−	1.12867i	−0.100442	−	0.0447195i
$638$	−44.8316	−	9.52924i	−1.77490	−	0.377266i
$639$	−15.1547	+	3.22123i	−0.599511	+	0.127430i
$640$	−11.5578	+	5.14588i	−0.456863	+	0.203409i
$641$	−5.03451	−	5.59139i	−0.198851	−	0.220847i	0.635470	−	0.772126i	$-0.280807\pi$
$641$	−5.03451	−	5.59139i	−0.198851	−	0.220847i	−0.834321	+	0.551279i	$0.814140\pi$
$642$	0.000822405		0.00782466i	3.24577e−5		0.000308815i
$643$	−6.68294	+	4.85544i	−0.263549	+	0.191480i	−0.711710	−	0.702473i	$-0.752079\pi$
$643$	−6.68294	+	4.85544i	−0.263549	+	0.191480i	0.448161	+	0.893953i	$0.352079\pi$
$644$	−1.43397	+	13.6433i	−0.0565062	+	0.537621i
$645$	−0.0128972	−	0.0223386i	−0.000507827	−	0.000879582i
$646$	−4.04438	+	7.00506i	−0.159124	+	0.275611i
$647$	−29.2394	−	21.2437i	−1.14952	−	0.835176i	−0.161104	−	0.986937i	$-0.551506\pi$
$647$	−29.2394	−	21.2437i	−1.14952	−	0.835176i	−0.988417	+	0.151761i	$0.951506\pi$
$648$	12.1569	−	13.5016i	0.477568	−	0.530393i
$649$	5.81316	−	17.8911i	0.228186	−	0.702285i
$650$	6.82015			0.267508
$651$	−0.0155336	+	0.0293129i	−0.000608811	+	0.00114886i
$652$	−7.43310			−0.291103
$653$	10.2715	−	31.6124i	0.401955	−	1.23709i	−0.521456	−	0.853278i	$-0.674611\pi$
$653$	10.2715	−	31.6124i	0.401955	−	1.23709i	0.923411	−	0.383812i	$-0.125389\pi$
$654$	0.0109175	−	0.0121251i	0.000426909	−	0.000474130i
$655$	−4.40952	−	3.20370i	−0.172294	−	0.125179i
$656$	−12.4542	+	21.5714i	−0.486256	+	0.842220i
$657$	18.9421	+	32.8086i	0.739000	+	1.27999i
$658$	2.08516	−	19.8389i	0.0812878	−	0.773402i
$659$	−6.02199	+	4.37523i	−0.234584	+	0.170435i	−0.698867	−	0.715252i	$-0.746312\pi$
$659$	−6.02199	+	4.37523i	−0.234584	+	0.170435i	0.464283	+	0.885687i	$0.346312\pi$
$660$	0.00136173	+	0.0129560i	5.30054e−5	+	0.000504313i
$661$	−17.7458	−	19.7087i	−0.690230	−	0.766579i	0.291559	−	0.956553i	$-0.405826\pi$
$661$	−17.7458	−	19.7087i	−0.690230	−	0.766579i	−0.981789	+	0.189974i	$0.939160\pi$
$662$	45.4937	−	20.2551i	1.76816	−	0.787238i
$663$	−0.00941278	+	0.00200075i	−0.000365562	+	7.77026e-5i
$664$	−11.5300	−	2.45078i	−0.447451	−	0.0951087i
$665$	2.62392	+	1.16824i	0.101751	+	0.0453025i
$666$	2.06386	+	6.35191i	0.0799729	+	0.246131i
$667$	−12.0622	−	37.1237i	−0.467051	−	1.43744i
$668$	−1.53888	−	0.685152i	−0.0595409	−	0.0265093i
$669$	0.0444781	+	0.00945412i	0.00171962	+	0.000365517i
$670$	−8.41202	+	1.78803i	−0.324985	+	0.0690776i
$671$	40.8371	−	18.1818i	1.57650	−	0.701902i
$672$	−0.0169226	−	0.0187944i	−0.000652802	−	0.000725010i
$673$	−1.33147	−	12.6681i	−0.0513244	−	0.488319i	−0.989747	−	0.142830i	$-0.954380\pi$
$673$	−1.33147	−	12.6681i	−0.0513244	−	0.488319i	0.938423	−	0.345489i	$-0.112287\pi$
$674$	−0.475895	+	0.345758i	−0.0183308	+	0.0133181i
$675$	0.00742062	−	0.0706025i	0.000285620	−	0.00271749i
$676$	−0.395914	−	0.685743i	−0.0152274	−	0.0263747i
$677$	−3.30309	+	5.72111i	−0.126948	+	0.219880i	−0.922493	−	0.386015i	$-0.873851\pi$
$677$	−3.30309	+	5.72111i	−0.126948	+	0.219880i	0.795545	+	0.605895i	$0.207185\pi$
$678$	0.0561900	+	0.0408244i	0.00215796	+	0.00156785i
$679$	16.2021	−	17.9943i	0.621779	−	0.690556i
$680$	−1.98444	+	6.10747i	−0.0760997	+	0.234211i
$681$	−0.0664014			−0.00254451
$682$	49.4922	−	24.2244i	1.89516	−	0.927599i
$683$	24.1533			0.924201			0.462100	−	0.886828i	$-0.347096\pi$
$683$	24.1533			0.924201			0.462100	+	0.886828i	$0.347096\pi$
$684$	−1.07044	+	3.29448i	−0.0409293	+	0.125967i
$685$	−0.997210	+	1.10751i	−0.0381014	+	0.0423159i
$686$	−27.1602	−	19.7330i	−1.03698	−	0.753410i
$687$	−0.00850310	+	0.0147278i	−0.000324413	+	0.000561900i
$688$	−23.0147	−	39.8626i	−0.877427	−	1.51975i
$689$	0.584526	−	5.56139i	0.0222687	−	0.211872i
$690$	−0.0316475	+	0.0229932i	−0.00120480	+	0.000875337i
$691$	1.15013	+	10.9428i	0.0437530	+	0.416282i	0.994374	+	0.105927i	$0.0337811\pi$
$691$	1.15013	+	10.9428i	0.0437530	+	0.416282i	−0.950621	+	0.310355i	$0.899552\pi$
$692$	3.98667	+	4.42765i	0.151550	+	0.168314i
$693$	−33.3668	+	14.8558i	−1.26750	+	0.564327i
$694$	−26.3425	+	5.59926i	−0.999946	+	0.212545i
$695$	−19.4846	−	4.14157i	−0.739092	−	0.157099i
$696$	0.0247570	+	0.0110225i	0.000938410	+	0.000417807i
$697$	5.15522	+	15.8661i	0.195268	+	0.600973i
$698$	0.677369	+	2.08473i	0.0256388	+	0.0789080i
$699$	−0.0411873	−	0.0183378i	−0.00155785	−	0.000693598i
$700$	6.49832	+	1.38126i	0.245613	+	0.0522067i
$701$	12.1938	−	2.59188i	0.460555	−	0.0978939i	0.0282093	−	0.999602i	$-0.491020\pi$
$701$	12.1938	−	2.59188i	0.460555	−	0.0978939i	0.432345	+	0.901708i	$0.357686\pi$
$702$	−0.0265479	+	0.0118199i	−0.00100199	+	0.000446114i
$703$	1.30009	+	1.44390i	0.0490339	+	0.0544576i
$704$	−1.74669	−	16.6186i	−0.0658308	−	0.626338i
$705$	0.0130521	−	0.00948291i	0.000491571	−	0.000357147i
$706$	3.53706	−	33.6529i	0.133119	−	1.26654i
$707$	13.1560	+	22.7868i	0.494782	+	0.856987i
$708$	0.00364493	−	0.00631320i	0.000136985	−	0.000237265i
$709$	12.1459	+	8.82450i	0.456148	+	0.331411i	0.792018	−	0.610497i	$-0.209030\pi$
$709$	12.1459	+	8.82450i	0.456148	+	0.331411i	−0.335870	+	0.941908i	$0.609030\pi$
$710$	5.53289	−	6.14490i	0.207646	−	0.230614i
$711$	−12.1469	+	37.3845i	−0.455546	+	1.40203i
$712$	−4.72183			−0.176958
$713$	38.9421	+	26.1880i	1.45839	+	0.980747i
$714$	−0.0330502			−0.00123687
$715$	1.75389	−	5.39793i	0.0655919	−	0.201871i
$716$	−4.24412	+	4.71357i	−0.158610	+	0.176154i
$717$	−0.0378455	−	0.0274964i	−0.00141337	−	0.00102687i
$718$	−0.146439	+	0.253640i	−0.00546506	+	0.00946576i
$719$	−0.879042	−	1.52254i	−0.0327827	−	0.0567813i	0.849169	−	0.528122i	$-0.177104\pi$
$719$	−0.879042	−	1.52254i	−0.0327827	−	0.0567813i	−0.881951	+	0.471341i	$0.843770\pi$
$720$	−1.48942	+	14.1709i	−0.0555075	+	0.528119i
$721$	−12.1930	+	8.85874i	−0.454091	+	0.329917i
$722$	−2.94703	−	28.0391i	−0.109677	−	1.04351i
$723$	0.0407255	+	0.0452302i	0.00151460	+	0.00168213i
$724$	17.7295	−	7.89368i	0.658912	−	0.293366i
$725$	−18.4902	+	3.93021i	−0.686709	+	0.145964i
$726$	−0.114094	−	0.0242514i	−0.00423442	−	0.000900053i
$727$	−8.62886	−	3.84181i	−0.320027	−	0.142485i	0.240435	−	0.970665i	$-0.422710\pi$
$727$	−8.62886	−	3.84181i	−0.320027	−	0.142485i	−0.560462	+	0.828180i	$0.689376\pi$
$728$	1.28225	+	3.94636i	0.0475233	+	0.146262i
$729$	−8.34332	−	25.6781i	−0.309012	−	0.951041i
$730$	−18.4708	−	8.22372i	−0.683634	−	0.304374i
$731$	−30.1549	−	6.40962i	−1.11532	−	0.237068i
$732$	0.0169441	−	0.00360157i	0.000626271	−	0.000133118i
$733$	23.6667	−	10.5371i	0.874148	−	0.389196i	0.0799099	−	0.996802i	$-0.474537\pi$
$733$	23.6667	−	10.5371i	0.874148	−	0.389196i	0.794238	+	0.607606i	$0.207870\pi$
$734$	32.8912	+	36.5294i	1.21404	+	1.34832i
$735$	−0.000805689	−	0.00766562i	−2.97183e−5	−	0.000282751i
$736$	−28.9433	+	21.0285i	−1.06686	+	0.775121i
$737$	3.32552	−	31.6402i	0.122497	−	1.16548i
$738$	12.5948	+	21.8149i	0.463622	+	0.803016i
$739$	22.9846	−	39.8105i	0.845503	−	1.46445i	−0.0396807	−	0.999212i	$-0.512634\pi$
$739$	22.9846	−	39.8105i	0.845503	−	1.46445i	0.885184	−	0.465242i	$-0.154033\pi$
$740$	−0.817891	−	0.594233i	−0.0300663	−	0.0218444i
$741$	−0.00282844	+	0.00314130i	−0.000103905	+	0.000115398i
$742$	5.93489	−	18.2657i	0.217877	−	0.670555i
$743$	9.53823			0.349924			0.174962	−	0.984575i	$-0.444020\pi$
$743$	9.53823			0.349924			0.174962	+	0.984575i	$0.444020\pi$
$744$	−0.0316019	+	0.00792600i	−0.00115858	+	0.000290581i
$745$	22.7468			0.833377
$746$	9.06324	−	27.8938i	0.331829	−	1.02126i
$747$	−11.7215	+	13.0180i	−0.428867	+	0.476305i
$748$	12.5963	+	9.15175i	0.460566	+	0.334621i
$749$	1.66950	−	2.89167i	0.0610024	−	0.105659i
$750$	0.0210749	+	0.0365027i	0.000769545	+	0.00133289i
$751$	3.19644	−	30.4121i	0.116640	−	1.10975i	−0.767021	−	0.641623i	$-0.778262\pi$
$751$	3.19644	−	30.4121i	0.116640	−	1.10975i	0.883660	−	0.468129i	$-0.155072\pi$
$752$	23.2911	−	16.9220i	0.849339	−	0.617081i
$753$	0.00499952	+	0.0475672i	0.000182193	+	0.00173345i
$754$	5.17777	+	5.75050i	0.188563	+	0.209421i
$755$	−13.5627	+	6.03849i	−0.493596	+	0.219763i
$756$	−0.0276890	+	0.00588549i	−0.00100704	+	0.000214053i
$757$	−3.86253	−	0.821006i	−0.140386	−	0.0298400i	0.137183	−	0.990546i	$-0.456195\pi$
$757$	−3.86253	−	0.821006i	−0.140386	−	0.0298400i	−0.277569	+	0.960706i	$0.589529\pi$
$758$	−15.2020	−	6.76835i	−0.552160	−	0.245837i
$759$	−0.0447191	−	0.137631i	−0.00162320	−	0.00499569i
$760$	0.871684	+	2.68277i	0.0316193	+	0.0973142i
$761$	9.94494	+	4.42777i	0.360504	+	0.160507i	0.578993	−	0.815333i	$-0.303446\pi$
$761$	9.94494	+	4.42777i	0.360504	+	0.160507i	−0.218489	+	0.975839i	$0.570113\pi$
$762$	0.0476462	+	0.0101275i	0.00172604	+	0.000366881i
$763$	−6.77304	+	1.43965i	−0.245201	+	0.0521190i
$764$	0.638307	−	0.284193i	0.0230931	−	0.0102817i
$765$	6.38576	+	7.09210i	0.230878	+	0.256416i
$766$	−1.38163	−	13.1453i	−0.0499201	−	0.474958i
$767$	−2.56945	+	1.86681i	−0.0927774	+	0.0674068i
$768$	0.00497468	−	0.0473309i	0.000179508	−	0.00170791i
$769$	−13.6692	−	23.6758i	−0.492924	−	0.853770i	0.507042	−	0.861921i	$-0.330739\pi$
$769$	−13.6692	−	23.6758i	−0.492924	−	0.853770i	−0.999967	+	0.00815111i	$0.997405\pi$
$770$	9.74657	−	16.8816i	0.351242	−	0.608369i
$771$	0.00217055	+	0.00157700i	7.81705e−5	+	5.67942e-5i
$772$	−3.64514	+	4.04834i	−0.131191	+	0.145703i
$773$	6.93312	−	21.3380i	0.249367	−	0.767473i	−0.745520	−	0.666483i	$-0.767799\pi$
$773$	6.93312	−	21.3380i	0.249367	−	0.767473i	0.994887	−	0.100990i	$-0.0322010\pi$
$774$	−46.5490			−1.67317
$775$	14.5840	−	17.4297i	0.523872	−	0.626095i
$776$	23.7803			0.853662
$777$	−0.00245323	+	0.00755026i	−8.80091e−5	+	0.000270864i
$778$	−10.2897	+	11.4279i	−0.368904	+	0.409709i
$779$	5.92850	+	4.30731i	0.212410	+	0.154325i
$780$	0.00109972	−	0.00190476i	3.93761e−5	−	6.82014e-5i
$781$	15.2947	+	26.4911i	0.547286	+	0.947928i
$782$	−4.88702	+	46.4969i	−0.174759	+	1.66272i
$783$	0.0651631	−	0.0473438i	0.00232874	−	0.00169193i
$784$	−1.43773	−	13.6791i	−0.0513475	−	0.488539i
$785$	14.4945	+	16.0977i	0.517329	+	0.574552i
$786$	0.0251675	−	0.0112053i	0.000897694	−	0.000399679i
$787$	52.9981	−	11.2651i	1.88918	−	0.401557i	0.890597	−	0.454793i	$-0.150287\pi$
$787$	52.9981	−	11.2651i	1.88918	−	0.401557i	0.998582	+	0.0532360i	$0.0169536\pi$
$788$	−13.8156	−	2.93660i	−0.492161	−	0.104612i
$789$	0.0451861	+	0.0201181i	0.00160867	+	0.000716225i
$790$	−6.48284	−	19.9521i	−0.230649	−	0.709865i
$791$	−9.10857	−	28.0333i	−0.323864	−	0.996750i
$792$	−32.7696	−	14.5900i	−1.16442	−	0.518431i
$793$	−7.38213	−	1.56912i	−0.262147	−	0.0557211i
$794$	−12.4565	+	2.64772i	−0.442066	+	0.0939640i
$795$	0.0141899	−	0.00631775i	0.000503264	−	0.000224067i
$796$	12.5857	+	13.9778i	0.446088	+	0.495431i
$797$	1.55487	+	14.7936i	0.0550762	+	0.524015i	0.986926	+	0.161172i	$0.0515273\pi$
$797$	1.55487	+	14.7936i	0.0550762	+	0.524015i	−0.931850	+	0.362843i	$0.881806\pi$
$798$	−0.0117450	+	0.00853326i	−0.000415769	+	0.000302074i
$799$	2.01551	−	19.1763i	0.0713037	−	0.678409i
$800$	8.66267	+	15.0042i	0.306272	+	0.530478i
$801$	−3.50855	+	6.07698i	−0.123968	+	0.214720i
$802$	−8.47271	−	6.15579i	−0.299182	−	0.217368i
$803$	50.0490	−	55.5850i	1.76619	−	1.96155i
$804$	0.00380975	−	0.0117252i	0.000134360	−	0.000413516i
$805$	16.6015			0.585127
$806$	−9.16395	−	1.60269i	−0.322786	−	0.0564525i
$807$	0.0255858			0.000900662
$808$	−7.98532	+	24.5763i	−0.280923	+	0.864591i
$809$	−25.5233	+	28.3465i	−0.897350	+	0.996608i	0.102648	+	0.994718i	$0.467269\pi$
$809$	−25.5233	+	28.3465i	−0.897350	+	0.996608i	−0.999998	+	0.00189072i	$0.999398\pi$
$810$	11.6577	+	8.46985i	0.409611	+	0.297600i
$811$	−17.8275	+	30.8781i	−0.626008	+	1.08428i	0.362338	+	0.932047i	$0.381979\pi$
$811$	−17.8275	+	30.8781i	−0.626008	+	1.08428i	−0.988345	+	0.152230i	$0.951355\pi$
$812$	3.76882	+	6.52778i	0.132260	+	0.229080i
$813$	0.000779800	−	0.00741930i	2.73488e−5	−	0.000260206i
$814$	10.6680	−	7.75075i	0.373913	−	0.271664i
$815$	0.940259	+	8.94597i	0.0329358	+	0.313364i
$816$	−0.0319164	−	0.0354468i	−0.00111730	−	0.00124088i
$817$	−12.3710	+	5.50793i	−0.432807	+	0.192698i
$818$	−13.6760	+	2.90692i	−0.478170	+	0.101638i
$819$	6.03172	+	1.28208i	0.210765	+	0.0447995i
$820$	−3.48331	−	1.55087i	−0.121642	−	0.0541587i
$821$	0.470312	+	1.44747i	0.0164140	+	0.0505171i	0.958928	−	0.283649i	$-0.0915452\pi$
$821$	0.470312	+	1.44747i	0.0164140	+	0.0505171i	−0.942514	+	0.334167i	$0.891545\pi$
$822$	−0.00232774	−	0.00716405i	−8.11893e−5	−	0.000249875i
$823$	−13.6860	−	6.09339i	−0.477063	−	0.212402i	0.154095	−	0.988056i	$-0.450754\pi$
$823$	−13.6860	−	6.09339i	−0.477063	−	0.212402i	−0.631159	+	0.775654i	$0.717420\pi$
$824$	−14.4782	−	3.07743i	−0.504371	−	0.107207i
$825$	−0.0685499	+	0.0145707i	−0.00238660	+	0.000507288i
$826$	−9.96491	+	4.43666i	−0.346724	+	0.154371i
$827$	−15.3020	−	16.9946i	−0.532102	−	0.590959i	0.415826	−	0.909444i	$-0.363492\pi$
$827$	−15.3020	−	16.9946i	−0.532102	−	0.590959i	−0.947928	+	0.318485i	$0.896826\pi$
$828$	2.09287	+	19.9123i	0.0727323	+	0.692002i
$829$	−14.1552	+	10.2844i	−0.491632	+	0.357192i	−0.805812	−	0.592172i	$-0.798271\pi$
$829$	−14.1552	+	10.2844i	−0.491632	+	0.357192i	0.314180	+	0.949364i	$0.398271\pi$
$830$	0.977248	−	9.29790i	0.0339208	−	0.322735i
$831$	−0.0150497	−	0.0260669i	−0.000522069	−	0.000904251i
$832$	−1.41060	+	2.44323i	−0.0489037	+	0.0847037i
$833$	−7.45278	−	5.41476i	−0.258224	−	0.187610i
$834$	0.0673711	−	0.0748231i	0.00233287	−	0.00259091i
$835$	−0.629940	+	1.93876i	−0.0218000	+	0.0670934i
$836$	6.83923			0.236540
$837$	−0.0265620	+	0.0931219i	−0.000918116	+	0.00321877i
$838$	14.3545			0.495870
$839$	2.14300	−	6.59548i	0.0739846	−	0.227701i	−0.907225	−	0.420645i	$-0.861804\pi$
$839$	2.14300	−	6.59548i	0.0739846	−	0.227701i	0.981210	+	0.192944i	$0.0618037\pi$
$840$	−0.00771224	+	0.00856531i	−0.000266098	+	0.000295531i
$841$	6.11014	+	4.43928i	0.210694	+	0.153078i
$842$	10.6368	−	18.4235i	0.366569	−	0.634916i
$843$	0.0397283	+	0.0688114i	0.00136831	+	0.00236999i
$844$	0.319954	−	3.04416i	0.0110133	−	0.104784i
$845$	−0.775232	+	0.563239i	−0.0266688	+	0.0193760i
$846$	−3.04328	−	28.9549i	−0.104630	−	0.995489i
$847$	33.1234	+	36.7873i	1.13813	+	1.26402i
$848$	25.3215	−	11.2738i	0.869543	−	0.387145i
$849$	0.0376318	−	0.00799888i	0.00129152	−	0.000274521i
$850$	22.1465	+	4.70739i	0.759620	+	0.161462i
$851$	10.2594	+	4.56777i	0.351687	+	0.156581i
$852$	0.00366304	+	0.0112737i	0.000125494	+	0.000386230i
$853$	−3.45293	−	10.6270i	−0.118226	−	0.363862i	0.874380	−	0.485241i	$-0.161268\pi$
$853$	−3.45293	−	10.6270i	−0.118226	−	0.363862i	−0.992606	+	0.121379i	$0.961268\pi$
$854$	−23.6793	−	10.5427i	−0.810287	−	0.360763i
$855$	4.10041	+	0.871570i	0.140231	+	0.0298071i
$856$	3.20759	−	0.681794i	0.109633	−	0.0233032i
$857$	−33.4311	+	14.8845i	−1.14199	+	0.508445i	−0.888492	−	0.458892i	$-0.848246\pi$
$857$	−33.4311	+	14.8845i	−1.14199	+	0.508445i	−0.253494	+	0.967337i	$0.581580\pi$
$858$	0.0191959	+	0.0213192i	0.000655337	+	0.000727825i
$859$	−3.51332	−	33.4270i	−0.119873	−	1.14051i	−0.874725	−	0.484619i	$-0.838958\pi$
$859$	−3.51332	−	33.4270i	−0.119873	−	1.14051i	0.754853	−	0.655895i	$-0.227708\pi$
$860$	5.70043	−	4.14161i	0.194383	−	0.141228i
$861$	−0.00312979	+	0.0297779i	−0.000106663	+	0.00101483i
$862$	27.1721	+	47.0634i	0.925485	+	1.60299i
$863$	−3.10965	+	5.38607i	−0.105854	+	0.183344i	−0.914087	−	0.405519i	$-0.867091\pi$
$863$	−3.10965	+	5.38607i	−0.105854	+	0.183344i	0.808233	+	0.588863i	$0.200424\pi$
$864$	−0.0597237	−	0.0433918i	−0.00203184	−	0.00147622i
$865$	4.82451	−	5.35817i	0.164038	−	0.182183i
$866$	−15.5014	+	47.7084i	−0.526759	+	1.62120i
$867$	0.0173318			0.000588620
$868$	−8.40694	−	3.38301i	−0.285350	−	0.114827i
$869$	77.6090			2.63270
$870$	−0.00664193	+	0.0204418i	−0.000225182	+	0.000693040i
$871$	−3.59409	+	3.99164i	−0.121781	+	0.135251i
$872$	−5.50166	−	3.99719i	−0.186310	−	0.135362i
$873$	17.6699	−	30.6051i	0.598035	−	1.03583i
$874$	10.2684	+	17.7853i	0.347332	+	0.601597i
$875$	1.86980	−	17.7900i	0.0632109	−	0.601411i
$876$	0.0234494	−	0.0170370i	0.000792280	−	0.000575625i
$877$	−0.944127	−	8.98277i	−0.0318809	−	0.303327i	−0.998830	−	0.0483575i	$-0.984601\pi$
$877$	−0.944127	−	8.98277i	−0.0318809	−	0.303327i	0.966949	−	0.254969i	$-0.0820653\pi$
$878$	−45.2138	−	50.2150i	−1.52589	−	1.69467i
$879$	−0.0138562	+	0.00616918i	−0.000467358	+	0.000208081i
$880$	27.5179	−	5.84911i	0.927628	−	0.197173i
$881$	22.9971	+	4.88819i	0.774792	+	0.164687i	0.578307	−	0.815819i	$-0.303714\pi$
$881$	22.9971	+	4.88819i	0.774792	+	0.164687i	0.196486	+	0.980507i	$0.437047\pi$
$882$	−12.7071	−	5.65758i	−0.427871	−	0.190501i
$883$	0.343764	+	1.05800i	0.0115686	+	0.0356045i	0.956674	−	0.291161i	$-0.0940414\pi$
$883$	0.343764	+	1.05800i	0.0115686	+	0.0356045i	−0.945106	+	0.326765i	$0.894041\pi$
$884$	−0.812308	−	2.50003i	−0.0273209	−	0.0840850i
$885$	−0.00805921	−	0.00358819i	−0.000270907	−	0.000120616i
$886$	−20.1968	−	4.29296i	−0.678524	−	0.144225i
$887$	34.6461	−	7.36426i	1.16330	−	0.247268i	0.414493	−	0.910052i	$-0.363959\pi$
$887$	34.6461	−	7.36426i	1.16330	−	0.247268i	0.748810	+	0.662785i	$0.230626\pi$
$888$	−0.00712267	+	0.00317122i	−0.000239021	+	0.000106419i
$889$	−13.8325	−	15.3626i	−0.463928	−	0.515244i
$890$	−0.391462	−	3.72451i	−0.0131218	−	0.124846i
$891$	−43.1265	+	31.3332i	−1.44479	+	1.04970i
$892$	−1.29838	+	12.3533i	−0.0434729	+	0.413617i
$893$	−4.23489	−	7.33505i	−0.141715	−	0.245458i
$894$	−0.0574865	+	0.0995695i	−0.00192264	+	0.00333010i
$895$	6.20980	+	4.51168i	0.207571	+	0.150809i
$896$	−18.1593	+	20.1680i	−0.606660	+	0.673765i
$897$	−0.00754998	+	0.0232364i	−0.000252086	+	0.000775842i
$898$	43.6067			1.45517
$899$	25.7681	−	0.935782i	0.859415	−	0.0312101i
$900$	9.69616			0.323205
$901$	5.73666	−	17.6556i	0.191116	−	0.588194i
$902$	33.2782	−	36.9592i	1.10804	−	1.23061i
$903$	−0.0447637	−	0.0325227i	−0.00148964	−	0.00108229i
$904$	14.4742	−	25.0701i	0.481405	−	0.833818i
$905$	−11.7430	−	20.3395i	−0.390351	−	0.676108i
$906$	0.00784379	−	0.0746287i	0.000260592	−	0.00247937i
$907$	−37.3778	+	27.1566i	−1.24111	+	0.901720i	−0.997672	−	0.0681964i	$-0.978276\pi$
$907$	−37.3778	+	27.1566i	−1.24111	+	0.901720i	−0.243439	+	0.969916i	$0.578276\pi$
$908$	−1.89599	−	18.0391i	−0.0629206	−	0.598650i
$909$	25.6961	+	28.5384i	0.852287	+	0.946560i
$910$	−3.00653	+	1.33859i	−0.0996653	+	0.0443739i
$911$	5.32222	−	1.13127i	0.176333	−	0.0374808i	−0.118899	−	0.992906i	$-0.537936\pi$
$911$	5.32222	−	1.13127i	0.176333	−	0.0374808i	0.295232	+	0.955426i	$0.404603\pi$
$912$	−0.0204941	−	0.00435616i	−0.000678628	−	0.000144247i
$913$	31.5958	+	14.0674i	1.04567	+	0.465562i
$914$	8.01036	+	24.6534i	0.264959	+	0.815460i
$915$	−0.00647797	−	0.0199372i	−0.000214155	−	0.000659102i
$916$	−4.24387	−	1.88949i	−0.140221	−	0.0624306i
$917$	−11.4362	−	2.43083i	−0.377655	−	0.0802732i
$918$	−0.0943654	+	0.0200580i	−0.00311452	+	0.000662012i
$919$	24.4130	−	10.8694i	0.805310	−	0.358547i	0.0375582	−	0.999294i	$-0.488042\pi$
$919$	24.4130	−	10.8694i	0.805310	−	0.358547i	0.767752	+	0.640747i	$0.221375\pi$
$920$	10.9098	+	12.1165i	0.359684	+	0.399470i
$921$	−0.00478844	−	0.0455589i	−0.000157784	−	0.00150122i
$922$	35.0027	−	25.4309i	1.15275	−	0.837523i
$923$	0.539831	−	5.13614i	0.0177687	−	0.169058i
$924$	0.0139724	+	0.0242009i	0.000459657	+	0.000796150i
$925$	2.71927	−	4.70992i	0.0894091	−	0.154861i
$926$	37.9525	+	27.5741i	1.24720	+	0.906141i
$927$	−14.7186	+	16.3467i	−0.483423	+	0.536896i
$928$	−6.07439	+	18.6951i	−0.199402	+	0.613695i
$929$	43.5844			1.42996			0.714979	−	0.699146i	$-0.246436\pi$
$929$	43.5844			1.42996			0.714979	+	0.699146i	$0.246436\pi$
$930$	−0.00887187	−	0.0242700i	−0.000290920	−	0.000795845i
$931$	−4.04653			−0.132620
$932$	3.80575	−	11.7129i	0.124661	−	0.383669i
$933$	−0.0592476	+	0.0658011i	−0.00193968	+	0.00215423i
$934$	−18.4056	−	13.3724i	−0.602249	−	0.437559i
$935$	9.42104	−	16.3177i	0.308101	−	0.533646i
$936$	3.02805	+	5.24474i	0.0989750	+	0.171430i
$937$	−1.69204	+	16.0987i	−0.0552764	+	0.525920i	0.931489	+	0.363768i	$0.118510\pi$
$937$	−1.69204	+	16.0987i	−0.0552764	+	0.525920i	−0.986766	+	0.162152i	$0.948157\pi$
$938$	−14.9244	+	10.8432i	−0.487298	+	0.354043i
$939$	0.00574934	+	0.0547013i	0.000187623	+	0.00178511i
$940$	2.94889	+	3.27507i	0.0961821	+	0.106821i
$941$	−5.37643	+	2.39374i	−0.175267	+	0.0780337i	−0.492494	−	0.870316i	$-0.663915\pi$
$941$	−5.37643	+	2.39374i	−0.175267	+	0.0780337i	0.317228	+	0.948349i	$0.397248\pi$
$942$	−0.107096	+	0.0227639i	−0.00348936	+	0.000741687i
$943$	41.4304	+	8.80631i	1.34916	+	0.286773i
$944$	−14.3814	−	6.40303i	−0.468076	−	0.208401i
$945$	0.0105859	+	0.0325802i	0.000344361	+	0.00105983i
$946$	28.4001	+	87.4065i	0.923366	+	2.84183i
$947$	−18.0977	−	8.05760i	−0.588095	−	0.261837i	0.0910433	−	0.995847i	$-0.470980\pi$
$947$	−18.0977	−	8.05760i	−0.588095	−	0.261837i	−0.679139	+	0.734010i	$0.737646\pi$
$948$	0.0294175	+	0.00625288i	0.000955435	+	0.000203084i
$949$	−12.3521	+	2.62552i	−0.400967	+	0.0852281i
$950$	9.08559	−	4.04517i	0.294776	−	0.131243i
$951$	0.0125835	+	0.0139754i	0.000408048	+	0.000453183i
$952$	1.43990	+	13.6997i	0.0466674	+	0.444011i
$953$	6.07417	−	4.41314i	0.196762	−	0.142956i	−0.485042	−	0.874491i	$-0.661196\pi$
$953$	6.07417	−	4.41314i	0.196762	−	0.142956i	0.681804	+	0.731535i	$0.261196\pi$
$954$	2.93000	−	27.8771i	0.0948624	−	0.902555i
$955$	−0.422779	−	0.732274i	−0.0136808	−	0.0236958i
$956$	6.38927	−	11.0665i	0.206644	−	0.357918i
$957$	−0.0643278	−	0.0467369i	−0.00207942	−	0.00151079i
$958$	−16.4848	+	18.3083i	−0.532601	+	0.591513i
$959$	−0.987872	+	3.04036i	−0.0319001	+	0.0981783i
$960$	−0.00783634			−0.000252917
$961$	−23.6918	+	19.9925i	−0.764251	+	0.644919i
$962$	−2.22627			−0.0717778
$963$	1.50593	−	4.63476i	0.0485278	−	0.149353i
$964$	−11.1248	+	12.3553i	−0.358305	+	0.397938i
$965$	5.33340	+	3.87494i	0.171688	+	0.124739i
$966$	−0.0419560	+	0.0726699i	−0.00134991	+	0.00233812i
$967$	0.282447	+	0.489212i	0.00908288	+	0.0157320i	0.870531	−	0.492113i	$-0.163775\pi$
$967$	0.282447	+	0.489212i	0.00908288	+	0.0157320i	−0.861448	+	0.507845i	$0.830442\pi$
$968$	−5.08177	+	48.3498i	−0.163334	+	1.55402i
$969$	−0.0113527	+	0.00824825i	−0.000364703	+	0.000264972i
$970$	1.97150	+	18.7576i	0.0633010	+	0.602269i
$971$	−13.9136	−	15.4527i	−0.446510	−	0.495899i	0.477306	−	0.878737i	$-0.341613\pi$
$971$	−13.9136	−	15.4527i	−0.446510	−	0.495899i	−0.923816	+	0.382838i	$0.874947\pi$
$972$	−0.0566146	+	0.0252065i	−0.00181592	+	0.000808497i
$973$	−41.7959	+	8.88399i	−1.33991	+	0.284808i
$974$	−48.7662	−	10.3656i	−1.56257	−	0.332135i
$975$	0.0108090	+	0.00481248i	0.000346165	+	0.000154123i
$976$	−11.5598	−	35.5773i	−0.370019	−	1.13880i
$977$	−5.35124	−	16.4694i	−0.171201	−	0.526904i	0.828238	−	0.560376i	$-0.189343\pi$
$977$	−5.35124	−	16.4694i	−0.171201	−	0.526904i	−0.999440	+	0.0334723i	$0.989343\pi$
$978$	−0.0415355	−	0.0184928i	−0.00132816	−	0.000591335i
$979$	13.5515	+	2.88047i	0.433109	+	0.0920602i
$980$	2.05950	−	0.437760i	0.0657883	−	0.0139837i
$981$	−9.23237	+	4.11051i	−0.294767	+	0.131239i
$982$	−17.8896	−	19.8685i	−0.570881	−	0.634028i
$983$	−3.18145	−	30.2695i	−0.101473	−	0.965447i	−0.920249	−	0.391334i	$-0.872014\pi$
$983$	−3.18145	−	30.2695i	−0.101473	−	0.965447i	0.818776	−	0.574113i	$-0.194653\pi$
$984$	−0.0237900	+	0.0172844i	−0.000758397	+	0.000551008i
$985$	−1.78667	+	16.9990i	−0.0569279	+	0.541633i
$986$	12.8443	+	22.2470i	0.409045	+	0.708487i
$987$	0.0173036	−	0.0299706i	0.000550778	−	0.000953976i
$988$	−0.934152	−	0.678701i	−0.0297193	−	0.0215924i
$989$	−52.3738	+	58.1670i	−1.66539	+	1.84960i
$990$	8.79160	−	27.0578i	0.279415	−	0.859952i
$991$	5.99399			0.190405			0.0952027	−	0.995458i	$-0.469650\pi$
$991$	5.99399			0.190405			0.0952027	+	0.995458i	$0.469650\pi$
$992$	−8.11379	−	22.1962i	−0.257613	−	0.704730i
$993$	0.0863939			0.00274163
$994$	5.48108	−	16.8690i	0.173849	−	0.535053i
$995$	15.2307	−	16.9154i	0.482847	−	0.536255i
$996$	0.0108429	+	0.00787784i	0.000343571	+	0.000249619i
$997$	−22.7657	+	39.4314i	−0.720997	+	1.24880i	0.239603	+	0.970871i	$0.422983\pi$
$997$	−22.7657	+	39.4314i	−0.720997	+	1.24880i	−0.960601	+	0.277933i	$0.910351\pi$
$998$	−6.43931	−	11.1532i	−0.203833	−	0.353049i
$999$	−0.00242228	+	0.0230465i	−7.66376e−5	+	0.000729158i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.bi.b.14.4	✓	136
31.20	even	15	inner	403.2.bi.b.144.4	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.bi.b.14.4	✓	136	1.1	even	1	trivial
403.2.bi.b.144.4	yes	136	31.20	even	15	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.bi (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.516329 + 1.58910i) q^{2} +(-0.00193962 + 0.00215417i) q^{3} +(-0.640602 - 0.465424i) q^{4} +(-0.479120 + 0.829859i) q^{5} +(-0.00242170 - 0.00419451i) q^{6} +(-0.214858 + 2.04424i) q^{7} +(-1.63317 + 1.18657i) q^{8} +(0.313585 + 2.98356i) q^{9} +O(q^{10})\)	\(q+(-0.516329 + 1.58910i) q^{2} +(-0.00193962 + 0.00215417i) q^{3} +(-0.640602 - 0.465424i) q^{4} +(-0.479120 + 0.829859i) q^{5} +(-0.00242170 - 0.00419451i) q^{6} +(-0.214858 + 2.04424i) q^{7} +(-1.63317 + 1.18657i) q^{8} +(0.313585 + 2.98356i) q^{9} +(-1.07134 - 1.18985i) q^{10} +(5.41100 - 2.40913i) q^{11} +(0.00224513 - 0.000477216i) q^{12} +(-0.978148 - 0.207912i) q^{13} +(-3.13755 - 1.39693i) q^{14} +(-0.000858345 - 0.00264172i) q^{15} +(-1.53169 - 4.71407i) q^{16} +(-3.03276 - 1.35027i) q^{17} +(-4.90308 - 1.04218i) q^{18} +(-1.42638 + 0.303185i) q^{19} +(0.693162 - 0.308615i) q^{20} +(-0.00398688 - 0.00442788i) q^{21} +(1.03449 + 9.84251i) q^{22} +(-6.81891 + 4.95423i) q^{23} +(0.000611665 - 0.00581960i) q^{24} +(2.04089 + 3.53492i) q^{25} +(0.835438 - 1.44702i) q^{26} +(-0.0140706 - 0.0102229i) q^{27} +(1.08908 - 1.20954i) q^{28} +(-1.43110 + 4.40448i) q^{29} +0.00464113 q^{30} +(-1.91157 - 5.22933i) q^{31} +4.24456 q^{32} +(-0.00530561 + 0.0163290i) q^{33} +(3.71161 - 4.12217i) q^{34} +(-1.59349 - 1.15773i) q^{35} +(1.18774 - 2.05722i) q^{36} +(-0.666198 - 1.15389i) q^{37} +(0.254688 - 2.42319i) q^{38} +(0.00234511 - 0.00170382i) q^{39} +(-0.202200 - 1.92381i) q^{40} +(-3.36255 - 3.73449i) q^{41} +(0.00909488 - 0.00404930i) q^{42} +(9.08343 - 1.93074i) q^{43} +(-4.58756 - 0.975117i) q^{44} +(-2.62618 - 1.16925i) q^{45} +(-4.35195 - 13.3939i) q^{46} +(1.79484 + 5.52395i) q^{47} +(0.0131258 + 0.00584398i) q^{48} +(2.71430 + 0.576942i) q^{49} +(-6.67111 + 1.41799i) q^{50} +(0.00879111 - 0.00391405i) q^{51} +(0.529836 + 0.588442i) q^{52} +(0.584526 + 5.56139i) q^{53} +(0.0235103 - 0.0170812i) q^{54} +(-0.593274 + 5.64463i) q^{55} +(-2.07472 - 3.59352i) q^{56} +(0.00211351 - 0.00366072i) q^{57} +(-6.26022 - 4.54832i) q^{58} +(2.12517 - 2.36024i) q^{59} +(-0.000679661 + 0.00209178i) q^{60} +7.54705 q^{61} +(9.29692 - 0.337622i) q^{62} -6.16647 q^{63} +(0.871798 - 2.68312i) q^{64} +(0.641187 - 0.712110i) q^{65} +(-0.0232089 - 0.0168623i) q^{66} +(2.68564 - 4.65166i) q^{67} +(1.31434 + 2.27651i) q^{68} +(0.00255386 - 0.0242984i) q^{69} +(2.66252 - 1.93443i) q^{70} +(0.539831 + 5.13614i) q^{71} +(-4.05232 - 4.50056i) q^{72} +(11.5363 - 5.13630i) q^{73} +(2.17762 - 0.462867i) q^{74} +(-0.0115734 - 0.00245999i) q^{75} +(1.05485 + 0.469649i) q^{76} +(3.76224 + 11.5790i) q^{77} +(0.00149669 + 0.00460635i) q^{78} +(11.9700 + 5.32940i) q^{79} +(4.64588 + 0.987512i) q^{80} +(-8.80325 + 1.87119i) q^{81} +(7.67065 - 3.41519i) q^{82} +(3.90718 + 4.33936i) q^{83} +(0.000493160 + 0.00469210i) q^{84} +(2.57359 - 1.86982i) q^{85} +(-1.62190 + 15.4314i) q^{86} +(-0.00671218 - 0.0116258i) q^{87} +(-5.97848 + 10.3550i) q^{88} +(1.89232 + 1.37485i) q^{89} +(3.21402 - 3.56953i) q^{90} +(0.635183 - 1.95489i) q^{91} +6.67403 q^{92} +(0.0149726 + 0.00602507i) q^{93} -9.70482 q^{94} +(0.431803 - 1.32895i) q^{95} +(-0.00823283 + 0.00914349i) q^{96} +(-9.53019 - 6.92409i) q^{97} +(-2.31829 + 4.01539i) q^{98} +(8.88459 + 15.3886i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 6 q^{2} + 2 q^{3} - 34 q^{4} - 15 q^{5} - 10 q^{6} - 8 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) \) 136 * q - 6 * q^2 + 2 * q^3 - 34 * q^4 - 15 * q^5 - 10 * q^6 - 8 * q^7 - 6 * q^8 + 23 * q^9	\( 136 q - 6 q^{2} + 2 q^{3} - 34 q^{4} - 15 q^{5} - 10 q^{6} - 8 q^{7} - 6 q^{8} + 23 q^{9} + 7 q^{10} + 5 q^{11} + 28 q^{12} + 17 q^{13} - 3 q^{14} + 17 q^{15} - 78 q^{16} - 12 q^{17} + 34 q^{18} - 23 q^{19} + 8 q^{20} - 38 q^{21} + 8 q^{22} + 9 q^{23} + 46 q^{24} - 69 q^{25} - 12 q^{26} - 58 q^{27} + 7 q^{28} + 18 q^{29} + 60 q^{30} + 14 q^{31} + 212 q^{32} - 41 q^{33} - 30 q^{35} - 106 q^{36} + 6 q^{37} - 62 q^{38} + 6 q^{39} + 39 q^{40} - 5 q^{41} + 37 q^{42} + q^{43} - 88 q^{44} - 168 q^{45} + 6 q^{46} - 81 q^{47} - 101 q^{48} + 117 q^{49} - 20 q^{50} + 35 q^{51} + 7 q^{52} + 25 q^{53} + 57 q^{54} + 19 q^{55} - 63 q^{56} - 20 q^{57} - 44 q^{58} + 9 q^{59} + 113 q^{60} + 8 q^{61} + 57 q^{62} + 112 q^{63} - 146 q^{64} - 5 q^{65} + 70 q^{66} - 99 q^{67} - 56 q^{68} - 65 q^{69} + 169 q^{70} - q^{71} - 43 q^{72} + 50 q^{73} - 26 q^{74} - 18 q^{75} - 94 q^{76} + 114 q^{77} - 17 q^{79} + 217 q^{80} + 54 q^{81} - 25 q^{82} - 53 q^{83} - 22 q^{84} + 2 q^{85} - 54 q^{86} - 28 q^{87} + 70 q^{88} - 101 q^{89} + 165 q^{90} - 4 q^{91} + 64 q^{92} + 61 q^{93} - 90 q^{94} - 33 q^{95} - 217 q^{96} + 73 q^{97} + 33 q^{98} - 15 q^{99}+O(q^{100}) \) 136 * q - 6 * q^2 + 2 * q^3 - 34 * q^4 - 15 * q^5 - 10 * q^6 - 8 * q^7 - 6 * q^8 + 23 * q^9 + 7 * q^10 + 5 * q^11 + 28 * q^12 + 17 * q^13 - 3 * q^14 + 17 * q^15 - 78 * q^16 - 12 * q^17 + 34 * q^18 - 23 * q^19 + 8 * q^20 - 38 * q^21 + 8 * q^22 + 9 * q^23 + 46 * q^24 - 69 * q^25 - 12 * q^26 - 58 * q^27 + 7 * q^28 + 18 * q^29 + 60 * q^30 + 14 * q^31 + 212 * q^32 - 41 * q^33 - 30 * q^35 - 106 * q^36 + 6 * q^37 - 62 * q^38 + 6 * q^39 + 39 * q^40 - 5 * q^41 + 37 * q^42 + q^43 - 88 * q^44 - 168 * q^45 + 6 * q^46 - 81 * q^47 - 101 * q^48 + 117 * q^49 - 20 * q^50 + 35 * q^51 + 7 * q^52 + 25 * q^53 + 57 * q^54 + 19 * q^55 - 63 * q^56 - 20 * q^57 - 44 * q^58 + 9 * q^59 + 113 * q^60 + 8 * q^61 + 57 * q^62 + 112 * q^63 - 146 * q^64 - 5 * q^65 + 70 * q^66 - 99 * q^67 - 56 * q^68 - 65 * q^69 + 169 * q^70 - q^71 - 43 * q^72 + 50 * q^73 - 26 * q^74 - 18 * q^75 - 94 * q^76 + 114 * q^77 - 17 * q^79 + 217 * q^80 + 54 * q^81 - 25 * q^82 - 53 * q^83 - 22 * q^84 + 2 * q^85 - 54 * q^86 - 28 * q^87 + 70 * q^88 - 101 * q^89 + 165 * q^90 - 4 * q^91 + 64 * q^92 + 61 * q^93 - 90 * q^94 - 33 * q^95 - 217 * q^96 + 73 * q^97 + 33 * q^98 - 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more